Optimization of machinery operation modes from the point of view of their dynamics

Abstract

This paper presents an analysis and synthesis of optimization methods of machinery dynamic modes. Theoretical studies have shown that in order to find optimum, one must define a differential equation describing the motion of the system, which would ensure the most advantageous dynamic regime determined by the stationary value of the corresponding functional. The definition of this equation must be carried out while machinery construction is taking place, as its physical parameters and layout form the basis of these differential equations. Such approach requires the introduction of certain principles significantly affecting the development of optimization methods justified in this paper. To solve the problem of optimal machinery modes, it is more suitable to perform a separation of complex motion by its dynamic properties Suppose that the complex motion can be devided into the motion of the machinery unit as a whole, to the static displacements of its elements as solid bodies, to the increasing and damping components of motion and to the vibrational component. The findings of the study indicate that the most advantageous machinery dynamic mode is determined by the conditions of the technological process, which would ensure its highest productivity, the lowest energy consumption and other optimal technical and economic indicators. This regime corresponds to the motion of the unit as a whole, that is, to the variation in the quasi-cyclic coordinates. The vector of external forces applied to the machinery is reduced to the initial conditions of its motion; homogeneous differential equations are considered further. The fundamental system of their solutions depends on the initial conditions of motion generated by external systems.