一种基于刀倾全展成法滚切准双曲面齿轮的数学模型  

Mathematical model for hobbing hypoid gears based on Spiroflex method

作　　者：沈玲莉[1] 陆宝山[2] 季业益[2] 关集俱 SHEN Ling-li;LU Bao-shan;JI Ye-yi;GUAN Ji-ju(Department of Mechanical and Electrical Engineering,Suzhou Vocational Institute of Industrial Technology,Suzhou 215104;Department of Precision Manufacturing Engineering,Suzhou Vocational Institute of Industrial Technology,Suzhou 215104)

机构地区：[1]苏州工业职业技术学院机电工程系,江苏苏州215104 [2]苏州工业职业技术学院精密制造工程系,江苏苏州215104

出　　处：《机械设计》2023年第2期111-117,共7页Journal of Machine Design

基　　金：江苏省自然科学基金青年项目(BK20170373);国家自然科学基金青年项目(51805345);江苏高校“青蓝工程”资助项目(2019);苏州市重点实验室资助项目(SZS201815)。

摘　　要：以通用型摇台式切齿机的坐标系统为基础,推导出基于刀倾全展成法(Spiroflex)滚切准双曲面齿轮的数学模型。首先,对通用型摇台式机床的机械设定进行转换,使其适用于当前新式6轴齿轮切齿机的坐标系统;然后,计算出6轴齿轮切齿机的机械坐标,编制出准双曲面齿轮刀倾全展成法滚切加工的加工程序;最后,用VERICUT仿真软件模拟准双曲面齿轮的滚切加工,并比较模拟齿轮与理论齿轮间的齿面误差。结果表明,模拟齿轮与理论齿轮间的齿面点位置误差及齿厚误差值均小于50μm,验证了该数学模型在6轴CNC齿轮切齿机上实施准双曲面齿轮的刀倾全展成法加工具有较高的准确性。In this article,based on the coordinate system of the universal cradle-type gear-cutting machine,the mathematical model of hobbing the hypoid gears is derived based on the Spiroflex method.Firstly,the mechanical setting of the universal cradle-type machine is converted,which makes it suitable for the coordinate system of the new vertical six-axis gear-cutting machine;then,the mechanical coordinates of the six-axis gear-cutting machine are calculated,and the machining process of hobbing the hypoid gears by means of the the Spiroflex method is formulated.Finally,the VERICUT software is used to simulate how to hob the hypoid gears and compare the tooth-surface error between the simulated gear and the theoretical gear.The results show that both the tooth-surface position error and the tooth-thickness error between the simulated gear and the theoretical gear are less than 50μm.It is proved that the mathematical model has high accuracy in hobbing the hypoid gears on the six-axis CNC gear-cutting machine with the help of the Spiroflex method.

关 键 词：刀倾全展成法 准双曲面齿轮 数学模型 齿面误差 

分 类 号：TG156[金属学及工艺—热处理]