A Study on Tool Path Generation in 2D Contour Milling of Cycloidal Discs and Rings Used in Cycloidal Reducers

Abstract

This paper presents a study on the determination of the tool paths in manufacturing by external or internal 2D contour milling (using an end mill cutter as tool) of a cycloidal disc and a cycloidal ring used inside a cycloidal reducer in two versions: with rotary pins as gear teeth placed on stator (in gear with cycloidal disc) and with rotary pins placed on rotor (in gear with cycloidal ring). These tool paths should be described by the Cartesian coordinates of the points on the 2D closed trajectory of the tool axis. The 2D profiles of a cycloidal disc (or a cycloidal ring) in transverse section and an analytic geometric approach are used in order to find out these tool paths, having a shape of distorted epicycloids or hypocycloids. Even though this goal is simply solvable on CNC milling machines by cutting radius compensation, some particularities of 2D profiles for a cycloidal disc (or a cycloidal ring) impose a specific theoretical approach on this topic. Some algorithms for tool path detection were proposed, verified and validated by simulation in Matlab on both 2D profiles.