Accurate spiral tool path generation of ultraprecision three-axis turning for non-zero rake angle using symbolic computation

Abstract

An accurate spiral tool path generation method of ultraprecision three-axis turning free form surface is proposed based on symbolic computation in this paper. Many analytic optical free form surfaces often need to be machined to submicron in form error, such as optical nonaxisymmetric aspheric surfaces, but current mainstream CAM systems usually use nonuniform rational basis spline (NURBS) to describe the designed surface and generate tool path. If we want to use these systems, the analytical optical surfaces must be approximated using NURBS surfaces, but it will introduce approximation error and may be difficult to achieve the approximation error less than submicron. More importantly, there is no effective tool path generation method for the special three-axis turning machine tool in current mainstream CAM systems. In this context, we propose to calculate the tool path directly from these analytic surfaces by using symbolic math. The proposed method can be used to generate accurate spiral tool paths for zero/negative/positive rake angle in a unified way. Finally, several examples are given to prove its effectiveness.