To gain a thorough understanding of the load state of parallel kinematic machines(PKMs), a methodology of elastodynamic modeling and joint reaction prediction is proposed. For this purpose, a Sprint Z3 model is used a...To gain a thorough understanding of the load state of parallel kinematic machines(PKMs), a methodology of elastodynamic modeling and joint reaction prediction is proposed. For this purpose, a Sprint Z3 model is used as a case study to illustrate the process of joint reaction analysis. The substructure synthesis method is applied to deriving an analytical elastodynamic model for the 3-PRS PKM device, in which the compliances of limbs and joints are considered. Each limb assembly is modeled as a spatial beam with non-uniform cross-section supported by lumped virtual springs at the centers of revolute and spherical joints. By introducing the deformation compatibility conditions between the limbs and the platform, the governing equations of motion of the system are obtained. After degenerating the governing equations into quasi-static equations, the effects of the gravity on system deflections and joint reactions are investigated with the purpose of providing useful information for the kinematic calibration and component strength calculations as well as structural optimizations of the 3-PRS PKM module. The simulation results indicate that the elastic deformation of the moving platform in the direction of gravity caused by gravity is quite large and cannot be ignored. Meanwhile, the distributions of joint reactions are axisymmetric and position-dependent. It is worthy to note that the proposed elastodynamic modeling method combines the benefits of accuracy of finite element method and concision of analytical method so that it can be used to predict the stiffness characteristics and joint reactions of a PKM throughout its entire workspace in a quick and accurate manner. Moreover, the present model can also be easily applied to evaluating the overall rigidity performance as well as statics of other PKMs with high efficiency after minor modifications.展开更多
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....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.展开更多
基金Project(Kfkt2013-12)supported by Open Research Fund of Key Laboratory of High Performance Complex Manufacturing of Central South University,ChinaProject(2014002)supported by the Open Fund of Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures,ChinaProject(51375013)supported by the National Natural Science Foundation of China
文摘To gain a thorough understanding of the load state of parallel kinematic machines(PKMs), a methodology of elastodynamic modeling and joint reaction prediction is proposed. For this purpose, a Sprint Z3 model is used as a case study to illustrate the process of joint reaction analysis. The substructure synthesis method is applied to deriving an analytical elastodynamic model for the 3-PRS PKM device, in which the compliances of limbs and joints are considered. Each limb assembly is modeled as a spatial beam with non-uniform cross-section supported by lumped virtual springs at the centers of revolute and spherical joints. By introducing the deformation compatibility conditions between the limbs and the platform, the governing equations of motion of the system are obtained. After degenerating the governing equations into quasi-static equations, the effects of the gravity on system deflections and joint reactions are investigated with the purpose of providing useful information for the kinematic calibration and component strength calculations as well as structural optimizations of the 3-PRS PKM module. The simulation results indicate that the elastic deformation of the moving platform in the direction of gravity caused by gravity is quite large and cannot be ignored. Meanwhile, the distributions of joint reactions are axisymmetric and position-dependent. It is worthy to note that the proposed elastodynamic modeling method combines the benefits of accuracy of finite element method and concision of analytical method so that it can be used to predict the stiffness characteristics and joint reactions of a PKM throughout its entire workspace in a quick and accurate manner. Moreover, the present model can also be easily applied to evaluating the overall rigidity performance as well as statics of other PKMs with high efficiency after minor modifications.
文摘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.
