Coordinate changeover and terminal differentiate problem

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1. The principle that the law compares of place discussion to undertake reaching circular arc interpolation point-blank with pointwise before quadrant and coordinate commutation and computation are formulary, apply to Ⅰ quadrant to be mixed point-blank only Ⅰ quadrant is anticlockwise circular arc the sort of specific situation. Quadrantal to differring mix point-blank for the circular arc of different quadrant, different trend, formula of its interpolation computation and pulse feed direction are different. To unite the interpolation formula with each straight quadrant the formula at Ⅰ quadrant, the interpolation formula of 8 kinds of circular arc of will different quadrant, different trend unites the computational formula that goes against a circle at Ⅰ quadrant, what wait according to quadrant with respect to need general coordinate and feed direction is different and undertake alternating, such, no matter which quadrantal circular arc is mixed,press Ⅰ quadrant to go against point-blank circle and undertake interpolation is calculated point-blank. And the direction of feed pulse is mixed by actual quadrant line will decide, use logistic circuit or program to deliver feed pulse respectively + X, - X, + Y, - Y4 the passageway goes up, mix in order to control machine tool workbench along X Y to motion. We use SR1, SR2, SR3, SR4 expresses Ⅰ respectively, Ⅱ , Ⅲ , the clockwise arc of Ⅳ quadrant, with NR1, NR2, NR3, NR4 expresses Ⅰ respectively, Ⅱ , Ⅲ , the anticlockwise circular arc of Ⅳ quadrant, if pursue 2, 6 (A) be shown; With L1, l2, l3, l4 expresses Ⅰ respectively, Ⅱ , Ⅲ , of Ⅳ quadrant linear, if pursue 2, 6 (B) be shown. By the graph 2, 6 can see: Press Ⅰ quadrant when operation of line of NR1 of anticlockwise trend circular arc interpolation, if the feed X axis is retrorse, walk out of Ⅱ quadrant to arrange hour hand to move toward circular arc SR2 namely; The feed Y axis is retrorse, walk out of SR4 namely; X and Y axis both feed is retrorse, walk out of NR3 namely. Right now NR1, NR3, SR2, SR4 4 kinds of lines take same deviation operation formula, beardless change. Graph 2-6 differs with circular arc point-blank quadrantal trend still can see, when pressing NR1 line interpolation, the coordinate X of operation formula and Y exchange, make Y with X, make X with Y, have to arrive so the trend of SR1. Press afore-mentioned principles, use formula of SR1 same operation, direction of proper change feed also can obtain the others line SR3, NR2, the trend of NR4. This that is to say, if be aimed at different quadrant to build the coordinate that is similar to Ⅰ quadrant, attainable as linear as Ⅰ quadrant the similar case that goes against a circle with Ⅰ quadrant, can make interpolation calculation with unified formula thereby, give out the pulse of different way according to differring quadrantally next. Graph 2, 6 (A) , (B) it is 8 kinds of circular arc and 4 kinds of linear coordinate to build a case respectively, can get expressing accordingly 2, the feed pulse of 3 distributes a kind. Normal Align=center> expresses X of 2-3 △ , distributive of △ Y pulse 12 sort <DIV Align=center>normal > graph Normal > pulse Normal Align=center> quadrantal Normal > Ⅰ Normal > Ⅱ Normal > Ⅲ Normal > Ⅳ Normal >G03normal > △ Xnormal > △ Ynormal >-Xnormal >+Ynormal >-Ynormal >+Xnormal >+Xnormal >-Ynormal >+Xnormal >+Ynormal >G02normal > △ Xnormal > △ Ynormal >-Ynormal >+Xnormal >+Xnormal >+Ynormal >+Ynormal >-Xnormal >-Xnormal >-Ynormal >G01normal > △ Xnormal > △ Ynormal >+Xnormal >+Ynormal >+Ynormal >-Xnormal >-Xnormal >-Ynormal >-Ynormal Style="TEXT-INDENT: 24pt; LINE-HEIGHT: 150%">+X</DIV> from the watch 2, 3 can see, to linear (G01) for, the Δ X that according to Ⅰ quadrant formula of linear deviation computation gets and Δ Y pulse, according to different quadrant, allocate a machine tool different coordinate (X, y) losing direction to go up. Namely if Ⅱ is quadrantal linear, criterion Δ X should be sent toward + Y coordinate; If Ⅲ is quadrantal linear, criterion Δ X should be sent toward - X coordinate, etc. Express from this can get sending past ± X, the pulse of direction of ± Y coordinate allocates logical pattern to be + Ⅰ of · of Y of X=G02 · Δ + Ⅰ of · of X of G01 · Δ + Ⅱ of · of X of G02 · Δ + Ⅲ of · of X of G03 · Δ + Ⅳ of · of Y of G03 · Δ + · Ⅳ of Y of G01 · Δ - . The terminal differentiate method that pointwise compares the terminal differentiate pointwise of the law to compare a standard has roughly following a few kinds: (1) install tally of a terminal subtration JE, the treatment overall length that this program X and Y coordinate write down before interpolation operation begins (namely the displacement total situation of X and Y is counted) , in interpolation process, x or Y to every make a move, subtract from inside total situation number 1, till number is put to be decreased in JE,be 0, express to arrive at terminus. This kind of method, precedent already made the introduction. (2) install two tally JEX and JEY, control the treatment length of two reference axis respectively. Axis of the X that be like an edge is mobile one pace, decrease from inside JEX 1; Same, axis of the Y that be like an edge is mobile one pace, decrease from inside JEY 1. Number should be put to all be decreased to be zero hour in JEX and JEY, express to arrive at terminus. (3) install tally of a terminal subtration JE, reference axis of this program X is written down before interpolation operation begins (or Y axis) axial umbriferous treatment overall length spends Ex (or Ey) -- the greater coordinate value in should choosing Ex and Ey regards terminal differentiate as coordinate. In interpolation process, if of the check in JE is Ex, criterion every time make a move of edge X axis, put from JE namely subtract in number 1 (Ey of the check in be like JE, criterion every time make a move of edge Y axis, subtract from inside JE namely 1) , till JE puts number to be decreased to be 0, express to arrive at terminus. Pointwise compares a law to divide can interpolation is mixed point-blank besides circular arc, still can 2 curves such as interpolation ellipse, parabola and hyperbola. Rate of this law feed is stable, precision is taller, no matter be,still be in common NC system in CNC system having very wide application. The feed rate problem when pointwise compares law interpolation is analysed below. CNC Milling CNC Machining