Numerical solution of critical force of n-step telescopic boom with superlift device

The installation of a superlift device on the telescopic boom of a crane is the main method to improve the stress condition of the telescopic boom and to effectively improve the lifting performance of the crane. However, there is a lack of an effective and accurate numerical method to solve the critical force of a crane telescopic boom with a superlift device. Therefore, the telescopic boom with a superlift device is reasonably simplified as a stepped column and double cable model. Based on the longitudinal and transverse bending theory, the differential equations of the deflection of the n-stepped column with double cables model are established, the buckling characteristic equation and its recurrence formula of the n-stepped column with double cables model are derived, and the combined superlift equations are established. The Levenberg–Marquardt optimization algorithm is used to solve the critical force and length coefficient. A large amount of data were compared and analyzed between the numerical solution results and the ANSYS finite element simulation results. The error result analysis proved the correctness of the deduced buckling characteristic equation and its derived formula and the accuracy of the numerical solution. The numerical solution method in this paper can be used to calculate the critical force and length coefficient under any number of boom sections, boom section length, sectional moment of inertia, cable length, and included angle between the two cables of the telescopic boom with a superlift device. The numerical solution method can provide a technical support for the structural design of a telescopic boom with a superlift device in practical projects.