Please wait a minute...
浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (12): 2307-2314    DOI: 10.3785/j.issn.1008-973X.2021.12.010
    
Simplified calculation method for friction coefficient in point contact with arbitrary entrainment vector
Wei CAO1,2(),Wei PU3,Yi-pin WAN1,Di WANG1,*(),Cun-bo LIU2
1. School of Construction Machinery, Chang’an University, Xi’an 710064, China
2. Shantui Construction Machinery Limited Company, Ji’ning 272073, China
3. School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China
Download: HTML     PDF(1548KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

Owing to the complexity of friction coefficient calculations in spatial point contact, such as spiral bevel gear and hypoid gear transmissions, a simplified calculation method for friction coefficient in point contact with arbitrary entrainment vector was proposed, considering the coupling between inlet temperature rise and center film thickness as well as the interaction between friction coefficient and temperature rise in contact zone. Based on the proposed method, the oil film thickness and friction coefficient of point contact were analyzed under different working conditions, and the oil film thickness and friction coefficient were compared with the experimental data in literatures. Results show that the temperature rise at inlet area and contact area is significant at high speed, hence the prediction results of oil film thickness and friction coefficient are large if the influence of temperature rises are ignored. The entrainment angle has great influence on the oil film thickness, but little effect on the friction coefficient. Under arbitrary entrainment angles, the predicted oil film thickness and friction coefficient for point contact agree well with experimental results from literatures, verifying the reliability of the simplified calculation method for friction coefficient.

Key words： friction coefficient      oil film thickness      point contact      entrainment vector      simplified method     
Received: 25 January 2021      Published: 31 December 2021
CLC:  TH 117.2  
Fund:  国家自然科学基金资助项目(52005047)；中国博士后科学基金资助项目（2020M672129）；陕西省自然科学基础研究计划资助项目（2020JQ-367, 2020JQ-345）；中央高校基本科研业务费专项资助项目（300102250301）；陕西省高校科协青年人才托举计划资助项目（20210420）
Corresponding Authors: Di WANG     E-mail: cw334926@163.com;wangdi@chd.edu.cn
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Wei CAO
Wei PU
Yi-pin WAN
Di WANG
Cun-bo LIU
Cite this article:

Wei CAO,Wei PU,Yi-pin WAN,Di WANG,Cun-bo LIU. Simplified calculation method for friction coefficient in point contact with arbitrary entrainment vector. Journal of ZheJiang University (Engineering Science), 2021, 55(12): 2307-2314.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2021.12.010     OR     https://www.zjujournals.com/eng/Y2021/V55/I12/2307


任意卷吸速度矢量点接触摩擦系数简化计算方法

针对弧齿锥齿轮和准双曲面齿轮传动的空间点接触摩擦系数求解复杂问题，考虑油膜入口区温升与中心油膜厚度以及接触区温升与摩擦系数间的耦合关系，提出任意卷吸速度矢量点接触的摩擦系数简化计算方法. 基于所提方法分析在不同工况下的点接触中心油膜厚度和摩擦系数，并将油膜厚度和摩擦系数与文献实验数据进行对比. 结果表明：在高速工况下，入口区温升和接触区温升显著，忽略温升影响将使油膜厚度和摩擦系数预测结果偏大；卷吸速度夹角对油膜厚度影响较大，对摩擦系数影响相对较小；在任意卷吸速度夹角工况下，点接触油膜厚度和摩擦系数预测结果与文献实验结果一致，验证摩擦系数简化计算方法的可靠性.


关键词： 摩擦系数,  油膜厚度,  点接触,  卷吸速度矢量,  简化方法 
Fig.1 Point contact with entrainment vector
Fig.2 Solution coordinates and grids of fluid shear stress
Fig.3 Approximation calculation of pressure gradient at inlet
Fig.4 Procedure of simplified calculation method for friction coefficient
Fig.5 Changes of central oil film thickness with entrainment under different thermal influence factors
Fig.6 Changes of inlet temperature of oil film with entrainment under different bulk temperatures
Fig.7 Changes of friction coefficient with slide-roll ratio under different thermal influence factors
Fig.8 Changes of friction coefficient with slide-roll ratio under different bulk temperatures
Fig.9 Changes of central oil film thickness with entrainment angle under different thermal influence factors
计算方法 hc/nm
θe= 0° θe= 45° θe= 90°
文献[11] 495.3 440.0 375.3
文献[33] 457.0 419.0 393.0
文献[13] 457.0 415.0 357.8
本研究 461.5 429.9 383.2
Tab.1 Central oil film thickness corresponding to entrainment angle in different calculation methods
Fig.10 Changes of friction coefficient, temperature rise of inlet oil film and maximum temperature rise in contact zone with entrainment under different thermal influence factors
Fig.11 Comparison of friction coefficient and experimental result under different entraining velocity angles
Fig.12 Changes of friction coefficient with entrainment angle under different conditons
[1]   蒲伟, 王家序, 朱东, 等 卷吸速度为任意方向的椭圆接触弹流润滑复合迭代解法[J]. 机械工程学报, 2014, 50 (13): 106- 112
PU Wei, WANG Jia-xu, ZHU Dong, et al Semi-system approach in elastohydrodynamic lubrication of elliptical contacts with arbitrary entrainment[J]. Journal of Mechanical Engineering, 2014, 50 (13): 106- 112
[2]   王家序, 胡如康, 周广武, 等 双圆弧谐波减速器共轭啮合区混合润滑分析[J]. 哈尔滨工业大学学报, 2018, 50 (7): 169- 178
ANG Jia-xu, HU Ru-kuang, ZHOU Guang-wu, et al Analysis on mixed lubrication at the conjugate meshing domain of harmonic gear with double-circular-arc tooth profile[J]. Journal of Harbin Institute of Technology, 2018, 50 (7): 169- 178
doi: 10.11918/j.issn.0367-6234.201709160
[3]   刘奕壕, 黄柏林, 付忠学, 等 基于Circular模型的大剪应变率点接触弹流界面滑移数值分析[J]. 摩擦学学报, 2018, 38 (2): 129- 137
LIU Yi-hao, HUANG Bo-lin, FU Zhong-xue, et al Numerical analysis of EHL boundary slip effect applying circular model under big shear strain rate[J]. Tribology, 2018, 38 (2): 129- 137
[4]   WANG H, ZHOU C, LEI Y, et al An adhesive wear model for helical gears in line-contact mixed elastohydrodynamic lubrication[J]. Wear, 2019, 426-427: 896- 909
doi: 10.1016/j.wear.2019.01.104
[5]   ZAPLETAL T, SPERKA P, KRUPKA I, et al The effect of surface roughness on friction and film thickness in transition from EHL to mixed lubrication[J]. Tribology International, 2018, 128: 356- 364
doi: 10.1016/j.triboint.2018.07.047
[6]   MASJEDI M, KHONSARI M M Film thickness and asperity load formulas for line-contact elastohydrodynamic lubrication with provision for surface roughness[J]. Journal of Tribology, 2012, 134 (1): 011503
doi: 10.1115/1.4005514
[7]   MASJEDI M, KHONSARI M M On the effect of surface roughness in point-contact EHL: formulas for film thickness and asperity load[J]. Tribology International, 2015, 82: 228- 244
doi: 10.1016/j.triboint.2014.09.010
[8]   MASJEDI M, KHONSARI M M Mixed elastohydrodynamic lubrication line-contact formulas with different surface patterns[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2014, 228 (8): 849- 859
doi: 10.1177/1350650114534228
[9]   MASJEDI M, KHONSARI M M An engineering approach for rapid evaluation of traction coefficient and wear in mixed EHL[J]. Tribology International, 2015, 92: 184- 190
doi: 10.1016/j.triboint.2015.05.013
[10]   JALALI-VAHID D, RAHNEJAT H, GOHAR R, et al Prediction of oil-film thickness and shape in elliptical point contacts under combined rolling and sliding motion[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2000, 214 (5): 427- 437
doi: 10.1243/1350650001543304
[11]   WANG J, QU S, YANG P Simplified multigrid technique for the numerical solution to the steady-state and transient EHL line contacts and the arbitrary entrainment EHL point contacts[J]. Tribology International, 2001, 34 (3): 191- 202
doi: 10.1016/S0301-679X(01)00020-2
[12]   STAHL K, MICHAELIS K, MAYER J, et al Theoretical and experimental investigations on EHL point contacts with different entrainment velocity directions[J]. Tribology Transactions, 2013, 56 (5): 728- 738
doi: 10.1080/10402004.2013.785624
[13]   PU W, WANG J, ZHANG Y, et al A theoretical analysis of the mixed elastohydrodynamic lubrication in elliptical contacts with an arbitrary entrainment angle[J]. Journal of Tribology, 2014, 136 (4): 041505
doi: 10.1115/1.4028126
[14]   蒲伟, 王家序, 杨荣松, 等 重载下准双曲面齿轮传动界面润滑机理分析[J]. 西安交通大学学报, 2015, 49 (11): 55- 61
PU Wei, WANG Jia-xu, YANG Rong-song, et al Analysis on lubrication performance of hypoid gears at heavy loads[J]. Journal of Xi'an Jiaotong University, 2015, 49 (11): 55- 61
[15]   CAO W, PU W, WANG J, et al Effect of contact path on the mixed lubrication performance, friction and contact fatigue in spiral bevel gears[J]. Tribology International, 2018, 123: 359- 371
doi: 10.1016/j.triboint.2018.03.015
[16]   KOLIVAND M, LI S, KAHRAMAN A Prediction of mechanical gear mesh efficiency of hypoid gear pairs[J]. Mechanism and Machine Theory, 2010, 45 (11): 1568- 1582
doi: 10.1016/j.mechmachtheory.2010.06.015
[17]   SIMON V V Improvements in the mixed elastohydrodynamic lubrication and in the efficiency of hypoid gears[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2020, 234 (6): 795- 810
doi: 10.1177/1350650119866027
[18]   XU H, KAHRAMAN A Prediction of friction-related power losses of hypoid gear pairs[J]. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 2007, 221 (3): 387- 400
doi: 10.1243/14644193JMBD48
[19]   李飞, 袁茹, 朱慧玲, 等 计及齿面摩擦的弧齿锥齿轮动态特性[J]. 航空动力学报, 2020, 35 (8): 1687- 1694
LI Fei, YUAN Ru, ZHU Hui-ling, et al Dynamic characteristics of spiral bevel gear considering tooth surface friction[J]. Journal of Aerospace Power, 2020, 35 (8): 1687- 1694
[20]   PU W, WANG J, ZHU D Friction and flash temperature prediction of mixed lubrication in elliptical contacts with arbitrary velocity vector[J]. Tribology International, 2016, 99: 38- 46
doi: 10.1016/j.triboint.2016.03.017
[21]   ZHU D. Thermal effect on EHL film thickness [M]. [S.l.]: Springer US, 2013: 3602-3606.
[22]   曹伟, 蒲伟, 王家序, 等. 弧齿锥齿轮摩擦系数与啮合效率研究[J]. 摩擦学学报, 2018, 38(3): 247-255.
CAO Wei, PU Wei, WANG Jia-xu, et al. Friction coefficient and mesh efficiency in spiral bevel gears [J], Tribology, 2018, 38(3): 247-255.
[23]   CHITTENDEN R J, DOWSON D, DUNN J F, et al A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. II. General case, with lubricant entrainment along either principal axis of the Hertzian contact ellipse or at some intermediate angle[J]. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1985, 397 (1813): 271- 294
doi: 10.1098/rspa.1985.0015
[24]   BAIR S, WINER W O A rheological model for elastohydrodynamic contacts based on primary laboratory data[J]. Journal of Tribology, 1979, 101 (3): 258- 264
[25]   ZHU D, HU Y Z A computer program package for the prediction of EHL and mixed lubrication characteristics, friction, subsurface stresses and flash temperatures based on measured 3-D surface roughness[J]. ASLE Transactions, 2001, 44 (3): 383- 390
[26]   HOUPERT L Fast numerical calculations of EHD sliding traction forces; application to rolling bearings[J]. Journal of Tribology, 1985, 107 (2): 234- 239
doi: 10.1115/1.3261030
[27]   JOHNSON K L, TEVAARWERK J L Shear behaviour of elastohydrodynamic oil films[J]. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1977, 356 (1685): 215- 236
doi: 10.1098/rspa.1977.0129
[28]   CASTRO J, SEABRA J Global and local analysis of gear scuffing tests using a mixed film lubrication model[J]. Tribology International, 2008, 41 (4): 244- 255
doi: 10.1016/j.triboint.2007.07.005
[29]   GREENWOOD J A, KAUZLARICH J J Inlet shear heating in elastohydrodynamic lubrication[J]. Journal of Lubrication Technology, 1973, 95 (11): 287- 362
[30]   PAOURIS L, RAHMANI R, THEODOSSIADES S, et al An analytical approach for prediction of elastohydrodynamic friction with inlet shear heating and starvation[J]. Tribology Letters, 2016, 64: 10
doi: 10.1007/s11249-016-0730-7
[31]   GUPTA P K, CHENG H S, ZHU D, et al Viscoelastic effects in MIL-L-7808-type lubricant, part I: analytical formulation[J]. Tribology Transactions, 1992, 35 (2): 269- 274
doi: 10.1080/10402009208982117
[32]   KATYAL P, KUMAR P Effect of arbitrary entrainment angle in elastohydrodynamic lubrication elliptical and circular contacts[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2020, 234 (3): 424- 434
doi: 10.1177/1350650119863998
[33]   PU W, WANG J, ZHOU G, et al Effect of surface topography associated with arbitrary velocity direction on the lubrication film thickness in elliptical contacts[J]. Industrial Lubrication and Tribology, 2018, 70 (2): 444- 452
doi: 10.1108/ILT-09-2016-0206
[1] Xian-rong DAI,Lu WANG,Chang-jiang WANG,Xiao-yang WANG,Rui-li SHEN. Anti-slip scheme of full-vertical friction plate for multi-pylon suspension bridge[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(9): 1697-1703.
[2] LIAO Xiang ping, GONG Guo fang, PENG Xiong bin, WU Wei qiang. Jam breakout characteristic of tunnel boring machine based on hydro viscous drive mechanism[J]. Journal of ZheJiang University (Engineering Science), 2016, 50(5): 902-912.