Analysis of the start-up process of the tower crane slewing mechanism with a steady state motion mode of its load trolley
Keywords:mathematical model, slewing, tower crane, load oscillations, analysis, Lagrange equations
provided that the load trolley moves at a constant velocity. On the basis of the second-order Lagrange equations, a corresponding mathematical model is obtained, which also describes the oscillations of the load on a flexible suspension in tangential and radial directions. The driving torque applied to the system is modeled using the Kloss equation. The obtained mathematical model is represented by a system of four second-order nonlinear differential equations, so numerical methods are used to integrate it. To assess the level of dynamic and energy loads in the system elements, we propose a set of indicators that reflect the maximum and root-mean-square values. It is suggested to consider the evolution of the system in two cases: the position of the trolley near the tower (the trolley moves from it) and the position of the trolley near the end of the boom (the trolley moves towards the tower). For both cases, the values of the estimation parameters were calculated, which together with the corresponding graphical dependencies allowed to identify the most significant factors that have an impact on the energetic, dynamic and kinematic processes of the system. In particular, these include: centrifugal force, Coriolis force, damping ability of the asynchronous electric drive of the crane slewing mechanism. The analysis of the load oscillation on a flexible suspension, which was carried out on the basis of phase portraits in the plane of the trolley movement and perpendicular to it, revealed their dependence on the initial position of the trolley on the boom. Apart from this, the drive power consumption, a part of which is spent on overcoming the centrifugal force which acts on the trolley and the load, significantly depends on this factor.
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