MATHEMATICAL MODELING OF A MAGNETIC CIRCUIT OF AN ELECTROMAGNETIC SYSTEM WITH A MAGNETORHEOLOGICAL FLUID
A electromagnetic system with magnetorheological fluid is investigated. Unlike the previous works of the authors, where the shape of the particles of magnetic material in the oil of the magnetorheological fluid was taken in the form of a cube, in this work, it is assumed that these particles (hereinafter referred to as balls) have the shape of a ball - closer to the real shape of the particles. It is assumed that the balls magnetized under the influence of an external magnetic field create elementary columns, which are combined in columns. The mathematical model of the magnetic circuit of the electromagnetic system is compiled (the electromagnetic system of the magnetorheological brake is adopted as the object under study)․ Expressions of magnetic conductivities (resistances) of characteristic sections of the passage of magnetic flux are obtained. In this case, the area occupied by the balls was represented by the nth number of magnetic flux tubes in the form of a cylinder (one tube) and a hollow cylinder ((n-1) tubes), and the area occupied only by non-magnetic materials - oil and non-magnetic coating - one tube. As a result, an equivalent circuit of the magnetic circuit is constructed in which there is an nth number of parallel branches with linear and nonlinear magnetic resistances and one branch with linear magnetic resistance. To solve a nonlinear system with (n + 1) equations compiled according to the first and second Kirchoff laws, and describing the equivalent circuit, the generalized reduced gradient method is used. For an electromagnetic system with the given sizes and particle material, numerical solutions of the system of equations are obtained and analyzed. In this case, the number of parallel branches of the equivalent circuit was taken to be six (n = 5), respectively, a non-linear system of equations of the 6th order was obtained and solved.