渐开线斜齿轮齿面点偏差求解及三维齿面偏差评定

Tooth surface point deviation calculation of involute helical gear and 3D tooth surface deviation evaluation

针对渐开线斜齿轮三维齿面偏差的求解过程不明确、基于三维齿面数据与基于齿面点线数据的偏差评定关系不确定的问题,提出一种计算齿面点偏差和三维齿面偏差评定的方法。将齿面偏差视为由标准齿形偏转形成,在柱坐标系下推导渐开线斜齿圆柱齿轮齿面点与设计齿面垂直偏差的计算公式。根据现行齿面偏差定义标准建立齿面坐标系,在该坐标系下,利用二维勒让德正交多项式前6项函数图像与常见齿面偏差类型特征相似的性质,对齿面偏差点云进行拟合,推算二维勒让德正交多项式项系数与对应类型基于齿面点线数据偏差评估量值的比例关系。使用三坐标测量机对含有径向变位的6级精度斜齿渐开线圆柱齿轮进行测量试验,将试验结果与齿轮测量中心报告对比,以验证该方法的可行性。

In order to solve the problems that the solution process of the 3D tooth surface deviation of involute helical gear is not clear,and the deviation evaluation relation between the data based on the 3D tooth surface and the data based on the tooth surface point-line is uncertain,a method for calculating the tooth surface deviation and for evaluating the 3D tooth surface deviation was presented.In this method,the tooth surface deviation was regarded as the deflection of the standard tooth shape,and the calculation formula of the vertical deviation between the tooth surface and the designed tooth surface were derived in a cylindrical coordinate system.The tooth surface coordinate system was established according to the current tooth surface deviation definition standard.In this coordinate system,based on the similarity between the first 6 terms function images of 2D Legendre orthogonal polynomials and the characteristics of common tooth surface deviation types,the deviation point cloud of the tooth surface was fitted as a whole.The proportional relationship between the coefficients of 2D Legendre orthogonal polynomials and the corresponding deviation evaluation values based on tooth surfacepoint-line data was calculated.The CMM was used to measure a 6-level helical involute cylindrical gear with radial displacement,and the experimental results were compared with the gear measuring center report to verify the feasibility of the method.