Mathematical modeling energy losses and dynamic loads during operation of the crane lifting mechanism

Abstract

A mathematical model of an overhead crane has been developed to calculate energy losses and dynamic loads during the operation of the lifting mechanism. The mathematical model of the crane, which is presented in the form of a three-mass design scheme, takes into account all the main parameters of the electromechanical system "electric drive - metal structure – load". The reduced to the ropes force of the asynchronous electric motor of the load lifting mechanism is taken into account using non-linear speed-torque characteristics. Differential and integral equations in the mathematical model of the crane make it possible to calculate energy losses in an asynchronous motor during a transient process due to constant losses, variable losses in the stator and rotor. Using the developed multifunctional computer program (in the Delphi environment), it is possible to calculate with high accuracy the values and build dependencies of all components of energy losses, as well as displacements, velocities, and accelerations of reduced masses, loads in the crane steel structure and ropes when lifting loads in transient processes. Using the presented mathematical model, studies of energy losses in the electric drive of the lifting mechanism and dynamic loads in the steel structures and ropes of an overhead crane with a lifting capacity of 20 (t) and spans from 19.5 to 31.5 (m) were carried out. The article presents the results of studies of transient processes when lifting a load "with pickup". Three stages of lifting the load are considered: the choice of gaps in the mechanism of lifting the load and the sagging of the ropes with a stationary load; change in effort in the ropes from zero to a value equal to the gravity of the load; the movement of all three masses after the separation of the load from the base.