弹流润滑条件下陶瓷轴承粗糙表面重复接触稳定性研究

Aiming at the failure problem of friction and wear on silicon nitride bearing for high-speed machining centers and precision machine tool, and in order to improve silicon nitride bearing capacity and service life, the shakedown analysis on rough surface repeated contact with elastohydrodynamic lubrication is developeded. The derivation of the contact model is facilitated through the definition of plastic asperities that are assumed to be embedded at a critical depth within the actual surface asperities. The elastohydrodynamic lubrication theory and Hertz theory on rough surface are extented, and a shakedown model on on rough surface repeated contact with elastohydrodynamic lubrication is obtained, and numerical algorithms about the model are presented. The multigrid method, stress and strain release method and linear programming method are given to solve the mathematical model. The relations between deformation of asperity, evolvement of rough surface geometry, elastoplastic deformation, lubricating oil film thickness, the bearing stress, cumulation of residual stress and repeat contact cycle are studied. The shakedown limited of model of rough surface contact under elastohydrodynamic lubrication condition is calculated, and the sensitive factors for affecting the lubricated contact stability are revealed. the necessary conditions for rough surface repeated contact stability under the elastohydrodynamic lubrication condition are obtained. According to the theoretical and experimental results, the geometric parameters of rough surface and elastohydrodynamic lubrication are obtained, and the macro contact equivalent model is developed. The inner relationship is revealed between microscopic rough surfaces comtact model and macroscopic contact model. Eventually the relatively The unified model contact mechanical model under elastohydrodynamic lubrication condition is established, which is suitable for areas of the contact element design, for the development of high speed and heavy load contact element design method. The research results will provide a theoretical foundation and scientific evidence for design of silicon nitride bearing,processing and application of technology of bearing and increase of bearing service life.

瞄准高速加工中心、精密机床等重大装备电主轴陶瓷轴承的摩擦磨损失效问题，以提高陶瓷轴承的承载能力和使用寿命为目的，围绕弹流润滑条件下陶瓷轴承粗糙表面重复接触安定性问题展开研究。通过发展弹流润滑理论、粗糙表面弹塑性接触理论，建立弹流润滑条件下陶瓷轴承粗糙表面接触安定模型，采用多重网格法、应力应变释放法和线性规划法，探究轴承滚道粗糙表面形貌、润滑油膜厚度、油膜承载压力、残余应力场随接触次数的演化规律，确定轴承滚道粗糙表面在弹流润滑条件下的接触安定极限，揭示影响润滑接触稳定性的敏感因素，获得弹流润滑条件下陶瓷轴承粗糙表面重复接触稳定性的必要条件。综合理论计算和实验测试结果，抽取滚道粗糙表面几何参数和润滑特征参数，构建有规可循的宏观接触等效模型，揭示微观粗糙表面接触与宏观接触之间的内在关系。为发展高速重载陶瓷轴承的设计方法、加工与应用技术，延长陶瓷轴承使用寿命，提供理论基础和科学依据。

瞄准高速加工中心、精密机床等重大装备电主轴陶瓷轴承的摩擦磨损失效问题，以提高陶瓷轴承的承载能力和使用寿命为目的，围绕弹流润滑条件下陶瓷轴承粗糙表面重复接触安定性问题展开研究，获得了以下研究成果。建立了尺度相关的分形接触模型。基于分形几何理论，利用双变量的Weierstrass-Mandelbrot函数模拟二维、三维分形粗糙表面，建立了三维分形粗糙表面弹塑性接触模型。推导出各等级微凸体发生弹性、弹塑性以及完全塑性变形的存在条件。确定了粗糙表面上各等级微凸体的面积分布密度函数，获得了总接触载荷和真实接触面积之间的关系式。建立了点、线接触的粗糙表面接触模型。推导出每份接触区域上各个频率指数的微凸体的截断面积密度分布函数，获得了真实接触面积与总接触载荷的解析表达式。建立粗糙表面接触的雷诺方程。将传统的润滑模型简化为一个半无限大的粗糙表面和一半无限大与其作相对运动的光滑表面组成的微弹流问题。采用有限差分法求解其方程，获得油膜厚度与油膜压力。建立了粗糙表面加卸载接触力学模型，对传统的微凸体面积密度分布函数进行变换，分别给出了加、卸载接触过程中不同频率指数微凸体的面积密度分布函数，最终得到加、卸载接触过程中粗糙表面真实接触面积与总接触载荷之间的关系。以上模型中，单个微凸体的临界接触面积与其尺寸相关，随着微凸体等级的增大，微凸体的高度和峰顶曲率半径减小。微凸体的变形顺序为弹性变形、弹塑性变形和完全塑性变形，与经典的赫兹模型保持一致。粗糙表面的力学性能仅与最小等级及后续的六个等级微凸体相关，其余微凸体基本上对整个粗糙表面的力学性能影响很小。设计了粗糙表面接触实验。通过测量表面形貌的分形参数、粗糙度及下压量与接触面压的关系，验证了以上模型的正确性。根据以上理论与实验测试的结果，建立了粗糙表面接触的安定性条件。