Ease-off修形准双曲面齿轮齿面动态抗磨设计与分析

doi:10.3901/JME.2021.19.015

摘要/Abstract

摘要： 为了改善准双曲面齿轮动态性能、减小齿面磨损提出齿面动态抗磨修形设计与分析方法。小轮修形齿面表示为共轭齿面与法向Ease-off曲面两个矢量的和，Ease-off曲面通过预置抛物线修形参数及几何传动误差参数表达。提出考虑磨损深度影响的齿面承载接触分析（Tooth contact analysis with wear，WLTCA）数值方法，该方法通过承载接触分析（Tooth contactanalysis，LTCA）方法获得啮合刚度及齿面静载荷，在此基础上根据动力学分析获得齿面动载荷，结合Archard磨损公式进一步获得齿面磨损量，将齿形更新时的同时啮合齿对的磨损量叠加到齿对的初始间隙，为磨损后的LTCA计算提供准确的参数，重复以上循环可得到齿形更新后齿面上任一点的磨损深度及次数。以无磨损时法向相对振动加速度均方根最小、齿面磨损量最小进行修形优化获得最优Ease-off曲面；分析齿面磨损与系统动态响应之间的耦合作用。结果表明最优Ease-off齿面主要通过齿廓修形减少了磨损量，有效改善了系统动态响应。该方法充分考虑了齿面修形、磨损、动态响应的耦合性且计算效率较高，为高性能准双曲面齿轮齿面抗磨、减振设计与分析提供理论参考。

关键词: 准双曲面齿轮, Ease-off修形, 动态磨损, 承载接触分析, 振动

Abstract: Methods of ease-off flank modification are developed to improve the dynamic performances and reduce tooth wear for hypoid gears. Firstly，the modified pinion are expressed by a sum of two vector of conjugate tooth of the gear and its normal ease-off modification represented by functions of both profile modification curves and predesigned transmission error. Secondly，a numerical method of loaded tooth contact analysis with wear(WLTCA) is proposed，and its principle are that: meshing stiffness and static loads are obtained based on loaded tooth contact analysis(LTCA)，and then based on which the dynamic loads are achieved by dynamic analysis，and then tooth wear depth are acquired based on Archard wear formula，and then the wear depth of simultaneous meshing tooth pairs are added to the initial clearances which provided with accurate parameters for the next LTCA，and then the both wear times and depths are calculated by repeating the above steps. Thirdly，the best ease-off deviations are determined by minimizing mean square value of normal vibration and tooth wear depths based on optimization algorithm. Finally，coupling action between tooth wear and dynamic responses are revealed. Besides，results show that the best ease-off tooth is mainly characterized by profile modification，and reduces the wear and improves the dynamic response. The approach fully considers the coupling of dynamic responses，tooth surface modification and wear，and provides with a theoretical reference of dynamic anti-wear and vibration reduction for the high performances hypoid gears.

Key words: hypoid gear, ease-off modified, tooth dynamic wear, LTCA, vibration

中图分类号:

TH132
TH117

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.

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.

参考文献

[1] FLODIN A,ANDERSSON S. Simulation of mild wear in spur gears[J]. Wear,1997,207(12):16-23.
[2] 朱丽莎,向磊,邹常青.齿间动态载荷分配下的齿轮磨损分析[J].西安交通大学学报,2018,52(5):80-85. ZHU Lisha,XIANG Lei,ZOU Changqing.Wear analysis of gears under dynamic load distribution between gear teeth[J]. Journal of Xi'an Jiao Tong University,2018,52(5):80-85.
[3] MASJEDI M,KHONSARI M M. On the prediction of steady-state wear rate in spur gears[J]. Wear,2015,342:234-243.
[4] 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.
[5] 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.
[6] KAHRAMAN A,BAJPAI P,ANDERSON N E. Influence of tooth profile deviations on helical gear wear[J]. Journal of Mechanical Design,2005,127(4):656-663.
[7] BAJPAI P,KAHRAMAN A,ANDERSON N E. A surface wear prediction methodology for parallel-axis gear pairs[J]. Journal of Tribology,2004,126(3):597-605.
[8] HüSEYIN I,HAYRETTIN D. Relation between wear and tooth width modification in spur gears[J]. Wear,2007,262(3-4):390-394.
[9] 张俊,卞世元,鲁庆,等.准静态工况下渐开线直齿轮齿面磨损建模与分析[J].机械工程学报,2017,53(5):136-144. ZHANG Jun,BIAN Shiyuan,LU Qing,et al. Quasi-static-model-based wear analysis of spur gears[J]. Journal of Mechanical Engineering,2017,53(5):136-144.
[10] 潘冬,赵阳,李娜,等.齿轮磨损寿命预测方法[J].哈尔滨工业大学学报,2012,44(9):29-33. PAN Dong,ZHAO Yang,LI Na,et al. The wear life prediction method of gear system[J]. Journal of Harbin Institute of Technology,2012,44(9):29-33.
[11] 周长江,汪红兵,雷玉英.齿轮磨损计算与测试方法及抑制技术[J].北京工业大学学报,2018,44(7):987-1000. ZHOU Changjiang,WANG Hongbing,LEI Yuying,et al. Calculating and measuring methods for gear wear and its suppression techniques[J]. Journal of Beijing University of Technology,2018,44(7):987-1000.
[12] PARK D,KAHRAMAN. A surface wear model for hypoid gear pairs[J]. Wear,2009,267(9-10):1595-1604.
[13] YUKSEL C,KAHRAMAN A. Dynamic tooth loads of planetary gear sets having tooth profile wear[J]. Mechanism and Machine Theory,2004,39(7):695-715.
[14] DING H,KAHRAMAN A. Interactions between nonlinear spur gear dynamics and surface wear[J]. Journal of Sound and Vibration,2007,307(3-5):662-679.
[15] OSMAN T,VELEX P. Static and dynamic simulations of mild abrasive wear in wide-faced solid spur and helical gears[J]. Mechanism and Machine Theory,2010,45(6):911-924.
[16] 杨勇,王家序,周青华,等.考虑摩擦的磨损和修形齿轮啮合刚度计算[J].工程科学与技术,2018,50(2):212-219. YANG Yong,WANG Jiaxu,ZHOU Qinghua,et al. Stiffness calculation considering friction for a spur gear with tooth wear and profile modification[J] Advanced Engineering Sciences,2018,50(2):212-219.
[17] 冯松,毛军红,谢友柏.齿面磨损对齿轮啮合刚度影响的计算与分析[J].机械工程学报,2015,51(15):27-32. FENG Song,MAO Junhong,XIE Youbai. Analysis and calculation of gear mesh stiffness with tooth wear[J]. Journal of Mechanical Engineering,2015,51(15):27-32.
[18] 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):24-36. 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):24-36.
[19] 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.
[20] KOLIVAND M,KAHRAMAN A. An ease-off based method for loaded tooth contact analysis of hypoid gears having local and global surface deviations[J]. Journal of Mechanical Design,2010,132(7):071004.
[21] ARTONI A,KOLIVAND M,KAHRAMAN A. An ease-off based optimization of the loaded transmission error of hypoid gears[J]. Journal of Mechanical Design. 2010,132:011010-1-9.
[22] 蒋进科,方宗德,刘钊. Ease-off拓扑修形准双曲面齿轮齿面多目标优化设计方法[J].西安交通大学学报,2019,53(6):44-53. JIANG Jinke,FANG Zongde,LIU Zhao. Design of multi-objective tooth optimization for hypoid gear with ease-off topological modification[J]. Journal of Xi'an Jiao Tong University,2019,53(6):44-53.
[23] PRIEST M,TAYLOR C M. Automobile engine tribology-approaching the surface[J].Wear,2000,241(2):193-203.