弧线齿圆柱齿轮四阶传动误差设计与分析

Design and Analysis of Fourth Order Transmission Error of Circular-arc Curvilinear of Cylindrical Gear

为了改善弧线齿圆柱齿轮传动的平稳性和轮齿强度,采用四阶传动误差曲线设计齿轮副。首先确定四阶传动误差曲线的系数,用有具有刀倾的刀盘形成的弧线产形齿条和假想小轮的方法,根据坐标变换和啮合方程,分别推导大轮和小轮的齿面方程。由两齿面在啮合中的连续相切条件,建立了考虑安装误差的轮齿接触分析(TCA)模型。齿轮副啮合仿真的结果表明,该方法可实现四阶传动误差,增大啮合转换点处夹角可使齿轮副平稳过渡,减小齿根的修形量可提高轮齿强度,可降低传动误差曲线对安装误差的敏感性。

The fourth order transmission error is applied to improve the transmission stability and tooth strength of circular--arc curvilinear of cylindrical gear. The coefficient of fourth order transmis- sion error curve is determined, the curvilinear shaped imaginary rack cutter is formed by the tilted head cutter, and the imaginary pinion is introduced to establish the tooth surface equation of pinion and gear by the coordinate systems transformation and the mesh equation, respectively. And the tooth contact analysis model which also considered assembly errors is established on the conditions of continuous tangency of two contact surfaces. The computerized simulation of meshing and contact shows that the fourth order transmission error can be achieved by the proposed method, and the stability transmission can be performed by increasing the angle of the transformation point between the adjacent meshing cy- cles, the tooth fillet strength can be enhanced for decreasing the modification amounts nearby tooth root, finally, the sensitivity of assemble errors of the transmission curve can be reduced.