Undercutting mechanism of worm wheel in offsetting normal arc-toothed cylindrical worm drive  

偏置法向圆弧齿蜗杆副的蜗轮根切机理

作　　者：MENG Qing-xiang JIAO Yu-ge ZHAO Ya-ping MU Shi-bo CUI Jian ZHANG Ming-hua 孟庆祥;焦宇鸽;赵亚平;穆士博;崔健;张明华

机构地区：[1]School of Mechanical Engineering,Yanshan University,Qinhuangdao 066004,China [2]School of Mechanical Engineering and Automation,Northeastern University,Shenyang 110819,China [3]School of Mechanical Engineering,Shenyang University of Technology,Shenyang 110870,China [4]Hebei Innovation Center for Equipment Lightweight Design and Manufacturing,Yanshan University,Qinhuangdao 066004,China

出　　处：《Journal of Central South University》2025年第2期495-508,共14页中南大学学报(英文版)

基　　金：Projects(52205069,52075083,52304049)supported by the National Natural Science Foundation of China;Project(2021-BS-164)supported by the Liaoning Province Doctoral Research Startup Fund,China;Project(LJKZ0264)supported by the Science and Technology Research Projects of Education Department of Liaoning Province,China;Project(G2022003010L)supported by the High-end Foreign Experts Recruitment Plan of China;Project(E2021203095)supported by the Natural Science Foundation for Young Scholars of Hebei Province,China。

摘　　要：The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The normal vector used to calculate the first-type limit function is determined in the natural frame without the aid of the curvature parameter of worm helicoid.The first-type limit line is ascertained via solving the nonlinear equations iteratively.It is discovered that one first-type limit line exists on the tooth surface of worm wheel by numerical simulation,and such a line is normally located out of the meshing zone.Only one intersection point exists between the first and second-types of limit lines,and this point is a lubrication weak point.The undercutting mechanism is essentially that a part of the meshing zone near the conjugated line of worm tooth crest will come into the undercutting area and will be cut off during machining the worm wheel.The machining simulation verifies the correctness of undercutting mechanism.Moreover,a convenient and practical characteristic quantity is proposed to judge whether the undercutting exists in the whole meshing zone via computing the first-type limit function values on the worm tooth crest.本文主要研究了偏置法向圆弧齿蜗杆副的蜗轮根切机理。蜗杆在其偏置法截面内的齿廓为一段圆弧。借助于蜗杆螺旋面的曲率参数,在自然标架内求得了蜗杆副的瞬时接触线的法矢量,并将其用于计算蜗杆副的一类界限函数。在此基础上,通过迭代求解非线性方程组计算得到了蜗杆副的一类界线,即曲率干涉界线。数值计算结果表明,在蜗轮齿面上存在一条曲率干涉界线,该曲率干涉界线与二类界线存在唯一的交点,且该点通常为润滑弱点。一般情况下,曲率干涉界线不会进入蜗杆副啮合区,若蜗杆副参数不合理,曲率干涉界线则将会进入啮合区,并将啮合区分为干涉区与非干涉区,从而使蜗轮产生根切。蜗轮的根切在本质上是蜗杆齿顶的部分共轭线和蜗杆副的部分啮合区进入了干涉区,并且在加工蜗轮时它们都会被切除掉。并通过仿真加工验证了根切机理的正确性。此外,通过计算蜗杆齿顶处一类界限函数值,本文还提出了一个简洁实用的特征量用于判断蜗杆副啮合区内是否存在曲率干涉。

关 键 词：cylindrical worm drive undercutting mechanism limit line nonlinear equations meshing zone 

分 类 号：TH132.4[机械工程—机械制造及自动化]