齿条刀加工渐开线圆柱外齿轮的切制机理研究

Machining mechanism of involute cylindrical external gear by rack cutter

鉴于精确的齿廓曲线方程对于齿轮修形、有限元分析、抗疲劳特性分析及动力学计算的重要性,对齿条型刀具加工渐开线圆柱外齿轮的切制机理进行了深入研究。在加工过程中,刀具直线部分齿廓首先进入啮合并切制齿轮毛坯生成渐开线,然后当刀具齿顶圆弧与齿轮毛坯齿根圆相切时,刀具齿顶圆弧开始切制齿根过渡曲线,并与渐开线加工汇于一点,然后退出啮合。在不同啮合位置,通过坐标变换,推导了圆柱外齿轮精确的渐开线方程和齿根过渡曲线方程,最后在ANSYS中利用APDL语言画出了所推导齿廓曲线方程的几何形状,提供了参数化方程在给定齿轮参数下应用的算例。

In light of the significance of an exact tooth profile curve equation for gear modification,finite element analysis,fatigue resistance analysis and dynamic calculation,we researched the machining mechanism of involute cylindrical external gear by rack cutter.In the course of processing,the straight tooth profile of the rack cutter firstly comes into mesh,and generates the involute by cutting the gear blank.After that,when the addendum arc of the cutter is tangent to the dedendum circle of the gear blank,the addendum arc of the cutter starts to create the dedendum transition curve,which gathers together with the involute.Afterwards,the cutter exits the mesh.In different mesh positions,through coordinate transformation,the precise involute equation and dedendum transition curve equation of the cylindrical external gear were derived.Finally,the derived geometric graphics of the tooth profile curve equation was generated by using APDL parameter design language in ANSYS software.This study has provided an example of the parametric equation applied under the given gear parameters.