Stability Research About Telescopic Box Boom Of Crane With Cylinder Supporting

At present, stability analysis for telescopic boom still limitation to the design rules for cranes《GB3811/83》national standards of People's Republic of China.In the original design rules for cranes, effective length of telescopic boom is confirmed by energy method without considering effect of cylinder, which is not precise; In the new revised design rules for cranes, considering the model as tapered stepped column, the result is more precise in theory,and still not considering effect of cylinder. Stability analysis and checking for telescopic boom with cylinder is still puzzling the designer, though many expert and scholar have done much research, till now, there is no accurate conclusion.Crane telescopic boom is made up of many tapered box sections which can axially slip relatively, only the boom is subject to bending moment, while supporting cylinder in boom bears axial force, which offers a non-conservative force, and the friction between booms is not taken account, therefore, its mechanical model cannot be equivalent to tapered stepped column's, and Euler's critical load is different. In the precondition of stability for cylinder, loading capability of telescopic boom depends on section inertia moment of boom and supporting form. As different placement and supporting form of cylinder for various telescopic booms, effective length coefficients are different too. The capability is irrespective with inertia moment of cylinder. The paper will emphasis this problem.The two method of differential equation and precise theoretical solution of Euler's critical load at out-of-lifting-plane for crane multi-telescopic-boom with cylinder supporting is provided in this paper. Differential equation applicable for less pitch number(two-three),that doesn't need finite element knowledge, provide a portable formula; precise finite element method applicable for multi-telescopic-boom, because it's trouble to calculation and have no regularity, so this method provide the designer corresponding theory, but that need software and hardware to support.In the precondition of stability for cylinder in the paper, deduced a recurrence formula with single cylinder supporting at the top; and the critical force of telescopic boom is calculated with three different methods, including differential equation method, elastic support method and finite element method; getting destabilizing characteristic equation with different supporting type; meanwhile, solved variable cross-section length coefficient; then detailed represent using precise finite element method to solve critical force of telescopic boom.Corresponding to parameter and graph table about the rules for cranes GB3811-83,the paper give more accurate parameter, and then get the effect of cylinders to global stability, which is more accurate in theory. The result is compared with that of methods which did not take account of the effect of cylinders using the model of tapered stepped column. Euler's critical load of the model considering the effect of supporting cylinder is greater than those neglecting it. In the previous design rules for cranes national standards of People's Republic of China, the mechanical model to calculate crane multi-telescopic-boom's stability is tapered stepped column neglecting the effect of supporting cylinder, thus the result generally incline to safety. The paper provide accurate data, and believe this can provide reference to the rules for cranes perfectly. The author really hope this can complement and motivation the theory developing in this realm.