Modelling methods for end mill grooves based on different wheel geometries

Abstract

Helical groove of end mill has great influence on its cutting performance. It is normally ground by disk wheels and the groove geometry varies with different wheel geometries. To improve the machining accuracy and reduce the cost of the groove machining process, establishing the groove model with the known wheel geometry and the wheel movement locus before the actual grinding is necessary. In this paper, according to the characteristics of wheel geometry, two different methods are introduced to build the groove model. One is based on the enveloping theory, taking into account the fact that the groove is generated by the enveloping movement of the wheel. Contact lines between the wheel and the groove are firstly deduced. Then, the expressions of the groove and the groove section lines are obtained. This method works well for wheels with straight generatrices. However, if the generatrix consists of quadric curves, a complex transcendental equation needs to be solved to satisfy the enveloping condition. Thus, the other modified graphical method is needed. The wheel is expressed in piecewise. During the grinding process, every part of the wheel will form a family of surfaces. By solving the intersections of these families and the end mill cross-section plane, a point set is obtained. Obviously, the outline of the set is the groove section line. Using this method, the result will be a set of points, but it has no wheel geometry limitation. The calculation procedures of these two methods are programmed with the MATLAB language and have good agreements with the Boolean result.