9
RESEARCH ON SELF-LOOSENING MECHANISM OF BOLTED JOINTS UNDER TRANSVERSAL VIBRATION Wei Wang State Key Laboratory for Manufacturing System Engineering, Xi'an Jiaotong University, 710049, School of Air and Missile Defense Air Force Engineering University, 710051, Xi'an ,China [email protected] Qingli Wang School of Air and Missile Defense, Air Force Engineering University, 710051, Xi'an ,China [email protected] Shuai Zheng State Key Laboratory for Manufacturing System Engineering, Xi'an Jiaotong University, 710049, Xi'an ,China [email protected] Xiaowei Liu School of Air and Missile Defense , Air Force Engineering University, 710051,Xi'an ,China [email protected] Haiping Liu School of Air and Missile Defense, Air Force Engineering University, 710051,Xi'an ,China [email protected] ABSTRACT Bolted joints are widely used in the auto industry, energy field and Construction, and so on. Due to the wide use of the bolted joints, the degradation of bolts has significant effect on the performance of a whole machine. Under transversal vibration, the self-loosening of bolted joints, which is the biggest form of failure ranked only second to fatigue failure [1], will happen, due to the cyclic shear load. This paper is to study the mechanism of bolted jointsself-loosening. Aiming at analyzing the self-loosening mechanism of bolted joints under vibration, a three dimensional FEA model of bolted joints , which had taken thread into consideration, was built with the application of APDL, and the preload was applied on the bolted joints by dropping temperature, then FEA transient analysis of the bolted joints under transverse cyclic excitation was conducted. Effect of transverse cyclic excitations amplitude, initial preload, thread and bearing friction coefficients, the jointssurface friction coefficient, the thread pitch and the hole clearance on self-loosening was investigated. The results show that the complete thread slip occurs prior to the complete bearing surface slip under transverse vibration; the smaller amplitude, the smaller thread pitch and the smaller hole clearance is, and the greater initial preload, thread and bearing friction coefficients are, the more difficult self-loosening is to happen; the jointssurface friction coefficient has little relationship with self-loosening, however, the larger jointssurface friction coefficient makes the needed shearing force, which induces the transversal vibration, larger. These are of great significance for understanding of fastenersself-loosening and designing of bolted jointsanti-loosening. Keyword: Bolted joints; Vibration; Transient Analysis; Preload; Friction Coefficient INTRODUCTION The self-loosening of bolted joints will cause leakage, failure due to the uneven stress, the lowering of the complete machine dynamic performance, and other bad effects, even lead to accident. Thus it is of significant for studying on self-loosening. 1 Copyright © 2014 by ASME Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition IMECE2014 November 14-20, 2014, Montreal, Quebec, Canada IMECE2014-37971

Research on Self-Loosening Mechanism of Bolted Joints

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RESEARCH ON SELF-LOOSENING MECHANISM OF BOLTED JOINTS

UNDER TRANSVERSAL VIBRATION

Wei Wang

State Key Laboratory for Manufacturing System

Engineering, Xi'an Jiaotong University, 710049,

School of Air and Missile Defense Air Force

Engineering University, 710051,

Xi'an ,China

[email protected]

Qingli Wang

School of Air and Missile Defense,

Air Force Engineering University, 710051,

Xi'an ,China

[email protected]

Shuai Zheng

State Key Laboratory for

Manufacturing System Engineering,

Xi'an Jiaotong University, 710049,

Xi'an ,China

[email protected]

Xiaowei Liu

School of Air and Missile Defense ,

Air Force Engineering University,

710051,Xi'an ,China

[email protected]

Haiping Liu

School of Air and Missile Defense,

Air Force Engineering University,

710051,Xi'an ,China

[email protected]

ABSTRACT

Bolted joints are widely used in the auto industry, energy

field and Construction, and so on. Due to the wide use of the

bolted joints, the degradation of bolts has significant effect on

the performance of a whole machine. Under transversal

vibration, the self-loosening of bolted joints, which is the

biggest form of failure ranked only second to fatigue failure

[1], will happen, due to the cyclic shear load. This paper is to

study the mechanism of bolted joints’ self-loosening.

Aiming at analyzing the self-loosening mechanism of

bolted joints under vibration, a three dimensional FEA model

of bolted joints , which had taken thread into consideration,

was built with the application of APDL, and the preload was

applied on the bolted joints by dropping temperature, then

FEA transient analysis of the bolted joints under transverse

cyclic excitation was conducted. Effect of transverse cyclic

excitation’s amplitude, initial preload, thread and bearing

friction coefficients, the joints’ surface friction coefficient, the

thread pitch and the hole clearance on self-loosening was

investigated. The results show that the complete thread slip

occurs prior to the complete bearing surface slip under

transverse vibration; the smaller amplitude, the smaller thread

pitch and the smaller hole clearance is, and the greater initial

preload, thread and bearing friction coefficients are, the more

difficult self-loosening is to happen; the joints’ surface friction

coefficient has little relationship with self-loosening, however,

the larger joints’ surface friction coefficient makes the needed

shearing force, which induces the transversal vibration, larger.

These are of great significance for understanding of fasteners’

self-loosening and designing of bolted joints’ anti-loosening.

Keyword: Bolted joints; Vibration; Transient Analysis;

Preload; Friction Coefficient

INTRODUCTION

The self-loosening of bolted joints will cause leakage,

failure due to the uneven stress, the lowering of the complete

machine dynamic performance, and other bad effects, even

lead to accident. Thus it is of significant for studying on

self-loosening.

1 Copyright © 2014 by ASME

Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition IMECE2014

November 14-20, 2014, Montreal, Quebec, Canada

IMECE2014-37971

The self-loosening and anti-loosening of bolted joints has

been studied by many scholars. Junker [2]designed the famous

tester, called Junker tester, to study the loosening behavior of

bolted joints and found that the bolted joints under transversal

vibration relaxed more easily, due to the transversal cyclic

shearing load, than under other conditions. Hess and his

co-workers [3] [16] studied the self-loosening of bolted joints

under transversal cyclic shearing load by using experimental

and FEA method, and they put forward that there are four

apparent stages in the self-loosening. Nassar, Housari and

other co-workers [4]-[6] studied the effects of the thread pitch,

the initial preload, the hole clearance, the thread and bearing

friction coefficients on self-loosening through the application

of line linear model. Then, Nassar, Yang and other co-workers

[1], [7]-[11] proposed a more accurate analytical model to

analyze the self-loosening under transversal vibration, and

designed a series of corresponding experiments to validate the

analytical model.The scholars mentioned above got plenty of

achievement on self- loosening study, however, both their

theoretical models and the experimental models were based

on the Junker tester, which did not match the actual for

ignoring the frictional condition of the joints’ surface.

Jiang and his co-workers [12]-[14] designed a new

experimental facility to study on self-loosening. They studied

the self-loosening of bolted joints under transversal cyclic

load by using experimental and FEA method and proposed

that self-loosening should be divided into two stages: the first

loosening due to the short-time and acute plastic ratchet

effect of the material of thread, the second loosening due to

the clamping force loss caused by the nut’s turning back. Jiang

and his co-workers considered the frictional condition of the

joints’ surface, nevertheless, they didn’t consider the spiral

effect of the thread in their finite element simulation,so their

study cannot explain the self-loosening due to nut’s turning

back clearly. Yang Guangxue and her co-workers [15] studied

the effects of the addition bending moment, initial preload and

anti-loosening nut on loosening of bolted joints under

transversal vibration with the application of 3D FEA method

in their research on anti-loosening mechanism of a new type

of nut.

On the foundation of the former sholars, this paper built a

three-dimensional finite element model of bolted joints,

applied preload on the bolted joints model by using cooling

pre-tightening algorithm, then conducted the FEA transient

analysis of the bolted joints under transverse cyclic excitation,

and investigated the effects of the transverse cyclic

excitation’s amplitude, the initial preload, the thread and

bearing friction coefficients, the joints’ surface friction

coefficient, the thread pitch and the hole clearance on

self-loosening.

CORRELATIVE ALGORITHM

Augmented Lagrangian contact algorithm

Contact algorithm is used to dealing with the relationship

of the interaction between the contact body. Effective contact

algorithm should be able to pass the contact force to ensure

that there is no penetration between the two contact surfaces.

General contact algorithms in ANSYS are Penalty Function

algorithm, Lagrange algorithm and Augmented Lagrangian

algorithm. The Augmented Lagrangian algorithm is an

algorithm with easily converging and accurately calculating

based on the former kinds of algorithms.Before calculating

each load step, it will check the penetration between the

contact surface and the target surface and manage the

penetration. when there is a penetration , it will set up a

normal contact force between the contact surface and the

target surface, the size of the force is determinded by the

component proportionately to the contact stiffness and

penetration size, and the Lagrange coefficient, being

equivalent to set a spring which can be adjust its stiffness

between the two surfaces to limit the size of the penetration

and to prevent pathological integral stiffness, which will lead

to the solving divergence, caused by excessive contact

stiffness matrix. The algorithm is described as follows.

The finite element contact equation:

[ ][ ] { } { }K u P R (1)

In Eq.(1), [ K ] is the stiffness matrix, [ u ] is the unit

displacement matrix, {P} is the unit load vector, {R} is the

unit contact force vector.

The portion iR of {R} is determined by Augmented

Lagrangian contact algorithm, as followed:

1

0 , 0, 0i

n i

Rk

(2)

In Eq.(2), nk is normal contact stiffness, i is the

space between the contact surface and target surface, 1i is

Lagrange coefficient. If 0 , which means penetration,

coefficient 1i will modify nk according to the actual

contact stiffness, the concrete can be determined by Lagrange

iterative method:

1

,

,i n

ii

k e

e

(3)

2 Copyright © 2014 by ASME

In Eq.(3),i is the Lagrange coefficient of the previous

step, e is the contact tolerance (the allowed maximum

penetration for convergence).

So we can solve equation (1), and control penetration

and transfer contact force between two contact surfaces.

Cooling pre-tightening algorithm

In FEA, the general pre-tightening algorithm are

Preload Element algorithm, Equivalent Force algorithm and

Cooling algorithm.The pretightening unit can't bear shear

load,so it cannot be used in the transient analysis under

transverse vibration; the loading by Equivalent Force

algorithm is complex, and it cannot simulate the response of

the joints under preloading [17]. To pre-tighten the bolt joints

with shear force, the Cooling algorithm must be used. Cooling

algorithm: setting the bolt material thermal expansion

coefficient, then lowering the temperature of the

pre-tightening bolt part, the bolt will elongate, while the joints

will restrict the deformation of the bolt,which will cause the

inside tension of the bolt ,so the pretightening is simulated.

The algorithm is described as follows.

As shown in figure 1, in the free stage, the temperature

of the bolt part (length l ), which will be pretightened, is

lowered for T . There will be a contraction deformation,

whose size is 0l , due to the heat bilges cold shrink effect. In

the cooling preloaded stage, the existence of joints reduces the

deformation of bolt, there will be a clamping force between

bolt and joints, this force decrease bolt shrinkage deformation

for 1l and cause the joints deformation for 2l .

l

1l

2l0l

Initial stage Cooling pre-tightening Free cooling Fig.1: The deformation corresponding relationship of bolted

joints under cooling pre-tightening

As the figure shows, the axial deformation of bolt joints

has a deformation corresponding relationship:

0 1 2l l l (4)

According to the heat-expansion and cold- contraction,

there is a relationship:

0 0l l T (5)

In Eq.(5), 0 is the linear expansion coefficient of bolt

material.

As the deformation relationship of the bolt and joints

under pre-tightening shows:

1 / bl F K (6)

2 / cl F K (7)

In the above , F is the pre-tightening force on bolt

connection, bK is the stiffness of bolt,

cK is the stiffness of

the joints.

Taking Eq.(4), (5) and Eq.(6) into Eq.(7), and calculating

them , the lowering temperature of bolts when loaded

prestressing force F will be given:

0

1 1( )

b c

FT

K K l (8)

STUDYING ON THE SELF-LOOSENING SIMULATION

Finite element analysis modeling

In order to study the self-loosening mechanism of bolted

joints under transversal vibration based on FEA, the

corresponding finite element model must consider the spiral

effect of the thread, in other words, a three dimensional FEA

model of bolted joints , which takes thread into consideration,

must be built.

In this paper, the ANSYS parametric language is used

to build the FEA model of bolted joints. As Fig.2 shows, the

bolt is made up of two parts: haulm and thread, and is meshed

after using the command VGLUE. The FEA model of the nut

can be obtained in the similar way. The sizes of the model are

follows: the nominal diameter D is 12mm, the bolt head

diameter D1 is 16.6mm, the height of the bolt head KW is

7.5mm, the height of the nut H is 13mm, the thread pitch p is

1.75mm, the length of the bolt L is 64mm, joints’ sizes is

80mm×80mm×20mm(both boards are the same), the hole

clearance ' / 2 is 0.5mm, the profile angle is 60 degree. In

the model, the bolt material is high strength steel, whose

Young’s modulus 1E is 210GPa, Poisson ratio 1 is 0.3,

density 1 is 7.9×103Kg/m3, yield limit is 640Mpa. While the

joints material is Q235 steel, whose Young’s modulus 2E is

210GPa, Poisson ratio 2 is 0.3, density 2 is 7.9×103Kg/m3,

yield limit is 235Mpa.

3 Copyright © 2014 by ASME

Fig.2: Three dimensional FEA model of bolted joints

Constraints applying

This paper consider the slippage between contact

surfaces, so the contact pairs is built by using TARGE170 as

the target unit and the CONTA173 as the contact unit. When

building the contact pairs, the friction coefficients of the

thread engagement surfaces, bearing surfaces and joints

surfaces is defined as 1 、 2 and 3 by defining material

friction factor. Each friction coefficients is obtained from

literature [6] and literature [16], namely the paraffin

lubrication (0.05), the MoS2 grease lubrication (0.1),

mechanical lubricating oil (0.17) and dry friction (0.2).

Bolted joints pre-tightening

In the static solver, the normal temperature is setted by

using command TREF, the temperature load according to

Eq.(8) is loaded on the bolt by using command BFV to

pre-tighten the bolt. Fig.3 shows the stress nephogram of nut

thread after preloaded.As shows in the figure, the first circle

thread stress is the largest, the followed decreases one by one,

which fits to the actual stress distribution of bolt joints.

The

first

circle

Fig.3: The stress nephogram of nut thread after preloaded

Transversal vibration transient analyzing

In order to conduct the FEA of bolted joints self-loosening,

the transversal excitation x should be loaded and the transient

analysis should be conducted. The x is determined by the

formula:

0 sin( )x t (9)

In Eq.(9), the excitation amplitude is 0 ('

0 / 2 ),

is angular frequency.

Concretely, the joint surface friction coefficients are

setted as 1 2 3 =0.1, the FEA model of bolted joints,

showed in figure 1, is pre-tightened by the load of

F(F=10730N) to conduct static analysis. After the solution, the

displacement load 0.2sin(3600 )x t is loaded, and the

transient analysis is conducted for time step t=0.0125s and

end time=0.325s.

ANALYSIS OF SELF-LOOSENING MECHANISM

Analysis of self-loosening process

The curve in the Figure 4 shows the shearing load

changing over transverse displacement, called shearing load

hysteretic curve. As the transversal stiffness of bolted joints

can be explained by 0/transverse shearingK F ( shearingF means

the biggest shearing load, which equals to the half the vertical

span of the curve), thus the transversal stiffness of bolted

joints can be measured by the vertical span of the curve: the

bigger the vertical span is, the bigger the transversal stiffness

is.

O

A

B

C

D

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-2

-1.5

-1

-0.5

0

0.5

1

2

1.5

Th

e sh

eari

ng

lo

ad/K

N

Transverse displacement/mm

Fig.4: The relationship between shearing load and transverse

displacement

What shows in Figure 5 are the contact status of thread

engagement surface and bearing surface at point A, B, C and

D in Figure 4. In the figure, we can know that the thread

engagement surface slips completely, while the bearing

surface slips incompletely at point A and C, and the slippage

parts of bearing surface at point A and C are opposite,

suggesting that the bearing surface can slip in a whole circle.

However, both thread engagement surface and bearing surface

slip incompletely at point B and D. It suggests that the

slippage at the amplitude of transverse displacement is the

acutest, and the complete slippage of thread engagement

surface happens before that of bearing surface.

Near contact slip stick

(a)Point A (b)Point B

4 Copyright © 2014 by ASME

(c)Point C (d)Point D

Fig.5: The contact status of thread and nut bearing surface

The Curve in the Figure 6 shows the residual preload

change over time. In the figure, we can know that the preload

loses a little in a circle (for decreasing only 0.7% per circle).

Integrating with the Figure 5, we can know that the

incompletely slippage can also cause relaxation

0 0.05 0.1 0.15 0.2 0.25 0.3 0.3510

10.1

10.2

10.3

10.4

10.5

10.6

10.7

10.8

Res

idue

pre

load

/KN

Time/s

Fig.6: Residue preload VS time

Effect of excitation amplitude on self-loosening

In order to investigate into the effect of amplitude of

transversal vibration on self-loosening, referring to the

simulation of section 3.4, we only modify the parameter 0

to 0.02, 0.1, 0.2, 0.3 and 0.4. Then the comparison simulation

of bolted joints with different excitation amplitude under

transverse vibration is conducted. The curves in the Figure 7

show residual preload change for different excitation

amplitudes. In the figure, we can know that the curves of 0.02

and 0.1 are nearly parallel with the coordinate axis, which

indicates that there is little preload loss when the excitation

amplitude is 0.02 and 0.1. However, the preload loss is very

visible when the excitation amplitude is 0.2, 0.3 and 0.4. It

suggests that the self-loosening of bolted joints can happen

only when the excitation amplitude is big enough. When

comparing the preload loss of 0.2, 0.3 and 0.4, we can know

that the greater the amplitude is, the more likely to happen the

self-loosening is. The Figure 8 shows shearing load hysteretic

curves under different amplitudes. In the figure, we can know

that the greater the amplitude is, the bigger the shearing load

needed is.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.359.4

9.6

9.8

10

10.2

10.4

10.6

10.8

Pre

load

/KN

Time/s

0.020.10.20.30.4

Fig.7: Residue preload VS time under different amplitudes

-0.4 -0.3 -0.2 -0.1 0 0.2 0.3 0.40.1-3

-2

-1

0

1

2

3

The

sher

ing l

oad

/KN

Transvers displacement/mm

0.020.10.20.30.4

Fig.8: Shearing load hysteretic curves under different

amplitudes

Effect of initial preload on self-loosening

In order to investigate into the effect of initial preload on

self-loosening, referring to the simulation of section 3.4, we

only modify the parameter F to 3, 10.73, 21.32 and

29.93.Then the comparison simulation of bolted joints with

different initial preloads under transverse vibration is

conducted. The curves in the Figure 9 show the losing preload

percentage change for different initial preloads. In the figure,

we can know that the greater initial preload is, the smaller

percentage of preload loss is, the less likely to happen the

self-loosening is. The Figure 10 shows shearing load

hysteretic curves under different initial preloads. In the figure,

we can know that the greater initial preload is, the bigger

vertical span is. It suggests that the greater initial preload is,

the greater transversal stiffness of bolted joints is.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

s-1

0

1

2

3

4

5

67

Per

centa

ge

of

losi

ng p

relo

ad/%

Time/s

3KN10.73KN21.32KN29.93KN

Fig.9: Curves of losing preload percentage under different

initial preloads

5 Copyright © 2014 by ASME

-0.2 -0.15 -0.1 -0.05 0 0.1 0.15 0.20.05-5

-4

-3

-2

-1

0

1

2

3

45

The

sher

ing l

oad

/KN

Transvers displacement/mm

3KN10.73KN21.32KN29.93KN

Fig.10: Shearing load hysteretic curves under different initial

preloads

Effect of coefficients on self-loosening

(1) Effect of coefficient1 on self-loosening

In order to investigate into the effect of thread

engagement surface friction coefficient (1 ) on

self-loosening, referring to the simulation of section 3.4, we

only modify the parameter 1 to 0.05, 0.1, 0.17 and

0.2.Then the comparison simulation of bolted joints with

different thread engagement surface friction coefficient under

transverse vibration is conducted. The curves in the Figure 11

show residual preload change. In the figure, we can know

there are little preload loss when the coefficient is 0.17 and

0.2. However, the preload loss is very visible when the

coefficient is 0.05 and 0.1. Because the bigger coefficient is,

the bigger frictional force is, and the less likely to happen the

self-loosening is. The Figure 12 shows shearing load

hysteretic curves under different thread engagement surface

friction coefficients. In the figure, we can know that the

shearing load hysteretic curves are nearly the same. It suggests

that the thread engagement surface friction coefficient has

small effect on the transversal stiffness of bolted joints.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

10.3

10.4

10.5

10.6

10.7

Res

idue

pre

load

/KN

s

Time/s

0.050.10.170.2

Fig.11: Residue preload VS time under different 1

-0.2 -0.15 -0.1 -0.05 0 0.1 0.15 0.20.05-2.5

-1.5

-1

-0.5

0

0.5

1

1.5

22.5

-2

0.050.10.170.2

Th

e sh

erin

g l

oad

/KN

Transvers displacement/mm

Fig.12: Shearing load hysteretic curves under different 1

(2) Effect of coefficient 2 on self-loosening

In order to investigate into the effect of bearing surface

friction coefficient ( 2 ) on self-loosening, referring to the

simulation of section 3.4, we only modify the parameter 2

to 0.05, 0.1, 0.17 and 0.2.Then the comparison simulation of

bolted joints with different bearing surface friction coefficient

under transverse vibration is conducted. The curves in the

Figure 13 show residual preload change. In the figure, we can

know that the bigger coefficient is, the greater preload loss is,

when the bearing surface friction coefficient is 0.1, 0.17 and

0.2. However, there is little preload loss when the bearing

surface friction coefficient is such small as 0.05, which is

contrary to other scholars’ results, but is also correct. Because

the bolt head’s and nut’s DOFs are not constrained in this

paper, but constrained in other scholars’ analysis to fit with

Junker test. When the bearing surface friction coefficient is

very small, the slippage, caused by transversal movement of

the board, will be very slight, thus the self-loosening speed is

very slow. The Figure 14 shows shearing load hysteretic

curves under different bearing surface friction coefficients. In

the figure, we can know that the bearing surface friction

coefficient has as small effect as thread engagement surface

friction coefficient on the transversal stiffness of bolted joints.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.3510.3

10.4

10.5

10.6

10.7

10.8

s

Res

idu

e p

relo

ad/K

N

Time/s

0.050.10.170.2

Fig.13: Residue preload VS time under different 2

-0.2 -0.15 -0.1 -0.05 0 0.1 0.15 0.20.05-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0.050.10.170.2

Th

e sh

erin

g l

oad

/KN

Transvers displacement/mm

Fig.14: Shearing load hysteretic curves under different 2

(3) Effect of coefficient 3 on self-loosening

In order to investigate into the effect of joints’ surface

friction coefficient ( 3 ) on self-loosening, referring to the

simulation of section 3.4, we only modify the parameter 3

to 0.05, 0.1, 0.17 and 0.2.Then the comparison simulation of

bolted joints with different joints’ surface friction coefficient

under transverse vibration is conducted. The curves in the

Figure 15 show residual preload change. In the figure, we can

know these curves are nearly the same. It suggests that the

joints’ surface friction coefficient nearly has no effect on

self-loosening under the same transversal vibration amplitude.

The Figure 16 shows shearing load hysteretic curves under

different joints’ surface friction coefficients. In the figure, we

6 Copyright © 2014 by ASME

can know that the bigger the joints’ surface friction coefficient

is, the bigger vertical span is. It suggests that the bigger the

joints’ surface friction coefficient is, the bigger transversal

stiffness of bolted joints is, the less likely to happen

self-loosening is.

0 0.05 0.1 0.15 0.2 0.25 0.310.3

10.4

10.5

10.6

10.7

s0.35

0.05

0.2

0.10.17

Res

idu

e p

relo

ad/K

N

Time/s

Fig.15: Residue preload VS time under different3

-0.2 -0.15 -0.1 -0.05 0 0.1 0.15 0.20.05-3

-2

-1

0

1

2

30.05

0.2

0.10.17

The

sher

ing l

oad

/KN

Transvers displacement/mm

Fig.16: Shearing load hysteretic curves under different 3

Effect of thread pitch on self-loosening

In order to investigate into the effect of thread pitch on

self-loosening, referring to the simulation of section 3.4, we

only modify the parameter p to 1.5(Fine thread) and

1.75(Coarse thread).Then the comparison simulation of bolted

joints with different pitches under transverse vibration is

conducted. The curves in the Figure 17 show residual preload

change for different thread pitches. In the figure, we can know

that the preload of fine thread loses slower than the coarse

thread’s. It suggests that the anti-loosening performance of

fine thread is better than coarse thread. The Figure 18 shows

shearing load hysteretic curves under different thread pitches.

In the figure, we can know that the shearing load hysteretic

curve of fine thread has the same vertical span with the coarse

thread. It suggests that the thread pitch has small effect on the

transversal stiffness of bolted joints.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.3510.3

10.4

10.5

10.6

s

10.7

Res

idu

e p

relo

ad/K

N

Time/s

fine

coarse

Fig.17: Residue preload VS time under different thread pitches

-0.2 -0.15 -0.1 -0.05 0 0.1 0.15 0.20.05-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Th

e sh

erin

g l

oad

/KN

Transvers displacement/mm

fine

coarse

Fig.18: Shearing load hysteretic curves under different thread

pitches

Effect of hole clearance on self-loosening

In order to investigate into the effect of hole clearance on

self-loosening, referring to the simulation of section 3.4, we

only modify the parameter ' / 2 to 0.5, 0.75 and 1.25. Then

the comparison simulation of bolted joints with different

clearance under transverse vibration is conducted. The curves

in the Figure 19 show residual preload change for different

hole clearance. In the figure, we can know that the bigger the

hole clearance is, the faster the preload loses, which proves

that the better the assemblage is, the better anti-loosening

performance is. The Figure 20 shows shearing load hysteretic

curves under different hole clearance. In the figure, we can

know that the shearing load hysteretic curve of bigger hole

clearance has the smaller vertical span than the smaller ones’.

It suggests that the bigger hole clearance has smaller

transversal stiffness of bolted joints. At the same time, the

difference between three shearing load hysteretic curves is not

unconspicuous. It suggests that the hole clearance has small

effect on the transversal stiffness of bolted joints.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.3510

10.1

10.2

10.3

10.4

10.5

10.6

10.8

10.7

Res

idue

pre

load

/KN

Time/s

0.751.25

0.5

Fig.19: Residue preload VS time under different hole clearance

-0.2 -0.15 -0.1 -0.05 0 0.1 0.15 0.20.05-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Th

e sh

erin

g l

oad

/KN

Transvers displacement/mm

0.751.25

0.5

Fig.20: Shearing load hysteretic curves under different hole

clearance

CONCLUSIONS

The self-loosening mechanism of bolted joints under

7 Copyright © 2014 by ASME

transversal vibration is studied based on FEA. And the

transverse vibration amplitude, the initial preload, thread and

bearing friction coefficients, the joints’ surface friction

coefficient, the thread pitch and the hole clearance on

self-loosening is investigated. The results show that:

(1)Both the slippage of thread engagement surface and

the slippage of bearing surface can lead to the preload loss of

bolted joints under transversal vibration. The complete

slippage of thread engagement surface is priority to bearing

surface.

(2)The greater the vibration amplitude is, the more likely

to happen the self-loosening is.

(3)The greater initial preload is, the smaller percentage of

preload loss is, the less likely to happen the self-loosening is.

(4)The greater thread and bearing friction coefficients is,

the less likely to happen the self-loosening is. The joints’

surface friction coefficient has small influence on self-

relaxation under the same transversal vibration. But it has a

big impact on the transversal stiffness of bolted joints.

(5)The self-loosening of bolt with coarse thread is more

likely to happen than that with fine thread.

(6)The paper proves that the better the assemblage, the

better locking performance of fine thread.

In conclusion, when designing bolted joints’

anti-loosening, we should put how to change the thread

engagement surface friction first. We should also consider

bearing surface friction. We should give the biggest preload

within the strength and increase joints’ surface friction without

leakage.

All in all, this paper is of great significance for

understanding of fasteners’ self-loosening and designing of

bolted joints’ anti-loosening.

ACKNOWLEDGMENT

This work is supported by Postdoctoral Science

Foundation of China (No.2014M552430) and a grant from the

National High Technology Research and Development

Program of China (863 Program) (No.2013AA040604).

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