Research On Spline Curve Interpolation Algorithm And Adaptive Speed Control

With the development of science and technology, spline curve has an increasinglyimportant role in the design and manufacture of complex curves and surfaces in theautomotive, aerospace, ships, mold and other industries. Spline curve interpolationtechnology is under increasing scrutiny in recent years, and more and more researcherslaunch the research, development and application of it, it has also become one of themain research directions of the numerical control technology. Interpolation technologyis the core of the numerical control system, and the algorithm of it will directly affectthe performance of the numerical control system. The performance of interpolationfunction has been a major index for the performance of the numerical control system.This thesis studies the specific form of the parametric representation of space curveand analyses the parametric representation’s advantages compared to the non-parametricrepresentation. And this thesis analyzes the source of the space spline curve, thedefinition of the space spline curve and the value of researching on the space splinecurve. With analyzing the insufficient of the interpolation algorithm based on Taylorexpansion which is commonly used in the numerical control system now, this thesisadopts a new interpolation algorithm which composes the Taylor expansion and thedifferential equation of Adams. The algorithm uses differential to replace derivativecalculation of the Taylor expansion, avoiding the complex derivative calculation, anduses the difference to replace the differential for the further simplification. It ensures thereal-time of the interpolation. At the same time, this thesis adopts aprediction-correction method to calibrate the interpolation parameter in order to ensurethe iterative accuracy of the spline curve interpolation.Acceleration and deceleration control is an important part of the interpolationalgorithm. This thesis adopts acceleration and deceleration control algorithm on thecubic polynomial model, based on the analysis of the advantages and disadvantages ofseveral acceleration and deceleration control algorithms which are used currently in thenumerical control system. And this thesis uses the pre-acceleration and decelerationspeed control, which ensures the contour accuracy of the spline curve interpolation andavoids the impact of the machine during the motion process effectively. Meanwhileconsidering the spline curve interpolation process chord error and acceleration controlto control speed adaptively, which ensures the interpolation accuracy of the spline curveinterpolation well. This thesis carries out research on the quintic spline interpolation algorithm, whichhas a unique advantage in the processing of the spline curve. And this thesis studies thebasic parametric expressions structure of the quintic spline. This thesis introduces thehardware platform of the quintic spline interpolation and the realization principles of thehardware platform. According to the spline curve interpolation algorithm and theacceleration and deceleration control algorithm which are presented in this thesis, usingthe software platform CCS to program experiment on the hardware platform ofTMS320C6713. And experimental analysis of an instance verifies the correctness andthe effectiveness of the designed spline curve interpolation algorithm.