Mathematical model of a linear motor controlled by a periodic magnetic field considering dry and viscous friction

Abstract

The paper deals with a drive concept that uses the controllable mechanical properties of a magnetorheological fluid (MRF). The biologically inspired operating principle is based on crawling using anisotropic friction, as of worms, and non-Newtonian fluids, as of snails. The MRF located between a slider and two slide-blocks is functionally relevant for the drive system to generate a translational motion. A controlled magnetic field is utilized to change the friction conditions in the drive system by varying the properties of the MRF. An extended friction model takes the dry friction into account, along with the viscous friction. In this case, apart from the ratio of the coefficients of viscous friction, it is necessary to introduce two more parameters: the ratio of the coefficients of dry friction in the absence and presence of the magnetic field, and the ratio of the characteristic forces of viscous and dry frictions. These parameters allow refining the mathematical model that governs the behavior of a linear motor. Using asymptotic methods of non-linear mechanics, an expression for the average velocity of the slider is obtained for the case when the friction force is assumed to be small in comparison with the driving force of the slide-blocks. The theoretical results are verified experimentally on a prototype.