Analytical Method for Obtaining Cutter Workpiece Engagement in Five-Axis Milling. Part 3: Flat-End Cutter and Free-Form Workpiece Surface

Abstract

In five-axis milling of 3D free form surface, determination of instantaneously changing cutter workpiece engagement for supporting force and surface quality prediction is still a challenge. In order to predict cutting force accurately, precise geometric information on cutter workpiece engagement is very important. Solid model and discrete model are the most common method used to predict the engagement region. Both methods give the result with the accuracy as the tolerance set in the beginning. However, the methods are suffering with the long computational time. This paper presents a new simple method to define Cutter Workpiece Engagement between flat-end cutter and free form workpiece surface. The engagement is calculated by using a combination of discretization and analytical method. Despite workpiece is discretized by normal vectors, but there is no calculation to check the intersection between cutter and normal vector. They are only used as the reference to define the shape of the surface at every Cl-point, mathematically. The engagement point is obtained based on predicted surface shape and tool orientation at instantaneous location. The formula were derived and implemented in a computer simulation. The program simulation can generate instantaneous cut shape and its size. To ensure the accuracy of the developed method, it was tested by compared the depth of cut generated by the program simulation with the depth of cut measured in Unigraphic. A test on sculptured part surface and workpiece surface was performed. The result indicates that the proposed method is very accurate.