Kinetic Energy-Based Indicators to Compare Different Load Models of a Mobile Crane

Abstract

This paper presents a proposal for the use of energy indicators to evaluate the load modelling methods on the dynamics of a mobile crane. Three different variants of mathematical models of a load carried were examined and compared: as a lumped mass on one hook-sling, as a sphere on one hook-sling, and as a box on four hook-slings. The formalism of joint coordinates and homogeneous transformation matrices were applied to define the kinematics of the system. The equations of motion were derived using the Lagrange equations of the second kind. These equations were supplemented by the Lagrange multipliers and constraint equations formulated for the cut-joints and drives. The energy indicators were proposed to evaluate the behavior of the crane and the carried load. The authors proved that modeling a load in the form of a lumped mass is a great simplification in the analysis of crane dynamics.