内齿轮刮齿刀修形设计及优化  

Modification Design and Optimization of Internal Gear Skiving Tool

作　　者：苏进展[1] 王远庆 魏刚 杨羽 常乐浩[1] SU Jinzhan;WANG Yuanqing;WEI Gang;YANG Yu;CHANG Lehao(Key Laboratory of Road Construction Technology and Equipment of MOE,Chang’an University,Xi’an 710064,China)

机构地区：[1]长安大学道路施工技术与装备教育部重点实验室,西安710064

出　　处：《西安交通大学学报》2021年第11期147-153,共7页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(51805405);陕西省自然科学研究计划资助项目(2019JQ-695,2020JQ-383)。

摘　　要：为了降低内齿轮刮齿的原理性误差,提出了一种刮齿刀修形设计新方法。从具有齿廓修形的齿条刀出发,结合变位渐开线斜齿轮的展成原理,推导了连续变位刮齿刀的齿面方程;联立刮齿刀齿面和前刀面方程,求解刮齿刀切削刃的数学表达式,根据双自由度包络理论和齐次坐标变换,建立内齿轮的刮齿模型,获得内齿轮齿面方程。算例表明,刮齿刀的变位方式、前角和螺旋角是造成原理性误差的主要影响因素;相比于公式法,基于修形齿条刀法的切削刃更接近于反向包络法的切削刃;建立以齿面偏差平方和最小为目标函数,通过优化齿条刀的齿廓修形系数,能够将齿面偏差最大值从18μm降低到3μm,有效地减小原理性误差。此研究可为刮齿刀设计提供一种更简单、精度更高的新方法。In order to reduce the principle error of a skiving tool in generation of internal gears,a new type of modified skiving tool is proposed.Starting from the rack cutter with profile modification,and combining with the principle of the generation of the shifting involute,the tooth surface equation of the continuous shifting skiving tool is derived,and the equations of the skiving tooth surface and rake surface are combined to obtain a mathematical expression of the cutting edge of skiving tool.A mathematical model of internal gear is established based on the double-DOF envelope theory and homogeneous coordinate transformation,then the tooth surface equation can be obtained consequently.A numerical example shows that the shifting mode,rake angle and helix angle of the skiving tool are the main factors causing the principle error.Compared with the formula method,the cutting edge of the new type of skiving tool profile based on the rack-cutter method is closer to the reversely-enveloped cutting edge,and the tooth surface deviation can be reduced by optimizing the profile modification coefficient of rack-cutter with the minimum square sum of tooth surface deviations as the objective function,and the maximum value of the tooth surface deviations can be reduced from 18μm to 3μm,resulting in a obvious decrease of the principle error of skiving tool.

关 键 词：刮齿刀 内齿轮 齿廓修形 齿面偏差 切削刃 

分 类 号：TH161[机械工程—机械制造及自动化]