滚刀几何误差与齿轮几何精度的映射规律研究  

Research on Mapping Rules of Hob Geometric Errors and Gear Geometric Precision

作　　者：王时龙[1] 孙守利 周杰[1] 康玲[1] 程成[1] 

机构地区：[1]重庆大学机械传动国家重点实验室

出　　处：《机械工程学报》2013年第19期119-125,共7页Journal of Mechanical Engineering

基　　金：国家杰出青年科学基金(50925518);国家科技支撑计划(2012BAF13B09);重庆市科技攻关(cstc2012gg-yyjsB60001);机械传动国家重点实验室自主研究课题资助项目

摘　　要：高精度齿轮是高端装备满足高速、重载、冲击、低噪声(静音)等极端环境要求的必要支撑,为提高滚齿加工精度,实现部分'以滚带磨',降低加工成本,针对滚刀几何误差与齿轮几何精度之间的定量映射规律研究不足,分别开展考虑机床运动精度的滚刀齿廓误差、滚刀螺旋线误差、滚刀安装角径向圆跳动误差与齿轮齿廓误差、基节误差之间的定量映射规律研究。通过产形齿条法,由渐开线滚刀齿廓方程包络生成齿轮齿廓方程。依据微分几何、包络原理,建立滚刀齿廓误差与齿轮齿廓误差之间的定量映射关系模型;建立滚刀螺旋线误差、滚刀安装角径向圆跳动误差与齿轮齿廓误差之间的定量映射规律模型。并根据齿轮齿廓误差与齿轮基节误差间的几何关系,计算得到上述因素对基节误差的映射规律。依据高斯分布规律,建立在考虑机床运动误差影响下,上述三种主要的滚刀误差对齿轮齿廓误差、齿轮基节误差的综合影响规律模型。最终通过仿真,并与实际加工经验进行对比,验证上述模型方法的正确性。从而揭示出滚齿加工过程中考虑机床运动误差的滚刀误差与影响齿轮主要几何精度的齿廓误差、基节误差的本质规律。为滚切更高精度的齿轮副打下理论基础。High precision gear is an necessary support of high-end equipment to meet the requirements of high-speed, heavy-duty, impact, low noise （mute） and other extreme environments. In order to improve the accuracy of hobbing manufacture, to partly achieve ＂replacing grinding with rolling＂, and to reduce processing costs, focusing on the insufficient quantitative mapping rules between hob geometry errors and gear geometric error, the quantitative mapping role research between gear hob tooth profile error, helix error, gear hob installation angle of the radial runout error and the gear tooth profile error, base pitch error with the consideration of machine tool movement error are carried out respectively. Utilizing the counterpart rack law, the gear tooth profile equation enveloping from involute curve hob tooth profile equation is generated, quantitative mapping relational model of hob pitch error and pitch deviation based on differential geometry and envelope principle is builded. At the same time quantitative mapping relational model between hob helix error, radial runout error of hob installation angle and the gear tooth profile error are established respectively. According to the geometric relations between gear tooth profile error and gear base pitch error, the mapping rule of base pitch error is calculated based on the factors mentioned above. A joint equation model between the above three main errors of gear hob and the tooth profile error based on Gaussian distribution with the consideration of machine tool movement error are builded. At last the correctness of the above model by comparing the result of model simulation method with empirical data is verified, so the essential mapping rules of hob error and the main factors which affect tooth geometric precision such as tooth profile error, base pitch error with the consideration of machine tool movement error are revealed, thus a theoretical foundation for roll cutting gear with higher precision is layed.

关 键 词：滚刀几何误差 齿轮几何精度 产形齿条法 包络原理 

分 类 号：TH161[机械工程—机械制造及自动化]