基于精确齿廓建模的内啮合齿轮参数化设计

Parametric Design of Internal Gears Based on Accurate Tooth Profile Modeling

针对当前内啮合齿轮参数化设计和开发过程中普遍存在的建模精度不足及设计校验计算效率低的问题,使用Matlab GUI开发了基于精确齿廓建模的内啮合齿轮参数化设计系统。依据齿轮展成原理,生成内啮合齿轮渐开线齿廓;应用齿廓法线法,建立内齿轮齿根过渡曲线方程,实现了内啮合齿轮的全齿廓精确建模;计算内啮合齿廓过渡点压力角α_(M)、α_(N),通过参数化设计程序完成内啮合齿轮设计参数的几何计算及干涉校验等工作,其中,过渡曲线干涉校验部分,利用齿廓过渡点压力角α_(M)、α_(N),在加工刀具任意齿顶圆角(或非特定圆角)情况下,计算出内啮合齿轮副过渡曲线干涉的校验公式。最后,将设计目标齿轮副全齿廓数据导入Catia界面中,建立了齿轮副三维实体模型,为后续齿轮系统的应力分析及动力学性能检测等研究奠定基础。

Aiming at the problems of insufficient modeling accuracy and low efficiency of design verification and calculation in the current parametric design and development of internal gears,a parametric design system of internal gears based on accurate tooth profile modeling is developed by using Matlab GUI.According to the principle of gear generating machining theory,the involute tooth profile of internal gears is generated.The tooth profile-normal method is used to establish the tooth root transition curve equation of internal gears,realizing the accurate modeling of the whole tooth of internal gears,and the pressure anglesαM andαN at the transition point of the internal gear profile are calculated.The geometric calculation and interference verification of the design parameters of internal gear pairs are completed through the parametric design program.In the transition curve interference verification part,using the pressure anglesαM andαN of the tooth profile transition point,the verification formula of the transition curve interference of the internal gear pair is calculated under the condition of any size tooth top fillet(or unspecified fillet)of the cutter.Finally,the whole tooth profile data of the designed target gear pairs is imported into the Catia interface,and the three-dimensional solid model of the gear pairs is established,which lays a foundation for the subsequent research on the stress analysis and dynamic performance detection of the gear system.