Optimization of the trolley mechanism acceleration during tower crane steady slewing

The article describes optimization of the process of acceleration of the tower crane trolley movement mechanism during the steady mode of the slewing mechanism. A mathematical model of the boom system of the tower crane was used for the optimization of the trolley movement. The model was reduced to a sixth-order linear differential equation with constant coefficients, which represents the relationships between the drive torque and the coordinate of the load and its time derivatives. Non-dimensional complex criterion (objective function), which takes into account the drive torque and its rate of change in time during the transient process, was developed to optimize the mode of the trolley movement mechanism. Based on that, a variational problem was formulated and solved in an analytical form in which root-mean-square (RMS) values of the quantiles were applied. A complex optimal mode of acceleration of the trolley movement mechanism was obtained and compared with the modes optimized based on different criteria. Advantages and disadvantages of the solutions were discussed based on the analysis of the obtained optimal modes of motion. The analysis revealed low- and high-frequency elements oscillations of the trolley movement mechanism during the transient processes. The conditions for their elimination were formulated.