CAD画齿轮的渐开线程序 (LSP)和渐开线齿轮关系

一、CAD中齿轮画法有下面一段渐开线程序：

;;;begain suprgear.lsp

;************************************************* ;SPURGEAR.LSP-a lisp program by Tony Hotchkiss

;-------------------------------------------------

;This routine draws a spur gear using joined

;polylines.It lets you use any pressure angle

;to design the gear teeth.

;************************************************* (defun err(s)

(if(=s"Function cancelled")

(princ"\nSPURGEAR-cancelled:")

(progn(princ"\nSPURGEAR-Error:")(princ s) (terpri))

);if

(resetting)

(princ"SYSTEM VARIABLES have been reset\n")

(princ)

);err

(defun setv(systvar newval)

(setq x(read(strcat systvar"1")))

(set x(getvar systvar))

(setvar systvar newval)

);setv

(defun setting()

(setq oerr*error*)

(setq*error*err)

(setv"CMDECHO"0)

(setv"BLIPMODE"0)

);end of setting

(defun rsetv(systvar)

(setq x(read(strcat systvar"1")))

(setvar systvar(eval x))

);restv

(defun resetting()

(rsetv"CMDECHO")

(rsetv"BLIPMODE")

(setq*error*oerr)

);end of resetting

(defun dxf(code ename)

(cdr(assoc code(entget ename)))

);dxf

(defun spurgear(/D N phi DO RO A B DR DB inv-plst p1 trimcode invent p0p curvent linent linent2ent2p2) (setq D(getreal"\nPitch diameter:")

N(getint"\nNumber of teeth:")

phi(getreal"\nPressure angle:")

phi(*(/phi180)pi);Pressure angle

DO(*D(+(/2.0N)1.0));Outside diameter

RO(/DO2.0);Outside radius

A(/D N);Addendum

B(*1.25A);Dedendum

DR(-D(*B2.0));Root diameter

DB(*D(cos phi));Base circle dia.

inv-plst(involute DB N phi);involute points

trimcode nil

);setq

(command"ZOOM"(list0(-B))

(list RO(/RO1.5))

);command

(setq invent(draw-inv inv-plst));Draw involute.

(setq p0(car inv-plst)

trimcode(ext-trim p0DR D);trim or extend

);setq;the involute.

(if(and trimcode(=trimcode0))

(progn;Joins the involute to the extension.

(setq p(list(/DR2.0)0)) (command"PEDIT"p"Y""J"invent"""X")

(setq curvent(entlast))

);progn

(setq curvent(entlast))

);if

(if(null trimcode)(setq curvent invent))

(setq linent(draw-top-line D DB N RO));top line. (command"COPY"linent"""0,0""0,0")

(setq linent2(entlast))

(setq ent2(mir-it curvent linent));mirror curve (command"PEDIT"curvent"J"linent ent2"""X") (segment DR N linent2);Finish the job!

(setq p1(list(-RO)(-RO)))

(setq p2(list RO RO))

(command"ZOOM"p1p2)

(prompt"\nConverting to POLYLINE,please wait...") (command"PEDIT"(entlast)"J""C"p1p2"""X") (prompt"\nAll done!")

);spurgear

(defun involute(DB N phi/numer denom frac theta2max thetamax theta-inc theta plist RB xval yval p)

(setq invfact3)

(setq numer(+N2.0)

denom(*N(cos phi))

frac(/numer denom)

theta2max(-(*frac frac)1)

thetamax(sqrt theta2max)

theta-inc(/thetamax(float invfact)) theta0

plist nil

RB(/DB2.0)

);setq

(repeat(1+invfact)

(setq xval(do-x RB theta)

yval(do-y RB theta)

p(list xval yval)

plist(append plist(list p))

);setq

(setq theta(+theta theta-inc))

);repeat

plist

);involute

(defun do-x(RB theta)

(*RB(+(cos theta)(*theta(sin theta)))) );do-x

(defun do-y(RB theta)

(*RB(-(sin theta)(*theta(cos theta)))) );do-y

(defun draw-inv(inv-plst/dirpt plist p) (command"PLINE"(nth0inv-plst))

(setq dirpt(polar(nth0inv-plst)01)) (command"A""D"dirpt)

(setq plist(cdr inv-plst))

(foreach p plist(command p))

(command"")

(entlast)

);draw-inv

(defun ext-trim(p0DR D/trimcode dist endr)

(if(>(car p0)(/DR2.0));Extends the involute (progn

(command"LINE"(list(/DR2.0)0)p0"")

(setq trimcode0)

);progn

);if

(if(<(car p0)(/DR2.0));Trims the involute (progn

(command"CIRCLE""0,0""D"DR);Root circle (setq dist(-(/D2.0)(car p0))) (command"ZOOM"p0

(polar p00.6dist))

(setq endr(entlast)) (command"TRIM"endr""p0"") (command"ZOOM""P")

(entdel endr)

(setq trimcode1)

);progn

);if

trimcode

);ext-trim

(defun draw-top-line(D DB N RO/theta-p xp yp alpha

beta tang angend inv-endpt lend)

(setq theta-p(sqrt(-(*(/D DB)(/D DB))1.0))

xp(do-x(/DB2.0)theta-p);This section

yp(do-y(/DB2.0)theta-p);sets up angles

alpha(atan yp xp);for drawing a

abeta(angle(list00)(last inv-plst))

beta(-abeta alpha);line across the

tang(/pi N);top of a tooth

angend(-(+alpha tang)beta)

inv-endpt(last inv-plst);This also creates

lend(polar(list00)angend RO);the tooth

);setq;thickness.

(command"LINE"inv-endpt lend"");Draws the line (redraw)

(entlast)

);draw-top-line

(defun mir-it(cvent linent/pt)

(setq pt(dxf11linent)) (command"MIRROR"cvent"""MID"pt"0,0""") (entlast)

);mir-it

(defun segment(DR N en/p1p2ang dist midp p0pang pang2p p3ent3entl1entl2en1en2)

(setq p1(dxf10en)

p2(dxf11en)

ang(angle p1p2)

dist(/(distance p1p2)2.0)

midp(polar p1ang dist)

p0(list00)

pang(angle p0midp)

pang2(/pi N)

p(polar p0pang(/DR2.0))

p1(polar p0(-pang pang2)(/DR2.0))

p2(polar p0(+pang pang2)(/DR2.0))

p3(polar p0(+pang pang2pang2)(/DR2.0)) ent3(entlast);This is the tooth p-line

);setq

(command"ZOOM""W"p3p1) (command"CIRCLE""0,0""D"DR);Root circle (command"TRIM"ent3""p"");Trim the root circle (command"ZOOM""P") (command"LINE"p0p1"")

(setq entl1(entlast))

(command"LINE"p0p2"")

(setq entl2(entlast)) (command"TRIM"entl1entl2""p3"")

(entdel entl1)

(entdel entl2)

(entdel en)

(command"ZOOM""W"p3p1) (command"PEDIT"p1"Y""X")

(setq en1(entlast))

(command"PEDIT"p2"Y""X")

(setq en2(entlast)) (command"PEDIT"en1"J"midp en2"""X") (command"ZOOM""P") (command"ARRAY"p1"""P""0,0"N"360""Y") );segment

(defun c:sg()

(setting)

(spurgear)

(resetting)

(princ)

);c:sg

(prompt"\n**SPURGEAR.LSP Loaded!")

(prompt"\n Enter'SG'to start")

;;;end suprgear.lsp

将上述代码保存成lsp文档格式，最好存入cad目录下的Support文件夹下。

打开CAD图形后点击“工具”菜单→AutoLISP→加载→找到自己所存的".LSP"文件位置点“加载”、点“关闭”。

在CAD环境下“命令”状态栏里输入“sg”命令后就可以调用。

二、渐开线关系式（开始建模就要加入此关系式）

m=(模数)

za=(齿数)

alpha=20压力角

db=0.5*m*za*cos(20)基园（m<1的模数需手动输入）

da=m*(za+2*1)齿顶园

df=m*(za-2*1.25)分度园

渐开线(方程式）卡迪尔坐标

t0=t*40

x0=(cos(t0)+t0*pi/180*(sin(t0)))*db

y0=(sin(t0)-t0*pi/180*(cos(t0)))*db

theta=-(tan(alpha)-alpha*pi/180)*180/pi-90/za

x=x0*cos(theta)-y0*sin(theta)

y=x0*sin(theta)+y0*cos(theta)

z=0