A High-Precision Surface Grinding Model for General Ball-End Milling Cutters

Abstract

The paper presents a high-precision manufacturing model for grinding the surface profiles of general ball-end milling (GBEM) cutters. The geometric shape of the grinding wheel is derived with a positive cone angle specifically for grinding the GBEM cutters. The concepts of radial equidistant lines and oblique equidistant surfaces are employed to model the front ball-end profile, the front cutting surface, the rear cutting surface, and the cutting-edge curve of the GBEM cutter. The front cutting surface model is obtained by computing the intersection of the rotating tool surface and the motion envelope of the grinder. The cutting-edge curve model is estimated by computing the intersection curve of the front cutting surface and the ball head of the GBEM cutter. A special model of the grinding mechanism is also derived and used to produce the rear surface of the cutter. Both the cutting-edge curve and the surface model are solved simultaneously in order to ensure that the cutting-edge curve leans physically against the rear-cutting surface. The geometry of the full front-end cutter shape and the parameters of the associated manufacturing processes are numerically optimised to ensure best grinding quality is achieved on the surfaces of the GBEM cutter. The concept of oblique equidistant surfaces is applied to produce a family of cutters of similar shapes with an accuracy corresponding to a user-specified allowable tolerance. One numerical example is presented to illustrate the usefulness and effectiveness of the proposed modelling methodology. Numerical results indicate that the proposed manufacturing model and grinding procedure are capable of producing a family of GBEM cutters accurate to a specified tolerance.