Improved Stiffness Modeling for An Exechon-Like Parallel Kinematic Machine (PKM) and Its Application

Abstract

Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy, stiffness and workspace of machining equipment. Therefore, a 5-DOF (degrees of freedom) parallel kinematic machine (PKM) with redundant constraints is proposed. Based on the kinematics analysis of the parallel mechanism using intermediate variables, the kinematics problems of the PKM are solved through equivalent kinematics model. The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM, where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis. And the stiffness model of the parallel mechanism is improved by correction coefficient matrix, each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism. The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively. The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism. To enhance the machining accuracy of the PKM, the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece. A plate workpiece taken as example is examined in the case study section, which demonstrates the effectiveness of optimization method.