A Parameter Adaptive Interpolation Algorithm of Three-Point Circle Method Applied to CNC Machine Tool

Abstract

The invention relates to a three-point circle method parameter self-adaptive interpolation algorithm applied to a numerical control machine tool. The three-point circle method parameter self-adaptive interpolation algorithm comprises the steps of: expressing a non-circle curve equation with parameter formulas, and ensuring that each parameter is corresponding to each function value; successively getting three points D, E and F on the curve in an isoparametric manner; calculating coordinates of a circle center point of an arc passing the three points and the radius R of the arc; then deriving a discriminant for determining whether the arc is clockwise or anticlockwise, and determining whether arc interpolation at this time is clockwise or anticlockwise; finding an intermediate point H between the D point and the E point, calculating the distance [Rho]1 from the point H to the circle center, and similarly, finding an intermediate point I between the E point and the F point, and calculating the distance [Rho]2 from the point H to the circle center; respectively calculating [delta]1 and [delta]2, wherein [delta]1=absolute([Rho]1-R), [delta]2=absolute([Rho]2-R), and [delta]1 and [delta]2 are used as interpolation errors; and comparing [delta]1 and [delta]2 with an allowable error [delta]<allowable>. The three-point circle method parameter self-adaptive interpolation algorithm has the advantages that the interpolation calculation is simplified, the solving process is simple, the solving difficulty is small, the interpolation quality and efficiency are improved, etc.

Description

technical field [0001] The invention belongs to the technical field of numerical control machine tools, and relates to a three-point circle method parameter adaptive interpolation algorithm applied to numerical control machine tools. Background technique [0002] Interpolation is the core of CNC technology. It can determine some intermediate points between known points on the ideal trajectory or contour according to certain mathematical methods according to the contour size of the part, combined with the requirements of precision and technology, so that Approaching the ideal workpiece contour, interpolation is also called "densification of data points". [0003] The interpolation algorithm needs to solve two problems, one is node selection, that is, according to what rules and conditions to select points on the curve; the other is the interpolation method of adjacent nodes, that is, what kind of interpolation movement is performed between adjacent nodes. For the selection o...

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Problems solved by technology

The calculation of equal parameter interpolation is simple and convenient, but the number of points will be a lot; the equal error method can well control the interpolation error in each place and reduce the number of interpolation points, but this method involves four times The calculation of the equation is very large, and the solution process is complicated; the interpolation method of equal chord length will produce a large interpolation error when the curvature of the interpolation curve changes greatly

The above three interpolation methods have their own advantages and disadvantages. If the three interpolation point selection methods can be combined, it can not only satisfy the error of the interpolation algorithm, but also reduce the amount of calculation. This is also the direction we want to study

[0004] Ordinary CNC machine tools have linear and circular interpolation functions. For non-circular curves, the traditional interpolation method uses linear interpolation between selected adjacent nodes, that is, small straight line segments are used to connect adjacent two points. When nodes When the quantity is obtained enough, the contour connected by several broken lines is very close to the real contour of the curve. This interpolation method is simple to calculate and convenient to interpolate. Interpolation mass and interpolation feedrate are detrimental

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