Abstract: In view of the problem that some subway line fastener anchor bolts break and affect the operation safety, the field test was carried out and the relationship between bolt torque and axial force was obtained. Based on the measured data, considering the spatial shape irregularity of the spring washer, the non-uniformity of the contact stress, and the nonlinear contact between different parts, the finite element model of the refined fastener bolt is established, and the single and double spring washers are respectively installed. The mechanical properties of the bolt parts are compared and analyzed. The results show that the double washer is more than a single washer. Since the shear deformation can be provided under the compression state, the bolt axial force increases little under the train load and the possibility of damage. Greatly reduced; due to the special shape of the spring washer, there is stress concentration in the local contact position between the nut and the washer, and the nut is subjected to a large eccentric load, which is an important cause of cracks and expansion damage at the joint position of the bolt and the nut. It is consistent with the actual situation on site.
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As the main artery of urban public transportation, rail transit is directly related to the travel, work, shopping and life of urban residents, and its safety is of vital importance. The track structure is the lower foundation of urban rail transit. The fastener is one of the core components of the track structure. Its function is to tightly press the rail and the lower track bed to form a stable and reliable overall structure to ensure the safe operation of the train. The fastener is composed of a plurality of components, and the function of the elastic strip buckle rail needs to be realized by the anchor bolt. Once the bolt fails, the integrity and stability of the rail structure and the safety of the train operation are affected.
In recent years, with the opening and operation of a large number of rail transit lines in China, the problem of fasteners for fastener anchor bolts (hereinafter referred to as bolts) is quite prominent. It has developed from random and sporadic faults to a large number of faults in some sections, which seriously affects driving safety. For example, the total number of fastener bolt breaks in a 40km long subway line in Beijing in February 28d was 33. It can be said that there are breaks every day, and according to the investigation of the site location, whether it is a straight line or a curve, the ordinary monolithic bed is still The floating plate damping track bed, whether it is down or up, has the problem of bolt breakage. However, in general, the bolt breaks in the curved section are significantly more than the straight sections.
For the bolt components, domestic and foreign scholars have conducted some research. Sethuraman et al. [1] obtained the stiffness interval of the joint surface of the joint by simplifying the contact of the bolt head or nut bearing surface to the rigid surface and the pressure equalizing surface; Musto et al. [2-3] obtained the finite element analysis and data fitting. The calculation formula of the stiffness of the connected parts corresponding to different size combinations, but neglecting the influence of Poisson's ratio factor, can not be accurately calculated. Tang Xiaoping et al [4] experimented on the pull-out resistance of fastener bolts, and obtained the influence bolts through multiple regression analysis. The main factor of pull resistance. Zhang Zhiyuan [5-6] obtained the axial force of the fastener bolt by calculation, and combined with the on-site corner test result, the attenuation law of the bolt axial force was obtained. E Strengthening, Li Xiuzhen et al [7-8] used ABAQUS to establish the bolt contact model, and analyzed the static performance of the yaw process of the yaw ring gear bolt connection of the wind turbine. Wang Ning et al [9] used the ANSYS parametric design language to construct a finite element model, and studied the factors affecting the effective radius of the bolt bearing surface.
It can be seen from the above research status that the existing research mainly analyzes the bolts from loosening and anchoring, and the research uses various degrees of simplification and assumptions, ignoring the influence of the spring washer on the bolt. In fact, the working condition of the fastener bolt is very complicated. It not only interacts with the iron pad, the elastic bar, etc., but also suffers from the long-term train vibration load, and the spring washer has a great influence on the force. Therefore, in order to reveal the cause of the fracture of the fastener bolt, it is necessary to carry out refined modeling of the bolt system, reasonably handle the boundary conditions and the contact relationship between the components, and propose feasible solutions through analysis to optimize the design and reduce the fastener. Provide a basis for small maintenance repairs.
1 Fastener system force analysis
In the fastener system, the iron pad is screwed and fixed on the integral track bed, and the rail is pressed on the iron pad by the fastener spring bar. The interaction of the rail, the elastic bar, the iron pad and the bolt is as shown in Fig. 1. Show. Among them, the iron pad is subjected to the pressure and lateral force of the rail, the pull-up force and the heel pressure of the elastic bar, the support force of the track bed and the friction force, and the pre-tightening force of the bolt [10]. According to the force and reaction force, the iron pad will produce an upward pulling force on the bolt, and the bolt sleeve has a pull-out resistance to the bolt. According to the static balance condition, there is
Under the action of the train, the track structure will vibrate. At this time, the fastener system will have a certain dynamic deformation. The compression of the rubber under the rail will cause the elastic stroke of the spring to change. The compression state of the spring washer changes, and the axial force of the bolt also changes. It changes accordingly. For fasteners, the performance of the spring washer exerts a critical influence on the force state of the bolt due to the high rigidity of the bolt.
According to the site investigation, the fasteners in the broken section of the bolt damage are all single spring washers. After analysis, it is found that the force of the bolts is improved when the double spring washers are used, and it is verified by field verification. Therefore, this paper will focus on the analysis of the state of the two spring washers to explore the reasons for bolt breakage.
2 fastener bolt field test
Testing of on-site fastener bolts is divided into static and dynamic parts. The static part is mainly to clarify the pre-stress of the bolt after the fastener is installed; the dynamic part is to test the vibration displacement of the iron plate of the fastener, and to provide the load application condition for the analysis of the theoretical model. The static test described below is a single washer.
2.1 Static test analysis
The track structure fastener bolts must be tightened during assembly, ie pre-tensioned before being subjected to working loads. The pre-tightening force can increase the rigidity, tightness and anti-loose ability of the fastener system. The size of the fastener system has a direct influence on the stress state during the service of the bolt. Therefore, the pre-tightening force of the fastener bolt is first tested in the field.
There is currently no measured data on the pre-tightening force of fastener bolts in the industry. In this paper, the needle-shaped sensor is used to test the pre-tightening force of the fastener bolt first, as shown in Figure 2 and Figure 3. Before the start of the experiment, a hole with a diameter of 2 mm is placed in the middle of the top of the bolt to be tested, and the needle strain gauge is installed into the hole, and the special wall is used to make the hole wall completely close to each other and waterproof. During the test, the bolt to be tested and the temperature compensation piece are connected into a Wheatstone bridge, and the bolt is placed in the bolt hole and tightened with a torque wrench. The strain gauge is used to collect the strain of the bolt to obtain the torque and preload of the bolt. The relationship curve is shown in Figure 4. 　　
According to the requirements of the subway line, the torque of the fastener bolt should be controlled at 200~250N·m. Table 1 shows the measured values ​​of the bolt torsion moment in the curve section of a Beijing subway line. From the results in Table 1, it can be seen that the torque value is relatively discrete. The torque is too small and the over-tightening phenomenon is relatively high, and some of the over-bolted bolts even reach 300 N·m. In this paper, the adverse situation is 300N·m for analysis. According to the test results, Figure 4 shows that the pre-tightening force corresponding to the 300N·m torque is 50kN. Therefore, subsequent analysis will take values ​​at 50kN.
2.2 Dynamic test analysis
When the train passes at high speed, the fastener iron pad will produce a certain amount of vibration displacement. This vibration displacement has a great influence on the stress state of the bolt, so it is necessary to carry out test tests on site. According to the actual situation of the test site, the German IMC dynamic acquisition instrument is used, and the self-made displacement meter is used for testing, including different displacement indexes such as rails and fasteners. As shown in Fig. 5, this paper mainly focuses on the vertical displacement of the fastener iron pad. The analysis was carried out and the test results are shown in Table 2.
3 Calculation model establishment
In the past, the bolt force analysis method usually applied a circular uniform load to the nut of the bolt to simulate the pull-up force [12-13], and replaced the spring washer with a flat plate, which is inconsistent with the actual bolt. The force status does not match. In order to accurately simulate the service state of the bolt, a fine finite element model is established, in which the components of the fastener are modeled according to the actual size and discretely processed by the solid element.
The model determines the assembly method according to the actual installation and working state of the bolts and gaskets in the fastener system. As shown in Figure 6, the shape of the spring washer is three-dimensional irregular during the actual service, and it is with the nut and The contact force of the iron pad is non-uniform. In order to realistically simulate the stress state of the bolt under working conditions, the contact is in the surface contact mode, that is, the nonlinear contact theory is applied [14-15]. For the single gasket case, the upper surface of the gasket and the lower surface of the nut are established. In the contact pair, the lower surface of the gasket establishes a contact pair with the upper surface of the iron pad; and for the double gasket, the contact of the inner upper surface of the first layer gasket with the inner lower surface of the second layer gasket is also considered.
When setting the contact pair, the normal contact adopts "hard contact", that is, when the gap between the two faces becomes zero, the contact constraint starts to function; when the contact pressure becomes zero or a negative value, the contact face is separated The constraint is lifted. The normal contact force between the contact algorithms can only be pressure, and the two objects are not allowed to penetrate or invade each other; the tangential contact adopts the Coulomb friction model, refer to the existing research [16], the friction coefficient between the contact pairs is 0.2; A penalty friction formula that allows "elastic sliding" to deal with non-convergence problems that may result from discontinuities between the two states of slip and bond. “Elastic sliding†refers to the small amount of relative motion that occurs when the surfaces are bonded together. The calculation model selects the penalty stiffness (the slope of the dashed line), so that the elastic value of this allowed “elastic sliding†is only the length of the unit feature. As shown in Figure 7.
According to the actual working force of the bolt, it can be considered that the threaded portion of the bolt is fixed, and the iron backing plate is movable, so when the model is established, the threaded portion of the lower part of the bolt is fixedly restrained, and the displacement load is applied to the iron backing plate. on. The magnitude of the applied displacement is determined based on the previously measured values ​​in the field. The material parameters of the fastener bolts are shown in Table 3.
4 analysis of bolt calculation results
4.1 Analysis of gasket deformation
For the coil spring washer, the distance between the upper surface of the first ring and the upper surface of the second ring is 11 mm, and the thickness of the gasket is 9 mm, so the compressible distance between the two layers of the gasket is 2 mm. In the case of a single washer, when the bolt is tightened, the washer is flattened, ie the stroke is 11 mm; for the double washer, when it is tightened, the lower surface of the first turn is in contact with the upper surface of the second ring, the whole The washer has a stroke of 2 x 1, 75 = 3.5 mm. However, the difference is that when the double spring washer is pressed, a certain amount of shear deformation can still occur.
When the bolting amount of the single washer is less than 11 mm, the single washer acts as a spring and provides a linear elastic force. When the bolt tightening amount of the single washer exceeds 11 mm, the single washer is no longer elastic. If the loading continues, the washer acts as an iron washer. Due to its relatively high rigidity, the bolts and washers are subjected to relatively large stresses, as shown in Fig. 8.
For the double washer case, when the bolt tightening amount is less than 3.5mm, the double washer provides a linear elastic force; when the bolt tightening amount exceeds 3.5mm, the double washer is pressed and no linear elasticity is generated, as shown in Fig. 9. Show. However, the first ring will be subjected to shearing force to the second turn, and there is still a certain shear deformation, which can continue to provide elasticity, thereby reducing the stress on the bolt.
4.2 Bolt axial force analysis
Fig. 10 and Fig. 11 are diagrams showing the relationship between the axial force of the bolt and the amount of bolt tightening when assembling the single washer and the double washer, respectively. It can be seen from the figure that for a single spring washer, when the tightening amount of the bolt is less than 11 mm, the axial force increases slowly with the increase of the tightening amount, and the spring coefficient is about 2 kN·mm -1 , when the tightening amount is greater than 11 In the case of mm, the axial force increases sharply with the increase of the tightening amount; when the double washer is assembled, when the tightening amount is more than 3.5 mm, the axial force of the bolt increases and increases with the increase of the bolt tightening amount. Linear, but the axial force increases significantly slower than a single washer.
Referring to the previous measured results, when the bolt tightening force is set to zero when the bolt axial force is 50kN, the relationship between the axial force and the equivalent tightening amount can be obtained, as shown in Fig. 12.
When the train passes at a high speed, the rail drives the iron pad to vibrate through the fastener to generate a certain vibration displacement. If the single washer is tightened, this vibration will have an impact on the bolt, and even if the vibration displacement of the iron pad is small, the axial force of the bolt will change abruptly. According to the field test results, it can be seen that the average vertical dynamic displacement of the iron pad is 0.29 mm on the side of the inner rail with a large number of bolt breaks. The axial force of the iron pad increases by nearly 3 times corresponding to the model calculation of Fig. 12. It can be seen that the main reason for the damage of the fastener bolt at the single washer is that the fastener bolt is excessively tightened for a long time, and the elasticity is almost lost, and the small displacement causes a large impact.
The double spring washer can still produce shear deformation and provide elasticity after the bolt axial force reaches 50kN. Therefore, when the iron pad is vibrated and displaced, the double spring washer acts as a shock absorbing buffer, and the axial force in the bolt The increase is not significant. Similarly, according to Fig. 12, when the vertical vibration displacement of the iron pad is 0.29 mm, the axial force of the bolt is increased by only about 40%. Therefore, the double washer can better adapt to the adverse conditions such as vibration and shock reduction, and the bolt service state is obviously superior to the single spring washer condition.
4.3 Bolt Stress Analysis
Whether a single washer or a double washer, the shape is spiral. Due to the special shape, the spring washer is in point contact with the nut and the iron pad at the beginning of the installation. As the bolt is tightened, the spring washer deforms and the contact with the nut and the iron pad gradually becomes surface contact. Therefore, when the bolt is in service, the position where the nut is in contact with the spring washer is relatively large, and a stress concentration point is generated on the nut, and the nut is subjected to a relatively large eccentric load. Figure 13 is a stress cloud diagram of the bolt.
It can be seen from Fig. 13 that since the nut is subjected to eccentric load and stress concentration is generated, here is also a relatively weak point where the size of the bolt and the nut is drastically changed, and under the action of long-term vibration, cracks are easily generated and the damage is expanded. The form of bolt failure found at the site is consistent with the analysis, see Figure 14.
5 Conclusion
(1) The first test design scheme was adopted. The field test of the fastener bolt was carried out by using the needle strain gauge. The data curve of the relationship between the torque and the bolt axial force was obtained. When the fastener torque was 300 N·m, the bolt was determined. The pre-tightening force is based on 50kN.
(2) Abandoning the traditional method of simulating contact with uniform pressure, using nonlinear contact theory to deal with the interaction between different parts such as bolts and spring washers, and establishing refined finite element for subway fastener bolts according to actual size. The model can well analyze the stress and deformation of bolts under single and double spring washers.
(3) The main reason for the breakage of the anchor bolts of the subway is that the torsion moment is too large, and the spring path provided by the single spring washer is used up. The bolts are subjected to a large impact force under the vibration load of the train, and finally the nuts and bolts are finally applied. The local contact position is subjected to a large force, thereby causing cracks and expanding the damage. For the double spring washer, since the shear deformation can be provided after the spring is used up, the axial force change of the bolt is relatively small and is not easy to be broken. This reveals that the use of double washers in the field can well solve the problem that the single washer bolt is prone to fracture damage.
(4) According to the research results, it is recommended to adopt a double washer scheme for the high-rise section of the subway line bolt breakage. Since the adoption in November 2015, there has been almost no bolt breakage. This further indicates that the results of the refined model analysis are correct.
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