三軸連動銑削加工(X軸+Y軸+A軸)
在工件為圓柱的前題下，要用圓柱表面上，使用直徑較小的銑刀(以直徑20mm為例)，銑出較大圓溝(溝寬64mm)，基本上只要兩軸連動及G41或G42補正就可以，不過，如果要用較小直徑20mm銑刀銑出較大圓溝直徑64mm，並要求此圓溝的溝壁如同64mm銑刀銑出的效果，就得以三軸連動(X軸+Y軸+A軸)的方式來加工才行。
三軸連動加工要訣是先找出圓溝的每一處外形是以直徑64mm銑刀圓周邊的哪一個部位所銑出來的，然後透過移動X及Y軸的方法，將直徑20mm銑刀圓周邊移到該位置，如下圖所示，並將A軸如同二軸連動那樣旋轉，即可用直徑20mm銑刀銑出像直徑64mm銑刀所銑出的圓溝。
用AutoLisp模擬較小的銑刀來銑出像直徑64mm銑刀所銑出的圓溝，並輸出CNC程式:
(defun c:kk() ;;for variable diameter of r1
(setq r1 10.0 xc 0.0 yc 0.0 d 0.0)
(setq r1 (/ (getreal "Enter the dia of finishing milling : ") 2))
(setq r0 32.0 x1 0.0 y1 0.0 x2 0.0 y2 0.0 z2 0.0 xp 0.0 yp 0.0 zp 0.0 )
(setq xp 121.205 yp 0 zp 110.)
(setq file01 (open "C://test.nc" "w"))
(princ "%\n" file01)
(princ "O0005\n" file01)
(princ "G0X121.205 Y0. Z110. A0. F600\n" file01)
(princ "S800 M03\n" file01)
(princ "M08 F70\n" file01)
(setq x2 121.205 y2 0.0 z2 75.0 ctype 1)
(princ "G1 " file01)
(pp1)
(setq y2 (- r0 r1) )
(princ " " file01)
(pp1)
(setq x2 90.)
(princ " " file01)
(pp1)
(setq y2 (* -1 y2) ctype 3 ppr (- r0 r1) )
(princ "G3 " file01)
(pp1)
(setq x2 121.205 ctype 1)
(princ "G1 " file01)
(pp1)
(setq radChg (/ 180.0 3.1415926) angChg (/ 3.1415926 180.0))
(setq cosCta (cos angChg) sinCta (sin angChg))
(setq iniCta 0.0 cta0 0.0 cta1 0.0 ctaTatal 0.0 iniAxial 0.0 wkAxial 0.0)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(setq xp 121.2051 yp -32 x2 149.9004 y2 -46.2611)
(setq ctype 2 ppr 36.0)
(scir) ;obtain xc, yc, iniCta, cta0, cta1,
(setq pillarDia (* 3.1415926 210) )
(setq i1 1 x1wk (- xp xc) y1wk (- yp yc))
(setq x2mem x2 y2mem y2 a2 0.0)
(while (< i1 ctaTatal)
(setq x2wk (+ (* x1wk cosCta) (* y1wk sinCta) ))
(setq y2wk (- (* y1wk cosCta) (* x1wk sinCta) ))
(setq ycc (+ yc (* (+ r0 ppr) (/ y2wk ppr))) )
(setq x2 (+ xc (* (+ r1 ppr) (/ x2wk ppr))) )
(setq y2 (+ yc (* (+ r1 ppr) (/ y2wk ppr))) )
(if (= i1 1)
(princ "G1 " file01)
(princ " " file01) )
(setq y2 (- y2 ycc) a2 (* 360 (/ ycc pillarDia)) )
(ppAxial)
(setq i1 (+ i1 1) x1wk x2wk y1wk y2wk) )
;;;;;;;;;the last endpoint of Arc
(setq ycc (+ yc (* (+ 32 ppr) (/ (- y2mem yc) ppr))) )
(setq x2 (+ xc (* (+ r1 ppr) (/ (- x2mem xc) ppr))) )
(setq y2 (- (+ yc (* (+ r1 ppr) (/ (- y2mem yc) ppr))) ycc) )
(setq a2 (* 360 (/ ycc pillarDia)) )
(ppAxial)
;;;;;;;;; ;for slant line
(setq mem y2 x2 254.4931 y2 -184.3234)
(setq d12 (sqrt (+ (* (- x2 x2mem)(- x2 x2mem)) (* (- y2 y2mem)(- y2 y2mem)) )))
(setq x3 (- x2 (* r1 (/ (- y2 y2mem) d12) )))
(setq y3 (+ y2 (* r0 (/ (- x2 x2mem) d12) )))
(setq x2 x3 y2 mem)
(setq a2 (* 360 (/ y3 pillarDia)))
(ppAxial)
;;;;;;;;;; milling a hole
(setq x2 254.4931 y2 -184.3234 ctype 3 ppr (- r0 r1))
(setq x3 (- x2 (* (- (+ r0 r0) r1) (/ (- y2 y2mem) d12) )))
(setq y2 (abs mem) x2 x3)
(princ "G3 " file01)
(pp1)
;;;;;;;;;;;;revering
;;;;;;;;;;;;obtain arc data
(setq x2 121.205 y2 r0 )
(setq xp 200.9143 yp -7.6142 ctype 3 ppr (+ 36. (* 2 r0)) )
(scir) ;obtain xc, yc, iniCta, cta0, cta1,
(setq x2mem x2 y2mem y2 a2 0.0)
;;;;;;;;; ;for revering slant line
(setq x2 (+ xc (* (- ppr r1) (/ (- xp xc) ppr))) )
(setq y2 (abs mem) a2 (* 360 (/ ycc pillarDia)))
(ppAxial)
;;;;;;;;;;milling revering arc
(setq x2 121.205 y2 r0 xp 200.9143 yp -7.6142)
(setq i1 1 x1wk (- xp xc) y1wk (- yp yc))
(while (< i1 ctaTatal )
(setq x2wk (- (* x1wk cosCta) (* y1wk sinCta) ))
(setq y2wk (+ (* y1wk cosCta) (* x1wk sinCta) ))
(setq ycc (+ yc (* (- ppr r0) (/ y2wk ppr))) )
(setq x2 (+ xc (* (- ppr r1) (/ x2wk ppr))) )
(setq y2 (* (- r0 r1) (/ y2wk ppr)) )
(if (= i1 1)
(princ "G1 " file01)
(princ " " file01) )
(setq a2 (* 360 (/ ycc pillarDia)) )
(ppAxial)
(setq i1 (+ i1 1) x1wk x2wk y1wk y2wk) )
;;;;;;;;;the last endpoint of Arc
(setq ycc (+ yc (* (- ppr r0) (/ (- y2mem yc) ppr))) )
(setq y2 (* (- r0 r1) (/ (- y2mem yc) ppr)) )
(setq x2 x2mem a2 (* 360 (/ ycc pillarDia)) )
(ppAxial)
(princ "G0 Z150.\n" file01) ;raising tool
(princ "M99\n" file01)
(princ "%\n" file01)
(close file01)
(setvar "osmode" 1)
)
;;;;;;;;;;;;;;;;;;;;;;;以下是子程式;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defun pp1()
(setq pxs(rtos x2 2 3) pys(rtos y2 2 3) pzs(rtos z2 2 3))
(setq pxl(strlen pxs) pyl(strlen pys) pzl(strlen pzs))
(setq pxn(- 7 pxl) pyn(- 7 pyl) pzn(- 7 pzl))
(if (> (abs (- xp x2)) 0.001)
(progn
(princ " X" file01) (princ pxs file01)
(if ( or (< (abs (- (fix x2) x2)) 0.001) (< (- 1 (abs (- (fix x2) x2))) 0.001) ) (princ "." file01) )
(repeat pxn (princ " " file01)) ))
(if (> (abs (- yp y2)) 0.001)
(progn
(princ " " file01) (princ "Y" file01) (princ pys file01)
(if ( or (< (abs (- (fix y2) y2)) 0.001) (< (- 1 (abs (- (fix y2) y2))) 0.001) ) (princ "." file01) )
(repeat pyn (princ " " file01)) ))
(if (> (abs (- zp z2)) 0.001)
(progn
(princ " " file01) (princ "Z" file01) (princ pzs file01)
(if ( or (< (abs (- (fix z2) z2)) 0.001) (< (- 1 (abs (- (fix z2) z2))) 0.001) ) (princ "." file01) )))
(if (> ctype 1 )
(progn
(float ppr)
(princ " " file01) (princ "R" file01) (princ ppr file01) ))
(princ "\n" file01)
(setq xp x2 yp y2 zp z2)
)
(defun ppAxial()
(setq pxs(rtos x2 2 3) pys(rtos y2 2 3) pzs(rtos a2 2 3))
(setq pxl(strlen pxs) pyl(strlen pys) pzl(strlen pzs))
(setq pxn(- 7 pxl) pyn(- 7 pyl) pzn(- 7 pzl))
(princ " X" file01) (princ pxs file01)
(if ( or (< (abs (- (fix x2) x2)) 0.001) (< (- 1 (abs (- (fix x2) x2))) 0.001) ) (princ "." file01) )
(repeat pxn (princ " " file01))
(princ " Y" file01) (princ pys file01)
(if ( or (< (abs (- (fix y2) y2)) 0.001) (< (- 1 (abs (- (fix y2) y2))) 0.001) ) (princ "." file01) )
(repeat pyn (princ " " file01))
(princ " A" file01) (princ pzs file01)
(if ( or (< (abs (- (fix a2) a2)) 0.001) (< (- 1 (abs (- (fix a2) a2))) 0.001) ) (princ "." file01) )
(princ "\n" file01)
)
(defun scir ()
(setq d (/ (distance (list xp yp) (list x2 y2)) 2))
(if (> d 0)
(progn
(setq k1 (sqrt (- (* ppr ppr) (* d d))) )
(if (< ctype 2.5)
(setq xc (+ (/ (+ xp x2) 2) (/ (* k1 (- y2 yp)) d 2))
yc (- (/ (+ yp y2) 2) (/ (* k1 (- x2 xp)) d 2)))
(setq xc (- (/ (+ xp x2) 2) (/ (* k1 (- y2 yp)) d 2))
yc (+ (/ (+ yp y2) 2) (/ (* k1 (- x2 xp)) d 2))) )))
(setq ctaTatal (* radChg (atan (/ d k1)) 2))
(setq x0 xp iniCta 0.0 cta0 0.0)
(if (< (abs (- xc xp )) 0.01)
(if (> yp yc)
(setq iniCta 90.0)
(setq iniCta 270.0) )
(if (< (abs (- yc yp )) 0.01)
(if (> xp xc)
(setq iniCta 0.0)
(setq iniCta 180.0) )
(progn
(setq cta0 (* radChg (atan (abs (/ (- yp yc) (- xp xc))))))
(if (> xp xc )
(if (> yp yc )
(setq iniCta cta0)
(setq iniCta (- 360.0 cta0) cta0 iniCta) )
(if (> yp yc )
(setq iniCta (- 180.0 cta0) cta0 iniCta)
(setq iniCta (+ 180.0 cta0) cta0 iniCta) )))))
)
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