Ease-off拓扑修形斜齿轮齿面黏着磨损计算方法

王永强; 魏冰阳; 谢学凯; 李家琦

doi:10.13224/j.cnki.jasp.20210568

Ease-off拓扑修形斜齿轮齿面黏着磨损计算方法

doi: 10.13224/j.cnki.jasp.20210568

河南科技大学机电工程学院，河南洛阳 471003

基金项目: 国家自然科学基金（51875174）

详细信息

作者简介:
王永强（1987-），男，讲师，博士生，主要从事摆线针轮、谐波齿轮减速器摩擦学计算及仿真分析方面的研究

中图分类号: V231；TH132
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- 被引次数: 0
出版历程
- 收稿日期: 2021-10-09
- 网络出版日期: 2023-09-14

Ease-off surface topological modification of helical gear tooth surface calculation method of adhesive wear

School of Mechatronics Engineering， Henan University of Science and Technology，Luoyang Henan 471003，China

摘要

摘要:
从ease-off差曲面拓扑修形出发，对变位斜齿轮啮合参数进行了解析，获得了齿面接触、运动与力学参数；应用离散接触线有限元，拟赫兹点接触仿真，解决了齿面边缘接触应力集中的求解问题；利用经典摩擦磨损计算模型，快捷求解了齿面瞬时接触线上的动态磨损系数，获得了两齿面磨损量三维分布云图。结果表明：主动轮齿根处磨损量远超齿顶处，从动轮齿顶处磨损略大于齿根处;主动轮啮入区磨损变化剧烈，啮出区磨损均匀，从动轮啮入区与啮出区磨损量无明显差异；抛物线修形，使齿面的磨损向齿宽中部集中，有利于改善齿面的磨损分布。选用合适的变位系数、修形量能够调整齿面的磨损分布，延长齿面的精度寿命。为变位、修形多变量耦合斜齿轮磨损计算、减摩设计提供了理论方法。
- 拓扑修形 /
- 斜齿轮 /
- 动态磨损系数 /
- 磨损计算 /
- 三维
Abstract:
Based on ease-off surface topology, the meshing parameters of modified helical gear were analyzed, and the tooth contact, motion and mechanical parameters of gear surface were obtained. The discrete contact line finite element method simulating the point contact of Quasi Hertz was used, and the problem of stress concentration in instantaneous contact zone of tooth surface boundary was solved; using the classical friction and wear modthe dynamic wear coefficient on the instantaneous contact line of tooth surface was solved quickly. The 3D distribution nephogram wear of two tooth surfaces was obtained. The results showed that the wear at the root of the pinion gear was far greater than that at the tip, and the wear at the top of the gear was slightly greater than that at the root of the tooth. Engaging-in of the pinion wore a lot, while the engaging-out wore uniformly. The wear change of the gear in the meshing area was not obvious. Parabolic modification made the wear of tooth surface concentrated to the middle part of tooth width, helping to improve the wear distribution of tooth surface. The wear distribution of the tooth surface can be adjusted and the precision life of the tooth surface can be prolonged by selecting appropriate modification coefficient and modification quantity. It could provide a theoretical method for wear calculation and friction reduction design of modified and multivariable coupling helical gear conditions such as displacement modification.
- topology modification /
- helical gear /
- dynamic wear coefficient /
- wear calculation /
- 3D

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图 1 齿面坐标映射

Figure 1. Coordinate mapping of tooth surface

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图 2 Ease-off曲面

Figure 2. Ease-off surface

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图 3 差曲面ease-off

Figure 3. Ease-off for gear surface

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图 4 主动轮和从动轮滑移比计算

Figure 4. Calculation of driving wheel and slave wheel slip ratio

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图 5 啮合点的运动矢量图

Figure 5. Motion vector diagram of meshing point

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图 6 瞬时接触形变区假设

Figure 6. Instantaneous contact deformation region hypothesis

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图 7 离散单元接触模型

Figure 7. Discrete element contact model

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图 8 齿面累积磨损计算流程图

Figure 8. Calculation flow chart of cumulative wear on tooth surface

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图 9 回归公式磨损系数分布

Figure 9. Regression formula wear coefficient distribution

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图 10 赫兹接触应力与接触半宽

Figure 10. Hertz contact stress and contact half width

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图 11 两齿轮滑移比

Figure 11. Slip ratio of two gears

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图 12 两齿轮滑移距离

Figure 12. Slip distance of two gears

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图 13 两齿轮磨损深度

Figure 13. Wear depth of two gears

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图 14 不同变位系数两齿轮磨损分布

Figure 14. Wear distribution of two gears with different modification

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图 15 不同转矩两齿轮磨损分布

Figure 15. Wear distribution of two gears with different torques

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图 16 不同传动比小齿轮磨损分布

Figure 16. Wear distribution of pinion with different transmission ratio

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图 17 不同传动比大齿轮磨损分布

Figure 17. Wear distribution of gear with different transmission ratio

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表 1 斜齿轮副基本参数

Table 1. Basic parameters of helical gear pair

基本参数	数值
传动比${i_{12}}$	29/21
齿宽$B/{\text{mm}}$	80
模数${m_n}/{\text{mm}}$	5
泊松比$v$	0.3
压力角${\alpha _{{n} } }/ （{\text{°}}）$	20
表面粗糙度${R_{\rm{a}}}/{\text{μm} }$	0.2
润滑油压黏系数${\alpha _0}/10^{-8} （{ {\text{m} }^2}/{\text{N} }）$	1.39
顶隙系数${c^ * }$	0.25
齿顶高系数$h_{\rm{a}}^ *$	1
螺旋角$\,\beta / （^\circ ）$	13
变位系数${x_1}$	0.1
变位系数${x_2}$	−0.098
转速n/（r/min）	3000
弹性模量$E/{\text{GPa}}$	209

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参考文献(21)

[1]	DING H. Dynamic wear models for gear systems [D]. Columbus, US: The Ohio State University, 2007.
[2]	BRANDÃO J A,MARTINS R,SEABRA J H O,et al. An approach to the simulation of concurrent gear micropitting and mild wear[J]. Wear,2015,324/325: 64-73. doi: 10.1016/j.wear.2014.12.001
[3]	ARCHARD J F. Contact and rubbing of flat surfaces[J]. Journal of Applied Physics,1953,24(8): 981-988. doi: 10.1063/1.1721448
[4]	FLODIN A,ANDERSSON S. Simulation of mild wear in spur gears[J]. Wear,1997,207(1/2): 16-23.
[5]	FLODIN A,ANDERSSON S. Simulation of mild wear in helical gears[J]. Wear,2000,241(2): 123-128. doi: 10.1016/S0043-1648(00)00384-7
[6]	FLODIN A,ANDERSSON S. A simplified model for wear prediction in helical gears[J]. Wear,2001,249(3/4): 285-292.
[7]	PRIEST M,TAYLOR C M. Automobile engine tribology—approaching the surface[J]. Wear,2000,241(2): 193-203. doi: 10.1016/S0043-1648(00)00375-6
[8]	JANAKIRAMAN V,LI S,KAHRAMAN A. An investigation of the impacts of contact parameters on wear coefficient[J]. Journal of Tribology,2014,136(3): 031602. doi: 10.1115/1.4027440
[9]	王晓笋,巫世晶,陈杰,等. 考虑动载荷与动态磨损系数的直齿轮传动系统动态磨损特性[J]. 中南大学学报(自然科学版),2014,45(2): 408-413. WANG Xiaosun,WU Shijing,CHEN Jie,et al. Dynamic surface wear characteristics in spur gear transmission system with dynamic loads and wear coefficients[J]. Journal of Central South University (Science and Technology),2014,45(2): 408-413. (in Chinese)
[10]	张建阁,刘少军,方特. 混合润滑下齿面磨损预测研究及试验验证[J]. 华南理工大学学报(自然科学版),2018,46(2): 22-30. ZHANG Jiange,LIU Shaojun,FANG Te. Prediction of gear wear rate in mixed lubrication and experimental verification[J]. Journal of South China University of Technology (Natural Science Edition),2018,46(2): 22-30. (in Chinese)
[11]	何荣国,江亲瑜,姚一富. 渐开线斜齿圆柱齿轮磨损的数值仿真[J]. 润滑与密封,2007,32(3): 88-91, 130. HE Rongguo,JIANG Qinyu,YAO Yifu. Numerical simulation of tooth wearing for involute helical cylindrical gears[J]. Lubrication Engineering,2007,32(3): 88-91, 130. (in Chinese)
[12]	刘先增,鲁庆,张鹏,等. 斜齿圆柱齿轮齿面磨损建模与数值分析[J]. 安徽工业大学学报(自然科学版),2015,32(2): 147-151. LIU Xianzeng,LU Qing,ZHANG Peng,et al. Modeling and numerical simulation of surface wear for helical gears[J]. Journal of Anhui University of Technology (Natural Science),2015,32(2): 147-151. (in Chinese)
[13]	周长江,雷玉英,汪红兵,等. 准静态与动态载荷下斜齿轮齿面粘着磨损计算[J]. 机械工程学报,2018,54(23): 10-22. doi: 10.3901/JME.2018.23.010 ZHOU Changjiang,LEI Yuying,WANG Hongbing,et al. Adhesive wear models for helical gears under quasi-static and dynamic loads[J]. Journal of Mechanical Engineering,2018,54(23): 10-22. (in Chinese) doi: 10.3901/JME.2018.23.010
[14]	曹雪梅,邓效忠,聂少武. 基于共轭齿面修正的航空弧齿锥齿轮高阶传动误差齿面拓扑结构设计[J]. 航空动力学报,2015,30(1): 195-200. CAO Xuemei,DENG Xiaozhong,NIE Shaowu. Ease-off flank topography design for aviation spiral bevel gears with higher-order transmission errors by modification of conjugate flank[J]. Journal of Aerospace Power,2015,30(1): 195-200. (in Chinese)
[15]	曹雪梅,孙宁,邓效忠. 直齿锥齿轮低安装误差敏感性设计与实验验证[J]. 航空动力学报,2016,31(1): 227-232. CAO Xuemei,SUN Ning,DENG Xiaozhong. Design for straight bevel gear based on low installation error sensitivity and experiment tests[J]. Journal of Aerospace Power,2016,31(1): 227-232. (in Chinese)
[16]	魏冰阳,杨建军,仝昂鑫,等. 基于等距Ease-off曲面的轮齿啮合仿真分析[J]. 航空动力学报,2017,32(5): 1259-1265. WEI Bingyang,YANG Jianjun,TONG Angxin,et al. Tooth meshing simulation and analysis based on isometric mapping Ease-off surface[J]. Journal of Aerospace Power,2017,32(5): 1259-1265. (in Chinese)
[17]	魏冰阳,王振,杨建军,等. Ease-off拓扑修形齿面拟赫兹接触与摩擦特性分析[J]. 机械工程学报,2021,57(1): 61-67. doi: 10.3901/JME.2021.01.061 WEI Bingyang,WANG Zhen,YANG Jianjun,et al. Analysis on quasi hertzian contact and friction characteristics of tooth surface modified by ease-off topology[J]. Journal of Mechanical Engineering,2021,57(1): 61-67. (in Chinese) doi: 10.3901/JME.2021.01.061
[18]	蒋进科,刘钊,刘红梅. Ease-off修形准双曲面齿轮齿面动态抗磨设计与分析[J]. 机械工程学报,2021,57(19): 155-164. doi: 10.3901/JME.2021.19.015 JIANG Jinke,LIU Zhao,LIU Hongmei. Dynamic anti-wear design and analysis for hypoid gears with ease-off flank modification[J]. Journal of Mechanical Engineering,2021,57(19): 155-164. (in Chinese) doi: 10.3901/JME.2021.19.015
[19]	蒋进科,刘钊,刘红梅. 齿面磨损最小直齿锥齿轮Ease-off修形设计与分析[J]. 西安交通大学学报,2020,54(6): 99-106. JIANG Jinke,LIU Zhao,LIU Hongmei. Design and analysis for straight bevel gears with ease-off flank modification based on minimal wear[J]. Journal of Xi’an Jiaotong University,2020,54(6): 99-106. (in Chinese)
[20]	魏冰阳,李家琦,王文胜. 基于差齿面拓扑的轮齿承载拟赫兹接触分析[J]. 中国机械工程,2021,32(18): 2174-2180. WEI Bingyang,LI Jiaqi,WANG Wensheng. Quasi-hertz loaded tooth contact analysis of gears based on ease-off surface topology[J]. China Mechanical Engineering,2021,32(18): 2174-2180. (in Chinese)
[21]	徐大伟,奔霖,沈伟. 直齿齿轮机构齿面磨损估算[J]. 航天工艺,2001(6): 4-8. XU Dawei,BEN Lin,SHEN Wei. Estimation of tooth surface wear of spur gear mechanism[J]. Aerospace Manufacturing Technology,2001(6): 4-8. (in Chinese)