A novel tool path generation algorithm for plane envelope grinding convex surface based on constant scallop height method

Abstract

This paper introduces a discovery about the geometric property of the tangent vectors of a constant scallop height (CSH) curve. Based on this discovery, a new tool path generation algorithm for plane envelope grinding a convex surface is presented, which aims at grinding convex surface with a cup wheel on five-axis NC machine tool. First, the envelop surface generated by a family of tangent planes of the convex surface is researched. Based on the research result, a method for computing the characteristic lines of the envelope surface is proposed, and then, an algorithm for searching the points of a CSH curve is presented. Second, the geometric properties of a CSH curve are researched, and an important discovery that the tangent vectors of a CSH curve are perpendicular to its corresponding normal vectors of the convex surface is made, which gives a method for precisely calculating the tangent vectors. Finally, on the basis of the research above, especially the tangent vectors of a CSH curve, a tool path generation algorithm is constructed. This algorithm can avoid computing the closed form expression of envelope surface and derive the largest width of grinding row with maintaining a CSH.