MATHEMATICAL MODELS OF A NEW LUMPED-PARAMETR MAGNETOELASTIC ACCELERATION TRANSDUCER
Keywords:
acceleration, magnetoelastic effect, magnetoelastic transducer, magnetic circuit, ferromagnetic material, equivalent substitution circuit, differential circuit, mathematical model, magnetic core, mechanical stress, magnetic flux, magnetic potential difference, magnetomotive force, magnetic reluctance, relative magnetic permeability, air gap, constraints, algebraic equation, Maclaurin series.Abstract
In this article, based on the theory of lumped-parameter circuits, algebraic and differential equations describing the mechanical, electrical, and magnetic circuits of new magnetoelastic acceleration transducers, their analytical solutions, as well as mathematical models establishing the relationship between the electromotive forces at the outputs of the transducers and acceleration, which is the input quantity of the transducer, have been developed. Analysis of these mathematical models and the graphs constructed on their basis shows that under the influence of acceleration applied to the transducers, with an increase in the mechanical stresses arising in the magnetic circuit of the transducer, a redistribution of magnetic fluxes occurs between the branches of the magnetic circuit. An increase in mechanical stress leads to an increase in the magnetic flux in one branch of the magnetic circuit and a decrease in the other branch. It has been established that this is explained by the different changes in the magnetic reluctances of the corresponding parts of the magnetic core. The analysis of the graphs showed that all the considered dependences are nonlinear in nature, and the degree of this nonlinearity takes different values: if in one half of the differential magnetic circuit the degree of nonlinearity is approximately 7.93%, then in the second half of the circuit it is approximately 5.67%. The analysis of the developed mathematical models also showed that they can be used to theoretically investigate the main technical characteristics of the new acceleration transducers with sufficiently high accuracy.
