Optimization of clamping conditions in thin-walled part machining to minimize forced vibrations, Part I: Model for the single tool –workpiece contact location

Abstract

Machining thin-walled, highly flexible parts is challenging due to excessive deflection, chatter, and forced vibrations, which can violate tolerance and surface finish requirements. These flexible parts are attached to the fixture or machine tool table using clamps. The location of the clamps and the clamping forces are usually selected intuitively in industry, although they affect the natural frequencies and magnitudes of the Frequency Response Functions (FRFs) of the part hence the deflections. This paper presents an algorithm to optimize the placement of clamps and the clamping forces to minimize static deflections and forced vibrations induced by milling forces at the fundamental tooth-passing frequency and its harmonics. The FRF at the tool-workpiece contact zone is calculated by analytically reducing the size of the full Finite Element (FE) model. The effect of clamping forces, and consequently the clamp stiffnesses, is considered in the model. It is shown that optimal clamping forces and clamp placements can lead to a reduction in both static deflections and forced vibrations. While this paper presents an optimal clamping condition model at a fixed tool path location, Part II extends the optimization to the entire tool path by considering the variation of workpiece dynamics caused by metal removal.