Transformation of Tracking Error in Parallel Kinematic Machining

Abstract

One emerging application of Parallel Kinematic Mechanisms (PKM) is in the computerized numerical control (CNC) machine tools and, recently, several prototypes of such CNC machines have been developed.In Cartesian machine tools, motion properties like velocity and acceleration of the individual drives are directly transferred to the tool center point (TCP). With PKM, the axes motions are transformed by nonlinear transfer functions as a general rule. The goal of the present study is to study the transformation of dynamic properties in PKM based machine tools.Transformation of tracking error and velocity gain from machine coordinates to Cartesian coordinates in workspace is, initially, investigated by a one axis mechanism (Monopod). In this study, the PKM behavior is simplified to a single degree of freedom (DOF) motion system with a nonlinear transformation of dynamic properties like position and velocity. The test bench of Monopod is calibrated by a neural network (NN) method and the model is simulated in the Matlab/Simulink environment. The results of transformation illustrate the relative velocity gain between TCP and drive axis, and are developed to multi axis PKM such as Bipod and Tripod. The effect on trace accuracy is discussed in light of these mechanisms. In the simulation phase, models are performed with constant length of strut, and the mechanical effects like inertia, flexibility, friction and backlash are neglected. This ensures to study uncoupled closed loop controller effects.A contour error algorithm is developed and verified by the Bipod and the Tripod to predict the contour error of a generalized machine tool by the Jacobian matrix and estimated tracking errors in the drives.The experimental results are obtained using a method for star contouring test that consists of straight lines in the workspace with varying orientations and the double ball bar in circular trajectory.An accurate trajectory control is a fundamental requirement for CNC machine tools. To eliminate the contour error, a compensated path method is introduced that generates a setpoint path, with a programmed deviation equal in amount but negative in direction to the calculated contour error. The real transfer function can be identified by the NN approach.