Analytical dynamic of a rotating prismatic actuator with variable stiffness and validation with finite element method

Precise Prismatic actuators are one of the most important actuators used in robotic industry and the main base of parallel robots as 6PUS Stewart-Gough robot. Because of bearing large axial forces by this actuators, elastic deformations are inevitable in the main parts of them. This results in elongation and compression of the piston and ball screw, which deteriorates the dynamic linear positioning accuracy of these actuators. The existence of accurate dynamic equations can seriously help to control these errors. Most of the dynamic models which have been used for these actuators based on lumped parameter approach have one DOF for rigid and two or three DOF for flexible state and the stiffness of parts are considered as constant. In this study, the direct dynamic equations of a rotating prismatic actuator which has three DOF in axial direction and ball screw drive system, are proposed using the Lagrange method. In addition to the flexibility of the moving piston, the ball screw is considered with variable stiffness. The important point of this study is the variability of ball screw stiffness. As the nut moves along the shaft, the active length and stiffness of the shaft change; which is very similar to the reality. In addition to the analytical method, the actuator is modeled in the finite element software, ABAQUS and the results of the analytical method and the finite element method are compared.