点啮合齿面安装误差敏感性的定量评价方法

Quantitative analysis of sensitivity of point-contact tooth surface meshing characteristics to gears mounting errors

针对以往同类研究中点啮合齿面安装误差的敏感性没有综合定量评价方法的不足,提出了一种定量评价齿面啮合特性对齿轮安装位置误差的敏感性的方法,其步骤为:利用矢量的齐次坐标矩阵和齐次坐标方阵表达啮合问题中啮合点在不同坐标系之间的变换关系;通过求解啮合方程对安装位置参数的全微分,推导关于齿面啮合点的位置误差与齿轮安装位置误差的线性方程组;由该线性方程组系数矩阵的条件数来定量评价齿面啮合点的位置误差对齿轮安装位置误差的敏感性。最后,通过实例说明所提出的方法在齿面设计中的应用。

According to the deficiency of the previous study on sensitivity of point - contact tooth surface meshing characteristics to mounting errors, a new method of quantitative analysis on sensitivity of point - contact tooth sur- face meshing characteristics to mounting errors was presented, the procedures were as follows： Representing co- ordinate transformation of the contact point in the theory of meshing with the homogeneous coordinates; Deriving linear equations related to the position errors of the contact point on the tooth surface and the mounting errors from calculating total differential of equations of meshing; Evaluating sensitivity of gears mounting errors to con- tact point position errors; Illustrating the developed method with numerical examples.