Process modeling of end mill groove machining based on Boolean method

Abstract

Helical groove is one of the key structures of end mills. Its grinding process is the hardest and most time-consuming in end mill machining. According to the practical groove-grinding process, a Boolean method to simulate the groove-grinding process is proposed in this paper. The groove model is obtained with the known wheel geometry by a sequence of Boolean operations. Accordingly, the wheel used to machine a desired groove is deduced with the similar method. Based on the Boolean operation results and principles of differential geometry, contact lines of the wheel and groove are illustrated and calculated to optimize the groove-grinding process. Wheel positions relative to the blank are described by a sequence of mathematical coordinates. Wheel profile expressions are built with the corresponding transformation matrixes including groove geometry transformation matrix, cutter tip transformation matrix, and start processing position transformation matrix. Some simulated examples are included to illustrate the presented method.