球轴承多体接触动力学研究
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摘要
球轴承被广泛用于机械系统的旋转支撑部件,对机械系统动力学性能有着重要的影响。目前,国内外滚动轴承力学研究主要运用静力学和拟动力学方法,深入研究润滑、摩擦、温度、波纹度或保持架的影响。在当今国际制造水平向静音轴承发展的过程中,为了降低球轴承振动、优化轴承动态性能和探索轴承工程应用环境的影响,精确的轴承动力学设计与动力学分析是球轴承的理论研究和工程应用亟待解决的关键问题。本文主要研究目的是提出一种快速有效的球轴承多体接触动力学分析的新方法,忽略润滑和保持架接触冲击的影响,建立球轴承的三维多参数耦合多体接触动力学分析模型,深入研究球轴承的接触振动机理。
本文基于云南省省院省校合作项目“数控万能工具铣床XK8140动态数字样机建模与仿真分析关键技术研究”(批准号：2004YX12)的资助,从多体系统动力学观点出发,围绕球轴承多体接触动力学问题进行了相关研究。在轴承外圈等效方法、球轴承刚柔多体接触动力学模型、新型广义-α法、动力学分析和球轴承柔性多体接触振动分析等方面取得了研究成果。论文的主要研究工作包括：
(1)基于柔性多体动力学理论,提出了以等效刚体单元的相对坐标和曲线铁木辛柯梁单元描述球轴承外圈的运动和结构弹性变形的新方法。结合球轴承套圈滚道的表面方程,研究了套圈滚道表面的三角网格模型,从而运用基于罚函数法的接触力显式表达式,建立了钢球和套圈的接触动力学模型。在此基础上,建立了考虑钢球和套圈动态接触关系的球轴承多参数耦合刚柔多体接触动力学模型。
(2)针对球轴承多体接触动力学分析中涉及的多体接触冲击、游隙等非线性因素和具有套圈单元离散引起的高频振荡特征,结合隐式数值积分解耦法,提出了适用于球轴承接触动力学分析的新型广义-α法。通过数值实例讨论了新型广义-α法的阻尼耗散特性、数值精度、收敛阶次、稳定性和计算效率。
(3)运用新型广义-a法对球轴承刚柔多体接触动力学模型进行了仿真研究,计算了运转状态下球轴承的接触非线性振动特性。分析了不同结构参数、转速和载荷等因素对球轴承的接触载荷分布、弹性变形、接触角、振动位移、加速度和频率等动力学特性和接触振动响应的影响。计算并探讨了运转状态下球轴承的接触非线性振动频率的变化规律,表明运转状态下在径向力作用时的球轴承接触非线性振动频率比在预紧力作用时的具有更加明显的非线性、时变性和周期性等特点。以固定式加速度计安装方式实现了球轴承振动真实信号的测量,实验验证了球轴承刚柔多体接触动力学的理论研究方法、计算分析结果的正确性和有效性。进一步丰富了球轴承振动理论,为球轴承动态设计和动态性能改善提供了参考。
(4)结合有限元方法与柔性多体动力学方法,考虑套圈结构弹性变形、钢球和套圈动态接触关系,建立了新的球轴承柔性多体接触动力学分析模型。在不同载荷条件下计及转速、游隙和离心力影响时,分别讨论了运转状态下球轴承的动态接触应力、弹性变形、接触角等接触振动特性。进一步认识了滚动轴承变支承刚度下的柔性接触振动规律和载荷分布规律。
理论研究方法和研究结果是多体接触动力学方法在球轴承动力学中的新尝试,丰富和完善了滚动轴承的振动理论,对以振动和疲劳寿命为目标的滚动轴承与轴承系统的动态设计、动力学分析和工程应用不仅具有重要的实用价值,而且具有重要的理论意义。
Ball bearings, as a kind of basic supporting components, are widely used in rotating machines. Their vibration and performances have an important influence on dynamic behavior of mechanical systems. The statics and quasi-dynamic method have been applied to study the effect of lubrication, friction, temperature, waviness or pockets on rolling bearings mechanics at present. With the trend of making quiet running bearings in today's world, in order to reduce vibration, optimize dynamic performances and research the effect of working conditions, accurate dynamic design and analysis of ball bearings have to be studied in the theoretical research and engineering application of ball bearings. The major purpose of this thesis is to provide a new, rapid and effective method on the multi-bodies contact dynamics of ball bearings. Without the effect of lubrication and pockets impact, the three dimensional multi-bodies contact dynamics analysis models of ball bearings have been constructed with multi-parameters coupling. The contact vibration mechanism of ball bearings has been studied thoroughly.
This thesis is based on the Yunnan Province Fund Cooperative Project" Reseaching on the key technologies of modeling and dynamic simulation analysis for virtual prototype of CNC universal tool milling machine"(Authorize number: 2004YX12). According to dynamics of multibody systems, the focus of this thesis is on multibody contact dynamics problem of ball bearings. Some progress and accomplishment have been made on the key issues such as equivalent method of outer ring, the multi-rigid-flexible bodies contact dynamics model of ball bearings, new generalized-a algorithms, dynamics analysis and the multi-flexible bodies contact vibrations analysis of ball bearings. The major focus of this thesis is listed as follow:
(1)A new method for outer ring's motion and structural elastic deformation is studied by the relative coordinates of equivalent rigid elements and curved Timoshenko beam elements based on multi-flexible bodies dynamics. The triangle mesh model for ring's races is established based on the surface equations. The rolling contact dynamics models are constructed and the calculation programme is written for dynamic contact force based on penalty method. Therefore, the multi-rigid-flexible bodies contact dynamics analysis models of ball bearings are established with multi-parameters coupling and dynamic contact between balls and rings.
(2)It takes account of the nonlinear factors such as multibody contact-impact, clearances and the essential characteristics such as high frequency vibration resulting from discrete rings. A new generalized-a algorithm is studied by implicit numerical integration decoupling algorithms for contact dynamics analysis of ball bearings. The new generalized-a algorithm's numerical dissipation, convergence, precision, stability and efficiency have been discussed by famous numerical experiments.
(3) The new generalized-a algorithm was applied to simulate contact nonlinear dynamics and vibrations of ball bearings. The effect of different structural and load parameters, rotating speeds on dynamics characteristics and contact vibration rules such as contact load distribution, elastic deformation, contact angle, vibration displacements, accelerations and frequencies of ball bearings has been analyzed. The curves of contact nonlinear vibration frequencies were calculated and discussed. It is found that the nonlinear frequencies of contact vibration with radial load are more obvious to nonlinearity, time variety and period than that with axial preload. The contact dynamics theoretical models, numerical algorithms and research results have been verified experimentally by the digital measurement system of ball bearings' vibration and fixed measurement method with the use of accelerometer. The contact dynamics models and results have been further enriched vibration theory of ball bearings and given to reference for dynamic design and improving dynamic characteristics of ball bearings.
(4)Considering ring's elastic deformation and dynamic contact between balls and ring's races, the new multi-flexible bodies contact dynamics analysis models of ball bearings are established, which are based on finite element method and multi-flexible bodies dynamics. Considering the effect of different load parameters, rotate speed, clearances and centrifugal force and so on, the distributions and rules of dynamic contact stress, elastic deformation and contact angle have been discussed. The flexible contact vibrations rules and load distributions rules of ball bearings under the varying supporting stiffness have been understood further by the research results.
The theoretical methods and research results are a new try of multi-bodies contact dynamics for vibration of ball bearings and have significances not only in perfecting and enriching the vibration theory of rolling element bearings but also in guiding the design, analysis and application of ball bearings and bearings systems with the purpose of vibration and fatigue life.
本文基于云南省省院省校合作项目“数控万能工具铣床XK8140动态数字样机建模与仿真分析关键技术研究”(批准号：2004YX12)的资助,从多体系统动力学观点出发,围绕球轴承多体接触动力学问题进行了相关研究。在轴承外圈等效方法、球轴承刚柔多体接触动力学模型、新型广义-α法、动力学分析和球轴承柔性多体接触振动分析等方面取得了研究成果。论文的主要研究工作包括：
(1)基于柔性多体动力学理论,提出了以等效刚体单元的相对坐标和曲线铁木辛柯梁单元描述球轴承外圈的运动和结构弹性变形的新方法。结合球轴承套圈滚道的表面方程,研究了套圈滚道表面的三角网格模型,从而运用基于罚函数法的接触力显式表达式,建立了钢球和套圈的接触动力学模型。在此基础上,建立了考虑钢球和套圈动态接触关系的球轴承多参数耦合刚柔多体接触动力学模型。
(2)针对球轴承多体接触动力学分析中涉及的多体接触冲击、游隙等非线性因素和具有套圈单元离散引起的高频振荡特征,结合隐式数值积分解耦法,提出了适用于球轴承接触动力学分析的新型广义-α法。通过数值实例讨论了新型广义-α法的阻尼耗散特性、数值精度、收敛阶次、稳定性和计算效率。
(3)运用新型广义-a法对球轴承刚柔多体接触动力学模型进行了仿真研究,计算了运转状态下球轴承的接触非线性振动特性。分析了不同结构参数、转速和载荷等因素对球轴承的接触载荷分布、弹性变形、接触角、振动位移、加速度和频率等动力学特性和接触振动响应的影响。计算并探讨了运转状态下球轴承的接触非线性振动频率的变化规律,表明运转状态下在径向力作用时的球轴承接触非线性振动频率比在预紧力作用时的具有更加明显的非线性、时变性和周期性等特点。以固定式加速度计安装方式实现了球轴承振动真实信号的测量,实验验证了球轴承刚柔多体接触动力学的理论研究方法、计算分析结果的正确性和有效性。进一步丰富了球轴承振动理论,为球轴承动态设计和动态性能改善提供了参考。
(4)结合有限元方法与柔性多体动力学方法,考虑套圈结构弹性变形、钢球和套圈动态接触关系,建立了新的球轴承柔性多体接触动力学分析模型。在不同载荷条件下计及转速、游隙和离心力影响时,分别讨论了运转状态下球轴承的动态接触应力、弹性变形、接触角等接触振动特性。进一步认识了滚动轴承变支承刚度下的柔性接触振动规律和载荷分布规律。
理论研究方法和研究结果是多体接触动力学方法在球轴承动力学中的新尝试,丰富和完善了滚动轴承的振动理论,对以振动和疲劳寿命为目标的滚动轴承与轴承系统的动态设计、动力学分析和工程应用不仅具有重要的实用价值,而且具有重要的理论意义。
Ball bearings, as a kind of basic supporting components, are widely used in rotating machines. Their vibration and performances have an important influence on dynamic behavior of mechanical systems. The statics and quasi-dynamic method have been applied to study the effect of lubrication, friction, temperature, waviness or pockets on rolling bearings mechanics at present. With the trend of making quiet running bearings in today's world, in order to reduce vibration, optimize dynamic performances and research the effect of working conditions, accurate dynamic design and analysis of ball bearings have to be studied in the theoretical research and engineering application of ball bearings. The major purpose of this thesis is to provide a new, rapid and effective method on the multi-bodies contact dynamics of ball bearings. Without the effect of lubrication and pockets impact, the three dimensional multi-bodies contact dynamics analysis models of ball bearings have been constructed with multi-parameters coupling. The contact vibration mechanism of ball bearings has been studied thoroughly.
This thesis is based on the Yunnan Province Fund Cooperative Project" Reseaching on the key technologies of modeling and dynamic simulation analysis for virtual prototype of CNC universal tool milling machine"(Authorize number: 2004YX12). According to dynamics of multibody systems, the focus of this thesis is on multibody contact dynamics problem of ball bearings. Some progress and accomplishment have been made on the key issues such as equivalent method of outer ring, the multi-rigid-flexible bodies contact dynamics model of ball bearings, new generalized-a algorithms, dynamics analysis and the multi-flexible bodies contact vibrations analysis of ball bearings. The major focus of this thesis is listed as follow:
(1)A new method for outer ring's motion and structural elastic deformation is studied by the relative coordinates of equivalent rigid elements and curved Timoshenko beam elements based on multi-flexible bodies dynamics. The triangle mesh model for ring's races is established based on the surface equations. The rolling contact dynamics models are constructed and the calculation programme is written for dynamic contact force based on penalty method. Therefore, the multi-rigid-flexible bodies contact dynamics analysis models of ball bearings are established with multi-parameters coupling and dynamic contact between balls and rings.
(2)It takes account of the nonlinear factors such as multibody contact-impact, clearances and the essential characteristics such as high frequency vibration resulting from discrete rings. A new generalized-a algorithm is studied by implicit numerical integration decoupling algorithms for contact dynamics analysis of ball bearings. The new generalized-a algorithm's numerical dissipation, convergence, precision, stability and efficiency have been discussed by famous numerical experiments.
(3) The new generalized-a algorithm was applied to simulate contact nonlinear dynamics and vibrations of ball bearings. The effect of different structural and load parameters, rotating speeds on dynamics characteristics and contact vibration rules such as contact load distribution, elastic deformation, contact angle, vibration displacements, accelerations and frequencies of ball bearings has been analyzed. The curves of contact nonlinear vibration frequencies were calculated and discussed. It is found that the nonlinear frequencies of contact vibration with radial load are more obvious to nonlinearity, time variety and period than that with axial preload. The contact dynamics theoretical models, numerical algorithms and research results have been verified experimentally by the digital measurement system of ball bearings' vibration and fixed measurement method with the use of accelerometer. The contact dynamics models and results have been further enriched vibration theory of ball bearings and given to reference for dynamic design and improving dynamic characteristics of ball bearings.
(4)Considering ring's elastic deformation and dynamic contact between balls and ring's races, the new multi-flexible bodies contact dynamics analysis models of ball bearings are established, which are based on finite element method and multi-flexible bodies dynamics. Considering the effect of different load parameters, rotate speed, clearances and centrifugal force and so on, the distributions and rules of dynamic contact stress, elastic deformation and contact angle have been discussed. The flexible contact vibrations rules and load distributions rules of ball bearings under the varying supporting stiffness have been understood further by the research results.
The theoretical methods and research results are a new try of multi-bodies contact dynamics for vibration of ball bearings and have significances not only in perfecting and enriching the vibration theory of rolling element bearings but also in guiding the design, analysis and application of ball bearings and bearings systems with the purpose of vibration and fatigue life.
引文
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