On vibrations in the dynamical systems of controlled machine units with discrete parameters

Abstract:
Vibrations in the controlled machine units with discrete parameters were studied. Such dynamical systems, used for materials processing, transportation etc., consist of motor, some mechanical part and system of process control. Functioning of such machine units showed that different complex dynamical processes were possible including dual-frequency vibrations. The mathematical models of such systems are nonlinear boundary value problems with non-classical boundary conditions. Such a model is a system of ordinary differential equations of the fifth order and one of the boundary conditions is a nonlinear one. This allowed to apply for the investigations some kinds of homogenization methods. Such methods made possible to determine conditions of stability of both one-frequency stationary modes and dual-frequency ones. Besides frequencies and amplitudes of the vibrations as well as the character of transient to stationary modes were obtained. Such calculations allowed to study the dependence of stationary modes characteristics in the considered controlled machine units on the different parameters of the systems including the dependence of frequencies and amplitudes on electromagnetic sluggishness of motor. After such investigations using of feedbacks, which allow to change purposefully electromagnetic sluggishness of motor, is proposed. This allows to optimize functioning of the controlled machine units with discrete parameters. The results may be applied in industry for design of new improved technical systems.