An efficient multipoint 5-axis tool positioning method for tensor product surfaces

Abstract

In this work, a robust tool-drop algorithm coupled with the bisection method is used to speed up the computations in the drop and tilt method (DTM), a multipoint tool positioning technique for 5-axis machining with a toroidal end mill. In the DTM, the tool is dropped on the surface along a predetermined tool-axis direction until it touches the surface tangentially. The position of the circular tool insert (pseudo-insert circle) through the first point of contact is then used to compute the tool-tilt angle that causes the tool to touch the surface tangentially at a second point. A previous implementation of DTM used Newton’s method to solve the system of equations for tilting the tool, but took many iterations and multiple initial seed solutions to converge to a valid solution for tool-tilt orientation. Using the bisection method coupled with the generalized tool-drop algorithm instead of a direct use of Newton’s method to determine the tool-tilt angle improves performance without compromising the accuracy. The method was implemented in C+ +, and a comparative study with an earlier method for several bi-quadratic and bi-cubic Bezier surfaces demonstrates the reliability of the developed method.