Prediction of tool tip dynamics for generalized milling cutters using the 3D model of the tool body

Abstract

In general, chatter is the main limitation to proper material removal in milling operations. Stability lobes are good tools to determine chatter-free cutting conditions in terms of spindle speed and cutting depth, which require the frequency response function (FRF) at the tool tip to be known. There are experimental methods to measure the tool tip FRF but this may be time consuming or even impossible for each tool and tool holder combination. Receptance coupling substructure analysis (RCSA) is a widely used approach to predict tool tip dynamics. This paper proposes the use of the RCSA approach with a stereolithographic (STL) slicing algorithm to enable the exact calculation of cross sectional properties such as area and area moment of inertia of the cutting tool from its 3D model opposed to the approximation methods. So that, the effect of flutes on cutting tool structure introduced in an exact manner and the RCSA approach becomes feasible for more complicated tool geometries with varying cross-sectional properties, i.e., tapered ball end mills, end mills with variable flute geometries, and so on. The solid model of the tool can be available by either the tool manufacturer or 3D measurement. Although, at the presence of 3D models, finite element methods (FEM) offer accurate simulation of the dynamic response for solid bodies, they suffer from the compromise between accuracy and computation time, as high number of elements is needed for accuracy. Thus, the use of analytical methods where possible improves the simulation time significantly. The proposed STL slicing algorithm is integrated with a previously developed RCSA method. The experimental results show that the proposed algorithm works more accurate in calculation of the cross-sectional properties and hence free-free response of the tool compared to the existing arc approximation methods. It is also shown that the proposed approach performs better than FEM solutions in terms of the computation time and the compromise between accuracy and computation performance. Finally, the proposed approach in prediction of tool tip dynamics for a robotic machining platform.