航空滚动轴承力学特性分析研究
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摘要
滚动轴承在航空发动机和航空传动装置中有着广泛的应用。航空滚动轴承的转速一般很高。由于离心效应的影响,轴承滚动体与内外套圈之间的接触角会产生变化,进而影响到轴承的变形与载荷分布特性,所以必须建立航空滚动轴承的力学模型进行载荷分布特性的研究。此外,滚动轴承的一些主要性能,如刚度、变形和承载能力、润滑状态、摩擦等,都是在进行滚动轴承力学分析之后获得的。因此,针对轴承的力学分析研究具有重要的工程应用价值。
本文利用拟动力学法,并采用套圈控制理论的假定,分析了复合负载作用下航空球轴承的载荷分布与变形;编制了低速和高速轴承的计算程序,同时分析了外载和转速对轴承载荷分布影响。在航空应用中柔性内外套圈影响轴承的载荷分布,有限元法能更好地分析这种情况。本文在ANSYS软件中建立了航空向心短圆柱滚子轴承的二维有限元模型,分析了径向力和转速对轴承载荷分布的影响和摩擦对于轴承接触变形的影响,并与拟动力学法计算结果进行了比较。根据上述计算所获得的航空滚动轴承的载荷分布结果,对载荷、转速、游隙、材料等参数对接触角、接触变形、接触刚度、油膜厚度和旋滚比等的影响进行了分析。
研究表明:采用套圈控制理论计算得到的轴承载荷分布是相当可信的;有限元法计算的变形大于拟动力学法所得的结果;两种方法均能有效地解决滚动轴承载荷分布问题。
Rolling bearings are widely used in areoengine and aerial transmission device. High rotational speed of aerial bearing leads to high centrifugal effect, which change outer and inner contact angle between rollers and rings. The deformation and load distribution also change. To find the load distribution, the mechanical model of rolling bearing must be set up. In addition, the performance and properties of bearing, such as stiffness, deformation, load capacity, lubrication condition, friction, etc, are calculated on the basis of its load distribution. Therefore, the research of mechanical properties of bearing has significant value in aviation engineering areas.
By qusi-dynamic method, the deformation and load distribution of rolling bearing under combined load are analyzed through the use of ring-controlled theory. The calculation programme is developed for the low speed and high speed models. And the influence of force and rotational speed to load distribution is studied. In aviation, some bearings have flexible rings, which change the load distribution. Finite element matheod can set up the mechanical model. By finite element matheod, a 2-D model of short cylindrical roller bearing is set up in ANSYS to analyze its load distribution under radial force. And the influence of radial force, rotational speed and friction on deformation is discussed. After calculating load distribution, the changing of contact angle, deformation, contact stiffness, oil film thickness and ratio of revolution and rolling is studied with different speeds, loads, materials and clearances.
It is found that load distribution of rolling bearing based on ring-controlled theory is reliable. The result of finite element matheod is larger than result ofqusi-dynamic method. Both of them can solve the load distribution of bearings.
本文利用拟动力学法,并采用套圈控制理论的假定,分析了复合负载作用下航空球轴承的载荷分布与变形;编制了低速和高速轴承的计算程序,同时分析了外载和转速对轴承载荷分布影响。在航空应用中柔性内外套圈影响轴承的载荷分布,有限元法能更好地分析这种情况。本文在ANSYS软件中建立了航空向心短圆柱滚子轴承的二维有限元模型,分析了径向力和转速对轴承载荷分布的影响和摩擦对于轴承接触变形的影响,并与拟动力学法计算结果进行了比较。根据上述计算所获得的航空滚动轴承的载荷分布结果,对载荷、转速、游隙、材料等参数对接触角、接触变形、接触刚度、油膜厚度和旋滚比等的影响进行了分析。
研究表明:采用套圈控制理论计算得到的轴承载荷分布是相当可信的;有限元法计算的变形大于拟动力学法所得的结果;两种方法均能有效地解决滚动轴承载荷分布问题。
Rolling bearings are widely used in areoengine and aerial transmission device. High rotational speed of aerial bearing leads to high centrifugal effect, which change outer and inner contact angle between rollers and rings. The deformation and load distribution also change. To find the load distribution, the mechanical model of rolling bearing must be set up. In addition, the performance and properties of bearing, such as stiffness, deformation, load capacity, lubrication condition, friction, etc, are calculated on the basis of its load distribution. Therefore, the research of mechanical properties of bearing has significant value in aviation engineering areas.
By qusi-dynamic method, the deformation and load distribution of rolling bearing under combined load are analyzed through the use of ring-controlled theory. The calculation programme is developed for the low speed and high speed models. And the influence of force and rotational speed to load distribution is studied. In aviation, some bearings have flexible rings, which change the load distribution. Finite element matheod can set up the mechanical model. By finite element matheod, a 2-D model of short cylindrical roller bearing is set up in ANSYS to analyze its load distribution under radial force. And the influence of radial force, rotational speed and friction on deformation is discussed. After calculating load distribution, the changing of contact angle, deformation, contact stiffness, oil film thickness and ratio of revolution and rolling is studied with different speeds, loads, materials and clearances.
It is found that load distribution of rolling bearing based on ring-controlled theory is reliable. The result of finite element matheod is larger than result ofqusi-dynamic method. Both of them can solve the load distribution of bearings.
引文
[1] G.Bankmann.航空和宇航轴承润滑[J].国外轴承技术,1996,4:19～22.
[2]林基恕.航空发动机主轴滚动轴承的技术进展[J].燃气涡轮试验与研究,2003,16(4):52～56.
[3]武俊生(摘译).SKF航空滚动轴承技术(上)[J].轴承工业,2003,(5):21～24.
[4]武俊生(摘译).SKF航空滚动轴承技术(下)[J].轴承工业,2003,(6):22～25.
[5]万长森.滚动轴承的分析方法[M].北京:机械工业出版社,1987:44～138.
[6] T. A. Harris,Michael Kotzalas.Rolling Bearing Analysis [M].5th Edition,New York:John Wiley & Sons,2006:46～268.
[7]汪久根,王庆九,章维明.滚动轴承动力学的研究[J].轴承,2007,3:40～45.
[8]吴昊,安琦.弹流润滑圆柱滚子轴承径向刚度的计算[J].轴承,2008,1:1～4.
[9] P.K. Gupta, Transient Ball Motion and Skid in Ball Bearing [J]. ASME, Journal of Lubrication Technology,1975,97:261～268.
[10] Zeki Kiral.Vibration Analysis of Rolling Element Bearings with Various Defects Under the Action of an Unbalanced Force [J].Mechanial Systems and Signal Proccessing.2006,20:667～678.
[11]罗继伟.滚动轴承受力分析及其发展[J].轴承,2001,9:28～31.
[12]陈家庆,周海,徐琳琳.滚动轴承载荷分布问题的理论研究进展[J].北京石油化工学报,2000,8(1):47～51.
[13] J. H. Rumberger.Thrust Bearings with Eccentric Loads [J].Machinery Design,1962,15:27～31.
[14] A.B. Jones, T.A. Harris, Analysis of a Rolling Element Idler Gear Bearing Having a Deformable Outer Race Structure[J].ASME, Journal of Basic Engineering, 1963,6:273～278.
[15] C.T. Walters, The Dynamics of Ball Bearings [J]. ASME, Journal of Lubrication Technology, 1971,93:1～10.
[16] P.K. Gupta,Dynamic of Rolling-element Bearings partⅢ:Ball Bearing Analysis [J]. Transaction of ASME,1979,101(3):298～326.
[17] C.R. Meeks, Ball Bearing Dynamic Analysis Using Computer Methods [J]. Transaction of ASME, 1996,118(1):52～58.
[18] A.Bourdon,J.F.Rigal.Static Rolling Bearing Models in A CAD Environment for the Study of Complex Mechanisms [J]. ASME,Journal of Tribology,1999,121:205～213.
[19]罗祝三,吴林丰,孙心德.轴向受载的高速球轴承的拟动力学分析[J].航空动力学报,1996,11(3):257～260.
[20]贾群义.柔性支承轴承的负荷分布与疲劳寿命计算[J].轴承,1991,5:32～34.
[21]杜辉.航空发动机主轴高速圆柱滚子轴承三位瞬态拟动力学分析[D].洛阳:河南科技大学硕士学位论文,2005.
[22] M.Cao,J.Xiao. A Comprehensive Dynamic Model of Double-Row Spherical Roller Bearing Model Development and Case Studies on Surface Defects,Preloads and Radial Clearance [J]. Mechanical Systems and Signal Processing,July,2007:123～131.
[23] T. A. Harris,J. L. Broschard. Analysis of an Improved Planetary Gear-transmission Bearing[J]. Journal of Basic Engineering,Transactions of ASME,1964,86(3):457～462.
[24]王大力,孙立明,单服兵,徐浩. ANSYS在求解轴承接触问题中的应用[J].轴承,2002,9:1～4.
[25]刘宁,张钢,高刚.赵志峰.基于ANSYS的圆柱滚子轴承有限元应力分析[J].轴承,2006,12:8～10.
[26] El-Sayed H R. Stiffness of Deep-grooved Ball Bearings[J]. Wear,1980,63(1):89～94.
[27] Hernot X,Sartor M,Guillot J. Calculation of the Stiffness Matrix of Angular Contact Ball Bearings by Using the Analytical Approach [J]. Journal of Mechanical Design,Transactions of ASME,2000,122(1):83～90.
[28]桃野达信.滚动轴承的刚性[J].国外轴承技术,2002,(3):56～64.
[29]刘卫群,罗继伟,吴长春,等.滚动轴承刚度分析程序[J].计算力学学报,2001,18(3):375～378.
[30]杜迎辉,丘明,蒋兴奇,等.高速精密角接触球轴承刚度计算[J].轴承,2001,(11):5～8.
[31]黄浩.航空发动机主轴滚动轴承的接触刚度特性分析[D].哈尔滨:哈尔滨工业大学博士论文,2000.
[32]王刚,郭茂林.航空航天滚动轴承刚度[J].哈尔滨工业大学学报,2001,33(5):644～650.
[33]唐云冰.航空发动机轴承动力学特性研究[D].南京:南京航空航天大学博士学位论文,2005.
[34]黄乾贵,邓四二,腾弘飞.滚动轴承系统仿真技术的现状及发展[J].轴承,2002,4:34～37.
[35]李兴林,王成焘.滚动轴承弹流润滑的新进展[J].轴承,1999,3:38～40.
[36]邓四二,腾弘飞.高速圆柱滚子轴承弹流润滑研究现状与发展[J].轴承,2004,1:41～43.
[37]郑学普,周彦伟,邓四二.航空发动机主轴圆柱滚子轴承弹流动态性能仿真[J].润滑与密封,2006,3:97～99.
[38] T.Nakamura, S.Yoshimoto.Static Tilt Characteristics of Aerostatic Retangular Double-pad ThrustBearings with Compound Restritors[J]. Tribology International,1996,29(2):149～152.
[39]徐芝纶.弹性力学[M].北京:高等教育出版社,1990:305～309.
[40]陈锦江,任成祖,徐燕申.基于Matlab的球轴承接触应力与变形和负载分布的计算[J].机械研究与应用,2004,17(1):59～60.
[41] Hoeprich, R. Micheal. Rolling Element Bearing Contact Geometry Analysis[J]. Tribology Transactions,1995,38(4):879～882.
[42]徐从儒.航空发动机附件传动轴承组件的设计[J].航空发动机,1999,4:12～15.
[43]薛毅.数值分析与实验[M].北京:北京工业大学出版社,2005:19～23.
[44]马天兵.基于ANSYS的滚动轴承有限元分析[J].煤矿机械,2004,2:66～69.
[45]刘相新,孟宪颐.ANSYS基础与应用教程[M].北京:科学出版社,2006:240～265.
[46] Bugra Ertas,John Vance.The Effect of Static and Dynamic Misalignment on Ball Bearing Radial Stiffness. AIAA-2002-4160,2002.
[47] Fujio Hirano.Motion of A Ball in Angular-Contact Ball Bearing[J].Wear,1966,9(5):406～415.
[48]张文轩.基于ANSYS的混合陶瓷球轴承分析与试验研究[D].天津:天津大学硕士学位论文,2004:45～46.
[49]《航空发动机设计手册》总编委会.航空发动机设计手册第19册[M].北京:航空工业出版社,2000:54～58.
[50]周延泽,陆震.高速球轴承球/保持架碰撞模型与冲击特性研究[J].机械设计,2001,9:33～37.
[51]郑德志,王黎钦.航空发动机用高速滚动轴承性能考核及失效分析[J].润滑与密封,2006,7:52～54.
[2]林基恕.航空发动机主轴滚动轴承的技术进展[J].燃气涡轮试验与研究,2003,16(4):52～56.
[3]武俊生(摘译).SKF航空滚动轴承技术(上)[J].轴承工业,2003,(5):21～24.
[4]武俊生(摘译).SKF航空滚动轴承技术(下)[J].轴承工业,2003,(6):22～25.
[5]万长森.滚动轴承的分析方法[M].北京:机械工业出版社,1987:44～138.
[6] T. A. Harris,Michael Kotzalas.Rolling Bearing Analysis [M].5th Edition,New York:John Wiley & Sons,2006:46～268.
[7]汪久根,王庆九,章维明.滚动轴承动力学的研究[J].轴承,2007,3:40～45.
[8]吴昊,安琦.弹流润滑圆柱滚子轴承径向刚度的计算[J].轴承,2008,1:1～4.
[9] P.K. Gupta, Transient Ball Motion and Skid in Ball Bearing [J]. ASME, Journal of Lubrication Technology,1975,97:261～268.
[10] Zeki Kiral.Vibration Analysis of Rolling Element Bearings with Various Defects Under the Action of an Unbalanced Force [J].Mechanial Systems and Signal Proccessing.2006,20:667～678.
[11]罗继伟.滚动轴承受力分析及其发展[J].轴承,2001,9:28～31.
[12]陈家庆,周海,徐琳琳.滚动轴承载荷分布问题的理论研究进展[J].北京石油化工学报,2000,8(1):47～51.
[13] J. H. Rumberger.Thrust Bearings with Eccentric Loads [J].Machinery Design,1962,15:27～31.
[14] A.B. Jones, T.A. Harris, Analysis of a Rolling Element Idler Gear Bearing Having a Deformable Outer Race Structure[J].ASME, Journal of Basic Engineering, 1963,6:273～278.
[15] C.T. Walters, The Dynamics of Ball Bearings [J]. ASME, Journal of Lubrication Technology, 1971,93:1～10.
[16] P.K. Gupta,Dynamic of Rolling-element Bearings partⅢ:Ball Bearing Analysis [J]. Transaction of ASME,1979,101(3):298～326.
[17] C.R. Meeks, Ball Bearing Dynamic Analysis Using Computer Methods [J]. Transaction of ASME, 1996,118(1):52～58.
[18] A.Bourdon,J.F.Rigal.Static Rolling Bearing Models in A CAD Environment for the Study of Complex Mechanisms [J]. ASME,Journal of Tribology,1999,121:205～213.
[19]罗祝三,吴林丰,孙心德.轴向受载的高速球轴承的拟动力学分析[J].航空动力学报,1996,11(3):257～260.
[20]贾群义.柔性支承轴承的负荷分布与疲劳寿命计算[J].轴承,1991,5:32～34.
[21]杜辉.航空发动机主轴高速圆柱滚子轴承三位瞬态拟动力学分析[D].洛阳:河南科技大学硕士学位论文,2005.
[22] M.Cao,J.Xiao. A Comprehensive Dynamic Model of Double-Row Spherical Roller Bearing Model Development and Case Studies on Surface Defects,Preloads and Radial Clearance [J]. Mechanical Systems and Signal Processing,July,2007:123～131.
[23] T. A. Harris,J. L. Broschard. Analysis of an Improved Planetary Gear-transmission Bearing[J]. Journal of Basic Engineering,Transactions of ASME,1964,86(3):457～462.
[24]王大力,孙立明,单服兵,徐浩. ANSYS在求解轴承接触问题中的应用[J].轴承,2002,9:1～4.
[25]刘宁,张钢,高刚.赵志峰.基于ANSYS的圆柱滚子轴承有限元应力分析[J].轴承,2006,12:8～10.
[26] El-Sayed H R. Stiffness of Deep-grooved Ball Bearings[J]. Wear,1980,63(1):89～94.
[27] Hernot X,Sartor M,Guillot J. Calculation of the Stiffness Matrix of Angular Contact Ball Bearings by Using the Analytical Approach [J]. Journal of Mechanical Design,Transactions of ASME,2000,122(1):83～90.
[28]桃野达信.滚动轴承的刚性[J].国外轴承技术,2002,(3):56～64.
[29]刘卫群,罗继伟,吴长春,等.滚动轴承刚度分析程序[J].计算力学学报,2001,18(3):375～378.
[30]杜迎辉,丘明,蒋兴奇,等.高速精密角接触球轴承刚度计算[J].轴承,2001,(11):5～8.
[31]黄浩.航空发动机主轴滚动轴承的接触刚度特性分析[D].哈尔滨:哈尔滨工业大学博士论文,2000.
[32]王刚,郭茂林.航空航天滚动轴承刚度[J].哈尔滨工业大学学报,2001,33(5):644～650.
[33]唐云冰.航空发动机轴承动力学特性研究[D].南京:南京航空航天大学博士学位论文,2005.
[34]黄乾贵,邓四二,腾弘飞.滚动轴承系统仿真技术的现状及发展[J].轴承,2002,4:34～37.
[35]李兴林,王成焘.滚动轴承弹流润滑的新进展[J].轴承,1999,3:38～40.
[36]邓四二,腾弘飞.高速圆柱滚子轴承弹流润滑研究现状与发展[J].轴承,2004,1:41～43.
[37]郑学普,周彦伟,邓四二.航空发动机主轴圆柱滚子轴承弹流动态性能仿真[J].润滑与密封,2006,3:97～99.
[38] T.Nakamura, S.Yoshimoto.Static Tilt Characteristics of Aerostatic Retangular Double-pad ThrustBearings with Compound Restritors[J]. Tribology International,1996,29(2):149～152.
[39]徐芝纶.弹性力学[M].北京:高等教育出版社,1990:305～309.
[40]陈锦江,任成祖,徐燕申.基于Matlab的球轴承接触应力与变形和负载分布的计算[J].机械研究与应用,2004,17(1):59～60.
[41] Hoeprich, R. Micheal. Rolling Element Bearing Contact Geometry Analysis[J]. Tribology Transactions,1995,38(4):879～882.
[42]徐从儒.航空发动机附件传动轴承组件的设计[J].航空发动机,1999,4:12～15.
[43]薛毅.数值分析与实验[M].北京:北京工业大学出版社,2005:19～23.
[44]马天兵.基于ANSYS的滚动轴承有限元分析[J].煤矿机械,2004,2:66～69.
[45]刘相新,孟宪颐.ANSYS基础与应用教程[M].北京:科学出版社,2006:240～265.
[46] Bugra Ertas,John Vance.The Effect of Static and Dynamic Misalignment on Ball Bearing Radial Stiffness. AIAA-2002-4160,2002.
[47] Fujio Hirano.Motion of A Ball in Angular-Contact Ball Bearing[J].Wear,1966,9(5):406～415.
[48]张文轩.基于ANSYS的混合陶瓷球轴承分析与试验研究[D].天津:天津大学硕士学位论文,2004:45～46.
[49]《航空发动机设计手册》总编委会.航空发动机设计手册第19册[M].北京:航空工业出版社,2000:54～58.
[50]周延泽,陆震.高速球轴承球/保持架碰撞模型与冲击特性研究[J].机械设计,2001,9:33～37.
[51]郑德志,王黎钦.航空发动机用高速滚动轴承性能考核及失效分析[J].润滑与密封,2006,7:52～54.
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