精度主导的大重合度齿轮动态设计理论与实验研究

It can effectively reduce the loading of single tooth when the contact-ratio of gears is greater than 2. The high-contact-ratio gear has significant effect in reducing the weight, vibration and noise. However, because the number of teeth participating in meshing is more than the normal, the dynamic meshing performance of the high-contact-ratio gear is very sensitive to the accuracy parameters. Therefore, this project will focus on the insufficiency of the existing theoretical system of gear dynamic design which does not take the contact ratio and the accuracy parameters fully into account. We analyze the influence of the accurate tooth surface model of the high-contact-ratio gear, the contact condition and the gear’s dynamic excitation by the accuracy parameters which contain the tooth surface morphology and the geometric deviation. Sufficient consideration is given to the contact ratio. We establish the accuracy-dominant contact model and dynamic model of the high-contact-ratio gear and conduct the accuracy-dominant high-contact-ratio gear's bearing capacity research and nonlinear dynamics research by using theoretical method such as the fractal theory and the experiment method. Then, we explore nonlinear mapping between accuracy parameters and bearing and vibration noise characteristics. Based on the research, we proceed to study modification method and multi-objective optimization of high-contact-ratio gear’s parameters and establish the design theory system of high-contact-ratio gear's parameters, especially the design theory system of accuracy parameters, which will be suitable for the work condition of high speed and heavy loading. This is supposed to lay a foundation of developing the excellent performance gear product. In conclusion, this project has important theoretic and practical value.

重合度大于2.0的齿轮传动能有效地减小单齿载荷，对传动系统的减重、减振和降噪有着显著的作用，但由于同时参与啮合的轮齿对数多，导致大重合度齿轮副的动态啮合性能对精度参数十分敏感。为此，本项目提出针对现有齿轮动态设计理论体系中未充分考虑重合度及精度因素这一不足，研究包括齿面形貌及几何偏差等在内的各种精度参数并充分考虑重合度因素对精确齿面模型、接触状态以及动态激励的影响，建立适合于大重合度齿轮的接触模型，进而建立起其动力学模型，应用分形理论等理论方法并结合实验手段开展精度主导的大重合度齿轮系统承载能力和非线性动力学研究，探索精度参数对承载特性和振动噪声特性之间的非线性映射关系，并以此为基础进行修形理论研究和系统参数的多目标优化，建立起适合于高速重载工况下的大重合度齿轮设计，尤其是精度设计理论体系，为开发性能优良的重载齿轮产品打下基础。因此本项目有着重要的理论和实际意义。

齿轮作为最为常用的传动基础件之一，其性能直接影响机械系统性能。采用大重合度齿轮能有效地减小单齿载荷，对传动系统的减重、减振和降噪有着显著的作用。但重合度增加意味着同时参与啮合的轮齿对数多，导致大重合度齿轮副的动态啮合性能对精度参数十分敏感。为此，本项目针对大重合度齿轮副的啮合特性以及目前理论研究的不足，开展精度主导的大重合度齿轮传动动态设计理论与实验研究。主要研究内容及研究结果如下：1）基于齿轮精度标准和GPS标准体系，将分形理论与几何偏差建模技术相结合，对综合考虑表面形貌和几何偏差等精度参数的大重合度齿轮齿面进行建模研究，形成了精确的齿面数学模型；分析接触面在载荷作用下的变形性质，利用分形理论中两粗糙曲面的M-B分形接触模型，建立了考虑精度参数的大重合度齿轮接触模型；基于考虑精度参数的接触模型，研究了大重合度齿轮的齿间载荷分配及齿面接触应力等承载能力特性。2）根据大重合度齿轮接触和受载情况，计算出轮齿的弹性变形和齿侧间隙，建立了大重合度齿轮时变啮合刚度、传动误差计算模型；基于前述齿轮动态内部激励计算模型，建立考虑精度参数的大重合度齿轮的动力学模型，并进行动力学特性分析。3）计算齿轮系统功重比，同时根据大重合度齿轮动力学模型，分析大重合度齿轮系统振动噪声特性，非线性降维后，建立了大重合度齿轮基本参数、精度参数与功重比、振动噪声之间的非线性映射关系，完成了参数的多目标优化；根据大重合度齿轮承载接触分析和振动噪声分析结果进行齿廓修形设计，确定最大修形量，选择不同的修形曲线以及修形长度，并进行综合性能对比分析，从而获得最佳的齿廓修形参数，建立了适合于大重合度齿轮的齿廓修形方法。本项目的实施为开发低噪声、大承载的高性能齿轮产品奠定了科学理论基础。