风电变桨轴承柔性支承研究与设计参数分析
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摘要
风电变桨轴承作为风电装备关键零部件之一,其设计和制造是制约我国重大装备业实力整体提升的一个瓶颈。本文选取某典型兆瓦级风电机组的变桨轴承——双排四点接触球转盘轴承为研究对象,根据赫兹弹性接触理论对承受径向力、轴向力和倾覆力矩的该转盘轴承建立力学模型,并利用Newton-Raphson方法对该模型进行数值仿真。该模型不仅考虑三个方向的联合载荷的作用,同时考虑了包括径向游隙、沟曲率半径系数、接触角和双排滚动体间距等参数在内的众多重要轴承设计参数。在该模型的基础上,以弹性力学等理论为基础,详细推导了在轴承外载荷和滚动体接触力等负荷下转盘轴承内、外套圈的弯曲变形公式,联立多非线性超越方程组求解四点接触球转盘轴承的相关力学问题。对赫兹弹性接触理论下建立的刚性套圈模型和弹性力学下建立的柔性套圈模型进行数值仿真,考量两个模型下轴承四个接触对的载荷分布以及载荷分布范围、内、外套圈上滚动体的接触应力分布、套圈弯曲变形与力矩分布等问题。着重对影响轴承承载能力的重要设计参数径向游隙、接触角、沟曲率半径系数等进行了仿真,并给予了详细的分析,提出了对应的轴承设计建议。文章所做以上工作为四点接触球转盘轴承,甚至转盘轴承的设计提供了重要的理论依据,具有一定的工程实际应用价值。
Wind turbine pitch bearing is one of the key components of wind power equipment, whose design and manufacturing is a bottleneck restricting to enhance the overall strength of major equipment industry in China. This paper selected a typical MW wind turbine pitch bearings-double row four point contact ball slewing bearing for the study. A pitch bearing mechanical model was established according to the Hertz elastic contact theory that consider radial force, axial force and overturning moment, and use Newton-Raphson method for numerical simulation of the model. The model is not only consider the three directions of the load, but also take into account a number of important design parameters, including radial clearance, groove radius of curvature coefficient, contact angle and double roller bearings spacing, etc. Based on the theory of elasticity, the equations about the bearing internal and outer ring bending deformation under the rolling contact load and the bearing load were detailed induced, and multiple non-linear transcendental equation group were solved to analyze four-point contact ball bearing related mechanical problems. The rigid ring model based on the theory of Hertz elastic contact and the flexible ring model based on the theory of elasticity were taken to numerical simulation, researching on the load distribution and distribution span of the four bearing contact diagonal, rolling element contact stress distribution, ring bending and torque distribution problems, etc.. Focusing on the research of some important design parameters impacting the carrying capacity of the bearing, including radial clearance, contact angle and groove radius of curvature coefficient, a detailed analysis was given, and the corresponding bearing design recommendations were presented. Work done by this paper provides an important theoretical basis for four-point contact ball slewing bearing, and even slewing bearing, and has some practical application value of engineering.
Wind turbine pitch bearing is one of the key components of wind power equipment, whose design and manufacturing is a bottleneck restricting to enhance the overall strength of major equipment industry in China. This paper selected a typical MW wind turbine pitch bearings-double row four point contact ball slewing bearing for the study. A pitch bearing mechanical model was established according to the Hertz elastic contact theory that consider radial force, axial force and overturning moment, and use Newton-Raphson method for numerical simulation of the model. The model is not only consider the three directions of the load, but also take into account a number of important design parameters, including radial clearance, groove radius of curvature coefficient, contact angle and double roller bearings spacing, etc. Based on the theory of elasticity, the equations about the bearing internal and outer ring bending deformation under the rolling contact load and the bearing load were detailed induced, and multiple non-linear transcendental equation group were solved to analyze four-point contact ball bearing related mechanical problems. The rigid ring model based on the theory of Hertz elastic contact and the flexible ring model based on the theory of elasticity were taken to numerical simulation, researching on the load distribution and distribution span of the four bearing contact diagonal, rolling element contact stress distribution, ring bending and torque distribution problems, etc.. Focusing on the research of some important design parameters impacting the carrying capacity of the bearing, including radial clearance, contact angle and groove radius of curvature coefficient, a detailed analysis was given, and the corresponding bearing design recommendations were presented. Work done by this paper provides an important theoretical basis for four-point contact ball slewing bearing, and even slewing bearing, and has some practical application value of engineering.
引文
[1]廖明夫,R.Gasch, J.Twele风力发电技术[M].西安：西北工业大学出版社,2009.
[2]Tony Burton, David Sharpe, Nick Jenkins. Wind energy handbook[J]. England:John Wiley & Sons, Ltd.2001.
[3]世界风能协会.2010年度世界风能发展报告[R]. Germany世界风能协会,2011.
[4]杨晓蔚.风电产业、风电设备及风电轴承[J].轴承,2009,12：54-59.
[5]International Electrotechnical Commission. Wind turbines-Part1:Design requirements (IEC61400-1)[Z].2005-08.
[6]芮晓明,柳亦兵,马志勇.风力发电机组设计[M].北京：机械工业出版社,2010.
[7]Julia KOller,Johann Koppel, Wolfgang Peters.Offshore Wind Energy[M]. Berlin: Springer-Verlag.2006.
[8]Jose Ignacio Amasorrain, Xabier Sagartzazu,Jorge Damian.Load distribution in a four contact-point slewing bearing [J]. Mechanism and Machine Theory,2003,(38): 479-496.
[9]S.Zupan, I.Prebil. Carrying Angle and Carrying Capacity of a Large Single Row Ball Bearing as a Function of Geometry Parameters of The Rolling Contact and the Supporting Structure Stiffness [J]. Mechanism and Machine Theory,2001,(36):1087-1103.
[10]Neng Tung Liao,Jen Fin Lin. A New Method for the Analysis of Deformation and Load in a Ball Bearing With Variable Contact Angle[J]. Journal of Mechanical Design,2001,(123):304-312.
[11]李云峰,吴宗彦.游隙对单排四点接触球转盘轴承载荷分布的影响[J].机械传动,2010,34(3)：56-58.
[12]陈龙,张慧,邱明,等.转盘轴承螺栓连接特性分析[J].轴承,2009,(8)：10-13,37.
[13]Chen Long, Zhang Yaping, Xia Xintao. Contact Stress and Deformation of Blade Bearing in Wind Turbine[J].2010 International Conference on Measuring Technology and Mechatronics Automation,2010,833-836.
[14]陈龙,赵联春,夏新涛,等.变桨轴承载荷分布分析[J].轴承,2010,(1)：1-4,9.
[15]汪洪,陈原.转盘轴承承载能力及额定寿命的计算方法[J].轴承,2008,(2)：7-9.
[16]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京：清华大学出版社,2003.
[17]Jorge Damian,Alberto Serna.Design of Four Contact-Point Slewing Bearing with a New Load Distribution Procedure to Account for Structural Stiffness[J]. Journal of Mechanical Design,2010,(132):021006-1-10.
[18]Rok Potocnik, Peter Goncz, Joze Flasker, et,al. Fatigue life of double row slewing ball bearing with irregular geometry[J]. Procedia Engineering,2010,(2):1877-1886.
[19]Liu Hongbin, Li Jishun, Xue Yujun, et,al. Study on Load Distribution Calculating Method of Link Slewing Bearing with the Elements[J]. Advanced Science Letters,2011,(4):2759-2763.
[20]Gao XH, Huang XD,Wang H. Modelling of ball-raceway contacts in a slewing bearing with non-linear springs[J]. Journal Of Mechanical Engineering Science,2011, 225(C4):827-831.
[21]Grochmal TR, Forbrich CP, Lynch AF. Nonlinear bearing force and torque model for a toothless self-bearing servomotor [J]. IEEE Transactions On Magnetics,2008, 44(7):1805-1814.
[22]Ludwik Kania. Modelling of Rollers in Calculation of Slewing Bearing with the Use of Finite Elements [J]. Mechanism and Machine Theory,2006, (41):1359-1376.
[23]Tadeusz Smolnicki, Eugeniusz Rusin'ski. Superelement-Based Modeling of Load Distribution in Large-Size Slewing Bearings [J]. Journal of Mechanical Design, 2007, (129):459-463.
[24]Aurelian Vadean, Dimitri Leray, Jean Guillot. Bolted joints for very large bearings numerical model development[J].Finite Elements in Analysis and Design, 2006,(42):298-313.
[25]王大力,孙立明,单服兵,等ANSYS在求解轴承接触问题中的应用[J].轴承,2002,(9)：1-4.
[26]张淑锋.塔式起重机回转支承系统的有限元分析[D].湖南：湘潭大学,2003.
[27]刘丹丹,韩红彪,刘红彬.三排滚柱式回转支承有限元分析[J].矿山机械,2010,(14)：58-62.
[28]唐云冰,高德平,罗贵火.航空发动机滚动轴承的载荷分布研究[J].航空学报,2006,27(6)：1117-1121.
[29]万长森.滚动轴承的分析方法[M].北京：机械工业出版社,1987.
[30]冈本纯三.球轴承的设计计算[M].北京：机械工业出版社,2003.
[31]T.A.Harris, M.N.Kotzalas. Rolling bearing analysis[M]. New York:Taylor& Francis Group,2006.
[32]邓思二,贾群义.滚动轴承设计原理[M].北京：中国标准出版社,2008.
[33]姚振强,王成焘.薄壁轴承座中滚动轴承载荷分布的分析与计算[J].机械设计与制造,1991,(1)：31-34.
[34]Tadeusz Smolnicki, Damian Derlukiewicz, Mariusz Stanco. Evaluation of load distribution in the superstructure rotation joint of single-bucket caterpillar excavators[J]. Automation in Construction,2008,17:218-223.
[35]Robert Kunc, Andrej Zerovnik, Matej Zvokelj, Ivan Prebil. Numerical determination of the carrying capacity of rolling rotational connections[J]. Materials and technology,2007,41 (2):73-76.
[36]S.P Timoshenko,J.M Gere.Theory of elastic stability[M].New York:Dover Pubn Inc,1961.
[37]S.P Timoshenko. Strength of materials[M]. New York:D.VAN Nostrand Company,1940.
[38]J. Y. LIU,Y. P. CHIU.Analysis of a Thin Elastic Ring Under Arbitrary Loading [J]. Journal of Engineering for Industry,1974,870-876.
[39]乐可锡,全永听,周桂如,等.谐波轴承负荷分布的一种新算法[J].浙江大学学报,1994,28(4)：306-404.
[40]郭宝霞.柔性支承滚动轴承负荷分布的光弹性实验研究[J].轴承,1984,5：5-10.
[41]徐立民,陈卓.回转支承[M].合肥：安徽科学技术出版社,1988.
[42]刘宏伟,刑振平,刘河,等.兆瓦级风电机组变桨轴承设计与技术要求[J].风能,2010,9：46-49.
[43]侯宁.影响回转支承承载能力的四个参数[J].建筑机械,2002,1：21-22.
[44]杨晓蔚.沟曲率半径系数fi(e)对深沟和角接触球轴承载荷能力的影响[J].轴承,1995,6：5-7.
[2]Tony Burton, David Sharpe, Nick Jenkins. Wind energy handbook[J]. England:John Wiley & Sons, Ltd.2001.
[3]世界风能协会.2010年度世界风能发展报告[R]. Germany世界风能协会,2011.
[4]杨晓蔚.风电产业、风电设备及风电轴承[J].轴承,2009,12：54-59.
[5]International Electrotechnical Commission. Wind turbines-Part1:Design requirements (IEC61400-1)[Z].2005-08.
[6]芮晓明,柳亦兵,马志勇.风力发电机组设计[M].北京：机械工业出版社,2010.
[7]Julia KOller,Johann Koppel, Wolfgang Peters.Offshore Wind Energy[M]. Berlin: Springer-Verlag.2006.
[8]Jose Ignacio Amasorrain, Xabier Sagartzazu,Jorge Damian.Load distribution in a four contact-point slewing bearing [J]. Mechanism and Machine Theory,2003,(38): 479-496.
[9]S.Zupan, I.Prebil. Carrying Angle and Carrying Capacity of a Large Single Row Ball Bearing as a Function of Geometry Parameters of The Rolling Contact and the Supporting Structure Stiffness [J]. Mechanism and Machine Theory,2001,(36):1087-1103.
[10]Neng Tung Liao,Jen Fin Lin. A New Method for the Analysis of Deformation and Load in a Ball Bearing With Variable Contact Angle[J]. Journal of Mechanical Design,2001,(123):304-312.
[11]李云峰,吴宗彦.游隙对单排四点接触球转盘轴承载荷分布的影响[J].机械传动,2010,34(3)：56-58.
[12]陈龙,张慧,邱明,等.转盘轴承螺栓连接特性分析[J].轴承,2009,(8)：10-13,37.
[13]Chen Long, Zhang Yaping, Xia Xintao. Contact Stress and Deformation of Blade Bearing in Wind Turbine[J].2010 International Conference on Measuring Technology and Mechatronics Automation,2010,833-836.
[14]陈龙,赵联春,夏新涛,等.变桨轴承载荷分布分析[J].轴承,2010,(1)：1-4,9.
[15]汪洪,陈原.转盘轴承承载能力及额定寿命的计算方法[J].轴承,2008,(2)：7-9.
[16]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京：清华大学出版社,2003.
[17]Jorge Damian,Alberto Serna.Design of Four Contact-Point Slewing Bearing with a New Load Distribution Procedure to Account for Structural Stiffness[J]. Journal of Mechanical Design,2010,(132):021006-1-10.
[18]Rok Potocnik, Peter Goncz, Joze Flasker, et,al. Fatigue life of double row slewing ball bearing with irregular geometry[J]. Procedia Engineering,2010,(2):1877-1886.
[19]Liu Hongbin, Li Jishun, Xue Yujun, et,al. Study on Load Distribution Calculating Method of Link Slewing Bearing with the Elements[J]. Advanced Science Letters,2011,(4):2759-2763.
[20]Gao XH, Huang XD,Wang H. Modelling of ball-raceway contacts in a slewing bearing with non-linear springs[J]. Journal Of Mechanical Engineering Science,2011, 225(C4):827-831.
[21]Grochmal TR, Forbrich CP, Lynch AF. Nonlinear bearing force and torque model for a toothless self-bearing servomotor [J]. IEEE Transactions On Magnetics,2008, 44(7):1805-1814.
[22]Ludwik Kania. Modelling of Rollers in Calculation of Slewing Bearing with the Use of Finite Elements [J]. Mechanism and Machine Theory,2006, (41):1359-1376.
[23]Tadeusz Smolnicki, Eugeniusz Rusin'ski. Superelement-Based Modeling of Load Distribution in Large-Size Slewing Bearings [J]. Journal of Mechanical Design, 2007, (129):459-463.
[24]Aurelian Vadean, Dimitri Leray, Jean Guillot. Bolted joints for very large bearings numerical model development[J].Finite Elements in Analysis and Design, 2006,(42):298-313.
[25]王大力,孙立明,单服兵,等ANSYS在求解轴承接触问题中的应用[J].轴承,2002,(9)：1-4.
[26]张淑锋.塔式起重机回转支承系统的有限元分析[D].湖南：湘潭大学,2003.
[27]刘丹丹,韩红彪,刘红彬.三排滚柱式回转支承有限元分析[J].矿山机械,2010,(14)：58-62.
[28]唐云冰,高德平,罗贵火.航空发动机滚动轴承的载荷分布研究[J].航空学报,2006,27(6)：1117-1121.
[29]万长森.滚动轴承的分析方法[M].北京：机械工业出版社,1987.
[30]冈本纯三.球轴承的设计计算[M].北京：机械工业出版社,2003.
[31]T.A.Harris, M.N.Kotzalas. Rolling bearing analysis[M]. New York:Taylor& Francis Group,2006.
[32]邓思二,贾群义.滚动轴承设计原理[M].北京：中国标准出版社,2008.
[33]姚振强,王成焘.薄壁轴承座中滚动轴承载荷分布的分析与计算[J].机械设计与制造,1991,(1)：31-34.
[34]Tadeusz Smolnicki, Damian Derlukiewicz, Mariusz Stanco. Evaluation of load distribution in the superstructure rotation joint of single-bucket caterpillar excavators[J]. Automation in Construction,2008,17:218-223.
[35]Robert Kunc, Andrej Zerovnik, Matej Zvokelj, Ivan Prebil. Numerical determination of the carrying capacity of rolling rotational connections[J]. Materials and technology,2007,41 (2):73-76.
[36]S.P Timoshenko,J.M Gere.Theory of elastic stability[M].New York:Dover Pubn Inc,1961.
[37]S.P Timoshenko. Strength of materials[M]. New York:D.VAN Nostrand Company,1940.
[38]J. Y. LIU,Y. P. CHIU.Analysis of a Thin Elastic Ring Under Arbitrary Loading [J]. Journal of Engineering for Industry,1974,870-876.
[39]乐可锡,全永听,周桂如,等.谐波轴承负荷分布的一种新算法[J].浙江大学学报,1994,28(4)：306-404.
[40]郭宝霞.柔性支承滚动轴承负荷分布的光弹性实验研究[J].轴承,1984,5：5-10.
[41]徐立民,陈卓.回转支承[M].合肥：安徽科学技术出版社,1988.
[42]刘宏伟,刑振平,刘河,等.兆瓦级风电机组变桨轴承设计与技术要求[J].风能,2010,9：46-49.
[43]侯宁.影响回转支承承载能力的四个参数[J].建筑机械,2002,1：21-22.
[44]杨晓蔚.沟曲率半径系数fi(e)对深沟和角接触球轴承载荷能力的影响[J].轴承,1995,6：5-7.