本文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，验证了本文提出的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。
Abstract
In this paper, the lateral-torsional coupled nonlinear dynamic model of gear transmission is taken as the research object. Firstly, the time-varying pressure angle caused by the bending displacement of gears was proposed. Secondly, based on the characteristics of involute gear transmission, the instantaneous meshing point speed analysis was carried out, and the meshing point pressure angles were used to determine the boundary condition of single and double teeth mesh, combined the above analysis with the weber mechanics of materials we obtained the feedback model of time-varying mesh stiffness which considered the speed fluctuations and bending displacement of gear pairs, which can provide more accurate description of the engagement in the gear transmission process. Then, the computer program of gear meshing feedback model was translated into Fortran code. Finally, the lateral-torsional coupled nonlinear lumped mass model of two-stage gear transmission was established, taking the eccentric, backlash , time-varying mesh angle and mesh stiffness feedback model into consideration, with the help of Lagrange method. Then solve the nonlinear model using the RK4 method. The results show that: the gear bending deformation can cause the changing of gears meshing angle related to the changing of gear pairs central distance，and the frequency mainly domain by the rotation frequency; the gear speed fluctuations as well as the bending displacement of the gears cause the frequency of mesh stiffness consist of rotation frequency and the meshing frequency and their combined frequency, also the centrifugal force caused by eccentrics can increase the rotation frequency amplitudeof all dynamic response, the eccentrics also play a significant impact on the time-varying meshing angle and gear axis trajectories.
关键词
齿轮 /
非线性 /
试验验证 /
间隙 /
啮合角
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