四軸連動(X軸+Y軸+ Z軸+A軸)
想要在圓筒上的圓溝周邊稜線加以倒角，以去除毛邊，這就需四軸連動(X軸+Y軸+ Z軸+A軸)，才能達成的加工，下圖的綠色線條是球銑刀倒角時的刀具路徑，由於CNC程式是控制球銑刀的中心最低點，所以倒角的刀具路徑看起來是在圓溝周邊稜線的上方內側。
四軸連動的倒角刀具路徑的計算
如前所敘，圓筒上的這個圓溝最初是以直徑64mm銑刀所銑出，待這個圓溝銑好之後，要用直徑較小的球銑刀(以直徑12mm為例)，銑出這個圓溝周邊的稜線的倒角，加工要訣也是要先找出圓溝的每一處稜線是以直徑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軸及Z軸的方法，將直徑較小的球銑刀的刀球圓周邊移到該位置，並以過切的手法來達到倒角的目的，如下圖所示，至於A軸則如同前述之二軸連動那樣旋轉，即可用直徑較小的球銑刀銑出圓溝周邊的稜線的倒角。
球銑刀倒角的刀具路徑側視圖
球銑刀倒角的刀具路徑端視圖
四軸連動Autolisp程式
(defun c:kk() ;;chamfering by variable diameter of r1;; including the other groove
(setq r0 32.0 r1 10.0 xc 0.0 yc 0.0 d 0.0)
(setq r1 (/ (getreal "Enter the dia of the ball-endmilling: ") 2))
(setq chm (getreal "Enter the size of chamfer: "))
(setq delr (/ r1 1.414) xp 99.0 yp 99.0 zp 99.0)
(setq file01 (open "C://test.nc" "w"))
(princ "%\n" file01)
(princ "O0005\n" file01)
(princ "G0X121.205 Y0. Z120. A0. F600\n" file01)
(princ "S800 M03\n" file01)
(setq r1 (- r1 (/ chm 1.414)))
(setq x2 121.205 y2 (- r0 r1) z2 (+ 105.0 r1) ctype 1)
(princ "G1 " file01)
(pp1)
(princ " F70\n" file01)
(setq x2Pre x2 y2Pre r0 z2Pre (sqrt (- (* 105 105) (* y2Pre y2Pre))) )
(setq y2 (- y2Pre delr) z2 (+ z2Pre delr))
(princ " " file01)
(pp1)
(setq x2 90.0 )
(princ "G1 " file01)
(pp1)
;;;;;;;;;setting variables////////////////////////////////
(setq radChg (/ 180.0 3.1415926) angChg (/ 3.1415926 180.0))
(setq cosCta (cos (* 2 angChg)) sinCta (sin (* 2 angChg)))
(setq iniCta 0.0 cta0 0.0 cta1 0.0 ctaTatal 0.0 iniAxial 0.0 wkAxial 0.0)
;;;;;;;;;chamfering the half circle ;;;;;;;;;;;;;;;;;;;
(setq i1 1 xp 90.0 yp r0 x2 90.0 y2 (* -1 r0) ppr r0)
(scir) ;obtain xc, yc, iniCta, cta0, cta1,
(setq x2mem x2 y2mem y2 a2 0.0 x1wk (- xp xc) y1wk (- yp yc) )
(while (< i1 91)
(setq x2wk (- (* x1wk cosCta) (* y1wk sinCta) ))
(setq y2wk (+ (* y1wk cosCta) (* x1wk sinCta) ))
(setq y2Pre (+ yc y2wk))
(setq x2Pre (+ xc x2wk))
(setq z2Pre (sqrt (- (* 105 105) (* y2Pre y2Pre))))
(setq x2 (- x2Pre (* delr (/ (- x2Pre xc) ppr))))
(setq y2 (- y2Pre (* delr (/ (- y2Pre yc) ppr))))
(setq z2 (+ z2Pre delr))
(princ " " file01)
(pp1)
(setq i1 (+ i1 1) x1wk x2wk y1wk y2wk xp x2 yp y2 zp z2) )
;;;;;;;;;chamfering a horizontal line;;;;;;;;;;;;;;;;;;;
(setq x2 121.205 )
(princ " " file01)
(pp1)
;;;;;;;;;;;chamfering arc 36 ;;;;;;;;;;;;;;;;;;;
(setq x2mem 121.205 y2mem y2 z2mem z2 xp 121.2051 yp -32.0 zp z2 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 x2mem x2 y2mem y2 a2 0.0 )
(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 (* (+ r0 ppr) (/ y2wk ppr))) )
(setq xcc (+ xc (* (+ r0 ppr) (/ x2wk ppr))) )
(setq a2 (* 360 (/ ycc pillarDia)))
(setq y2Pre (- 0 (* r0 (/ y2wk ppr))))
(setq x2pre (- xcc (* r0 (/ x2wk ppr))))
(setq z2Pre (sqrt (- (* 105 105) (* y2Pre y2Pre))))
(setq x2 (- x2Pre (* delr (/ (- x2Pre xcc) r0))))
(setq y2 (- y2Pre (* delr (/ (- y2Pre 0) r0))))
(setq z2 (+ z2Pre delr))
(princ " " file01)
(ppAxial4)
(setq i1 (+ i1 2) x1wk x2wk y1wk y2wk xxmem x2 yymem yy zzmem zz) )
;;;;;;;;;chamfering the last endpoint of Arc 32;;;;;;;;;;;;;;;;;;;
(setq ycc (+ yc (* (+ r0 ppr) (/ (- -46.2611 yc) ppr))) )
(setq xcc (+ xc (* (+ r0 ppr) (/ (- 149.9004 xc) ppr))) )
(setq a2 (* 360 (/ ycc pillarDia)))
(setq y2Pre (- 0 (* r0 (/ (- -46.2611 yc) ppr))))
(setq x2pre (- xcc (* r0 (/ (- 149.9004 xc) ppr))))
(setq z2Pre (sqrt (- (* 105 105) (* y2Pre y2Pre))))
(setq x2 (- x2Pre (* delr (/ (- x2Pre xcc) r0))))
(setq y2 (- y2Pre (* delr (/ (- y2Pre 0) r0))))
(setq z2 (+ z2Pre delr))
(princ " " file01)
(ppAxial4)
;;;;;;;;;chamfering slant line ;;;;;;;;;;;;;;;;;;;
(setq x2mem x2 y2mem y2)
(setq xxmem x2 yymem yy zzmem zz )
(setq d12 (sqrt (+ (* (- 254.4931 149.9004)(- 254.4931 149.9004)) (* (- -184.3234 -46.2611)(- -184.3234 -46.2611)) )))
(setq i1 2 xdel (/ (- 254.4931 149.9004) d12) ydel (/ (- -184.3234 -46.2611) d12) )
(setq x2 254.4931)
(setq y2 -184.3234)
(setq xcc (- x2 (* r0 ydel)))
(setq ycc (+ y2 (* r0 xdel)))
(setq a2 (* 360 (/ ycc pillarDia)))
(setq x2pre (+ xcc (* ydel r0)))
(setq y2Pre (- 0 (* xdel r0)))
(setq z2Pre (sqrt (- (* 105 105) (* y2Pre y2Pre))))
(setq x2 (- x2Pre (* delr (/ (- x2Pre xcc) r0))))
(setq y2 (- y2Pre (* delr (/ (- y2Pre 0) r0))))
(setq z2 (+ z2Pre delr))
(princ " " file01)
(ppAxial4)
;;;;;;;;;;chamfering the lower circle;;;;;;;;;;;;;;;;;;;
(setq x2mem x2 y2mem y2Pre xp x2Pre yp y2Pre ctype 3 ppr r0)
(setq x2 (- x2Pre (* ydel 2 r0)))
(setq y2 (abs y2Pre))
(scir) ;obtain xc, yc, iniCta, cta0, cta1,
(setq i1 2 x1wk (- xp xc) y1wk (- yp yc) ctype 1)
(while (< i1 181)
(setq x2wk (- (* x1wk cosCta) (* y1wk sinCta) ))
(setq y2wk (+ (* y1wk cosCta) (* x1wk sinCta) ))
(setq x2Pre (+ xc x2wk) )
(setq y2Pre (+ yc y2wk) )
(setq z2Pre (sqrt (- (* 105 105) (* y2Pre y2Pre)) ))
(setq x2 (- x2Pre (* delr (/ (- x2Pre xc) r0))))
(setq y2 (- y2Pre (* delr (/ (- y2Pre 0) r0))))
(setq z2 (+ z2Pre delr))
(princ " " file01)
(pp1)
(setq i1 (+ i1 2) x1wk x2wk y1wk y2wk xxmem x2Pre yymem yy zzmem zz) )
;;;;;;;;;;;;revering;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;chamfering the revering slant line ;;;;;;;;;;;;;;;;;;;
(setq d12 (sqrt (+ (* (- 254.4931 149.9004)(- 254.4931 149.9004)) (* (- -184.3234 -46.2611)(- -184.3234 -46.2611)) )))
(setq i1 2 xdel (/ (- 149.9004 254.4931) d12) ydel (/ (- -46.2611 -184.3234) d12) )
(setq x2 299.8698)
(setq y2 -110.2882)
(setq xcc (- x2 (* r0 ydel)))
(setq ycc (+ y2 (* r0 xdel)))
(setq a2 (* 360 (/ ycc pillarDia)) )
(setq x2Pre (+ xcc (* r0 ydel)))
(setq y2Pre (- 0 (* r0 xdel)))
(setq z2Pre (sqrt (- (* 105 105) (* y2Pre y2Pre)) ))
(setq x2 (- x2Pre (* delr (/ (- x2Pre xcc) r0))))
(setq y2 (- y2Pre (* delr (/ (- y2Pre 0) r0))))
(setq z2 (+ z2Pre delr))
(princ " " file01)
(ppAxial4)
;;;;;;;;;;;;obtain the data of the revering arc 100
(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)
;;;;;;;;;;chamfering the revering arc 100;;;;;;;;;;;;;;;;;;;
(setq x2 121.205 y2 r0 xp 200.9143 yp -7.6142)
(setq i1 1 x1wk (- xp xc) y1wk (- yp yc))
(setq cosCta (cos (* 1 angChg)) sinCta (sin (* 1 angChg)))
(while (< i1 ctaTatal)
(setq x2wk (- (* x1wk cosCta) (* y1wk sinCta) ))
(setq y2wk (+ (* y1wk cosCta) (* x1wk sinCta) ))
(setq xcc (+ xc (* (- ppr r0) (/ x2wk ppr))) )
(setq ycc (+ yc (* (- ppr r0) (/ y2wk ppr))) )
(setq a2 (* 360 (/ ycc pillarDia)))
(setq y2Pre (+ 0 (* r0 (/ y2wk ppr))))
(setq x2pre (+ xcc (* r0 (/ x2wk ppr))))
(setq z2Pre (sqrt (- (* 105 105) (* y2Pre y2Pre))))
(setq x2 (- x2Pre (* delr (/ (- x2Pre xcc) r0))))
(setq y2 (- y2Pre (* delr (/ (- y2Pre 0) r0))))
(setq z2 (+ z2Pre delr))
(princ " " file01)
(ppAxial4)
(setq i1 (+ i1 1) x1wk x2wk y1wk y2wk xxmem x2 yymem yy zzmem zz) )
(setq xcc 121.205)
(setq ycc 0)
(setq a2 (* 360 (/ ycc pillarDia)))
(setq y2Pre r0)
(setq x2pre 121.205)
(setq z2Pre (sqrt (- (* 105 105) (* y2Pre y2Pre))))
(setq x2 (- x2Pre (* delr (/ (- x2Pre xcc) r0))))
(setq y2 (- y2Pre (* delr (/ (- y2Pre 0) r0))))
(setq z2 (+ z2Pre delr))
(princ " " file01)
(ppAxial4)
(princ "G0 Z150.\n" file01) ;raising tool
(princ "M99\n" file01)
(princ "%\n" file01)
(close file01)
(setvar "osmode" 1)
)
;;;;;;;;;;;;;;;;;;;;;;;以下是AutoLisp之子程式;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(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 ppAxial4()
(setq pxs(rtos x2 2 3) pys(rtos y2 2 3) pzs(rtos z2 2 3) pas(rtos a2 2 3))
(setq pxl(strlen pxs) pyl(strlen pys) pzl(strlen pzs) pal(strlen pas))
(setq pxn(- 7 pxl) pyn(- 7 pyl) pzn(- 7 pzl) pan(- 7 pal))
(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 " 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 " Z" file01) (princ pzs file01)
(if ( or (< (abs (- (fix z2) z2)) 0.001) (< (- 1 (abs (- (fix z2) z2))) 0.001) ) (princ "." file01) )
(repeat pyn (princ " " file01))
(princ " A" file01) (princ pas file01)
(if ( or (< (abs (- (fix a2) a2)) 0.001) (< (- 1 (abs (- (fix a2) a2))) 0.001) ) (princ "." file01) )
(princ "\n" file01)
(setq yp y2)
)
(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))) )))
(if(< k1 0.001)
(setq ctaTatal 90.0 )
(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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