斜齿面齿轮传动齿面主动修形与边缘接触分析

Tooth surface active modification and edge contact analysis for face gear drives with helical pinion

为了预控斜齿面齿轮传动的啮合性能并消除边缘接触,提出齿面主动修形方法。利用几何啮合性能的定量参数建立了小轮主动修形齿面的数学模型;阐述了小轮的数控加工方法并确立了数控运动规律多项式系数,建立了由该系数增量、该系数单位增量影响齿面位置矢量变化的敏感矩阵,以及小轮主动修形齿面相对其理论齿面的修形量组成的敏感矩阵方程;通过奇异值分解法迭代求解敏感矩阵方程获得加工小轮主动修形齿面的数控规律。数值计算实例说明,数控规律求解方法可行,主动修形齿面可再现预置的几何啮合性能,而且避免了不考虑安装误差时的边缘接触,但有安装误差时将出现新的边缘接触。

For a face gear drive with a helical pinion to pre-control its meshing performance and avoid its edge contact,a method of tooth surface active modification was proposed.The quantitative parameters of geometry meshing performance were applied to establish the mathematical model of the pinion's modified tooth surface.The coefficients of CNC motion rule polynomials were derived according to the pinion generation by CNC machining method,then the sensitive matrix represented the influence of incremental coefficients and unit increment on the position vector variation of tooth surface was established,and the cutting volume of the modified tooth surface respecting with the theoretical one of the pinion formed a sensitive matrix equation,which was iteratively solved by Singular Value Decomposition(SVD)to correct CNC motion rule for generating the active modified tooth surface of the pinion.Numerical example illustrated the application of the proposed method and showed that the method of motion rule correction was feasible,and the modified surface was able to reproduce the pre-designed geometry meshing performance to avoid the edge contact without misalignment,but the edge contact would occurred again with misalignment.