Influence of wheel-rail excitation on contact characteristics and stress intensity factors of cracked gears for locomotives
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摘要: 使用数值法求解了齿根裂纹故障齿轮的时变啮合刚度，建立了六自由度齿轮动力学模型；采用Newmark法求解裂纹深度为1、2、3 mm齿轮传动系统动态响应，对时域信号进行了分析，计算了不同统计指标对不同故障程度的敏感度；结合多体动力学，建立了机车多体动力学模型，求解了18、19、24阶数车轮多边形激励以及0.5、1.0、1.5 mm波深钢轨波磨激励工况下含齿根裂纹齿轮传动系统接触特性，模拟了不同激励工况下的齿面接触状态。分析结果表明：时变啮合刚度随着裂纹扩展角度和裂纹深度的增加逐渐下降；随着裂纹深度的加深，传动系统的振动冲击愈加剧烈；脉冲因子对裂纹故障特征较为敏感，适合作为裂纹故障特征评价指标；随着车轮多边形阶数和钢轨波磨波深的增加，含裂纹单齿齿面接触力最大值分别约为无激励工况下的3.0和6.4倍，当车轮多边形阶数为24阶时，齿面接触合力和单齿齿面接触力均达到最大值，分别为4 125、1 178 N；Ⅰ型裂纹应力强度因子数量级远大于Ⅱ型裂纹应力强度因子，Ⅰ型裂纹在裂纹扩展中占主导地位，且应力强度因子随着载荷和扩展程度增加而增大，说明轮轨激励的存在会导致含裂纹齿裂纹扩展速率增加，缩短其使用寿命，影响机车的安全运行。Abstract: The time-varying meshing stiffness of gears with root crack faults was solved by the numerical method, a 6-DOF gear dynamics model was established, and the Newmark method was used to solve the dynamic responses of the gear transmission systems with crack depths of 1, 2, and 3 mm. The time domain signal was analyzed, and the sensitivities of different statistical indexes to different fault degrees were calculated. A multi-body dynamics model of the locomotive was built based on the multi-body dynamics. The contact characteristics of the gear transmission system with tooth root cracks were solved under wheel polygon excitations of 18th, 19th, and 24th orders and rail corrugations of 0.5, 1.0, and 1.5 mm wave depths. The contact states of tooth surfaces under different excitation conditions were simulated. Analysis results indicate that the time-varying meshing stiffness gradually decreases with the increase of crack propagation angle and crack depth. With the deepening of crack depth, the vibration and shock of the transmission system become increasingly severe. The pulse factor is sensitive to the crack fault characteristics and is suitable as an evaluation index of crack fault characteristics. With the increase of wheel polygon order and rail corrugation depth, the maximum contact force of a single tooth surface with cracks is about 3.0 times and 6.4 times that under the no excitation, respectively. When the wheel polygon order is 24, the contact resultant force of the tooth surface and the contact force of the single tooth surface both reach maximum values, which are 4 125 and 1 178 N, respectively. The value of the mode Ⅰ crack stress intensity factor is much larger than that of the mode Ⅱ crack stress intensity factor. Mode Ⅰ crack is dominant in crack propagation, and the stress intensity factor increases with the increase of load and expansion degree, indicating that the existence of wheel-rail excitation can increase the crack propagation rate of cracked teeth, shorten its service life, and affect the safe operation of locomotives.
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图 1 时变啮合刚度数值计算模型
Figure 1. Numerical calculation model of time-varying meshing stiffness
图 2 不同初始裂纹深度的齿轮时变综合啮合刚度
Figure 2. Time-varying composite meshing stiffnesses of gears with different initial crack depth
图 3 不同初始裂纹扩展角度的齿轮时变综合啮合刚度
Figure 3. Time-varying composite meshing stiffnesses of gears with different initial crack propagation angles
图 5 不同裂纹深度齿轮传动系统垂向振动位移
Figure 5. Vertical vibration displacements of gear transmission system with different crack depths
图 6 不同裂纹深度时域统计指标趋势
Figure 6. Time domain statistical index trends of different crack depths
图 12 不同车轮多边形激励工况下机车从动齿轮振动位移
Figure 12. Vibration displacements of locomotive driven gear under different wheel polygon excitation conditions
图 13 不同车轮多边形激励工况下齿面接触合力
Figure 13. Contact resultant forces of gear tooth surface under different wheel polygon excitation conditions
图 14 不同车轮多边形激励工况下含裂纹齿的齿面接触力
Figure 14. Contact forces of gear tooth surface with crack under different wheel polygon excitation conditions
图 15 不同车轮多边形激励工况下裂纹尖端应力
Figure 15. Crack tip stresses under different wheel polygon excitation conditions
图 17 不同钢轨波磨激励工况下机车从动齿轮垂向振动位移
Figure 17. Vertical vibration displacements of locomotive driven gear under different rail corrugation excitation conditions
图 18 不同钢轨波磨激励工况下齿面接触合力
Figure 18. Contact resultant forces of gear tooth surface under different rail corrugation excitation conditions
图 19 不同钢轨波磨激励工况下含裂纹齿的齿面接触力
Figure 19. Contact forces of gear tooth surface with crack under different rail corrugation excitation conditions
图 20 不同钢轨波磨激励工况下裂纹尖端应力
Figure 20. Crack tip stresses under different rail corrugation excitation conditions
图 21 不同载荷条件下的应力强度因子
Figure 21. Stress intensity factors under different load conditions
表 1 机车齿轮基本几何参数
Table 1. Basic geometric parameters of locomotive gear
基本参数 主动齿轮 从动齿轮 模数/mm 8 8 压力角/(°) 20 20 螺旋角/(°) 0 0 齿顶高系数 1 1 顶隙系数 0.25 0.25 齿宽/mm 140 140 齿数/个 23 120 
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表 2 机车齿轮材料参数
Table 2. Material parameters of locomotive gear
密度/(g·cm-3) 弹性模量/GPa 泊松比 7.85 209 0.3
下载: 导出CSV
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