Natural frequencies and modal shapes of machine tools have position-dependent characteristics owing to their dynamic behaviors changing with the positions of moving parts. It is time-consuming and difficult to evaluate the dynamic behaviors of machine tools and their machining accuracy at different positions. In this paper, a Kriging approximation model coupled with finite element method is proposed to substitute the dynamic equations for obtaining the position-dependent natural frequencies of a machine tool, as well as relative positions between the tool and the workpiece during the machining process. Based on the proposed method, dynamic performance optimization design of the machine tool is conducted under the condition of minimum relative positions. Three case studies are illustrated to demonstrate the implementation of the proposed method.

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