DYNAMIC ANALYSIS OF THE FORESTRY CRANE BOOM IN INTEGRATED LOGGING EQUIPMENT USING PHASE PORTRAITS

Abstract

This article presents the results of a dynamic analysis of the forestry crane boom as a key component of integrated logging equipment operating under variable technological loads. The relevance of the study stems from the need to improve the reliability and service life of forestry machinery, which is subject to significant dynamic overloads during timber skidding operations. A mathematical model of the boom dynamics has been proposed, based on second-order Lagrange equations and incorporating the elastic-dissipative properties of structural elements, the inertial characteristics of the load, and the kinematic features of the winch drive. The model includes three degrees of freedom and accounts for the interaction between the boom, the cable-drive system, and the timber payload.

The system of nonlinear second-order differential equations was solved numerically using the Wolfram Mathematica environment. Particular attention was given to the construction and analysis of phase portraits representing the oscillations of the boom’s reduced mass and the load under varying loading conditions (ranging from 5,0 to 20,0 kN). It was found that as the load mass increases, the system transitions from a linear damped regime to a nonlinear one, exhibiting quasi-periodicity, asymmetry, and irregular oscillatory behaviour. For loads exceeding 14,0 kN, the boom demonstrates increased sensitivity to initial conditions and external disturbances, posing risks of loss of controllability and necessitating the implementation of stabilisation measures.

The results obtained have practical significance for optimising the structural parameters of the boom, selecting appropriate winch drive modes, and developing adaptive control algorithms. Future research prospects include extending the model to spatial oscillations, accounting for cable flexibility and variable soil characteristics, and conducting experimental validation of the numerical results. The proposed approach can be applied in the design and modernisation of specialised logging equipment to enhance its reliability, energy efficiency, and operational durability under real-world industrial conditions.