Avoiding Self-loosening Failure of Bolted Joints With Numerical

Engineering Failure Analysis 18 (2011) 2188–2200

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Engineering Failure Analysis

journal homepage: www.elsevier .com/locate /engfai lanal

Avoiding self-loosening failure of bolted joints with numericalassessment of local contact state

G. Dinger ⇑, C. FriedrichUniversity of Siegen, Department of Mechanical Engineering, Institute of Engineering Design MVP, Paul-Bonatz-Str. 9-11, D 57076 Siegen, Germany

a r t i c l e i n f o a b s t r a c t

Article history:Received 10 June 2011Received in revised form 11 July 2011Accepted 13 July 2011Available online 23 July 2011

Keywords:Finite element analysisJoint failuresThreaded fastenersSelf-looseningLocalized slip

1350-6307/$ - see front matter � 2011 Elsevier Ltddoi:10.1016/j.engfailanal.2011.07.012

⇑ Corresponding author. Tel.: +49 271 740 4399;E-mail address: [email protected] (G. D

Fatigue and rotational self-loosening are two most widespread reasons for failure ofdynamically loaded bolted joints, especially due to external loading perpendicular to thebolt axis (transverse loading). More and more component systems show self-looseningin light weight design. The aim of this paper is to provide a numerical design method withfinite element analysis for detecting and understanding of the self-loosening process atbolted joints and the influences of the preload generation for the residual shank torquein the numerical simulation.

A three-dimensional finite element (FE) model is established to study details of the rota-tional self-loosening process. Such processes are characterized by either complete or local-ized slip at the screw head and thread contact surfaces. Detailed information is given aboutthe modelling. The computational results of the numerical simulation are compared withexperimental investigations of the cyclic transverse load–displacement behaviour. Theseshow that rotational self-loosening can also occur for only localized slip without completeslipping at the head contact surface.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction and background

Bolted joints are widely used in mechanical products and structures due to their possibility for easy disassembly and theirrelatively low cost [1,15]. Fatigue and rotational self-loosening are the two most widespread reasons of failures during oper-ation. Whereas the mechanism for failure in fatigue or preload relaxation of a bolted joint can be analysed with the help ofanalytic guidelines [1,2] and design tools [11], no established and verified design method exists in case of preload loss causedby rotational self-loosening of the screw.

Since nearly 60 years research on loosening of threaded fasteners is performed [4]. Many studies are based on the studiesby Junker [3] in the late 1960s and the vibration test apparatus developed by Junker which is also used in DIN 65151 [5]. Incontrast to the classical theory that loosening starts with the transverse complete slip of the bolt head surface, Pai and Hess[6,7], Izumi et al. [8] and Koch et al. [9] showed that critical slight loosening appears prior to the bolt head slip. These studiesare performed experimentally or with numerical simulations of the vibration test setup (no friction between clamped parts).Pai and Hess [6] been the first authors who identified that a fastener could turn loose under dynamic shear loading only dueto the accumulation of localized slip at the fastener contact surfaces and introduced the term ‘localized slip’ for the self-loos-ening process.

In this paper a real fastened component system (friction between clamped parts) is used for the further understanding oflocalized or complete slip at the fastener contact surfaces. Also additional performance variables are defined.

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G. Dinger, C. Friedrich / Engineering Failure Analysis 18 (2011) 2188–2200 2189

For additional details of the loosening process, the reader is referred to Koch et al. [9]. A comprehensive review of theliterature is given by Bickford [10] and Sakai [13]. A bibliographical review of finite element methods for the analysis of fas-tening and joining is given by Mackerle [14].

The focus in this paper is directed to the evolution of residual shank torque for loosening after preload generation andloading and the self-loosening behaviour of a real threaded connection due to complete or localized slip at the fastener sur-faces. In contrast to the vibration test setup the real threaded connection shows friction force between the clamped parts.Such component systems can be found at bolted clutches, brake callipers, connections of steel constructions, bolted fly-wheels and in wheel suspensions of cars. The increase of the nonlinear behaviour, by the frictional contact between theclamped parts, leads to significant efforts for the simulation and experimental study of real dynamic loaded threaded fas-tener systems. The fastener geometry, stiffness, geometrical tolerances and contact with friction are the most important fac-tors that influence slip and the resulting self-loosening behaviour of the screw.

2. Simulation

With the aim of developing a general simulation method for rotational self-loosening of screws all important influencesfor the self-loosening mechanism have to be considered in the numerical simulation. A three-dimensional finite element (FE)model is established for detection and understanding of self-loosening at bolted joints and the influences of the preload gen-eration for the residual shank torque.

2.1. Model description

The general purpose finite element analysis software Abaqus/Standard 6.9.1 has been used to model a real threaded con-nection with component interface. The geometry is simplified to include only the essential parts of the assembly (Fig. 1). Themovable clamped part is sinusoidal moved in x-direction and the nut thread component remains fixed. The geometry of themodelled screw with external hexagon drive and plain support type is given by DIN 6921 M10 � 60 – 10.9. The three-dimen-sional helical thread geometry is based on ISO 965 and DIN 13 including the tolerances given for 6 g/6 H (centre values used).The helix of the thread (P = 1.5 mm) is attached to the bolt shank and the nut thread component using tie constraints be-tween the surfaces to minimize the number of elements in the shank and the nut thread. The thread flanks need a finer meshto increase the simulation accuracy of the contact state and to minimize stiffness problems due to locking behaviour. Fullintegrated hexahedral eight node elements (C3D8) were used for the thread flanks and reduced integrated hexahedral eightnode elements (C3D8R) for the remaining parts. The mesh density was checked by convergence tests and comparison withanalytical calculations of the axial stiffness of the fastener system according to VDI 2230 [2].

All the analysis in this study does not aim to obtain detailed stress distribution, but understanding of the mechanicalmechanism based of rotational self-loosening. Therefore, the curvature of the thread root and the radius of the head–shank-transition are not taken into account. The bearing surface angle is modelled according to DIN 6921 with e = 0.75�(Fig. 2). The preload Fp is restricted to 25 kN (elastic range) to avoid the influence of large-volume yielding at the screw.The elastic–plastic behaviour of screw steel (property class 10.9) was determined in tension tests according to DIN 50125– B – 5 � 25. Elastic material behaviour was assumed for the nitrided steel parts (moveable clamped part and nut threadcomponent). Young’s modulus and Poisson’s ratio are 210 GPa and 0.3, respectively, for all steel materials.

Further description of the threaded component system, the contact surfaces and boundary conditions of the model aregiven in Figs. 1 and 2.

Fig. 1. Three-dimensional finite element model with component interface for simulation of preload generation and self-loosening.

cross section of screw head

cross section of thread

Abaqus/Standard 6.9.1

steel

C3D8R, C3D882434 elements

surface to surfacepressure-overclosure: hard contactnormal behaviour: Penaltytangential behaviour: Penaltycritical slip: γcrit = 0.0004 µh = 0.15µt = 0.2µc = 0.13

DIN 6921 M10 x 60 - 10.9pitch P = 1.5 mmme = 1.2 . dthread tolerance: centre of 6g/6H

clamp lengh lc = 40 mmdiameter of bore dh = 12 mm

- software:

- material:

- elements:

- contact:

- screw:

- clamped part:

model characteristics:

y

x

ε=

0.7 5

°

Fig. 2. Cross section of screw head and thread contact as well as model characteristics.

2190 G. Dinger, C. Friedrich / Engineering Failure Analysis 18 (2011) 2188–2200

The nut thread component was restrained in the x, y and z directions at the surface marked in Fig. 1. For anchoring theclamped part, the plate was restrained at the reference point RP1 (Fig. 1) so that it could not move in any other direction thanthe direction in which it was displaced. For the self-loosening simulation the reference point RP1 is moved in x directionsinusoidal. A second reference point (RP2) is connected to the bolt head to estimate the displacement of the bolt head srad

and the rotational angle #h. The screw was initially restrained in the x and z directions at RP2 so that it could not move inorder to position it when the bolt preload was generated (this restraint was removed during simulation of the self-looseningbehaviour). The preload Fp = 25 kN is generated through a pre-tension section created in the bolt shank or by a rotation angleat RP2 (chapter 3).

The vibration frequency in the experiment is 0.5 Hz, compared to the eigenfrequency the system can be treated as a qua-si-static process.

2.2. Contact formulation

Contact modelling is of great importance for self-loosening simulation because of the effects associated with local stick–slip behaviour of the contact surfaces. The most common algorithms for solving contact problems are the penalty approachand the method of Lagrangian multipliers. Other procedures, such as a combined method called the augmented Lagrangiantechnique and the perturbed Lagrangian method can also be applied. The contact condition is not fulfilled exactly in the pen-alty approach. In contrast to the penalty formulation, the Lagrangian multipliers method ensures exact satisfaction of therequired contact constraints. The multipliers can be interpreted as contact forces. However, it increases the number of vari-ables in the numeric simulation with the introduction of Lagrange multipliers.

The surface constraint approach used in these studies is a master–slave, finite sliding, surface-to-surface assignment. Thecontact normal behaviour was modelled with a penalty approach.

Friction based tangential contact is considered at the bolt head surface, thread flanks and the interface between clampedpart and nut thread component. The friction coefficients for grease lubricated contacts at screw head lh and the thread flankslt were measured on a multi-channel assembly test stand for screw assemblies (similar to DIN EN ISO 16047 [12]) with iden-tical screw, clamped part and nut thread component as being used for the vibration test. The friction coefficient of interfacelc was determined directly in the vibration test setup.

The standard isotropic Coulomb law of friction assumes that no relative motion occurs if the frictional shear stress s is lessthan the critical stress scirt which is proportional to the contact pressure p, i.e. scirt = l . p, where l is the related coefficient offriction (Fig. 3).

This nonlinear behaviour of sticking and slipping in the absence of slip can be made exactly zero with the use of a La-grange multiplier formulation. This procedure seems to be attractive because of the exact sticking condition for self-loosen-ing simulations. Disadvantages are the increase in analysis cost due to additional Lagrange multipliers; the presence of rigidconstraints tends to slow or sometimes prevent convergence of the Newton solution technique used in Abaqus/Standard.This is likely to occur in contact areas where the contact status changes.

In the penalty formulation of Coulomb friction, the condition of no relative sliding motion is approximated with a ‘‘stiffelastic behaviour’’ as shown in the Fig. 3. Therefore, a small amount of elastic slip |cel| 6 ccrit is permitted although there

Fig. 3. Frictional tangential behaviour between two contacting bodies for the penalty and Lagrange method.


should be no slipping at all. The elastic slip is related to the frictional shear stress through the relation si ¼ kp � celi for i = 1, 2

(sliding directions in three-dimensional problem). The influence of the penalty stiffness kp, concerning the rotational self-loosening, has been discovered in previous studies [9]. All tangential contacts in the numerical simulations use the penaltymethod with a critical slip ccrit = 0.0004 to avoid unrealistic rotation angles of the screw.

3. Residual shank torque as origin for self-loosening

This chapter discusses the influences of three different methods of preload generation in the numerical simulation forself-loosening. The difference in rotation angle between screw head #h and screw end #t describes the twisting of the screwshank. The calculated residual shank torque for self-loosening Tre is associated with this twisting deformation. The analyticalrelation between total tightening torque Ttot and preload Fp is well-known (Eq. (1)). During operating the residual shank tor-que Tre changes asymptotically from the sum of Tt_pitch and Tt_friction directly after tightening to Tt_pitch.

Ttot ¼ Tt pitch þ Tt friction þ Th ð1Þ

Ttot ¼ Fp � 0:159 � P þ Fp � 0:577 � d2 � lt þ Fpdkm

2lh ðfor metric thread profile and plain head support areaÞ

where Ttot is the total tightening torque, Tt_pitch the screw thread torque due to thread pitch, Tt_friction the screw thread torquedue to friction, Th the head torque, Tre the residual shank torque, Fp the preload, P the thread pitch, d2 the pitch diameter ofscrew thread, dKm the equivalent friction diameter under the screw head, lt the friction coefficient of thread contact and lh isthe friction coefficient of head contact.

In this example:

dKm ¼ 19:55 mm ðfor Fp ¼ 25 kNÞ; d2 ¼ 8:93 mm; Fp ¼ 25 kN; P ¼ 1:5 mm; lt ¼ 0:2; lh ¼ 0:15

Ttot ¼ 25 kN � ð0:159 � 1:5þ 0:577 � 8:93 mm � 0:2þ 19:55 mm2

0:15Þ

Ttot ¼ 5:96 Nmþ 25:76 Nmþ 36:64 Nm ¼ 68:36 Nm

Analysed methods of preload generation in simulation:

V1: Axial preload generation with pre-tension function; with thread friction lt = 0.2.V2: Axial preload generation with pre-tension function; without thread friction lt = 0.0 by preload generation (Steps 1and 2).V3: Rotational assembling by turning the screw head (Step 2); with thread friction lt = 0.2.

The tightening preload Fp = 25 kN is generated through a pre-tension section (axial elongation) created in the bolt shankfor version V1 and V2. In the first step the adjustments of the pre-tensioning is used for closing all contacts. In the second

ksentini

Texte surligné


step the length of the bolt is automatically adjusted at the pre-tension section to achieve the prescribed amount of pre-ten-sion. The related length changing is fixed for further steps. The state of equilibrium is calculated in Step 3 for the self-loos-ening simulation in the further steps. In contrast to this a real tightening process with a tightening angle instead of the pre-tension section is used for version V3. The equivalent friction diameter under the head dKm is also determined by simulationresults from version V3 and Eq. (2) for the analytical calculation of Eq. (1). With increasing preload Fp the equivalent frictiondiameter dKm decreases due to elastic bearing surface deformation of the screw head (bearing surface angle is shown inFig. 2).

Fi

Fig. 5.cycles a

dkm ¼2 � Th

Fp � lhð2Þ

For example:

dkm ¼2 � 13:51 Nm9:13 kN � 0:15

¼ 19:73 mm

dkm ¼2 � 36:64 Nm

24:98 kN � 0:15¼ 19:55 mm

The resulting preload and the angle at screw head and end for version V1, V2 and V3 for a transverse displacementsQmax = 0.55 mm show Figs. 4 and 5. The corresponding residual shank torque for self-loosening Tre after preload generationand transverse load cycles for three different transverse displacements sQmax is shown in Figs. 6–8, respectively, for versionV1, V2 and V3.

24000

24500

25000

25500

26000

26500

27000

3 4 5 6 7Step [-]

Prel

oad

F p [N

]

V1 V2 V3

Fp

increase

in preload through

tighten up at screw end

decrease in preloadthrough buildupof shank torque

g. 4. Simulation of preload Fp for version V1, V2 and V3; transverse displacement sQmax = 0.55 mm; only first four load cycles are visualised.

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

3 4 5 6 7Step [-]

Ang

le [°

]

V1_screw head V1_screw endV2_screw head V2_screw end

ϑh

ϑt

difference results in Tt_pitch= 5.96 Nm

loosening angle ϑLh

(a) ϑt

ϑt

ϑh

ϑh

-1,4

-1,2

-1

-0,8

-0,6

-0,4

-0,2

0

0,2

3 4 5 6 7

Step [-]

Ang

le [°

]

V3_screw head V3_screw end

difference is based onTt_friction= 25.75 Nm

tighten up angle at screw end

without tightening angles

(b) ϑtϑh

ϑt

Simulation of rotation angle at screw head #h and end #t for version V1, V2 and V3; transverse displacement sQmax = 0.55 mm; only first four loadre visualised.


An increase in preload (Fig. 4) and a tighten up angle (Fig. 5b) at the screw end #t (angle at the screw head #h remainconstant) is observed for assembling by turning the screw head (V3). The difference in rotation angles after tightening be-tween screw head #h and screw end #t (Fig. 5b) describes the twisting of the screw shank due to the screw thread torque Tt

(Fig. 8). The screw thread friction torque Tt_friction decreases after a few load cycles (Fig. 5b); the gradient of decrease dependson the transverse displacement sQmax (Fig. 8).

If the pre-tension function is used for preload generation, the preload decreases for preload generation with thread fric-tion lt (V1) and remains constant without thread friction V2 (Fig. 4). The difference in rotation angle is equal to the screwthread torque due to the screw thread pitch Tt_pitch after preload generation for version V2 (Fig. 5a). The build-up of the resid-ual shank torque Tre for V1 (Fig. 6) results in a decrease in preload (Fig. 4) due to an increase of the angle at the screw end #t

(Fig. 5a) for repeated transverse loading.A significant self-loosening angle at screw head is observed for the transverse displacement sQmax = 0.55 mm (Fig. 5a).

With the assessment (constant self-loosening at screw head #Lh > 0.01� per load cycle) from [9], this displacement is equalto the critical displacement scrit (localized head slipping) described in chapter 4. On the other hand, entire slip at screw headcontact surface (sQmax = 0.9 mm) induces a large self-loosening angle (0.38� per load cycle) and a large decrease in preload Fp

(Figs. 6–8). Once the entire screw head surface slips, the torsion in the bolt shank is reduced for each half cycle (sQmax = 0.9 inFigs. 6–8). This effect is enlarged for smaller preloads or by clamp load loss due to self-loosening. The residual shank torqueTre takes an asymptotic increase towards the thread pitch torque Tt_pitch, when the deflection of the sinusoidal displacementchanges, through the self-loosening of the screw thread. The head loosening angle #Lh shows nearly a step increase whencomplete slip at the bearing surface occurs, while the thread angle #Lt increases more gradually. The thread angle is leadingthe head angle; this is expected since the entire residual shank torque Tre is developed by the thread pitch.

0

1

2

3

4

5

6

7

3 4 5 6 7 8 9 10Step [-]

Res

idua

l sha

nk to

rque

Tre

[Nm

]

sQmax = 0.30 sQmax = 0.55 sQmax = 0.90 Tt_pitch

sQmax

sQdue to decrease of preload

Tre

Fig. 6. V1: Development of residual shank torque during self-loosening Tre after preload generation and three transverse displacements sQmax; analyticalcalculation of Tt_pitch with constant preload Fp = 25 kN.

0

1

2

3

4

5

6

7

3 4 5 6 7 8 9 10Step [-]

Res

idua

l sha

nk to

rque

Tre

[Nm

]]


TresQmax

sQdue to decrease of preload

Fig. 7. V2: Development of residual shank torque during self-loosening Tre after preload generation and three transverse displacements sQmax; analyticalcalculation of Tt_pitch with constant preload Fp = 25 kN.

0

5

10

15

20

25

30

35

3 4 5 6 7 8 9 10Step [-]

Res

idua

l sha

nk to

rque

Tre

[Nm

]


Tt=Tt_pitch+Tt_friction= 31.72 Nm

Tre

Fig. 8. V3: Development of residual shank torque during self-loosening Tre after tightening and three transverse displacements sQmax; analytical calculationof Tt_pitch with constant preload Fp = 25 kN.


The build-up (V1) or decrease (V3) of residual shank torque Tre is influenced by the method of preload generation in thenumerical simulation and the transverse displacement sQmax. For displacements less than the critical displacement scrit (inthis example sQmax = 0.55 mm) it takes over 7 (sQmax = 0.3 mm) load cycles until the residual shank torque Tre has converged.The converged residual shank torque Tre which is necessary for the self-loosening simulation is available in version V2 afterpreload generation. This saves analysis cost and therefore is used for the following self-loosening simulations. It is acceptableto skip the real tightening process (V3) for self-loosening simulations. The understanding and proper illustration of the resid-ual shank torque in the numerical simulation is important for self-loosening simulations.

4. Determination of local contact state

In experimental studies for fasteners under transverse load only phenomenological results by analysing the self-looseningangle #L can be obtained. For the understanding of self-loosening with numerical simulations the classification of slip at thefastener surfaces can be classified in complete slip when the entire contact surface at the head or thread slides or localized slipwhen only partitions of the contact surface slide as suggested by Pai and Hess [6]. If the loads acting on the screw are suf-ficiently large to overcome friction over the entire contact surface, complete slip will occur. Before the entire contact surfacestarts complete slipping, localized slip occurs in partitions of the contact surface where the localized friction force has beenovercome. The slip state is influenced by the residual shank torque Tre (chapter 3), transverse displacement sQ, other externalloads, fastener geometry, stiffness, contact and friction conditions.

In the numerical simulation only a few load cycles are computed and very small calculated self-loosening angle in thenumerical simulation still leads to no self-loosening angle in experiment. Koch et al. [9] defined in his work with the Junkertest setup a critical displacement scrit (displacement of the moveable top part) for the simulation and experiment at whichsignificant self-loosening angle can be detected for localized head slipping. The maximum displacement smax (in this studysmax = sQmax = 0.86 mm) defines the maximum displacement of the screw head (entire slip at screw head contact surface).The risk for rotational self-loosening already starts when the critical displacement scrit (in this study scrit = sQmax = 0.55 mm;Fig. 5a) is reached, which differs significantly from the maximum displacement smax. For additional details to the critical dis-placement scrit, the reader is referred to Koch et al. [9].

In this paper a real fastener system is used for further understanding of localized slip and complete slip at the fastenercontact surfaces. Also additional a local key figure gn and global key figures for the entire contact gC and kC to characterisethe contact situation and for understanding of the self-loosening due to localized slip are defined.

The utilization of transferable friction force to normal force and friction coefficient per contact node gn of the contact sur-face (Eq. (3)) allows the evaluation of the ratio from ‘‘almost’’ sliding local (finite) contact areas, slipping contact areas andareas without contact. This is a useful qualitative extension to the pure observation of sticking, slipping and no contact from[7,8].

gn ¼Fshear n

Fnormal n � l100 ¼ s

p � l100 ½%� ð3Þ

where gn = 0%, represent no contact; 0% < gn < 100%, represent stick at contact node; gn = 100%, represent slip at contactnode; Fshear_n the magnitude of frictional shear force per contact node; Fnormal_n the magnitude of contact normal forceper contact node; s the shear stress; p the contact pressure and l is the friction coefficient.


The ratio of the transferable friction force to normal force and friction coefficient per contact surface at the screw head orthread defines the variable gC (Eq. (4)) for every increment.

gC ¼

PNtotal

n¼0Fshear n

ðPNtotal

n¼0Fnormal nÞl

100 ½%� ð4Þ

where Ntotal is the total number of nodes in contact (Fnormal_n > 0; p > 0) at contact surface (head or thread).kC defines the ratio of sticking contact area to slipping contact area at the screw head or thread surface (Eq. (5)) for every

increment.

kC ¼

PNstick

n¼0An

PNtotal

n¼0An

100 ½%� ð5Þ

where Nstick is the number of sticking nodes at contact surface (head or thread), Ntotal the total number of nodes in contact(Fnormal_n > 0; p > 0) at contact surface (head or thread) and An is the nodal contact area.

The evaluation of the key figures for every increment of the simulation is carried out with a self-developed python pro-gram for Abaqus, and can therefore easily be applied to other self-loosening problems. Below, these performance variablesgn, gC and kC are applied to different loading states of the real fastening system.

The utilization of transferable friction force to normal force and friction coefficient per contact node gn at the screw headand thread for three transverse displacements sQmax show Figs. 9 and 10 from the second transverse load cycle (Steps 4–5).Due to different localized or complete slipping at the screw contact surfaces in the first load cycle (Steps 3–4) differ the val-ues (FQ, Fp, Tre, kC, gC and A) and contour plots (gn) in the second load cycle for the same transverse displacements sQ, as it canbe seen in Figs. 9 and 10.

Increasing transverse displacement sQ leads to bending and tilting of the screw. This creates an unsymmetrical contactstate with an increase of the head contact area Ah and a decrease of the thread contact area At.

For the critical displacement scrit (sQmax = 0.55 mm) only kCh = 19% of the head surface is sticking (81% slipping) and thecomplete thread surface is already slipping (kct = 0%). The utilization of transferable friction force to normal force and frictioncoefficient at the head surface is very high (gCh = 92%), even for the sticking areas (kCh = 19%) which is shown by the local keyfigure gn. A fastener can show self-loosening under dynamic transverse loading due to the accumulation of localized slip atthe fastener contact surfaces. Head contact regions that stick during the first period of cyclic loading, slip during the secondperiod. This enables the entire head contact to slip over a complete cycle. The phenomenon of localized slip at the partitionsof the screw head surface from the right dead point to the left dead point, leads to small self-loosening angle. The stickingregion at the left dead point transforms into a slip region at the right dead point, the resultant cyclic variation in contact anddeformation states induce a small turn angle. The accumulation of this small angle at the screw head will induce the de-crease in preload, which finally results in the transverse complete screw head slip after various cycles. Self-loosening dueto localized slip is critical since it can occur at a significantly lower transverse load FQ or transverse displacement sQ thanthat required for complete slip.

As expected entire slip at the screw head contact surface is observed for the transverse displacement sQmax = 0.90.Complete slip at the thread surface (Fig. 10) occurs for all three transverse displacements sQmax. This does not necessarily

lead to a self-loosening of the screw; however the slipping affects the evolution of the residual shank torque Tre. The ratio ofthe transferable friction force to normal force and friction coefficient for the thread contact surface gCt is always greater than70% if the real fastener connection is transverse loaded.

The magnitude of the transverse force FQ is the sum of the transverse load acting at the bolt head FQ_head and the force atthe interface between the moveable clamped part and the nut thread component FQ_interface (Eq. (6)).

FQ ¼ FQ head þ FQ interface ð6Þ

where FQ is the transverse load, FQ_head the transverse load acting at the bolt head and FQ_interface is the transverse load actingat the contact interface.

As expected the total transverse force at the bolt head FQ_head, where complete sliding at the head support area begins, canbe derived from the sum of nodal shear forces Fshear_n (Eq. (7)).

FQ head ¼XNtotal

n¼0

Fshear n ¼XNtotal

n¼0

Fnormal n

!lh ð7Þ

Consider that immediately before reaching this force already slipping in the largest part of the head contact area takesplace (can be seen in Fig. 9). When the transverse load at the bolt head reaches Eq. (7) it shows not a transition from sticking

sQmax=0.9= 0.0 mm= 0.3 mm= 0.55 mm= 0.9 mm

sQ(t) = sQmax.sin(ω.t)

sQmax=0.55sQmax=0.3

4 5 Step

direction of transverse displacement sQ

x

z

TreFQ = 2825 NFp = 24746 NTre = 5.75 NmηCh = 52 %λCh = 98 %Ah = 63.3 mm²

sQmax = 0.9 mm

s Q =

0.0

mm

s Q =

0.3

mm

s Q =

0.5

5 m

ms Q

= 0

.9 m

mslip

no contact

stick

ηn [%]

FQ = 3438 NFp = 24678 NTre = 5.32 NmηCh = 57 %λCh = 66 %Ah = 63.3 mm²







FQ = 6277 NFp = 25470 NTre = 2.39 NmηCh = 100 %λCh = 0.0 %Ah = 69.7 mm²

no contact

stick

slip

complete surfaceis slipping

unsymmetrical contact state;increase in contact area

x

z

sQmax = 0.55 mmsQmax = 0.3 mm

slip

stick

x

z

FQ = Transverse loadFp = PreloadTre = Residual shank torqueηCh= Ratio of the transferable friction force to normal force and friction coefficient per contact surface at the screw head surfaceλCh= Ratio of sticking contact area to slipping contact area at the screw head surfaceAh = Head contact surface

bending ofshank

Fig. 9. Utilization of transferable friction force to normal force and friction coefficient per contact node gn at the screw head for three transversedisplacements sQmax for the second load cycle (deformed visualisation, screw displayed without thread).


to slipping but a transition from localized slip to complete sliding. Even if no self-loosening occurs for periodic transversedisplacement less than the critical displacement scrit material is worn in areas with localized slip (head-, thread- and inter-face contact). This phenomenon is known as fretting. This leads to a reduced preload by increasing periodic loading and thefriction coefficient can change.

slip

no contact

stick

ηn [%]

direction of transverse

displacement sQ

FQ = 2825 NFp = 24746 NTre = 5.75 NmηCt = 91 %λCt = 43 %At = 151.8 mm²

sQmax = 0.9 mmFQ = 3438 NFp = 24678 NTre = 5.32 NmηCt = 98 %λCt = 2 %At = 132.6 mm²

FQ = 3625 NFp = 23892 NTre = 4.14 NmηCt = 100 %λCt = 0.0 %At = 146.8 mm²







no contact

stick

slipthread engage-ment


unsymmetricalcontact statedue to bending;decrease in contact area

sQmax = 0.55 mmsQmax = 0.3 mm

y

xz

y

xz

y

xz


complete surfaceis slippings Q

= 0

.0 m

ms Q

= 0

.3 m

ms Q

= 0

.55

mm

s Q =

0.9

mm

FQ = Transverse loadFp = PreloadTre = Residual shank torqueηCt= Ratio of the transferable friction force to normal force and friction coefficient per contact surface at the screw thread surface

λCt= Ratio of sticking contact area to slipping contact area at the screw thread surfaceAt = Thread contact surface

Fig. 10. Utilization of transferable friction force to normal force and friction coefficient per contact node gn at the screw thread for three transversedisplacements sQmax for the second load cycle (undeformed visualisation, thread displayed without screw shank).



The self-loosening is influenced by several factors and the behaviour is a result of their non-linear interactions. Thenumerical simulation includes the primary factors that cause loosening and provides a useful method for analysing detailsof fastener loosening.

5. Verification of simulation results

The simulated mechanical behaviour of the real threaded connection including friction at the contact interface is verifiedwith experimental results. The real threaded connection is given by Fig. 11; it consists of the components described in Fig. 1.The clamped part is sinusoidal moved with a servo-hydraulic cylinder and the transverse force FQ, displacement of screwhead srad and the self-loosening angle of the screw head #Lh are measured. An ultrasonic axial tension gauge is used for mea-suring of the preload Fp = 25 kN during tightening and after operation.

The transverse load–displacement behaviour is influenced by the stiffness of the different parts, contact conditions, fric-tion coefficient, dimensional tolerances and self-loosening behaviour. The diagram in Fig. 12 compares the hysteresis curves

sQ(t) = sQmax.sin(ω.t); FQ

measurement ofloosening angle ϑLh

contact interface µc

screw moveable clamped part

nut thread component

measurement of screw head displacement srad

Fig. 11. Experimental test setup for a real threaded connection with interface contact between clamped part and nut thread component.

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Transverse displacement sQ [mm]

Tran

sver

se fo

rce

FQ [N

]

Simulation- sQmax=0.30 Simulation - sQmax=0.55 Simulation - sQmax=0.90Experimental - sQmax=0.30 Experimental - sQmax=0.55 Experimental - sQmax=0.90

sQmax

sQ

a

b

ce

d

b

dd

d

b

complete slip under screw head

b

Fig. 12. Verification of transverse load–displacement-functions for three different displacements sQmax.


between simulation (continuous line) and measurement (discontinuous line). In the diagram different displacements(sQmax = 0.30/0.55/0.90 mm) are drawn. They are matching very well and show point of gradient change when complete slipat the screw head surface occurs.

The simulation of the transverse behaviour including friction at the contact interface reproduces the real behaviour in agood approximation when including a detailed modelling of the contact conditions.

6. Discussion and conclusions

The preload generation and self-loosening process of a real fastener connection with component interface was investi-gated by a three-dimensional FE model and with experiments for verification. The results show that local contact state variessignificantly dependent on system parameters and load profile. Important is the exact knowledge of the residual shank tor-que Tre for self-loosening simulations. The following results are shown:

1. The numerical simulation of the transverse behaviour shows close agreement to the experimental observed behaviour.2. The self-loosening rate by localized slip is fairly low and increases as the loosening transitions from localized to complete

slip at the screw head surface takes place.3. The build-up (V1) or decrease (V3) of residual shank torque Tre and the preload evolution are influenced by the method of

preload generation in the numerical simulation and the transverse displacement sQmax. For displacements smaller thanthe critical displacement scrit (sQmax = 0.55 mm) it takes over 7 (sQmax = 0.3 mm) load cycles until the residual shank torqueTre has converged.

4. The converged residual shank torque Tre which is decisive for the self-loosening simulation is available in version V2instantaneous after preload generation. This saves analysis time and cost.

5. The residual shank torque Tre remains unchanged for self-loosening that occurs prior to complete slip at the head surface.6. A new local key figure gn and global key figures for the entire contact gC and kC to characterise the contact situation and

for understanding of the self-loosening due to localized slip are defined and introduced.7. For the critical displacement scrit (sQmax = 0.55 mm) only kCh = 19% of the head surface is sticking and the complete thread

surface is already slipping (kCt = 0%). The utilization of the head surface is very high (gCh = 92%), even for the sticking areaswhich is shown by the local key figure gn.

8. Complete slip at the thread surface (Fig. 10) occurs for all three transverse displacements sQmax. This does not necessarilylead to a self-loosening of the screw; however the slipping affects the evolution of the residual shank torque Tre.

Linking these results with simulations and experience form self-loosening, following conclusions can be drawn:The con-verged residual shank torque Tre is necessary for the self-loosening numerical simulation and is influenced by the method ofpreload generation. Self-loosening is initiated when complete thread slip is achieved and localized slip at the screw headsurface takes place. Self-loosening caused by localized slip occurs at significantly lower transverse displacements thanself-loosening caused by complete screw head slip. Failure behaviour due to self-loosening can be theoretical predicted withthe new introduced key figures which characterise the contact situation. The common consideration for analysing the risk ofself-loosening by quantifying the maximum transverse displacement smax (complete slip) of the screw head is an inadvisablemethod. So, considering no localized slip can lead to insufficient safety against self-loosening. In future, investigations due tomulti-screws-connections are in progress [16].

Appendix A. Supplementary material

Supplementary video data associated with this article for the visualisation of the self-loosening prozess of the realthreaded connection including friction at the contact interface can be found, in the online version, at doi:10.1016/j.engfail-anal.2011.07.012. Video (1) shows the self-loosening prozess due to lokalized slip at the head surface (sQmax = 0.55 mm) andvideo (2) shows the self-loosening prozess due to complete slip at the head surface (sQmax = 0.9 mm).

References

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[12] DIN EN ISO 16047. Fasteners – torque/clamp force testing, Berlin: Beuth; 2005.[13] Sakai T. Bolted joint engineering fundamentals and applications. Berlin: Beuth; 2008.[14] Mackerle J. Finite element analysis of fastening and joining: a bibliography (1990–2002). Int J Pres Ves Pip 2003;80:253–71.[15] Friedrich C, Koch D, Dinger G. Force transfer behaviour of fastened structures in light weight design. American Society of Mechanical Engineers ASME;

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Documents

Avoiding Self-loosening Failure of Bolted Joints With Numerical