The Mathematical Macro-Model of the States of the Actuator with Shape Memory Effect and Its Applications

Abstract

The article is devoted to solving the actual problem of synthesizing actuators based on materials with the shape memory effect. A macro-model of the state of the actuator is constructed, taking into account the dependence of the deformation of the active element of the actuator on the magnetic properties of the material and the external load. The magnetic state of the actuator is described by a set of equations of a stationary magnetic field. The direct and inverse problems of synthesis of the actuator are solved. The computational algorithm of the direct problem of determining the deformation of an element is based on the finite element method for calculating the magnetic field and approximating the dependence of magnetic induction on the deformation of the active element. The solution of the inverse problem of determining the magnetomotive force in the actuator control coils consists in solving the direct problem of calculating the magnetic field and minimizing the functional, taking into account the element deformation condition, by the gradient descent method. The application of the mathematical macro-model for determining the indicated parameters of a linear actuator is shown. The obtained results allow to effectively solving the problems of synthesis of electrical devices, a feature of which is the use of ferromagnetic materials with the shape memory effect.