Optimization of rotate mode at constant change of departure in the level-luffing crane with geared sector

Abstract

The results of optimization of the rotation mode of the level-luffing boom system of the crane at the launch site, with the steady-state mode of departure change. The object of the study is a boom system with a sector drive of the mechanism of change of departure. The mechanism of rotation consists of an electric motor, a planetary mechanism and an open gear. Variation calculus methods were used to optimize the mode of rotation of the boom system. In this case, a variational problem is formed, which includes the equation of motion of the boom system when turning and changing the departure, the optimization criterion and boundary conditions of motion. The optimization criterion has the form of an integral functional that reflects the root mean square value of the driving torque of the drive mechanism of rotation during start-up. The study was carried out at the starting point of the electric motor of the turning mechanism from the state of rest to reach the nominal speed and at a steady speed of rotation of the electric motor of the mechanism of change of departure. The solution of the problem is presented in the form of a polynomial with two terms, the first of which provides boundary conditions of motion, and the second minimizes the criterion of optimization through unknown coefficients. To do this, use a software package. Graphs of change of kinematic characteristics of cargo and boom system at work of mechanisms of turn and change of departure, and also the driving moment in the course of start of the mechanism of turn which correspond to an optimum mode of movement are constructed. The resulting mode of movement allowed to eliminate the oscillations of the load on the suspension. Based on research, recommendations for the use of the obtained optimal start-up mode have been developed.