非圆齿轮滚齿包络误差建模及抑制研究

Research on Modeling and Suppression of the Tooth Profile Envelope Error of Non-circular Gear Hobbing

非圆齿轮节曲线各位置的齿廓具有等模数、不等曲率半径和极径的特点,在滚切过程中形成的各齿廓的包络线分布特性不同,导致不同位置的齿廓具有不等的包络误差。对此,以滚切基本联动模型为运动约束,构建滚刀断续切削齿廓的几何仿真方案,给出包络线分布与节曲线曲率半径和极径之间的关联特征;引入当量滚刀概念,建立了包络误差与当量齿轮齿数和当量滚刀槽数的关系模型;研究整周不同齿廓最大包络误差的计算和位置分布,提出了一种改善包络误差的滚切模型。该模型通过窜刀运动实现非圆节曲线不同位置当量滚刀槽数的改变,进而抑制包络误差的最大值及不均分布。研究工作为非圆齿轮滚切齿廓包络误差分析提供了理论支撑,可对包络误差进行预判并指导合理加工方案的制订。

The tooth profiles at different positions of the non-circular gear pitch curve have the characteristics of equal modulus but unequal curvature radius and polar diameter.The distribution characteristics of the envelope curve of each tooth profile formed during the hobbing process are different,which lead to the unequal envelope error of the tooth profile at different positions.Taking the basic linkage model of hobbing as the motion constraint,the geometric simulation scheme of the tooth profile generated by the intermittent cutting of the hob is constructed,and the correlation characteristics between the envelope distribution and the curvature radius of the pitch curve and the polar diameter are analyzed.The concept of equivalent hobs is introduced,the relationship model between envelope error and equivalent gear tooth number and equivalent hob groove number is built,and the calculation and position distribution of the maximum envelope error of different tooth profiles are analyzed.A hobbing model to improve the envelope error is proposed.The model can realize the change of the equivalent hob groove number at different positions of the non-circular curve through the hob shifting method,thereby the maximum value and uneven distribution of the envelope error are improved.This study provides theoretical support for the analysis of the tooth profile envelope error of the non-circular gear hobbing,which can predict the envelope error and guide the formulation of a reasonable machining plan.