摘要
工程中应用十分广泛的滚子类摩擦副通常在润滑条件下工作,其压力分布、膜厚膜形及温度分布对机器零部件的性能和寿命有很大影响,需进行凸度设计以改善此类摩擦副的承载能力和润滑状况。本文以滚子类摩擦副为应用对象,研究了有限长线接触弹性流体动力润滑问题,探讨了凸度滚子的稳态热弹流设计和动态等温特性,考察了润滑剂、载荷、速度等工况参数和凸度修形参数对压力分布、膜厚膜形、温度分布的影响,讨论了加减速、起停、急停以及摆动等特殊变速运动下的压力分布和成膜特性。完成的主要工作如下:
一.基于多重网格技术,通过引入附加项强制构造温度分析矩阵主对角优势,限制压力温度的合理范围以及对于苛刻工况由工况参数接近的相对温和工况的计算结果提供良好初值等数值技巧,构建了适用于有限长线接触热弹流分析的高效稳定的计算方法,可在接触长宽比达到100,接触压力达到2.0 GPa的苛刻工况下得到收敛解。以此为工具,系统完整的定量模拟了Wymer等在此领域完成的经典光干涉试验,分析结果与试验结果吻合很好,从而验证了分析程序的正确性。
二.系统深入分析了工程中常用的相交圆弧修形滚子的重载稳态热弹流特性,包括此种滚子的两个修形参数:修形长度和修形半径的影响;速度、载荷和滑滚比等工况参数的影响;Eyring非牛顿效应的影响;并探讨了弹流温度场与压力场分布规律的相似性以说明凸度设计对弹流温度分布的影响。研究表明:只要修形参数合适,相交圆弧修形滚子将分别在修形起始位置以及靠近轴向出口位置出现两次轴向颈缩,轴向颈缩与径向颈缩共同阻碍了润滑油流出接触区从而增加膜厚,即“封油效应”。合理修形的此类滚子可对工况有较好的自适应性,从成膜的角度讲,润滑失效与“封油效应”的无法建立是对应的;端部的压力集中程度主要由修形半径和载荷决定。使用Eyring非牛顿流体有利于改善此类接触副的承载能力和润滑状况,但Eyring非牛顿效应对这种滚子的凸度设计没有明显影响。压缩功是导致弹流温度梯度与压力梯度相似性的主要原因。凸度设计在改善压力分布的同时也将改善温度分布,进而改善由热效应导致的各种疲劳现象。
The widely used line contact friction pairs work mostly under lubrication conditions. The pressure, film thickness, and temperature distributions play important role in the performance and service life of such friction pairs. Therefore, crowning design is necessary to increase their load capacity and improve lubrication condition. In this dissertation, the line contact EHL of finite length is studied. Crowning designs based on steady thermal and transient isothermal EHL of profiled rollers are discussed. The effects of lubricants, applied load, velocity as well as crowning parameters on pressure, film thickness and temperature distributions are investigated. The pressure distribution and oil film structure of several types of non-steady state motion, including acceleration/deceleration, stop/start, rapid deceleration and oscillation are obtained. The main work is as follows:
1. An effective, robust and stable algorithm is established based on the multi-level multi-integration technique and several numerical skills: introducing additive items to construct the temperature matrix, constricting the pressure and temperature in a reasonable range during the calculation process, and using the solutions of some similar operating conditions as the initial values for more severe operating conditions. Numerical trials show that convergent solutions could be obtained under severe working conditions (the contact pressures exceed 2.0 GPa and the length-width ratio of contact area is over 100). Using this algorithm, systematic and complete numerical simulations of the classical interferometry experiments by Wymer’s group are carried out. The numerical and experimental results agree quite well with each other. Therefore, the reliability of the calculation program is verified.
2. The steady thermal EHL behavior for cylindrical rollers with crown-profiled ends at heavy load is systematically analyzed, including the following aspects: the effects of crowning length and crowning radius; the effects of velocity, applied load and slip-slide ratio; and the effects of the Eyring non-Newtonian fluids. Moreover, the similarity of the pressure and temperature distribution is investigated to discover the influence of the crowning design on the temperature distribution. It has been concluded that, if the crowning parameters are suitable, such rollers could establish two times of constriction in the cylindrical direction, the
引文
[1] Jost H P. Lubrication (Tribology) education and research ? a report on the present position and industry’s needs, D. E. S. Report. HM Stationary Office, London, 1966
[2] 霍林 J. 摩擦学原理 [M]. 上海交通大学摩擦学研究室译. 北京: 机械工业出版社, 1981
[3] 温诗铸. 摩擦学原理 [M]. 北京: 清华大学出版社,1990
[4] 张嗣伟. 关于我国摩擦学发展方向的探讨 [J]. 摩擦学学报. 2001, 21(5): 321~323
[5] Martin H M. The lubrication of gear teeth [J], Enginerring, 1916: 10
[6] 温诗铸, 杨沛然. 弹性流体动力润滑 [M]. 北京: 清华大学出版社, 1992
[7] 杨沛然. 流体润滑数值分析 [M]. 北京: 国防工业出版社, 1998
[8] Dowson D, Higginson G R. Elasto-hydrodynamic lubrication [M]. London: Pergamon Press,1977
[9] Dowson D,Higginson G R. A numerical solution to the elastohydrodynamic problems [J]. Journal of Mechanical Engineering Science. 1959, 1(1): 6~15
[10] Hamrock B J, Dowson D. Isothermal elastohydrodynamic lubrication of point contacts, Part I-theoretical formulation [J]. ASME Journal of Lubrication Technology, 1976, 98(2): 223~229
[11] Hamrock B J, Dowson D. Isothermal elastohydrodynamic lubrication of point contacts, Part III-fully flooded results [J]. ASME Journal of Lubrication Technology, 1977, 99(2): 264~276
[12] 朱东. 弹性流体动力润滑椭圆接触问题的热分析 [D]. 清华大学博士学位论文. 1984
[13] Xiaolan Ai, Herbert S Cheng and Linqing Zheng. Transient model for micro-elastohydrodynamic lubrication with three-dimensional irregularities [J]. ASME Journal of Tribology, 1993, 115(1): 102~110
[14] 杨沛然. 非稳态热弹性流体动力润滑研究 [D]. 清华大学博士学位论文. 1989
[15] Johnson K L, Higginson J G. Non-Newtonian effect for sliding in miro-EHL [J]. Wear, 1988, 128(3): 249~264
[16] Gohar R, Cameron A. The mapping of Elastohydrodynamic contacts [J]. ASME Journal of Lubrication, 1967, 10: 215~225
[17] Israelachvili J N. Thin film studies using multiple-beam interferometry [J]. Journal of Colloid and Interface Science. 1973, 44: 259~271
[18] Spikes H A, Gao G. Properties of ultra-thin lubricating using wedged spacer layer optical interferometery in: Dowson D. Eed [C]. Proceedings of the Leeds-lyon Sympoo on Tribology, Interface Dynamics, Netherlands: Elsevier Science Publisher B. V. 1987, 275~279
[19] Johnston G J, Wayte R and Spikes H A. Measurement and study of very thin lubricant films in concentrated contacts [J]. Tribology Transactions. 1991, 34(2): 187~194
[20] 雒建斌. 薄膜润滑实验技术和特性研究 [D]. 清华大学博士学位论文. 1994
[21] Luo Jianbin, Wen Shizhu and Huang Ping. Thin film lubrication, Part I: The transtion between EHL and thin Film Lubrication [J]. Wear, 1996; 194(1-2): 107~115
[22] Kaneta M, Nishikawa H, Kameishi K, Sakai T, Ohno, N. Effects of elastic moduli of contact surfaces in Elastohydrodynamic lubrication [J]. ASME Journal of Tribology, 1992(1), 114: 75~80
[23] Yang Peiran, Qu Shiyue, Kaneta M, Nishikawa H. Formation of steady in point TEHL contacts [J]. ASME Journal of Tribology, 2001,123(1): 42~49
[24] 陈晓阳, 张直明, 马家驹. 有限长线接触弹流润滑的现状与展望 [J]. 摩擦学学报, 1997, 17 (3): 281~288
[25] 濮良贵, 纪名刚. 机械设计 [M]. 北京: 高等教育出版社,2001
[26] Johnson K L. Contacts Mechanic [M]. Cambridge University Press, 1995
[27] Lurdberg G. Elastische beruhrung zweier halbraume[J]. Forchung auf dem Gebiete des Ingenicurwesns. Sept/okt 1939, 10(5): 201~221
[28] 王振华. 圆柱滚子轴承的使用性能分析 [J]. 轴承, 1989, 2: 57~62
[29] 马家驹. 滚子凸度设计 [J]. 轴承, 1992, 1: 11~15
[30] 马家驹. 线接触副凸度设计的研究 (I) 计算方法 [C]. 第五届全国摩擦学学术会议论文集(上册), 武汉, 1992, 167 ~174
[31] 马家驹. 线接触副凸度设计的研究 (II) 凸度设计 [C]. 第五届全国摩擦学学术会议论文集(下册). 武汉, 1992, 175 ~179
[32] 陈晓阳, 马家驹. 滚子凸形对接触应力和疲劳寿命的影响 [J]. 机电工程, 1993, 3: 21~24
[33] 孙浩洋, 陈晓阳. 凸度设计及有限长弹流理论的进展 [J].中国机械工程,2004,15(9):
[17] Israelachvili J N. Thin film studies using multiple-beam interferometry [J]. Journal of Colloid and Interface Science. 1973, 44: 259~271
[18] Spikes H A, Gao G. Properties of ultra-thin lubricating using wedged spacer layer optical interferometery in: Dowson D. Eed [C]. Proceedings of the Leeds-lyon Sympoo on Tribology, Interface Dynamics, Netherlands: Elsevier Science Publisher B. V. 1987, 275~279
[19] Johnston G J, Wayte R and Spikes H A. Measurement and study of very thin lubricant films in concentrated contacts [J]. Tribology Transactions. 1991, 34(2): 187~194
[20] 雒建斌. 薄膜润滑实验技术和特性研究 [D]. 清华大学博士学位论文. 1994
[21] Luo Jianbin, Wen Shizhu and Huang Ping. Thin film lubrication, Part I: The transtion between EHL and thin Film Lubrication [J]. Wear, 1996; 194(1-2): 107~115
[22] Kaneta M, Nishikawa H, Kameishi K, Sakai T, Ohno, N. Effects of elastic moduli of contact surfaces in Elastohydrodynamic lubrication [J]. ASME Journal of Tribology, 1992(1), 114: 75~80
[23] Yang Peiran, Qu Shiyue, Kaneta M, Nishikawa H. Formation of steady in point TEHL contacts [J]. ASME Journal of Tribology, 2001,123(1): 42~49
[24] 陈晓阳, 张直明, 马家驹. 有限长线接触弹流润滑的现状与展望 [J]. 摩擦学学报, 1997, 17 (3): 281~288
[25] 濮良贵, 纪名刚. 机械设计 [M]. 北京: 高等教育出版社,2001
[26] Johnson K L. Contacts Mechanic [M]. Cambridge University Press, 1995
[27] Lurdberg G. Elastische beruhrung zweier halbraume[J]. Forchung auf dem Gebiete des Ingenicurwesns. Sept/okt 1939, 10(5): 201~221
[28] 王振华. 圆柱滚子轴承的使用性能分析 [J]. 轴承, 1989, 2: 57~62
[29] 马家驹. 滚子凸度设计 [J]. 轴承, 1992, 1: 11~15
[30] 马家驹. 线接触副凸度设计的研究 (I) 计算方法 [C]. 第五届全国摩擦学学术会议论文集(上册), 武汉, 1992, 167 ~174
[31] 马家驹. 线接触副凸度设计的研究 (II) 凸度设计 [C]. 第五届全国摩擦学学术会议论文集(下册). 武汉, 1992, 175 ~179
[32] 陈晓阳, 马家驹. 滚子凸形对接触应力和疲劳寿命的影响 [J]. 机电工程, 1993, 3: 21~24
[33] 孙浩洋, 陈晓阳. 凸度设计及有限长弹流理论的进展 [J].中国机械工程,2004,15(9):Journal of Tribology, 1983, 105(3): 598~604
[48] Bahadoran H, Gohar R. End closure in elastohydrodynamic line contact [J]. Journal of Mechanical Engineering Science, 1974, 16:276~278
[49] Shigeaki Kuroda, Kazuyoshi Arai. Elastohydrodynamic lubrication between two rollers (finite width analysis) [J]. Bulletin of JSME, 1985, 28,1367~1372
[50] 陈晓阳. 等温有限长线接触弹性流体动力润滑 [D]. 浙江大学博士学位论文, 1993
[51] 陈晓阳. 修形滚子凸型对润滑油膜的影响 [J]. 机械设计与研究, 1996, (2):2~3
[52] 刘双表. 滚子摩擦副润滑分析中的几个问题 [D]. 浙江大学硕士学位论文, 1994
[53] 徐文. 滚子摩擦副弹流特性及其应用 [D]. 浙江大学博士学位论文, 1996
[54] Chen Xiaoyang, Shen Xuejin, Xu Wen, Ma Jiaju, Liu Shuangbiao. EHL studies on the effects of crowning value in roller bearing [C]. Proceedings of the first Asia international conference on tribology. 1998, 1: 76~80
[55] 马家驹, 徐文, 陈晓阳. 滚子摩擦副弹流特性及其应用 [J]. 摩擦学学报, 2000, 20(1): 63~66
[56] 崔子伟, 张和豪, 华东耘. 重载有限宽滚子弹流润滑的逆解法 [J]. 上海工业大学学报, 1991,12(4): 301~311
[57] 莫云辉. 正反圆锥滚子弹流润滑 [D]. 上海工业大学硕士学位论文, 1994
[58] Park, Kim. The Elastohydrodynamic lubrication of profiled cylindrical roller [C]. Proceedings of the international tribology conference, Yokohama, 1995. 1043~1048
[59] Park, Kim. Elastohydrodynamic lubrication of finite line contact [J]. Wear, 1998, 223: (1-2), 102~109
[60] Barragan de Ling F dM, Evans H P, Snidle R W. Thrust cones lubrication. Part 1: Elastohydrodynamic analysis of conical rims [J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 1996, 210(2): 85~96
[61] Barragan de Ling F dM, Evans H P, Snidle RW. Thrust cones lubrication. Part 2: Elastohydrodynamic analysis of crown rims [J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 1996, 210(2): 97~105
[62] Barragan de Ling F dM, Evans H P, Snidle R W. Thrust cones lubrication. Part 3: a test facility and preliminary measured data [J]. Proceedings of the Institution of MechanicalEngineers, Part J: Journal of Engineering Tribology, 1996, 210(2): 107~112
[63] Arthur Francisco, Jean Frene, Antoinette Blouin. Multilevel solution of the elastohydrodynamic contact for the water lubricated silicon carbide 3D line contact [J]. Tribology Transactions, 2002, 45(1): 110~116
[64] Lubrecht A A, Ten Napel W E and Bosma R. Multigrid, an alternative method for calculation film thickness and pressure profiles on the Elastohydrodynamic lubricated line contacts [J]. ASME Journal of Tribology. 1986, 108(4): 551~556
[65] Venner C H. Multilevel solutions of the EHL line and piont contact problems [D]. Ph.D thesis, Enschede: University of Twente, 1991
[66] Liu Xiaoling, Yang Peiran. Analysis of the thermal elastohydrodynamic lubrication of a finite line contact [J]. Tribology International. 2002, 35(3): 137~144
[67] 刘晓玲, 杨沛然. 有限长滚子线接触热弹流润滑分析 [J]. 摩擦学学报, 2002, 22(4): 295~299
[68] Kushwaha M, Rahnejat H. Transient elastohydrodynamic lubrication of finite line conjunction of cam to follower concentrated contact [J]. Journal of physics D: Applied physis, 2002, 35(21): 2872~2890
[69] Kushwaha M, Rahnejat H, Gohar R. Aligned and misaligned contacts of rollers to races in elastohydrodynamic finite line conjunctions [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2002, 216(11): 1051~1070
[70] Yang Peiran, Wen Shizhu. A generalized Reynolds equation for non-Newtonian thermal elastohydrodynamic lubrication [J]. ASME Journal of Tribology, 1990, 112 (4): 631~636
[71] Roelands C J A. Correlation aspects of viscosity-temperature-pressure relationship of lubricating oils [D]. PhD thesis, Delft University of Technology, Netherland, 1966
[72] 郭峰. 椭圆接触微观热弹性流体动力润滑求解的多重网格算法研究 [D]. 青岛建筑工程学院硕士学位论文, 1998
[73] 刘超群. 多重网格法及其在计算流体力学中的应用 [M]. 北京:清华大学出版社, 1995
[74] 陆今甫, 关治. 偏微分方程数值解法 [M]. 北京: 清华大学出版社, 1987
[75] 王文中, 胡元中, 王慧. 混合润滑中弹性变形的快速数值计算[J]. 摩擦学学报,2002, 22(5): 390-394
[76] 王文中. 混合润滑的数值模拟和试验研究 [D]. 清华大学博士学位论文, 2003
[77] Colin F, Lubrecht A A. Comparison of FFT-MLMI for elastic deformation calculations [J]. ASME Journal of Tribology, 2001, 123(4): 884-887
[78] 刘晓玲. 有限长线接触及非牛顿点接触热弹流润滑分析 [D]. 青岛建筑工程学院硕士学位论文, 2002
[79] Yang Peiran, Qu Shiyue, Chang Qiuying, Guo Feng. On the theory of thermal Elastohydrodynamic lubrication at high slide-roll ratios?line contact solution [J]. ASME Journal of Tribology, 2001, 123(1): 36~41
[80] Stejskal E O, Cameron A. Optical interferometry study of film formation in lubrication of sliding and/or rolling contacts, 1972, NASA report, Lewis Research Center.
[81] Panger A P, Ettles C M M, Cameron A. The solution of the point contact Elastohydrodynamic problem [J]. Proceedings of Royal Society, 1975,346: 227~244
[82] 刘晓玲, 杨沛然, 兼田桢宏. 基于表面凹陷现象的非牛顿热弹流润滑分析 [J], 摩擦学学报,2003, 23(5), 406-410
[83] 孙浩洋. 高速极重载热弹流润滑分析 [D]. 青岛建筑工程学院硕士学位论文, 2002
[84] Yagi K, Kyogoku K, Nakahara T. Temperature measurements of oil film and surface in point contact EHL under high slip ratio condition [C]. Proceedings of the International Tribology Conference. Nagsaki, 2000, 567~572
[85] Zhang Y, Zhang X, Tabler W. A systematic model for the analysis of contact,slide slip and traction of toroidal drives [J]. ASME Journal of Tribology, 2000, 122: 523-528
[86] 王静, 杨沛然. 时变等温线接触弹流润滑问题求解的多重网格技术 [J]. 润滑与密封. 2000, (3): 9~11
[87] Suginura J, Jones W R, Spikes H A. EHD film thickness in non-steady state contacts [J]. ASME Journal of Tribology, 1998, 120(3): 442~452
[88] Glovnea R P, Spikes H A. The influence of lubricant on film collapse rate in high pressure thin film behavior during sudden halting of motion [J]. Tribology Transactions, 2000, 43(4): 731-739
[89] Glovnea R P, Spikes H A. Elastohydrodynamic film formation at the start-up of the motion [J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of EngineeringTribology, 2001, 215: 125~138
[90] Glovnea R P, Spikes H A. Elastohydrodynamic film collapse during rapid deceleration. Part I: experimental results [J]. ASME Journal of Tribology, 2001, 123(2): 254~261
[91] Glovnea R P. Behavior of EHD films during reversal of entrainment in cyclically accelerated/decelerated motion [J]. Tribology Transactions, 2002, 45(2):177~184
[92] Glovnea R P, Spikes H A. Oscillations induced in EHD film thickness by a step in entrainment speed [J]. Lubrication Science, 2003, 15(4): 311~320
[93] Qu Shiyue, Yang Peiran and Guo Feng. Theoretical investigation on the dimple occurrence in the thermal EHL of simple sliding steel-glass circular contacts [J]. Tribology International, 2000, 33(1): 59~65
[94] Sun Haoyang, Chen Xiaoyang. Simulation of an optical interferometry experiments in EHL study of cylindrical roller [C]. Abstracts of the papers presented at the regular sessions of the sixth world congress on computational mechanics in conjunction with the Second Asian-pacific Congress on computional mechanics, Beijing, China, 2004, volume II, 491
[95] 陈晓阳. 凸度滚子轴承的摩擦学设计综述 [J]. 中国矿业大学学报,1999, 28: 摩擦学专辑, 132-134
[96] 陈晓阳, 沈雪瑾. 滚针凸度抛窜工艺及评价技术研究 [J]. 上海大学学报 (自然科学版),增刊,1997, (3): 142-146
[97] 高海涛, 王景东. 滚子凸度加工技术的研究 [J]. 轴承技术, 2003, (3): 10-11
[98] 董晖, 王雪珍. 滚子轴承套圈滚道凸度的磨削加工 [J]. 轴承, 2004, (7): 20-22
[99] 王世锋, 段富宣, 姚志国. 圆柱滚子凸度设计应用 [J]. 制造技术与机床, 2004, (7): 91-92
[100] 段明德 , 李济顺 , 孙其林 . 凸度滚子超精辊廓形曲面的加工方法 [J]. 轴承 , 2004,(12):16-17
[101]F. Schmelz, Graf von H.-C. Seherr-Thoss, E. Aucktor 著, 伍德荣, 肖生发, 陶健民 译, 万向节和传动轴 [M]. 北京: 北京理工大学出版社, 1997
[102]冈本纯三 著, 黄志强译, 罗继伟 校. 球轴承的设计计算 [M]. 北京: 机械工业出版社, 2003