Study on initial self-relaxation behavior of face gear coupling bolts Jiang Xiangjun1, Zhu Yongsheng2a翟qiang2a Hongjun2b(1 College of Mechanical Engineering, Chongqing University, Chongqing 401331, China; 2Xi'an Jiaotong University, Department of Modern Design and Rotor Bearing System, Ministry of Education. The material is isotropic, and the modulus of elasticity is E=209 GPa. The thread of the bolt and nut is built into a true thread geometry, which is beneficial to improve the reliability of the self-relaxation analysis of the bolt. In the finite element mesh model There are 6 bolts and 24 face teeth. Since the load and geometry are cyclically symmetric along the direction of the 6 bolts, only 1/6 of the structural model is established. The displacement nodes at the end of the wheel are all constrained. Cannot move in the z direction, and the torsional displacement load is applied to the other end of the wheel. According to the previous finite element simulation, the contact thread load of the first ring is more than 30% of the total load; therefore, it is possible to tighten the root of the first ring. The most critical area of ​​plastic deformation occurs, and the behavior of this area should be carefully studied.
There are a total of 4.104 nodes and 7.5955X104 eight-node 3D solid elements in the mesh model. The analysis including surface contact generally uses an eight-node unit. The contact problem of the bolt structure is simulated by the penalty function method, and is realized by the APDL input program in ANSYS. The contact surface is simulated by the contact coupling pair: nut and wheel Contact between the disc surfaces, contact between the faces of the two disc faces, contact between the bolt head and the surface of the disc. To simulate the bond between the nut and bolt contact threads, the nodes on the two threaded contact surfaces of the nut and bolt are coupled together by the APDL program. The coefficient of friction of all contact faces is set to 0.3. In the definition of the contact pair, the bolt head with the fine mesh and the nut contact surface are used as the target faces, and the wheel contact surface with the rough mesh is used as the contact face.
2.2 Plastic model The self-relaxing finite element simulation of bolt fastening uses the Ab-delKarim-hno cyclic plastic model. The constitutive mathematical equations in the basic plasticity theory are as follows: the strain and plastic strain rate; D is the fourth-order elastic tensor; K is the material parameter, which is determined by the test at different load rates as the stress tensor is the deviation stress tensor ;a is the back stress; Q is the isotropic deformation impedance; F is the key state function; <> is the Macauley symbol;: is the double dot product symbol.
Abdel-Karim and Ohno superimposed the OW-I enhanced model and the AF enhanced model, and proposed a superimposed enhanced combination model with the following expression =. The plastic model is obtained by embedding the user-defined program USERMA into the general finite element software package ANSYS. The specific stress correction uses the EULAR implicit backoff algorithm, which simplifies the plastic model into a nonlinear equation that can be solved by the Newton-Raphson method. In order to achieve global iterative equilibrium, the quadratic convergence of Newton-Raphson iteration is guaranteed by solving the corresponding consistent tangential stiffness matrix.
2.3 Calculation of initial parameters of the simulation In order to carry out the bolt self-relaxing simulation analysis of the face gear coupling structure, the simulation parameters of the ratcheting effect constitutive plastic model must be determined. The calculation method of the material parameters of the plastic model is as described above, first according to the material. The uniaxial tensile test curve obtains the formula for calculating C and r as follows: =Q According to the calculation method, the elastic modulus E=209GPa, Poisson's ratio=0.3, and the calculation results of C and r of 45拈 steel of the test material obtained in this paper are obtained. :rr is 152.1, 20.0, 15.2, 10.5, 305. Then the finite element analysis model is established. The finite element simulation calculation results determine that the ratchet strain rate control parameter a can be taken as an eight-node hexahedral element on three coordinate planes. The symmetry constraint and the stress loading are substituted into the obtained initial material parameters Ci and ri. According to the ratchet strain rate obtained by the experiment, the simulation result of the ratcheting strain is determined as shown in the figure. In the figure: N is the cyclic loading number as the total strain size loading condition. From the simulation results, it can be known that the selected initial material parameters can simulate the single-axis ratchet effect of 45SCO, in two loads. Under the condition, the increase of the ratchet strain can be well predicted. When the load amplitude is larger or the load average value is larger, the ratchet strain is more obvious.
2.4 The finite element simulation results are known: the uniaxial ratchet effect of the material. The simulation parameters of the constitutive plastic model can be used for the ratcheting effect of the structure. The finite element simulation calculates the loading condition of the finite element simulation P0=5. The torsional displacement load amplitude A0=0.2 In each loading case, a total of 20 torsional cyclic loadings were simulated after the initial preload. The application of the preload force of the bolted joint is achieved by shortening the true distance between the bolt head and the nut. When the torsional load is simulated, the end of one of the discs is fixed and the other end of the disc has a uniformly distributed displacement. The loading method of the torsional load is increased by 0.02°0.04° in each substep according to the magnitude of the load. The bolt preload can be listed by calculating the sum of the axial stresses of the bolt cross-sectional area. Ruler=5.55kN, 2 working conditions The lower preload is reduced as the cyclic loading increases. The figure shows the bolt clamping force; NT is the number of times the torsional load is loaded. It can be found that the self-relaxation of the bolt is obvious under the initial cyclic load and gradually stabilizes in the later stage. The equivalent stress on the cross section of the face tooth surface is shown as the change of the number of cyclic loads. The figure shows the equivalent stress on the face tooth surface; SN is the node sequence of the selected face tooth section. From the distribution of the equivalent stress on the face tooth surface, the equivalent stress value is close to the peak at the tooth surface contact surface separation, and the center position stress value of the contact surface is low. The top end of the tooth is not subjected to load and the equivalent stress is low. The change from the inclination angle of the face tooth to the second cycle load is not significant, and the equivalent stress of the face tooth does not change significantly. However, after the end of the first cycle, the change in equivalent stress is more pronounced.
1 - 1st cycle, A (9 = equivalent stress after the end face tooth is shown as a schematic diagram of the bolt contact surface. In order to study the change of the bolt head contact surface stress with the cyclic loading, the contact surface is unfolded along 0360, first take The contact stress at the outermost edge of the contact surface of the bolt head is analyzed. As shown in the figure, ah is the joint angle bh of the bolt head is the contact stress of the bolt head. The contact stress of the outermost edge of the contact surface of the bolt head is selected for analysis. Because this part of the stress is most sensitive to the external load, it can best reflect the influence of the external load on the contact surface stress of the bolt head. It can be seen that the initial contact stress distribution is relatively uniform and there is no large fluctuation, when the first cycle is twisted and loaded to A0= At 0.2, the contact stress at the outer edge of the bolt head is reduced at ah = 90 and 270. After the torsional load is unloaded, the contact stress decreases at the position of ah = 180, while the other positions are almost restored to the original state due to the elastic deformation. The end of the head joint contact surface near the hub axis receives less contact stress, while the end away from the shaft end receives greater contact stress. The separation between the bolt head and the wheel contact surface
=7.9kN, the smaller the bolt stress equivalent stress cloud diagram (color code unit: MPa) at A=0. The maximum equivalent stress occurs at the root of the first turn. Due to the stress concentration, it can be observed that plastic deformation first occurs near the root of the thread. This is because there is an adaptive and self-distributing process for the bearer of the structure. In the pre-tightening process, the first load bearing is the contact surface of the bolt head or the nut and the wheel, and then the load on the contact surface is transmitted to the thread, firstly carried by the first thread, and after reaching a certain limit, the load is 2nd. The thread is transferred and then gradually transferred to the rear thread until it is balanced.
The main reason for the self-relaxation behavior of the bolt due to structural ratcheting deformation is that the bolt thread exhibits plastic strain after being loaded, resulting in plastic accumulation or ratcheting deformation under cyclic loading. The material near the root of the first thread of the bolt has the greatest cyclic plasticity, and the stress and strain in this area also vary with the number of cycles of loading. It shows the change of the strain at the root of the first turn of the bolt with the cyclic loading, which is the equivalent strain of the root of the thread. It can be found that at this particular position, the axial strain is always increasing, thus also causing a reduction in the bolt preload. From the analysis results of the cyclic plasticity, it is known that the stress strain is continuously redistributed with time in a small area of ​​the root of the thread. It can be seen from the calculation results that the closer to the position of the clamped member, the faster the rate of equivalent strain increases; the first cyclic loading causes the amplitude of the equivalent strain at all positions to increase the most.
Variation of equivalent strain at the root of the thread
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