Mathematical Model of Linear Motor Stage with Non-Linear Friction Characteristics

Abstract

This paper proposes a mathematical model of a feed drive system consisting of a cylindrical linear motor and linear ball guides. The friction model consists of two components; a model for the relationships between displacement and friction force under microscopic motion (non-linear spring characteristic), and a model for the relationship between velocity and friction force (Stribeck curve). The non-linear spring is modeled from the results of very low frequency simple harmonic motion experiments. The Stribeck curve is modeled from the results of friction force experiments conducted for various constant velocities. The parameters in the model were derived from machine specifications of the feed drive system and experimental results. In addition, in order to account for the quantization error of the linear scale, the controller and amplifier were modeled as a discrete time system. To evaluate the proposed model, step responses and circular motion under various conditions were measured and simulated. The influence of the friction characteristics on dynamic behavior was then investigated. In the experiment, the friction characteristics were changed and compared using three greases with differing viscosities. As a result, it was confirmed that differences in grease viscosity strongly influence the damping of vibrations for the step responses. Furthermore, it was clarified that quadrant glitches do not appear in the microscopic displacement region. For many simulation results, it was verified that the proposed model accurately reflects the real behavior.

Keywords

• linear motor stage
• linear ball guide
• mathematical model
• non-linear friction
• friction model