Low-order dynamic model for flexible hydraulic cranes

Abstract

A method to obtain a low-order but accurate dynamic model for multilink flexible hydraulic cranes is presented. An efficient model is achieved by using the assumed modes method with consistent kinematics and by a careful selection of assumed modes. A special type of assumed modes, namely force modes, is presented. These modes consider pointwise forces and moments caused by hydraulic cylinders. The finite element method is used in the calculation of assumed modes, which allows non-uniform links to be modelled with the same accuracy as uniform links. The guidelines for the selection of the number and type of assumed modes are also given. A commercial log loader is used as an example. Three flexible links and two cylinders are modelled. Compared with a high-order finite element model, it is found that, altogether, five force modes are sufficient to achieve a high degree of agreement in the three lowest natural frequencies of the crane. Simulated open-loop responses also show good agreement with measured responses. The structural flexibility has a strong effect on the response of the crane and neglecting flexibility yields incorrect values of the natural frequency, amplitude and damping of force responses of cylinders.