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

Abstract

The object of the study is a level-luffing boom system with a drive mechanism for changing the departure in the form of a toothed sector. The turning mechanism consists of a drive 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 the boundary conditions of motion. The Lagrange’s equation of the second kind was used to compile the equations of motion. The optimization criterion is presented in the form of an integral functional, which reflects the root mean square value of the driving moment of the drive mechanism of rotation during start-up.