一种改进的非线性接触齿廓修形直齿轮啮合刚度分析方法

An improved method for analyzing meshing stiffness of nonlinear contact spur gear with tooth profile modification

时变啮合刚度是齿轮副的周期性内部激励,是齿轮传动系统振动和噪声问题的主要来源。针对齿廓修形的直齿轮啮合刚度计算问题,从能量等效思想出发,结合悬臂梁模型,考虑接触对间的非线性接触,提出了一种改进的非线性接触齿廓修形直齿轮啮合刚度解析模型。首先,在已有文献的基础上,将轮齿简化为齿根圆上的悬臂梁,三维的齿轮副传动模型转换为二维的平面齿廓,进行了接触分析,考虑齿对间的非线性接触,通过能量法构建了齿廓修形直齿轮单齿啮合刚度半解析模型;然后,补充了变形协调与力平衡方程,导出了齿廓修形直齿轮副综合啮合刚度模型;最后,将采用该方法所得结果与有限元计算结果进行了对比,完成了对该计算方法的验证,并分析了不同摩擦系数与齿轮参数对齿轮啮合刚度的影响规律。研究结果表明:相较于传统的有限元计算结果,采用该解析模型得到的计算误差在3%以内,计算速度提高150倍,在精度损失较小的情况下,能够实现对非线性接触齿廓修形圆柱齿轮啮合刚度的快速求解。

Time-varying meshing stiffness was the periodic internal excitation of the gear pair,which was the main source of the vibration and noise of the gear transmission system.Aiming at the calculation of the meshing stiffness of spur gears with tooth profile modification,an improved analytical model of the meshing stiffness of spur gears with nonlinear contact profile modification was proposed based on the idea of energy equivalence,combined with the cantilever beam model and considering the nonlinear contact between contact pairs.Firstly,based on the existing literature,the gear tooth was simplified as a cantilever beam on the root circle and the three-dimensional transmission model of spur gear pair was transformed into two-dimensional plane tooth profile for contact analysis,a semi-analytical model of single tooth meshing stiffness was constructed by energy method considering the nonlinear contact between tooth pairs.Then,the equations of deformation coordination and force balance were supplemented to derive the time-varying meshing stiffness model of spur gear pair with tooth profile modification.Finally,compared with the finite element calculation results,the calculation method was verified and the influence rules of friction and different gear parameters on meshing stiffness were analyzed.The research results show that,compared with the traditional finite element calculation results,the calculation error obtained by using this analytical model is less than 3%,and the calculation speed is 150 times higher,and the rapid solution of meshing stiffness of the spur gear with nonlinear contact can be realized under the condition of little precision loss.