Analysis on inverse method for design parameters of involute spur gears with unilateral tooth profile wear

LI Xueyi; WU Zongkun; NIU Xingwang; ZHANG Zhenhang; YANG Tong

doi:10.16578/j.issn.1004.2539.2026.03.007

您当前的位置：

首页 >

文章列表页 >

Analysis on inverse method for design parameters of involute spur gears with unilateral tooth profile wear

Structural Design and Parameter Optimization | 更新时间：2026-05-27

- Analysis on inverse method for design parameters of involute spur gears with unilateral tooth profile wear
- Journal of Mechanical Transmission Vol. 50, Issue 3, Pages: 53-60(2026)
- 作者机构：
  
  山东科技大学机械电子工程学院，青岛 266590
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2026.03.007
  CLC： TH132.413
- Received：07 December 2024，
  
  Revised：2025-02-11，
  
  Published：15 March 2026
- 稿件说明：
移动端阅览
李学艺，吴宗坤，牛兴旺，等. 单侧齿廓磨损的渐开线直齿轮设计参数反求方法分析［J］. 机械传动，2026，50（3）：53-60.

LI Xueyi，WU Zongkun，NIU Xingwang，et al. Analysis on inverse method for design parameters of involute spur gears with unilateral tooth profile wear［J］. Journal of Mechanical Transmission，2026，50（3）：53-60.
李学艺，吴宗坤，牛兴旺，等. 单侧齿廓磨损的渐开线直齿轮设计参数反求方法分析［J］. 机械传动，2026，50（3）：53-60. DOI： 10.16578/j.issn.1004.2539.2026.03.007.

LI Xueyi，WU Zongkun，NIU Xingwang，et al. Analysis on inverse method for design parameters of involute spur gears with unilateral tooth profile wear［J］. Journal of Mechanical Transmission，2026，50（3）：53-60. DOI： 10.16578/j.issn.1004.2539.2026.03.007.

摘要

目的

进口设备和老旧设备中的传动齿轮磨损失效后，因缺乏原始设计资料往往无法修复和更换，导致整个设备提前报废。为此，提出一种基于视觉检测的单侧齿廓磨损渐开线直齿轮设计参数反求方法。

方法

首先，采用高精度视觉检测系统获取齿轮的端面齿廓图像，基于齿轮结构原理有效提取并分割齿廓特征点列；然后，利用渐开线齿廓的几何特性对磨损齿廓进行有效识别，并用未磨损侧标准齿廓对磨损齿廓进行重构，获得原始设计齿廓；最后，利用重构渐开线直齿轮齿廓的结构尺寸求解出齿轮的设计参数。

结果

试验结果表明，采用所提方法求得的齿轮模数、压力角与理论值一致，变位系数及其他基本参数的绝对误差均小于0.035 mm，满足制造精度的要求。此外，所提方法具有无接触、操作简便、检测结果稳定、受齿轮磨损程度影响小的优势。

Abstract

Objective

The failure of transmission gears in imported and aged equipment due to tooth flank wear often leads to premature scrapping of the entire machine

as original design data is frequently unavailable for repair or replacement. To address this issue

a method for reverse-engineering the design parameters of involute spur gears with unilateral tooth flank wear based on visual inspection was proposed.

Methods

Firstly

a high-precision visual inspection system was used to obtain the end face tooth profile images of the gear. Based on the principle of the gear structure

the tooth profile feature point sequences were effectively extracted and segmented. Then

the geometric characteristics of the involute tooth flank were utilized to accurately identify the worn tooth flank

which was then reconstructed using the standard tooth flank from the unworn side to obtain the original design tooth flank. Finally

the design parameters of the gear were solved by using the structural dimensions of the reconstructed involute spur gear tooth profile.

Results

The test results show that the gear modulus and pressure angle obtained by the proposed method are consistent with the theoretical values

and the absolute errors of the profile shift coefficient and other basic parameters are all less than 0.035 mm

meeting the requirements of manufacturing precision. In addition

the proposed method has the advantages of non-contact

simple operation

stable detection results

and being less affected by the degree of gear wear.

关键词

Keywords

references

GOCH G ， GUENTHER A ， PENG Y ， et al . Gear metrology-an update ［J］. CIRP Annals ， 2023 ， 72 （ 2 ）： 725 - 751 .

石照耀，于渤，宋辉旭，等 . 20年来齿轮测量技术的发展［J］. 中国机械工程， 2022 ， 33 （ 9 ）： 1009 - 1024 .

SHI Zhaoyao ， YU Bo ， SONG Huixu ， et al . Development of gear measurement technology during last 20 years ［J］. China Mechanical Engineering ， 2022 ， 33 （ 9 ）： 1009 - 1024 .

陈朝伟，范芳蕾，黄伟莉 . 基于机器视觉的齿轮参数测量系统［J］. 机电工程技术， 2023 ， 52 （ 5 ）： 113 - 116 .

CHEN Zhaowei ， FAN Fanglei ， HUANG Weili . Gear parameter measurement system based on machine vision ［J］. Mechanical & Electrical Engineering Technology ， 2023 ， 52 （ 5 ）： 113 - 116 .

程敏杰，王建文 . 利用机器视觉的直齿轮在线测量方法研究［J］. 机械设计， 2020 ， 37 （ 3 ）： 19 - 22 .

CHENG Minjie ， WANG Jianwen . Research on the in-site measurement of spur gears based on machine vision ［J］. Journal of Machine Design ， 2020 ， 37 （ 3 ）： 19 - 22 .

MORU D K ， BORRO D . A machine vision algorithm for quality control inspection of gears ［J］. The International Journal of Advanced Manufacturing Technology ， 2020 ， 106 （ 1 ）： 105 - 123 .

汤洁，刘小兵，李睿 . 未知参数小模数齿轮齿距和齿廓偏差视觉测量［J］. 光学精密工程， 2021 ， 29 （ 1 ）： 100 - 109 .

TANG Jie ， LIU Xiaobing ， LI Rui . Vision measurement of pitch and profile deviations for small modulus gears with unknown parameters ［J］. Optics and Precision Engineering ， 2021 ， 29 （ 1 ）： 100 - 109 .

方一鸣，石照耀 . 小模数直齿轮免参数并行快速测量［J］. 光学精密工程， 2024 ， 32 （ 6 ）： 792 - 805 .

FANG Yiming ， SHI Zhaoyao . Parameter-free parallel fast measurement of fine-pitch spur gears ［J］. Optics and Precision Engineering ， 2024 ， 32 （ 6 ）： 792 - 805 .

刘小霞 . 逆向工程在渐开线圆柱直齿轮测绘中的应用［J］. 煤矿机电， 2019 ， 40 （ 5 ）： 67 - 70 .

LIU Xiaoxia . Application of reverse engineering in surveying and mapping of involute cylindrical gears ［J］. Colliery Mechanical & Electrical Technology ， 2019 ， 40 （ 5 ）： 67 - 70 .

陆国 . 齿轮测绘的最优化方法研究及其系统实现［D］. 北京：北京交通大学， 2010 ： 25 - 31 .

LU Guo . Research on optimization method of gear mapping and its system realization ［D］. Beijing ： Beijing Jiaotong University ， 2010 ： 25 - 31 .

尤红丹 . 基于逆向工程技术的零件磨损检测与分析［D］. 南昌：南昌大学， 2009 ： 54 - 64 .

YOU Hongdan . Inspection and analysis of parts wear based on reverse engineering technology ［D］. Nanchang ： Nanchang University ， 2009 ： 54 - 64 .

GROMPONE VON GIOI R ， RANDALL G . A sub-pixel edge detector：an implementation of the Canny/Devernay algorithm ［J］. Image Processing on Line ， 2017 （ 7 ）： 347 - 372 .

ZHANG Z . A flexible new technique for camera calibration ［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence ， 2000 ， 22 （ 11 ）： 1330 - 1334 .

魏建杰，汤洁，石照耀 . 基于齿廓测量点的渐开线齿轮基圆圆心反求方法［J］. 航空制造技术， 2019 ， 62 （ 20 ）： 70 - 76 .

WEI Jianjie ， TANG Jie ， SHI Zhaoyao . Reverse calculation method of base circle center based on involute profile measuring points ［J］. Aeronautical Manufacturing Technology ， 2019 ， 62 （ 20 ）： 70 - 76 .

全国齿轮标准化技术委员会 . 通用机械和重型机械用圆柱齿轮标准基本齿条齿廓： GB/T 1356—2001 ［S］. 北京：中国标准出版社， 2001 ： 12 - 17 .

National Technical Committee of Gear Standardization . Cylindrical gears for general and heavy engineering—standard basic rack tooth profile ： GB/T 1356—2001 ［S］. Beijing ： Standards Press of China ， 2001 ： 12 - 17 .

《齿轮手册》编委会 . 第2篇渐开线圆柱齿轮传动［M］// 齿轮手册（上册） . 北京：机械工业出版社， 2013 ： 3 - 34 .

Gear Handbook Editorial Board . Chapter 2 ： involute cylindrical gear transmission ［M］//Gear handbook （volume I）. Beijing ： China Machine Press ，2013： 3 - 34 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Bearing Feature Extraction Method Based on the Time Subsequence

Fault Diagnosis of Fan Bearings Based on an Improved Grey Wolf Optimization Algorithm and SVM

Gear Pitting Fault Diagnosis Based on Improved Variational Modal Decomposition

Feature Extraction of Weak Fault for Rolling Bearing based on Improved SSD Denoising

Gearbox Fault Diagnosis based on Time-frequency Combination Feature Extraction and Manifold Learning of MS-LTSA

Related Author

Yu Yongsheng

Zheng Zhifei

Nie Fei

Wang Dexue

Xie Lirong

Xiang Zhicheng

Abulizi Maimaitireyimu

Liu Jinyan

Related Institution

IOT Engineering College, Wuxi City College of Vocational Technology

School of Information Management, Wuxi Institute of Communications Technology

School of Electrical Engineering, Xinjiang University

First Military Representative Office of the Army Equipment Office in Beijing

School of Mechanical Engineering，Beijing Institute of Technology

⁰