基于MATLAB的滑动轴承压力分布的数值计算
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摘要
以往人们大多是在假设轴瓦为刚性的前提下进行滑动轴承的研究和设计。而现代滑动轴承常在高速、重载条件下运行,产生很高的油膜压力,加上由于薄壁瓦的兴起和轴瓦材料向低弹性模量方向的发展,使得轴瓦的弹性变形变得不容忽视。
本文采用有限差分法求解刚性轴承的各项润滑性能,并将所得结果与有关经典研究结论进行对比,结果十分吻合,证明所采用的算法、编程语言、编程原理都十分可靠。在考虑轴瓦弹性变形条件下,通过数学建模,建立了一种新型的耦合算法,即:将差分法和有限元法有机组合应用于数值求解滑动轴承油膜压力分布和弹性变形分布的问题。
该算法与其它算法相比更为科学、合理,同时具有收敛快、精度高的特点。通过对一个具体轴承计算研究,分析了在考虑弹性变形和不考虑弹性变形两种情况下润滑性能的变化。研究结果表明,在大偏心率的情况下,弹性变形对滑动轴承润滑性能的影响不容忽视。
In the past, the research and design of journal bearing were taken on the premise of assuming the bearing is rigid . However, due to more and more journal bearings nowadays so operating under conditions of high speed and heavy load would produce higher oil film pressure than before, as well as the prevalence of thin bearing and the developing tendency of lower elasticity modulus of bearing material, the elastic deformation of bearing can no longer be neglectedThis paper employs the finite difference method to study the performance of rigid journal bearing and compares the results to some classical research conclusions accepted widely. The outcomes are very consistent and further prove that the applied algorithm and programming language and principle are very reliable.In the condition of considering the elastic deformation of bearing, a new coupling algorithm is developed through applying the difference method and the finite-element method simultaneously to numerically solve the problem of the pressure distribution in the oil film and the elastic deformation of journal bearing. This algorithm features high speed of convergence and precision and is more reasonable compared with others. By calculating a practical journal bearing, the changes of each lubrication performance of journal bearing with and without considering the effect of elastic deformation are studied and analyzed in detail.The analysis results show that the influences of elastic deformation of bearing on the performance of journal bearing should no longer be neglected, especially in the case of high eccentricity ratio.
本文采用有限差分法求解刚性轴承的各项润滑性能,并将所得结果与有关经典研究结论进行对比,结果十分吻合,证明所采用的算法、编程语言、编程原理都十分可靠。在考虑轴瓦弹性变形条件下,通过数学建模,建立了一种新型的耦合算法,即:将差分法和有限元法有机组合应用于数值求解滑动轴承油膜压力分布和弹性变形分布的问题。
该算法与其它算法相比更为科学、合理,同时具有收敛快、精度高的特点。通过对一个具体轴承计算研究,分析了在考虑弹性变形和不考虑弹性变形两种情况下润滑性能的变化。研究结果表明,在大偏心率的情况下,弹性变形对滑动轴承润滑性能的影响不容忽视。
In the past, the research and design of journal bearing were taken on the premise of assuming the bearing is rigid . However, due to more and more journal bearings nowadays so operating under conditions of high speed and heavy load would produce higher oil film pressure than before, as well as the prevalence of thin bearing and the developing tendency of lower elasticity modulus of bearing material, the elastic deformation of bearing can no longer be neglectedThis paper employs the finite difference method to study the performance of rigid journal bearing and compares the results to some classical research conclusions accepted widely. The outcomes are very consistent and further prove that the applied algorithm and programming language and principle are very reliable.In the condition of considering the elastic deformation of bearing, a new coupling algorithm is developed through applying the difference method and the finite-element method simultaneously to numerically solve the problem of the pressure distribution in the oil film and the elastic deformation of journal bearing. This algorithm features high speed of convergence and precision and is more reasonable compared with others. By calculating a practical journal bearing, the changes of each lubrication performance of journal bearing with and without considering the effect of elastic deformation are studied and analyzed in detail.The analysis results show that the influences of elastic deformation of bearing on the performance of journal bearing should no longer be neglected, especially in the case of high eccentricity ratio.
引文
[1] 邱宣怀.机械设计(第三版).北京:高等教育出版社,1991.
[2] 徐灏,邱宣怀等.机械设计手册.第4卷.北京:机械工业出版社,1992.
[3] 张直明.滑动轴承的流体动力润滑理论.北京:高等教育出版社,1986.
[4] 全永听.工程摩擦学.杭州:浙江大学出版社,1990.
[5] 余俊,徐真,赵冬初,刘珍莲.摩擦学.长沙:湖南科学技术出版社,1984.
[6] 王兆伍,杨家富,许尚贤.流体润滑轴承静动态特性的有限分析法.南京林业大学学报,1996,20(4):21-25.
[7] 高创宽,秀梅.雷诺方程数值解中的几个问题.太原重型机械学院学报,1993,14(3):96-102.
[8] 周桂如,马骥,全永昕.流体润滑理论.杭州:浙江大学出版社,1990.
[9] K.P.Oh, K.H.Huebner.Solution of the Elastohydrodynamic Finite Journal Bearing Problem.Trans.ASME, journal of lubrication Technology, 1973, 95: 342-352.
[10] 张鹏顺,陆思聪.弹性流体动力润滑及其应用.北京:高等教育出版社,1995.
[11] 孙大成.润滑力学讲义.北京:中国友谊出版公司,1991.
[12] 郑林庆.摩擦学原理.北京:高等教育出版社,1994.
[13] 张直明.流体动压轴承润滑理论,1979年2月(于上海交大讲学记录讲义).
[14] 周长新.有限元方法在径向滑动轴承计算中的几个数学问题的处理,西安交通大学科技报告.1978.8.
[15] D.Dowson.History of Tribology, 1979.
[16] J.O' Donoghue, D.K.Brighton, C.J.K.Hooke.The Effect of Elastic Distortions on Journal Bearing Performance.TRANS.ASME, Journal of Lubrication Technology, Series F.1967, 89(4): 409-417.
[17] C.J.K.Hooke, D.K.Brighton, J.O' Donoghue.The Effect of Elastic Distortions on the performance of Thin Shell Bearings.Proc.I.Mech.E, 1966, 181(Part 38): 63-69.
[18] S.Timoshenko.Strength of Materials, 3rd Edition, 1956.
[19] H.D.Conway, H.C.Lee.The Analysis of the Lubrication of a Flexible Journal Bearing, Trans.ASME, Journal of lubrication Technology, 1975, 97: 599-604.
[20] H.D.Conway, P.A.Engel.The Elastohydrodynamic Lubrication of a Thin Layer.Journal of Lubrication Technology, TRAMS.ASME, Series F, 1973, 95(3): 381-385.
[21] H.D.Conway, P.A.Engel.A Grubin-type Formula for the Elastohydrodynamic Lubrication of a Thin Elastic Layer.Journal of Lubrication Technology, TRANS.ASME, Series F, 1974, 96(2): 300-302.
[22] Higginson.G.R.The Theoretical Effect of Elastic Deformation Liner on journal Bearing Performance.Proceeding of the of the Bearing symposium on Elastohydrodynamic Lubrication, Institution of Mechanical Engeers, 1965, 180(Part3B): 31-38.
[23] A.E.H.Love.A Treatise on the Mlathematical Theory of Elasticity, 4th Edition, 1927.
[24] 张冠坤,钟洪.液体动静压轴承.广州:科学普及出版社广州分社,1988.
[25] 钟洪,张冠坤,罗健.轧钢机油膜轴承巴氏合金层接触变形的理论计算与实验研究摩擦学第三届全国学术交流会论文集,流体的润滑部分,1982.
[26] 岑少起,陈瀚,唐照民.重载径向轴承润滑力学问题数值解.西安交通大学学报,1982,(2):119-126.
[27] 楼志文,陈瀚,马小士.弹性流体动力润滑理论有限元解.西安交通大学学报,1979,(2):75-85.
[28] 张国贤,金键,吴白羽.EMP径向滑动轴承弹性变形的有限元求解.润滑与密封,2000,(6):2-4.
[29] 张颖,张国贤.EMP径向滑动轴承热弹变形对润滑特性的影响.机械设计与研究,2000,(2):48-49.
[30] 石晓祥,张颖,张国贤.EMP径向滑动轴承三维热弹流有限元分析与研究.机械设计,2000,(10):27-29.
[31] 董勋.润滑理论.上海:上海交通大学出版社,1984.
[32] 苏荭.基于质量守恒边界条件的油膜空穴研究:(上海大学硕士学位论文),2003.
[33] 陈伯贤,裘祖干,张慧生.流体润滑理论及其应用.北京:机械工业出版社,1991.
[34] 孙恭寿,冯明.液体动静压混合轴承设计.北京:世界图书出版公司,1993.
[35] 黄民毅.液体动压滑动轴承设计的数值计算.四川工业学院学报,1998,17(3):37-41.
[36] 高诚,王永生.液体动压向心滑动轴承的数值解 甘肃工业大学学报,1993,19(1):60-67.
[37] 兴丽,王培俊,吴鹿鸣.用MATLAB求解动静压混合轴承的承载能力.机械设计与制造工程,2002,31(5):72-73.
[38] 温诗铸,黄平.摩擦学原理(第二版).北京:清华大学出版社,2002.
[39] 刘则毅等.科学计算技术与MATLAB.北京:科学出版社,2001.
[40] 吴德龄,马进.弹性变形对滑动轴承工作性能的影响.北京工业大学学报,1989,15(4):67-71.
[41] 段芳莉,韦云隆弹性变形对径向轴承弹流润滑性能的影响.润滑与密封,2000,(6):28-29.
[42] 周仲荣,谢友柏.摩擦学设计.成都:西南交通大学出版社,2000.
[43] Kenshi Ushijima, Takayuki Arai, Takaharu Goto, Shunichi Aoyama.A study on engine bearing performance using EHL analysis and experimental analysis, JSAE Review.1997, 18: 263-269.
[44] U.M.Mokhiamer, W.A.Crosby, H.A.El-Gamal.A study of journal bearing lubricated by fluids with couple stress considering the elastic of the liner.WEAR, 1999, 224: 194-201.
[45] Satish C.Sharma, Vi jay Kumar, S.C.Jain, R.Sinhasan, M.Subramanian.A study finite element method, of slot-entry hydrostatic/hybrid journal bearing using the Tribology International, 1999, 32: 185-196.
[46] 孟庆逢,王忠祥.流体动压润滑轴承的有限元分析法,天津轻工业学院学报,1994,(2):54-59.
[47] 王韵成,邵敏.有限单元法基本原理和数值方法(第二版).北京:清华大学出版社,1997.
[48] 孙菊芳,荣王伍.有限元法及其应用.北京:北京航空航天大学出版社,1990.
[49] 吴永礼.计算固体力学方法.北京:科学出版社,2003.
[50] 徐教,邱宣怀等.机械设计手册.第1卷.北京:机械工业出版社,1992.
[51] Satish C.Sharma, S.C.Jain, N.Madhu Mohan Reddy.Influence of elastic effects on the performance of slot-entry journal bearings.Tribology International, 1999, 32: 537-551.
[52] Yutaka Okamoto, Minoru Hanahashi, Takeshi Katagiri.Theoretical analysis of bearing considering elastic deformation-effects of the housing stiffness and bearing length on bearing performance.JASE Review, 1999, 20: 203-209.
[2] 徐灏,邱宣怀等.机械设计手册.第4卷.北京:机械工业出版社,1992.
[3] 张直明.滑动轴承的流体动力润滑理论.北京:高等教育出版社,1986.
[4] 全永听.工程摩擦学.杭州:浙江大学出版社,1990.
[5] 余俊,徐真,赵冬初,刘珍莲.摩擦学.长沙:湖南科学技术出版社,1984.
[6] 王兆伍,杨家富,许尚贤.流体润滑轴承静动态特性的有限分析法.南京林业大学学报,1996,20(4):21-25.
[7] 高创宽,秀梅.雷诺方程数值解中的几个问题.太原重型机械学院学报,1993,14(3):96-102.
[8] 周桂如,马骥,全永昕.流体润滑理论.杭州:浙江大学出版社,1990.
[9] K.P.Oh, K.H.Huebner.Solution of the Elastohydrodynamic Finite Journal Bearing Problem.Trans.ASME, journal of lubrication Technology, 1973, 95: 342-352.
[10] 张鹏顺,陆思聪.弹性流体动力润滑及其应用.北京:高等教育出版社,1995.
[11] 孙大成.润滑力学讲义.北京:中国友谊出版公司,1991.
[12] 郑林庆.摩擦学原理.北京:高等教育出版社,1994.
[13] 张直明.流体动压轴承润滑理论,1979年2月(于上海交大讲学记录讲义).
[14] 周长新.有限元方法在径向滑动轴承计算中的几个数学问题的处理,西安交通大学科技报告.1978.8.
[15] D.Dowson.History of Tribology, 1979.
[16] J.O' Donoghue, D.K.Brighton, C.J.K.Hooke.The Effect of Elastic Distortions on Journal Bearing Performance.TRANS.ASME, Journal of Lubrication Technology, Series F.1967, 89(4): 409-417.
[17] C.J.K.Hooke, D.K.Brighton, J.O' Donoghue.The Effect of Elastic Distortions on the performance of Thin Shell Bearings.Proc.I.Mech.E, 1966, 181(Part 38): 63-69.
[18] S.Timoshenko.Strength of Materials, 3rd Edition, 1956.
[19] H.D.Conway, H.C.Lee.The Analysis of the Lubrication of a Flexible Journal Bearing, Trans.ASME, Journal of lubrication Technology, 1975, 97: 599-604.
[20] H.D.Conway, P.A.Engel.The Elastohydrodynamic Lubrication of a Thin Layer.Journal of Lubrication Technology, TRAMS.ASME, Series F, 1973, 95(3): 381-385.
[21] H.D.Conway, P.A.Engel.A Grubin-type Formula for the Elastohydrodynamic Lubrication of a Thin Elastic Layer.Journal of Lubrication Technology, TRANS.ASME, Series F, 1974, 96(2): 300-302.
[22] Higginson.G.R.The Theoretical Effect of Elastic Deformation Liner on journal Bearing Performance.Proceeding of the of the Bearing symposium on Elastohydrodynamic Lubrication, Institution of Mechanical Engeers, 1965, 180(Part3B): 31-38.
[23] A.E.H.Love.A Treatise on the Mlathematical Theory of Elasticity, 4th Edition, 1927.
[24] 张冠坤,钟洪.液体动静压轴承.广州:科学普及出版社广州分社,1988.
[25] 钟洪,张冠坤,罗健.轧钢机油膜轴承巴氏合金层接触变形的理论计算与实验研究摩擦学第三届全国学术交流会论文集,流体的润滑部分,1982.
[26] 岑少起,陈瀚,唐照民.重载径向轴承润滑力学问题数值解.西安交通大学学报,1982,(2):119-126.
[27] 楼志文,陈瀚,马小士.弹性流体动力润滑理论有限元解.西安交通大学学报,1979,(2):75-85.
[28] 张国贤,金键,吴白羽.EMP径向滑动轴承弹性变形的有限元求解.润滑与密封,2000,(6):2-4.
[29] 张颖,张国贤.EMP径向滑动轴承热弹变形对润滑特性的影响.机械设计与研究,2000,(2):48-49.
[30] 石晓祥,张颖,张国贤.EMP径向滑动轴承三维热弹流有限元分析与研究.机械设计,2000,(10):27-29.
[31] 董勋.润滑理论.上海:上海交通大学出版社,1984.
[32] 苏荭.基于质量守恒边界条件的油膜空穴研究:(上海大学硕士学位论文),2003.
[33] 陈伯贤,裘祖干,张慧生.流体润滑理论及其应用.北京:机械工业出版社,1991.
[34] 孙恭寿,冯明.液体动静压混合轴承设计.北京:世界图书出版公司,1993.
[35] 黄民毅.液体动压滑动轴承设计的数值计算.四川工业学院学报,1998,17(3):37-41.
[36] 高诚,王永生.液体动压向心滑动轴承的数值解 甘肃工业大学学报,1993,19(1):60-67.
[37] 兴丽,王培俊,吴鹿鸣.用MATLAB求解动静压混合轴承的承载能力.机械设计与制造工程,2002,31(5):72-73.
[38] 温诗铸,黄平.摩擦学原理(第二版).北京:清华大学出版社,2002.
[39] 刘则毅等.科学计算技术与MATLAB.北京:科学出版社,2001.
[40] 吴德龄,马进.弹性变形对滑动轴承工作性能的影响.北京工业大学学报,1989,15(4):67-71.
[41] 段芳莉,韦云隆弹性变形对径向轴承弹流润滑性能的影响.润滑与密封,2000,(6):28-29.
[42] 周仲荣,谢友柏.摩擦学设计.成都:西南交通大学出版社,2000.
[43] Kenshi Ushijima, Takayuki Arai, Takaharu Goto, Shunichi Aoyama.A study on engine bearing performance using EHL analysis and experimental analysis, JSAE Review.1997, 18: 263-269.
[44] U.M.Mokhiamer, W.A.Crosby, H.A.El-Gamal.A study of journal bearing lubricated by fluids with couple stress considering the elastic of the liner.WEAR, 1999, 224: 194-201.
[45] Satish C.Sharma, Vi jay Kumar, S.C.Jain, R.Sinhasan, M.Subramanian.A study finite element method, of slot-entry hydrostatic/hybrid journal bearing using the Tribology International, 1999, 32: 185-196.
[46] 孟庆逢,王忠祥.流体动压润滑轴承的有限元分析法,天津轻工业学院学报,1994,(2):54-59.
[47] 王韵成,邵敏.有限单元法基本原理和数值方法(第二版).北京:清华大学出版社,1997.
[48] 孙菊芳,荣王伍.有限元法及其应用.北京:北京航空航天大学出版社,1990.
[49] 吴永礼.计算固体力学方法.北京:科学出版社,2003.
[50] 徐教,邱宣怀等.机械设计手册.第1卷.北京:机械工业出版社,1992.
[51] Satish C.Sharma, S.C.Jain, N.Madhu Mohan Reddy.Influence of elastic effects on the performance of slot-entry journal bearings.Tribology International, 1999, 32: 537-551.
[52] Yutaka Okamoto, Minoru Hanahashi, Takeshi Katagiri.Theoretical analysis of bearing considering elastic deformation-effects of the housing stiffness and bearing length on bearing performance.JASE Review, 1999, 20: 203-209.