Mathematical model of the dynamics varying the radius jib system loader crane at adjustment movement arm and telescopic section

## Keywords

mathematical model
combination of movements
Lagrange equations of the second kind

## Abstract

In the paper considers the method of constructing a mathematical model in the plane of change of departure of the jib system of a link loader crane with a load. The mathematical model is built with three simultaneous movements, namely, the simultaneous angular movement of the arm, the linear movement of the telescopic section and the oscillatory movement of the gripping device with a load. The functions of changing the kinematic and dynamic characteristics of the jib system while simultaneously moving its links are calculated. The construction of a mathematical model is performed using the Lagrange equations of the second kind. In this case, for the generalized coordinates of the model of a loader crane, the angular coordinates of the position of the links of the jib system and the angular deviation of the load, and the position of the telescopic section is determined by the linear generalized coordinate of the extension of the rod of the drive hydraulic cylinder.
The mechanical characteristics of the drive, presented in the form of quadratic dependencies between the acting forces and the speeds of movement of the rods of the power hydraulic cylinders. The control of the drive elements is represented as equations of the working fluid flow rate with a change in the flow area of the according to a linear law.
As a result, the equation of motion of the loader crane was obtained, taking into account the influence of the inertial component of each link of the jib system and the influence of the oscillatory movement of the load on the dynamic loads of the metal construction and the hydraulic drive elements. The developed mathematical model makes it possible to theoretically determine the effect of the simultaneous movement of the jib and arm on the oscillations of the load, and the effect of the oscillation of the load on the dynamic loads arising in the jib system and elements of the loader crane drive.