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

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.

Evolution of convex structure during counter-rotating electrochemical machining based on kinematic modeling

Counter-rotating electrochemical machining(CRECM)is a novel electrochemical machining(ECM)method,which can be used to machine convex structures with complex shapes on the outer surface of casings.In this study,the evolution of the convex structure during CRECM is studied.The complex motion form of CRECM is replaced by an equivalent kinematic model,in which the movement of the cathode tool is realized by matrix equations.The trajectory of the cathode tool center satisfies the Archimedes spiral equation,and the feed depth in adjacent cycles is a constant.The simulation results show that the variations of five quality indexes for the convex structure:as machining time increases,the height increases linearly,and the width reduces linearly,the fillets at the top and root fit the rational function,and the inclination angle of the convex satisfies the exponential function.The current density distributions with different rotation angles is investigated.Owing to the differential distribution of current density on workpiece surface,the convex is manufactured with the cathode window transferring into and out of the processing area.Experimental results agree very well with the simulation,which indicates that the proposed model is effective for prediction the evolution of the convex structure in CRECM.