考虑轮辐刚度和齿廓修形的渐开线直齿轮动载荷研究

doi:10.3969/j.issn.1000-1093.2018.06.026

兵工学报 ›› 2018, Vol. 39 ›› Issue (6): 1239-1248.doi: 10.3969/j.issn.1000-1093.2018.06.026

• 研究简报 • 上一篇

考虑轮辐刚度和齿廓修形的渐开线直齿轮动载荷研究

李春明¹，王成¹，杜明刚¹，赵志刚²

(1.中国北方车辆研究所车辆传动重点实验室，北京 100072； 2.陆军装备部项目管理办公室，北京 100072）

收稿日期:2017-09-08 修回日期:2017-09-08 上线日期:2018-07-29
作者简介:李春明(1964—)，男，研究员，博士。E-mail: chmli@noveri.com.cn；
杜明刚(1973—)，男，研究员。E-mail:mgdu@noveri.com.cn
基金资助:
国家国防科技工业局基础产品创新科研项目(2018年)；武器装备预先研究项目(41402050202)

Analysis of Dynamic Load of Spur Gears Considering the Gear Body Stiffness and Tooth Profile Modification

LI Chun-ming¹, WANG Cheng¹, DU Ming-gang¹, ZHAO Zhi-gang²

(1.Science and Technology on Vehicle Transmission Laboratory, China North Vehicle Research Institute, Beijing 100072, China; 2.Project Management Office, Department of Army Equipment, Beijing 100072, China)

Received:2017-09-08 Revised:2017-09-08 Online:2018-07-29

摘要/Abstract

摘要： 为解决高速重载车辆渐开线直齿轮功率密度低和振动载荷大问题，开展轮辐刚度和齿廓修形对齿轮动载荷影响规律研究。考虑轮辐刚度、齿廓修形和齿轮实际运动状态，结合解析法建立了齿轮啮合刚度模型，将该模型与10自由度横-扭-摆耦合非线性动力学模型进行耦合计算。结果表明：随着转速增加，齿轮动载荷均呈驼峰状变化，多数转速下薄壁轮缘齿轮动载荷较大，其中，动态啮合力第2阶和第6阶啮频对应的幅值明显增加；随着转矩增加，齿轮动载荷总体均呈抛物线减小，但薄壁轮缘齿轮存在局部峰值；随着修形量增加，齿轮动载荷均呈U形变化；存在最优修形量使动载荷达到最小，当修形量超过最优值时薄壁轮缘齿轮动载荷变化平缓；当修形量超过某临界值时修形齿轮动载荷大于无修形齿轮，且薄壁轮缘齿轮临界修形量较大；短修形齿轮动载荷总体均呈U形变化，长修形齿轮动载荷急剧减小，说明长修形可更有效地减弱齿轮振动。

关键词: 渐开线直齿轮, 啮合刚度, 齿廓修形, 动载荷

Abstract: The influences of gear bodies, input speed, torque and tip relief on dynamic load of gear pair are studied to solve the low power density and high dynamic load of spur gear for high speed heavy-duty vehicles. A gear mesh stiffness model is established for spur gear, in which the gear body stiffness, profile modification and actual motion state of gear are considered. The gear mesh stiffness model is coupled into the 10 degrees-of-freedom lateral-torsional-rocking nonlinear dynamic model of a single stage gear system. The results show that the dynamic load of gear changes in the form of hump-like shape with the increase in speed, and the change trend of dynamic load remain almost the same at many rotating speeds. While the dynamic load of light-weight gear are much larger at various speeds, especially the amplitudes corresponding to the second- and sixth-order harmonics of mesh frequency of dynamic mesh force are obviously increased. With the increase in torque, the dynamic load of gear body is reduced in the form of a parabola, while the dynamic load of light-weight gear reaches to its local maximum. With the increase in tip relief amount, the dynamic load changes in the form of “U” type, and an optimal amount of tip relief exists to make the dynamic load reach to the minimum. While the amount of tip relief exceeds the optimal value, the dynamic load of light-weight gear changes more slightly. For short length of tip relief, the dynamic load appears in the form of “U” type. For long length of tip relief, the dynamic load factor is sharply reduced, which means that the long length of tip relief can more effectively reduce the dynamic load.Key

Key words: spurgear, meshstiffness, profilemodification, dynamicload

中图分类号:

TH132.413

李春明，王成，杜明刚，赵志刚. 考虑轮辐刚度和齿廓修形的渐开线直齿轮动载荷研究[J]. 兵工学报, 2018, 39(6): 1239-1248.

LI Chun-ming, WANG Cheng, DU Ming-gang, ZHAO Zhi-gang. Analysis of Dynamic Load of Spur Gears Considering the Gear Body Stiffness and Tooth Profile Modification[J]. Acta Armamentarii, 2018, 39(6): 1239-1248.

参考文献

［1］刘辉, 蔡仲昌, 曹华夏, 等. 基于iSIGHT平台的车辆动力传动系统联轴器刚度优化研究[J]. 兵工学报, 2012, 33(2):228-231.
LIU Hui, CAI Zhong-chang, CAO Hua-xia, et al. The optimization study on the stiffness of coupling in vehicle powertrain based on iSIGHT platform[J]. Acta Armamentarii, 2012, 33(2):228-231. (in Chinese)
[2］项昌乐, 何韡, 刘辉, 等. 履带车辆传动系统换挡工况瞬态动力学分析[J]. 农业机械学报, 2016, 47(4):288-293.
XIANG Chang-le, HE Wei, LIU Hui, et al. Transient dynamic analysis of tracked vehicle transmission during gear shift process[J]. Transactions of the Chinese Society for Agricultural Machinery, 2016, 47(4):288-293.(in Chinese)
[3］刘辉, 项昌乐, 孙恬恬. 车辆动力传动系统弯扭耦合振动模型的建立及复模态分析[J]. 机械工程学报, 2010, 46(24):67-74.
LIU Hui, XIANG Chang-le, SUN Tian-tian. Construction of bending-torsional coupled vibration model and complex modal analysis of the vehicle powertrain[J]. Journal of Mechanical Engineering, 2010, 46(24):67-74.(in Chinese)
[4］ Liu H, Wang C, Xiang C L. Dynamic characteristic optimization of vehicle transmission based on lateral-torsional coupled nonlinear dynamic model[C]∥Proceedings of the 6th International Conference on Modelling, Identification & Control. Melbourne, Australia: IEEE, 2014: 149-154.
[5］刘辉, 蔡仲昌, 朱丽君, 等. 多挡条件下单级行星传动非线性振动特性研究[J]. 兵工学报, 2012, 33(10):1153-1161.
LIU Hui, CAI Zhong-chang, ZHU Li-jun, et al. Study on nonli- near vibration behavior of simple single stage planetary gears in multiple work conditions[J]. Acta Armamentarii, 2012, 33(10): 1153-1161. (in Chinese)
[6］李润方. 齿轮传动的刚度分析和修形方法[M]. 重庆:重庆大学出版社, 1998.
LI Run-fang. Mesh stiffness analysis and modification method of gear transmission[M]. Chongqing: Chongqing University Press, 1998. (in Chinese)
[7］ Chen Z G, Shao Y M. Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack[J]. Mechanism and Machine Theory, 2013, 62: 63-74.
[8］唐进元, 蔡卫星, 王志伟. 修形圆柱齿轮啮合刚度计算公式[J]. 中南大学学报:自然科学版, 2017, 48(2):337-342.
TANG Jin-yuan, CAI Wei-xin, WANG Zhi-wei. Meshing stiffness formula of modification gear[J]. Journal of Central South University: Science and Technology, 2017, 48(2):337-342. (in Chinese)
[9］ Lin H H, Oswald F B, Townsend D P. Dynamic loading of spur gears with linear or parabolic tooth profile modifications[J]. Mechanism and Machine Theory, 1994, 29:1113-1129.

[10］ Liu G, Parker R G. Dynamic modeling and analysis of tooth profile modification for multimesh gear vibration[J]. Journal of Mechanical Design, 2008, 130(12):
121402-1-121402-12.
[11］ Bahk C J, Parker R G. Analytical investigation of tooth profile modification effects on planetary gear dynamics[J]. Mechanism and Machine Theory, 2013, 70:298-319.
[12］王成, 刘辉, 项昌乐. 波动扭矩下渐开线直齿轮传动齿廓修形研究[J].振动与冲击, 2014, 33(24):32-38, 53.
WANG Cheng, LIU Hui, XIANG Chang-le. Influences of profile modification on dynamic characteristics of involute spur gears under a fluctuating torque[J]. Journal of Vibration and Shock, 2014, 33(24):32-38, 53. (in Chinese)
[13］ Marcello F, Farhad S, Gabrieie B, et al. Dynamic optimization of spur gears[J]. Mechanism and Machine Theory, 2011, 46: 544-557.
[14］陈思雨, 唐进元, 王志伟, 等. 修形对齿轮系统动力学特性的影响规律[J]. 机械工程学报, 2014, 50(7):39-45.
CHEN Si-yu, TANG Jin-yuan, WANG Zhi-wei, et al. Effect of modification on dynamic characteristics of gear[J]. Journal of Mechanical Engineering, 2014, 50(7):39-45.(in Chinese)
[15］马辉, 逄旭, 宋溶泽, 等.考虑齿顶修缘的齿轮-转子系统振动响应分析[J]. 机械工程学报, 2014,50(7)：39-45.
MA Hui, PANG Xu, SONG Rong-ze, et al. Vibration response analysis of a geared rotor system considering the tip relief[J]. Journal of Mechanical Engineering, 2014, 50(7):39-45.(in Chinese)
[16］杨玉良, 魏静, 赖育彬, 等. 考虑齿顶修缘的斜齿轮传动振动响应分析[J]. 重庆大学学报, 2017, 40(1):31-40.
YANG Yu-liang, WEI Jing, LAI Yu-bin, et al. Vibration response analysis of helical gear transmission considering the tip relief[J]. Journal of Chongqing University, 2017, 40(1):31-40.(in Chinese)
[17］王成, 刘辉, 项昌乐. 基于齿轮传动系统横-扭-摆耦合非线性动力学模型的齿廓修形优化设计[J]. 振动与冲击, 2016, 35(1): 142-148.
WANG Cheng, LIU Hui, XIANG Chang-le. Optimal profile modification for spur gear systems based on their lateral-torsional-rocking coupled nonlinear dynamic model[J]. Journal of Vibration and Shock, 2016, 35(1): 142-148.(in Chinese)
[18］ Liu H, Zhang C, Xiang C L, et al. Tooth profile modification based on lateral-torsional-rocking coupled nonlinear dynamic model of gear system[J]. Mechanism and Machine Theory, 2016, 105: 606-619.
[19］ Chaari F, Fakhfakh T, Haddar M. Analytical modelling of spur gear tooth crack and influence on gear mesh stiffness[J]. European Journal of Mechanics A/Solids, 2009, 28(3):461-468.
[20］刘辉, 张晨, 王成. 两级渐开线齿轮传动系统横-摆-扭耦合非线性动力学建模与试验验证[J]. 振动与冲击, 2017, 36(15): 124-132.
LIU Hui, ZHANG Chen, WANG Cheng. Nonlinear dynamic modeling and test validation for a two-stage involute gear system[J]. Journal of Vibration and Shock, 2017, 36(15): 124-132. (in Chinese)
[21］王成. 渐开线直齿轮传动系统非线性动力学研究[D].北京：北京理工大学, 2015.
WANG Cheng.Nonlinear dynamic research of involute spur gear system [D]. Beijing: Beijing Institute of Technology, 2015. (in Chinese)

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考虑轮辐刚度和齿廓修形的渐开线直齿轮动载荷研究

Analysis of Dynamic Load of Spur Gears Considering the Gear Body Stiffness and Tooth Profile Modification

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