无侧隙双滚子包络环面蜗杆传动的参数优化

Parameter Optimization of the Non-backlash Double-roller Enveloping Hourglass Worm Gearing

无侧隙双滚子包络环面蜗杆传动是一种能同时满足高精度、大载荷要求的新型环面蜗杆传动。为获得啮合性能优良的无侧隙双滚子包络环面蜗杆传动,提出综合考虑传动齿面接触性能和润滑性能对该新型传动的几何参数进行优选。通过对蜗杆副齿面啮合参数如诱导法曲率、卷吸速度、润滑角以及滚子自转角等的数值计算,分析表征传动啮合性能的齿面接触参数的影响因素,进而确定该新型蜗杆传动优化设计变量的取值范围。以此为基础,建立以蜗杆副的滚子自转角及齿面综合系数为优化目标,建立以传动齿面润滑角、蜗杆轴的强度与刚度以及几何不干涉等为约束的优化设计数学模型,并用Matlab的遗传算法工具箱对数值算例进行求解。数值实例表明,经过几何参数优化的蜗杆传动,其齿面接触性能和润滑性能明显得到改善和提高。

Non-backlash double-roller enveloping hourglass worm gearing is a new-type hourglass worm gearing,which can be used in high precision and big load applications domain. To obtain a non-backlash double-roller enveloping hourglass worm gearing with perfect meshing performance,the optimization design of the worm gearing is presented with the contact and lubrication performances of the gearing taken into consideration. By numerical calculation of the tooth contact parameters that includes lubrication angle,induced normal curvature,entrainment velocity and roller rotation angle,the effect factor of the meshing performance are discussed and the value range of design variables is determined. Then,the optimization model of the worm gearing is built,in which the roller rotation angle and comprehensive coefficient of tooth for elastohydrodynamic lubrication condition are taken as optimization objectives,and the lubrication angle,the strength and stiffness of the worm axis and geometric non-interference are considered as constraint conditions. The GA toolbox in the Matlab software is utilized to obtain the optimal solution. A numerical example shows that this method can be used to effectively improve the meshing performance of the non-backlash double-roller enveloping hourglass worm gearing.