# The error waits to approach the computational method of node point-blank in numerical control process designing

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Machine tool of most numerical control does not have the interpolation of the curve that be not a circle to dictate, pass commonly when the work out is not program of round curve numerical control be replaced point-blank with circular arc, because linear substitution method is intuitionistic simple, below the condition that asks in contented precision, replace the curve that be not a circle with broken line of straight line segment normally, the crucial question of process designing of such numerical control language is node is affirmatory. Machine tool of most numerical control does not have the interpolation of the curve that be not a circle to dictate, pass commonly when the work out is not program of round curve numerical control be replaced point-blank with circular arc, because linear substitution method is intuitionistic simple, below the condition that asks in contented precision, replace the curve that be not a circle with broken line of straight line segment normally, the crucial question of process designing of such numerical control language is node is affirmatory. The node of linear substitution method uses span more certainly law and wait for a pace to grow a way two kinds. Below the condition that is less than tolerance in academic curve and linear the biggest error, waiting for span law is the distance between X axis node Δ X is equal. And waiting for a pace to grow a way is the linear length Δ L between each node equal. Wait for span law and waiting for a pace to grow the characteristic with common law is computation simple, but it is calm value as a result of Δ X and Δ L, when the curvature when the curve is bigger, division check the number is more, paragraph of number that creates a program is overmuch, when curvature change of the curve is bigger at the same time, the surface roughness change that brings a spare parts to machine the surface is big also, the surface that affects a part machines precision. The error such as attached drawing is approached point-blank 1 waiting for an error to approach the error such as round curve of Central Africa of principle CNC Machining to approach a way point-blank point-blank is each curve and linear error δ are equal between node, if attached drawing place is shown. Allow the round equation of the error certainly, namely with start A(xa, ya) is the centre of a circle, δ makes a circle for radius: (X-xa)2+(y-ya)2= δ 2(1) begs circle and curvilinear common tangent the slope K of PT: K=(yT-yp)(xT-xp)(2) is beg XT, YT, Xp, Yp, demand solves simultaneous equations: YT-yp=f(xp)(xT-xp)yp=f1(xp)yT-yp=f2(xT)(xT-xp)yT=f2(xT)(3) among them F1(x) is error round function, f2(X) is treatment curve function. By type (3) gets YT, Yp, XT, Xp, press type (the slope K that 2) begs an as parallel as PT bowstring Ab. Criterion the linear equation of bowstring Ab is: Y-ya=K(x-xa)(4) couplet establishs equation of curvilinear equation chord to get B to nod coordinate: Y=f2(x)y-ya=K(x-xa)(5) gets C, D, E by above move in succession... each bits of coordinate. Waiting for an error to approach a way point-blank is the method with node and numerical control least block in CNC Machining of the curve that be not a circle, and the treatment surface precision of the spare parts is mixed dimension precision is tall. But because wait for an error to approach a way point-blank,computation is compared trival, if use handiwork to solve 4 yuan of quadratic equation to get accurate solution very hard commonly, reason is used at the to program of numerical control machine tool rarely. The 2 node algorithm citing that wait for an error to approach a way point-blank take parabola with the academic curve of CNC Machining right half branch Y=ax2(a>0, x>0) is exemple, have Y=2ax. Differ round equation according to allow (1) gets: Group of equation of reason of 2-(x-xa)2y=(x-xa)(y-ya)(6) of Y=ya- √ δ (3) can write for: 2-(x-xa)2yT-yp=2axT(xT-xp)yT=axT2(7) of δ of YT- Yp=-(xp-xa)(xT-xp)(yp-ya)y=ya- √ passes equation series (after the first node that 7) begs, serve as new start with this node, beg repeatedly go down, can get all node. CNC Milling

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