交错轴双滚子包络环面蜗杆传动啮合分析

为了消除环面蜗杆传动的齿侧间隙,提高其传动的精度和效率,分析了传统消隙蜗轮副的不足,在无侧隙双滚子包络环面蜗杆传动研究基础上提出一种交错轴双滚子包络环面蜗杆传动,采取双排滚子错位布置,且滚子轴线与蜗轮径向偏转一定角度。阐述了交错轴双滚子包络环面蜗杆传动的工作原理,依据空间齿轮啮合理论和微分几何理论,采用运动学法建立了蜗杆副的动静坐标系及接触点处的活动坐标系,推导了该新型环面蜗杆齿面方程和蜗轮齿面接触线方程,并导出了该传动的一界函数、诱导法曲率、润滑角及自转角等齿面啮合参数计算公式。最后运用matlab软件进行了数值仿真,并分析了滚柱偏置距离c2、滚柱半径R、交错角γ等参数对该蜗杆传动啮合性能的影响。仿真实例表明:要使该传动保持良好的接触性能和润滑性能,c2不宜超过10 cm,R在8～15 cm之间,γ在28°～50°之间。

Meshing Analysis of Non-parallel Double-roller Enveloping Hourglass Worm Gearing

To eliminate the backlash and improve the precision and efficiency of enveloping worm,by analyzing the shortcomings in the existing non-backlash worm gear sets,non-parallel double-roller enveloping hourglass worm gearing was proposed based on the research of non-backlash double-roller enveloping hourglass worm gearing.Two rows of rollers were assigned to misplace and there was a certain defection angle between the roller axis and the radial.The working principle was introduced.According to the theories of differential geometry and space engagement theory,the dynamic and static coordinate system based on worm gear pair and the moving coordinate system based on the contacting point were established.The tooth surface equations of worm and contacting line equations of worm gear were deduced.The formulas of meshing limit function,induced normal curvature,lubrication angle and rotation angle of the non-parallel double-roller enveloping hourglass worm gearing were derived by means of the theory of differential geometry.The simulation was conducted using MATLAB software,c2,R and γ,which impacted the engagement performance of this transmission,were analyzed.The numerical example showed that c2 should not be more than 10 cm,R should be controlled within 8 to 15 cm,and should be controlled within 28° to 50°,for effectively improving the meshing performance of the non-parallel double-roller enveloping hourglass worm gearing.