Power Criterion Optimization of Concurrent Start of Trolleying and Slewing Mechanisms in Tower Crane

An optimization problem has been formulated and solved for the concurrent start of the trolleying and slewing mechanisms in a tower crane with a saddle jib. A dynamic model of the crane trolleying system with six degrees of freedom has been employed. The model incorporates the primary motion of the mechanisms as well as the oscillations of the slewing structure, trolley, and load, induced by the elastic properties of the structural components and cables. The differential equations governing the concurrent motion of the mechanisms have been derived based on the dynamic model. The optimization criterion is defined as the root-mean-square value of the total power. The generalized coordinates and velocities of the trolleying system at the start and end of the motion have been used to define the boundary conditions for the optimal motion trajectory. These coordinates are expressed in terms of the load position and its higher-order time derivatives. As a result of the optimization, the motion conditions that minimize the power of the drive mechanisms, reduce dynamic loads, and eliminate oscillations of links and load when transitioning to steady-state motion of the mechanisms have been obtained.