真实微观齿面的动态接触模型与滚-滑复合摩擦因数计算方法研究

Study on the model, quantitative calculation and process simulation of tooth surface friction, is the basis of active design of gear tribology and accurate analysis of dynamic of gear drive. As the aim of the gear system in unlubrication friction, dynamic contact model on tooth microsurface including errors and calculation method for rolling-rubbing friction and dash friction are studied, by theoretical research, system simulation, optimization and test technical, and the frictional process is simulated and optimized. Composite error function is built based on the influence of teeth errors to engaging force.The flank data is get by 3D roughness teater. The right tooth microsurface including errors is get by the composition of the error function and the above flank data. The elastic dynamic model on asperity contact is built after the discretization and simulation of friction surfaces, and the multi-tip contact problem and the stress, deformation, friction force on the micsurface are studied. The kinemics, loads and frictional states studied, the calculation method for the composite friction coefficient of rolling-rubbing friction is studied, which can descript accurately the varied rule of rolling friction and rubbing friction on the engaged teeth, and then the models and calculating methods of pitch and corner dash researched in special position as well. After system state parameters gotten and the typical load spectrum including errors worked out, the frictional process is simulated and then optimized. These studies are very important to explore the friction and wear mechanism of gear drive, to improve the design and manufacture level of high-end gear products.

齿面复杂的摩擦机理建模、定量预测与过程仿真，是齿轮摩擦学主动设计和动力学精确计算的基础。本课题以无润滑齿轮系统为研究对象，理论研究、系统仿真、优化反求与试验技术相结合，研究真实微观齿面动态接触模型和滚-滑复合摩擦及冲击摩擦因数计算方法，模拟并优化摩擦过程。根据齿面误差对啮合力的影响，构造法向与齿向综合误差函数；利用粗糙度仪测得微观齿面数据并重构，与误差函数耦合获得真实微观齿面的数据模型。在分片摩擦表面上构建粗糙面弹性动态接触模型，研究多峰接触问题及微观表面上的应力、变形、摩擦等。根据齿面运动、载荷及摩擦状态，建立描述齿面滚动与滑动摩擦变化规律的滚-滑复合摩擦因数计算模型及其计算方法，研究特殊啮合位置发生的节点冲击和线外啮合冲击摩擦。构建系统运行状态参数序列，编制典型的有摩擦载荷谱，对啮合周期内的摩擦过程进行模拟和优化。上述研究，对提升高端齿轮产品的设计制造水平具有重要理论价值和工程意义。

本项目以无润滑齿轮传动系统为对象，将理论研究、数值模拟、反求方法与测试技术相结合，研究了含误差微观齿面的弹塑性动态接触模型和滚滑复合摩擦及啮合冲击摩擦因数的计算方法。基于局部坐标变换法，将测出的微观齿貌和蒙特卡洛法计算出的传动误差进行合成，得到了含误差宏观齿形与粗糙齿面的合成模型。根据重构的微齿面和微凸峰的统计分布率，在分片摩擦表面上建立了正/侧接触的单微凸体弹塑性理论计算模型和正接触多微凸体的弹塑性理论模型，并通过有限元接触分析研究了啮合齿面的应力、变形与接触面积的变化规律。根据齿根最大拉应力的数值计算解和试验测试值，基于隔代映射小种群遗传算法反求出齿面摩擦因数的多项式代理模型，进而计算出沿齿高方向及全齿面上的摩擦因数。基于齿轮传动线外啮合冲击原理，提出在啮合线方向上构建含系统误差和轮齿变形的啮入与啮出冲击摩擦计算模型，求解出冲击点的速度、冲击力与摩擦因数。另外，考虑齿面摩擦分别基于Lewis悬臂梁模型和第四强度理论推导出弧齿锥齿轮的弯曲与接触强度计算式，与ISO齿轮强度计算标准及有限元分析结果进行了对比验证。上述研究对于真实微观齿面几何建模、粗糙齿面微接触理论分析与数值模拟、滚滑复合摩擦因数的定量计算、线外啮合冲击摩擦建模及有摩擦齿轮弯曲与接触强度的计算具有一定的参考价值，对高端齿轮产品的设计制造具有一定的工程意义。