CN1888992A - Variable separation orthometric subalgebric curve composition difference interpolating digital processing method - Google Patents

Variable separation orthometric subalgebric curve composition difference interpolating digital processing method Download PDF

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CN1888992A
CN1888992A CN 200610045552 CN200610045552A CN1888992A CN 1888992 A CN1888992 A CN 1888992A CN 200610045552 CN200610045552 CN 200610045552 CN 200610045552 A CN200610045552 A CN 200610045552A CN 1888992 A CN1888992 A CN 1888992A
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curve
interpolation
difference
cutter
cutter circle
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CN100462879C (en
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王敏
赵玉刚
单东日
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Shandong Institute of Light Industry
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王敏
赵玉刚
单东日
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Abstract

The invention is concerned with the positive higher-order algebraic curve synthesis difference interpolation numerical control processing method that the variable may separate. The invention solves the problems in the present numerical controlling system, such that the interpolation method can not satisfy the process need, the precision is low when processing the beeline or arc fitting, the meeting point is not continuous, the computing program is big, the advantages of the invention are that the interpolation function is strong, the controlling precision is high and the operation is easy. The method is: uses the difference interpolation method to achieve the direct interpolation of the beeline, the ellipse, the hyperbola and the parabola by the unified computing chart, thereby the interpolation function of the numerical controlling system improves a lot, uses the curve fold principle to achieve the automatic creation of the he non-circular curve isometry curve.

Description

The separable positive high order algebraic curve of variable synthesizes the difference interpolating numerical-control processing method
Technical field
The present invention relates to a kind of digital control system job operation, relate in particular to the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of a kind of variable.
Background technology
Numerically-controlled machine is typical electromechanical integrated product, be the main flow equipment of modern manufacturing industry, it is the important symbol that embodies the machinery manufacturing industry technological level, be involve the interests of the state and the people, the most advanced and sophisticated strategic materials of building of national defence, it is the important motivity of China's economic development, its large-scale promotion and application are for increasing effect is just being brought into play in the manufacturing development of China.
Digital control system is the control and the drive unit of numerically-controlled machine, it is the core of numerically-controlled machine, the power of digital control system function and the quality of performance are directly determining the power of numerically-controlled machine function and the quality of performance, so the development of digital control system is the basis of numerically-controlled machine development.From the world, through the development of five more than ten years, though digital control system in kind, or on function and performance, all obtained development at full speed, the various digital control systems as lathe, milling machine, grinding machine, line cutting, machining center etc. have appearred.Although present digital control system is of a great variety, superior performance, but the interpolation function that nearly all digital control system has has only two kinds: the one, and linear interpolation, the 2nd, circular interpolation, the curve of processing other can only carry out match by straight line or circular arc as circular cone or high order curve except that circle.And for conic section or high order curve, carry out straight line or circular fitting and all have three shortcomings: the one, the first order derivative at node place is discontinuous, and promptly contact is unsmooth; The 2nd, in order to reach the fitting precision of regulation, the program hop count that match is used can be very big, exceeds the program capacity of digital control system through regular meeting in the occasion of Machining of Curved Surface; The 3rd, contact place unsmooth also caused the discontinuous of speed.The existence of these three problems all can have certain influence to machining precision and crudy.From domestic, although the numerically-controlled machine industry development of China rapidly, play an important role to machinery manufacturing industry and development and national economy, but the most of employed digital control system of nearly all The advanced CNC and low-grade numerically-controlled machine is the digital control system of import, the development of China NC Machine industry is being subjected to Hesperian restriction always, and the import of the digital control system of some specific use (as military use) is restricted.
Summary of the invention
Purpose of the present invention is exactly that used interpolating method can not well satisfy process requirements in the present digital control system in order to solve, precision is low when carrying out straight line or circular fitting, contact is discontinuous, problems such as operation program is big, provide a kind of and have that interpolation function is stronger, control accuracy is higher, manipulate the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of variable of advantage such as easier.
For achieving the above object, the present invention has adopted following technical scheme: the separable positive high order algebraic curve of a kind of variable synthesizes the difference interpolating numerical-control processing method, and its step is:
A, be that the separable positive high order algebraic curve machining starting point of variable is a true origin with contour curve, the tangent line at starting point place is set up " curve relative coordinate system " at first quartile, and calculates positive high order algebraic curve P m(x)=Q n(y) equation in relative coordinate system;
B, foundation " cutter circle relative coordinate system ", and provide the equation of cutter circle in relative coordinate system;
C, with the parameter initialization of contour curve to be processed and cutter circle;
D, determine interpolation mode according to the numerical value of parameter S bz and synthetic interpolation slope deviation discriminant function δ:
As Sbz=0 and δ 〉=0, then carry out difference interpolating by the cutter circle, calculate new deviation δ and, return steps d Sbz assignment again;
As Sbz=0 and δ＜0, then carry out difference interpolating by contour curve, calculate new deviation δ;
As Sbz ≠ 0 and δ 〉=0, then, calculate new deviation δ by carrying out difference interpolating by contour curve;
As Sbz ≠ 0 and δ＜0, then carry out difference interpolating by the cutter circle, calculate new deviation δ and, return steps d Sbz assignment again;
E, as curve counting step=0, finish interpolation; Otherwise, return steps d.
The equation of contour curve in relative coordinate system that obtains through coordinate transform among the described step a is P m(x)=Q n(y).Wherein
P m(x)=a mx m+ a M-1x M-1+ ... a1 x, Q n(y)=b ny n+ b N-1y N-1+ ... b 1Ya mBe coefficient, b nBe coefficient, m, n are natural number, and x, y are variable.
Work as m, n≤2 o'clock, curve is a SECOND ORDER ALGEBRAIC CURVE, in relative coordinate system, it is P that curve is converted to positive SECOND ORDER ALGEBRAIC CURVE 2(x)=Q 2(y), P wherein 2(x)=a 2x 2+ a 1X, Q 2(y)=b 2y 2+ b 1Y.
Among the described step b, cutter circle relative coordinate system is determined by following three principles:
A, cutter circle relative coordinate system is identical with the coordinate axis forward of contour curve relative coordinate system among the step a, and quadrant instructs identical, and true origin can not overlap;
B, cutter circle and contour curve are tangent at the starting point place;
C, cutter circle relative coordinate system true origin, the center of circle, contour curve starting point be straight line altogether, all on the normal direction at spring of curve place.
Parameter S bz=0 in the described steps d represents cutter circle second order difference j sX2 is for just and j sY2 is for negative; Sbz=1 represents cutter circle second order difference j sX2 is negative and j sY2 is for just.
Synthetic interpolation slope deviation discriminant function δ in the described steps d is the contour curve slope k lWith cutter circle slope k sPoor k l - k s = j l x 1 - j l x 2 2 j l y 1 - j l y 2 2 - j s x 1 - j s x 2 2 j s y 1 - j s y 2 2 Molecule after the reduction of fractions to a common denominator, promptly
δ=j lX1j sY1-j sX1j lY1+0.5 (j sX2j lY1-j lX1j sY2+j sX1j lY2-j lX2j sY1)+0.25 (j lX2j sY2-j sX2j lY2) wherein, j lX1: polynomial expression P m(x) in x place first order difference; j lX2: polynomial expression P m(x) in x place second order difference;
j lY1: polynomial expression Q n(y) in y place first order difference; j lY2: polynomial expression Q n(y) in y place second order difference;
j sX1: the cutter circle is in x place first order difference; j sX2: the cutter circle is in x place second order difference;
j sY1: the cutter circle is in y place first order difference; j sY2: the cutter circle is in y place second order difference.
About described processing quadrant instruction L, cutter partially, the curve concavity and convexity determines that jointly the cutter of digital control processing is partially inside and outside, promptly synthetic moving interpolation adds or subtracts during cutter radius compensation; Differentiating inside and outside inclined to one side method based on left and right sides offset tool, the instruction of processing quadrant and curve concavity and convexity is (TA=0 is that straight line is done outer processing partially):
The left avertence cutter The quadrant instruction TA Partially inside and outside The right avertence cutter The quadrant instruction TA Partially inside and outside
L1 ＞0 Partially interior L1 ≥0 Partially outer
≤0 Partially outer ＜0 Partially interior
L2 ≥0 Partially outer L2 ＞0 Partially interior
＜0 Partially interior ≤0 Partially outer
L3 ＞0 Partially interior L3 ≥0 Partially outer
≤0 Partially outer ＜0 Partially interior
L4 ≥0 Partially outer L4 ＞0 Partially interior
＜0 Partially interior ≤0 Partially outer
Wherein, TA = ( jy 1 - jy 2 2 ) jx 2 - ( jx 1 - jx 2 2 ) jy 2 .
During the outer cutting curve partially of cutter circle, the moving interpolation of cutter circle and curve all drives the motion of lathe coordinate axis, when the curve interpolating motion when numeration direction coordinate makes a move, the curve length jj that counts subtracts 1; Partially during cutting curve, the moving interpolation of cutter circle does not drive the motion of lathe coordinate axis in the cutter circle, also will deduct just to drive the lathe coordinate axis behind the moving interpolation of cutter circle and move in the moving interpolation of curve, but jj still subtracts 1.
Cutter circle and contour curve in the described steps d all can be expressed as the positive high order algebraic curve of separable geometries form P in relative coordinate system separately m(x)=Q n(y), the difference interpolating method of cutter circle and curve is unified.The positive high order algebraic curve of concrete separable geometries difference interpolating step is,
A, carry out curve (contour curve, cutter circle) coordinate transform, obtain the curvilinear equation in the relative coordinate system;
B, parameter initialization: calculate P m(x) at the 1～m of x=0 place jump branch: jx1, jx2 ..., jxm; Calculate Q n(y) at the 1～n of y=0 place jump branch: jy1, jy2 ..., jyn; Initialization deviation F=Q n(y)-P m(x), at the F=P of starting point place m(0)=Q n(0)=0; Determine counting direction G; Count initialized length jj; Determine processing quadrant instruction L i
C, as counting step jj=0, finish interpolation; Otherwise, change steps d;
D, as jy1＜jx1, then interpolation parameters is changed to Fy=F+jy1, Fxy=Fy-jx1, jy1=jy1+jy2, jy2=jy2+jy3 ..., jy (n-1)=jy (n-1)+jyn changes step e; Otherwise interpolation parameters is changed to Fx=F+jx1, Fxy=Fy-jy1, and jx1=jx1+jx2, jx2=jx2+jx3 ..., jx (m-1)=jx (m-1)+jxm changes step f;
E, as | Fy|＜| Fxy|, Y makes a move, and makes F=Fy, as G=Gy, then counting step jj=jj-1 changes step c; Otherwise X, Y respectively make a move, F=Fxy, and jx1=jx1+jx2, jx2=jx2+jx3 ..., jx (m-1)=jx (m-1)+jxm, counting step jj=jj-1 changes step c;
F, as | Fx|＜| Fxy|, X makes a move, and makes F=Fx, as G=Gx, then technology length jj=jj-1 changes step c; Otherwise, X, Y respectively makes a move, F=Fxy, jy1=jy1+jy2, jy2=jy2+jy3 ..., jy (n-1)=jy (n-1)+jyn, counting step jj=jj-1 changes step c;
Counting step jj is for when the tangent line of End of Curve and X-axis angle≤45 ° among the described step 6b, and counting direction is G=Gx, and the projection of curve on X-axis superposes and be counting step jj; Otherwise G=Gy, the curve projection on Y-axis superposes and is counting step jj;
In the described curve difference interpolating process,, then process quadrant instruction and be Li, i=1 wherein, 2,3,4 as the i quadrant of machining starting point place tangent line in absolute coordinate system; In the interpolation process, when jx1＜0, be to cross quadrant, it is anti-that the Y-axis direction of feed becomes, and interpolation parameters is changed to: jx1=-jx1, jx2=-jx2, jy2=-jy2, jy1=jy1+jy2, F=-F; When jy1＜0, also be quadrant, it is anti-that the X-axis direction of feed becomes, and interpolation parameters is changed to: jy1=-jy1, jy2=-jy2, jx2=-jx2, jx1=jx1+jx2, F=-F.
Beneficial effect of the present invention is:
1, adopts synthetic difference interpolating technology, realized the direct interpolation of the separable geometries high order curves such as straight line, circular arc, ellipse, para-curve, hyperbolic curve under unified algorithm;
2, utilization curve superposition principle has realized the automatic generation method of non-circular curve equidistant curve, has avoided the complicated calculations of central track of cutter.
Description of drawings
Fig. 1 is a synthetic difference interpolating method flow block diagram of the present invention;
Fig. 2 is a difference interpolating method flow block diagram of the present invention;
Fig. 3 is the functional value calculation process block diagram based on difference of the present invention.
Embodiment
The invention will be further described below in conjunction with accompanying drawing and example.
Fig. 1 is synthetic difference interpolating method flow block diagram principle explanation.
According to two different physical systems of essence of similarity theory, if can describe with same mathematical equation (group), these two systems are exactly similar system, and amount corresponding in the equation (group) is an analog quantity, and similar system has similar character.
The point-to-point comparison method interpolation principle of straight line y=kx is: to the first quartile straight line, as interpolated point (x l, y l) the ratio of coordinate in length and breadth during more than or equal to k, walk+one step of x, and walk+one step of y during less than k; To the second quadrant straight line, as (x l, y l) the ratio of coordinate in length and breadth during more than or equal to k, walk+one step of y (walking-x on indivedual books, is because the inclination angle of straight line does not have unified Definition), and during less than k, walk-one step of x, just all make (x like this i, y l) coordinate levels off to k, i.e. y=kx than all the time in length and breadth.
On contour curve, cutter circle tangent slope k sSlope k with contour curve L lBe tending towards equal, respectively represent contour curve and the round parameter of cutter with subscript l, s, the constraint condition that must synthesize interpolation is:
k l＝λk s (λ＝1)
Know k by similarity theory l=λ k sWith y=kx be similar system, the two similar performance.For cutter circle, the second order difference j of x and y sX2 and j sThe y2 equal and opposite in direction, opposite in sign.Work as j sX2 is negative, j sY2 is timing, k sMore and more littler; Work as j sX2 for just, j sWhen y2 is negative, k sIncreasing.For contour curve L, k is arranged all the time in relative coordinate system l〉=0, so use the similar analogy principle, it is as follows to synthesize interpolation bias judge conclusion:
1. work as k l〉=k sThe time, if cutter circle second order difference j sX2 is being for just, j sY2 should be by the interpolation of cutter circle for negative; If j sX2 is negative j sY2 is timing, should be by the contour curve interpolation; Work as k l＜k sThe time, if cutter circle second order difference j sX2 for just, j sWhen y2 is negative, should be by the contour curve interpolation; If j sX2 is negative j sY2 is timing, should so all make k by the interpolation of cutter circle l=λ k s(λ=1).
2. represent cutter circle j with sbz=0 sX2 is positive j sY2 is for negative; Represent j with sbz=1 sX2 is negative j sY2 is being for just, k l-k sGet molecule δ after the reduction of fractions to a common denominator and be synthetic interpolation slope deviation discriminant function:
δ＝j lx1j sy1-j sx1j ly1+0.5(j sx2j ly1-j lx1j sy2+j sx1j ly2-j lx2j sy1)+0.25(j lx2j sy2-j sx2j ly2)
According to as above conclusion, must synthesize difference interpolating method flow block diagram such as Fig. 1.
Fig. 2 is the explanation of difference interpolating method flow block diagram principle.
The core concept of separable geometries high order curve difference interpolating is: when X coordinate axis or the feeding of Y coordinate axis during one step corresponding coordinate figure add 1, the function P of simultaneously corresponding coordinate m(x) or Q n(y) add this first order difference value, keep P in the feeding process as far as possible m(x)=Q n(y).But feeding mode X or the independent feeding of Y coordinate axis, also can two coordinate axis feeding simultaneously, require feeding mode feeding by interpolation error minimum.Wherein, deviation F=Q n(y)-P m(x), at the P of starting point place m(0)=Q n(0)=0.Concrete FB(flow block) such as Fig. 2.
The cutter circle is all the separable geometries algebraic curve with contour curve, and its interpolating method all can carry out according to Fig. 2, and this is exactly contour curve and the round interpolating method of cutter in the block diagram 1.
Fig. 3 is the functional value calculation process block diagram principle explanation based on difference, is to begin each positive integer point function P (x)=ax from x=1 mThe value block diagram.
Functional value P m(x) divide calculating by function at starting point 1～m jump, the recursion computing formula is P (x l)=P (x L-1)+jx L-11, concrete computing method such as Fig. 3.
Functional value calculates and is mainly used in deviation F=Q in the block diagram 2 n(y)-P m(x) calculating.

Claims (10)

1, the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of a kind of variable is characterized in that: its step is,
A, be that the separable positive high order algebraic curve machining starting point of variable is a true origin with contour curve, the tangent line at starting point place is set up " curve relative coordinate system " at first quartile, and calculates the equation P of contour curve in relative coordinate system m(x)=Q n(y);
B, foundation " cutter circle relative coordinate system ", and provide the equation of cutter circle in relative coordinate system;
C, with the parameter initialization of contour curve to be processed and cutter circle;
D, determine interpolation mode according to the location parameter Sbz of cutter circle and the numerical value of synthetic interpolation slope deviation discriminant function δ:
As Sbz=0 and δ 〉=0, then carry out difference interpolating by the cutter circle, calculate new deviation δ and, return steps d Sbz assignment again;
As Sbz=0 and δ＜0, then carry out difference interpolating by contour curve, calculate new deviation δ;
As Sbz ≠ 0 and δ 〉=0, then, calculate new deviation δ by carrying out difference interpolating by contour curve;
As Sbz ≠ 0 and δ＜0, then carry out difference interpolating by the cutter circle, calculate new deviation δ and, return steps d Sbz assignment again;
When synthesizing interpolation, judge the inside and outside inclined to one side of numerical control machining cutter based on left and right sides offset tool, the instruction of processing quadrant with the curve concavity and convexity, the synthetic moving interpolation of the inside and outside inclined to one side decision of cutter adds or subtracts;
E, as curve counting step=0, finish interpolation; Otherwise, return steps d.
2, the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of variable according to claim 1 is characterized in that: the equation P of contour curve in relative coordinate system among the described step a m(x)=Q n(y) in
P m(x)=a mx m+ a M-1x M-1+ ... a 1X, Q n(y)=b ny n+ b N-1y N-1+ ... b 1Ya mBe coefficient, b nBe coefficient, m, n are natural number, and x, y are variable.
3, the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of variable according to claim 2 is characterized in that: described equation P m(x)=Q n(y) in, at m, n≤2 o'clock, curve is a SECOND ORDER ALGEBRAIC CURVE, in relative coordinate system, it is P that curve is converted to positive SECOND ORDER ALGEBRAIC CURVE 2(x)=Q 2(y), P wherein 2(x)=a 2x 2+ a 1X, Q 2(y)=b 2y 2+ b 1Y.
4, the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of variable according to claim 1 is characterized in that: among the described step b, cutter circle relative coordinate is:
A, cutter circle relative coordinate system is identical with the coordinate axis forward of contour curve relative coordinate system among the step a, and quadrant instructs identical, and true origin can not overlap;
B, cutter circle and contour curve are tangent at the starting point place;
C, cutter circle relative coordinate system true origin, the center of circle, contour curve starting point be straight line altogether, all on the normal direction at spring of curve place.
5, the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of variable according to claim 1 is characterized in that: the parameter S bz=0 in the described steps d is cutter circle second order difference j sX2 is for just and j sY2 is for negative; Sbz=1 is cutter circle second order difference j sX2 is negative and j sY2 is for just.
6, the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of variable according to claim 1, it is characterized in that: the synthetic interpolation slope deviation discriminant function δ in the described steps d is the contour curve slope k lWith cutter circle slope k sPoor k l - k s = j l x 1 - j l x 2 2 j l y 1 - j l y 2 2 - j s x 1 - j s x 2 2 j s y 1 - j s y 2 2 Molecule after the reduction of fractions to a common denominator, promptly
δ＝j lx1j sy1-j sx1j ly1+0.5(j sx2j ly1-j lx1j sy2+j sx1j ly2-j lx2j sy1)+0.25(j lx2j sy2-j sx2j ly2)
Wherein, j lX1: polynomial expression P m(x) in x place first order difference; j lX2: polynomial expression P m(x) in x place second order difference;
j lY1: polynomial expression Q n(y) in y place first order difference; j lY2: polynomial expression Q n(y) in y place second order difference;
j sX1: the cutter circle is in x place first order difference; j sX2: the cutter circle is in x place second order difference;
j sY1: the cutter circle is in y place first order difference; j sY2: the cutter circle is in y place second order difference.
7, the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of variable according to claim 1, it is characterized in that: in the described steps d, the inside and outside folk prescription method of judging numerical control machining cutter when synthesizing interpolation is, based on left and right sides offset tool, instruction of processing quadrant and the employing of curve concavity and convexity TA = ( jy 1 - jy 2 2 ) jx 2 - ( jx 1 - jx 2 2 ) jy 2 , Synthetic moving interpolation adds or subtracts when judging cutter radius compensation, is processing partially straight line is done outside at TA=0;
During the outer cutting curve partially of cutter circle, the moving interpolation of cutter circle and curve all drives the motion of lathe coordinate axis, when the curve interpolating motion when numeration direction coordinate makes a move, the curve length jj that counts subtracts l; Partially during cutting curve, the moving interpolation of cutter circle does not drive the motion of lathe coordinate axis in the cutter circle, also will deduct just to drive the lathe coordinate axis behind the moving interpolation of cutter circle and move in the moving interpolation of curve, but curve counting step jj still subtracts l.
8, the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of variable according to claim 1 is characterized in that: cutter circle and contour curve in the described steps d all can be expressed as the positive high order algebraic curve of separable geometries form P in relative coordinate system separately m(x)=Q n(y), the difference interpolating method of cutter circle and curve is unified, and the positive high order algebraic curve of concrete separable geometries difference interpolating step is,
A, carry out the coordinate transform that curve is contour curve, a cutter circle, obtain the curvilinear equation in the relative coordinate system;
B, parameter initialization: calculate P m(x) at the 1～m of x=0 place jump branch: jx1, jx2 ..., jxm; Calculate Q n(y) at the 1～n of y=0 place jump branch: jy1, jy2 ..., jyn; Initialization deviation F=Q n(y)-P m(x), at the F=P of starting point place m(0)=Q n(0)=0; Determine counting direction G; Count initialized length jj; Determine processing quadrant instruction L i
C, as counting step jj=0, finish interpolation; Otherwise, change steps d;
D, as jy1＜jx1, then interpolation parameters is changed to Fy=F+jy1, Fxy=Fy-jx1, jy1=jy1+jy2, jy2=jy2+jy3 ..., jy (n-1)=jy (n-1)+jyn changes step e; Otherwise interpolation parameters is changed to Fx=F+jx1, Fxy=Fy-jy1, and jx1=jx1+jx2, jx2=jx2+jx3 ..., jx (m-1)=jx (m-1)+jxm changes step f;
E, as | Fy|＜| Fxy|, Y makes a move, and makes F=Fy, as G=Gy, then counting step jj=jj-1 changes step c; Otherwise X, Y respectively make a move, F=Fxy, and jx1=jx1+jx2, jx2=jx2+jx3 ..., jx (m-1)=jx (m-1)+jxm, counting step jj=jj-1 changes step c;
F, as | Fx|＜| Fxy|, X makes a move, and makes F=Fx, as G=Gx, then technology length jj=jj-1 changes step c; Otherwise, X, Y respectively makes a move, F=Fxy, jy1=jy1+jy2, jy2=jy2+jy3 ..., jy (n-1)=jy (n-1)+jyn, counting step jj=jj-1 changes step c.
9, the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of variable according to claim 8, it is characterized in that: counting step jj is for when the tangent line of End of Curve and X-axis angle≤45 ° among the described step b, counting direction is G=Gx, and the projection of curve on X-axis superposes and be counting step jj; Otherwise G=Gy, the curve projection on Y-axis superposes and is counting step jj.
10, the synthetic difference interpolating numerical-control processing method of the separable positive high order algebraic curve of variable according to claim 8 is characterized in that: as the i quadrant of machining starting point place tangent line in absolute coordinate system, then process the quadrant instruction and be Li, i=1 wherein, 2,3,4; In the interpolation process, when jx1＜0, be to cross quadrant, it is anti-that the Y-axis direction of feed becomes, and interpolation parameters is changed to: jx1=-jx1, jx2=-jx2, jy2=-jy2, jy1=jy1+jy2, F=-F; When jy1＜0, also be quadrant, it is anti-that the X-axis direction of feed becomes, and interpolation parameters is changed to: jy1=-jy1, jy2=-jy2, jx2=-jx2, jx1=jx1+jx2, F=-F.
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