Digital Simulation of Worm Gear Machining with Oversize Hob Using Discrete Envelope Method

GUO Xiang; CHANG Haifeng; ZHENG Pantuo; JIA Kang

doi:10.7652/xjtuxb202610020

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Digital Simulation of Worm Gear Machining with Oversize Hob Using Discrete Envelope Method

更新时间：2026-09-29

- Digital Simulation of Worm Gear Machining with Oversize Hob Using Discrete Envelope Method
- Journal of Xi'an Jiaotong University Vol. 60, Issue 10, Pages: 231-241(2026)
- 作者机构：
  
  西安交通大学现代设计与轴承转子系统教育部重点实验室，710049，西安
  西安交通大学机械工程学院，710049，西安
  汉江工具责任有限公司，723000，陕西汉中
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202610020
  CLC： TH132
- Received：24 February 2026，
  
  Online First：09 May 2026，
  
  Published：10 October 2026
- 稿件说明：
移动端阅览
GUO Xiang, CHANG Haifeng, ZHENG Pantuo, et al. Digital Simulation of Worm Gear Machining with Oversize Hob Using Discrete Envelope Method[J/OL]. Journal of Xi'an Jiaotong University,2026,60 (10):231-241. https://doi.org/10.7652/xjtuxb202610020.
DOI：

GUO Xiang, CHANG Haifeng, ZHENG Pantuo, et al. Digital Simulation of Worm Gear Machining with Oversize Hob Using Discrete Envelope Method[J/OL]. Journal of Xi'an Jiaotong University,2026,60 (10):231-241. https://doi.org/10.7652/xjtuxb202610020. DOI：

摘要

针对传统解析法处理蜗轮修形边界易数值发散，且实体仿真效率低、难获底层数据等问题，提出一种基于离散包络原理的增径滚刀蜗轮加工数字仿真建模方法。通过构建增径滚刀加工蜗轮的运动数学模型，基于蜗轮齿面栅格划分，对蜗轮多截面进行离散切削交线族数值包络以构建蜗轮齿面；采用VERICUT仿真软件验证了方法的有效性，系统分析了增径系数和蜗杆头数对齿面拓扑形貌的影响规律。研究结果表明：与经典空间啮合解析法相比，该离散包络算法在全齿面域内的最大绝对法向逼近误差可严格收敛至1μm数量级，仿真有效工作区域的几何误差可严格控制在0.001mm以内，局部残余误差不超过0.01mm；增径系数主导修形量级，当增径系数从1.05提升至1.20时，单头与三头蜗杆边缘的最大负偏差分别由-0.03、-0.04mm增大至-0.1184、-0.1537mm；蜗杆头数决定误差分布形态，多头蜗杆导程角效应使得啮入与啮出端修形呈现非对称扭曲。该研究可为工程中增径工艺参数选取、蜗轮副加载齿面接触分析以及抗磨损主动修形设计提供三维几何基础。

Abstract

To address the issues of traditional analytical methods

such as numerical divergence when handling worm gear modification boundaries

as well as the low efficiency and difficulty in obtaining underlying data in solid simulations

a digital simulation modeling method for worm gear machining with an oversize hob based on the discrete envelope principle is proposed. A kinematic mathematical model for worm gear machining with an oversize hob is constructed. Based on the grid division of the worm gear tooth flank

the tooth flank is generated through the numerical envelope of discrete cutting intersection line families across multiple sections of the worm gear. The validity of the proposed method is verified using VERICUT simulation software

and the influence patterns of the oversize coefficient and the number of worm threads on the tooth flank topography are systematically analyzed. The results show that compared with the classical spatial meshing analytical method

the maximum absolute normal approximation error of the discrete envelope algorithm over the entire tooth flank domain strictly converges to the order of 1μm; the geometric error in the effective working region of the simulation is strictly controlled within 0.001mm

with local residual errors not exceeding 0.01mm. The oversize coefficient dominates the modification magnitude: when the oversize coefficient increases from 1.05to 1.20

the maximum negative deviations at the edges of single- and triple-thread worms increase from -0.03mm and -0.04mm to -0.1184mm and -0.1537mm

respectively. The number of worm threads determines the error distribution pattern; the lead angle effect of multi-thread worms causes asymmetric distortion of the modification at the mesh-in and mesh-out ends. This study provides a three-dimensional geometric foundation for the selection of oversize process parameters

loaded tooth contact analysis of worm gear pairs

and proactive modification design for wear resistance in engineering practice.

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