Abstract
The paper deals with the modeling and optimization of the processes of movement and acceleration of a bridge crane trolley in the mode of damping uncontrolled oscillations of the load. For the dynamic system of a flat pendulum with vibration damping, which describes the oscillations of a bridge crane load on a flexible rope suspension in a separate vertical plane, it is proposed to use third-order time splines that model the motion and acceleration of the load suspension point in the horizontal direction of the trolley's movement. To determine the time dependence of the angle of deviation of the crane from the gravitational ver-tical, it is proposed to use the methods of classical calculus of variations (Euler-Poisson equation), which allow optimizing (minimizing) the value of this angle in the process of accelerating a trolley with a load sus-pended from the ropes of an overhead crane. An analytical solution to the problem of damping residual uncontrollable oscillations of the overhead crane load, which usually occur after full acceleration or braking of the load suspension point on the trolley, is obtained. To derive the dependencies, an analytical approach was used to calculate the value of the angle of deviation of the overhead crane's cargo rope from the gravitational vertical, depending on the acceleration and displacement of the load suspension point. The problem of loosening of a load moved by an overhead crane is considered and solved in a new way that allows to completely avoiding pendulum spatial oscillations of the load on a rope suspension. The mathematical apparatus of linear algebra (Kramer's rule, in particular) is used, which allows us to establish analytically the law of time motion of a rope with a load, the angle of deviation of which from the vertical takes minimum values in the process of acceleration of the cargo trolley.
Published Version
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