DESIGN AND RELIABILITY INFLUENCES ON SELF-LOOSENING OF MULTI-BOLTED JOINTSirf/Proceedings_IRF2016/data/... · 2016-05-31 · paper focuses on the reliability influence on self-loosening

Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal 24-28 July 2016

Editors J.F. Silva Gomes and S.A. Meguid

Publ. INEGI/FEUP (2016)

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PAPER REF: 6302

DESIGN AND RELIABILITY INFLUENCES ON SELF-LOOSENING

OF MULTI-BOLTED JOINTS

Shiva Kumar Manoharan(*), Christoph Friedrich

Institute of Engineering Design- MVP, Department of Mechanical Engineering, University of Siegen, Germany. (*)Email: [email protected]

ABSTRACT

Research into self-loosening has till date focused on a few of the joint parameters of a one-

bolt-joint, namely, bolt preload/bolt force, clamp length, friction coefficients at different

interfaces, length of thread engagement, diameter of bolt and that of head support. Recent

developments have indicated that there is a significant difference in self-loosening behavior

between laboratory tests with a single bolt joint without interface friction (Junker’s test) and

behavior of real component systems. This paper deals with design influences on self-

loosening behavior of bolted joints which have so far been neglected, like, different clamped

materials, difference between single and multi-bolted joints, influence of distance between the

bolts, influence of component stiffness and influence of an offset load. Another part of this

paper focuses on the reliability influence on self-loosening behavior. Bolted joints often have

deviations between the designed/desired preload level and the actual clamping force due to

friction deviations, seating loss, thermal/mechanical (over)loading, creep of materials etc. As

a method to develop reliable and robust bolted joints for components, investigations have

been performed with not only the maximum design preload but also minimum possible

clamping force in application.

Keywords: Self-loosening, multi-bolted joints, finite element analysis, design, reliability.

INTRODUCTION

Self-loosening is a predominant failure mode for bolted joints experiencing dynamic loads.

Research into this phenomenon intensified since 1960s with the invention of Junker’s test,

where a single bolt under tension, with no interface friction, was subjected to transverse

vibrations (perpendicular to bolt axis) using an eccentric cam drive that produced a sinusoidal

displacement [2]. Such loading led to rotational loosening of the bolt without external aid,

hence the term self-loosening. Self-loosening can lead to complete loss of tension in the bolt

thereby compromising the joint integrity. The phenomenon is normally not integrated in

design process for prediction in applications. Vibration test standard DIN 65151 has been

created from Junker’s test [20].

Research into self-loosening has till date focused mainly on the mechanism leading to

rotational self-loosening and few of the joint parameters of a single bolt joint, namely, bolt

force, clamp length, friction coefficients at different interfaces, length of thread engagement,

diameter of bolt and that of head support [1, 2, 5, 7, 9]. The mechanism for self-loosening that

is widely accepted is understood as follows: Due to transverse vibrations in the components

that are clamped together, small relative displacements can take place in the components; this

leads to bending of the bolt and contact instability (partial slipping of contact surfaces) in the

Symposium_17: Mechanical Connections

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head and thread region. Under the presence of these contact instabilities, the off torque from

the pitch of the threads is sufficient to cause small rotations. Details of the mechanism can be

found in literature like [1, 2, 6, 8] and published books [5, 18,19].

DIFFERENT METHODS FOR ASSESSMENT OF SELF-LOOSENING

IN BOLTED JOINTS

Several methods to analyze a joint for self-loosening failure have been presented by

researchers in the past. This include analytical method using formulae, laboratory experiments

in controlled environment and finite element analysis of a bolted joint. A few interesting

analytical formulae and their comparison can be found in [13]. The general form for the

analytical formulae that are available in the literature is as follows:

scrit = f (bolt preload FP, clamp length lC, friction coefficient at bolt

head µH, stiffness of the bolt, radial clearance between the threads) Eq. 1

Where scrit is the relative transverse displacement of clamped components that leads to

complete loosening of bolt preload. Based on their own research different researchers have

presented different magnitudes of scrit [2, 3, 5, 7]. From the research findings of Koch, a

criterion for analyzing a joint for self-loosening is when the gradient of the rotational

loosening curve reaches 0.03° per load cycle in an FE (finite element) simulation within the

first 10 load cycles [7]. This had been derived by statistically analyzing experimental work

(with Junker’s test stand) and simulations.

However, for a given design task, it is difficult to assess the relative displacement between

components (due to the material stiffness and geometric non-linearities). At best the designer

has the knowledge of the forces and moments acting in different locations and directions,

based on the preload that prevails in a bolted joint, these forces and moments may or may not

cause relative displacements. Another important point worth mentioning is that the analytical

formulae generally do not include a function of the pitch angle of threads (off-torque

generation comes from threads), which theoretically would be a parameter based on the

mechanism of self-loosening. Hence one can conclude that there needs to be further

investigation in this regards.

From experiments point of view, most popular is Junker’s test stand which has also been

adopted into standards such as DIN 65151. There are several limitations to this test setup,

such as friction-less interface of clamped components [2], limited number of parameters that

can be varied, influences from real component systems like more than one bolt in a joint and

stiffness of clamped materials cannot be assessed directly. Most of all, the loading is a very

ideal case of transverse loading whereas other types of loading such as torsional [16] and

combination of axial and transverse [17] have also shown to produce rotational self-

loosening. Another notable test stand is NAS 1312-7 [25] which produces impact loading on

the bolt and nut combination mounted on a vibrating table. The best way to test a joint for

self-loosening would be to test it at the component level with the loading from application.

Summarizing the introduction, there are no concrete measures that will help a designer to

predict the safety of a bolted joint against self-loosening. One useful method is that of

simulations, where a complete component system can be analyzed three dimensionally with

reduced efforts of analytical design and experiments. In this work several design parameters

are assessed with finite element analysis and their influence on self-loosening behavior is

discussed. Simulations are often time consuming in nature and several parameters of FEA

Proceedings of the 5th International Conference on Integrity-Reliability-Failure

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(finite element analysis) and numerical methods themselves can become influencing factors.

A good solution to the self-loosening problem would be in the direction of analytical

calculation such that designers have the chance to predict the phenomena in advance.

Combination of experimental results and simulation results to bring up a modified analytical

formula is a future need.

SIMULATION OF ROTATIONAL SELF-LOOSENING IN BOLTED JOINTS

In the last two decades, simulation of self-loosening behavior can be found in the literature.

Most researchers have proposed simulations as an alternative to Junker’s test and as a means

to study the mechanism which normally cannot be realized from experiments without much

efforts. For the simulation of rotational self-loosening, three dimensional helical threads must

be modelled [4, 7, 8, 16]. Apart from this, the influence of various contact interfaces must be

taken into account e.g. bolt head bearing surface, interface between clamped components, nut

bearing surface and mating threads. A simple check of the joint model can be performed with

comparing the bolt stiffness from the FE model to analytical calculation (e.g. from [19]). The

behavior, in simulation, is found to be quite sensitive to the stiffness of bolt and to that of the

clamped components [9]. In this work results are presented by using Abaqus 6.9 – a

commercial FE solver. For the right influence of stiffness, elastic-plastic material data is used.

For realistic simulation, modelling the bolt head with the respective inclination of the bearing

surface is important as it would determine the level of resistance against loosening moment at

head.

Fig. 1 - A FE model for simulation of self-loosening, here example of a single bolt joint.

In Fig. 1 above, a cut section of a meshed model used to study the characteristics of self-

loosening is shown. Some simplifications are made by neglecting the radius at head-shank

transition region, neglecting the thread root radius and modelling a separate thread part which

is attached with tie function to the bolt shank. This is done because the focus of the

investigation is on the loosening behavior and not the stress distribution. In this work an M10

bolt is modelled according to DIN EN 1665 [21] with a pitch of 1.5 mm and 60° thread angle

and 0.75° head bearing surface inclination angle. The threads are modelled as per DIN ISO

965 [22] with average values of tolerance combination 6g, 6H from DIN 13-20 [23].

Clearance at the bore of clamped parts is set to 1 mm as per DIN EN 20273 [24]. Selective

usage of reduced and fully integrated elements provides an optimal computation time. Mesh


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match technique was used in order to facilitate initial contact between the various contact

regions. Surface-to-surface contact formulation with finite sliding and penalty algorithm for

both normal and tangential contacts are used. When using penalty algorithm, care must be

taken to define a small elastic slip factor in order to achieve exact stick-slip effects. Penalty

algorithm is preferred here for its speed.

Boundary conditions for the investigations are inspired from Junker’s test. Preload is

introduced in the form of a pretension section which is a built-in function of the FE package.

Sensitivity analysis can be performed with varying amplitudes of transverse displacements in

sinusoidal form to replicate the effects of vibration. An important assumption is that the

process of self-loosening is quasi-static based on Junker’s work from 1969 wherein the state

of stick-slip and the number of transverse load cycles are the main influencing factors [2]. The

critical output parameters monitored in this analysis are the preload FP, rotation at head of the

bolt ϑLh and transverse force FQ causing the sinusoidal displacement. The major advantage of

this method is that critical force levels can be established for different preload levels, hence

providing an input for the designer to check his joint against the possibility of self-loosening.

The term scrit has been defined as the minimum relative slip between the clamped components

that sets up a constant loosening gradient of 0.03° per load cycle in the first ten cycles of

simulation [7], the same is used in this work. This generally leads only to partial slip in the

bolt head bearing surface [4, 6, 7, 8, 9]. Static friction coefficients are defined as 0.15 at head

bearing surface, 0.07 at component interface and 0.2 at threads. Clamp length of the joint is

15 mm.

RESULTS AND DISCUSSION

In the last years, efforts have been redirected towards the design stage assessment of self-

loosening [11, 12, 13]. Simulation method involving finite element analysis have been

improved to predict and avoid self-loosening in the design phase of real components. The

principle is to apply a displacement load (sinusoidal) to the structure and evaluating the

resulting behavior of the bolts. Displacement load is preferred because from the mechanism, a

relative movement of the clamped components is essential in causing self-loosening. In this

work a comprehensive study is performed with single bolted joints and multi-bolted joints

(with two bolts) to assess the parameters that are additionally important from design

perspective for components.

Self-loosening behavior of multi-bolted joints

The prediction for self-loosening with FEA involves conducting sensitivity analysis of a

single bolt joint in order to determine the smallest (critical) amplitude of transverse vibration

that may cause complete loosening of the joint. However significant difference is observed in

the behavior of a single bolt joint and a multi-bolted joint as shown in Fig. 2. The source for

the difference in behavior for the same amplitude of relative transverse displacement comes

from the combined preload of two bolts, the deformation behavior of the clamped parts and

the stiffness of the clamped parts in the transverse direction under the influence of bolts

clamping the plates. Due to this the transverse load is unable to produce the required shear

under the bolt head that corresponds to the single bolt model as shown in Fig. 3. There also

exists a difference in the maximum transverse force (FQmax) that is required to create the

displacement of 0.2 mm due to the fact that the force only needs to be high enough to cause

the deformation at the point of loading and not till the other end of the joint.


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Fig. 2 - Difference in self-loosening behavior of a single bolt joint (a) and a multi-bolted

joint (b1, b2) with aluminum clamped part (red) and steel nut component (green) subjected

to same amplitude of transverse vibration SQmax = 0.2 mm (in the form of load cycles with

sinusoidal displacement) here the clamp length is 10 mm [13].

Fig. 3 - Shear force under bolt head for a single bolt joint (a), multi bolted joint (b1) and

(b2) corresponding to Fig. 2 above.

Influence of clamped material on self-loosening behavior

Light weight components are often vibration critical in application. In this section a

comparison is made between the self-loosening behavior of bolted joint with steel and

aluminum clamped part during the search for the critical relative displacement of component

from simulation, scrit. As discussed earlier, the search for the critical relative displacement

involves varying the amplitude of displacement such that the resulting gradient of self-

loosening achieves or crosses 0.03°/load cycle. Regarding this criterion, when the clamped

part is made of steel, scrit = 0.18 mm and when it is made of aluminum it is scrit = 0.195 mm.

However, the transverse force value that causes the critical self-loosening gradient are similar.


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This means that that a value of critical displacement calculated by analytical formulae does

not hold true for different clamped materials. The comparison can be seen in Fig 4. The

reason for the difference could be associated to the elastic strain energy that is absorbed by

aluminum to deform due to the presence of the bolt force, hence a greater relative

displacement is required in order to produce sufficient shear force under the bolt head.

Moreover, for aluminum clamped part with lower strength and modulus of elasticity, there

can been seen a greater embedment of the bolt head into the clamped part (Fig. 5), this gives a

small resistance to self-loosening.

Fig. 4 - Evaluation to determine scrit for a single bolt joint, with change in material of the

clamped part. M10 bolt according to dimensions from DIN 1665 with 25 kN preload via a

pretension section and clamp length of 15 mm.

Fig. 5 - Embedment of bolt head (modelled with bearing angle of 0.75°) into clamped part

(modelled flat) with aluminum and steel material under a preload of FP = 25 kN.


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Influence of component stiffness/geometry on self-loosening behavior of multi-

bolted joints

From the previous section, a significant influence of the stiffness of the clamped part can be

seen on self-loosening behavior of bolted joints based on material of clamped part. With this

motivation, an extended evaluation with a multi-bolted joint was conducted. Two bolts of

M10 according to DIN EN 1665, separated by a distance of seven times the nominal diameter

(7D) was modelled to simulate self-loosening behavior for assessment of geometrical

stiffness. Two geometries of the clamped part are assessed, one with rectangular plates (stiff

component) and another with a small portion of the clamped parts cut away resulting in C like

plates (reduced stiffness). For comparison, both geometries are loaded with the same

amplitude of relative transverse displacement between components, sQ= 0.2 mm (which is

greater than scrit from previous section). The same test is performed for steel clamped part and

aluminum clamped part.

The results are shown in Fig. 6 and 7. For both materials, sum of the rotational loosening for

two bolts increases when the stiffness of the component in between the bolts reduces. On the

other hand, for the aluminum clamped part, the scrit from previous section was = 0.195 mm,

even though the sQmax in this section is greater than scrit, only bolt 1 (B1) reaches the critical

gradient but not bolt 2 (B2). This is due to the stiffness of the clamped part and the energy

absorbed for elastic strain between the two bolts in the rectangular plates. Hence when

reducing this cross section, the C plates show increased loosening in both B1 and B2 for the

aluminum plates. However, for steel plates with reduced cross section, the stiffness goes

down and the force absorbed for deformation is higher hence B1 rotates more and B2 rotates

less than the rectangular plates.

Fig. 6 - Influence of geometrical stiffness on self-loosening behavior of a multi-bolted joint

with two M10 bolts according to DIN EN 1665 and aluminum clamped part. Clamp length

here is 15 mm.


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Fig. 7 - Influence of geometrical stiffness on self-loosening behavior of multi-bolted joint

with two M10 bolts according to DIN EN 1665 and steel clamped part. Clamp length here

is 15 mm.

Influence of distance between the bolts on self-loosening behavior of multi-bolted joints

Taking the investigation with multi-bolted joints further, another variation is made with

distance between the bolts. For the C-plates, two distances were evaluated, four times the

nominal diameter (4D) and seven times the nominal diameter (7D). From Fig. 8 and Fig. 9, it

can be seen that reducing the distance between the bolts, increases the rotational loosening of

bolt 2 (B2), whereas the rotational loosening of bolt 1 (B1) remains almost the same. This

means that the influence of the stiffness reduces with decreasing distance between the bolts in

a multi bolted joint. As a result, the force absorbed for elastic strain is less, the transmission to

second bolt is higher. This behavior can be better understood with example of an imaginary

spring with length l, thickness t and a very low stiffness, connecting the two bolts B1 and B2.

When l = ∞, all the force pushing B1 towards B2 will be utilized for deflection of the spring,

no force will be transferred to B2. At l = 0, force on B1 = force on B2. When ∞ > l > 0, some

amount of energy is absorbed for elastic strain of the spring before part of the force is

transferred to B2. This behavior leads to an increase in the deflection of bolt head about the

bolt axis in the 4D model as compared to the 7D model as shown in Fig. 10. The reason for

increase in bolt head rotation of B2 in the 4D model is the presence of a torsional moment in

addition to the transverse load due to the geometry of the clamped part.


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Fig. 8 - Influence of distance between the bolts on self-loosening behavior of the multi-

bolted joint with C-plates from previous section and aluminum clamped part

Fig. 9 - Influence of distance between the bolts on self-loosening behavior of the multi-

bolted joint with C-plates from previous section and steel clamped part.


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Fig. 10 - Deflection of bolt head about the bolt axis for the two distance variations between

the bolts with aluminum clamped part.

Influence of offset load on self-loosening behavior of multi-bolted joints

In this section another experiment is performed by considering an offset loading to the C-

plates via a small lever arm at 20 mm above the plane of bolt head bearing surface. Aluminum

has been defined as the material for the clamped component. Loading is the same

displacement based loading of sQmax = 0.2 mm. The results are shown in Fig. 11. It can be

seen that no self-loosening has occurred in the joint. The reason can be associated with the

strain energy absorbed by the by the lever arm itself to deform, hence there is no significant

slipping of the components that takes place. Additionally, when the clamped part deforms, the

transverse load generates a bending moment which leads to higher pressure in the component

contact; therefore, more component deformation and less relative movements of surfaces in

contact. This can be seen in the global deformation behavior in Fig. 12.


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Fig. 11 - Comparison of self-loosening angles when loading is in plane of the bolt head

contact surface and when loading is at an offset of 20 mm, both variation with aluminum

clamped part.

Fig. 12 - Global deformation behavior of the clamped parts for studying the influence of

load offset on self-loosening behavior of the multi bolted joint with C-plates.


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Reliability influence on self-loosening behavior of multi-bolted joints

Bolted joints often have deviations in assembly preload due to frictional stability, tightening

torque and other deviations in assembly. Once assembled, further deviations can come from

effects like seating of roughness, thermal and mechanical (over-)loading. A detailed view of

different reliability aspects can be found in [10, 15]. A typical range of deviation of preload

resulting from relaxation of bolted joints is 15% to 40% of the design preload for light weight

components tightened close to the yield point [10]. Hence it is essential to perform the

investigation with not only the maximum assembly preload but also the worst case of

minimum clamping force in application. To illustrate the influence of these reliability issues

on self-loosening behavior, a simple test is carried out by taking a multi-bolted joint with

dissimilar preload levels in the bolts. For the C-plates, two simulations are compared in Fig.

13, one with preload FP1 = FP2 = 25 kN and another with FP1 = 25 kN and FP2 = 15 kN. The

results show that for a multi-bolted joint, reduction in preload of even one bolt can lead to

greater self-loosening in both the bolts. This could be attributed directly to the decrease of

total preload in the joint which thereby makes self-loosening to proceed at a higher rate as

preload determines the main resisting torque at bolt head that needs to be overcome by thread

off-torque for self-loosening.

Fig. 13 - Influence of reliability of preload on the self-loosening behavior in the multi-bolted joint with C-plates

and two M10 bolts according to DIN EN 1665.

CONCLUSION AND OUTLOOK

Self-loosening behavior of multi-bolted joints show significant differences from that of a

single bolt joint. Additionally, factors like material of clamped part, geometry of clamped part

(stiffness and load offset), distance between the bolts and deviations in bolt preload can lead

to difference in the self-loosening behavior of the joint. Following points can be concluded

from above:

• Assessment of self-loosening for a single bolt joint is not transferrable directly to

multi-bolted joints.


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• Lightweight materials like aluminum can give a better resistance to self-loosening

than stiff materials like steel due to their ability to store higher strain energy.

• Distance between the bolts must be assessed for obtaining the right combination of

material and resistance to self-loosening based on geometry of clamped parts.

• Geometric shapes of the clamped components and load offsets can be crucial in

determining the self-loosening behavior of a multi bolted joint.

• Deviations of preload in application must be assessed beforehand in order to guarantee

a joint safe against self-loosening.

Integrity of a multi-bolted joint, against self-loosening failure, is subject to design and

reliability influences. It is also quite clear that analytical formulae are not sufficient to

encompass the vast influences of design. For component systems with particular load cases, a

simple laboratory test with one bolt, does not necessarily guarantee the safety against self-

loosening.

The method of simulation with finite element analysis is robust enough to assess components

for individual load cases, design and reliability influences. For the future, a need exists for

enhancement of analytical methods for prediction of self-loosening which could result from

combination of assessments from FE simulation and laboratory experiments.

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technik, Vol. 1, pp. 25-30, Ingenieur Digest Verlag, 1969.

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Documents

DESIGN AND RELIABILITY INFLUENCES ON SELF-LOOSENING OF MULTI-BOLTED JOINTSirf/Proceedings_IRF2016/data/... · 2016-05-31 · paper focuses on the reliability influence on self-loosening