Purpose

The purpose of this paper is to calculate the meshing stiffness of nutation face gear considering the roughness, establish the calculation method of time-varying meshing stiffness of rough tooth surface and analyze the influence of roughness, load and other factors on the meshing stiffness of tooth surface.

Design/methodology/approach

The Weierstrass–Mandelbrot (W-M) function in the Majumdar–Bhushan model is used to characterize the rough contact line of the tooth surface, the normal height and radius of the micro convex body are calculated and the contact flexibility of the contact point of the tooth surface is obtained. The contact flexibility and the bending shear deformation flexibility obtained previously are substituted into the improved deformation compatibility equation for iterative calculation, and the time-varying meshing stiffness of the nutation face gear considering the roughness is obtained.

Findings

Compared with ABAQUS finite element simulation results, it is found that the meshing stiffness curve of rough tooth surface is more gentle than that of smooth tooth surface, the meshing stiffness value is smaller and the meshing stiffness change is smaller at the position where the number of gear teeth coincide changes.

Originality/value

In the process of calculating contact deformation, the fractal theory W-M function is used to characterize the contact line of the rough nutation face gear, and the deformation coordination condition considering roughness is improved. Therefore, the method of time-varying meshing stiffness considering roughness can obtain more accurate results, which provides theory and data for the subsequent dynamics analysis of the nutation face gear transmission.

中文翻译：

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考虑粗糙度的章动端面齿轮刚度分析

目的

本文的目的是计算考虑粗糙度的章动端面齿轮的啮合刚度，建立粗糙齿面时变啮合刚度的计算方法，并分析粗糙度、载荷等因素对轮齿啮合刚度的影响表面。

设计/方法论/途径

利用Majumdar-Bhushan模型中的Weierstrass-Mandelbrot（WM）函数来表征齿面的粗糙接触线，计算微凸体的法向高度和半径以及齿面接触点的接触柔度获得表面。将先前获得的接触柔度和弯曲剪切变形柔度代入改进的变形协调方程中进行迭代计算，得到考虑粗糙度的章动面齿轮时变啮合刚度。

发现

与ABAQUS有限元仿真结果对比发现，粗糙齿面的啮合刚度曲线比光滑齿面的啮合刚度曲线更加平缓，啮合刚度值更小，且在齿数个数处啮合刚度变化更小。齿轮齿数重合变化。

原创性/价值

在计算接触变形过程中，利用分形理论WM函数来表征粗糙章动面齿轮的接触线，改进了考虑粗糙度的变形协调条件。因此，考虑粗糙度的时变啮合刚度方法可以获得更为准确的结果，为后续章动端面齿轮传动动力学分析提供理论和数据。