Dynamic simulation of a high altitude gantry crane with cable hoisting. Part one. 2D model

Introduction. Simulation of the 2D dynamic motion of a high altitude wide span gantry crane with a rope hoisting mechanism is addressed. Such large gantry cranes with a height of more than 50 meters, have been unstudied very well so far. A small swing angle of the payload, it's fast hoisting, and the fast motion of the trolley are critical for these cranes and, hence, they need to be analyzed in detail. Materials and methods. The generalized formulation of the two-dimensional crane dynamics is efficiently performed and simulated in Mathcad. This is a single mass model that has a non-elastic cable. The formulation is derived using the Lagrange method, and differential equations are correctly solved using the Runge-Kutta method in Mathcad. In this model the crane is fixed, and all the subsystems are considered as rigid bodies without any deflection in terms of the trolley and the payload. Results. The results are verified using MSC ADAMS (Academic) that indicates satisfactory convergence. The considerable influence of the payload oscillation on the trolley motion is visible in both Mathcad and ADAMS models. The implemented Mathcad code can be useful for students and researchers. Conclusions. The maximum speed of the trolley is 1.716 m/s to prevent the payload swinging angle from exceeding 0.5 deg. The calculated velocity of the trolley is reasonable for such a large crane if limitations like wind effects and resonance are ignored.