高阶传动误差函数的面齿轮传动设计新方法

摘要

In order to avoid edge contact and enhance dynamic property and to be less sensitive to misalignment for bearing contact ,a design process for face gear drive that is provided with a high order polynomial function of transmission errors is proposed in this paper .Considering the differential teeth between shaper and spur pinion ,the mathematical models for a high order polynomial function of transmission error that reflect the relationship between the rotation angle of the input gear and output gear is created .Based on the theory of gearing ,the coordinate systems are set up for the face gear generated and a pre-designed fourth order polynomial function of transmission error is assigned to the face gear drive .The tooth face of the spur gear is longitudinally crowned by employing a form disk grinding wheel that is driven by a parabolic motion .The mathematical models of tooth contact analysis (TCA) for face gear drive are created .Mathematical models of principle curvatures and directions for face gear pair are developed and contact ellipses are determined ,and computer simulation is performed . The results show that the perfect bearing contact is obtained and transmission errors of output are correspondence with that of pre-designed .%为了提高面齿轮传动的动态性能和降低啮合对安装误差的敏感性，提出具有高阶传动误差函数的面齿轮齿面设计方法，描述了齿轮传动反映输出和输入角度关系的四阶传动误差函数的数学模型，考虑刀具齿轮与圆柱齿轮齿数差，推导了面齿轮数控加工过程中具有四阶传动误差函数的齿面方程．利用盘形砂轮对渐开线圆柱齿轮齿向修形，发展圆柱齿轮齿向修形的鼓形齿面．建立面齿轮副轮齿接触分析条件，对具有四阶传动误差函数的面齿轮和齿向鼓形的渐开线圆柱齿轮的啮合进行了计算机仿真和啮合分析．研究结果表明，设计传动误差幅值为10″，在对准安装和轴夹角误差为0．02°的条件下，齿轮副输出的高阶传动误差幅值为0″，其他形位参数与预置的参数完全一致；齿面接触区域对安装误差不敏感，接触迹线始终稳定在齿轮半径的172 mm附近。