The imminent discussion of the data item parameters on the table line body during NC operation

The mathematical description of the parameter spline is the one-parameter cubic spline curve equation shown by the parameter t: P(t)=B1+B2t+B3t2+B4t3(1) As shown, n value points (xj, Yj), j=1, 2, 3,, n. In the formula (1), P(t)= The position vector of any point on the spline, tj If P(tj)=Pj, P′j=dpdt|t=tj=0; P(tj+1)=Pj+1, P′j+1=dpdt|t=tj+1=0(2) :P(t)=Pj+P'jt+3Pj+1-P'jt2j+1-2P'jP'j+1tj+1t2+2Pj-Pj+1t3j+1-P'j+P'j+1t2j+ 1t3(3) adjacent two line segments have the same curvature at the node, and its second derivative is equal on both sides of the node, namely: P′′jtj+1=P′′j+10. Therefore: tj+2P′j+2tj +2+tj+1P'j+1+tj+1P'j+2=3tj+1tj+2×04t2j+1Pj+2-Pj+1+t2j+2Pj+1-Pj(4)

Let: λj=tjtj+tj-1, μj=1-λj, Cj=3λjPj-Pj-1tj-1+μjPj+1-Pjtj(5) Then equation (4) can be written as: λjP'j-1+2P' j+μjP'j+1=Cj=1,2,,(n-1)(6)

Tool position data calculation <5> Most CNC machine tools have a tool compensation function, which can be directly programmed with the numerical values ​​of the points obtained by the above method. However, many parts are not suitable for the parameter cubic spline curve and the core point envelope. For the tool compensation function, the tool point must be obtained to program.

P→(t) is the parameter cubic spline curve, l is a curve which is equidistant from P→(t), which is enveloped by the centroid point. P and P1 are corresponding to P→(t) and l respectively. The two points on the same normal line have the coordinates {x(t), y(t)}, {x1(t), y1(t)}, T→ is the point P-cut, and R is the tool radius.

Conclusion In NC programming, using the spline curve to approximate the column curve is one of the commonly used methods, but because its shape does not have geometric invariance, and the processing error is affected by the large error when dealing with large deflection curves. In this paper, the shape spline curve has the characteristics that the shape has nothing to do with the coordinate system, and the error is small when dealing with large deflection. The mathematical interpolation is used to give the interpolation algorithm, and then the calculation of the tool position data solves the problem that some parts are not suitable. The disadvantage of using the knife compensation function and having to use the point of the knife to program.

(Finish)

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