Research On The Algorithm Of Forward Adaptive Interpolation Based On NURBS Curve

One of the key technologies in manufacturing is now digital technology of CNC, and the core technology of CNC is the interpolation algorithm. Interpolation algorithm is based on the requirements of the feed speed, based on the known outline discrete point data directly to calculate the coordinates of a number of intermediate points, and then according to the interpolation of the coordinate values, control the movement of the tool. Interpolation of the intermediate point coordinates relate to the interpolation point generation algorithm and interpolation point distance control. Complex interpolation curve generation algorithm will be described generally with spline and control acceleration and deceleration control algorithm is generally used to control interpolation point distance.This paper studies that the generation algorithm and related properties spline curve, relate to the node vector, the weighting factors to calculate the basis functions as well as spline curve derivation, inverse control points. To reduce the amount of computation a NURBS curve simplification algorithm is applied to the spline interpolation algorithm; doing in-depth research for acceleration and deceleration control algorithm. S-type speed control algorithms is derived in detail and time planning is solved with the acceleration classified mode.A dozen change speed curve which is involved in the complex S type speed curve with the beginning and the end speed non zero, are divided into three stages that includes seven time periods, which simplify the calculation process and avoid complicated calculations.Newton iterative method is used to solve high order equation that includes second iteration correction, finally get planning values correspond processing requirements. Convergence value error is bigger from direct use of the Newton iteration method, so need to consume a long time for correction, and then proposed an improved Newton iterative method. As the acceleration and deceleration control process is divided into three stages, According to the mathematical analysis of the acceleration time change equations, the higher order equations is simplified, and in accordance with its constitution monotonic change,construct its square function, to convert it into a single convex function, and then take advantage of the convergence of Newton iteration to solve its value. The algorithm solves the problems which the S-type acceleration and deceleration time of the planning is complex, complicated and provide a simple, efficient deceleration time planning algorithms.According to the requirements of the spline interpolation forward adaptive interpolation algorithm is used and pre-sentence segment is based on changes of the contour of the curve to determine the deceleration section, and then the speed of each sampling period is calculated with the S-type acceleration and deceleration planning, according to the best principles of efficiency, and then determine whether the plan speed meets curve machining accuracy, and the final trajectory planning program meet the requirements of high speed and high precision.According to acceleration and deceleration control algorithm proposed and prospective adaptive interpolation algorithm, MATLAB software is used for real-time CNC machining simulation, to analyze interpolation algorithm efficiency 、interpolation precision and time plan, then correctness of the algorithm, practicality, efficiency is proved, then conduct experiments on the motor test platform to verify the feasibility of the algorithm, effectiveness. Some technical preparation for the development of numerical control system is made based on research.