空间非渐开线变厚齿轮传动及参数激励同伦分析方法研究

The new type of beveloid gear pair design science problems will be refined based on the key factors of spacial beveloid gear system with nonlinear oscillations which limited its working performance. The theory of parametric design will be established and new type of beveloid gear pair will be developped furthermore with improvement of its bearing capacity because of the line contact and with theoretical breakthrough of traditional involute cylindrical gear category. The homotopy analysis method (HAM) will be used to analyze the response of the nonlinear dynamics equations to gear systems with parametric excitations. And those nonlinear dynamics phenomena with different parameters and loads will be analyzed such as primary resonances, superharmonic resonances, subharmonic resonances and bifurcation. Moreover, vibration and noise mehanism of gear systems will be studied by HAM. The influence and change rule on the amplitude-frequency response curves will be studied by means of the tooth modificaton expression of nonlinear dynamics of gear systems and by means of theoretical analysis, numerical simulation and experimental varification. All of these studies will not only provide theoretical guidance to the improvement of gear system reliability and their performance lives, but also can develop into the innovation design theory and the new research directions of tooth modification of spacial non-involute beveloid gears. This project is expected to provide a basic technical support to resolve those key design problems about low vibration and low noise gear systems.

将制约空间变厚齿轮传动系统性能的关键非线性振动因素，凝练为新型变厚齿轮副设计科学问题，突破传统的渐开线圆柱齿轮范畴，在提高其承载能力的同时，实现新型非渐开线变厚齿轮空间传动线接触承载功能，建立其结构参数化设计理论，探索设计加工出新型高性能变厚齿轮副。将改进的同伦分析方法（HAM）引入到该参数激励齿轮系统非线性动力学方程中分析其振动响应特性，探索出不同参数和不同载荷激励作用下，该系统中存在的主共振、超谐波共振、次谐波共振、分叉等非线性动力学特性，分析其振动和噪声的产生机理。通过研究该齿轮系统的修形非线性动力学特性，并采取理论分析、数值仿真和实验验证相结合的方法得出轮齿修形对幅频响应曲线的影响机理和变化规律，为提高齿轮系统的可靠性，延长其性能寿命提供理论指导，创新出非渐开线空间变厚齿轮传动设计新理论和轮齿修形研究新方向，为解决低振动、低噪声齿轮系统的关键设计难题提供基础技术支撑。

变厚齿轮是齿轮传动的最一般形式，因其变位系数沿轴向变化，导致不同端截面上具有不同的齿厚。变厚齿轮由于具有消隙功能，可以实现平行轴、相交轴、交错轴之间的传动，因而特别适用于对回差要求严格的精密传动中。由于渐开线齿轮在空间传动中属于点接触而限制了承载能力的提高，本项目突破了传统的渐开线圆柱齿轮范畴，将制约空间变厚齿轮传动系统性能的关键因素，凝练为新型变厚齿轮副设计科学问题，利用空间啮合原理建立了参数化设计理论，推导和分析了新型空间变厚齿轮的齿廓形状。在提高其承载能力的同时，实现了新型非渐开线变厚齿轮空间传动线接触承载功能，探索设计加工出了新型高性能变厚齿轮副，提出了产业化加工方法，并搭建了齿轮系统综合实验台。在此基础上利用改进的同伦分析方法（HAM）分析和研究该参数激励齿轮系统非线性振动响应特性，探索出不同参数和不同载荷激励作用下，该系统中存在的各种非线性动力学特性，分析其振动和噪声的产生机理。通过研究该齿轮系统的修形非线性动力学特性，采取理论分析、数值仿真和实验验证相结合的方法得出轮齿修形对幅频响应曲线的影响机理和变化规律，为提高齿轮系统的可靠性，延长其性能寿命提供理论指导，创新出非渐开线空间变厚齿轮传动设计新理论和轮齿修形研究新方向，为解决低振动、低噪声齿轮系统的关键设计难题提供基础技术支撑。