基于共轭曲线的新型交错轴齿轮啮合理论与设计方法研究

The researches about the design theories and methods of crossed-axis gears are always intensive in the field of gear transmission. In order to meet the needs of critical equipment, this project aims to develop novel meshing theory and design methods of crossed-axis gears based on conjugate curve meshing theory. In previous studies, the applicant has found that conjugate curve meshing theory can be applied to design point-contact gears in the field of gear transmission of parallel axis and intersecting axis. Corresponding prototype gearboxes represented high-performance characteristics. Therefore, this project tries to complete further researches on the conjugate curve gear in the field of crossed-axis gear transmission by mathematical analysis, numerical analysis, simulation and experiments. In this research project, first, the meshing principles of conjugate curves will be investigated in mathematics. Then, from gear meshing theory, the meshing surface construction methods from conjugate curves and corresponding surface optimization methods will be developed. Besides, the mechanical analysis will be completed by elastic mechanics and computational mechanics methods. Next, based on computer numerical control milling machines, the manufacture methods of tooth surfaces of these gears will be researched. At last, the experiments about prototype gearboxes will be completed to verify developed theory and investigate their performance characteristics. All the research results will construct a complete theory of crossed-axis conjugate curve gears. This project will expand the applications of conjugate curve meshing theory in the field of gear transmission and provide innovative theory and design methods for developing novel high-performance crossed-axis gear transmission devices.

交错轴齿轮的设计理论与方法一直是齿轮传动领域研究热点。本项目针对重大装备的迫切需求，以共轭曲线啮合思想为基础，发展新型交错轴齿轮啮合理论和设计方法。申请人在前期研究中已发现共轭曲线理论可有效应用于平行轴和相交轴点接触齿轮设计中，相关样机展现出优良的运行特性。因此，本项目拟采用数理解析、数值分析、仿真计算与试验验证相结合的研究方法，进一步完成交错轴领域共轭曲线齿轮研究：在数理层面发展交错轴齿轮的共轭曲线啮合原理；以齿轮啮合理论为基础，形成曲线至齿面的构建方法，并提出曲线载体设计优化理论；通过弹性力学和计算力学方法完成齿轮强度理论研究；以加工中心为基本装备，发展齿面成形方法；开展样机性能试验，完成理论验证并检测其基础性能。最终形成相对完整的交错轴共轭曲线齿轮理论。项目实施将进一步拓展共轭曲线理论在齿轮传动领域的应用，并为开发新型高性能交错轴齿轮传动装置提供理论支撑和设计工具。

交错轴齿轮传动是空间齿轮传动最为复杂的一种布置形式，由于其结构紧凑、承载能力强，被广泛应用于汽车、工程机械、轨道交通等动力传动领域。为实现交错轴齿轮全啮合周期接触特性分析与控制，本项目围绕高性能交错轴的关键要素，基于共轭曲线啮合的基本思想，对交错轴齿轮啮合原理与设计方法等开展研究。.本项目主要开展了以下四个方面研究：1）探寻了交错轴空间共轭曲线啮合原理，提出空间共轭曲线的一般求解方法，论证了空间共轭曲线基本运动学性质，考察了空间共轭曲线与齿轮齿面间的联系；2）提出了空间共轭曲线、接触方向及相对运动参量与齿面二阶接触特性参量的显式表达式，从而能够在实际齿面未定的情况下对点接触齿轮齿面可能的二阶接触情况进行分析，为点接触齿轮齿面优化提供了可计算的指导公式；3）完成了共轭曲线齿轮的力学特性研究，提出共轭曲线齿轮的有限寿命计算方法，发展了直线型和一般点接触齿轮的时变啮合刚度快速准确计算方法，帮助实现复杂传动系统动力学快速分析和优化；4）开展了基于五轴加工中心非球头刀的交错轴共轭曲线齿轮加工方法研究，实现较为高效且可通用化的共轭曲线齿轮加工工艺。.相关研究成果将进一步丰富齿轮啮合理论体系，为高性能齿轮传动装置开发提供一定的技术创新思路，此外，本项目的主要理论成果已编制成为软件模块，为本项目理论研究成果的应用提供了具体技术工具。