基于印刷机滚筒轴承接触问题的有限元分析
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摘要
印刷机滚筒上的圆柱滚子轴承是印刷机的重要部件之一,它应能满足高速、重载、工作精度高等要求。因此,如何保证印刷机轴承处于良好的工作状态对整个印刷生产具有重大的意义。本文主要以赫兹接触理论和有限元法为理论基础,对印刷机滚筒轴承接触问题的分析方法进行了分析和研究。
首先,运用了赫兹公式和有限元法对外形规则、接触状态简单的模型进行接触应力和接触变形计算。其次,重点分析了有限元法处理接触问题的一般过程,给出了如何选择接触单元、建立有限元模型,如何划分网格、建立接触对,如何加载、求解。提出了分析过程中应注意的关键问题,如网格单元大小的选择,载荷施加问题等。最后,以高宝科美特70(KBA COMET 70)报纸轮转印刷机压印滚筒上的轴承为例分析了三维单圆柱轴承和全尺寸轴承的受力变形情况。本论文研究的主要内容有：
1、基于圆柱滚子轴承力学分析的理论及原则、单体接触问题中的Hertz理论,以高宝科美特70 (KBA COMET 70)报纸轮转印刷机滚筒用NN3024ASK.M.P型双排圆柱滚子轴承为例,详细分析了轴承的接触应力、变形、载荷分布情况。
2、建立了接触分析的有限元模型,采用接触问题的拉格朗日乘子法,分别讨论了二维接触模型在不同单元长度不同载荷作用下的一系列的结果,得到了接触变形图,讨论了网格疏密对求解结果的影响,提出了解决接触问题的有效方法,为分析三维接触问题打下基础。
3、建立了最大载荷滚动体处的接触模型,得出了滚动体、套圈的接触应力变形图,利用有限元数值方法对接触弹性变形量与作用载荷的关系指数进行了修正。
4、在单个滚子轴承的基础上建立了全尺寸三维圆柱滚子轴承NN3024ASK.M.P的有限元模型,详细论述了ANSYS提供的边界条件设置以及轴承载荷的施加情况。对轴承进行数值模拟并分析,得到了轴承性能分析的有效方法,为该轴承承载能力动力学分析研究奠定了基础。
5、应用有限元数值模拟技术对圆柱滚子进行了凸度设计。
本文的研究方法和结果对印刷机滚筒轴承的可靠性分析和优化设计具有一定的参考价值。
The Cylindrical Roller Bearing is one of the important components of the printing machine. Not only the roller Bearing is working in high precision, but also it must meet the challenge of over loading and high speed. Therefore, it is significant for entire printing production to ensure the normal work and life of the cylindrical Roller Bearing. The analyzing method of the contact Problems and engineering application is researched basing on Hertz contacting theory and finite element method.
First contact stress and deformation of Parts which have normal shapes and simple contacting status are calculated using Hertz formula and finite element method. Then process of finite element method dealing with contact problem is discussed. Choice of contact elements, establishing finite element model, portion of gridding, establishing contact Pairs, loading and solution are expatiated. At last, The distorted deform of the one cylindrical Roller Bearing and entire cylindrical Roller Bearing is given.
The thesis includes the main contents in the listed below:
1、Take the NN3024ASK.M.P bearing which produced by KBA used on roller for example, based on the power analysis and Hertz theory with cylinder roller contact problem, the contact stress, displacement, and the load distributed is analyzed in detailed.
2、Finite element model of the contact analysis is established. based on the contact theory with Lagrange, the results of the 2d finite element contact model in different length and different load is discussed. The contact stress is got, and the results influence by different mesh is given, which make a good guide for 3d contact problems.
3、The contact model which take the biggest load is established, and the contact stress between the cylindrical roller and ring is demonstrated. The index between the displacement and load is modified based on the FEM methods and theory.
4、The whole model and finite element model of the NN3024 bearing is established, and the math simulation and analysis of the border and load is made, the method of the properties of the bearing is given, and make a foundation for dynamic analysis.
5、Based on the Finite element numerical simulation technology, the cylinder roller convexity is designed.
The method and outcome will bring important effect on optimization design and reliable of the cylindrical Roller Bearing.
首先,运用了赫兹公式和有限元法对外形规则、接触状态简单的模型进行接触应力和接触变形计算。其次,重点分析了有限元法处理接触问题的一般过程,给出了如何选择接触单元、建立有限元模型,如何划分网格、建立接触对,如何加载、求解。提出了分析过程中应注意的关键问题,如网格单元大小的选择,载荷施加问题等。最后,以高宝科美特70(KBA COMET 70)报纸轮转印刷机压印滚筒上的轴承为例分析了三维单圆柱轴承和全尺寸轴承的受力变形情况。本论文研究的主要内容有：
1、基于圆柱滚子轴承力学分析的理论及原则、单体接触问题中的Hertz理论,以高宝科美特70 (KBA COMET 70)报纸轮转印刷机滚筒用NN3024ASK.M.P型双排圆柱滚子轴承为例,详细分析了轴承的接触应力、变形、载荷分布情况。
2、建立了接触分析的有限元模型,采用接触问题的拉格朗日乘子法,分别讨论了二维接触模型在不同单元长度不同载荷作用下的一系列的结果,得到了接触变形图,讨论了网格疏密对求解结果的影响,提出了解决接触问题的有效方法,为分析三维接触问题打下基础。
3、建立了最大载荷滚动体处的接触模型,得出了滚动体、套圈的接触应力变形图,利用有限元数值方法对接触弹性变形量与作用载荷的关系指数进行了修正。
4、在单个滚子轴承的基础上建立了全尺寸三维圆柱滚子轴承NN3024ASK.M.P的有限元模型,详细论述了ANSYS提供的边界条件设置以及轴承载荷的施加情况。对轴承进行数值模拟并分析,得到了轴承性能分析的有效方法,为该轴承承载能力动力学分析研究奠定了基础。
5、应用有限元数值模拟技术对圆柱滚子进行了凸度设计。
本文的研究方法和结果对印刷机滚筒轴承的可靠性分析和优化设计具有一定的参考价值。
The Cylindrical Roller Bearing is one of the important components of the printing machine. Not only the roller Bearing is working in high precision, but also it must meet the challenge of over loading and high speed. Therefore, it is significant for entire printing production to ensure the normal work and life of the cylindrical Roller Bearing. The analyzing method of the contact Problems and engineering application is researched basing on Hertz contacting theory and finite element method.
First contact stress and deformation of Parts which have normal shapes and simple contacting status are calculated using Hertz formula and finite element method. Then process of finite element method dealing with contact problem is discussed. Choice of contact elements, establishing finite element model, portion of gridding, establishing contact Pairs, loading and solution are expatiated. At last, The distorted deform of the one cylindrical Roller Bearing and entire cylindrical Roller Bearing is given.
The thesis includes the main contents in the listed below:
1、Take the NN3024ASK.M.P bearing which produced by KBA used on roller for example, based on the power analysis and Hertz theory with cylinder roller contact problem, the contact stress, displacement, and the load distributed is analyzed in detailed.
2、Finite element model of the contact analysis is established. based on the contact theory with Lagrange, the results of the 2d finite element contact model in different length and different load is discussed. The contact stress is got, and the results influence by different mesh is given, which make a good guide for 3d contact problems.
3、The contact model which take the biggest load is established, and the contact stress between the cylindrical roller and ring is demonstrated. The index between the displacement and load is modified based on the FEM methods and theory.
4、The whole model and finite element model of the NN3024 bearing is established, and the math simulation and analysis of the border and load is made, the method of the properties of the bearing is given, and make a foundation for dynamic analysis.
5、Based on the Finite element numerical simulation technology, the cylinder roller convexity is designed.
The method and outcome will bring important effect on optimization design and reliable of the cylindrical Roller Bearing.
引文
[1]王时任,周都刚,彭文生.轴承基础知识[M].上海科学技术出版社出版,1983.5
[2]郭敦霖,谢志强.国外轴承工业概况[M].机械工业部第十设计研究院.机械工业科技情报课题92100302号
[3]罗继伟.滚动轴承受力分析及其进展[J].轴承,2001.9
[4]万长森.滚动轴承的分析方法.北京：机械工业出版社,1987
[5]T. A. Harris. Rolling Bearing Analysis(4th edition).New York:John Wiley and Sons, Inc.,2001
[6]A. Choudhury and N. A. Tandon. A Theoretical Model to Predict Vibration Response to Rolling Bearings to Distributed Defects under Radial Load. Trans ASME, J Vibr Acoust,1998,120(1):214-220
[7]丁长安.圆柱滚子轴承的受载变形.轴承,1996,(9)：6-9
[8]H. Hertz," Uber die Beruhrung Fester Elastischer Korrper(On the contact of elastic solids), "[M]J. Reine Angew.Math.,92,156-171,1882.
[9]K. L. Johnson, "Contact Mechanics,"[M]Cambridge University Press,London,1985.
[10]俞茂宏,工程强度理论.北京：高等教育出版社,1998
[11]濮良贵,级名刚.机械设计.高等教育出版社,1996
[12]P.A 别捷尔曼,Б.В茨伯金.滚动轴承手册.北京：机械工业出版社,1966
[13]L. E. Goodman. Contact Stress Analysis of Normally Loaded Rough Spheres. Joumal of Mechanics, 1962,515-522
[14]冯登泰.磨耗型轮轨弹塑性机静力接触的解析解.铁道学报,1988,10(2)：1-13
[15]A. Ekberg. H. Bjamched, R. Lun den. A Fatigue Litc Model for General Rolling Contact with Application to Wheel/Rail Damage, Fatigue Fract. Engng Mater,1995,18(10):1189-1199
[16]雷任静,颜秉善.减缓轨头接触疲劳损伤的对策研究铁道学报1992,13(2)：5-9
[17]R. Smallwood. J. C. Sinclair, KJ. Sawley. An Optimization Technique to Minimize Rail Contac Stresses.Wear,1999,(144):373-384
[18]A. P. Boresi, O. M. Sidebottom F. D. Seely, J. O. Smith. ADVANCED MECHANICS OF MATERIALS.THIRD EDITION. John Wiley and Sons,1978
[19]加林.弹性理论的接触问题.北京：科学出版社,1958
[20]G M. L. Glabwell,范天佑译.经典弹性理论中的接触问题.北京：北京理工大学出版社,1991
[21][英]K. L. Johnson著.徐秉业,罗学富,刘信声等译.接触力学[M].高等教育出版社.1992.5
[22]孔祥安,江晓禹,金学松.固体接触力学[M].北京：中国铁道出版社,1999
[23]冯登泰.接触力学的发展概况.力学进展,1987,4
[24]S. K. Chan, and I. S. Tuba, "A finite element method for contact problems of solid bodies-part I:Theory and validation; part Ⅱ:Application to turbine blade fastenings,"[J]International Journal of Mechanical Sciences,13,pp.615-625;pp.627-639,1971.
[25]K. J. Bathe, and A. Chaudhary," A solution method for planar and axisymmetric contact problems," [M]International Journal for Numerical Methods in Engineering,21,pp.65-88,1985.
[26]H. Parisch," A consistent tangent stiffness matrix for three-dimensional non-linear contact analysis," [M]International Journal for Numerical Methods in Engineering,28,pp.1803-1812,1989.
[27]M. Bartos, and Z. Kestranek," Numerical solution of the contact problem. Application to a simple model of the human hip joint,"[M]Journal of Computational and Applied Mathematics,63, pp.439-447,1995.
[28]S. H. Ju, J. J. Stone, and R. E. Rowlands, "A new symmetric contact element stiffness matrix for frictional contact problems,"[M]Computers&Structures,54(2),pp.289-301,1995.
[29]R. E. Jones, and J. M. Solberg, "A novel finite element formulation for frictionless contact problems,"[M]International Journal for Numerical Methods in Engineering,38,pp.2603-2617 1995.
[30]M. Sassi, and M. Desvignes, "A seminumerical method for three-dimensional frictionless contact problems," [M]Mathl.Comput.Modelling,28(4-8),pp.413-425,1998
[31]D. Barlam, and E. Zahavi, "The reliability of solutions in contact problems,"[M]Computers& Structures,70,pp.35-45,1999.
[32]冯登泰.磨耗型轮轨弹塑性静力接触的解析解.铁道学报,1988,10(2)：1-13
[33]雷腾.轮轨接触应力的计算和分析.中国铁道科学,1985,6(1)：53-65
[34]Paul B, Hashemi J. Rail-wheeigeometry geometry associated with contact stress analysis. Repo-rt no.FRD/ORD-78/41,Sept.1979,1-13
[35]颜秉善.钢轨伤损及换轨周期的预侧.铁道学报,1988,10(2)：86-95
[36]Lawn BR, Wiederhorn SM. Contact Fracture in Brittle Materiais,Contact Mechanics and Wear Rail/Wheel System, Waterloo USA:University of Waterloo PreSS,1982,133-146
[37]魏先祥.轮轨静接触时的应力状态.铁道学报,1991,13(2)：1-11
[38]张焱,孔祥安,金学松等.轮轨三维弹塑性接触应力的算法研究.力学与实践,2000,22(1)：23-27
[39]张焱.铁路轮轨接触应力研究：[学位论文].四川：西南交通大学,1998
[40]罗继伟.滚动轴承中的弹性接触问题及其数值求解：[博士学位论文].北京：清华大学,1989
[41]冈本纯三著,黄志强译.球轴承的设计计算.北京：机械工业出版社,2003
[42]霍林文编.上海交通大学摩擦学研究室译.摩擦学原理.北京：机械工业出版社,1981
[43]S. P. Timoshenko and J. N. Goodier. Theory of Elasticity.北京：清华大学出版社,2004
[44]白葳,喻海良.通用有限元分析ANSYS8.0基础教程[M].清华大学出版社,2005.5
[45]张胜民.基于有限元软件ANSYS7.0的结构分析[M].清华大学出版社,2003.12
[46]杜平安,甘娥忠,于亚婷.有限元法原理、建模及应用[M].国防工业出版社,2004.8
[47]张朝晖.ANSYS工程应用范例入门与提高[M].清华大学出版社.2004.10
[48]叶先磊,史亚杰.ANSYS工程分析软件应用实例[M].北京：清华大学出版社,2003
[49]王勖成.有限单元法.[M].清华大学出版,2003.7
[50]J. C. Simo, T. A. Laursen. An Augmented Lagrangian Treatment of contact Problems Involving Friction.Computer and Structures,1992,43(1):97-116
[51]李皓月,周天朋.ANSYS工程计算应用教程[M].北京：中国铁道出版社,2003,1：427-489.
[52]王国强.实用工程数值模拟技术及在ANSYS上的实践[M].西安：西北工业大学出版社,1999,8.
[53]杨生华.齿轮接触有限元分析[J].计算力学学报.2003,20(2)：189-194.
[54]陈家瑞.汽车构造[M].人民交通出版社,1996,第2版.
[55]GLundberg & A.Palmgren:Dynamic Capacity of Rolling Bearings[M]. Jngeniors-vetenskademiens Nr.196(1947)
[56]李润方,龚剑霞.接触问题数值方法及在机械设计中的应用[M].重庆：重庆出版社,1991,2.
[57]王国强.实用工程数值模拟技术及在ANSYS上的实践[M].西安：西北工业大学出版社,1999,8
[58]余俊.滚动轴承计算[M].北京：高等教育出版社,1993,7.
[59]刘泽九.滚动轴承应用手册[M].北京：机械工业出版社,2007,7
[60]商跃进.有限元原理与ANSYS应用指南[M].北京：清华大学出版社,2005,6
[61][美]罗伯特.D.库克等.关正西等译.有限元分析的概念与应用[M].西安：西安交通大学出版社,2007
[62]周宁等.ANSYS APDL高级工程应用实例分析与二次开发[M].北京：中国水利水电出版社,2007
[63]张亚欧等.ANSYS 7.0有限元分析实用教程[M].北京：清华大学出版社,2004,7
[64]张朝晖.ANSYS 11.0结构分析工程应用实例解析[M].北京：机械工业出版社,2008,1
[2]郭敦霖,谢志强.国外轴承工业概况[M].机械工业部第十设计研究院.机械工业科技情报课题92100302号
[3]罗继伟.滚动轴承受力分析及其进展[J].轴承,2001.9
[4]万长森.滚动轴承的分析方法.北京：机械工业出版社,1987
[5]T. A. Harris. Rolling Bearing Analysis(4th edition).New York:John Wiley and Sons, Inc.,2001
[6]A. Choudhury and N. A. Tandon. A Theoretical Model to Predict Vibration Response to Rolling Bearings to Distributed Defects under Radial Load. Trans ASME, J Vibr Acoust,1998,120(1):214-220
[7]丁长安.圆柱滚子轴承的受载变形.轴承,1996,(9)：6-9
[8]H. Hertz," Uber die Beruhrung Fester Elastischer Korrper(On the contact of elastic solids), "[M]J. Reine Angew.Math.,92,156-171,1882.
[9]K. L. Johnson, "Contact Mechanics,"[M]Cambridge University Press,London,1985.
[10]俞茂宏,工程强度理论.北京：高等教育出版社,1998
[11]濮良贵,级名刚.机械设计.高等教育出版社,1996
[12]P.A 别捷尔曼,Б.В茨伯金.滚动轴承手册.北京：机械工业出版社,1966
[13]L. E. Goodman. Contact Stress Analysis of Normally Loaded Rough Spheres. Joumal of Mechanics, 1962,515-522
[14]冯登泰.磨耗型轮轨弹塑性机静力接触的解析解.铁道学报,1988,10(2)：1-13
[15]A. Ekberg. H. Bjamched, R. Lun den. A Fatigue Litc Model for General Rolling Contact with Application to Wheel/Rail Damage, Fatigue Fract. Engng Mater,1995,18(10):1189-1199
[16]雷任静,颜秉善.减缓轨头接触疲劳损伤的对策研究铁道学报1992,13(2)：5-9
[17]R. Smallwood. J. C. Sinclair, KJ. Sawley. An Optimization Technique to Minimize Rail Contac Stresses.Wear,1999,(144):373-384
[18]A. P. Boresi, O. M. Sidebottom F. D. Seely, J. O. Smith. ADVANCED MECHANICS OF MATERIALS.THIRD EDITION. John Wiley and Sons,1978
[19]加林.弹性理论的接触问题.北京：科学出版社,1958
[20]G M. L. Glabwell,范天佑译.经典弹性理论中的接触问题.北京：北京理工大学出版社,1991
[21][英]K. L. Johnson著.徐秉业,罗学富,刘信声等译.接触力学[M].高等教育出版社.1992.5
[22]孔祥安,江晓禹,金学松.固体接触力学[M].北京：中国铁道出版社,1999
[23]冯登泰.接触力学的发展概况.力学进展,1987,4
[24]S. K. Chan, and I. S. Tuba, "A finite element method for contact problems of solid bodies-part I:Theory and validation; part Ⅱ:Application to turbine blade fastenings,"[J]International Journal of Mechanical Sciences,13,pp.615-625;pp.627-639,1971.
[25]K. J. Bathe, and A. Chaudhary," A solution method for planar and axisymmetric contact problems," [M]International Journal for Numerical Methods in Engineering,21,pp.65-88,1985.
[26]H. Parisch," A consistent tangent stiffness matrix for three-dimensional non-linear contact analysis," [M]International Journal for Numerical Methods in Engineering,28,pp.1803-1812,1989.
[27]M. Bartos, and Z. Kestranek," Numerical solution of the contact problem. Application to a simple model of the human hip joint,"[M]Journal of Computational and Applied Mathematics,63, pp.439-447,1995.
[28]S. H. Ju, J. J. Stone, and R. E. Rowlands, "A new symmetric contact element stiffness matrix for frictional contact problems,"[M]Computers&Structures,54(2),pp.289-301,1995.
[29]R. E. Jones, and J. M. Solberg, "A novel finite element formulation for frictionless contact problems,"[M]International Journal for Numerical Methods in Engineering,38,pp.2603-2617 1995.
[30]M. Sassi, and M. Desvignes, "A seminumerical method for three-dimensional frictionless contact problems," [M]Mathl.Comput.Modelling,28(4-8),pp.413-425,1998
[31]D. Barlam, and E. Zahavi, "The reliability of solutions in contact problems,"[M]Computers& Structures,70,pp.35-45,1999.
[32]冯登泰.磨耗型轮轨弹塑性静力接触的解析解.铁道学报,1988,10(2)：1-13
[33]雷腾.轮轨接触应力的计算和分析.中国铁道科学,1985,6(1)：53-65
[34]Paul B, Hashemi J. Rail-wheeigeometry geometry associated with contact stress analysis. Repo-rt no.FRD/ORD-78/41,Sept.1979,1-13
[35]颜秉善.钢轨伤损及换轨周期的预侧.铁道学报,1988,10(2)：86-95
[36]Lawn BR, Wiederhorn SM. Contact Fracture in Brittle Materiais,Contact Mechanics and Wear Rail/Wheel System, Waterloo USA:University of Waterloo PreSS,1982,133-146
[37]魏先祥.轮轨静接触时的应力状态.铁道学报,1991,13(2)：1-11
[38]张焱,孔祥安,金学松等.轮轨三维弹塑性接触应力的算法研究.力学与实践,2000,22(1)：23-27
[39]张焱.铁路轮轨接触应力研究：[学位论文].四川：西南交通大学,1998
[40]罗继伟.滚动轴承中的弹性接触问题及其数值求解：[博士学位论文].北京：清华大学,1989
[41]冈本纯三著,黄志强译.球轴承的设计计算.北京：机械工业出版社,2003
[42]霍林文编.上海交通大学摩擦学研究室译.摩擦学原理.北京：机械工业出版社,1981
[43]S. P. Timoshenko and J. N. Goodier. Theory of Elasticity.北京：清华大学出版社,2004
[44]白葳,喻海良.通用有限元分析ANSYS8.0基础教程[M].清华大学出版社,2005.5
[45]张胜民.基于有限元软件ANSYS7.0的结构分析[M].清华大学出版社,2003.12
[46]杜平安,甘娥忠,于亚婷.有限元法原理、建模及应用[M].国防工业出版社,2004.8
[47]张朝晖.ANSYS工程应用范例入门与提高[M].清华大学出版社.2004.10
[48]叶先磊,史亚杰.ANSYS工程分析软件应用实例[M].北京：清华大学出版社,2003
[49]王勖成.有限单元法.[M].清华大学出版,2003.7
[50]J. C. Simo, T. A. Laursen. An Augmented Lagrangian Treatment of contact Problems Involving Friction.Computer and Structures,1992,43(1):97-116
[51]李皓月,周天朋.ANSYS工程计算应用教程[M].北京：中国铁道出版社,2003,1：427-489.
[52]王国强.实用工程数值模拟技术及在ANSYS上的实践[M].西安：西北工业大学出版社,1999,8.
[53]杨生华.齿轮接触有限元分析[J].计算力学学报.2003,20(2)：189-194.
[54]陈家瑞.汽车构造[M].人民交通出版社,1996,第2版.
[55]GLundberg & A.Palmgren:Dynamic Capacity of Rolling Bearings[M]. Jngeniors-vetenskademiens Nr.196(1947)
[56]李润方,龚剑霞.接触问题数值方法及在机械设计中的应用[M].重庆：重庆出版社,1991,2.
[57]王国强.实用工程数值模拟技术及在ANSYS上的实践[M].西安：西北工业大学出版社,1999,8
[58]余俊.滚动轴承计算[M].北京：高等教育出版社,1993,7.
[59]刘泽九.滚动轴承应用手册[M].北京：机械工业出版社,2007,7
[60]商跃进.有限元原理与ANSYS应用指南[M].北京：清华大学出版社,2005,6
[61][美]罗伯特.D.库克等.关正西等译.有限元分析的概念与应用[M].西安：西安交通大学出版社,2007
[62]周宁等.ANSYS APDL高级工程应用实例分析与二次开发[M].北京：中国水利水电出版社,2007
[63]张亚欧等.ANSYS 7.0有限元分析实用教程[M].北京：清华大学出版社,2004,7
[64]张朝晖.ANSYS 11.0结构分析工程应用实例解析[M].北京：机械工业出版社,2008,1