Nonlinear dynamic characteristics analysis of planar flexible rotating beams with clearance joint

This paper presents a dynamic modeling method for studying dynamic behavior of planar flexible rotating beams with clearance joint. The Hamilton method is introduced to establish a dynamic model of the planar flexible rotating beams. The coupling relationship among the planar revolute joint clearance, the elastic deformation and wide range motion is taken into account. To address the problem of dynamic stiffening under the situation of high-speed rotation, the second-order coupling quantity of the longitudinal contraction caused by the transverse bending deformation is taken into account. To illustrate this method, two examples are presented: a typical planar rotating flexible beam with clearance revolute joint, and an engineering rotating manipulator arm. The typical planar rotating flexible beam example illustrates the efficiency and the accuracy of the dynamic modeling method. Results show that clearance joint leads to dynamic irregular fluctuation. The second example is the engineering problem that we have to deal with, in which the structure of manipulator arm is modeled as a clamped-free beam. Simulation results indicate that the motion of manipulator arm is nonlinear, and it is unreasonable to employ the model of ideal rigid body to build the controller of manipulator arm. Compared to the stage of oscillation, the dynamic fluctuation is small in the process of continuous contact. Besides, the contact force of clearance joint is higher than the constraint force of ideal joint during the process of contact.