偏航变桨轴承力学特性分析及结构优化设计
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摘要
偏航、变桨轴承广泛使用大型四点接触球轴承,工作时承受轴向载荷、径向载荷及倾覆力矩的联合作用,具有工况载荷复杂、结构尺寸大、整体刚度低及工作转速低的特点,因此不能采用普通轴承的分析方法,而有必要针对其展开专门的研究与分析。本文采用数值分析法和有限元仿真法,研究偏航、变桨轴承的力学特性和结构参数的优化设计。
首先,简要分析了偏航、变桨轴承的工作环境、载荷特征、结构形式等特点,详细阐述了以Hertz弹性接触理论为条件的偏航、变桨轴承接触变形和接触应力的非线性关系,推导了偏航、变桨轴承接触载荷和接触刚度的计算方法,并介绍了其静强度和疲劳强度的计算理论。
其次,根据偏航、变桨轴承的使用工况条件、几何结构特点和变形协调关系,建立了考虑实际接触角、游隙、滚道沟曲率半径系数等因素的偏航、变桨轴承力学模型,并给出了采用牛顿—拉夫森迭代法求解力学模型的详细过程,并以某一型号偏航、变桨轴承为例,研究了不同工况条件下轴承的载荷分布规律及实际接触角的变化情况。
接着,采用力学模型与经验公式两种方法计算偏航、变桨轴承的最大接触载荷并进行对比分析,初步验证了偏航、变桨轴承力学模型求解最大接触载荷及计算静强度的正确性。基于力学模型计算接触载荷的方法,实现了偏航、变桨轴承承载曲面和承载曲线的精确绘制。
然后,分析了滚道排距、游隙、接触角、沟曲率半径等结构参数对轴承接触载荷、接触应力、实际接触角、承载滚动体个数等力学性能的影响规律,完成了以最小接触应力为目标函数的偏航、变桨轴承优化模型建立,并采用遗传算法进行求解,从而实现了偏航、变桨轴承结构参数的优化设计。
最后,采用有限元分析法对比分析了无支撑结构和含支撑结构的偏航、变桨轴承两种模型的载荷分布及实际接触角变化规律,并通过与力学模型计算结果进行对比分析,进一步验证了偏航、变桨轴承力学模型求解载荷分布方法的正确性。
The large-scale four-point contact ball bearing is usually used as the yaw and pitch bearing, which are mainly loaded with axial force, radial force and turnover moment, in a wind turbine. The traditional analysis method of rolling element bearing is not useful for the four-point contact ball bearing any more because the bearing is with different structure and low stiffness. So it is necessary to develop a new method for analyzing the mechanical performances of a four-point contact ball bearing. In this study, the mechanical performances analysis and structural optimization design of a yaw and pitch bearing are accomplished based on the new mathematical model developed in this paper. Then, the model and results are verified by the finite element method.
First, the characteristics of yaw and pitch bearing, such as the working environment, load, structure, are analyzed. The nonlinear relationship between the Hertz contact stress and deformation of a rolling bearing is introduced. The calculation method for the contact load and contact stiffness of the yaw and pitch bearing is given. And calculation theories of the static and fatigue strengths are introduced.
Second, according to the working conditions, geometry structure characteristics and deformation compatibility relation of yaw and pitch bearing, a mathematical model considering all kinds of factors, such as the actual contact angle, play and groove curvature coefficients, is developed. And the detail process to solve the mathematical model using the Newton-Raphson iterative method is given. Taking one kind of four-point contact ball bearing as an example, the load distribution and the actual contact angle are researched under the different working conditions.
Then, the maximal contact forces calculated by the mathematical model are compared with those gotten by the empirical formula. The validity of the mathematical model for calculating the maximal contact force and static strength is verified. The load curve and surface are drawn exactly based on the mathematical model of four-point contact ball bearing.
After that, the influence of the structure parameters (groove row distances, play, contact angle, groove curvature coefficients, diameter and number of roller, etc) on the mechanical performances (contact load, contact stress, actual contact angle, number of loaded rollers, etc) is analyzed. The optimization model of four-point contact ball bearing is established taking the minimum contact stress as an objective. The optimized values of key structural parameters are obtained by the optimization model adopting genetic algorithm.
Finally, using the finite element method, load and actual contact angle distributions when the finite model is with support structure or no support structure are analyzed, respectively. The results gotten by the finite element method are compared with those calculated by the mathematical model developed in this paper. The validity of the mathematical model for analyzing the mechanical performances of a four-contact ball bearing is further verified.
首先,简要分析了偏航、变桨轴承的工作环境、载荷特征、结构形式等特点,详细阐述了以Hertz弹性接触理论为条件的偏航、变桨轴承接触变形和接触应力的非线性关系,推导了偏航、变桨轴承接触载荷和接触刚度的计算方法,并介绍了其静强度和疲劳强度的计算理论。
其次,根据偏航、变桨轴承的使用工况条件、几何结构特点和变形协调关系,建立了考虑实际接触角、游隙、滚道沟曲率半径系数等因素的偏航、变桨轴承力学模型,并给出了采用牛顿—拉夫森迭代法求解力学模型的详细过程,并以某一型号偏航、变桨轴承为例,研究了不同工况条件下轴承的载荷分布规律及实际接触角的变化情况。
接着,采用力学模型与经验公式两种方法计算偏航、变桨轴承的最大接触载荷并进行对比分析,初步验证了偏航、变桨轴承力学模型求解最大接触载荷及计算静强度的正确性。基于力学模型计算接触载荷的方法,实现了偏航、变桨轴承承载曲面和承载曲线的精确绘制。
然后,分析了滚道排距、游隙、接触角、沟曲率半径等结构参数对轴承接触载荷、接触应力、实际接触角、承载滚动体个数等力学性能的影响规律,完成了以最小接触应力为目标函数的偏航、变桨轴承优化模型建立,并采用遗传算法进行求解,从而实现了偏航、变桨轴承结构参数的优化设计。
最后,采用有限元分析法对比分析了无支撑结构和含支撑结构的偏航、变桨轴承两种模型的载荷分布及实际接触角变化规律,并通过与力学模型计算结果进行对比分析,进一步验证了偏航、变桨轴承力学模型求解载荷分布方法的正确性。
The large-scale four-point contact ball bearing is usually used as the yaw and pitch bearing, which are mainly loaded with axial force, radial force and turnover moment, in a wind turbine. The traditional analysis method of rolling element bearing is not useful for the four-point contact ball bearing any more because the bearing is with different structure and low stiffness. So it is necessary to develop a new method for analyzing the mechanical performances of a four-point contact ball bearing. In this study, the mechanical performances analysis and structural optimization design of a yaw and pitch bearing are accomplished based on the new mathematical model developed in this paper. Then, the model and results are verified by the finite element method.
First, the characteristics of yaw and pitch bearing, such as the working environment, load, structure, are analyzed. The nonlinear relationship between the Hertz contact stress and deformation of a rolling bearing is introduced. The calculation method for the contact load and contact stiffness of the yaw and pitch bearing is given. And calculation theories of the static and fatigue strengths are introduced.
Second, according to the working conditions, geometry structure characteristics and deformation compatibility relation of yaw and pitch bearing, a mathematical model considering all kinds of factors, such as the actual contact angle, play and groove curvature coefficients, is developed. And the detail process to solve the mathematical model using the Newton-Raphson iterative method is given. Taking one kind of four-point contact ball bearing as an example, the load distribution and the actual contact angle are researched under the different working conditions.
Then, the maximal contact forces calculated by the mathematical model are compared with those gotten by the empirical formula. The validity of the mathematical model for calculating the maximal contact force and static strength is verified. The load curve and surface are drawn exactly based on the mathematical model of four-point contact ball bearing.
After that, the influence of the structure parameters (groove row distances, play, contact angle, groove curvature coefficients, diameter and number of roller, etc) on the mechanical performances (contact load, contact stress, actual contact angle, number of loaded rollers, etc) is analyzed. The optimization model of four-point contact ball bearing is established taking the minimum contact stress as an objective. The optimized values of key structural parameters are obtained by the optimization model adopting genetic algorithm.
Finally, using the finite element method, load and actual contact angle distributions when the finite model is with support structure or no support structure are analyzed, respectively. The results gotten by the finite element method are compared with those calculated by the mathematical model developed in this paper. The validity of the mathematical model for analyzing the mechanical performances of a four-contact ball bearing is further verified.
引文
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[5]罗继伟.滚动轴承受力分析及其进展[J].轴承,2001,7：28-31.
[6]吴云鹏,张文平,孙立红.滚动轴承力学模型的研究及其发展趋势[J].轴承,2004,7：44-46.
[7]杜睿,吴志军.单排球式回转支承的承载能力分析[J].机械设计与制造,2006,9：56-58.
[8]王思明等.四点接触转盘轴承轴向静力分析[J].起重运输机械,2009(10)：14-16.
[9]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.
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[11]徐绍仁,杨友中,白宇光等.特大型负游隙四点接触球轴承拟静力学分析[J].轴承,2009,9：1-3.
[12]S. Zupan, I.Prebil. Carrying angel and capacity of a large single row hall bearing as a function of geometry parameter of the rolling contact and the supporting structure stiffness[J]. Mechanism and Machine Theory,2001(36):1087-1103.
[13]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.
[14]Robert Kunc, Ivan Prebil. Numerical determination of carrying capacity of large rolling bearings [J]. Journal of Materials Processing Technology,155-156 (2004):1696-1703.
[15]Potocnic R, Gocnz P, Flasker J, et al. Fatigue life of double row slewing ball bearing with irregular geometry[J]. Procedia engineering,2010,2:1877-1886.
[16]李建征.盾构机主轴承的有限元分析及寿命研究[D].河南：河南科技大学,2011.
[17]王新荣,陈永波.有限元法基础及ANSYS应用[M].北京：科学出版社,2000.
[18]郑兰疆,李彦等.大型回转轴承的承载性能分析[J].机械设计与研究,2008,2：82-86.
[19]唐艳华,赵云峰.变位机用转盘轴承的载荷分析与仿真[J].机械设计,2011,5：10-14.
[20]丁龙建,洪荣晶.基于ABAQUS的回转支承非线性接触研究[J].煤矿机械,2010,12：68-70.
[21]徐弘毅.重载滚动轴承的仿真与优化设计[D].北京：清华大学,2010.
[22]Ludwik Kania. Modeling of rollers in calculation of slewing bearing with the use of finite elements. Mechanism and Machine Theory,41 (2006) 1359-1376.
[23]Kania L. Modeling of rollers in calculation of slewing bearing with the use of finite elements[J]. Mechanism and machine theory,2006,41:1359-1376.
[24]Smolnicki T, Rusinski E. Superelement-based modeling of load distribution in large-size slewing bearings[J]. Journal of mechanical design,2007,129(4):459-463.
[25]Smolnicki T, Derlukiewicz D, Stanco M. Evaluation of load distribution in the superstructure rotation joint of single-bucket caterpillar excavators [J]. Automation in construction,2008,17:218-223.
[26]Alain Daidie, Zouhair Chaib, Antoine Ghosn.3D Simplified Finite Elements Analysis of Load and Contact Angle in a Slewing Ball Bearings [J]. Journal of Mechanical Design,2008(26):1-8.
[27]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,2010,2:1-10.
[28]孙靖民.现代机械设计方法[M].哈尔滨工业大学出版社,2003.
[29]查全.滚动轴承优化设计方法分析[J].轴承,1985,5：1-3.
[30]高琳.机械优化设计方法综述[J].技术创新,2010(3)：14.
[31]周晴.风力发电机主轴轴承的优化设计及可靠性研究[D].河南：河南科技大学,2011.
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