Motion of anisotropic magnetizable elastomer body in the electromagnetic coil field with consideration of interaction with inclined plane

D. I. Merkulov ; D. A. Pelevina ; I. I. Merkulova ; V. A. Turkov ; V. A. Naletova

Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2025), pp. 60-66

Résumé

In this paper the motion of a spherical body with anisotropic magnetizable elastomer under the action of the magnetic field of an electromagnetic coil is studied experimentally and theoretically when the motion of the body is limited from below by an inclined plane. The dependencies of the current in the coil on the angle of inclination of the plane, which separate the regions in which the body is either at rest, or moves along an inclined plane, or first moves along an inclined plane and then breaks away from it, or immediately breaks away from the inclined plane, are constructed experimentally. Based on the previously proposed mathematical model, which takes into account the interaction of the body (rolling, sliding) with the inclined plane and does not take into account the deformation of the body and surface roughness, similar dependencies are calculated. The qualitative difference between the experiment and the theory proposed earlier is shown: in the experiment the body on the horizontal surface begins to move when the current in the coil reaches a certain value, while according to the previously proposed theory, the body begins to move at arbitrarily small currents. An improvement of the previously proposed theory has been carried out: the moment of support reaction associated with the roughness of surfaces and the presence of a certain area of contact between the body and the plane has been taken into account. The new model is shown to better describe the experimental results.