Research On Error And Stiffness Characteristic Of Cross-Link6-DOF Parallel Machine Tool

To address the two issues of error and stiffness for cross-links6-DOFs parallel machine tool BJ-04-02(A), the characteristic that both error and stiffness are related to the pose (position and orientation) of cutter platform is considered. Some key themes, such as full inverse position analysis, workspace (position space and orientation space) analysis, mapping between joint clearance and pose error, distribution of static stiffness, driving force analysis based on rigid-body dynamics, are researched.The main research works in this dissertation include:Based on screw theory and exponential forward position mapping expressions, the full inverse position anlysis is completed and all active and passive joints variables are obtained. Using virtual3D assembly model of BJ-04-02(A), the motion screws of all joints for given referential cutter platform pose are measured and the exponential mapping expressions from joint variables to cutter platform pose are built for six links respectively. By solutions of Paden-Kahan subproblem, the full inverse position solution are derived and all36joint variables from given referential pose to arbitrarily given pose are calculated. The variations of joint variables for four typical trajectories are researched.To obtain the distribution of error and stiffness, the workspace of BJ-04-02(A) are calculated by considering three type constraints, the stretch out and draw back scope of actuating link, the rotating scope of revolute joint and interference of cross links. Firstly reachable point set for given referential cutter platform pose is obtained. Secondly maximal all-around reachable tilting angle is calculated for each point in above set. Thirdly the position space for given tilting angle, i.e., orientation space, is obtained. Finally the recommended spherical, cylindrical and cuboid workspaces are provided.To investigate error and stiffness variations to pose, the error mapping expressions and stiffness matrix containing pose are derived by combining two rotation transformations based on Euler angles (precession, notation and rotation) and rotation angles around three inertial coordinate axes (be equivalent to rotating around a spatial axis) respectively. As to error mapping from joint clearance to pose, Euler angles are used for ideal pose discription without joint clearance while rotating around a spatial axis is added for pose discription with joint clearance, and joint clearance is converted into link length. As to stiffness matrix, Euler angles are used for pose discription without external load while rotating around a spatial axis is added for pose discription with external load. Some variations are investigated, such as error and stiffness distribution in given layers, variations of error and stiffness to z coordinate, variations of error and stiffness to tilting direction and tilting angle.To estimate the fluctuction of actuating forces in six links, the rigid-body dynamics analysis is completed using Newton-Euler method. The analytical expressions of actuating forces are derived and the fluctuctions are investigated for typical trajectory. Combining with cutting force test, the fluctuction of actuating forces during cutting process is obtained.Tests of manufacturing error are taken on BJ-04-02(A), the results are compared with corresponding theoretical results, which has verified the validity of theoretical researches.