Modeling of logging machine stability operating with a vertically held tree

Abstract

The article presents the results of mathematical modeling of the stability of a logging machine with a vertically held tree when it is removed from the canopy of the forest. The calculation schemes for two positions of a vertically held tree are described. The substantiation of the idealization for the calculation schemes of a vertically held tree is given. The dynamic stability equations of a logging machine with a vertically held tree are constructed on the basis of second kind Lagrange equations system. Due to analyze the interrelationships between dynamic parameters and processes of a logging machine with a vertically held tree, motion differential equations were integrated taking into account external influences and initial conditions. Using the MATLAB program, the integration operations of second kind Lagrange equations system were carried out for two cases: 1) The vertical tree is rigidly fixed and repeats the deviations of the logging machine; 2) The tree is perfectly held vertically with any deviations of the logging machine. The input parameters for the calculation were the rigidity of the connections, the parameters of the logging machine, the gripping cutting device (GCD) and the tree. The parameters of the slope of the logging machine were set using the implementation of a Gaussian random process with a given correlation and variance. The dynamic stability study of a logging machine with a vertical tree showed that the ideal tree alignment in a vertical position leads to a decrease in the inertia moment of the system and to a significant decrease in the frequency of angular and linear oscillations compared with a rigidly fixed tree.