斜齿轮的有效长度和收尾长度的计算  

Calculation of the Effective Length and the Run-Out Length of Helical Gears

作　　者：陈涛 CHEN Tao(Zhejiang Wanda Steering Gear Co.,Ltd,Hangzhou 311258,Zhejiang,China)

机构地区：[1]浙江万达汽车方向机有限公司,浙江杭州311258

出　　处：《机械研究与应用》2024年第5期110-113,共4页Mechanical Research & Application

摘　　要：文章基于理论分析并应用Lagrange乘数法以及求解一个一元四次方程,推导得到了与圆柱型齿条配合的斜齿轮所需要的有效长度的解析表达式,并通过SolidWorks软件验证了其正确性。再通过求解一元四次方程,推导得到了斜齿轮的滚齿收尾部分最远端到垂直于工件轴线且包含退刀时滚刀轴线和工件轴线的最短距离线所在平面的距离,即滚齿收尾长度的解析表达式,并通过SolidWorks软件验证了其正确性。这两个表达式为与斜齿轮相关的机械产品的设计提供了重要依据。Based on theoretical analysis,through applying the Lagrange multiplier method and solving a quartic equation of one variable,the analytic expression of the effective length of a helical gear fitted with a cylindrical rack is derived;then the correctness is verified by the SolidWorks software.Based on theoretical analysis,and through solving a quartic equation with one variable,the analytic expression of distance between the farthest end of hobbing and the plane perpendicular to the workpiece axis and containing the shortest distance line between the hobbing axis and the workpiece axis is derived,this distance is the hobbing run-out length of a helical gear.Then the correctness is verified by SolidWorks software.These two expressions provide an important basis for design of the helical gear related mechanical products.

关 键 词：斜齿轮 滚齿 有效长度 收尾长度 

分 类 号：TH132.41[机械工程—机械制造及自动化] O29[理学—应用数学]