渐开线蜗轮的精确建模与修形

为了适应单件、小批量生产模式,文章提出了一种新的渐开线蜗轮修形建模技术。根据微分几何与齿轮啮合原理依次推导得出蜗杆齿面方程、蜗轮副啮合方程,进而得出蜗轮齿面方程。将蜗轮齿面方程计算出的齿面点云沿齿面法向偏移,得出修形后的齿面。对蜗杆与修形蜗轮的动态啮合进行有限元分析,得出接触区与传动误差。分析结果表明,文中的修形建模方法精度高、啮合性能良好、调整方便。这种修形建模方法还可以用于其它类型的圆柱蜗轮副。

Accurate Modeling and Modification of Involute Worm Gear

In order to adapt to single piece and small batch production model,a new modeling technique of involute worm gear modification is proposed in this paper.According to the differential geometry and the gear meshing principle,the equation of the tooth surface of the worm and the meshing equation of the worm gear pair are derived,and then the equation of the tooth surface of the worm gear is obtained.The points of worm gear surface,which are calculated by worm gear tooth surface equation,are deviated in normal direction so that the modified tooth surface is obtained.The dynamic meshing of the worm and the worm gear is analyzed by finite element method,then the contact area and the transmission error are obtained.The analysis results show that the modeling method of this paper is of high accuracy,good meshing performance and convenient adjustment.This method can also be used for other types of cylindrical worm gear pair.