16
Research Article Self-Loosening Failure Analysis of Bolt Joints under Vibration considering the Tightening Process Yan Chen, Qiang Gao, and Zhenqun Guan State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China Correspondence should be addressed to Zhenqun Guan; [email protected] Received 19 July 2017; Revised 20 October 2017; Accepted 24 October 2017; Published 6 December 2017 Academic Editor: Sergio De Rosa Copyright © 2017 Yan Chen et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. By considering the tightening process, a three-dimensional elastic finite element analysis is conducted to explore the mechanism of bolt self-loosening under transverse cyclic loading. According to the geometrical features of the thread, a hexahedral meshing is implemented by modifying the node coordinates based on cylinder meshes and an ABAQUS plug-in is made for parametric modeling. e accuracy of the finite element model is verified and validated by comparison with the analytical and experimental results on torque-tension relationship. And, then, the fastening states acquired by different means are compared. e results show that the tightening process cannot be replaced by a simplified method because its fastening state is different from the real process. With combining the tightening and self-loosening processes, this paper utilizes the relative rotation angles and velocities to investigate the slip states on contact surfaces instead of the Coulomb friction coefficient method, which is used in most previous researches. By contrast, this method can describe the slip states in greater detail. In addition, the simulation result reveals that there exists a creep slip phenomenon at contact surface, which causes the bolt self-loosening to occur even when some contact facets are stuck. 1. Introduction e bolt joint, as a very common component in engineering, is widely used in a variety of industrial machines because of its simple configuration, convenient operation, and low cost [1]. A typical diagram of the bolt joint structure is shown in Figure 1. In practical applications, the bolt joint always requires a sufficiently large preload to guarantee a reliable force transmission between the clamped components. How- ever, due to the complex working environment, bolt joints oſten experience self-loosening (gradual loss of preload) with increasing service time, which can cause a decrease in the structure stiffness and in some cases may even lead to fatal consequences if it remains undetected [2]. In 1969, Junker [3] first indicated that transverse or shear loading (perpendicular to the fastener axis) is the most dangerous form of loading on self-loosening. Since then, self-loosening of bolted joints under cyclic transverse loads has become a popular topic in the study of bolt science. Pai and Hess [4, 5] introduced the concept of localized slip and classified the self-loosening process into four different types: (1) localized head slip with localized thread slip; (2) localized head slip with complete thread slip; (3) complete head slip with localized thread slip; (4) complete head slip with complete thread slip. However, the friction coefficients on the two surfaces are usually close, and, in this case, the complete thread slip is achieved prior to bolt head slip, which leads to the rare occurrence of the third type [6, 7]. Kasei [8] and Izumi et al. [9] investigated the mechanism of self-loosening due to micro bearing-surface slip. e results showed that a small degree of loosening occurs when transverse load reaches the range 50 to 60% of the critical loading for the bearing-surface slip. Recently, the cycle rotation load has been accepted as another reason to cause self-loosening [10, 11]. e results by Yokoyama et al. [10] revealed that loosening occurs only when the rotation angle around bolt axis which is applied to clamped component reaches a critical value, and the thread surface undergoes a complete slip. For a further understanding of localized slip and complete slip at contact surfaces, Dinger and Friedrich [7] proposed a local Hindawi Shock and Vibration Volume 2017, Article ID 2038421, 15 pages https://doi.org/10.1155/2017/2038421

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Research ArticleSelf-Loosening Failure Analysis of Bolt Joints underVibration considering the Tightening Process

Yan Chen Qiang Gao and Zhenqun Guan

State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics Dalian University ofTechnology Dalian 116024 China

Correspondence should be addressed to Zhenqun Guan guanzhqdluteducn

Received 19 July 2017 Revised 20 October 2017 Accepted 24 October 2017 Published 6 December 2017

Academic Editor Sergio De Rosa

Copyright copy 2017 YanChen et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

By considering the tightening process a three-dimensional elastic finite element analysis is conducted to explore the mechanismof bolt self-loosening under transverse cyclic loading According to the geometrical features of the thread a hexahedral meshingis implemented by modifying the node coordinates based on cylinder meshes and an ABAQUS plug-in is made for parametricmodeling The accuracy of the finite element model is verified and validated by comparison with the analytical and experimentalresults on torque-tension relationship And then the fastening states acquired by different means are compared The resultsshow that the tightening process cannot be replaced by a simplified method because its fastening state is different from the realprocess With combining the tightening and self-loosening processes this paper utilizes the relative rotation angles and velocitiesto investigate the slip states on contact surfaces instead of the Coulomb friction coefficient method which is used in most previousresearches By contrast this method can describe the slip states in greater detail In addition the simulation result reveals that thereexists a creep slip phenomenon at contact surface which causes the bolt self-loosening to occur even when some contact facets arestuck

1 Introduction

The bolt joint as a very common component in engineeringis widely used in a variety of industrial machines because ofits simple configuration convenient operation and low cost[1] A typical diagram of the bolt joint structure is shownin Figure 1 In practical applications the bolt joint alwaysrequires a sufficiently large preload to guarantee a reliableforce transmission between the clamped components How-ever due to the complex working environment bolt jointsoften experience self-loosening (gradual loss of preload) withincreasing service time which can cause a decrease in thestructure stiffness and in some cases may even lead to fatalconsequences if it remains undetected [2]

In 1969 Junker [3] first indicated that transverse or shearloading (perpendicular to the fastener axis) is the mostdangerous form of loading on self-loosening Since thenself-loosening of bolted joints under cyclic transverse loadshas become a popular topic in the study of bolt science Paiand Hess [4 5] introduced the concept of localized slip and

classified the self-loosening process into four different types(1) localized head slip with localized thread slip (2) localizedhead slip with complete thread slip (3) complete headslip with localized thread slip (4) complete head slip withcomplete thread slip However the friction coefficients on thetwo surfaces are usually close and in this case the completethread slip is achieved prior to bolt head slip which leadsto the rare occurrence of the third type [6 7] Kasei [8] andIzumi et al [9] investigated the mechanism of self-looseningdue to micro bearing-surface slip The results showed thata small degree of loosening occurs when transverse loadreaches the range 50 to 60 of the critical loading for thebearing-surface slip Recently the cycle rotation loadhas beenaccepted as another reason to cause self-loosening [10 11]The results by Yokoyama et al [10] revealed that looseningoccurs only when the rotation angle around bolt axis whichis applied to clamped component reaches a critical valueand the thread surface undergoes a complete slip For afurther understanding of localized slip and complete slip atcontact surfaces Dinger and Friedrich [7] proposed a local

HindawiShock and VibrationVolume 2017 Article ID 2038421 15 pageshttpsdoiorg10115520172038421

2 Shock and Vibration

Bolt

Nut

Clampedcomponents

Figure 1 A typical bolt joint diagram

key parameter 120578119899 (obtained by (1)) to characterize the contactsituation 120578119899 = 0 represents no contact 0 lt 120578119899 lt 100represents sticking at the contact node 120578119899 = 100 representsslipping at the contact node In (1) 120591 is the shear stress 119901 isthe contact stress and 120583 is the friction coefficient

120578119899 = 120591119901 sdot 120583 times 100 (1)

Through the same method Jiang et al [12] focused onthe self-loosening of bolts in curvic coupling and notedthat the slip states at contact surfaces highly depend on thevalues of the preload of the bolt and the torque loads onthe disc Additionally Nassar and Housari [13 14] used asimplified mathematical model to investigate some factorson self-loosening of threaded fasteners such as the holeclearance thread fit thread pitch and initial tension Insubsequent work Nassar et al [15ndash17] proposed a moreaccurate mathematical model to predict the variation of thepreload during the self-loosening process by investigatingthe relationship between the bearing friction torque thethread friction torque and the pitch torque componentsHowever simplifications were used in the model that led toits difference from the real structure

With the development of computer technology the finiteelement method is accepted as the most useful numericalmethod for solving the bolt self-loosening problem [18]However it is difficult tomodel andmesh the helical structureconsidering the effects of the lead angle There are two mainapproaches one is to model the bolt body and the threadseparately and then connect them using a tie constraint [1920] In thisway the twoparts can bemodeledwith hexahedralmeshes However the transmission of force and displacementon the interface is achieved by the interpolation whichresults in low accuracy critical discontinuous stress and evenincorrect high stress at some nodesThe other approach treatsthe bolt body and the threads as a whole part which canbe meshed only by tetrahedron [9 10 21 22] Unfortunatelya tetrahedron is less accurate and more time-consuming incalculation compared with the hexahedral mesh Fukuokageneralized the mathematical expressions of helical threadthrough the analysis of geometry and proposed a feasiblehexahedral mesh generation method [23 24] neverthelessit is complex and cumbersome

In this paper we implement the hexahedral mesh gener-ation of the thread structure by modifying the node coordi-nates Besides an ABAQUS plug-in is made for parametricmodeling and further study Using this model we studythe differences between different fastening means and theireffects on bolt self-loosening Additionally the mechanismof bolt self-loosening is analyzed using the relative motion ofnodes and a creep slip phenomenon is illustrated

2 Finite Element Model

21 Mathematical Expressions of the Thread Cross-SectionProfile According to the geometry features of the threadshown in Figure 2 the shape is naturally identical at any cross-section along the bolt axis To another cross-section it can beobtained just by rotating a certain angle around the axis basedon Figure 2The surface of the external thread consists of fourparts A-B (thread shank) B-C (crest) C-D (thread shank)and D-A (root radius) The outer contour line of the cross-section is equivalent to the whole pitch Figure 3 shows thecross-section profile along the bolt axis including the threadroot radius

Assume that the diagram given by Figure 2 is the cross-section at 119911 = 0 which can be viewed as a datum plane Thedistance between the outer contour line and the axis of thebolt can then be expressed by the following equations119903 (120579 119911 = 0)

=

1198892 minus 78119867 + 2120588 minus radic1205882 minus 119875241205872 1205792 (0 le 120579 le 1205791) 119867120587 120579 + 1198892 minus 78119867 (1205791 le 120579 le 1205792) 1198892 (1205792 le 120579 le 1205793) 119867120587 (2120587 minus 120579) + 1198892 minus 78119867 (1205793 le 120579 le 1205794) 1198892 minus 78119867 + 2120588 minus radic1205882 minus 119875241205872 (2120587 minus 120579)2 (1205794 le 120579 le 2120587)

1205791 = radic3120587120588119875 1205792 = 71205878 1205793 = 91205878 1205794 = 2120587 minus 1205791

Shock and Vibration 3

R

B

C

A

D

r

Major diameter

Minor diameter

Thread root

1

2

3

4

Figure 2 The cross-section profile of external thread

120588 = radic311987512 119867 = radic31198752

(2)

where 119875 and 119889 represent the thread pitch and the nominaldiameter respectively 120588 is the root radius of the threadAnother cross-section which is a distance 119911 off the datumplane has the same shape as the datum one However in acylindrical coordinate itmust be rotated by an angle120593 whichcan be written as

120593 = 2120587119875 119911 (3)

In addition it can be known that the mathematicalexpression of the outer surface of thread is periodic

119903 (120579 119911) = 119903 (120579 + 2119899120587 119911 + 119898119875) (4)

In summary the complete expression of the thread cross-section profile can be expressed as follows

119903 (120579 119911)

=

120601 = 120579 + 120593 = 120579 + 2120587119875 1199111198892 minus 78119867 + 2120588 minus radic1205882 minus 119875241205872 1205792 (0 le 120601 le 1205791) 119867120587 120579 + 1198892 minus 78119867 (1205791 le 120601 le 1205792) 1198892 (1205792 le 120601 le 1205793) 119867120587 (2120587 minus 120579) + 1198892 minus 78119867 (1205793 le 120601 le 1205794) 1198892 minus 78119867 + 2120588 minus radic1205882 minus 119875241205872 (2120587 minus 120579)2 (1205794 le 120601 le 2120587)

1205791 = radic3120587120588119875 1205792 = 71205878 1205793 = 91205878 1205794 = 2120587 minus 1205791120588 le +radic311987512

(5)

Similarly the profile of the internal thread can beexpressed in the same manner and it also has the periodicalpiecewise function form

1199031015840 (120579 119911) = 1199031015840 (120579 + 2119899120587 119911 + 119898119875) 1199031015840 (120579 119911)

=

120601 = 120579 + 120593 = 2120587119875 11991111988912 = 1198892 minus 58119867 (0 le 120579 le 12057910158401) 119867120587 120579 + 1198892 minus 78119867 (12057910158401 le 120579 le 12057910158402) 1198892 + 78119867 minus 21205881015840 + radic12058810158402 minus 119875241205872 (120587 minus 120579)2 (12057910158402 le 120579 le 12057910158403) 119867120587 (2120587 minus 120579) + 1198892 minus 78119867 (12057910158403 le 120579 le 12057910158404) 11988912 (12057910158404 le 120579 le 2120587)

12057910158401 = 1205874 12057910158402 = 120587(1 minus radic31205881015840119875 )

4 Shock and Vibration

D

P pitchr

C

B

A

2

4

3

2

1

0

H

8

H

4

5

8Hd1

2

d

2minus

7

8H +

root radius

Figure 3 The cross-section profile along the bolt axis

12057910158403 = 120587(1 + radic31205881015840119875 ) 12057910158404 = 71205874 1205881015840 le radic324 119875

(6)

22 Automatic Mesh Generation of the Thread StructureThe mesh generation method Fukuoka proposed requiresmany cyclic operations on the two-dimensional elementssuch as ldquocopyrdquo ldquotranslaterdquo ldquorotaterdquo and ldquomergerdquo whicheasily cause the problem of expensive computation In thisstudy the thread structure is partitioned properly beforemeshing The hexahedral mesh generation is implementedby modifying the node coordinates based on cylindricalhexahedron meshes The detailed procedures are introducedbelow In addition a self-developedABAQUSplug-in ismadefor parametric modeling (Figure 4)

Step 1 Depending on the size of the bolt and nut the corre-sponding cylinders are modeled with hexahedral meshes inABAQUS To fit the shape of the thread well and improve thecalculation efficiency the model is divided into two parts thethread region and the nonthread region The thread regionis discretized with finer meshes to guarantee the simulationaccuracy of the contact state while the other region ismeshedwith relative coarse elements (Figure 5) The models are thenexported in the form of an INP file

Step 2 The node coordinates of the thread region areextracted from the INP file exported previously and theyare modified by a self-compiled program depending on the

Figure 4 The parametric modeling interface

mathematical expression of thread cross-section profile Themodified INP file is then imported to ABAQUS again andthe hexahedral models of threads are generated (Figure 6)

Step 3 The bolt shank and bolt head which are simplecylinders are built up andmeshed with hexahedral elementsThen they are merged with the thread part to obtain acomplete bolt model

Step 4 Finally the clamped components are modeled inABAQUS and all parts are assembled into a whole analysismodel of the bolt self-loosening problem (Figure 7)

Through the method described before the 3D finite ele-mentmodel which contains aM10lowast15 bolt and nut and twoclamped components is established using the commercialsoftware package ABAQUS There are a total of 58140 C3D8elements and 64731 nodes All components in this model areassumed to be purely elastic and Youngrsquos modulus Poissonrsquosratio and the density are 210GPa 03 and 7800 kgm3respectively

Contact interactions have been set between all slidingsurfaces including the interfaces between the threads boltunderhead surface and the upper part surface and nutsurface and the lower part surface Contact modeling isvery important to the simulation of the tightening andself-loosening process According to the work by Dingerand Friedrich [7] the augmented Lagrangian technique andthe penalty approach are applied to solve the normal andtangential contact problem respectively In this study thesurface constraint approach used for all contact pairs is amaster-slave finite sliding and node-to-surface assignmentConcretely to the interface between internal and externalthreads the surface of external threads is assigned the mastersurface to the interface between bolt and upper componentthe surface of upper component is assigned the mastersurface to the interface between nut and lower componentthe surface of lower component is assigned the mastersurface to the interface between clamped components thesurface of lower component is assigned the master surface

Shock and Vibration 5

Z

Y

X Z

Y

X

Figure 5 The hexahedral models of cylinders

X

Y

Z X

Y

Z

Figure 6 The hexahedral models of threads

X

Y

Z

Figure 7 The whole hexahedral model of a typical bolt joint

A nominal friction coefficient 01 is initially used for allsliding surfaces Considering the geometric nonlinearity theimplicit dynamicsmodule inABAQUS is used to simulate thetightening and self-loosening process

3 Analysis of the Tightening Process

31 Verification of the Accuracy of the FE Model The preloadrefers to the elastic restoring force of the bolt when it is

serving In engineering it is always controlled by tighteningtorque or rotation angle of the nut In this paper thetightening process analysis is performed by applying a rampcircumferential displacement 1205790 on the side surface of the nut(Figure 8) and then removing it after maintaining the valuefor a period The accuracy of finite element model is verifiedby contrast with the analytical and experimental results ontorque-tension relationship

Referring to the general rules of tightening for threadedfasteners given inGBT 168232 [25] the relationship betweentightening torque 119879119891 and bolt preload 119865119891 can be estimatedapproximately by

119879119891 = 119870119865119891119889 (7)

where 119870 is the torque coefficient and 119889 is the nominaldiameter of the bolt 119870 can be expressed as follows

119870 = 12119889 (119875120587 + 1205831199041198892 sec1205721015840 + 120583119882119863119882) (8)

where 119875 is the thread pitch 120583119904 is the coefficient of threadfriction 1198892 is the intermediate diameter 1205721015840 is half of the

6 Shock and Vibration

0

Figure 8 The loading diagram

FEA resultsFEM fitting resultsAnalytical results

times104

times1041 15 2 25 3 3505

Preload (N)

1

2

3

4

5

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 9 The contrast diagram of torque-tension relationships

thread profile angle (30 degrees for standard ISO threads)120583119882is the coefficient of underhead friction and119863119882 is the effectiveunderhead bearing contact radius which can be expressed asfollows when the underhead bearing face is circular

119863119882 = 23 times1198893119882 minus 1198893ℎ1198892119882 minus 1198892ℎ (9)

where 119889ℎ and 119889119882 are the internal diameter and the externaldiameter of the underhead bearing contact face respectively

To a M10 lowast 15 bolt and nut the torque-tension rela-tionship can be acquired by substituting relevant parametersinto (7)ndash(9) Figure 9 shows the comparison between theanalytical results and simulation results It can be seen thatthe FEA (finite element analysis) results are similar to theanalytical ones The torque coefficient 119870 by the analyticalmethod is 1453 while the value is 14749 by FEM (finiteelement method) The error between them is only 151

BoltBolted fixture

Load cellNut fixture

Locked spacer

Nut

Figure 10 The test rig

FEA resultsExperimental results

0

1

2

3

4

5

6

1 2 30Preload (N)

times104

times104

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 11 Comparison between the finite element method and theexperimental method

In addition a test rig has been developed as shown inFigure 10 with an aim to verify the accuracy of the FE modelIn this experiment two plates made of steel (30CrMnSiA)are clamped by a M10 lowast 15 bolt and nut Each plate has athickness of 10mmDuring the loading process the bolt headis fixed and a torque wrench is used to tighten the nut Thevalue of tightening torque is applied in the range of 0sim60NmBesides a load cell is attached between the bolt head andthe clamped component to measure the clamp force Thedata of fastener tension are recorded per 5Nm torque in thisexperiment

The curves in Figure 11 show the contrast results betweenfinite element method and the experimental method

Shock and Vibration 7

Δl Δl

Figure 12 The loading diagram of the simplified way

Through the comparison it can be seen that the differencebetween the finite element and the experimental resultsis tiny The accuracy of FEM is verified by analytical andexperimental study

32 Analysis of the Fastening States The preload is a veryimportant factor that should not be ignored in the study ofbolt self-loosening However few studies considered both thetightening process and the self-loosening process simulta-neously Most of them simulated the preload by stretchingthe bolt or using a cooling pretightening algorithm thatmakes the fastening state of bolt different from the realcase Therefore the differences of different fastening waysare discussed here followed by their effects on bolt self-loosening

To simulate the tightening process a circumferentialdisplacement 1205790 is applied on the side surface of the nutwhich is the same as the model validation process Besides asimplified way that stretches the bolt is made for comparisonThe two clamped components are separated by a distanceΔ119897 which is used to control the value of preload as shownin Figure 12 After the loading process the whole bolt jointbecomes static without external constraints and the resultanttorque at every contact surface is equal in magnitude Sothe resultant torque at contact surface between threads isregarded as the object Figure 13 presents the relationshipsbetween the torque and the preload in static state which areachieved by different fastening means

As shown before the value of the torque in the tighteningprocess is obviously higher than that obtained by stretchingthe bolt under the same preload which leads to makingthe self-loosening more likely to occur The resultant torqueon the thread interface consists of two parts the pitchtorque and the thread friction torque Figure 14 illustratesthe relationships between the preload the pitch torque thethread friction torque and the resultant torque by differentfastening means It can be noted that the pitch torque andthread friction torque possess the same direction whenconsidering the tightening process while it is opposite by

Simulating the tightening processStretching bolt

4000

8000

12000

16000

1 2 30

Preload (N)times104

Resu

ltant

torq

ue (N

middotmm

)Figure 13 The relationships between the torque and the preload

stretching the bolt which leads to a much smaller resultanttorque

4 Analysis of the Bolt Loosening Mechanism

Considering the influence of the tightening process thepreload is produced by applying a constrained circumferen-tial displacement on the side surface of the nut followed by itsremoval To conduct the FEA of bolt joints self-loosening atransversal excitation 119904 is loaded on the clamped components(Figure 15) which is determined by the following formula

119904 = 1199040 sin (120596119905) (10)

where 1199040 and 120596 represent the excitation amplitude andangular frequency which are 003mm and 2120587 in this paperrespectively The excitation amplitude is smaller than theclearance between the bolt body and the clamped partTo reduce computational cost the clamped componentsare assumed to be rigid bodies when simulating the self-loosening process of bolt joints Since the vibration frequencyis set to 1Hz which is low the system can be treated as aquasi-static process Because the self-loosening behavior ismainly caused by slip at contact surfaces the critical outputparametersmonitored in this analysis include the preload andthe motion of nodes at contact surfaces which are used toanalyze the slip state

41 Evolution of the Preload during Self-Loosening To inves-tigate the effects of different fastening means on the self-loosening process of the bolt joint the same preload isproduced by adjusting the circumferential displacement andthe separation distance in finite element analysis and theother attributes of the two models are completely identical Acyclic transversal displacement is then loaded on the clamped

8 Shock and Vibration

0

Resultant torquePitch torqueThread friction torque

4000

8000

12000

16000

2 31Preload (N) times104

Torq

ue (N

middotmm

)

(a) Simulating the tightening process

Resultant torquePitch torqueThread friction torque

2 31Preload (N) times104

minus8000

minus4000

0

4000

8000

Torq

ue (N

middotmm

)

(b) Stretching the bolt

Figure 14 The relationships between different kinds of torque and preload

s

s s

t (s)

003 mm

105

s = 003 MCH 2t

Figure 15 The diagrams of transversal harmonic load

components The evolutions of the preload of differentfastening means during the first 15 load cycles are illustratedin Figure 16 It shows that at the same load cycle the self-loosening is much easier to appear andmore preload gets lostwhen the preload is produced by the simplified way This isbecause the resultant torque at contact surface is smaller

It can be drawn from the above analysis that the approx-imate pretightening algorithm cannot take the place of thetightening process to study the self-loosening mechanism ofbolt joints To preform further analysis of the evolution ofthe preload during bolt self-loosening the number of loadingcycles is increased to 150 and the initial preload is set to 8 kNThe curve in Figure 17 displays the preload variation duringthe 150 cycles It can be seen that with the increase of theloading cycles the variation curve of the preload tends to be

flat after a rapid decline The whole process can be roughlydivided into two stages the rapid decline stage and the flatstage which is in accordance with the result of Junker

42 Analysis of the Slip State at Contact Surfaces The self-loosening behavior is mainly caused by slip at contactsurfacesTherefore the dynamics during self-loosening is themain focus of the following analysis This paper uses therelative motion of nodes to present the slip state which isdifferent from previous researches and it is proved to be ingreater detail by contrast with the traditional method usingthe friction relation

The process of the preload variation mainly consists oftwo stages (exampled in Section 41) Taking the bolt headbearing surface as an example the relative motion of nodes

Shock and Vibration 9

The assembling processThe simplified way

25

255

26

265

27

275

Prel

oad

(N)

10 150 5Time (s)

times104

Figure 16 The preload variations under different fastening ways

2000

4000

6000

8000

Prel

oad

(N)

50 100 1500Time (s)

Figure 17 The curve of preload variation during the 150 cycles

during the two stages is analyzed Because the clampedcomponents are assumed to be rigid bodies the relativerotation between contact surfaces is equivalent to the rotationof bolt around its axis In the calculations the uniformdistribution nodes 1sim8 are selected from the outside edge ofbolt and node A is the intersection point between the contactsurface and the axis of bolt The relative rotation at contactsurface can be simplified to the rotation angle of nodes 1sim8around node A (Figure 18)

According to Figure 19 the range of analysis time is 0sim1 s(the decline stage) and 145sim150 s (the flat stage) During thetwo stages the rotation angle of each calculation node aroundnode A is shown

As shown before all the nodes rotate along the loosedirection as a whole which causes the preload loss Howeverat the beginning of the self-loosening process not all of thenodes rotate at the same time but one node rotates firstlyand drives the rotation of the other nodes Moreover in theprocess of rotating the rotation angles of some nodes arelarge and some are small When the movement direction ofclamped component changes the rotation angles of thosewhose rotation angles are large previously begin to decreaseMeanwhile the rotation angles of thosewhose rotation anglesare small increase This presents a creep slip phenomenonat contact surface under reversed cyclic load With increaseof the loading cycles the preload continues to decline And

10 Shock and Vibration

1

82

3

4

5

6

7A

Figure 18 The diagrams of the contact surface and the calculation points

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

02 04 06 08 10Time (s)

1

15

2

25

3

35

Relat

ive r

otat

ion

angl

e (ra

d)

times10minus3

(a) The rapid decline stage

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

00425

00426

00427

Relat

ive r

otat

ion

angl

e (ra

d)

148 150146Time (s)

(b) The flat stage

Figure 19 The rotation angles of each point in different stages

finally all nodes present a back and forth rotation at one placewhich causes the flat stage

To analyze the slip state during the initial stage of self-loosening (when preload is 272 kN) all nodes along theouter edge are taken into account and their relative rotationvelocities around node A are carried out as shown inFigure 20 Figure 21 shows the relative rotation velocity ofeach calculation node at some moments It can be notedthat the contact surface is slipping in a creep form Forcomparison the frictionmethod is also applied in the analysisof the contact state Based on the local key parameter 120578119899calculated the slip state contours are displayed in Figure 22However there is no significant difference among the three

figures which reflects that this method cannot give a detaileddescription of the slip state for a short time Through theanalysis of a whole cycle it suggests that there are always tworegions whose velocity directions are opposite Owing to thecontinuity of motion it means that there is a stick region onthe contact surface at any moment and bolt self-loosing canoccur without complete slip on the bolt head bearing surface

In addition the relativemotion between thread interfacesis analyzed in a similar way Two helical segments are inter-cepted from the contact location of bolt and nut (Figure 23)respectivelyThe rotation velocities of nodes belonging to thetwo helical segments can be calculated to build the position-velocity fields of bolt and nut at any time and the velocity

Shock and Vibration 11

XY

Z

1 2 348

13

25

37

Figure 20 The node number along the outer edge

t = 02 st = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 st = 03 s

2 4 6 80Circumferential position (rad)

minus8

minus4

0

4

8

Relat

ive r

otat

ion

velo

city

(rad

s)

Figure 21 The relative rotation velocity of each node at different moment

between adjacent nodes can be obtained approximately bylinear interpolation Figure 24 shows the position-velocitycurve at 025 s

Based on the position-velocity curves of bolt and nut therelative position-velocity relationship between thread inter-faces can be acquired by subtracting them Figure 25 showsthe relative position-velocity relationships at some momentsIt can be seen that all curves intersect the horizontal linethat the value is zero This means that there is always a stick

region in the thread interfaces which is consistent with theconclusion presented on the bolt head bearing surface Theslip state contours between thread interfaces are also given forcomparison (Figure 26) However there is still no significantdifference among them

To further strengthen the trust in the results summedbefore the relation between transverse force (shear force)and transverse displacement during the initial fifteen cyclesis shown in Figure 27 It is noted that the hysteresis loop

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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International Journal of

Page 2: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

2 Shock and Vibration

Bolt

Nut

Clampedcomponents

Figure 1 A typical bolt joint diagram

key parameter 120578119899 (obtained by (1)) to characterize the contactsituation 120578119899 = 0 represents no contact 0 lt 120578119899 lt 100represents sticking at the contact node 120578119899 = 100 representsslipping at the contact node In (1) 120591 is the shear stress 119901 isthe contact stress and 120583 is the friction coefficient

120578119899 = 120591119901 sdot 120583 times 100 (1)

Through the same method Jiang et al [12] focused onthe self-loosening of bolts in curvic coupling and notedthat the slip states at contact surfaces highly depend on thevalues of the preload of the bolt and the torque loads onthe disc Additionally Nassar and Housari [13 14] used asimplified mathematical model to investigate some factorson self-loosening of threaded fasteners such as the holeclearance thread fit thread pitch and initial tension Insubsequent work Nassar et al [15ndash17] proposed a moreaccurate mathematical model to predict the variation of thepreload during the self-loosening process by investigatingthe relationship between the bearing friction torque thethread friction torque and the pitch torque componentsHowever simplifications were used in the model that led toits difference from the real structure

With the development of computer technology the finiteelement method is accepted as the most useful numericalmethod for solving the bolt self-loosening problem [18]However it is difficult tomodel andmesh the helical structureconsidering the effects of the lead angle There are two mainapproaches one is to model the bolt body and the threadseparately and then connect them using a tie constraint [1920] In thisway the twoparts can bemodeledwith hexahedralmeshes However the transmission of force and displacementon the interface is achieved by the interpolation whichresults in low accuracy critical discontinuous stress and evenincorrect high stress at some nodesThe other approach treatsthe bolt body and the threads as a whole part which canbe meshed only by tetrahedron [9 10 21 22] Unfortunatelya tetrahedron is less accurate and more time-consuming incalculation compared with the hexahedral mesh Fukuokageneralized the mathematical expressions of helical threadthrough the analysis of geometry and proposed a feasiblehexahedral mesh generation method [23 24] neverthelessit is complex and cumbersome

In this paper we implement the hexahedral mesh gener-ation of the thread structure by modifying the node coordi-nates Besides an ABAQUS plug-in is made for parametricmodeling and further study Using this model we studythe differences between different fastening means and theireffects on bolt self-loosening Additionally the mechanismof bolt self-loosening is analyzed using the relative motion ofnodes and a creep slip phenomenon is illustrated

2 Finite Element Model

21 Mathematical Expressions of the Thread Cross-SectionProfile According to the geometry features of the threadshown in Figure 2 the shape is naturally identical at any cross-section along the bolt axis To another cross-section it can beobtained just by rotating a certain angle around the axis basedon Figure 2The surface of the external thread consists of fourparts A-B (thread shank) B-C (crest) C-D (thread shank)and D-A (root radius) The outer contour line of the cross-section is equivalent to the whole pitch Figure 3 shows thecross-section profile along the bolt axis including the threadroot radius

Assume that the diagram given by Figure 2 is the cross-section at 119911 = 0 which can be viewed as a datum plane Thedistance between the outer contour line and the axis of thebolt can then be expressed by the following equations119903 (120579 119911 = 0)

=

1198892 minus 78119867 + 2120588 minus radic1205882 minus 119875241205872 1205792 (0 le 120579 le 1205791) 119867120587 120579 + 1198892 minus 78119867 (1205791 le 120579 le 1205792) 1198892 (1205792 le 120579 le 1205793) 119867120587 (2120587 minus 120579) + 1198892 minus 78119867 (1205793 le 120579 le 1205794) 1198892 minus 78119867 + 2120588 minus radic1205882 minus 119875241205872 (2120587 minus 120579)2 (1205794 le 120579 le 2120587)

1205791 = radic3120587120588119875 1205792 = 71205878 1205793 = 91205878 1205794 = 2120587 minus 1205791

Shock and Vibration 3

R

B

C

A

D

r

Major diameter

Minor diameter

Thread root

1

2

3

4

Figure 2 The cross-section profile of external thread

120588 = radic311987512 119867 = radic31198752

(2)

where 119875 and 119889 represent the thread pitch and the nominaldiameter respectively 120588 is the root radius of the threadAnother cross-section which is a distance 119911 off the datumplane has the same shape as the datum one However in acylindrical coordinate itmust be rotated by an angle120593 whichcan be written as

120593 = 2120587119875 119911 (3)

In addition it can be known that the mathematicalexpression of the outer surface of thread is periodic

119903 (120579 119911) = 119903 (120579 + 2119899120587 119911 + 119898119875) (4)

In summary the complete expression of the thread cross-section profile can be expressed as follows

119903 (120579 119911)

=

120601 = 120579 + 120593 = 120579 + 2120587119875 1199111198892 minus 78119867 + 2120588 minus radic1205882 minus 119875241205872 1205792 (0 le 120601 le 1205791) 119867120587 120579 + 1198892 minus 78119867 (1205791 le 120601 le 1205792) 1198892 (1205792 le 120601 le 1205793) 119867120587 (2120587 minus 120579) + 1198892 minus 78119867 (1205793 le 120601 le 1205794) 1198892 minus 78119867 + 2120588 minus radic1205882 minus 119875241205872 (2120587 minus 120579)2 (1205794 le 120601 le 2120587)

1205791 = radic3120587120588119875 1205792 = 71205878 1205793 = 91205878 1205794 = 2120587 minus 1205791120588 le +radic311987512

(5)

Similarly the profile of the internal thread can beexpressed in the same manner and it also has the periodicalpiecewise function form

1199031015840 (120579 119911) = 1199031015840 (120579 + 2119899120587 119911 + 119898119875) 1199031015840 (120579 119911)

=

120601 = 120579 + 120593 = 2120587119875 11991111988912 = 1198892 minus 58119867 (0 le 120579 le 12057910158401) 119867120587 120579 + 1198892 minus 78119867 (12057910158401 le 120579 le 12057910158402) 1198892 + 78119867 minus 21205881015840 + radic12058810158402 minus 119875241205872 (120587 minus 120579)2 (12057910158402 le 120579 le 12057910158403) 119867120587 (2120587 minus 120579) + 1198892 minus 78119867 (12057910158403 le 120579 le 12057910158404) 11988912 (12057910158404 le 120579 le 2120587)

12057910158401 = 1205874 12057910158402 = 120587(1 minus radic31205881015840119875 )

4 Shock and Vibration

D

P pitchr

C

B

A

2

4

3

2

1

0

H

8

H

4

5

8Hd1

2

d

2minus

7

8H +

root radius

Figure 3 The cross-section profile along the bolt axis

12057910158403 = 120587(1 + radic31205881015840119875 ) 12057910158404 = 71205874 1205881015840 le radic324 119875

(6)

22 Automatic Mesh Generation of the Thread StructureThe mesh generation method Fukuoka proposed requiresmany cyclic operations on the two-dimensional elementssuch as ldquocopyrdquo ldquotranslaterdquo ldquorotaterdquo and ldquomergerdquo whicheasily cause the problem of expensive computation In thisstudy the thread structure is partitioned properly beforemeshing The hexahedral mesh generation is implementedby modifying the node coordinates based on cylindricalhexahedron meshes The detailed procedures are introducedbelow In addition a self-developedABAQUSplug-in ismadefor parametric modeling (Figure 4)

Step 1 Depending on the size of the bolt and nut the corre-sponding cylinders are modeled with hexahedral meshes inABAQUS To fit the shape of the thread well and improve thecalculation efficiency the model is divided into two parts thethread region and the nonthread region The thread regionis discretized with finer meshes to guarantee the simulationaccuracy of the contact state while the other region ismeshedwith relative coarse elements (Figure 5) The models are thenexported in the form of an INP file

Step 2 The node coordinates of the thread region areextracted from the INP file exported previously and theyare modified by a self-compiled program depending on the

Figure 4 The parametric modeling interface

mathematical expression of thread cross-section profile Themodified INP file is then imported to ABAQUS again andthe hexahedral models of threads are generated (Figure 6)

Step 3 The bolt shank and bolt head which are simplecylinders are built up andmeshed with hexahedral elementsThen they are merged with the thread part to obtain acomplete bolt model

Step 4 Finally the clamped components are modeled inABAQUS and all parts are assembled into a whole analysismodel of the bolt self-loosening problem (Figure 7)

Through the method described before the 3D finite ele-mentmodel which contains aM10lowast15 bolt and nut and twoclamped components is established using the commercialsoftware package ABAQUS There are a total of 58140 C3D8elements and 64731 nodes All components in this model areassumed to be purely elastic and Youngrsquos modulus Poissonrsquosratio and the density are 210GPa 03 and 7800 kgm3respectively

Contact interactions have been set between all slidingsurfaces including the interfaces between the threads boltunderhead surface and the upper part surface and nutsurface and the lower part surface Contact modeling isvery important to the simulation of the tightening andself-loosening process According to the work by Dingerand Friedrich [7] the augmented Lagrangian technique andthe penalty approach are applied to solve the normal andtangential contact problem respectively In this study thesurface constraint approach used for all contact pairs is amaster-slave finite sliding and node-to-surface assignmentConcretely to the interface between internal and externalthreads the surface of external threads is assigned the mastersurface to the interface between bolt and upper componentthe surface of upper component is assigned the mastersurface to the interface between nut and lower componentthe surface of lower component is assigned the mastersurface to the interface between clamped components thesurface of lower component is assigned the master surface

Shock and Vibration 5

Z

Y

X Z

Y

X

Figure 5 The hexahedral models of cylinders

X

Y

Z X

Y

Z

Figure 6 The hexahedral models of threads

X

Y

Z

Figure 7 The whole hexahedral model of a typical bolt joint

A nominal friction coefficient 01 is initially used for allsliding surfaces Considering the geometric nonlinearity theimplicit dynamicsmodule inABAQUS is used to simulate thetightening and self-loosening process

3 Analysis of the Tightening Process

31 Verification of the Accuracy of the FE Model The preloadrefers to the elastic restoring force of the bolt when it is

serving In engineering it is always controlled by tighteningtorque or rotation angle of the nut In this paper thetightening process analysis is performed by applying a rampcircumferential displacement 1205790 on the side surface of the nut(Figure 8) and then removing it after maintaining the valuefor a period The accuracy of finite element model is verifiedby contrast with the analytical and experimental results ontorque-tension relationship

Referring to the general rules of tightening for threadedfasteners given inGBT 168232 [25] the relationship betweentightening torque 119879119891 and bolt preload 119865119891 can be estimatedapproximately by

119879119891 = 119870119865119891119889 (7)

where 119870 is the torque coefficient and 119889 is the nominaldiameter of the bolt 119870 can be expressed as follows

119870 = 12119889 (119875120587 + 1205831199041198892 sec1205721015840 + 120583119882119863119882) (8)

where 119875 is the thread pitch 120583119904 is the coefficient of threadfriction 1198892 is the intermediate diameter 1205721015840 is half of the

6 Shock and Vibration

0

Figure 8 The loading diagram

FEA resultsFEM fitting resultsAnalytical results

times104

times1041 15 2 25 3 3505

Preload (N)

1

2

3

4

5

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 9 The contrast diagram of torque-tension relationships

thread profile angle (30 degrees for standard ISO threads)120583119882is the coefficient of underhead friction and119863119882 is the effectiveunderhead bearing contact radius which can be expressed asfollows when the underhead bearing face is circular

119863119882 = 23 times1198893119882 minus 1198893ℎ1198892119882 minus 1198892ℎ (9)

where 119889ℎ and 119889119882 are the internal diameter and the externaldiameter of the underhead bearing contact face respectively

To a M10 lowast 15 bolt and nut the torque-tension rela-tionship can be acquired by substituting relevant parametersinto (7)ndash(9) Figure 9 shows the comparison between theanalytical results and simulation results It can be seen thatthe FEA (finite element analysis) results are similar to theanalytical ones The torque coefficient 119870 by the analyticalmethod is 1453 while the value is 14749 by FEM (finiteelement method) The error between them is only 151

BoltBolted fixture

Load cellNut fixture

Locked spacer

Nut

Figure 10 The test rig

FEA resultsExperimental results

0

1

2

3

4

5

6

1 2 30Preload (N)

times104

times104

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 11 Comparison between the finite element method and theexperimental method

In addition a test rig has been developed as shown inFigure 10 with an aim to verify the accuracy of the FE modelIn this experiment two plates made of steel (30CrMnSiA)are clamped by a M10 lowast 15 bolt and nut Each plate has athickness of 10mmDuring the loading process the bolt headis fixed and a torque wrench is used to tighten the nut Thevalue of tightening torque is applied in the range of 0sim60NmBesides a load cell is attached between the bolt head andthe clamped component to measure the clamp force Thedata of fastener tension are recorded per 5Nm torque in thisexperiment

The curves in Figure 11 show the contrast results betweenfinite element method and the experimental method

Shock and Vibration 7

Δl Δl

Figure 12 The loading diagram of the simplified way

Through the comparison it can be seen that the differencebetween the finite element and the experimental resultsis tiny The accuracy of FEM is verified by analytical andexperimental study

32 Analysis of the Fastening States The preload is a veryimportant factor that should not be ignored in the study ofbolt self-loosening However few studies considered both thetightening process and the self-loosening process simulta-neously Most of them simulated the preload by stretchingthe bolt or using a cooling pretightening algorithm thatmakes the fastening state of bolt different from the realcase Therefore the differences of different fastening waysare discussed here followed by their effects on bolt self-loosening

To simulate the tightening process a circumferentialdisplacement 1205790 is applied on the side surface of the nutwhich is the same as the model validation process Besides asimplified way that stretches the bolt is made for comparisonThe two clamped components are separated by a distanceΔ119897 which is used to control the value of preload as shownin Figure 12 After the loading process the whole bolt jointbecomes static without external constraints and the resultanttorque at every contact surface is equal in magnitude Sothe resultant torque at contact surface between threads isregarded as the object Figure 13 presents the relationshipsbetween the torque and the preload in static state which areachieved by different fastening means

As shown before the value of the torque in the tighteningprocess is obviously higher than that obtained by stretchingthe bolt under the same preload which leads to makingthe self-loosening more likely to occur The resultant torqueon the thread interface consists of two parts the pitchtorque and the thread friction torque Figure 14 illustratesthe relationships between the preload the pitch torque thethread friction torque and the resultant torque by differentfastening means It can be noted that the pitch torque andthread friction torque possess the same direction whenconsidering the tightening process while it is opposite by

Simulating the tightening processStretching bolt

4000

8000

12000

16000

1 2 30

Preload (N)times104

Resu

ltant

torq

ue (N

middotmm

)Figure 13 The relationships between the torque and the preload

stretching the bolt which leads to a much smaller resultanttorque

4 Analysis of the Bolt Loosening Mechanism

Considering the influence of the tightening process thepreload is produced by applying a constrained circumferen-tial displacement on the side surface of the nut followed by itsremoval To conduct the FEA of bolt joints self-loosening atransversal excitation 119904 is loaded on the clamped components(Figure 15) which is determined by the following formula

119904 = 1199040 sin (120596119905) (10)

where 1199040 and 120596 represent the excitation amplitude andangular frequency which are 003mm and 2120587 in this paperrespectively The excitation amplitude is smaller than theclearance between the bolt body and the clamped partTo reduce computational cost the clamped componentsare assumed to be rigid bodies when simulating the self-loosening process of bolt joints Since the vibration frequencyis set to 1Hz which is low the system can be treated as aquasi-static process Because the self-loosening behavior ismainly caused by slip at contact surfaces the critical outputparametersmonitored in this analysis include the preload andthe motion of nodes at contact surfaces which are used toanalyze the slip state

41 Evolution of the Preload during Self-Loosening To inves-tigate the effects of different fastening means on the self-loosening process of the bolt joint the same preload isproduced by adjusting the circumferential displacement andthe separation distance in finite element analysis and theother attributes of the two models are completely identical Acyclic transversal displacement is then loaded on the clamped

8 Shock and Vibration

0

Resultant torquePitch torqueThread friction torque

4000

8000

12000

16000

2 31Preload (N) times104

Torq

ue (N

middotmm

)

(a) Simulating the tightening process

Resultant torquePitch torqueThread friction torque

2 31Preload (N) times104

minus8000

minus4000

0

4000

8000

Torq

ue (N

middotmm

)

(b) Stretching the bolt

Figure 14 The relationships between different kinds of torque and preload

s

s s

t (s)

003 mm

105

s = 003 MCH 2t

Figure 15 The diagrams of transversal harmonic load

components The evolutions of the preload of differentfastening means during the first 15 load cycles are illustratedin Figure 16 It shows that at the same load cycle the self-loosening is much easier to appear andmore preload gets lostwhen the preload is produced by the simplified way This isbecause the resultant torque at contact surface is smaller

It can be drawn from the above analysis that the approx-imate pretightening algorithm cannot take the place of thetightening process to study the self-loosening mechanism ofbolt joints To preform further analysis of the evolution ofthe preload during bolt self-loosening the number of loadingcycles is increased to 150 and the initial preload is set to 8 kNThe curve in Figure 17 displays the preload variation duringthe 150 cycles It can be seen that with the increase of theloading cycles the variation curve of the preload tends to be

flat after a rapid decline The whole process can be roughlydivided into two stages the rapid decline stage and the flatstage which is in accordance with the result of Junker

42 Analysis of the Slip State at Contact Surfaces The self-loosening behavior is mainly caused by slip at contactsurfacesTherefore the dynamics during self-loosening is themain focus of the following analysis This paper uses therelative motion of nodes to present the slip state which isdifferent from previous researches and it is proved to be ingreater detail by contrast with the traditional method usingthe friction relation

The process of the preload variation mainly consists oftwo stages (exampled in Section 41) Taking the bolt headbearing surface as an example the relative motion of nodes

Shock and Vibration 9

The assembling processThe simplified way

25

255

26

265

27

275

Prel

oad

(N)

10 150 5Time (s)

times104

Figure 16 The preload variations under different fastening ways

2000

4000

6000

8000

Prel

oad

(N)

50 100 1500Time (s)

Figure 17 The curve of preload variation during the 150 cycles

during the two stages is analyzed Because the clampedcomponents are assumed to be rigid bodies the relativerotation between contact surfaces is equivalent to the rotationof bolt around its axis In the calculations the uniformdistribution nodes 1sim8 are selected from the outside edge ofbolt and node A is the intersection point between the contactsurface and the axis of bolt The relative rotation at contactsurface can be simplified to the rotation angle of nodes 1sim8around node A (Figure 18)

According to Figure 19 the range of analysis time is 0sim1 s(the decline stage) and 145sim150 s (the flat stage) During thetwo stages the rotation angle of each calculation node aroundnode A is shown

As shown before all the nodes rotate along the loosedirection as a whole which causes the preload loss Howeverat the beginning of the self-loosening process not all of thenodes rotate at the same time but one node rotates firstlyand drives the rotation of the other nodes Moreover in theprocess of rotating the rotation angles of some nodes arelarge and some are small When the movement direction ofclamped component changes the rotation angles of thosewhose rotation angles are large previously begin to decreaseMeanwhile the rotation angles of thosewhose rotation anglesare small increase This presents a creep slip phenomenonat contact surface under reversed cyclic load With increaseof the loading cycles the preload continues to decline And

10 Shock and Vibration

1

82

3

4

5

6

7A

Figure 18 The diagrams of the contact surface and the calculation points

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

02 04 06 08 10Time (s)

1

15

2

25

3

35

Relat

ive r

otat

ion

angl

e (ra

d)

times10minus3

(a) The rapid decline stage

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

00425

00426

00427

Relat

ive r

otat

ion

angl

e (ra

d)

148 150146Time (s)

(b) The flat stage

Figure 19 The rotation angles of each point in different stages

finally all nodes present a back and forth rotation at one placewhich causes the flat stage

To analyze the slip state during the initial stage of self-loosening (when preload is 272 kN) all nodes along theouter edge are taken into account and their relative rotationvelocities around node A are carried out as shown inFigure 20 Figure 21 shows the relative rotation velocity ofeach calculation node at some moments It can be notedthat the contact surface is slipping in a creep form Forcomparison the frictionmethod is also applied in the analysisof the contact state Based on the local key parameter 120578119899calculated the slip state contours are displayed in Figure 22However there is no significant difference among the three

figures which reflects that this method cannot give a detaileddescription of the slip state for a short time Through theanalysis of a whole cycle it suggests that there are always tworegions whose velocity directions are opposite Owing to thecontinuity of motion it means that there is a stick region onthe contact surface at any moment and bolt self-loosing canoccur without complete slip on the bolt head bearing surface

In addition the relativemotion between thread interfacesis analyzed in a similar way Two helical segments are inter-cepted from the contact location of bolt and nut (Figure 23)respectivelyThe rotation velocities of nodes belonging to thetwo helical segments can be calculated to build the position-velocity fields of bolt and nut at any time and the velocity

Shock and Vibration 11

XY

Z

1 2 348

13

25

37

Figure 20 The node number along the outer edge

t = 02 st = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 st = 03 s

2 4 6 80Circumferential position (rad)

minus8

minus4

0

4

8

Relat

ive r

otat

ion

velo

city

(rad

s)

Figure 21 The relative rotation velocity of each node at different moment

between adjacent nodes can be obtained approximately bylinear interpolation Figure 24 shows the position-velocitycurve at 025 s

Based on the position-velocity curves of bolt and nut therelative position-velocity relationship between thread inter-faces can be acquired by subtracting them Figure 25 showsthe relative position-velocity relationships at some momentsIt can be seen that all curves intersect the horizontal linethat the value is zero This means that there is always a stick

region in the thread interfaces which is consistent with theconclusion presented on the bolt head bearing surface Theslip state contours between thread interfaces are also given forcomparison (Figure 26) However there is still no significantdifference among them

To further strengthen the trust in the results summedbefore the relation between transverse force (shear force)and transverse displacement during the initial fifteen cyclesis shown in Figure 27 It is noted that the hysteresis loop

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

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Journal of

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Submit your manuscripts athttpswwwhindawicom

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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International Journal of

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Navigation and Observation

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DistributedSensor Networks

International Journal of

Page 3: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

Shock and Vibration 3

R

B

C

A

D

r

Major diameter

Minor diameter

Thread root

1

2

3

4

Figure 2 The cross-section profile of external thread

120588 = radic311987512 119867 = radic31198752

(2)

where 119875 and 119889 represent the thread pitch and the nominaldiameter respectively 120588 is the root radius of the threadAnother cross-section which is a distance 119911 off the datumplane has the same shape as the datum one However in acylindrical coordinate itmust be rotated by an angle120593 whichcan be written as

120593 = 2120587119875 119911 (3)

In addition it can be known that the mathematicalexpression of the outer surface of thread is periodic

119903 (120579 119911) = 119903 (120579 + 2119899120587 119911 + 119898119875) (4)

In summary the complete expression of the thread cross-section profile can be expressed as follows

119903 (120579 119911)

=

120601 = 120579 + 120593 = 120579 + 2120587119875 1199111198892 minus 78119867 + 2120588 minus radic1205882 minus 119875241205872 1205792 (0 le 120601 le 1205791) 119867120587 120579 + 1198892 minus 78119867 (1205791 le 120601 le 1205792) 1198892 (1205792 le 120601 le 1205793) 119867120587 (2120587 minus 120579) + 1198892 minus 78119867 (1205793 le 120601 le 1205794) 1198892 minus 78119867 + 2120588 minus radic1205882 minus 119875241205872 (2120587 minus 120579)2 (1205794 le 120601 le 2120587)

1205791 = radic3120587120588119875 1205792 = 71205878 1205793 = 91205878 1205794 = 2120587 minus 1205791120588 le +radic311987512

(5)

Similarly the profile of the internal thread can beexpressed in the same manner and it also has the periodicalpiecewise function form

1199031015840 (120579 119911) = 1199031015840 (120579 + 2119899120587 119911 + 119898119875) 1199031015840 (120579 119911)

=

120601 = 120579 + 120593 = 2120587119875 11991111988912 = 1198892 minus 58119867 (0 le 120579 le 12057910158401) 119867120587 120579 + 1198892 minus 78119867 (12057910158401 le 120579 le 12057910158402) 1198892 + 78119867 minus 21205881015840 + radic12058810158402 minus 119875241205872 (120587 minus 120579)2 (12057910158402 le 120579 le 12057910158403) 119867120587 (2120587 minus 120579) + 1198892 minus 78119867 (12057910158403 le 120579 le 12057910158404) 11988912 (12057910158404 le 120579 le 2120587)

12057910158401 = 1205874 12057910158402 = 120587(1 minus radic31205881015840119875 )

4 Shock and Vibration

D

P pitchr

C

B

A

2

4

3

2

1

0

H

8

H

4

5

8Hd1

2

d

2minus

7

8H +

root radius

Figure 3 The cross-section profile along the bolt axis

12057910158403 = 120587(1 + radic31205881015840119875 ) 12057910158404 = 71205874 1205881015840 le radic324 119875

(6)

22 Automatic Mesh Generation of the Thread StructureThe mesh generation method Fukuoka proposed requiresmany cyclic operations on the two-dimensional elementssuch as ldquocopyrdquo ldquotranslaterdquo ldquorotaterdquo and ldquomergerdquo whicheasily cause the problem of expensive computation In thisstudy the thread structure is partitioned properly beforemeshing The hexahedral mesh generation is implementedby modifying the node coordinates based on cylindricalhexahedron meshes The detailed procedures are introducedbelow In addition a self-developedABAQUSplug-in ismadefor parametric modeling (Figure 4)

Step 1 Depending on the size of the bolt and nut the corre-sponding cylinders are modeled with hexahedral meshes inABAQUS To fit the shape of the thread well and improve thecalculation efficiency the model is divided into two parts thethread region and the nonthread region The thread regionis discretized with finer meshes to guarantee the simulationaccuracy of the contact state while the other region ismeshedwith relative coarse elements (Figure 5) The models are thenexported in the form of an INP file

Step 2 The node coordinates of the thread region areextracted from the INP file exported previously and theyare modified by a self-compiled program depending on the

Figure 4 The parametric modeling interface

mathematical expression of thread cross-section profile Themodified INP file is then imported to ABAQUS again andthe hexahedral models of threads are generated (Figure 6)

Step 3 The bolt shank and bolt head which are simplecylinders are built up andmeshed with hexahedral elementsThen they are merged with the thread part to obtain acomplete bolt model

Step 4 Finally the clamped components are modeled inABAQUS and all parts are assembled into a whole analysismodel of the bolt self-loosening problem (Figure 7)

Through the method described before the 3D finite ele-mentmodel which contains aM10lowast15 bolt and nut and twoclamped components is established using the commercialsoftware package ABAQUS There are a total of 58140 C3D8elements and 64731 nodes All components in this model areassumed to be purely elastic and Youngrsquos modulus Poissonrsquosratio and the density are 210GPa 03 and 7800 kgm3respectively

Contact interactions have been set between all slidingsurfaces including the interfaces between the threads boltunderhead surface and the upper part surface and nutsurface and the lower part surface Contact modeling isvery important to the simulation of the tightening andself-loosening process According to the work by Dingerand Friedrich [7] the augmented Lagrangian technique andthe penalty approach are applied to solve the normal andtangential contact problem respectively In this study thesurface constraint approach used for all contact pairs is amaster-slave finite sliding and node-to-surface assignmentConcretely to the interface between internal and externalthreads the surface of external threads is assigned the mastersurface to the interface between bolt and upper componentthe surface of upper component is assigned the mastersurface to the interface between nut and lower componentthe surface of lower component is assigned the mastersurface to the interface between clamped components thesurface of lower component is assigned the master surface

Shock and Vibration 5

Z

Y

X Z

Y

X

Figure 5 The hexahedral models of cylinders

X

Y

Z X

Y

Z

Figure 6 The hexahedral models of threads

X

Y

Z

Figure 7 The whole hexahedral model of a typical bolt joint

A nominal friction coefficient 01 is initially used for allsliding surfaces Considering the geometric nonlinearity theimplicit dynamicsmodule inABAQUS is used to simulate thetightening and self-loosening process

3 Analysis of the Tightening Process

31 Verification of the Accuracy of the FE Model The preloadrefers to the elastic restoring force of the bolt when it is

serving In engineering it is always controlled by tighteningtorque or rotation angle of the nut In this paper thetightening process analysis is performed by applying a rampcircumferential displacement 1205790 on the side surface of the nut(Figure 8) and then removing it after maintaining the valuefor a period The accuracy of finite element model is verifiedby contrast with the analytical and experimental results ontorque-tension relationship

Referring to the general rules of tightening for threadedfasteners given inGBT 168232 [25] the relationship betweentightening torque 119879119891 and bolt preload 119865119891 can be estimatedapproximately by

119879119891 = 119870119865119891119889 (7)

where 119870 is the torque coefficient and 119889 is the nominaldiameter of the bolt 119870 can be expressed as follows

119870 = 12119889 (119875120587 + 1205831199041198892 sec1205721015840 + 120583119882119863119882) (8)

where 119875 is the thread pitch 120583119904 is the coefficient of threadfriction 1198892 is the intermediate diameter 1205721015840 is half of the

6 Shock and Vibration

0

Figure 8 The loading diagram

FEA resultsFEM fitting resultsAnalytical results

times104

times1041 15 2 25 3 3505

Preload (N)

1

2

3

4

5

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 9 The contrast diagram of torque-tension relationships

thread profile angle (30 degrees for standard ISO threads)120583119882is the coefficient of underhead friction and119863119882 is the effectiveunderhead bearing contact radius which can be expressed asfollows when the underhead bearing face is circular

119863119882 = 23 times1198893119882 minus 1198893ℎ1198892119882 minus 1198892ℎ (9)

where 119889ℎ and 119889119882 are the internal diameter and the externaldiameter of the underhead bearing contact face respectively

To a M10 lowast 15 bolt and nut the torque-tension rela-tionship can be acquired by substituting relevant parametersinto (7)ndash(9) Figure 9 shows the comparison between theanalytical results and simulation results It can be seen thatthe FEA (finite element analysis) results are similar to theanalytical ones The torque coefficient 119870 by the analyticalmethod is 1453 while the value is 14749 by FEM (finiteelement method) The error between them is only 151

BoltBolted fixture

Load cellNut fixture

Locked spacer

Nut

Figure 10 The test rig

FEA resultsExperimental results

0

1

2

3

4

5

6

1 2 30Preload (N)

times104

times104

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 11 Comparison between the finite element method and theexperimental method

In addition a test rig has been developed as shown inFigure 10 with an aim to verify the accuracy of the FE modelIn this experiment two plates made of steel (30CrMnSiA)are clamped by a M10 lowast 15 bolt and nut Each plate has athickness of 10mmDuring the loading process the bolt headis fixed and a torque wrench is used to tighten the nut Thevalue of tightening torque is applied in the range of 0sim60NmBesides a load cell is attached between the bolt head andthe clamped component to measure the clamp force Thedata of fastener tension are recorded per 5Nm torque in thisexperiment

The curves in Figure 11 show the contrast results betweenfinite element method and the experimental method

Shock and Vibration 7

Δl Δl

Figure 12 The loading diagram of the simplified way

Through the comparison it can be seen that the differencebetween the finite element and the experimental resultsis tiny The accuracy of FEM is verified by analytical andexperimental study

32 Analysis of the Fastening States The preload is a veryimportant factor that should not be ignored in the study ofbolt self-loosening However few studies considered both thetightening process and the self-loosening process simulta-neously Most of them simulated the preload by stretchingthe bolt or using a cooling pretightening algorithm thatmakes the fastening state of bolt different from the realcase Therefore the differences of different fastening waysare discussed here followed by their effects on bolt self-loosening

To simulate the tightening process a circumferentialdisplacement 1205790 is applied on the side surface of the nutwhich is the same as the model validation process Besides asimplified way that stretches the bolt is made for comparisonThe two clamped components are separated by a distanceΔ119897 which is used to control the value of preload as shownin Figure 12 After the loading process the whole bolt jointbecomes static without external constraints and the resultanttorque at every contact surface is equal in magnitude Sothe resultant torque at contact surface between threads isregarded as the object Figure 13 presents the relationshipsbetween the torque and the preload in static state which areachieved by different fastening means

As shown before the value of the torque in the tighteningprocess is obviously higher than that obtained by stretchingthe bolt under the same preload which leads to makingthe self-loosening more likely to occur The resultant torqueon the thread interface consists of two parts the pitchtorque and the thread friction torque Figure 14 illustratesthe relationships between the preload the pitch torque thethread friction torque and the resultant torque by differentfastening means It can be noted that the pitch torque andthread friction torque possess the same direction whenconsidering the tightening process while it is opposite by

Simulating the tightening processStretching bolt

4000

8000

12000

16000

1 2 30

Preload (N)times104

Resu

ltant

torq

ue (N

middotmm

)Figure 13 The relationships between the torque and the preload

stretching the bolt which leads to a much smaller resultanttorque

4 Analysis of the Bolt Loosening Mechanism

Considering the influence of the tightening process thepreload is produced by applying a constrained circumferen-tial displacement on the side surface of the nut followed by itsremoval To conduct the FEA of bolt joints self-loosening atransversal excitation 119904 is loaded on the clamped components(Figure 15) which is determined by the following formula

119904 = 1199040 sin (120596119905) (10)

where 1199040 and 120596 represent the excitation amplitude andangular frequency which are 003mm and 2120587 in this paperrespectively The excitation amplitude is smaller than theclearance between the bolt body and the clamped partTo reduce computational cost the clamped componentsare assumed to be rigid bodies when simulating the self-loosening process of bolt joints Since the vibration frequencyis set to 1Hz which is low the system can be treated as aquasi-static process Because the self-loosening behavior ismainly caused by slip at contact surfaces the critical outputparametersmonitored in this analysis include the preload andthe motion of nodes at contact surfaces which are used toanalyze the slip state

41 Evolution of the Preload during Self-Loosening To inves-tigate the effects of different fastening means on the self-loosening process of the bolt joint the same preload isproduced by adjusting the circumferential displacement andthe separation distance in finite element analysis and theother attributes of the two models are completely identical Acyclic transversal displacement is then loaded on the clamped

8 Shock and Vibration

0

Resultant torquePitch torqueThread friction torque

4000

8000

12000

16000

2 31Preload (N) times104

Torq

ue (N

middotmm

)

(a) Simulating the tightening process

Resultant torquePitch torqueThread friction torque

2 31Preload (N) times104

minus8000

minus4000

0

4000

8000

Torq

ue (N

middotmm

)

(b) Stretching the bolt

Figure 14 The relationships between different kinds of torque and preload

s

s s

t (s)

003 mm

105

s = 003 MCH 2t

Figure 15 The diagrams of transversal harmonic load

components The evolutions of the preload of differentfastening means during the first 15 load cycles are illustratedin Figure 16 It shows that at the same load cycle the self-loosening is much easier to appear andmore preload gets lostwhen the preload is produced by the simplified way This isbecause the resultant torque at contact surface is smaller

It can be drawn from the above analysis that the approx-imate pretightening algorithm cannot take the place of thetightening process to study the self-loosening mechanism ofbolt joints To preform further analysis of the evolution ofthe preload during bolt self-loosening the number of loadingcycles is increased to 150 and the initial preload is set to 8 kNThe curve in Figure 17 displays the preload variation duringthe 150 cycles It can be seen that with the increase of theloading cycles the variation curve of the preload tends to be

flat after a rapid decline The whole process can be roughlydivided into two stages the rapid decline stage and the flatstage which is in accordance with the result of Junker

42 Analysis of the Slip State at Contact Surfaces The self-loosening behavior is mainly caused by slip at contactsurfacesTherefore the dynamics during self-loosening is themain focus of the following analysis This paper uses therelative motion of nodes to present the slip state which isdifferent from previous researches and it is proved to be ingreater detail by contrast with the traditional method usingthe friction relation

The process of the preload variation mainly consists oftwo stages (exampled in Section 41) Taking the bolt headbearing surface as an example the relative motion of nodes

Shock and Vibration 9

The assembling processThe simplified way

25

255

26

265

27

275

Prel

oad

(N)

10 150 5Time (s)

times104

Figure 16 The preload variations under different fastening ways

2000

4000

6000

8000

Prel

oad

(N)

50 100 1500Time (s)

Figure 17 The curve of preload variation during the 150 cycles

during the two stages is analyzed Because the clampedcomponents are assumed to be rigid bodies the relativerotation between contact surfaces is equivalent to the rotationof bolt around its axis In the calculations the uniformdistribution nodes 1sim8 are selected from the outside edge ofbolt and node A is the intersection point between the contactsurface and the axis of bolt The relative rotation at contactsurface can be simplified to the rotation angle of nodes 1sim8around node A (Figure 18)

According to Figure 19 the range of analysis time is 0sim1 s(the decline stage) and 145sim150 s (the flat stage) During thetwo stages the rotation angle of each calculation node aroundnode A is shown

As shown before all the nodes rotate along the loosedirection as a whole which causes the preload loss Howeverat the beginning of the self-loosening process not all of thenodes rotate at the same time but one node rotates firstlyand drives the rotation of the other nodes Moreover in theprocess of rotating the rotation angles of some nodes arelarge and some are small When the movement direction ofclamped component changes the rotation angles of thosewhose rotation angles are large previously begin to decreaseMeanwhile the rotation angles of thosewhose rotation anglesare small increase This presents a creep slip phenomenonat contact surface under reversed cyclic load With increaseof the loading cycles the preload continues to decline And

10 Shock and Vibration

1

82

3

4

5

6

7A

Figure 18 The diagrams of the contact surface and the calculation points

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

02 04 06 08 10Time (s)

1

15

2

25

3

35

Relat

ive r

otat

ion

angl

e (ra

d)

times10minus3

(a) The rapid decline stage

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

00425

00426

00427

Relat

ive r

otat

ion

angl

e (ra

d)

148 150146Time (s)

(b) The flat stage

Figure 19 The rotation angles of each point in different stages

finally all nodes present a back and forth rotation at one placewhich causes the flat stage

To analyze the slip state during the initial stage of self-loosening (when preload is 272 kN) all nodes along theouter edge are taken into account and their relative rotationvelocities around node A are carried out as shown inFigure 20 Figure 21 shows the relative rotation velocity ofeach calculation node at some moments It can be notedthat the contact surface is slipping in a creep form Forcomparison the frictionmethod is also applied in the analysisof the contact state Based on the local key parameter 120578119899calculated the slip state contours are displayed in Figure 22However there is no significant difference among the three

figures which reflects that this method cannot give a detaileddescription of the slip state for a short time Through theanalysis of a whole cycle it suggests that there are always tworegions whose velocity directions are opposite Owing to thecontinuity of motion it means that there is a stick region onthe contact surface at any moment and bolt self-loosing canoccur without complete slip on the bolt head bearing surface

In addition the relativemotion between thread interfacesis analyzed in a similar way Two helical segments are inter-cepted from the contact location of bolt and nut (Figure 23)respectivelyThe rotation velocities of nodes belonging to thetwo helical segments can be calculated to build the position-velocity fields of bolt and nut at any time and the velocity

Shock and Vibration 11

XY

Z

1 2 348

13

25

37

Figure 20 The node number along the outer edge

t = 02 st = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 st = 03 s

2 4 6 80Circumferential position (rad)

minus8

minus4

0

4

8

Relat

ive r

otat

ion

velo

city

(rad

s)

Figure 21 The relative rotation velocity of each node at different moment

between adjacent nodes can be obtained approximately bylinear interpolation Figure 24 shows the position-velocitycurve at 025 s

Based on the position-velocity curves of bolt and nut therelative position-velocity relationship between thread inter-faces can be acquired by subtracting them Figure 25 showsthe relative position-velocity relationships at some momentsIt can be seen that all curves intersect the horizontal linethat the value is zero This means that there is always a stick

region in the thread interfaces which is consistent with theconclusion presented on the bolt head bearing surface Theslip state contours between thread interfaces are also given forcomparison (Figure 26) However there is still no significantdifference among them

To further strengthen the trust in the results summedbefore the relation between transverse force (shear force)and transverse displacement during the initial fifteen cyclesis shown in Figure 27 It is noted that the hysteresis loop

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

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Submit your manuscripts athttpswwwhindawicom

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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International Journal of

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DistributedSensor Networks

International Journal of

Page 4: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

4 Shock and Vibration

D

P pitchr

C

B

A

2

4

3

2

1

0

H

8

H

4

5

8Hd1

2

d

2minus

7

8H +

root radius

Figure 3 The cross-section profile along the bolt axis

12057910158403 = 120587(1 + radic31205881015840119875 ) 12057910158404 = 71205874 1205881015840 le radic324 119875

(6)

22 Automatic Mesh Generation of the Thread StructureThe mesh generation method Fukuoka proposed requiresmany cyclic operations on the two-dimensional elementssuch as ldquocopyrdquo ldquotranslaterdquo ldquorotaterdquo and ldquomergerdquo whicheasily cause the problem of expensive computation In thisstudy the thread structure is partitioned properly beforemeshing The hexahedral mesh generation is implementedby modifying the node coordinates based on cylindricalhexahedron meshes The detailed procedures are introducedbelow In addition a self-developedABAQUSplug-in ismadefor parametric modeling (Figure 4)

Step 1 Depending on the size of the bolt and nut the corre-sponding cylinders are modeled with hexahedral meshes inABAQUS To fit the shape of the thread well and improve thecalculation efficiency the model is divided into two parts thethread region and the nonthread region The thread regionis discretized with finer meshes to guarantee the simulationaccuracy of the contact state while the other region ismeshedwith relative coarse elements (Figure 5) The models are thenexported in the form of an INP file

Step 2 The node coordinates of the thread region areextracted from the INP file exported previously and theyare modified by a self-compiled program depending on the

Figure 4 The parametric modeling interface

mathematical expression of thread cross-section profile Themodified INP file is then imported to ABAQUS again andthe hexahedral models of threads are generated (Figure 6)

Step 3 The bolt shank and bolt head which are simplecylinders are built up andmeshed with hexahedral elementsThen they are merged with the thread part to obtain acomplete bolt model

Step 4 Finally the clamped components are modeled inABAQUS and all parts are assembled into a whole analysismodel of the bolt self-loosening problem (Figure 7)

Through the method described before the 3D finite ele-mentmodel which contains aM10lowast15 bolt and nut and twoclamped components is established using the commercialsoftware package ABAQUS There are a total of 58140 C3D8elements and 64731 nodes All components in this model areassumed to be purely elastic and Youngrsquos modulus Poissonrsquosratio and the density are 210GPa 03 and 7800 kgm3respectively

Contact interactions have been set between all slidingsurfaces including the interfaces between the threads boltunderhead surface and the upper part surface and nutsurface and the lower part surface Contact modeling isvery important to the simulation of the tightening andself-loosening process According to the work by Dingerand Friedrich [7] the augmented Lagrangian technique andthe penalty approach are applied to solve the normal andtangential contact problem respectively In this study thesurface constraint approach used for all contact pairs is amaster-slave finite sliding and node-to-surface assignmentConcretely to the interface between internal and externalthreads the surface of external threads is assigned the mastersurface to the interface between bolt and upper componentthe surface of upper component is assigned the mastersurface to the interface between nut and lower componentthe surface of lower component is assigned the mastersurface to the interface between clamped components thesurface of lower component is assigned the master surface

Shock and Vibration 5

Z

Y

X Z

Y

X

Figure 5 The hexahedral models of cylinders

X

Y

Z X

Y

Z

Figure 6 The hexahedral models of threads

X

Y

Z

Figure 7 The whole hexahedral model of a typical bolt joint

A nominal friction coefficient 01 is initially used for allsliding surfaces Considering the geometric nonlinearity theimplicit dynamicsmodule inABAQUS is used to simulate thetightening and self-loosening process

3 Analysis of the Tightening Process

31 Verification of the Accuracy of the FE Model The preloadrefers to the elastic restoring force of the bolt when it is

serving In engineering it is always controlled by tighteningtorque or rotation angle of the nut In this paper thetightening process analysis is performed by applying a rampcircumferential displacement 1205790 on the side surface of the nut(Figure 8) and then removing it after maintaining the valuefor a period The accuracy of finite element model is verifiedby contrast with the analytical and experimental results ontorque-tension relationship

Referring to the general rules of tightening for threadedfasteners given inGBT 168232 [25] the relationship betweentightening torque 119879119891 and bolt preload 119865119891 can be estimatedapproximately by

119879119891 = 119870119865119891119889 (7)

where 119870 is the torque coefficient and 119889 is the nominaldiameter of the bolt 119870 can be expressed as follows

119870 = 12119889 (119875120587 + 1205831199041198892 sec1205721015840 + 120583119882119863119882) (8)

where 119875 is the thread pitch 120583119904 is the coefficient of threadfriction 1198892 is the intermediate diameter 1205721015840 is half of the

6 Shock and Vibration

0

Figure 8 The loading diagram

FEA resultsFEM fitting resultsAnalytical results

times104

times1041 15 2 25 3 3505

Preload (N)

1

2

3

4

5

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 9 The contrast diagram of torque-tension relationships

thread profile angle (30 degrees for standard ISO threads)120583119882is the coefficient of underhead friction and119863119882 is the effectiveunderhead bearing contact radius which can be expressed asfollows when the underhead bearing face is circular

119863119882 = 23 times1198893119882 minus 1198893ℎ1198892119882 minus 1198892ℎ (9)

where 119889ℎ and 119889119882 are the internal diameter and the externaldiameter of the underhead bearing contact face respectively

To a M10 lowast 15 bolt and nut the torque-tension rela-tionship can be acquired by substituting relevant parametersinto (7)ndash(9) Figure 9 shows the comparison between theanalytical results and simulation results It can be seen thatthe FEA (finite element analysis) results are similar to theanalytical ones The torque coefficient 119870 by the analyticalmethod is 1453 while the value is 14749 by FEM (finiteelement method) The error between them is only 151

BoltBolted fixture

Load cellNut fixture

Locked spacer

Nut

Figure 10 The test rig

FEA resultsExperimental results

0

1

2

3

4

5

6

1 2 30Preload (N)

times104

times104

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 11 Comparison between the finite element method and theexperimental method

In addition a test rig has been developed as shown inFigure 10 with an aim to verify the accuracy of the FE modelIn this experiment two plates made of steel (30CrMnSiA)are clamped by a M10 lowast 15 bolt and nut Each plate has athickness of 10mmDuring the loading process the bolt headis fixed and a torque wrench is used to tighten the nut Thevalue of tightening torque is applied in the range of 0sim60NmBesides a load cell is attached between the bolt head andthe clamped component to measure the clamp force Thedata of fastener tension are recorded per 5Nm torque in thisexperiment

The curves in Figure 11 show the contrast results betweenfinite element method and the experimental method

Shock and Vibration 7

Δl Δl

Figure 12 The loading diagram of the simplified way

Through the comparison it can be seen that the differencebetween the finite element and the experimental resultsis tiny The accuracy of FEM is verified by analytical andexperimental study

32 Analysis of the Fastening States The preload is a veryimportant factor that should not be ignored in the study ofbolt self-loosening However few studies considered both thetightening process and the self-loosening process simulta-neously Most of them simulated the preload by stretchingthe bolt or using a cooling pretightening algorithm thatmakes the fastening state of bolt different from the realcase Therefore the differences of different fastening waysare discussed here followed by their effects on bolt self-loosening

To simulate the tightening process a circumferentialdisplacement 1205790 is applied on the side surface of the nutwhich is the same as the model validation process Besides asimplified way that stretches the bolt is made for comparisonThe two clamped components are separated by a distanceΔ119897 which is used to control the value of preload as shownin Figure 12 After the loading process the whole bolt jointbecomes static without external constraints and the resultanttorque at every contact surface is equal in magnitude Sothe resultant torque at contact surface between threads isregarded as the object Figure 13 presents the relationshipsbetween the torque and the preload in static state which areachieved by different fastening means

As shown before the value of the torque in the tighteningprocess is obviously higher than that obtained by stretchingthe bolt under the same preload which leads to makingthe self-loosening more likely to occur The resultant torqueon the thread interface consists of two parts the pitchtorque and the thread friction torque Figure 14 illustratesthe relationships between the preload the pitch torque thethread friction torque and the resultant torque by differentfastening means It can be noted that the pitch torque andthread friction torque possess the same direction whenconsidering the tightening process while it is opposite by

Simulating the tightening processStretching bolt

4000

8000

12000

16000

1 2 30

Preload (N)times104

Resu

ltant

torq

ue (N

middotmm

)Figure 13 The relationships between the torque and the preload

stretching the bolt which leads to a much smaller resultanttorque

4 Analysis of the Bolt Loosening Mechanism

Considering the influence of the tightening process thepreload is produced by applying a constrained circumferen-tial displacement on the side surface of the nut followed by itsremoval To conduct the FEA of bolt joints self-loosening atransversal excitation 119904 is loaded on the clamped components(Figure 15) which is determined by the following formula

119904 = 1199040 sin (120596119905) (10)

where 1199040 and 120596 represent the excitation amplitude andangular frequency which are 003mm and 2120587 in this paperrespectively The excitation amplitude is smaller than theclearance between the bolt body and the clamped partTo reduce computational cost the clamped componentsare assumed to be rigid bodies when simulating the self-loosening process of bolt joints Since the vibration frequencyis set to 1Hz which is low the system can be treated as aquasi-static process Because the self-loosening behavior ismainly caused by slip at contact surfaces the critical outputparametersmonitored in this analysis include the preload andthe motion of nodes at contact surfaces which are used toanalyze the slip state

41 Evolution of the Preload during Self-Loosening To inves-tigate the effects of different fastening means on the self-loosening process of the bolt joint the same preload isproduced by adjusting the circumferential displacement andthe separation distance in finite element analysis and theother attributes of the two models are completely identical Acyclic transversal displacement is then loaded on the clamped

8 Shock and Vibration

0

Resultant torquePitch torqueThread friction torque

4000

8000

12000

16000

2 31Preload (N) times104

Torq

ue (N

middotmm

)

(a) Simulating the tightening process

Resultant torquePitch torqueThread friction torque

2 31Preload (N) times104

minus8000

minus4000

0

4000

8000

Torq

ue (N

middotmm

)

(b) Stretching the bolt

Figure 14 The relationships between different kinds of torque and preload

s

s s

t (s)

003 mm

105

s = 003 MCH 2t

Figure 15 The diagrams of transversal harmonic load

components The evolutions of the preload of differentfastening means during the first 15 load cycles are illustratedin Figure 16 It shows that at the same load cycle the self-loosening is much easier to appear andmore preload gets lostwhen the preload is produced by the simplified way This isbecause the resultant torque at contact surface is smaller

It can be drawn from the above analysis that the approx-imate pretightening algorithm cannot take the place of thetightening process to study the self-loosening mechanism ofbolt joints To preform further analysis of the evolution ofthe preload during bolt self-loosening the number of loadingcycles is increased to 150 and the initial preload is set to 8 kNThe curve in Figure 17 displays the preload variation duringthe 150 cycles It can be seen that with the increase of theloading cycles the variation curve of the preload tends to be

flat after a rapid decline The whole process can be roughlydivided into two stages the rapid decline stage and the flatstage which is in accordance with the result of Junker

42 Analysis of the Slip State at Contact Surfaces The self-loosening behavior is mainly caused by slip at contactsurfacesTherefore the dynamics during self-loosening is themain focus of the following analysis This paper uses therelative motion of nodes to present the slip state which isdifferent from previous researches and it is proved to be ingreater detail by contrast with the traditional method usingthe friction relation

The process of the preload variation mainly consists oftwo stages (exampled in Section 41) Taking the bolt headbearing surface as an example the relative motion of nodes

Shock and Vibration 9

The assembling processThe simplified way

25

255

26

265

27

275

Prel

oad

(N)

10 150 5Time (s)

times104

Figure 16 The preload variations under different fastening ways

2000

4000

6000

8000

Prel

oad

(N)

50 100 1500Time (s)

Figure 17 The curve of preload variation during the 150 cycles

during the two stages is analyzed Because the clampedcomponents are assumed to be rigid bodies the relativerotation between contact surfaces is equivalent to the rotationof bolt around its axis In the calculations the uniformdistribution nodes 1sim8 are selected from the outside edge ofbolt and node A is the intersection point between the contactsurface and the axis of bolt The relative rotation at contactsurface can be simplified to the rotation angle of nodes 1sim8around node A (Figure 18)

According to Figure 19 the range of analysis time is 0sim1 s(the decline stage) and 145sim150 s (the flat stage) During thetwo stages the rotation angle of each calculation node aroundnode A is shown

As shown before all the nodes rotate along the loosedirection as a whole which causes the preload loss Howeverat the beginning of the self-loosening process not all of thenodes rotate at the same time but one node rotates firstlyand drives the rotation of the other nodes Moreover in theprocess of rotating the rotation angles of some nodes arelarge and some are small When the movement direction ofclamped component changes the rotation angles of thosewhose rotation angles are large previously begin to decreaseMeanwhile the rotation angles of thosewhose rotation anglesare small increase This presents a creep slip phenomenonat contact surface under reversed cyclic load With increaseof the loading cycles the preload continues to decline And

10 Shock and Vibration

1

82

3

4

5

6

7A

Figure 18 The diagrams of the contact surface and the calculation points

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

02 04 06 08 10Time (s)

1

15

2

25

3

35

Relat

ive r

otat

ion

angl

e (ra

d)

times10minus3

(a) The rapid decline stage

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

00425

00426

00427

Relat

ive r

otat

ion

angl

e (ra

d)

148 150146Time (s)

(b) The flat stage

Figure 19 The rotation angles of each point in different stages

finally all nodes present a back and forth rotation at one placewhich causes the flat stage

To analyze the slip state during the initial stage of self-loosening (when preload is 272 kN) all nodes along theouter edge are taken into account and their relative rotationvelocities around node A are carried out as shown inFigure 20 Figure 21 shows the relative rotation velocity ofeach calculation node at some moments It can be notedthat the contact surface is slipping in a creep form Forcomparison the frictionmethod is also applied in the analysisof the contact state Based on the local key parameter 120578119899calculated the slip state contours are displayed in Figure 22However there is no significant difference among the three

figures which reflects that this method cannot give a detaileddescription of the slip state for a short time Through theanalysis of a whole cycle it suggests that there are always tworegions whose velocity directions are opposite Owing to thecontinuity of motion it means that there is a stick region onthe contact surface at any moment and bolt self-loosing canoccur without complete slip on the bolt head bearing surface

In addition the relativemotion between thread interfacesis analyzed in a similar way Two helical segments are inter-cepted from the contact location of bolt and nut (Figure 23)respectivelyThe rotation velocities of nodes belonging to thetwo helical segments can be calculated to build the position-velocity fields of bolt and nut at any time and the velocity

Shock and Vibration 11

XY

Z

1 2 348

13

25

37

Figure 20 The node number along the outer edge

t = 02 st = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 st = 03 s

2 4 6 80Circumferential position (rad)

minus8

minus4

0

4

8

Relat

ive r

otat

ion

velo

city

(rad

s)

Figure 21 The relative rotation velocity of each node at different moment

between adjacent nodes can be obtained approximately bylinear interpolation Figure 24 shows the position-velocitycurve at 025 s

Based on the position-velocity curves of bolt and nut therelative position-velocity relationship between thread inter-faces can be acquired by subtracting them Figure 25 showsthe relative position-velocity relationships at some momentsIt can be seen that all curves intersect the horizontal linethat the value is zero This means that there is always a stick

region in the thread interfaces which is consistent with theconclusion presented on the bolt head bearing surface Theslip state contours between thread interfaces are also given forcomparison (Figure 26) However there is still no significantdifference among them

To further strengthen the trust in the results summedbefore the relation between transverse force (shear force)and transverse displacement during the initial fifteen cyclesis shown in Figure 27 It is noted that the hysteresis loop

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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International Journal of

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DistributedSensor Networks

International Journal of

Page 5: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

Shock and Vibration 5

Z

Y

X Z

Y

X

Figure 5 The hexahedral models of cylinders

X

Y

Z X

Y

Z

Figure 6 The hexahedral models of threads

X

Y

Z

Figure 7 The whole hexahedral model of a typical bolt joint

A nominal friction coefficient 01 is initially used for allsliding surfaces Considering the geometric nonlinearity theimplicit dynamicsmodule inABAQUS is used to simulate thetightening and self-loosening process

3 Analysis of the Tightening Process

31 Verification of the Accuracy of the FE Model The preloadrefers to the elastic restoring force of the bolt when it is

serving In engineering it is always controlled by tighteningtorque or rotation angle of the nut In this paper thetightening process analysis is performed by applying a rampcircumferential displacement 1205790 on the side surface of the nut(Figure 8) and then removing it after maintaining the valuefor a period The accuracy of finite element model is verifiedby contrast with the analytical and experimental results ontorque-tension relationship

Referring to the general rules of tightening for threadedfasteners given inGBT 168232 [25] the relationship betweentightening torque 119879119891 and bolt preload 119865119891 can be estimatedapproximately by

119879119891 = 119870119865119891119889 (7)

where 119870 is the torque coefficient and 119889 is the nominaldiameter of the bolt 119870 can be expressed as follows

119870 = 12119889 (119875120587 + 1205831199041198892 sec1205721015840 + 120583119882119863119882) (8)

where 119875 is the thread pitch 120583119904 is the coefficient of threadfriction 1198892 is the intermediate diameter 1205721015840 is half of the

6 Shock and Vibration

0

Figure 8 The loading diagram

FEA resultsFEM fitting resultsAnalytical results

times104

times1041 15 2 25 3 3505

Preload (N)

1

2

3

4

5

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 9 The contrast diagram of torque-tension relationships

thread profile angle (30 degrees for standard ISO threads)120583119882is the coefficient of underhead friction and119863119882 is the effectiveunderhead bearing contact radius which can be expressed asfollows when the underhead bearing face is circular

119863119882 = 23 times1198893119882 minus 1198893ℎ1198892119882 minus 1198892ℎ (9)

where 119889ℎ and 119889119882 are the internal diameter and the externaldiameter of the underhead bearing contact face respectively

To a M10 lowast 15 bolt and nut the torque-tension rela-tionship can be acquired by substituting relevant parametersinto (7)ndash(9) Figure 9 shows the comparison between theanalytical results and simulation results It can be seen thatthe FEA (finite element analysis) results are similar to theanalytical ones The torque coefficient 119870 by the analyticalmethod is 1453 while the value is 14749 by FEM (finiteelement method) The error between them is only 151

BoltBolted fixture

Load cellNut fixture

Locked spacer

Nut

Figure 10 The test rig

FEA resultsExperimental results

0

1

2

3

4

5

6

1 2 30Preload (N)

times104

times104

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 11 Comparison between the finite element method and theexperimental method

In addition a test rig has been developed as shown inFigure 10 with an aim to verify the accuracy of the FE modelIn this experiment two plates made of steel (30CrMnSiA)are clamped by a M10 lowast 15 bolt and nut Each plate has athickness of 10mmDuring the loading process the bolt headis fixed and a torque wrench is used to tighten the nut Thevalue of tightening torque is applied in the range of 0sim60NmBesides a load cell is attached between the bolt head andthe clamped component to measure the clamp force Thedata of fastener tension are recorded per 5Nm torque in thisexperiment

The curves in Figure 11 show the contrast results betweenfinite element method and the experimental method

Shock and Vibration 7

Δl Δl

Figure 12 The loading diagram of the simplified way

Through the comparison it can be seen that the differencebetween the finite element and the experimental resultsis tiny The accuracy of FEM is verified by analytical andexperimental study

32 Analysis of the Fastening States The preload is a veryimportant factor that should not be ignored in the study ofbolt self-loosening However few studies considered both thetightening process and the self-loosening process simulta-neously Most of them simulated the preload by stretchingthe bolt or using a cooling pretightening algorithm thatmakes the fastening state of bolt different from the realcase Therefore the differences of different fastening waysare discussed here followed by their effects on bolt self-loosening

To simulate the tightening process a circumferentialdisplacement 1205790 is applied on the side surface of the nutwhich is the same as the model validation process Besides asimplified way that stretches the bolt is made for comparisonThe two clamped components are separated by a distanceΔ119897 which is used to control the value of preload as shownin Figure 12 After the loading process the whole bolt jointbecomes static without external constraints and the resultanttorque at every contact surface is equal in magnitude Sothe resultant torque at contact surface between threads isregarded as the object Figure 13 presents the relationshipsbetween the torque and the preload in static state which areachieved by different fastening means

As shown before the value of the torque in the tighteningprocess is obviously higher than that obtained by stretchingthe bolt under the same preload which leads to makingthe self-loosening more likely to occur The resultant torqueon the thread interface consists of two parts the pitchtorque and the thread friction torque Figure 14 illustratesthe relationships between the preload the pitch torque thethread friction torque and the resultant torque by differentfastening means It can be noted that the pitch torque andthread friction torque possess the same direction whenconsidering the tightening process while it is opposite by

Simulating the tightening processStretching bolt

4000

8000

12000

16000

1 2 30

Preload (N)times104

Resu

ltant

torq

ue (N

middotmm

)Figure 13 The relationships between the torque and the preload

stretching the bolt which leads to a much smaller resultanttorque

4 Analysis of the Bolt Loosening Mechanism

Considering the influence of the tightening process thepreload is produced by applying a constrained circumferen-tial displacement on the side surface of the nut followed by itsremoval To conduct the FEA of bolt joints self-loosening atransversal excitation 119904 is loaded on the clamped components(Figure 15) which is determined by the following formula

119904 = 1199040 sin (120596119905) (10)

where 1199040 and 120596 represent the excitation amplitude andangular frequency which are 003mm and 2120587 in this paperrespectively The excitation amplitude is smaller than theclearance between the bolt body and the clamped partTo reduce computational cost the clamped componentsare assumed to be rigid bodies when simulating the self-loosening process of bolt joints Since the vibration frequencyis set to 1Hz which is low the system can be treated as aquasi-static process Because the self-loosening behavior ismainly caused by slip at contact surfaces the critical outputparametersmonitored in this analysis include the preload andthe motion of nodes at contact surfaces which are used toanalyze the slip state

41 Evolution of the Preload during Self-Loosening To inves-tigate the effects of different fastening means on the self-loosening process of the bolt joint the same preload isproduced by adjusting the circumferential displacement andthe separation distance in finite element analysis and theother attributes of the two models are completely identical Acyclic transversal displacement is then loaded on the clamped

8 Shock and Vibration

0

Resultant torquePitch torqueThread friction torque

4000

8000

12000

16000

2 31Preload (N) times104

Torq

ue (N

middotmm

)

(a) Simulating the tightening process

Resultant torquePitch torqueThread friction torque

2 31Preload (N) times104

minus8000

minus4000

0

4000

8000

Torq

ue (N

middotmm

)

(b) Stretching the bolt

Figure 14 The relationships between different kinds of torque and preload

s

s s

t (s)

003 mm

105

s = 003 MCH 2t

Figure 15 The diagrams of transversal harmonic load

components The evolutions of the preload of differentfastening means during the first 15 load cycles are illustratedin Figure 16 It shows that at the same load cycle the self-loosening is much easier to appear andmore preload gets lostwhen the preload is produced by the simplified way This isbecause the resultant torque at contact surface is smaller

It can be drawn from the above analysis that the approx-imate pretightening algorithm cannot take the place of thetightening process to study the self-loosening mechanism ofbolt joints To preform further analysis of the evolution ofthe preload during bolt self-loosening the number of loadingcycles is increased to 150 and the initial preload is set to 8 kNThe curve in Figure 17 displays the preload variation duringthe 150 cycles It can be seen that with the increase of theloading cycles the variation curve of the preload tends to be

flat after a rapid decline The whole process can be roughlydivided into two stages the rapid decline stage and the flatstage which is in accordance with the result of Junker

42 Analysis of the Slip State at Contact Surfaces The self-loosening behavior is mainly caused by slip at contactsurfacesTherefore the dynamics during self-loosening is themain focus of the following analysis This paper uses therelative motion of nodes to present the slip state which isdifferent from previous researches and it is proved to be ingreater detail by contrast with the traditional method usingthe friction relation

The process of the preload variation mainly consists oftwo stages (exampled in Section 41) Taking the bolt headbearing surface as an example the relative motion of nodes

Shock and Vibration 9

The assembling processThe simplified way

25

255

26

265

27

275

Prel

oad

(N)

10 150 5Time (s)

times104

Figure 16 The preload variations under different fastening ways

2000

4000

6000

8000

Prel

oad

(N)

50 100 1500Time (s)

Figure 17 The curve of preload variation during the 150 cycles

during the two stages is analyzed Because the clampedcomponents are assumed to be rigid bodies the relativerotation between contact surfaces is equivalent to the rotationof bolt around its axis In the calculations the uniformdistribution nodes 1sim8 are selected from the outside edge ofbolt and node A is the intersection point between the contactsurface and the axis of bolt The relative rotation at contactsurface can be simplified to the rotation angle of nodes 1sim8around node A (Figure 18)

According to Figure 19 the range of analysis time is 0sim1 s(the decline stage) and 145sim150 s (the flat stage) During thetwo stages the rotation angle of each calculation node aroundnode A is shown

As shown before all the nodes rotate along the loosedirection as a whole which causes the preload loss Howeverat the beginning of the self-loosening process not all of thenodes rotate at the same time but one node rotates firstlyand drives the rotation of the other nodes Moreover in theprocess of rotating the rotation angles of some nodes arelarge and some are small When the movement direction ofclamped component changes the rotation angles of thosewhose rotation angles are large previously begin to decreaseMeanwhile the rotation angles of thosewhose rotation anglesare small increase This presents a creep slip phenomenonat contact surface under reversed cyclic load With increaseof the loading cycles the preload continues to decline And

10 Shock and Vibration

1

82

3

4

5

6

7A

Figure 18 The diagrams of the contact surface and the calculation points

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

02 04 06 08 10Time (s)

1

15

2

25

3

35

Relat

ive r

otat

ion

angl

e (ra

d)

times10minus3

(a) The rapid decline stage

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

00425

00426

00427

Relat

ive r

otat

ion

angl

e (ra

d)

148 150146Time (s)

(b) The flat stage

Figure 19 The rotation angles of each point in different stages

finally all nodes present a back and forth rotation at one placewhich causes the flat stage

To analyze the slip state during the initial stage of self-loosening (when preload is 272 kN) all nodes along theouter edge are taken into account and their relative rotationvelocities around node A are carried out as shown inFigure 20 Figure 21 shows the relative rotation velocity ofeach calculation node at some moments It can be notedthat the contact surface is slipping in a creep form Forcomparison the frictionmethod is also applied in the analysisof the contact state Based on the local key parameter 120578119899calculated the slip state contours are displayed in Figure 22However there is no significant difference among the three

figures which reflects that this method cannot give a detaileddescription of the slip state for a short time Through theanalysis of a whole cycle it suggests that there are always tworegions whose velocity directions are opposite Owing to thecontinuity of motion it means that there is a stick region onthe contact surface at any moment and bolt self-loosing canoccur without complete slip on the bolt head bearing surface

In addition the relativemotion between thread interfacesis analyzed in a similar way Two helical segments are inter-cepted from the contact location of bolt and nut (Figure 23)respectivelyThe rotation velocities of nodes belonging to thetwo helical segments can be calculated to build the position-velocity fields of bolt and nut at any time and the velocity

Shock and Vibration 11

XY

Z

1 2 348

13

25

37

Figure 20 The node number along the outer edge

t = 02 st = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 st = 03 s

2 4 6 80Circumferential position (rad)

minus8

minus4

0

4

8

Relat

ive r

otat

ion

velo

city

(rad

s)

Figure 21 The relative rotation velocity of each node at different moment

between adjacent nodes can be obtained approximately bylinear interpolation Figure 24 shows the position-velocitycurve at 025 s

Based on the position-velocity curves of bolt and nut therelative position-velocity relationship between thread inter-faces can be acquired by subtracting them Figure 25 showsthe relative position-velocity relationships at some momentsIt can be seen that all curves intersect the horizontal linethat the value is zero This means that there is always a stick

region in the thread interfaces which is consistent with theconclusion presented on the bolt head bearing surface Theslip state contours between thread interfaces are also given forcomparison (Figure 26) However there is still no significantdifference among them

To further strengthen the trust in the results summedbefore the relation between transverse force (shear force)and transverse displacement during the initial fifteen cyclesis shown in Figure 27 It is noted that the hysteresis loop

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

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Shock and Vibration

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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International Journal of

Page 6: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

6 Shock and Vibration

0

Figure 8 The loading diagram

FEA resultsFEM fitting resultsAnalytical results

times104

times1041 15 2 25 3 3505

Preload (N)

1

2

3

4

5

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 9 The contrast diagram of torque-tension relationships

thread profile angle (30 degrees for standard ISO threads)120583119882is the coefficient of underhead friction and119863119882 is the effectiveunderhead bearing contact radius which can be expressed asfollows when the underhead bearing face is circular

119863119882 = 23 times1198893119882 minus 1198893ℎ1198892119882 minus 1198892ℎ (9)

where 119889ℎ and 119889119882 are the internal diameter and the externaldiameter of the underhead bearing contact face respectively

To a M10 lowast 15 bolt and nut the torque-tension rela-tionship can be acquired by substituting relevant parametersinto (7)ndash(9) Figure 9 shows the comparison between theanalytical results and simulation results It can be seen thatthe FEA (finite element analysis) results are similar to theanalytical ones The torque coefficient 119870 by the analyticalmethod is 1453 while the value is 14749 by FEM (finiteelement method) The error between them is only 151

BoltBolted fixture

Load cellNut fixture

Locked spacer

Nut

Figure 10 The test rig

FEA resultsExperimental results

0

1

2

3

4

5

6

1 2 30Preload (N)

times104

times104

Tigh

teni

ng to

rque

(Nmiddotm

m)

Figure 11 Comparison between the finite element method and theexperimental method

In addition a test rig has been developed as shown inFigure 10 with an aim to verify the accuracy of the FE modelIn this experiment two plates made of steel (30CrMnSiA)are clamped by a M10 lowast 15 bolt and nut Each plate has athickness of 10mmDuring the loading process the bolt headis fixed and a torque wrench is used to tighten the nut Thevalue of tightening torque is applied in the range of 0sim60NmBesides a load cell is attached between the bolt head andthe clamped component to measure the clamp force Thedata of fastener tension are recorded per 5Nm torque in thisexperiment

The curves in Figure 11 show the contrast results betweenfinite element method and the experimental method

Shock and Vibration 7

Δl Δl

Figure 12 The loading diagram of the simplified way

Through the comparison it can be seen that the differencebetween the finite element and the experimental resultsis tiny The accuracy of FEM is verified by analytical andexperimental study

32 Analysis of the Fastening States The preload is a veryimportant factor that should not be ignored in the study ofbolt self-loosening However few studies considered both thetightening process and the self-loosening process simulta-neously Most of them simulated the preload by stretchingthe bolt or using a cooling pretightening algorithm thatmakes the fastening state of bolt different from the realcase Therefore the differences of different fastening waysare discussed here followed by their effects on bolt self-loosening

To simulate the tightening process a circumferentialdisplacement 1205790 is applied on the side surface of the nutwhich is the same as the model validation process Besides asimplified way that stretches the bolt is made for comparisonThe two clamped components are separated by a distanceΔ119897 which is used to control the value of preload as shownin Figure 12 After the loading process the whole bolt jointbecomes static without external constraints and the resultanttorque at every contact surface is equal in magnitude Sothe resultant torque at contact surface between threads isregarded as the object Figure 13 presents the relationshipsbetween the torque and the preload in static state which areachieved by different fastening means

As shown before the value of the torque in the tighteningprocess is obviously higher than that obtained by stretchingthe bolt under the same preload which leads to makingthe self-loosening more likely to occur The resultant torqueon the thread interface consists of two parts the pitchtorque and the thread friction torque Figure 14 illustratesthe relationships between the preload the pitch torque thethread friction torque and the resultant torque by differentfastening means It can be noted that the pitch torque andthread friction torque possess the same direction whenconsidering the tightening process while it is opposite by

Simulating the tightening processStretching bolt

4000

8000

12000

16000

1 2 30

Preload (N)times104

Resu

ltant

torq

ue (N

middotmm

)Figure 13 The relationships between the torque and the preload

stretching the bolt which leads to a much smaller resultanttorque

4 Analysis of the Bolt Loosening Mechanism

Considering the influence of the tightening process thepreload is produced by applying a constrained circumferen-tial displacement on the side surface of the nut followed by itsremoval To conduct the FEA of bolt joints self-loosening atransversal excitation 119904 is loaded on the clamped components(Figure 15) which is determined by the following formula

119904 = 1199040 sin (120596119905) (10)

where 1199040 and 120596 represent the excitation amplitude andangular frequency which are 003mm and 2120587 in this paperrespectively The excitation amplitude is smaller than theclearance between the bolt body and the clamped partTo reduce computational cost the clamped componentsare assumed to be rigid bodies when simulating the self-loosening process of bolt joints Since the vibration frequencyis set to 1Hz which is low the system can be treated as aquasi-static process Because the self-loosening behavior ismainly caused by slip at contact surfaces the critical outputparametersmonitored in this analysis include the preload andthe motion of nodes at contact surfaces which are used toanalyze the slip state

41 Evolution of the Preload during Self-Loosening To inves-tigate the effects of different fastening means on the self-loosening process of the bolt joint the same preload isproduced by adjusting the circumferential displacement andthe separation distance in finite element analysis and theother attributes of the two models are completely identical Acyclic transversal displacement is then loaded on the clamped

8 Shock and Vibration

0

Resultant torquePitch torqueThread friction torque

4000

8000

12000

16000

2 31Preload (N) times104

Torq

ue (N

middotmm

)

(a) Simulating the tightening process

Resultant torquePitch torqueThread friction torque

2 31Preload (N) times104

minus8000

minus4000

0

4000

8000

Torq

ue (N

middotmm

)

(b) Stretching the bolt

Figure 14 The relationships between different kinds of torque and preload

s

s s

t (s)

003 mm

105

s = 003 MCH 2t

Figure 15 The diagrams of transversal harmonic load

components The evolutions of the preload of differentfastening means during the first 15 load cycles are illustratedin Figure 16 It shows that at the same load cycle the self-loosening is much easier to appear andmore preload gets lostwhen the preload is produced by the simplified way This isbecause the resultant torque at contact surface is smaller

It can be drawn from the above analysis that the approx-imate pretightening algorithm cannot take the place of thetightening process to study the self-loosening mechanism ofbolt joints To preform further analysis of the evolution ofthe preload during bolt self-loosening the number of loadingcycles is increased to 150 and the initial preload is set to 8 kNThe curve in Figure 17 displays the preload variation duringthe 150 cycles It can be seen that with the increase of theloading cycles the variation curve of the preload tends to be

flat after a rapid decline The whole process can be roughlydivided into two stages the rapid decline stage and the flatstage which is in accordance with the result of Junker

42 Analysis of the Slip State at Contact Surfaces The self-loosening behavior is mainly caused by slip at contactsurfacesTherefore the dynamics during self-loosening is themain focus of the following analysis This paper uses therelative motion of nodes to present the slip state which isdifferent from previous researches and it is proved to be ingreater detail by contrast with the traditional method usingthe friction relation

The process of the preload variation mainly consists oftwo stages (exampled in Section 41) Taking the bolt headbearing surface as an example the relative motion of nodes

Shock and Vibration 9

The assembling processThe simplified way

25

255

26

265

27

275

Prel

oad

(N)

10 150 5Time (s)

times104

Figure 16 The preload variations under different fastening ways

2000

4000

6000

8000

Prel

oad

(N)

50 100 1500Time (s)

Figure 17 The curve of preload variation during the 150 cycles

during the two stages is analyzed Because the clampedcomponents are assumed to be rigid bodies the relativerotation between contact surfaces is equivalent to the rotationof bolt around its axis In the calculations the uniformdistribution nodes 1sim8 are selected from the outside edge ofbolt and node A is the intersection point between the contactsurface and the axis of bolt The relative rotation at contactsurface can be simplified to the rotation angle of nodes 1sim8around node A (Figure 18)

According to Figure 19 the range of analysis time is 0sim1 s(the decline stage) and 145sim150 s (the flat stage) During thetwo stages the rotation angle of each calculation node aroundnode A is shown

As shown before all the nodes rotate along the loosedirection as a whole which causes the preload loss Howeverat the beginning of the self-loosening process not all of thenodes rotate at the same time but one node rotates firstlyand drives the rotation of the other nodes Moreover in theprocess of rotating the rotation angles of some nodes arelarge and some are small When the movement direction ofclamped component changes the rotation angles of thosewhose rotation angles are large previously begin to decreaseMeanwhile the rotation angles of thosewhose rotation anglesare small increase This presents a creep slip phenomenonat contact surface under reversed cyclic load With increaseof the loading cycles the preload continues to decline And

10 Shock and Vibration

1

82

3

4

5

6

7A

Figure 18 The diagrams of the contact surface and the calculation points

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

02 04 06 08 10Time (s)

1

15

2

25

3

35

Relat

ive r

otat

ion

angl

e (ra

d)

times10minus3

(a) The rapid decline stage

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

00425

00426

00427

Relat

ive r

otat

ion

angl

e (ra

d)

148 150146Time (s)

(b) The flat stage

Figure 19 The rotation angles of each point in different stages

finally all nodes present a back and forth rotation at one placewhich causes the flat stage

To analyze the slip state during the initial stage of self-loosening (when preload is 272 kN) all nodes along theouter edge are taken into account and their relative rotationvelocities around node A are carried out as shown inFigure 20 Figure 21 shows the relative rotation velocity ofeach calculation node at some moments It can be notedthat the contact surface is slipping in a creep form Forcomparison the frictionmethod is also applied in the analysisof the contact state Based on the local key parameter 120578119899calculated the slip state contours are displayed in Figure 22However there is no significant difference among the three

figures which reflects that this method cannot give a detaileddescription of the slip state for a short time Through theanalysis of a whole cycle it suggests that there are always tworegions whose velocity directions are opposite Owing to thecontinuity of motion it means that there is a stick region onthe contact surface at any moment and bolt self-loosing canoccur without complete slip on the bolt head bearing surface

In addition the relativemotion between thread interfacesis analyzed in a similar way Two helical segments are inter-cepted from the contact location of bolt and nut (Figure 23)respectivelyThe rotation velocities of nodes belonging to thetwo helical segments can be calculated to build the position-velocity fields of bolt and nut at any time and the velocity

Shock and Vibration 11

XY

Z

1 2 348

13

25

37

Figure 20 The node number along the outer edge

t = 02 st = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 st = 03 s

2 4 6 80Circumferential position (rad)

minus8

minus4

0

4

8

Relat

ive r

otat

ion

velo

city

(rad

s)

Figure 21 The relative rotation velocity of each node at different moment

between adjacent nodes can be obtained approximately bylinear interpolation Figure 24 shows the position-velocitycurve at 025 s

Based on the position-velocity curves of bolt and nut therelative position-velocity relationship between thread inter-faces can be acquired by subtracting them Figure 25 showsthe relative position-velocity relationships at some momentsIt can be seen that all curves intersect the horizontal linethat the value is zero This means that there is always a stick

region in the thread interfaces which is consistent with theconclusion presented on the bolt head bearing surface Theslip state contours between thread interfaces are also given forcomparison (Figure 26) However there is still no significantdifference among them

To further strengthen the trust in the results summedbefore the relation between transverse force (shear force)and transverse displacement during the initial fifteen cyclesis shown in Figure 27 It is noted that the hysteresis loop

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 7: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

Shock and Vibration 7

Δl Δl

Figure 12 The loading diagram of the simplified way

Through the comparison it can be seen that the differencebetween the finite element and the experimental resultsis tiny The accuracy of FEM is verified by analytical andexperimental study

32 Analysis of the Fastening States The preload is a veryimportant factor that should not be ignored in the study ofbolt self-loosening However few studies considered both thetightening process and the self-loosening process simulta-neously Most of them simulated the preload by stretchingthe bolt or using a cooling pretightening algorithm thatmakes the fastening state of bolt different from the realcase Therefore the differences of different fastening waysare discussed here followed by their effects on bolt self-loosening

To simulate the tightening process a circumferentialdisplacement 1205790 is applied on the side surface of the nutwhich is the same as the model validation process Besides asimplified way that stretches the bolt is made for comparisonThe two clamped components are separated by a distanceΔ119897 which is used to control the value of preload as shownin Figure 12 After the loading process the whole bolt jointbecomes static without external constraints and the resultanttorque at every contact surface is equal in magnitude Sothe resultant torque at contact surface between threads isregarded as the object Figure 13 presents the relationshipsbetween the torque and the preload in static state which areachieved by different fastening means

As shown before the value of the torque in the tighteningprocess is obviously higher than that obtained by stretchingthe bolt under the same preload which leads to makingthe self-loosening more likely to occur The resultant torqueon the thread interface consists of two parts the pitchtorque and the thread friction torque Figure 14 illustratesthe relationships between the preload the pitch torque thethread friction torque and the resultant torque by differentfastening means It can be noted that the pitch torque andthread friction torque possess the same direction whenconsidering the tightening process while it is opposite by

Simulating the tightening processStretching bolt

4000

8000

12000

16000

1 2 30

Preload (N)times104

Resu

ltant

torq

ue (N

middotmm

)Figure 13 The relationships between the torque and the preload

stretching the bolt which leads to a much smaller resultanttorque

4 Analysis of the Bolt Loosening Mechanism

Considering the influence of the tightening process thepreload is produced by applying a constrained circumferen-tial displacement on the side surface of the nut followed by itsremoval To conduct the FEA of bolt joints self-loosening atransversal excitation 119904 is loaded on the clamped components(Figure 15) which is determined by the following formula

119904 = 1199040 sin (120596119905) (10)

where 1199040 and 120596 represent the excitation amplitude andangular frequency which are 003mm and 2120587 in this paperrespectively The excitation amplitude is smaller than theclearance between the bolt body and the clamped partTo reduce computational cost the clamped componentsare assumed to be rigid bodies when simulating the self-loosening process of bolt joints Since the vibration frequencyis set to 1Hz which is low the system can be treated as aquasi-static process Because the self-loosening behavior ismainly caused by slip at contact surfaces the critical outputparametersmonitored in this analysis include the preload andthe motion of nodes at contact surfaces which are used toanalyze the slip state

41 Evolution of the Preload during Self-Loosening To inves-tigate the effects of different fastening means on the self-loosening process of the bolt joint the same preload isproduced by adjusting the circumferential displacement andthe separation distance in finite element analysis and theother attributes of the two models are completely identical Acyclic transversal displacement is then loaded on the clamped

8 Shock and Vibration

0

Resultant torquePitch torqueThread friction torque

4000

8000

12000

16000

2 31Preload (N) times104

Torq

ue (N

middotmm

)

(a) Simulating the tightening process

Resultant torquePitch torqueThread friction torque

2 31Preload (N) times104

minus8000

minus4000

0

4000

8000

Torq

ue (N

middotmm

)

(b) Stretching the bolt

Figure 14 The relationships between different kinds of torque and preload

s

s s

t (s)

003 mm

105

s = 003 MCH 2t

Figure 15 The diagrams of transversal harmonic load

components The evolutions of the preload of differentfastening means during the first 15 load cycles are illustratedin Figure 16 It shows that at the same load cycle the self-loosening is much easier to appear andmore preload gets lostwhen the preload is produced by the simplified way This isbecause the resultant torque at contact surface is smaller

It can be drawn from the above analysis that the approx-imate pretightening algorithm cannot take the place of thetightening process to study the self-loosening mechanism ofbolt joints To preform further analysis of the evolution ofthe preload during bolt self-loosening the number of loadingcycles is increased to 150 and the initial preload is set to 8 kNThe curve in Figure 17 displays the preload variation duringthe 150 cycles It can be seen that with the increase of theloading cycles the variation curve of the preload tends to be

flat after a rapid decline The whole process can be roughlydivided into two stages the rapid decline stage and the flatstage which is in accordance with the result of Junker

42 Analysis of the Slip State at Contact Surfaces The self-loosening behavior is mainly caused by slip at contactsurfacesTherefore the dynamics during self-loosening is themain focus of the following analysis This paper uses therelative motion of nodes to present the slip state which isdifferent from previous researches and it is proved to be ingreater detail by contrast with the traditional method usingthe friction relation

The process of the preload variation mainly consists oftwo stages (exampled in Section 41) Taking the bolt headbearing surface as an example the relative motion of nodes

Shock and Vibration 9

The assembling processThe simplified way

25

255

26

265

27

275

Prel

oad

(N)

10 150 5Time (s)

times104

Figure 16 The preload variations under different fastening ways

2000

4000

6000

8000

Prel

oad

(N)

50 100 1500Time (s)

Figure 17 The curve of preload variation during the 150 cycles

during the two stages is analyzed Because the clampedcomponents are assumed to be rigid bodies the relativerotation between contact surfaces is equivalent to the rotationof bolt around its axis In the calculations the uniformdistribution nodes 1sim8 are selected from the outside edge ofbolt and node A is the intersection point between the contactsurface and the axis of bolt The relative rotation at contactsurface can be simplified to the rotation angle of nodes 1sim8around node A (Figure 18)

According to Figure 19 the range of analysis time is 0sim1 s(the decline stage) and 145sim150 s (the flat stage) During thetwo stages the rotation angle of each calculation node aroundnode A is shown

As shown before all the nodes rotate along the loosedirection as a whole which causes the preload loss Howeverat the beginning of the self-loosening process not all of thenodes rotate at the same time but one node rotates firstlyand drives the rotation of the other nodes Moreover in theprocess of rotating the rotation angles of some nodes arelarge and some are small When the movement direction ofclamped component changes the rotation angles of thosewhose rotation angles are large previously begin to decreaseMeanwhile the rotation angles of thosewhose rotation anglesare small increase This presents a creep slip phenomenonat contact surface under reversed cyclic load With increaseof the loading cycles the preload continues to decline And

10 Shock and Vibration

1

82

3

4

5

6

7A

Figure 18 The diagrams of the contact surface and the calculation points

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

02 04 06 08 10Time (s)

1

15

2

25

3

35

Relat

ive r

otat

ion

angl

e (ra

d)

times10minus3

(a) The rapid decline stage

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

00425

00426

00427

Relat

ive r

otat

ion

angl

e (ra

d)

148 150146Time (s)

(b) The flat stage

Figure 19 The rotation angles of each point in different stages

finally all nodes present a back and forth rotation at one placewhich causes the flat stage

To analyze the slip state during the initial stage of self-loosening (when preload is 272 kN) all nodes along theouter edge are taken into account and their relative rotationvelocities around node A are carried out as shown inFigure 20 Figure 21 shows the relative rotation velocity ofeach calculation node at some moments It can be notedthat the contact surface is slipping in a creep form Forcomparison the frictionmethod is also applied in the analysisof the contact state Based on the local key parameter 120578119899calculated the slip state contours are displayed in Figure 22However there is no significant difference among the three

figures which reflects that this method cannot give a detaileddescription of the slip state for a short time Through theanalysis of a whole cycle it suggests that there are always tworegions whose velocity directions are opposite Owing to thecontinuity of motion it means that there is a stick region onthe contact surface at any moment and bolt self-loosing canoccur without complete slip on the bolt head bearing surface

In addition the relativemotion between thread interfacesis analyzed in a similar way Two helical segments are inter-cepted from the contact location of bolt and nut (Figure 23)respectivelyThe rotation velocities of nodes belonging to thetwo helical segments can be calculated to build the position-velocity fields of bolt and nut at any time and the velocity

Shock and Vibration 11

XY

Z

1 2 348

13

25

37

Figure 20 The node number along the outer edge

t = 02 st = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 st = 03 s

2 4 6 80Circumferential position (rad)

minus8

minus4

0

4

8

Relat

ive r

otat

ion

velo

city

(rad

s)

Figure 21 The relative rotation velocity of each node at different moment

between adjacent nodes can be obtained approximately bylinear interpolation Figure 24 shows the position-velocitycurve at 025 s

Based on the position-velocity curves of bolt and nut therelative position-velocity relationship between thread inter-faces can be acquired by subtracting them Figure 25 showsthe relative position-velocity relationships at some momentsIt can be seen that all curves intersect the horizontal linethat the value is zero This means that there is always a stick

region in the thread interfaces which is consistent with theconclusion presented on the bolt head bearing surface Theslip state contours between thread interfaces are also given forcomparison (Figure 26) However there is still no significantdifference among them

To further strengthen the trust in the results summedbefore the relation between transverse force (shear force)and transverse displacement during the initial fifteen cyclesis shown in Figure 27 It is noted that the hysteresis loop

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 8: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

8 Shock and Vibration

0

Resultant torquePitch torqueThread friction torque

4000

8000

12000

16000

2 31Preload (N) times104

Torq

ue (N

middotmm

)

(a) Simulating the tightening process

Resultant torquePitch torqueThread friction torque

2 31Preload (N) times104

minus8000

minus4000

0

4000

8000

Torq

ue (N

middotmm

)

(b) Stretching the bolt

Figure 14 The relationships between different kinds of torque and preload

s

s s

t (s)

003 mm

105

s = 003 MCH 2t

Figure 15 The diagrams of transversal harmonic load

components The evolutions of the preload of differentfastening means during the first 15 load cycles are illustratedin Figure 16 It shows that at the same load cycle the self-loosening is much easier to appear andmore preload gets lostwhen the preload is produced by the simplified way This isbecause the resultant torque at contact surface is smaller

It can be drawn from the above analysis that the approx-imate pretightening algorithm cannot take the place of thetightening process to study the self-loosening mechanism ofbolt joints To preform further analysis of the evolution ofthe preload during bolt self-loosening the number of loadingcycles is increased to 150 and the initial preload is set to 8 kNThe curve in Figure 17 displays the preload variation duringthe 150 cycles It can be seen that with the increase of theloading cycles the variation curve of the preload tends to be

flat after a rapid decline The whole process can be roughlydivided into two stages the rapid decline stage and the flatstage which is in accordance with the result of Junker

42 Analysis of the Slip State at Contact Surfaces The self-loosening behavior is mainly caused by slip at contactsurfacesTherefore the dynamics during self-loosening is themain focus of the following analysis This paper uses therelative motion of nodes to present the slip state which isdifferent from previous researches and it is proved to be ingreater detail by contrast with the traditional method usingthe friction relation

The process of the preload variation mainly consists oftwo stages (exampled in Section 41) Taking the bolt headbearing surface as an example the relative motion of nodes

Shock and Vibration 9

The assembling processThe simplified way

25

255

26

265

27

275

Prel

oad

(N)

10 150 5Time (s)

times104

Figure 16 The preload variations under different fastening ways

2000

4000

6000

8000

Prel

oad

(N)

50 100 1500Time (s)

Figure 17 The curve of preload variation during the 150 cycles

during the two stages is analyzed Because the clampedcomponents are assumed to be rigid bodies the relativerotation between contact surfaces is equivalent to the rotationof bolt around its axis In the calculations the uniformdistribution nodes 1sim8 are selected from the outside edge ofbolt and node A is the intersection point between the contactsurface and the axis of bolt The relative rotation at contactsurface can be simplified to the rotation angle of nodes 1sim8around node A (Figure 18)

According to Figure 19 the range of analysis time is 0sim1 s(the decline stage) and 145sim150 s (the flat stage) During thetwo stages the rotation angle of each calculation node aroundnode A is shown

As shown before all the nodes rotate along the loosedirection as a whole which causes the preload loss Howeverat the beginning of the self-loosening process not all of thenodes rotate at the same time but one node rotates firstlyand drives the rotation of the other nodes Moreover in theprocess of rotating the rotation angles of some nodes arelarge and some are small When the movement direction ofclamped component changes the rotation angles of thosewhose rotation angles are large previously begin to decreaseMeanwhile the rotation angles of thosewhose rotation anglesare small increase This presents a creep slip phenomenonat contact surface under reversed cyclic load With increaseof the loading cycles the preload continues to decline And

10 Shock and Vibration

1

82

3

4

5

6

7A

Figure 18 The diagrams of the contact surface and the calculation points

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

02 04 06 08 10Time (s)

1

15

2

25

3

35

Relat

ive r

otat

ion

angl

e (ra

d)

times10minus3

(a) The rapid decline stage

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

00425

00426

00427

Relat

ive r

otat

ion

angl

e (ra

d)

148 150146Time (s)

(b) The flat stage

Figure 19 The rotation angles of each point in different stages

finally all nodes present a back and forth rotation at one placewhich causes the flat stage

To analyze the slip state during the initial stage of self-loosening (when preload is 272 kN) all nodes along theouter edge are taken into account and their relative rotationvelocities around node A are carried out as shown inFigure 20 Figure 21 shows the relative rotation velocity ofeach calculation node at some moments It can be notedthat the contact surface is slipping in a creep form Forcomparison the frictionmethod is also applied in the analysisof the contact state Based on the local key parameter 120578119899calculated the slip state contours are displayed in Figure 22However there is no significant difference among the three

figures which reflects that this method cannot give a detaileddescription of the slip state for a short time Through theanalysis of a whole cycle it suggests that there are always tworegions whose velocity directions are opposite Owing to thecontinuity of motion it means that there is a stick region onthe contact surface at any moment and bolt self-loosing canoccur without complete slip on the bolt head bearing surface

In addition the relativemotion between thread interfacesis analyzed in a similar way Two helical segments are inter-cepted from the contact location of bolt and nut (Figure 23)respectivelyThe rotation velocities of nodes belonging to thetwo helical segments can be calculated to build the position-velocity fields of bolt and nut at any time and the velocity

Shock and Vibration 11

XY

Z

1 2 348

13

25

37

Figure 20 The node number along the outer edge

t = 02 st = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 st = 03 s

2 4 6 80Circumferential position (rad)

minus8

minus4

0

4

8

Relat

ive r

otat

ion

velo

city

(rad

s)

Figure 21 The relative rotation velocity of each node at different moment

between adjacent nodes can be obtained approximately bylinear interpolation Figure 24 shows the position-velocitycurve at 025 s

Based on the position-velocity curves of bolt and nut therelative position-velocity relationship between thread inter-faces can be acquired by subtracting them Figure 25 showsthe relative position-velocity relationships at some momentsIt can be seen that all curves intersect the horizontal linethat the value is zero This means that there is always a stick

region in the thread interfaces which is consistent with theconclusion presented on the bolt head bearing surface Theslip state contours between thread interfaces are also given forcomparison (Figure 26) However there is still no significantdifference among them

To further strengthen the trust in the results summedbefore the relation between transverse force (shear force)and transverse displacement during the initial fifteen cyclesis shown in Figure 27 It is noted that the hysteresis loop

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 9: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

Shock and Vibration 9

The assembling processThe simplified way

25

255

26

265

27

275

Prel

oad

(N)

10 150 5Time (s)

times104

Figure 16 The preload variations under different fastening ways

2000

4000

6000

8000

Prel

oad

(N)

50 100 1500Time (s)

Figure 17 The curve of preload variation during the 150 cycles

during the two stages is analyzed Because the clampedcomponents are assumed to be rigid bodies the relativerotation between contact surfaces is equivalent to the rotationof bolt around its axis In the calculations the uniformdistribution nodes 1sim8 are selected from the outside edge ofbolt and node A is the intersection point between the contactsurface and the axis of bolt The relative rotation at contactsurface can be simplified to the rotation angle of nodes 1sim8around node A (Figure 18)

According to Figure 19 the range of analysis time is 0sim1 s(the decline stage) and 145sim150 s (the flat stage) During thetwo stages the rotation angle of each calculation node aroundnode A is shown

As shown before all the nodes rotate along the loosedirection as a whole which causes the preload loss Howeverat the beginning of the self-loosening process not all of thenodes rotate at the same time but one node rotates firstlyand drives the rotation of the other nodes Moreover in theprocess of rotating the rotation angles of some nodes arelarge and some are small When the movement direction ofclamped component changes the rotation angles of thosewhose rotation angles are large previously begin to decreaseMeanwhile the rotation angles of thosewhose rotation anglesare small increase This presents a creep slip phenomenonat contact surface under reversed cyclic load With increaseof the loading cycles the preload continues to decline And

10 Shock and Vibration

1

82

3

4

5

6

7A

Figure 18 The diagrams of the contact surface and the calculation points

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

02 04 06 08 10Time (s)

1

15

2

25

3

35

Relat

ive r

otat

ion

angl

e (ra

d)

times10minus3

(a) The rapid decline stage

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

00425

00426

00427

Relat

ive r

otat

ion

angl

e (ra

d)

148 150146Time (s)

(b) The flat stage

Figure 19 The rotation angles of each point in different stages

finally all nodes present a back and forth rotation at one placewhich causes the flat stage

To analyze the slip state during the initial stage of self-loosening (when preload is 272 kN) all nodes along theouter edge are taken into account and their relative rotationvelocities around node A are carried out as shown inFigure 20 Figure 21 shows the relative rotation velocity ofeach calculation node at some moments It can be notedthat the contact surface is slipping in a creep form Forcomparison the frictionmethod is also applied in the analysisof the contact state Based on the local key parameter 120578119899calculated the slip state contours are displayed in Figure 22However there is no significant difference among the three

figures which reflects that this method cannot give a detaileddescription of the slip state for a short time Through theanalysis of a whole cycle it suggests that there are always tworegions whose velocity directions are opposite Owing to thecontinuity of motion it means that there is a stick region onthe contact surface at any moment and bolt self-loosing canoccur without complete slip on the bolt head bearing surface

In addition the relativemotion between thread interfacesis analyzed in a similar way Two helical segments are inter-cepted from the contact location of bolt and nut (Figure 23)respectivelyThe rotation velocities of nodes belonging to thetwo helical segments can be calculated to build the position-velocity fields of bolt and nut at any time and the velocity

Shock and Vibration 11

XY

Z

1 2 348

13

25

37

Figure 20 The node number along the outer edge

t = 02 st = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 st = 03 s

2 4 6 80Circumferential position (rad)

minus8

minus4

0

4

8

Relat

ive r

otat

ion

velo

city

(rad

s)

Figure 21 The relative rotation velocity of each node at different moment

between adjacent nodes can be obtained approximately bylinear interpolation Figure 24 shows the position-velocitycurve at 025 s

Based on the position-velocity curves of bolt and nut therelative position-velocity relationship between thread inter-faces can be acquired by subtracting them Figure 25 showsthe relative position-velocity relationships at some momentsIt can be seen that all curves intersect the horizontal linethat the value is zero This means that there is always a stick

region in the thread interfaces which is consistent with theconclusion presented on the bolt head bearing surface Theslip state contours between thread interfaces are also given forcomparison (Figure 26) However there is still no significantdifference among them

To further strengthen the trust in the results summedbefore the relation between transverse force (shear force)and transverse displacement during the initial fifteen cyclesis shown in Figure 27 It is noted that the hysteresis loop

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 10: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

10 Shock and Vibration

1

82

3

4

5

6

7A

Figure 18 The diagrams of the contact surface and the calculation points

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

02 04 06 08 10Time (s)

1

15

2

25

3

35

Relat

ive r

otat

ion

angl

e (ra

d)

times10minus3

(a) The rapid decline stage

Node 1Node 2Node 3Node 4

Node 5Node 6Node 7Node 8

00425

00426

00427

Relat

ive r

otat

ion

angl

e (ra

d)

148 150146Time (s)

(b) The flat stage

Figure 19 The rotation angles of each point in different stages

finally all nodes present a back and forth rotation at one placewhich causes the flat stage

To analyze the slip state during the initial stage of self-loosening (when preload is 272 kN) all nodes along theouter edge are taken into account and their relative rotationvelocities around node A are carried out as shown inFigure 20 Figure 21 shows the relative rotation velocity ofeach calculation node at some moments It can be notedthat the contact surface is slipping in a creep form Forcomparison the frictionmethod is also applied in the analysisof the contact state Based on the local key parameter 120578119899calculated the slip state contours are displayed in Figure 22However there is no significant difference among the three

figures which reflects that this method cannot give a detaileddescription of the slip state for a short time Through theanalysis of a whole cycle it suggests that there are always tworegions whose velocity directions are opposite Owing to thecontinuity of motion it means that there is a stick region onthe contact surface at any moment and bolt self-loosing canoccur without complete slip on the bolt head bearing surface

In addition the relativemotion between thread interfacesis analyzed in a similar way Two helical segments are inter-cepted from the contact location of bolt and nut (Figure 23)respectivelyThe rotation velocities of nodes belonging to thetwo helical segments can be calculated to build the position-velocity fields of bolt and nut at any time and the velocity

Shock and Vibration 11

XY

Z

1 2 348

13

25

37

Figure 20 The node number along the outer edge

t = 02 st = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 st = 03 s

2 4 6 80Circumferential position (rad)

minus8

minus4

0

4

8

Relat

ive r

otat

ion

velo

city

(rad

s)

Figure 21 The relative rotation velocity of each node at different moment

between adjacent nodes can be obtained approximately bylinear interpolation Figure 24 shows the position-velocitycurve at 025 s

Based on the position-velocity curves of bolt and nut therelative position-velocity relationship between thread inter-faces can be acquired by subtracting them Figure 25 showsthe relative position-velocity relationships at some momentsIt can be seen that all curves intersect the horizontal linethat the value is zero This means that there is always a stick

region in the thread interfaces which is consistent with theconclusion presented on the bolt head bearing surface Theslip state contours between thread interfaces are also given forcomparison (Figure 26) However there is still no significantdifference among them

To further strengthen the trust in the results summedbefore the relation between transverse force (shear force)and transverse displacement during the initial fifteen cyclesis shown in Figure 27 It is noted that the hysteresis loop

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 11: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

Shock and Vibration 11

XY

Z

1 2 348

13

25

37

Figure 20 The node number along the outer edge

t = 02 st = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 st = 03 s

2 4 6 80Circumferential position (rad)

minus8

minus4

0

4

8

Relat

ive r

otat

ion

velo

city

(rad

s)

Figure 21 The relative rotation velocity of each node at different moment

between adjacent nodes can be obtained approximately bylinear interpolation Figure 24 shows the position-velocitycurve at 025 s

Based on the position-velocity curves of bolt and nut therelative position-velocity relationship between thread inter-faces can be acquired by subtracting them Figure 25 showsthe relative position-velocity relationships at some momentsIt can be seen that all curves intersect the horizontal linethat the value is zero This means that there is always a stick

region in the thread interfaces which is consistent with theconclusion presented on the bolt head bearing surface Theslip state contours between thread interfaces are also given forcomparison (Figure 26) However there is still no significantdifference among them

To further strengthen the trust in the results summedbefore the relation between transverse force (shear force)and transverse displacement during the initial fifteen cyclesis shown in Figure 27 It is noted that the hysteresis loop

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 12: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

12 Shock and Vibration

+6000e minus 01+6333e minus 01+6667e minus 01+7000e minus 01+7334e minus 01+7667e minus 01+8000e minus 01+8334e minus 01+8667e minus 01+9001e minus 01+9334e minus 01+9668e minus 01+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 22 The slip state contours at different time

Figure 23 The schematic diagrams of helical segments

BoltNut

minus6

minus4

minus2

0

2

4

6

Relat

ive r

otat

ion

velo

city

(rad

s)

5 10 15 200Circumferential position (rad)

Figure 24 The position-velocity fields of bolt and nut at 025 s

only involves slope regions and has no flat region The slopeprovides an indication of the joint stiffness in the transversedirection and the reduction in slope is a sign of slip at contactsurfaces However in the slope region the figure indicatesthat the contact surfaces undergo localized slip No flat regionmeans that the complete slip does not occur at contactsurfaces during the initial self-loosening This is consistent

with the conclusion obtained by analyzing the relativemotionof nodes

5 Conclusions

The self-loosening process of bolt joints is investigatedcombining the tightening process by a three-dimensional

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 13: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

Shock and Vibration 13

t = 021 st = 022 st = 023 st = 024 st = 025 s

t = 026 st = 027 st = 028 st = 029 s

201612 240 4 8Circumferential position (rad)

minus4

minus2

0

2

4

Diff

eren

ce o

f rot

atio

n ve

loci

ty (r

ads

)

Figure 25 The relative rotation velocity of each node at different moment

+0000e + 00

+8334e minus 02

+1667e minus 01

+2500e minus 01

+3334e minus 01

+4167e minus 01

+5001e minus 01

+5834e minus 01

+6667e minus 01

+7501e minus 01

+8334e minus 01

+9168e minus 01

+1000e + 00

t = 02 s t = 025 s t = 03 s

n

Figure 26 The slip state contours between thread interfaces

finite element model in this paper The FE model is meshedwith hexahedral elements and its accuracy is verified andvalidated compared with the analytical and experimentalresults Followed by simulating different fastening meansthe differences between them and their effects on bolt self-loosening are discussed Finally we utilize the relativemotionof nodes to describe the contact states and the conventionalCoulomb friction method is also applied for contrast Basedon the FEA results the following conclusions are drawn

(1) Based on the mathematical expression the threadsare meshed with hexahedral elements by modifying

the node coordinates of the cylindrical hexahedralmeshes which is proved to be effective And a self-developed plug-in is made for parametric modelingand its functions can be expanded in further study

(2) Through comparing with a simplified pretighteningalgorithm it is demonstrated that the tighteningprocess cannot be replaced because the simplifiedway may cause a smaller resultant torque due to theopposite direction of the two torque components onthe thread interface For the same reason it will lead

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 14: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

14 Shock and Vibration

minus2500

minus1500

minus500

500

1500

2500

Tran

sver

se lo

ad (N

)

minus002 0 002 004minus004Transverse displacement (mm)

Figure 27 Hysteresis loops of transverse displacement and load

to a greater loss of preload than the value in realityunder the same number of load cycles

(3) By contrast the relative motion between nodes isfound in a greater detail to describe the slip stateat contact surfaces than Coulombrsquos law of frictionAccording to the simulation results of bolt self-loosening it reveals that there exists a creep slipphenomenon on the bolt head bearing surface whichcauses the bolt self-loosening to occur even whensome contact facets are stuck

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The paper is supported by National Science and TechnologyMajor Project of the Ministry of Science and Technology ofChina (no 2011ZX02403) National Natural Science Foun-dation of China (no 11302035 and no 11272074) and theFundamental Research Funds for the Central Universities

References

[1] D Liang and S-F Yuan ldquoDecision fusion system for bolted jointmonitoringrdquo Shock and Vibration vol 2015 Article ID 59204311 pages 2015

[2] L Zhu J Hong G Yang and X Jiang ldquoExperimental studyon initial loss of tension in bolted jointsrdquo Journal of MechanicalEngineering Science vol 230 no 10 pp 35ndash54 2015

[3] G H Junker ldquoNew criteria for self-loosening of fasteners undervibrationrdquoAircraft Engineeringampamp Aerospace vol 44 no 10pp 14ndash16 1969

[4] N G Pai and D P Hess ldquoExperimental study of looseningof threaded fasteners due to dynamic shear loadsrdquo Journal ofSound and Vibration vol 253 no 3 pp 585ndash602 2002

[5] N G Pai and D P Hess ldquoThree-dimensional finite elementanalysis of threaded fastener loosening due to dynamic shearloadrdquo Engineering Failure Analysis vol 9 no 4 pp 383ndash4022002

[6] X Yang and S Nassar ldquoAnalytical and Experimental Investi-gation of Self-Loosening of Preloaded Cap Screw FastenersrdquoJournal of Vibration and Acoustics vol 133 no 3 p 031007 2011

[7] G Dinger and C Friedrich ldquoAvoiding self-loosening failure ofbolted joints with numerical assessment of local contact staterdquoEngineering Failure Analysis vol 18 no 8 pp 2188ndash2200 2011

[8] S Kasei ldquoA study of self-loosening of bolted joints due to repe-tition of small amount of slippage at bearing surfacerdquo Journal ofAdvanced Mechanical Design Systems and Manufacturing vol1 no 3 pp 358ndash367 2007

[9] S IzumiM Kimura and S Sakai ldquoSmall Loosening of Bolt-nutFastener Due to Micro Bearing-Surface Slip A Finite ElementMethod Studyrdquo Journal of Solid Mechanics and Materials Engi-neering vol 1 no 11 pp 1374ndash1384 2007

[10] T Yokoyama M Olsson S Izumi and S Sakai ldquoInvestigationinto the self-loosening behavior of bolted joint subjected torotational loadingrdquo Engineering Failure Analysis vol 23 pp 35ndash43 2012

[11] Y Fujioka and T Sakai ldquoRotating looseningmechanism of a nutconnecting a rotary disk under rotating-bending forcerdquo Journalof Mechanical Design vol 127 no 6 pp 1191ndash1197 2005

[12] X Jiang Y Zhu J Hong X Chen and Y Zhang ldquoInvestigationinto the loosening mechanism of bolt in curvic couplingsubjected to transverse loadingrdquo Engineering Failure Analysisvol 32 pp 360ndash373 2013

[13] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology Transactions of the ASME vol 128no 4 pp 590ndash598 2006

[14] S A Nassar and B A Housari ldquoStudy of the effect of holeclearance and thread fit on the self-loosening of threaded

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 15: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

Shock and Vibration 15

fastenersrdquo Journal of Mechanical Design vol 129 no 6 pp 586ndash594 2007

[15] S A Nassar and P H Matin ldquoClamp load loss due to fastenerelongation beyond its elastic limitrdquo Journal of Pressure VesselTechnology Transactions of the ASME vol 128 no 3 pp 379ndash387 2006

[16] A M Zaki S A Nassar and X Yang ldquoEffect of conicalangle and thread pitch on the self-loosening performance ofpreloaded countersunk-head boltsrdquo Journal of Pressure VesselTechnology vol 134 no 2 pp 566ndash571 2013

[17] S A Nassar and B A Housari ldquoEffect of thread pitch and initialtension on the self-loosening of threaded fastenersrdquo Journal ofPressure Vessel Technology vol 128 no 4 pp 129ndash138 2010

[18] J Mackerle ldquoFinite element analysis of fastening and joiningA bibliography (1990ndash2002)rdquo International Journal of PressureVessels and Piping vol 80 no 4 pp 253ndash271 2003

[19] M Zhang Y Jiang and C-H Lee ldquoFinite element modelingof self-loosening of bolted jointsrdquo Journal of Mechanical Designvol 129 no 2 pp 218ndash226 2007

[20] R I Zadoks and D P R Kokatam ldquoInvestigation of the axialstiffness of a bolt using a three-dimensional finite elementmodelrdquo Journal of Sound and Vibration vol 246 no 2 pp 349ndash373 2001

[21] S Izumi T Yokoyama M Kimura and S Sakai ldquoLoosening-resistance evaluation of double-nut tightening method andspring washer by three-dimensional finite element analysisrdquoEngineering Failure Analysis vol 16 no 5 pp 1510ndash1519 2009

[22] S Izumi T Yokoyama A Iwasaki and S Sakai ldquoThree-dimensional finite element analysis of tightening and looseningmechanism of threaded fastenerrdquo Engineering Failure Analysisvol 12 no 4 pp 604ndash615 2005

[23] T Fukuoka M Nomura and Y Morimoto ldquoProposition ofhelical thread modeling with accurate geometry and finiteelement analysisrdquo Journal of Pressure Vessel Technology vol 130no 1 pp 135ndash140 2008

[24] T Fukuoka ldquoAnalysis of the tightening process of bolted jointwith a tensioner using spring elementsrdquo Journal of PressureVessel Technology Transactions of the ASME vol 116 no 4 pp443ndash448 1994

[25] The standard of Peoplersquos Republic of China ldquoGBT 168232-1997 General rules of tightening for threaded fastenersrdquo 1997(Chinese)

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 16: Self-Loosening Failure Analysis of Bolt Joints under …downloads.hindawi.com/journals/sv/2017/2038421.pdfSelf-Loosening Failure Analysis of Bolt Joints under Vibration considering

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of