Abstract
Genetic algorithms are used to parameter identification of the model of oscillatory processes in complicated motion transmission of electric drives containing long elastic shafts as systems of distributed mechanical parameters. Shaft equations are generated on the basis of a modified Hamilton–Ostrogradski principle, which serves as the foundation to analyse the lumped parameter system and distributed parameter system. They serve to compute basic functions of analytical mechanics of velocity continuum and rotational angles of shaft elements. It is demonstrated that the application of the distributed parameter method to multi-mass rotational systems, that contain long elastic elements and complicated control systems, is not always possible. The genetic algorithm is applied to determine the coefficients of approximation the system of Rotational Transmission with Elastic Shaft by equivalent differential equations. The fitness function is determined as least-square error. The obtained results confirm that application of the genetic algorithms allow one to replace the use of a complicated distributed parameter model of mechanical system by a considerably simpler model, and to eliminate sophisticated calculation procedures and identification of boundary conditions for wave motion equations of long elastic elements.
Highlights
IntroductionPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
Received: 5 November 2020Accepted: 23 December 2020Published: 28 December 2020Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.license.Electric drives are among the top consumers of electricity, estimated to use 60% of the energy generated at present
The mathematical model of electric drive motion transmission including long elastic elements is described with (2) and is the most accurate, which means results of computer simulation of functional dependences sought on its basis can be with great adequacy regarded as an experiment
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Velocity and rotation angle of shaft start (rotor)—ω1, φ1 and their equivalents for the parameters for determining the instant of supplying the control signal in precise electric shaft end—ωN, φN are the most interesting functions in (5)–(8). The mathematical model of electric drive motion transmission including long elastic elements is described with (2) and is the most accurate, which means results of computer simulation of functional dependences sought on its basis can be with great adequacy regarded as an experiment. The functions computed in this way will be approximated by Equation (18)
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