基于摩擦与润滑状态下的齿面形貌对其动力学行为影响之研究

Gear mechanism is widely used in the transmission system. In current gear dynamics method, "contact" is described as the "spring-damper" system, and research on gear dynamics influenced by the macro factors are discussed，while the influences by contact surface's micro topography are often ignored. In order to solve this problem, the basic character of "contact" is first studied, and then the gear surface profile is simulated through using the W-M function in the fractal theory. Combining with the M-B fractal contact model, the fractal contact model of gear pairs is set up considering the friction. The coupling method between the fractal contact model of gear pairs and the torsional vibration model of gear pairs is studied, and then the fractal model of gear dynamics is created, which can analyze the gear dynamic affected by the surface topography (fractal parameters); Furthermore, the way of testing the fractal parameters of gear surface is discussed and the gear dynamics behavior influenced by the wear and lubrication is also presented applying the fractal dynamic model. Through the dynamic character testing of gear pairs with different friction and lubrication, the above analysis and conclusion is verified. The research fruits here are a beneficial supplement to existing gear dynamic theory, which can be used to the design and improvement of gear products and has an important theoretical significance and application value.

齿轮机构在传动系统中应用广泛，其动力学分析方法常将接触描述成"弹簧-阻尼"系统，从宏观尺度讨论动力学的影响因素，但其忽视了接触表面的微观形貌的影响。本项目拟从齿轮"接触"本身这一基本特性出发，利用分形理论中的W-M函数模拟齿面轮廓，结合M-B分形接触模型，建立考虑摩擦的齿轮分形接触模型；研究该模型与齿轮副的扭转振动模型的耦合方法，建立齿轮副的分形动力学模型。通过该模型分析表面形貌（分形参数）对动力学特性的影响。同时研究不同磨损和润滑的齿面分形参数的测定方法，并应用上述动力学模型研究磨损和润滑的齿轮接触动力学行为。通过对不同润滑和磨损状态的齿轮振动、噪音等动力学特性测试，验证上述理论的科学性。该研究是对现有齿轮动力学理论的有益补充，对于指导齿轮设计和提高其产品性能，具有重要的理论意义和应用价值。

本项目研究摩擦和润滑状态下齿面形貌对其动力学的影响。主要工作如下：基于分形理论的表面形貌模拟方法，实现渐开线齿轮的齿面形貌模拟；完成圆柱体表面特征尺度系数的测定试验，获得特征尺度系数的准确数值，得到特征尺度系数与表面粗糙度之间的近似关系式，大大简化其求解过程。设计基于分形理论的齿面形貌绘制软件，可实现绘制不同分形维数、特定参数直齿轮和斜齿轮的二维及三维表面微观形貌。建立存在摩擦时的两圆柱表面接触承载能力分析的分形接触模型、考虑摩擦的两球体接触承载分析的分形接触模型、切向接触刚度的分形模型和法向接触刚度分形模型，上述模型为进一步研究考虑摩擦下的齿轮动力学建立理论基础。建立基于分形理论的考虑齿面形貌的单自由度齿轮间隙非线性动力学模型，研究不同表面形貌下分形特征及其动力学特性。推导考虑弹性流体动压润滑状态下的两圆柱体结合面分形接触模型，研究润滑对两圆柱体结合面接触承载能力的影响。设计齿轮动力学特性试验台，并结合分形动力学模型和试验，得出有利于动力学性能提高的润滑方式及其相应的齿面分形维数特征。本项目的研究成果是对现有齿轮动力学理论的有益补充，对于指导齿轮设计和提高其产品性能，具有重要的理论意义和应用价值。