Investigation of the influence of the length of the rope suspension of the bridge crane and the length of displacement of the cargo in the controlled sway mode on the time of displacement

The formulas for a complete analytical solution of the problem of moving cargo on a pendulum suspension of constant length along a given trajectory in a plane setting are presented. To set the desired trajectory as a time dependence of the linear horizontal coordinate of the cargo in a limited time interval, two-point Hermite polynomials are used. The field of application of the method is the automatic control of the movement of bridge and gantry cranes, as well as modeling of crane working processes. The application is limited to small angles of deviation of the cargo rope of the bridge crane from the gravitational vertical. The method makes it possible to quickly synthesize the optimal trajectory of the point of cargo suspension movement, which accurately provides the required trajectory of cargo movement. For a series of constant values of the maximum acceleration developed by the point of suspension of the cargo during a single transient process, graphs of the moving time dependences from moving length and cargo rope length are revealed. The functions obtained are not smooth and have a fracture. This makes it impractical to approximate them using the regression equation, due to the high error of the latter. The resulting graphs can be used to determine the time of movement of the cargo depending on the specified length of moving, the length of the cargo rope and the maximum acceleration developed by the drive of the cargo suspension. (paper)