Modeling of ball screw driven stage for drilling machines with lumped parameter system model and FEM model

Abstract

In this study, a method of modeling the frequency characteristic of a ball-screw-driven stage in a design phase is proposed, targeting a printed-circuit-board drilling machine. A ball-screw driven stage is widely used as a precise positioning mechanism mounted in inspection devices or manufacturing equipment. When a controller of the stage is being designed, the frequency response of the stage is needed first, and it is generally measured with actual stage equipment. Therefore, the positioning performance of the stage cannot be estimated in the design phase. A method for predicting the frequency characteristic of the stage on the basis of its design specification is required for developing the stage structure and controller and the method will be useful for shortening development period or lowering development costs. At the beginning of this study, it was revealed that the frequency response of the stage is affected by not only the stiffness of the ball screw but the natural modes of the structure, and it cannot be represented with just a lumped-parameter model of the ball- screw driving system. Subsequently, a modeling method for a ball-screw driven stage was proposed. The model consists of a lumped-parameter model of a ball-screw drive system and vibration models of its structural components (which are analyzed by FEM models), and these models are connected by mode synthesis. Finally the effectiveness of the proposed model was demonstrated in comparison with experimental results, and it is concluded that the proposed model can represent similar frequency-response characteristics as represented by measured values.