Global Stability Of Telescopic Boom With Impact Of Lap Between Booms And Friction

Telescopic boom is the most important component of wheel crane, whose stability calculation is the key of design and analysis. At present, stability calculation of telescopic boom mainly according to Chinese crane design specifications《GB3811-83》, and calculation length of telescopic arm is derived by energy method according to the variable cross-section ladder model without considering the impact of fuel tank, therefore, it is theoretically neither rigor nor precision. The revised crane design specifications still uses variable cross-section ladder model; although it got precise analytical solutions in the form of ladder recurrence formula, which is more rigor theoretically, it did not consider the friction impact of fuel tank and telescopic boom's lap so that it is completely not consistent with the actual working conditions. Therefore, it is very necessary to work out the stability of telescopic boom with considering fuel tank and friction.Crane's telescopic boom is usually composed of a number of variable cross-section box-arms that are connected by sliders, which allows axial expansion. Its fuel tank generally lies inside of the telescopic boom, and bears axial force together with box-arms, while the latter at the same time bear all the bearing moment. Therefore, telescopic boom's Euler critical force is different from that of both the variable cross-section ladder model and the multi-telescopic boom model only considering fuel tank. It depends on the moment of inertia of lazy arm's section and the axial force, friction, box-arm bears. Meanwhile, with different support forms of fuel tanks, Euler critical force would also be different. The issue mentioned above is that this paper will focus on.In this paper, two methods, differential equation method and precision FEM, are introduced to get Euler critical force's precision solution of telescopic boom with considering the effects of arm lap and friction outside the lifting plane. Then, elastic support method is applied to verify the accuracy of theory. In this paper, the recurrence formula of Euler critical force's precision solution of telescopic boom with a single fuel tank at its top is proposed; critical force of telescopic boom is determined by three methods: differential equations method, elastic support method and FEM; work out the instability characteristic equation of telescopic boom in different support; and describe in detail the solution process of telescopic boom's Euler critical force using precision FEM.According to the relevant parameters and charts in standard《GB3811-83》, comparison of results between this paper and both the variable cross-section ladder model and the telescopic boom model with considering fuel tank support in the standard shows that Euler critical force of telescopic boom with considering arm lap and friction is between that of those two models mentioned above, which is consistent with the real work of telescopic boom.