Wear 346-347 (2016) 66–77
Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Experimental and numerical studies of bolted joints subjected to axial excitation Jianhua Liu a, Huajiang Ouyang b, Jinfang Peng a, Chaoqian Zhang c, Pingyu Zhou c, Lijun Ma c, Minhao Zhu a,n a
Tribology Research Institute, Traction Power State Laboratory, Southwest Jiaotong University, Chengdu 610031, China School of Engineering, University of Liverpool, Liverpool L69 3GH, UK c Qingdao Sifang Locomotive and Rolling Stock Co., Qingdao 266111, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 2 June 2015 Received in revised form 12 October 2015 Accepted 16 October 2015 Available online 3 November 2015
The dynamic behaviour of bolted joints subjected to axial excitation is investigated using experimental and numerical methods. Firstly, the amount of reduction in clamp force is found by experiments. In addition, the damage of threads is analysed using scanning electron microscope (SEM) and Energy Dispersive X-ray (EDX). Secondly, by changing the tightening torque, the amplitude of the axial excitation, and coating lubricant (MoS2) on the threads, their effects on both the clamp load loss and the damage of threads are determined in experiments. It is found that the clamp force decreases rapidly in the early stage because of the cyclic plastic deformation, and then slowly because of fretting wear in the later stage. With the increase of the tightening torque and the decrease of the amplitude of the axial excitation, the clamp load loss decreases and the damage of threads becomes slight. The lubrication (MoS2) of bolt threads is useful to reduce bolt loosening and damage of threads. A three-dimensional finite element model used to simulate the bolted joint under axial excitation is created using ABAQUS, through which the frictional stress, slip amplitude and frictional work per unit area along two specified paths on the first thread are studied. It is found that the FE results agree with the experimental observations very well. & 2015 Elsevier B.V. All rights reserved.
Keywords: Bolted joint Loosening Wear mechanism Lubrication Finite element method
1. Introduction Bolted joints have found wide-spread use in many machines and structures. As basic fastening pieces, they have direct influences on the safety and reliability of a structural system. Assemblies which utilise bolted joints often work in vibratory environments. Most of past studies are focused on energy dissipation and damping of bolted joints [1–3], parameter uncertainties [4–6], failure and fatigue of structural joints [7–9], and loosening mechanisms [10–12]. When viewed from how the load is applied, bolted joints are subjected to four different types of loads: axial tensile load, transverse or shear load, torsional load, and prying load. Such vibratory loading conditions can lead to vibration-induced bolt loosening which can result in increased maintenance and/or failure. The loosening mechanism for an axial tension-loaded joint has been studied extensively in the literature. In general, there are two basic views of the loosening mechanism: (1) microslip occurs
n
Corresponding author. Tel.: þ 86 28 87600715; fax: þ 86 28 87600723. E-mail address:
[email protected] (M. Zhu).
http://dx.doi.org/10.1016/j.wear.2015.10.012 0043-1648/& 2015 Elsevier B.V. All rights reserved.
both on the screw thread and on the bearing surface; (2) fastener elongation is beyond its elastic limit. Vibration will increase loosening through wear and hammering. After a sufficient amount of friction force is lost, the nut actually starts to back off and the clamp load is completely lost [6]. Goodier et al. [13] seem to have been the first to study the loosening mechanism for a bolt under axial load. They pointed out that an increase in load caused a bolt thread to move radially inward and a nut thread radially outward. This action results in a radial microslip between the contact threads. Based on static equilibrium conditions, this theory predicted a loosening twisting during loading and a tightening twisting during unloading, with a loosening twisting per cycle. Hosokawa et al. [14] reported that during the loading and unloading process, relative microslippage occurred radially both on the screw thread surface and on the bearing surface due to Poisson's ratio effect. Izumi et al. [15] analysed the detailed loosening behaviour of bolt and nut under axial tension load using a threedimensional finite element method. Sakai [16] investigated the selfloosening mechanism based on the strength of materials. Experiments and analyses by Basava et al. [17] and Hess et al. [18] with thread fasteners loaded by gravity and subjected to axial harmonic vibration revealed that thread components can twist with or
J. Liu et al. / Wear 346-347 (2016) 66–77
against gravity in the presence of vibration. It was shown that the direction of twist depended on initial preload, the frequency and amplitude of the vibratory input, the component mass and material, and thread fit and friction. The physical explanation for this observed behaviour concerns the nonlinear dynamic interaction of vibration and friction, and the resulting patterns of repeated sliding, sticking, and separation between the thread components. The torque–tension relationship for a thread fastener is highly sensitive to friction variation between the turning surfaces at the head/nut interface and between male and female threads [19,20]. In some cases, the fastener's tensile stress may exceed its yield strength due to decrease of the coefficients of friction [21]. Karamiş et al. [22] used theoretical and experimental methods to study the friction behaviour of bolted joints. It was shown that the surface roughness of the joint members and joined materials had an important effect on self-loosening of the joint. When a bolted joint is put in service, it may be subjected to an external separating load, which will increase the fastener tension and simultaneously reduce the clamped load [23]. In a recent study, Nassar et al. [24] investigated the nonlinear behaviour of a bolted joint under cyclic separating tensile load using experimental and the finite element methods. The effects of the level and location of the separating load on the variation in clamp load and bolt tension were studied. Yang et al. [25] investigated the effects of separating load level, thread friction coefficient, and bolt preload level on the variations of the clamp load and bolt tension using experimental, analytical and the finite element methods. Aluminium alloy is widely used to reduce the weight of machines and structures. However, its low strength causes bolt loosening or joint fatigue failure in bolted connections. A thread insert is used to improve the mechanical properties of female threads made of aluminium alloy. In this paper, an extensive experimental study is conducted for investigating the behaviour of bolted joints (coated with a lubricant of MoS2), made of aluminium alloy and equipped with a thread insert, subjected to axial excitation. The effects of the excitation level, the tightening torque and the lubrication (MoS2) of bolt threads on the clamp load loss and the damage of threads are studied. Additionally, the levels of the clamp load loss and the damage of threads are investigated, while the bolted joints are subjected to longer-term excitation. The frictional stress, slip amplitude and frictional work per unit area along two specified paths on the first thread is analysed using the finite element method.
2. Experimental method The joint tested in the experimental investigation is shown in Fig. 1. Two bolt testing fixtures made of high strength steel are clamped with a bolt and a nut. One fixture is fixed at one end and an axial excitation is applied at the end of the other fixture. The
bolts used in the experiments are made of low-carbon steel (A283D, ASTM A283/A283M-03) and coated with zinc to protect them from rust. The thickness of coating is about 5 μm. The washer and the square nut are made of aluminium alloy (7050T7451, ASTM B209-04). A thread insert, which is made of stainless steel (316L, ASTM A580/A580M—2008), is used to improve the engagement between the threads of the bolt and the female threads of the square nut. Between the bottom bolt testing fixture and the nut, a load cell is used to measure the clamp force. In order to protect the load cell from fretting wear, a thin washer made of aluminium alloy is placed in between the load cell and the bolt testing fixture. In the experiments, five levels of tightening torque, M0, are used. They are 30 Nm, 35 Nm, 40 Nm, 45 Nm, and 50 Nm. The axial excitation, denoted as Fe, is the controlling parameter. The amplitude of the axial excitation, Fe, will be referred to as AF. A number of AF values are used, and they range from 7.5 kN to 12.25 kN. Furthermore, the frequency of the axial excitation is 30 Hz. A lubricant is used to study its effect on bolt loosening. It is made from lithium soap of a hydroxy fatty acid, antioxidant and molybdenum disulphide (MoS2). The procedure of application is as follows: 1) a thin layer of MoS2 grease is applied on the thread surface of the bolt and the surface of the upper fixture which is in contact with the bolt head; 2) the joint is assembled and the tightening torque is applied. The test conducted for each experimental condition is repeated for four separate times. All the experiments are conducted in air at room temperature. The axial excitation, the stroke (the displacement of the bolt testing fixture), and the clamping force are measured for every loading cycle continuously throughout an experiment. The morphologies of wear scar are examined using a scanning electron microscope (SEM, JOELJEM-6610LV), and chemical compositions of damage zone are analysed by Energy Dispersive X-ray (EDX, OXFORDXMAX50 INCA-250).
3. Distribution of preload Tightening a bolt to a torque value is the most popular means of controlling the preload provided by a threaded fastener. However, it is experimentally observed that the preload is not a constant value when the same tightening torque is applied on nominally identical bolted joints under the same condition. Therefore, a tightening torque of 30 Nm is applied on each of 45 bolted joints tested, and the distribution of preload is shown in Fig. 2. About 50% of these joints have achieved preload in the range of 13.5 kN 14.5 kN. This is one reason why many bolts joints work correctly but some get loose under the same condition.
Bolt Bolt Test Fixtures Thin Washer Load Cell Square Nut Fig. 1. Experimental setup.
67
Fig. 2. The distribution of preload (M0 ¼30 Nm).
68
J. Liu et al. / Wear 346-347 (2016) 66–77
Fig. 3. Effect of re-tightening the bolt on the clamp force generated (M0 ¼ 30 Nm).
Fig. 4. Experimental hysteresis loops (M0 ¼ 30 Nm, AF ¼10 kN, N ¼ 106 cycles).
Accordingly, the follow-up experiments are conducted on those bolt specimens having the following condition: the preload range is between 13.5 kN and 14.5 kN when a tightening torque of 30 Nm is applied. The change of preload during repeated tightening of electro-zinc plated joints has been studied by a number of researchers [26]. To investigate the effect of the number of tightening on preload, five bolted joints are tested, and each one is loaded in 12 repeated cycles of tightening and loosening. The trend observed is that the preload decreases as the number of tightening/loosening turns increases. It drops quickly in the first three cycles, and then stabilises after four cycles. This is illustrated in Fig. 3. In the subsequent experiments, bolted joints are only tightened once.
area ploughing with obvious plastic flow is the main wear phenomenon. The EDX analyses of wear scars show that point C presents a higher O-element peak than that of point B. Therefore, the main mechanisms are abrasive wear, adhesive wear and oxidative wear in this area. Due to the effect of fatigue wear, the damaged surface shows delamination phenomenon in the area denoted as II. The material components of point A are analysed. It is found that the region contains only iron and carbon. This suggests that electrozinc plated (EZP) coating of the bolt has been completely removed. Therefore, the main mechanism is delamination in this area. Above all, the wear mechanisms of the contact surface between threads are complicated. They contain all of the four basic wear mechanisms mentioned above. Likewise, similar damage characteristics also are observed in the test lasting 5 106 cycles. As shown in Fig. 6, seriously damaged areas, denoted as I, occur on the thread edge. The material components of point A are analysed. It is found that the region contains only iron and carbon without oxygen. Absence of corrosion suggests that the cause of the damage is not corrosion before the test but fretting wear between threads. Similarly, the main wear mechanism is delamination in this area. In the II area, abrasive wear, adhesive wear and delamination phenomena are very evident. The content of oxygen at point C is close to that at point B, so it cannot be determined whether there is oxidation wear. Above all, the main mechanisms are abrasive wear, adhesive wear and delamination.
4. Analysis of clamp force loss 4.1. Hysteresis loop A bolted joint displays a hysteresis loop for axial force, Fe, versus the relative displacement, δ, of the joint when subjected to axial excitation. The minimum axial displacement of every cycle is denoted as δmin. As the testing machine is unable to apply the axial tensile excitation in a steady manner in the first twenty cycles, the amplitude of the axial excitation is found to be less than its pre-set value, and the minimum of axial load is found to be greater than 0. This leads to two following consequences: the value of δmin is larger than the cyclic plastic deformation; and the clamp force measured by the load cell is also larger than its actual value without axial load. Therefore, the data of the first twenty cycles are not included in the following experimental results. As shown in Fig. 4, δmin increases obviously at the beginning of the experiment, in other words, the plastic deformation increases rapidly. Because of the ratchet effect of material, the plastic deformation increases slowly in the later period of the experiment, and δmin increases slowly during this period. 4.2. SEM investigation It is reported that the axial pressure distribution was so uneven that a serious stress concentration existed at the first thread which carried more than 30% [27,28] of the total axial load. So the damage of the first thread is analysed using SEM and EDX. In the past, four wear mechanisms were found to be abrasive wear, adhesive wear, oxidative wear and delamination [29,30]. The SEM morphologies and EDX patterns are shown in Fig. 5. As can be seen from the graphs damage is not continuous. In the I
4.3. Self-loosening curve Function RF is defined as the percentage of clamp force to preload. Under high value of RF, loosening of bolted joints is serious; while under low value of RF, it is slight. Among the many factors affecting bolted joints and fasteners are friction, surface hardness and finish, the relative dimensions of all interacting parts, and the creep of gaskets [20]. The importance of each factor will vary from bolt to bolt, and joint to joint because of usage or manufacturing tolerances. As a result all joints and jointed structures exhibit a degree of parametric uncertainty [6]. As shown in Fig. 7, the self-loosening curves of two bolted joints in the first one million cycles are different under the same working condition. At the beginning of the experiment, the clamp force drops rapidly, and then gradually. More than 15% reduction in clamp force occurs in the first 100 cycles. As previously mentioned, due to the ratchet effect of material, the plastic deformation increases rapidly, then slowly, and finally stabilises. Consequently, plastic deformation of threads is the main reason of reduction in clamp force in the initial stage of the experiment. In addition, less
J. Liu et al. / Wear 346-347 (2016) 66–77
Fig. 5. SEM morphologies and EDX patterns corresponding to wear scar of the first thread surface (M0 ¼ 30 Nm, AF ¼10 kN, N ¼ 106 cycles).
Fig. 6. SEM morphologies and EDX patterns corresponding to wear scar of the first thread surface (M0 ¼30 Nm, AF ¼ 10 kN, N ¼5 106 cycles).
69
70
J. Liu et al. / Wear 346-347 (2016) 66–77
than 5% reduction in clamp force is produced from the 105th cycle to the 106th cycle. Small increase in clamp force occurs from the 2.3 106th cycle to the 3.2 106th cycle. This may be caused by the abrasive dust piled up on the contact surfaces. When the abrasive dust is removed, the clamp force decreases again.
Fig. 7. Self-loosening curves for varying cycles (M0 ¼ 30 Nm, AF ¼ 10 kN).
5. Effects on clamp force loss 5.1. Effect of tightening torque Fig. 8 shows the wear morphologies and EDX patterns at two different levels of the tightening torque, namely, 40 Nm and 50 Nm. As shown in Fig. 8a), the damaged surface shows delamination phenomenon in a local area. EDX peaks of the scar show that point B contains only iron and carbon, and point A mainly contains zinc and oxygen. Likewise, the similar conclusions can be drawn from Fig. 8b). Delamination is also shown in a local area. EDX pattern of point D shows that it contains only iron and carbon in the spalling pit. Consequently, the main wear mechanism is delamination. Compared with Fig. 5, with the tightening torque increasing, the damage is reduced gradually. This is because the slippage between the contact surfaces is small and most of the contact region is in sticking condition under high tightening torque. Fig. 9a) shows the self-loosening curves at five levels of the tightening torque. Under higher tightening torque, the contact area between threads is larger and plastic deformation is smaller under the same axial excitation. Thus, the reduction of clamp force is less than that under lower tightening torque. As discussed before, the damage is slighter under higher tightening torque, so the clamp force decreases more slowly. In summary, the bolted
Fig. 8. SEM morphologies and EDX patterns corresponding to wear scar of the first thread surface for varying tightening torques (AF ¼ 10 kN, N ¼106 cycles) a) self-loosening curves and b) changes in torques and clamp forces.
J. Liu et al. / Wear 346-347 (2016) 66–77
joints subjected to higher tightening torque are not prone to loosening due to the smaller plastic deformation and the slighter damage. Obviously, tightening torque cannot be too large, since the shear stress produced by high tightening torque may exceed the strength of bolt material and the bolt will fracture. Function RT is defined as the percentage of the breakaway torque necessary to loosen the tightening torque. After 106 loading
71
cycles, RT is referred to as RT (106) and the percentage of clamp force to preload is referred to as RF (106). In practice, torque wrenches are commonly used to monitor whether bolted joints are loose. A bolted joint considered to work properly when the value of RT is larger than 80%. Fig. 9b) shows the changes in torques and clamp forces at three levels of the tightening torque after 106 loading cycles. When the tightening torque is 30 Nm, RT (106)
Fig. 9. Self-loosening curves and changes in torques and clamp forces for varying tightening torques (AF ¼10 kN, N ¼ 106 cycles).
Fig. 10. SEM morphologies and EDX patterns corresponding to wear scar of the first thread surface for varying amplitudes of axial excitations (M0 ¼ 30 Nm, N ¼ 106 cycles).
72
J. Liu et al. / Wear 346-347 (2016) 66–77
Fig. 11. Self-loosening curves and changes in torques and clamp forces for varying amplitudes of axial excitation (M0 ¼30 Nm, N ¼ 106 cycles).
is larger than 90%, but RF (106) is smaller than 70%. As discussed before, the damage caused by fretting wear is non-uniform and discontinuous pits occur on contacting threads. This causes the breakaway torque to become large. It is found that the breakaway torque is sometimes larger than the tightening torque. Consequently, it is not very suitable to use torque wrenches to monitor whether bolted joints are loose. As shown in Fig. 9b), with the increasing tightening torque, the degree of loosening reduces, while the change in the tightening torque is not obvious. 5.2. Effect of axial excitation Fig. 10 shows the wear morphologies and EDX patterns for two different levels of axial excitation, namely, at the amplitude of 7.5 kN and 12.5 kN. As shown in Fig. 10 a), electrozinc plated (EZP) coating of some regions is removed, and the surface damage of wear scar is very slight. Electrozinc plated (EZP) coating in most regions is removed at the higher excitation amplitude (see Fig. 10 b)). The main wear mechanism is delamination. Compared with Fig. 5, with the increasing amplitude of axial excitation, the surface damage of threads gets serious. Fig. 11a) shows the self-loosening curves for five levels of axial excitation. Under higher amplitude of axial excitation, plastic deformation is larger under the same tightening torque. Consequently, the reduction in the clamp force is more than that under lower amplitude of axial excitation. As discussed earlier, the wear of threads gets serious with the amplitude of axial excitation increasing. Anyhow, the degree of loosening of bolted joints subjected to higher amplitude of axial excitation gets larger due to the larger plastic deformation and the more serious damage. It is experimentally observed that some of bolts fail due to fatigue when the amplitude of axial excitation is 12.5 kN. Fig. 11b) shows the changes in tightening torques and clamp forces for three levels of the amplitude of axial excitation after 106 loading cycles. When the amplitude of axial excitation is 12.5 kN, the average value of RT (106) is less than 70%, and the breakaway torque exhibits great uncertainty. With the increasing amplitude of axial excitation, the degree of loosening increases under the same tightening torque. 5.3. Effect of a lubricant of MoS2 The friction coefficient between threads and that between bolt head face and bearing surface are evaluated using DIN 946 [31]
Table 1 Bolt dimensional details. Thread diameter, D Thread pitch, p Basic pitch diameter of thread, d2 Included thread flank angle Bearing diameter of bolt head, do Hole diameter of Bolt Test Fixture, di Effective bearing diameter of the bolt head, De
which gives: De M 0 ¼ P 0 0:159p þ 0:578μt d2 þ μh 2
12 mm 1.75 mm 10.863 mm 60° 18.5 mm 13.0 mm 15.75 mm
ð1Þ
The value of De is taken to be: De ¼
do þdi 2
ð2Þ
where M0 is the total tightening torque, P0 is the bolt preload, d2 is the basic pitch diameter of the threads, p is the pitch of the threads, De is the effective bearing diameter of the bolt head, do is the outer bearing diameter of the bolt head, di is the hole diameter of the clamped body, μt is the friction coefficient between threads, and μh is the friction coefficient between bolt head and the clamped body. In practice, the two friction coefficients are often assumed to be equal [32]. The dimensions of the bolts used in this series of tests are given in Table 1. Under a tightening torque of 30 Nm, the value of preload is about 14 kN; Taking them into Eq. (1), the friction coefficients are determined as
μt ¼ μh ¼ 0:132
ð3Þ
When a tightening torque of 30 Nm is applied on bolted joints coated with a lubricant of MoS2, the preload is about 20 kN. According to Eqs. (1) and (3), the friction coefficient at the interface between threads coated with lubricant, μ0t , is found to be
μ0t ¼ 0:029
ð4Þ
Fig. 12 shows the wear morphologies and EDX patterns corresponding to wear scar of the first thread surface of the MoS2lubricated bolt. According to the EDX analyses point A mainly contains zinc and oxygen, and a small amount of iron. This suggests that the surface damage of most regions was very slight. Compared with Fig. 5, the surface damage of the lubricated bolt is slighter than that of the unlubricated bolt due to the lower friction coefficient. The main wear mechanism is abrasive wear in this area. In addition, delamination is found in some areas. Consequently, the main wear mechanisms are abrasive wear and delamination.
J. Liu et al. / Wear 346-347 (2016) 66–77
73
Fig. 12. SEM morphologies and EDX patterns corresponding to wear scar of the first thread surface of the bolt coated with a lubricant of MoS2 (M0 ¼ 30 Nm, AF ¼ 20 kN, N ¼106 cycles).
Fig. 13. Self-loosening curves and changes in torques and clamp forces of bolted joints coated with/without a lubrication of MoS2 (M0 ¼ 30 Nm, AF ¼20 kN, N ¼ 106 cycles).
Fig. 13a) shows the self-loosening curves of bolted joints lubricated with MoS2. Generally speaking, lubrication of bolt threads causes the friction and torque coefficients to decrease and so the clamp force to increase. This makes the contact area between threads increase and the plastic deformation decrease
under the same level of axial excitation. As discussed before, the surface damage of the lubricated bolt is slighter than that of the unlubricated bolt. In summary, the bolted joints lubricated with MoS2 are not prone to loosening due to the smaller plastic deformation and slighter damage. Fig. 13b) shows the changes in
74
J. Liu et al. / Wear 346-347 (2016) 66–77
torques and clamp forces of bolted joints with/without a lubrication of MoS2. For the bolted joints with a lubrication of MoS2, very good agreement is achieved between the amount of reduction in clamp force and torque. In addition, the breakaway torque exhibits low uncertainty. Therefore, adding a lubrication of MoS2 on threads of bolted joints is a good method to prevent loosening.
6. Finite element analysis 6.1. Description of finite element model Fig. 14 shows the finite element models for the bolt and nut. Seven threads are created for both the external and internal threads in the models. The internal faces of external threads are tied with the bolt shank. Similarly, the external faces of internal threads are tied with the inner wall of the hole of the nut [33]. The internal threads are made of steel and the nut is made of aluminium alloy. Fig. 15a) shows the finite element meshes. The model consists of a bolt, a nut, a thin washer made of aluminium alloy, and two fixtures and a load cell made of high strength steel. The material of the bolt shank, the external threads, the thin washer and the nut is assumed to be elasto-plastic with linear strain-hardening and the constitutive equation can be written as [34]: ( E εe in elastic zone σ ¼ σ þ Hε in plastic zone ð5Þ s p
the lower fixture and the thin washer, the contact between the thin washer and the load cell, the contact between the load cell and nut, and the contact between the threads. The finite sliding formulation is used for the contact between the two fixtures. However, considering the small-scale relative motion of the contacting bodies for the other contact interfaces, the infinitesimal sliding formulation is used to improve the efficiency of the computation. Tetrahedral elements are used in the transition region between cylindrical part and the rectangular box of each of the two fixtures, while eight-node linear reduced-integration solid brick elements are used in other regions to improve the accuracy of the calculation. The finite element model consists of a total of 193,906 nodes and 152,622 elements. The loading process is shown in Fig. 15b). To avoid singularity in the numerical computation, the first step is to apply a small preload on the section that is the transition from the bolt head to the shank of the bolt. The actual bolt preload is applied in the next step. The first two steps are to create contact steadily and apply the bolt preload. The third step is to apply the axial excitation. A dynamic transient analysis is carried out. The FE simulations conducted are listed in Table 2.
For steel, Young's modules E ¼ 200000 MPa, Poisson's ratio
ν ¼ 0:3. The strain-hardening parameter H ¼ 2000 MPa, and yield stress σ s ¼ 350 MPa; For aluminium alloy, Young's modules E ¼70000 MPa, Poisson's ratio ν ¼ 0:3, the strain-hardening parameter H ¼ 400 MPa and yield stress σ s ¼ 480 MPa. For the other bodies, including the internal threads, the material is considered elastic. The lower fixture is fixed and the axial excitation, denoted as Fe, is applied on the top fixture. The density of steel is 7.8 10 9 t/mm3, and that of aluminium alloy is 2.7 10 9 t/mm3. In the finite element model, six contact pairs are defined: the contact between the top fixture and the head of the bolt, the contact between the two fixtures, the contact between
Fig. 15. Finite element model and loading process.
Fig. 14. Finite element models for bolt and nut.
J. Liu et al. / Wear 346-347 (2016) 66–77
75
Table 2 Finite element simulations. Loading case
Preload (kN) Axial excitation (kN)
friction coefficient between threads
1(Coated with MoS2) 2(M0 ¼ 30 Nm) 3(M0 ¼ 30 Nm) 4(M0 ¼ 30 Nm) 5(M0 ¼ 40 Nm) 6(M0 ¼ 50 Nm)
20 14 14 14 18 22
0.029 0.132 0.132 0.132 0.132 0.132
20 15 20 25 20 20
Fig. 17. Definition of the two paths on the first thread. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article)
the bolted joints without a lubrication of MoS2. The frictional work per unit area is largest at point X and it is not monotonically increasing or decreasing along path 2.
7. Discussions
Fig. 16. Variations of clamping force with applied axial excitation.
6.2. Finite element results Fig. 16 shows the variations of clamping force with applied axial excitation for different tightening torques. It is observed that the clamping force decreases rapidly with the increase of axial tensile excitation at the beginning. Then, when the axial excitation reaches a certain level (different level for a different tightening torque), due to the separation of the two fixtures, the clamping force decreases to zero and all the axial excitation will add to the bolt. In order to study the frictional stress and frictional work per unit area during a loading cycle in detail, the first thread of the bolt is shown in Fig. 17. Two paths on the upper surface of the thread, denoted by 1 (in the radial direction) and 2 (in the circumferential direction) in red colour, are defined in the figure. Fig. 18 shows the frictional stress at t1 and slip amplitude along the two paths. It is observed that the frictional stress and slip amplitude increase as the number of axial excitation turns increases. When the tightening torque is 30 Nm and 40 Nm, the clamping force is zero under an axial excitation of 20 kN (Fig. 16). Due to the separation of the two fixtures, the bolt force is the same for the two cases. Consequently, the frictional stress is the same at t1 when the tightening torque is 30 Nm and 40 Nm. When the tightening torque is 50 Nm, the frictional stress is larger than that with the tightening torque of 30 or 40 Nm. The slip amplitude decreases as the number of tightening torque turns increases. Under the same tightening torque and axial excitation, due to low friction coefficient between threads of a MoS2-lubricated bolt, the frictional stress is smaller than that of the bolt without a lubrication of MoS2. The frictional stress is largest at point X. Fig. 19 shows the frictional work per unit area during the second loading cycle along the two specified paths. It is observed that frictional work per unit area increases as the number of axial excitation turns increases, and it decreases with the increasing tightening torque. As shown in Fig. 19, under the same tightening torque and axial excitation, for the bolted joints with a lubrication of MoS2, the frictional work per unit area is smaller than that of
The degree of damage at a contact interface is usually characterized by wear volume. When the wear volume is small, the damage is considered slight; and vice versa. Fridrici et al. reported [35] that the wear volume has a linear relationship with cumulative dissipated friction energy. Fig. 19 illustrates that the frictional work per unit area decreases with the increasing tightening torque. In other words, during the same loading cycles, the cumulative dissipated friction energy decreases as the number of tightening torque turns increases. Consequently, the damage of threads is reduced gradually with the increasing tightening torque. This is in agreement with the experimental observations (Figs. 5 and 8). Fig. 19 also indicates that the frictional work per unit area increases with the amplitude of axial excitation. This suggests that the damage of threads becomes serious with increasing amplitude of axial excitation. This is also consistent with the experimental observations (Figs. 5 and 10). In addition, Fig. 19 shows that the frictional work per unit area, for the lubricated bolted joints, gets small compared with the unlubricated bolted joints. This suggests that the damage of threads gets slight. This is also in agreement with the experimental observations (Figs. 5 and 12).
8. Conclusions The reduction in clamp force and the surface damage of bolted joints subjected to axial excitation are studied in this paper. The following conclusions can be made from the experimental results. 1. The preload of nominally identical bolted joints is not a constant value even though it is generated under the same condition. The trend is that the preload decreases as the number of tightening turns increases. It drops quickly in the first three tightening turns, and then stabilizes after four tightening turns. 2. Plastic deformation of threads is the main reason of reduction in clamp force in the initial stage of the experiment. The clamp force decreases in the later stage of the test due to fretting wear between threads. Delamination and ploughing with obvious plastic flow are the main causes of wear. The main wear
76
J. Liu et al. / Wear 346-347 (2016) 66–77
Fig. 18. Maximum of frictional stress and displacement amplitude along the two paths.
Fig. 19. Frictional work per unit area along the two paths.
mechanism of the contact surface between threads is delamination, accompanied by abrasive wear, adhesive wear and oxidative wear. 3. With the increase of the tightening torque and the decrease of the amplitude of axial excitation, the damage of threads is reduced gradually, and the amount of reduction in clamp force decreases. Due to lubrication of bolt threads, the degree of loosening decreases and the damage of threads gets slight for lubricated bolts. 4. For the unlubricated bolted joints, breakaway torque is sometimes larger than tightening torque due to discontinuous pits caused by fretting wear between threads. In addition, the reduction in clamp force does not have a strong correlation with the difference between tightening torque and breakaway torque. For the bolted joints with a lubrication of MoS2, breakaway torque exhibits small uncertainty; the difference between tightening torque and breakaway torque is in good agreement with the reduction in clamp force.
The FE results agree with the third conclusion very well. With the increase of the tightening torque and the decrease of the amplitude of axial excitation, the frictional work per unit area decreases. The frictional work per unit area becomes small for lubricated bolts. In addition, the frictional work per unit area in the radial direction is largest near the crests of threads.
Acknowledgements The authors gratefully acknowledge the financial support provided by China National Funds for Distinguished Young Scientists (No. 51025519), the Changjiang Scholarships and Innovation Team Development Plan (No. IRT1178), the 2011 Doctoral Innovation Funds of Southwest Jiaotong University, and the Fundamental Research Funds for the Central Universities (Grant No. A0920502051410-4).
J. Liu et al. / Wear 346-347 (2016) 66–77
References [1] Y.S. Shin, J.C. Iverson, K.S. Kim, Experimental studies on damping characteristics of bolted joints for plates and shells, Am. Soc. Mech. Eng. J. Press. Vessel Technol. 113 (1991) 402–408. [2] L. Gual, R. Nitsche, The role of friction in mechanical joints, Appl. Mech. Rev. 54 (2001) 93–106. [3] J. Esteban, C.A. Rogers, Energy dissipation through joints: theory and experiments, Comput. Struct. 75 (2000) 347–359. [4] M. Hanss, S. Oexl, L. Gaul, Simulation and analysis of structural joint models with uncertainties, In: Proceedings of the International Conference on Structural Dynamics Modeling—Test, Analysis, Correlation and Validation, Madeira Island, Portugal, 2002, pp. 165–174. [5] M. Hanss, S. Oexl, L. Gaul, Identification of a bolted-joint model with fuzzy parameters loaded normal to the contact interface, Mech. Res. Commun. 29 (2002) 177–187. [6] R.A. Ibrahim, C.L. Pettit, Uncertainties and dynamic problems of bolted joints and other fasteners, J. Sound Vib. 279 (3–5) (2005) 857–936. [7] P. Lazzarin, V. Milani, M. Quaresimin, Scatter bands summarizing the fatigue strength of aluminum alloy bolted joints, Int. J. Fatigue 19 (1997) 401–407. [8] B. Atzori, P. Lazzarin, M. Quaresimin, A re-analysis on fatigue data of aluminum alloy bolted joints, Int. J. Fatigue 19 (1997) 579–588. [9] R.S. Birch, M. Alves, Dynamic failure of structural joint systems, Thin-Walled Struct. 36 (2000) 137–154. [10] G.H. Junker, New criteria for self-loosening faster under vibration, SAE Trans. 78 (1969) 314–335. [11] Y. Jiang, M. Zhang, T.W. Park, C.H. Lee, An experimental study of self-loosening of bolted joints, J. Mech. Design 126 (5) (2004) 925. [12] G.E. Ramey, R.C. Jenkins, Experimental Analysis of Thread Movement in Bolted Connections due To Vibrations, Marshall Space Flight Center, AL, 1995, Final Report NAS8-39131. [13] J.N. Goodier, R.J. Sweeney, Loosening by vibration of threaded fastenings, Mech. Eng. 67 (1945) 798–802. [14] S. Hosokawa, S. Sato, C. Miyata, T. Tsumura, Contraction deformation of bolt shank in threaded connection, Bull. Jpn. Soc. Precis. Eng. 53 (11) (1987) 1726–1732. [15] S. Izumi, T. Take, M. Kimura, S. Sakai, Self-loosening analysis of bolt-nut tightening system subjected to axial loading by three-dimensional finite element method, Trans. Jpn. Soc. Mech. Eng. Ser. A 73 (732) (2007) 869–876. [16] T. Sakai, Mechanism for a bolt and nut self-loosening under repeated bolt axial tensile load, J. Solid Mech. Mater. Eng. 5 (11) (2011) 627–639. [17] S. Basava, D.P. Hess, Bolted joint clamping force variation due to axial vibration, J. Sound Vib. 210 (2) (1998) 255–265.
77
[18] D.P. Hess, S.V. Sudhirkashyap, Dynamic analysis of threaded fasteners subjected to axial vibration, J. Sound Vib. 193 (5) (1996) 1079–1090. [19] J.H. Bickford, Handbook of Bolts and Bolted Joints, The Chemical Rubber Company Press, Florida, 1998. [20] J.H. Bickford, Introduction to the Design and Analysis of Bolted Joints, 4th ed., The Chemical Rubber Company Press, Florida, 2007. [21] S.A. Nassar, G.C. Barber, D. Zuo, Bearing friction torque in bolted joints, In: Proceedings of Society of Tribologists and Lubrications Engineers (STLE) Conference Transactions, Toronto, Canada, 2004 May, pp. 17–21. [22] M.B. Karamiş, B. Selçuk, Analysis of the friction behaviour of bolted joints, Wear 166 (1) (1993) 73–83. [23] R.C. Juvinall, K.M. Marshek, Fundamentals of Machine Component Design, 4th ed, Wiley, New York, 2011. [24] S.A. Nassar, X. Yang, S.V.T. Gandham, Z. Wu, Nonlinear deformation behavior of clamped bolted joints under a separating service load, J. Press. Vessel Technol. 133 (2) (2011) 021001. [25] X. Yang, S.A. Nassar, Z. Wu, A. Meng, Nonlinear behavior of preloaded bolted joints under a cyclic separating load, J. Press. Vessel Technol. 134 (1) (2012) 011206. [26] W. Eccles, I. Sherrington, R.D. Arnell, Frictional changes during repeated tightening of zinc plated threaded fasteners, Tribol. Int. 43 (4) (2010) 700–707. [27] H. Jiang, Analysis of bolt failure and fatigue life of reciprocating compressor, Petrochem. Saf. Technol. 22 (6) (2006) 22–24. [28] Z. Wang, B. Xu, Y. Jiang, A reliable fatigue prediction model for bolts under cyclic axial loading, in: Proceedings of the 5th ISSAT International Conference on Reliability Quality in Design, 1999, pp. 137–141. [29] N.P. Suh, The delamination theory of wear, Wear 25 (1973) 111–124. [30] R.B. Waterhouse, The role of adhesion and delamination in the fretting wear of metallic materials, Wear 45 (3) (1977) 355–364. [31] DIN 946, Determination of coefficient of friction of bolt–nut assemblies under specified conditions, Deutsche Norm, 1991. [32] D.X. Cheng, Handbook of Mechanical Design, 4th ed, Chemical Industry Press, Beijing, 2010. [33] M. Ishimura, T. Sawa, A. Karami, T. Nagao, Bolt-nut loosening in bolted flange connections under repeated bending moments, In: Proceedings of the ASME 2010 Pressure Vessels and Piping Conference, Bellevue, Washington, USA, 2010. [34] H. Zhao, Stress concentration factors within bolt–nut connectors under elastoplastic deformation, Int. J. Fatigue 20 (9) (1998) 651–659. [35] V. Fridrici, S. Fouvry, Ph Kapsa, Effect of shot peening on the fretting wear of Ti–6Al–4V, Wear 250 (2001) 642–649.
