Application of Genetic Algorithm Elements to Modelling of Rotation Processes in Motion Transmission Including a Long Shaft

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.

Mathematical Modelling of Transient Processes in an Asynchronous Drive with a Long Shaft Including Cardan Joints

“…In drive systems including long shafts, the susceptibility of these elements in distributed parameter systems must be additionally taken into consideration [4,6,[24][25][26]. Only the susceptibility of the middle shaft needs to be addressed in our system, since it is several times longer than the first or third shaft.…”

“…It concerns physical effects in motion transmission, where a drive motor's torque is transferred to a load system. When the distance between the drive motor and the load system is substantial, the torque is determined by describing a long shaft in a distributed mechanical parameters system [1][2][3][4][5][6]. Points of power receipt can obviously have varying practical configurations, which may in turn complicate kinematic and drive system equations.…”

Dynamics of Electromechanical Systems Containing Long Elastic Couplings and Safety of Their Operation

“…Depending on the length and cross section, transmission shafts may show different susceptibilities to the moment of torsion, the measure of which is the value of the angle of twist [6,13]. In the case of a short mechanical coupling, the value of the angle of twist is insignificant and may be neglected under the assumption of a rigid mechanical coupling, while this value cannot be omitted in the case of a longer mechanical coupling, and such coupling should be considered elastic [5,[13][14][15][16][17][18].…”

“…To model the transmission shafts, classical methods based on the d'Alembert principle and Newton's second law as well as the variational method are used. The variational method is based on a model with distributed parameters and consists of partial differential equations [13]. An example of a partial differential equation used to describe a long elastic element is the wave equation [25].…”

“…A step or overly rapid change in the speed reference for control systems of electric motors cause a temporary lock of the speed controller due to the applied limitations at its output. Particularly, the unfavorable effects of such a lock can be observed in drive systems where there is a long elastic coupling (transmission shaft) between the electric motor and the working machine [5,6,13,17]. As a consequence, shaft twists and accompanying torsional moments of considerable amplitudes appear.…”