Research Progress on Influencing Factors of Bolted Joint Structure Loosening

Loosening of bolted joint structure is a critical failure mode mainly caused by the slippage and friction behaviours on the thread and bearing surfaces. Domestic and foreign scholars have conducted a series of studies on the loosening mechanism and anti-loosening methods of bolted joint structures; however, there are fewer summaries on the influencing factors of loosening of bolted joint structures. This paper takes the phenomenon of loosening of bolted joint structure as the research object, summarizes the research method of loosening of bolt joint structure and the influencing factors, and summarizes the influencing law of loosening of bolted joint structure in four aspects, namely, preload force, external load factors, structural factors, and operating temperature, to provide references for the design of anti-loosening of bolted joint structure.


Introduction
Bolt fasteners, as the essential parts of mechanical equipment, have the characteristics of simple structure, easy disassembly, interchangeability, and so on, so they are widely used in aerospace, automobile, pressure vessels, and other engineering fields.However, in the joint structure, the bolt joint is the weakest link, and the common forms of bolt fastening joint failure are loosening, overload fracture, fatigue fracture, stress corrosion, hydrogen embrittlement, slippery teeth, etc [1].Loosening failure is extremely common in bolted joint structures.; its failure criterion is defined as a decline in the axial force to a certain extent, leading to the loss of work performance.In engineering applications, due to vibration, impact, and alternating loads, the bolt axial force inevitably decreases.The equipment lightly causes structural failures such as leakage and rattling, and heavily causes other forms of failure such as fracture, leading to the overall structural damage of the equipment and causing major safety accidents.In 2002, a derailment occurred in the UK when a train traveling via Potters Bar came into the station due to the loosening of the nuts on the rutters, resulting in 7 deaths and 16 injuries [2].In 2007, when China Airlines Flight 18616 landed, an explosion and fire occurred; the accident investigation revealed that during landing, an internal bolt on the wing leading edge flap loosened and fell off and poked through the fuel tank inside the wing, and fuel flowed out of the rupture in large quantities, which was then ignited by the high temperature of the engine [3].Loosening of bolted joint structures leads to frequent accidents, seriously affecting the reliability and safety of the equipment.
The loosening of bolted joint structures is affected by a variety of uncertainties, such as structural dimensions, external loads, and service environment.In recent years, scholars at home and abroad have studied the loosening behaviour, loosening mechanism, and anti-loosening methods of bolted structures by various means such as loosening test and finite element simulation [4][5][6][7], and some key results have been obtained.Still, no report has been reported on the systematic summarization of these research results.Given this, this paper summarises the factors affecting the loosening of bolted joint structures by 1) preload force; 2) external load factors (direction, amplitude, frequency); 3) structural factors (friction coefficient, pitch, thread clearance fit); 4) operating temperature, and put forward suggestions to improve the looseness of bolted joint structure, to provide a reference for the anti-loosening design of the bolted joint structure.

Experimental Work
Junker et al. [8] first designed a test device, which first applied transverse cyclic vibration to threaded fasteners.As shown in figure 1, the Junker test setup consists of a fixed base, movable plates, and several sensors that monitor preload, shear load, and lateral displacement.Through the lateral movement between the movable plates, the shear load will be applied to the joint structure between the bolt and the nut, causing transverse vibration of the whole experimental setup.The device is widely used in the study of bolted joint structure loosening.The test of bolt antiloosening ability in international standard DIN-65151 [9] and national standard GB / T 10431-1008 [10] is based on this device.
In addition, some scholars from Southwest Jiaotong University [11][12][13] designed a loosening test device of bolted joint structures under different working conditions, such as axial excitation, transverse excitation, and shear excitation by improving the fixture of the fatigue testing machine.As shown in figure 2 for the transverse vibration test device schematic diagram, the fatigue testing machine at both ends of the chuck was clamped upper and lower fixture, and the bolt through the fixture through-hole and nut with the formation of a complete bolted joint structure.Between the two fixtures set up pressure sensors and connected to the testing machine, the testing machine can control the experimental parameters and monitor the change of bolt axial force in real time.Compared with the Junker testing machine, this testing device has the advantages of simple structure, simplicity of operation, high testing precision, and accurate data collection.

FEA
Bolt joint structure exists threaded surface, bearing surface, and other groups of interfaces.Due to the complexity of the bolt structure, bolted joint structure loosening test is often used to test and observe the macroscopic loosening process, and it is very difficult to monitor the micro-behaviour of the loosening process and analyse the loosening mechanism, so the loosening test alone does not allow a comprehensive understanding of the loosening behaviour and loosening mechanism of the bolted joint structure, and it is necessary to carry out finite element modelling to carry out the simulation calculations.For the numerical modelling of a single bolt, two commonly used models are shown in figure 3 [14,15].Model (a) is the most complex model and is the closest to the actual structure in practical applications.Compared with the actual structure, the model ignores the geometry at the receding groove.However, due to the special characteristics of the screw structure, it is difficult to divide the whole structure directly by hexahedral mesh, so the commonly used mesh division method is tetrahedral mesh division or hexahedral division of the threaded screw respectively, and finally, the whole structure is modeled by binding.Because the influence of the screw rise angle is considered in the modelling process, the model is mainly used in the simulation of the actual assembly process and different positions of the contact friction and other anti-loosening research.
Model (b) ignores the effect of the lift angle during the modeling process and automatically generates a structured mesh by sweeping the ellipsis.However, since the thread lift angle is not considered, the phenomenon of rising or falling along the helix cannot be ignored.In the static analysis, the load distribution is not affected by the lift angle, so the model can be reduced to an axisymmetric model for analysis in two dimensions.This model is often used to study the loosening of bolted joints caused by stress concentration and plastic zone accumulation at the bottom of thread teeth.

Preload Force
Preload force refers to the bolt to ensure the reliability and tightness of the joint before the working load, to ensure the reliability and tightness of the joint, through the pre-existing force to make the joint structure force compression, to prevent the relative sliding between the connecting parts.When the preload increases, the friction between the contact interfaces also increases, which is conducive to resisting external loads, so that the bolted joint structure is not easy to loosen.As early as 1973, Walker et al. [16] through experimental verification, found that the size of the preload force on the bolt joint structure loosening has a greater impact.Scanclemente et al. [17] through the nested design and the application of statistical analysis techniques carried out 64 tests and found that increasing the preload force can effectively reduce the loosening.Xu et al. [18] studied the self-loosening behaviour of bolted joints using a combination of simplified bolted joint models and finite element simulations and similarly found that the larger the preload force, the stronger the bolt loosening resistance.However, the increase of preload should be controlled in a certain range.Jiang et al. [19] found that under the condition of a larger preload, the bolted joint structure has a better anti-loosening effect, but a larger preload will increase the possibility of bolt fatigue.Song et al. [20] pointed out that the bolt preload is too large to lead to premature fatigue fracture of the bolt, while the preload is too low in the external load is easy to occur under the action of shear fracture.
Therefore, it can be seen that a small preload is not enough to provide sufficient axial force to avoid bolt loosening, and a large preload allows the jointed structure to maintain a large force for a long time, which is prone to strength failure and thus leads to axial force degradation.Preloading more than the critical value of the bolt will cause fatigue or even fracture.Therefore, in the bolt preload, attention to the selection of preload torque, in the choice of greater bolt preload to improve the bolt joint of the antiloosening performance, should be considered at the same time, as the resulting fatigue failure, shear fracture, and other issues.Axial Load: Axial vibration load refers to the load applied along the direction parallel to the axis of the bolt or nut.In 1945, Goodier et al. [22] found that axial vibration causes the loosening of bolts.Using a microscope, it was observed that the nut rotated by 0.0055 rad after 500 cycles.They attributed the rotation to the influence of Poisson's ratio of the material, where the internal thread diameter becomes smaller, and the external thread diameter becomes larger during the loading cycle, resulting in the rotation of the nut in the direction of the thread.However, Saikai et al. [23] found experimentally that in the initial stage of loading, the loss of preload was mainly caused by plastic deformation, and the subsequent vibration process did not cause a decrease in preload.With the advancement of simulation technology, scholars have carried out more refined work.Izumi et al. [24], through three-dimensional finite element simulation, concluded that the deformation of the nut leads to the relative slippage of the bearing surface, and thus loosening when the longitudinal load is applied.In recent studies, more and more scholars believe that axial loading causes a decrease in preload force, but no significant rotational loosening occurs.For this phenomenon, it is speculated that the rotational loosening caused by axial vibration may be observed due to insufficiently high measurement accuracy in the early days, and at this stage, the theory [25][26][27][28] suggests that plastic deformation between the meshing thread surfaces and fretting wear between the contact interfaces are the main reasons for the decrease in the preload force under the condition of axial vibration.
Transverse load: Transverse vibration load is the load applied along the direction perpendicular to the axis of the bolt.Junker [8] first investigated the loosening behaviour of bolted joint structures under transverse vibration conditions, and found that transverse vibration can cause a large amount of preload decay as well as obvious rotational loosening behaviour, and put forward the idea that the relative motion between the threads can cause rotational loosening.That is, under transverse loading, the friction on the threaded surface is not enough to resist the external loading, which makes the threaded surface more prone to relative slippage, which leads to loosening.By establishing a simplified three-dimensional model of a threaded connection, Zhang et al. [29] simulated the periodic transverse vibration and found that under the action of transverse load, the cause of bolted joints loosening is the repeated microslippage of the thread contact interface, and the transverse vibration will exert the opposite cyclic bending moment on the bolt nut.At present, most scholars believe that transverse vibration is the main load form leading to the loosening of the bolted joint structure.Under the action of transverse vibration, local slippage or repeated micro-slippage occurs on the thread surface and end face, which leads to loosening through the gradual accumulation of slippage.
In addition, torsional and eccentric vibration loads can also cause the loosening of bolted joint structures, but there are fewer studies on this.At present, most of the studies focus on the loosening of bolted joints under transverse vibration conditions, which is due to the finding that periodic transverse vibration is the main factor for generating rotational loosening, while axial vibration almost does not cause rotational loosening.Scholars mainly use finite element simulation or theoretical modelling to reveal the tribological principle of loosening caused by external loads but lack in-depth research on tribological tests.

Load Amplitude.
For bolted joint structures, a larger load amplitude increases the plastic deformation between the threads, which leads to the reduction of the axial force.In addition, excessive load amplitude can easily lead to fatigue or even fracture of bolts.Liu et al. [28] verified through experiments and found that as the axial load amplitude increased, the thread surface damage and bolt loosening increased under the same preload condition, as shown in figure 5, and the thread surface was severely worn at higher amplitude, and the zinc-plating coating was removed in most areas.Wang et al. [30] investigated the impact of cyclic load amplitude on the bolted joint structure by establishing a threedimensional finite element model of the bolted joint structure, investigated the effect of cyclic load amplitude on the self-loosening of bolts, and found that the smaller the load amplitude, the less likely the bolted joint structure to loosen.In addition, Wu et al. [31] found that there is a threshold value for the shear load amplitude of the bolted joint structure.When the shear load amplitude is lower than the threshold value of its own existence, bolt loosening will not occur.In summary, the load amplitude has a greater impact on bolt loosening.A smaller load amplitude is beneficial to prevent loosening, while too large a load amplitude will make the bolted joint structure subjected to more intense shock and vibration the greater the fatigue stress it is subjected to, the bolt faces the risk of fatigue or even fracture.The larger the load amplitude, the larger the slippage amplitude of the thread contact interface, and the more likely the bolt will loosen.

Frequency of Loading.
Generally speaking, the loosening of bolted joint structure is more likely to occur at lower loading frequencies.Hess et al. [32] concluded that the change in bolt axial force is affected by the loading frequency, i.e., the axial force of bolts may become larger or smaller at different loading frequencies.Vinogradov [33] studied the influence of high-frequency vibration on loosening by establishing a kinematic model and using numerical methods.It was found that loosening may occur under certain high frequencies of dynamic excitation.Nassar [34] experimentally verified that the relative rotation time of the contact interface of the bolted joint structure is longer at lower frequencies.Therefore, under the condition that other conditions remain unchanged, low frequency is more likely to loosen the bolted joint structure than high frequency.As shown in figure 6 (1, 2, and 3 represent the first three turns of the bolt working threads), Li et al. [35] found that under the same number of cycles, with the increase of loading frequency, the damage degree of thread surface and the loosening degree of bolted joint structure become smaller.Therefore, it is considered that under lower loading frequency conditions, the friction time of each contact surface of the bolted joint structures becomes longer, which provides more time for the rotation of the bolted joint structure and makes it more prone to loosening.

Friction Coefficient.
The influence of the coefficient of friction on the loosening behaviour of the bolted joint structure is twofold.On the one hand, increasing the thread friction coefficient can increase the thread friction torque component, so that the bolted joint structure is not prone to relative rotation.On the other hand, the reduction of the thread friction coefficient (friction-reducing coatings, lubrication, etc.) results in less fretting wear between the threaded surfaces under external loads and improved bolt loosening behaviour.
Scanclemente et al. [17] found that the greater the friction coefficient between the thread pairs, the greater the pre-tightening torque required to tighten the bolt.Although the axial force of the bolt is increased, it will cause a large torsional deformation of the screw, and comprehensively, the bolted joint structure to resist the loosening of the structure has not been improved.Therefore, it can be inferred that under the same preload torque condition, the larger the thread friction coefficient, the lower the preload obtained by the connection structure, and the bolt is more likely to loosen.To obtain the appropriate pretightening force, it is necessary to apply a larger pre-tightening torque.At this time, the bolt material will face greater plastic deformation and even the risk of breaking.In addition, this study also found that the use of lubricants reduces the coefficient of friction, making the bolted joint structure more susceptible to loosening.The study by Zhou [36], however, found that the use of lubricant coatings (PTFE, MoS2) can significantly improve the anti-loosening performance of bolted joint structure when the bolted joint structure is subjected to a lower shear load under the same conditions of the initial torque as shown in figure 7.This is because, after the use of grease, the frictional dissipation energy per unit area of the thread surface and the relative displacement of the contact interface are reduced, increasing the loosening prevention performance.The coefficient of friction is an important factor affecting the loosening of bolted joint structures.When the coefficient of friction is large, the friction between the threaded parts is sufficient to resist the external load, so the bolted joint structure has a better anti-loosening effect.Too large a friction coefficient will make the bolt preload difficult to meet the design requirements, which in turn affects the stability of the bolted joint structure, making it easier to loosen.A smaller friction coefficient to a certain extent on the bolted joint structure of the anti-loosening plays a role in promoting, this is due to the smaller friction coefficient between the threaded vice, in the external load under the threaded surface of the damage degree is lighter, improve the bolted joint structure of the anti-loosening performance.The small friction coefficient makes the friction torque between the threads insufficient to resist the external load, and the bolted joint structure is more likely to loosen.Therefore, in practical application, the choice of friction coefficient needs to consider different working conditions and requirements in order to achieve the best anti-loosening effect.

Bolts Own Joint Structure. (1) Thread pitch
The force analysis of the threaded connection reveals that the torque required to loosen the bolt is roughly calculated in equation [37] as It can be seen from the formula that the loosening torque of the threaded connection is mainly used to overcome the friction at the thread and the friction on the support surface of the bolt head.Due to p T = /2 P  , Therefore, the larger the thread pitch is, the larger the relaxation moment is required, and the more prone to loosening of the bolted joint structure.Wang [38] established a three-dimensional bolted joint finite element model with threads and analyzed the effect of different pitches on the lateral vibration self-relaxation of the bolted joint structure, and found that the preload of fine threads decreased more slowly than that of coarse threads.The slip corresponding to the thick thread was more severe by observing the thread meshing surface.Noda et al. [39,40] found that a smaller pitch can effectively improve the anti-loosening and anti-fatigue properties of bolts.
Therefore, when selecting the thread structure, the thread with a smaller thread pitch should be selected as far as possible.When the thread pitch is small, the contact area between the threaded parts increases, and the friction increases, thus generating a resisting moment to prevent the relative rotation of the bolted joint structure.In addition, a smaller thread pitch will increase the normal pressure between the threaded parts, so that a positive pressure is generated between the threaded parts that does not change with the external load.
(2) Thread clearance fits A smaller thread clearance can achieve the effect of anti-loosening to a certain extent.Nassar et al. [41,42] investigated the effect of screw-screw hole fit and the degree of threaded sub-fit on the loosening of bolts through theoretical modeling and experiments.They found that the tighter the screw-screw hole fit and the threaded sub-fit are, the stronger the bolts are in resisting loosening.As shown in figure 8, Gong et al. [43] selected three different thread clearance fits of clearance, interference, and transition, and set five different gradient fit tolerances of -0.01, -0.005, 0, 0.005, and 0.01.Through finite element simulation, it was found that with the increase of the fit tolerance, the bolted joint structure resistance to loosening decreases, and the bolted joint structure with a smaller clearance distance is less prone to loosening.Under the action of external load, the tighter the degree of thread clearance, the smaller the distance of the relative slippage of the threaded surface, and the stronger the bolt's ability to resist loosening.There are two main reasons: one is the smaller the thread clearance fit, the larger the contact area between the bolt and the nut, and the friction between the threaded vice will then become larger, resulting in the resistance moment being more likely to resist the external load effect; two is the smaller the thread clearance fit, the larger the depth of the bolt and the nut engagement, thus improving the strength and stiffness of the bolted joint structure, reducing the deformation between the threads and the concentration of stresses.

Operating Temperatures
Temperature affects the loosening of bolted joint structures in two main ways.On the one hand, the increase in temperature will cause the plastic deformation of the material, such as the decrease of the elastic modulus of the material at higher temperatures and the creep of the material, which will cause the axial force attenuation of the bolted joint structure.On the other hand, due to the different coefficients of thermal expansion between different materials, the temperature difference will lead to relative sliding between the connecting part and the connected part, and between the inner and outer threads, and the bolted joint structure may loosen.
He et al. [44] obtained the creep law of Q460 steel at 450 ℃, 500 ℃, and 550 ℃ through hightemperature creep experiments.The finite element model of the bolt was established based on hightemperature creep and transverse vibration load, and the loosening behaviour of the bolted joint structure under high-temperature creep conditions was explored.The results show that under the action of high temperature and transverse vibration load, the axial force of the bolt decreases rapidly at first and then decreases at a stable rate.Sawa et al. [45,46] investigated the effects of the linear expansion coefficient and the number of cyclic temperatures on the axial force of bolts by experimental and finite element methods.The results show that under cyclic temperature load, due to the difference in thermal expansion coefficient between the connecting piece and the connected piece, the degree of thermal deformation is inconsistent, and relative slippage occurs between the contact surfaces.When the difference in thermal expansion coefficient between the connected piece and the connecting piece material, the internal and external thread material is small, the looseness is not easy to occur.

Conclusions
This paper summarises the research method of loosening of bolted joint structure from two aspects of experimental research and finite element modeling and summarises the influencing factors of loosening from four aspects of preload force, external load factors, structural factors, and operating temperature, through the analysis, the following conclusions can be drawn: (1) The bolted joint structure is prone to loosening under lateral vibration conditions.
(2) Controlling the range of preload force, applying smaller load amplitude, and selecting fine threads are all beneficial to the anti-loosening of the bolted joint structure.
(3) The influence of friction coefficient and thread clearance on the loosening of the bolted structure is two-fold, which needs further in-depth study.
(4) According to the specific operating conditions, choosing suitable materials with small differences in temperature resistance and coefficient of thermal expansion as the bolted joint structure can effectively prevent bolt loosening.At present, domestic and foreign scholars have conducted in-depth research on the loosening of bolted joints, and have a more systematic understanding of the loosening behaviour of bolted joints.However, there are still the following aspects of work that need to be improved: (1) Carry out a large number of simulations and experiments on the loosening behaviour, to quantitatively determine the influence of various factors on the loosening law.
(2) Combined with the actual working conditions, investigate the loosening behaviour of the bolted joint structure under multi-factor coupling conditions and extreme conditions.
(3) It is necessary to further construct the quantitative evaluation index system for thread joints' antiloosening performance

3. 2 .
External Load Factors 3.2.1.Load Direction.The force system is decomposed and synthesized, and the loads on the bolted joint structure are mainly divided into axial and transverse loads according to the direction, as shown in figure 4 [21].(a) Axial load (b) Transverse load
(a) SEM morphologies of surface abrasion at AF=7.5kN(b) SEM morphologies of surface abrasion at AF=12.5kN (c) Loosening curves of bolted structures under different load amplitudes

Figure 5 .
Figure 5. Self-loosening curves of bolts and the degree of axial force reduction under different amplitude [28].

Figure 7 .
Figure 7. Degree of looseness of three coated bolted structures under the same preload [36].
Friction moment at the thread b T --Frictional moment at the support surface of the head of the bolt P --Thread pitch t  --Friction coefficient at the thread b  --Friction coefficient of the supporting surface of the head of the bolt t r --Equivalent friction radius at the thread b r --Equivalent friction radius of the supporting surface of the head of the bolt  --Tooth angle