Mathematical model of the dynamics change departure of the jib system manipulator with the simultaneous movement of its links
DOI:
https://doi.org/10.32347/2410-2547.2020.104.175-190Keywords:
mathematical model, varying the radius, combination of movements, manipulator, Lagrange equations of the second kind, dynamic loads, load oscillationsAbstract
In order to increase the productivity and reliability of the manipulator according to the normative and technical documentation, which regulates the safe operation of the manipulators, it is allowed to combine movements with the simultaneous movement of several elements of the boom system. As a result, the paper methodology reviewed for constructing a mathematical model in the plane of the departure change of the boom system of a manipulator with a load. The mathematical model is constructed from the calculation of three simultaneous movements, namely, the simultaneous movement of the first jib section, the second jib section, the telescopic jib section and the oscillation of the cargo. The functions of changing the kinematic and dynamic characteristics of the boom system with the simultaneous movement of its links are calculated. The construction of a mathematical model is carried out using Lagrange equations of the second kind. Moreover, the generalized coordinates of the manipulator model are taken as the angular coordinates of the position of the links of the boom system and the angular deviation from the vertical of the cargo. And the mechanical characteristics of the hydraulic drive are presented in the form of square dependencies between the acting forces and the speeds of movement of the hydraulic cylinder rods. The control of the drive elements is presented in the form of equations of the flow rate of the working fluid with a change in the area of the flow cross-section of the hydraulic distributor according to a linear law. As a result, the equation of motion of the manipulator is obtained, taking into account the influence of the inertial component of each link of the boom system and the influence of cargo oscillations on the dynamic loads of metalware elements and hydraulic drive elements. The developed mathematical model allows one to theoretically determine the effect of simultaneous movement of the first jib section, the second jib section and the telescopic jib section on cargo oscillation, as well as the effect of cargo oscillation on dynamic loads that occur in the boom system and manipulator hydraulic drive elements.
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