两级渐开线齿轮传动系统横-摆-扭耦合非线性动力学建模与试验验证

Nonlinear dynamic modeling and test validation for a two-stage involute gear system

以两级渐开线齿轮传动系统为研究对象,分析了几何偏心、中心距安装误差以及齿轮中心支撑弯曲变形引起中心距的变化对啮合角和间隙的影响,引入非线性动态啮合刚度模型,得到了各级齿轮传动的非线性动态啮合力。采用拉格朗日方法建立了考虑偏心、间隙、时变啮合角以及非线性动态啮合刚度模型的两级齿轮传统系统横-摆-扭非线性动力学模型,采用4阶定步长龙哥库塔法求解非线性动力方程。针对一个两级齿轮传统系统试验装置进行理论计算和试验测试,安装在齿轮圆周对称位置的角加速度传感器,测试结果显示各工况下齿轮角加速度仿真值与实验值最大误差为23.51%;固定安装在箱体上的位移传感器测得振动位移仿真值与实验值最大误差为21.21%;粘贴在轴上的应变片测得扭转切应力仿真值与实验值最大误差为17.9%。研究结果表明:仿真结果与试验结果的变化趋势基本吻合,且误差在可接受范围内。分析了可能导致仿真结果与试验结果之间产生误差的原因,验证了渐开线直齿轮传动横-扭-摆耦合非线性动力学模型和非线性动态啮合模型的正确性。

Here, a two-stage involute gear system was taken as a study object, the effects of variation of distances between centers due to geometric eccentricity, installation errors of distances between centers and bending displacement of gear center bearings on pressure angle and backlash were analyzed, a nonlinear dynamic meshing stiffness model was introduced, nonlinear dynamic meshing forces of each gear pair were obtained. Adopting Lagrange method, the nonlinear lateral-shimmy-torsional coupled dynamic model of the two-stage involute gear system was established considering the effects of eccentricity, backlash, time-varying pressure angle and the nonlinear dynamic meshing stiffness model. The nonlinear dynamic equations were solved with the 4th order fixed step Runge-Kutta algorithm. The theoretical calculation and tests were performed for a test device of a two-stage gear system. The test results showed that the maximum error between simulated values of angular acceleration under various conditions and tested ones obtained with angular acceleration sensors installed at symmetric positions around gear circumference is 23. 51% ; the maximum error between simulated values of vibration displacements and tested ones obtained with displacement sensors installed at positions of thegear box is 21.21% ; the maximum error between simulated values of torsional shear stresses and tested ones obtained with strain gauges pasted on the gear shaft is 17. 9% . The study results indicated that the varying trend of simulated results agrees well with that of test ones, and errors are within an acceptable range, the reasons causing errors between simulated results and tested ones are analyzed; the correctness of the proposed dynamic model and the meshing stiffness model of the gear system is verified.