Pointwise compares law interpolation (on)

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Appearance of the spare parts in be being machined actually is sundry, still should use finally to these complex spare parts outline linear or circular arc undertakes so that,be imminented CNC machining. Interpolation computation: It is basic to input of numerical control system data (be like sharp starting point, terminal coordinate, coordinate of the start of circular arc, terminus, the centre of a circle) , use certain algorithmic calculation, according to computation the result issues feed statement to corresponding coordinate. The corresponding each instruction that enter Dai, the machine tool moves to be apart from certainly on corresponding coordinate direction, give workpiece treatment wants outline appearance thereby. Realize the device of operation of this one interpolation, call interpolation implement. The athletic contrail that controls cutting tool or workpiece is core of pilot of outline of numerical control machine tool, no matter be hardware numerical control (NC) system, still be computerized numerical control (CNC) system, have interpolation unit. In CNC, with software (namely program) interpolation perhaps realizes interpolation with hardware and software combination; And in Nc, realize interpolation completely by hardware. The commonly used interpolation algorithm in numerical control system has: Pointwise compares split plot design of integration method of law, number, time and way of the smallest error to wait, method of before this chapter basically introduces two kinds of interpolation. Pointwise compares a standard: It is system of control of every make a move want to will be machined dot and given graphical contrail photograph is compared, in order to decide the way of next feed, make approach treatment contrail. Pointwise compares a law to be approached with broken line linear or circular arc, its biggest error does not exceed unit of a the smallest set. Pointwise introduces to compare a standard respectively below the principle of linear interpolation and circular arc interpolation. One, pointwise compares a standard linear interpolation is like graph 3, L place is shown those who set linear OA to be the first quadrant is linear, start is coordinate origin. O(0, 0) , terminal coordinate is, a() , , p() is treatment dot. If P nods as it happens to lie on linear OA, by similar triangle relation criterion is had nod namely in linear OA upper part (the area that is linear OA and Y axis strictly to be being surrounded to place) , have be like P dot to be in namely linear OA lower part (the area that is linear OA and X axis strictly to be being surrounded to place) , have graph 3, 1 pointwise compares a standard even of the first quadrantal and linear interpolation (3-1) has: ① if, nod P to be on linear OA, already but to + X direction feed one pace, also but to + Y direction feed one pace; ② if, nod P to be in linear OA upper part, should to + X direction feed one pace, in order to approach OA linear; ③ if, nod P to be in linear OA lower part, should to + Y direction feed one pace, treat a kind of condition with approaching OA to will be reached commonly point-blank, instant, to + X direction feed one pace. When the pace number that takes when two direction place and terminal coordinate are equal, stop interpolation. This namely pointwise compares a standard the principle of linear interpolation. Linear to the first quadrant OA from start (namely coordinate origin) set out, when F 0, + X to make a move; When F<0, y to make a move. Characteristic: Each pace needs computational deviation, such computation is more troublesome. The methodological computation deviation of recurrence: The treatment deviation recurrence of before the new processes a dot error after every make a move is used a bit comes out. Use recurrence method, must know begin to process the error of the dot, and beginning to machine a dot is sharp starting point, reason. Below derivation its recurrence formula. Set in treatment to order P() part, , answer along + X direction feed one pace, the deviation that the coordinate value that right now new treatment nods nods for new treatment is machining bit of P() to be in to be like namely, , answer along + Y direction feed one pace, the deviation that the coordinate value that right now new treatment nods nods for new treatment is be narrated on put together namely, pointwise compares a standard every make a move should finish linear interpolation 4 measure (metre) , namely: (1) position differentiate is more than according to deviation value 0, be equal to 0, the position that is less than dot of 0 affirmatory and current treatment. (2) coordinate feed is more than according to deviation value 0, be equal to 0, be less than 0 affirmatory edges feed of wh which direction one pace. (The deviation that 3) deviation computation nods according to new treatment of recurrence formula cipher out is worth. (4) terminal differentiate uses certain treatment dot to whether arrive at terminus. If already arrived, should give out stop signal of new block of machine or changeover. The J of total situation number that wants with X and Y coordinate place commonly comes differentiate. Your J= , every make a move criterion J decreases 1, till J=0. Exemple 3-1 is set want treatment to see graph 3 for 0A (point-blank, 2) , its terminus coordinate is A(5, 3) , terminal computation is worth J= =5+3=8, if the operation metre that machines a process expresses 3, 1 is shown. Above discussed method of calculation of the first quadrantal and linear interpolation, to other quadrant linear, can get method of its interpolation calculation according to same principle. Watch 3, 2 listed direction of feed of each quadrantal and linear L1, L2, L3, L4 and deviation are calculated formulary, among them in deviation computation formula, all be absolute value. Graph 3, show 3 times for the first quadrant pointwise compares a standard the program block diagram of linear interpolation. CNC Milling CNC Machining