Adaptive Curvature Real-time Interpolation Technique Of Parametric Curves And Surfaces

Parametric curves and surfaces interpolaiton and velocity control are very important in the CNC system modules. More requirements for the CNC interpolation have been brought by application of free-form curves and surfaces theory in CAD/CAM and NC machining of components with characteristics of free-form curves and surfaces.The research on the development of a kind of CNC system which supports real-time interpolation for free-form curves and surfaces is of great significance on the improvement of the overall performance of the CNC system and the integration of the CAD/CAM/CNC technique.NURBS curve and surface class is developed for the application of the curve and surface interpolation technique of the CNC system. A flexible acceleration and deceleration algorithm based on the cubic spline function is proposed in this dissertation for curve and surface interpolation. By setting the terms of maximum acceleration and jerk, even the second derivative velocity curve can be obtained and the control objective that the velocity is in a smooth profile without jerk limit can be achieved.The predictor-corrector(预估-校正)parameter calculation method is bettered, and the predictor-iterative correction method is proposed based on the first-order Taylor expansion, which effectively reduces the impact of truncation error on the velocity, and improves the speed characteristics during the process of curve interpolation. A curvature adaptive parametric interpolation algorithm is presented in this thesis. The feed-rate sensitive areas on the curves are detected through offline interpolation preprocessing, where the velocity is planned in accordance with the flexible acceleration and deceleration control method, so that the velocity profile can be smooth as long as it can satisfy the chord error and meet the constraint of machine acceleration.In this paper, the commonly used tool path generating method for parametric surfaces is analyzed, and then an on-line tool path generation algorithm is presented, which takes iso-parametric as the prototype, and has made further improvements about it according to the current research at home and abroad. Based on its combination with the curvature adaptive parametric interpolation algorithm, reliable and continuous path generation and real-time interpolation properties can be gained. At last, the curvature adaptive parametric interpolation and tool path generation for NURBS surfaces are simulated using VC++ and Matlab, and then according to the simulation results, the velocity control effect and parametric interpolation error are analyzed and verified, also the validity and reliability of the tool path generation algorithm for surfaces are specified. The simulation results show that the algorithm is correct and valid, and has important significance for improving the parametric surface path processing ability and the curve interpolation ability of CNC system.