Adequacy Evaluation of the Synthesis of Mathematical Models for One Class of Linear Dynamic Systems With Parameters, Variable in Time and in Space

Abstract

The object of research: the authors of this work have synthesized in previous publications a mathematical model of one class of linear dynamic systems with variable parameters in time and space, which includes the system for lifting and lowering a load with a crane in the case of taking into account the influence of longitudinal vibrations that arise in the cable of the lifting mechanism, and shift in time of the moment of inertia of the rotating masses reduced to the motor shaft.
 Investigated problem: simulation models are synthesized in the Simulink graphical software environment of the MATLAB application package to assess the adequacy of the specified mathematical model. A calculation was carried out using the passport data and characteristics of all components of the crane structure to find the numerical values of the parameters of simulation models, including the electric motor, cable and gearbox.
 The main scientific results: the results of modeling the dynamics of the electric drive system during acceleration, deceleration, the prevailing velocity are given. By comparing the results obtained on the simulation model with the results of experimental studies of the same class of dynamical systems carried out by other authors, the adequacy of the mathematical models synthesized by the authors of this work is proved. It is proved that the use of the classical equation of the dynamics of the electric drive system, which contains a constant moment of inertia and a constant moment of load, leads to errors in the estimates of the processes accompanying the lifting and lowering of loads by cranes. And this, in turn, does not allow predicting the behavior of the system in various operating modes with sufficient accuracy.
 The area of practical use of the research results: enterprises of the machine-building industry, specializing in the production, modernization of lifting equipment.
 Innovative technological product: a simulation model of a crane mechanism, which makes it possible to take into account the influence of longitudinal vibrations that arise in the cable of the hoisting mechanism, and the shift in time of the moment of inertia of the rotating masses reduced to the motor shaft.
 Scope of application of the innovative technological product: design and development of control systems for electric drives of lifting equipment.