Mathematical Modeling of the Linear Drive for Research Viscoelastic Properties of Elastomer

Abstract

The article is devoted to solving the problem of mathematical and simulation modeling of linear magnetoelectric drive (LMED) for the research of rheological characteristics of elastomers. A special feature of the linear drive is lack of transmitting and convertive elements between the anchor, which is a clamping rod, and a test sample of the elastomer, what makes it necessary to include equations describing nonlinear viscosity processes in the General model of the LMED when solving the modeling problem. The possibility of using multi-circuit equivalent circuits, which can be synthesized on the basis of experimental data obtained for the test sample of a certain brand of elastomer under its loading to fixed values of the relative strain, is shown. As a result of the relaxation process of the test sample of the elastomer, the exponential time dependence of the mechanical stress is investigated, which can be subsequently represented by the sum of the exponents with different time constants. The analogy in the recording of the time dependence of the mechanical voltage and current in the electrical circuit containing RC-elements, as well as fixed deformation and constant voltage of the power supply makes it possible to establish a correspondence between the specified values and to create an equivalent circuit of substitution of the test sample of the elastomer. The number of parallel branches of the substitution scheme, as well as its parameters can be determined on the basis of an experiment to remove the time dependence of the mechanical stress at a fixed value of the relative strain. The article also presents a General mathematical model and its implementation in the software MATLAB/Simulink