Vector Synthesis Interpolation And C Function Cutter Radius Compensation For Cone Spline

Interpolation precision is one of the most important indicators for Numerical Control (NC) system, and the interpolation algorithm determines the performance of a NC system. In traditional interpolation algorithms, line and arc are the main interpolation targets. With the more applications of conic curves (elliptic and parabolic, etc) in NC machining, simple linear or circular interpolation algorithms can not satisfy the requirement of modern high precision NC processing. Cone Spline consists of conic curves which are connected with each other, and it now has become a general description form of complex work pieces in CAD system. By using cone spline to fit the work piece, the fitted curve is assured to have higher fitting precision. A general vector synthesis interpolation algorithm for cone spline is proposed, and on the basis of it, the sharp and internal auto-transition problems are solved. In this thesis, the main contents of vector synthesis interpolation and C function cutter radius compensation are as follows:(1) In this thesis, both at home and abroad researches of NC interpolation and C function cutter radius compensation are firstly introduced. The necessity of the research above is analyzed from the view of the machine user.(2) Based on the difference interpolation algorithm, vector analysis of the cutter location point's track of cone spline is proceeded by creating a normal vector circle. In conic curves machining, a universal interpolation algorithm for line (degradation of conic curve), arc, elliptic, parabolic is researched. In the meantime, some other problems regard to vector synthesis interpolation algorithm, such as machining allowance, are analyzed.(3) After comprehensive analyzing of the possible 25 cases in the connection of conic curves, sharp and internal corner transition theories for cone spline NC machining are proposed based on the vector synthesis interpolation algorithm. Other problems regard to C function cutter radius compensation for cone spline are solved.(4) Reverse coordinate system is established and reverse interpolation algorithm is proposed. After that, post-quadrant problem is resolved successfully. An error mathematic model is established, and error analyses are compared between difference interpolation and vector synthesis interpolation by the average error method.Experiment show that vector synthesis interpolation algorithm for cone spline has high interpolation precision.