少齿数渐开线齿轮根切半径的改进计算方法  

An Improved Method for Calculating Undercut Radius of Involute Spur Gear with Small Tooth Number

作　　者：孙付春 杨栗 吴昌明 杨涛 袁影 Sun Fuchun;Yang Li;Wu Changming;Yang Tao;Yuan Ying(School of Mechanical Engineering,Chengdu University,Chengdu 610106,China)

机构地区：[1]成都大学机械工程学院,四川成都610106

出　　处：《机械传动》2018年第11期180-183,共4页Journal of Mechanical Transmission

基　　金：四川省教育厅自然科学重点资助项目(16ZA0382)

摘　　要：为正确计算出少齿数渐开线齿轮由滚齿加工所引起的根切半径。首先,实例分析了现有计算方法的适用范围;其次,针对少齿数渐开线齿轮的滚齿加工特点,基于放宽齿廓在根切点上的相切连续条件,提出由刃心转置角度所决定的改进计算方法;最后,给出了该种齿轮的全参数化齿廓方程。结果表明,现有计算方法仅适用于弧刃半径系数上限(由齿刀几何结构所决定)大于其下限(由成功的滚齿加工所决定)的情况;少齿数齿轮的弧刃半径系数上限却小于其下限,现有的计算方法不适用;刃心转置角度却大于20°的直刃压力角;通过弧刃半径系数的标准化优选,可以实现少齿数齿轮的无根切滚齿加工;所给出的根切齿轮模型,正确可靠,参数化性能好。为少齿数渐开线齿轮的后续其他计算,提供正确的理论基础。For successful calculating undercut radius from hobbed machining of involute spur gear with small tooth number.Firstly,the application scope of the conventional calculation method is analyzed by two examples.Secondly,because of the special feature of gear hobbed machining with small tooth number,the tangent continuity condition of gear profile on undercut point must be neglected,and from center transposed angle of arc blade of undercut point,an developed method for calculating undercut radius is derived.Finally,all parameterized tooth profile equations of the gear is created.All results indicated that the conventional calculation method is applicable only the condition of upper radius coefficient limit determined by rack cutter geometry greater than its lower limit determined by successful gear hobbed machining,unfortunately,for the involute spur gear with small tooth number,its upper limit usually is less than its lower limit,so the conventional calculation method isn′t applicable for calculating undercut radius.The center transposed angle of arc blade really is greater than the pressure angle with 20°of straight blade,the hobbed machining is successful from optimized normative radius coefficient of arc blade for the gear with small tooth number.The created 3D gear model is reliability and fully parameterized,etc.It is concluded that the developed calculation method as an theoretical basis is provided for other followed calculating of involute spur gear with small tooth number.

关 键 词：少齿数 渐开线齿轮 根切半径 滚齿加工 

分 类 号：TH132.413[机械工程—机械制造及自动化]