齒輪范成程序MATLAB代碼

1、本人經過一個月的努力,寫出了以下齒輪展成程序,是matlab格式的。只要按照附圖的標注定義出滾刀刀齒的形狀,指定程序模擬的精度,就可以模擬出滾刀滾切齒輪的圖形.下圖為程序中定義刀具的尺寸示意圖以下為源程序%shape of hob%input areacls;alpha=deg2rad(21); %壓力角alphaf=deg2rad(31); %齒頂倒角壓力角W0=1.85; %節(jié)圓半齒寬H=6; %全齒高ha0=3; %齒頂高hf0=1.44; %齒根倒角起點高度H1=0.064; %觸角厚度hc=1.3; %觸角高度ht=0.65; %觸角凸部的高度rc=0.6; %齒頂圓角半徑R=30;

2、 %工件分度圓半徑P=7.54; %刀具齒距N=2; %刀齒數amount=10; %每段線上取點的個數step=100; %計算步數range=-pi*0.15,pi*0.15;%計算范圍%location of key-point yr=ha0-rc; %齒頂圓角圓心xr=W0+(H1-rc)/cos(alpha)-yr*tan(alpha);point=zeros(6,2);point(1,2)=ha0;point(1,1)=xr;point(2,2)=ha0-rc*(1-sin(alpha);point(2,1)=xr+rc*cos(alpha);point(3,2)=ha0-ht;p

3、oint(3,1)=(W0+H1/cos(alpha)-(ha0-ht)./cot(alpha);point(4,2)=ha0-hc;point(4,1)=W0-point(4,2)*tan(alpha);point(5,2)=-hf0;point(5,1)=W0-tan(alpha)*point(5,2);point(6,2)=ha0-H;point(6,1)=point(5,1)-tan(alphaf)*(point(6,2)-point(5,2);%-直線部分-theta=linspace(range(1),range(2),step);w11=linspace(point(4,1),p

4、oint(5,1),amount);h11=linspace(point(4,2),point(5,2),amount);w12=repmat(w11,1,step);h12=repmat(h11,1,step);theta2=repmat(theta,amount,1);x12=(h12-R).*sin(theta2)+(R.*theta2-w12).*cos(theta2);y12=(R.*theta2-w12).*sin(theta2)+(R-h12).*cos(theta2);theta13=(w11-h11/tan(alpha)/R;x13=sin(theta13).*(h11-R)

5、+cos(theta13).*(R.*theta13-w11);y13=sin(theta13).*(R*theta13-w11)+cos(theta13).*(R-h11);%-圓角部分-gama=linspace(pi/2,alpha,amount);w21=(xr+rc.*cos(gama);h21=(yr+rc.*sin(gama);w22=repmat(w21,1,step);h22=repmat(h21,1,step);x22=(h22-R).*sin(theta2)+(R.*theta2-w22).*cos(theta2);y22=(R.*theta2-w22).*sin(the

6、ta2)+(R-h22).*cos(theta2);theta23=(xr-yr.*cot(gama)/R);x23=sin(theta23).*(h21-R)+cos(theta23).*(R.*theta23-w21);y23=sin(theta23).*(R*theta23-w21)+cos(theta23).*(R-h21);rmin=R;for i=1:(length(x23)-2)XX,YY,RR=threepointcircle(x23(i),y23(i),x23(i+1),y23(i+1),x23(i+2),y23(i+2);if RRrmin rmin=RR;endend%-

7、凸角部分-w31=linspace(point(2,1),point(3,1),amount);h31=linspace(point(2,2),point(3,2),amount);w32=repmat(w31,1,step);h32=repmat(h31,1,step);theta2=repmat(theta,amount,1);x32=(h32-R).*sin(theta2)+(R.*theta2-w32).*cos(theta2);y32=(R.*theta2-w32).*sin(theta2)+(R-h32).*cos(theta2);theta33=(w31-h31/tan(alph

8、a)/R;x33=sin(theta33).*(h31-R)+cos(theta33).*(R.*theta33-w31);y33=sin(theta33).*(R*theta33-w31)+cos(theta33).*(R-h31);%-連接部分-alpha2=atan(point(4,1)-point(3,1)/(point(3,2)-point(4,2);w41=linspace(point(3,1),point(4,1),amount);h41=linspace(point(3,2),point(4,2),amount);w42=repmat(w41,1,step);h42=repma

9、t(h41,1,step);theta2=repmat(theta,amount,1);x42=(h42-R).*sin(theta2)+(R.*theta2-w42).*cos(theta2);y42=(R.*theta2-w42).*sin(theta2)+(R-h42).*cos(theta2);theta43=(w41-h41/tan(alpha2)/R;x43=sin(theta43).*(h41-R)+cos(theta43).*(R.*theta43-w41);y43=sin(theta43).*(R*theta43-w41)+cos(theta43).*(R-h41);%-倒角

10、部分-alpha3=atan(point(6,1)-point(5,1)/(point(5,2)-point(6,2);w51=linspace(point(5,1),point(6,1),amount);h51=linspace(point(5,2),point(6,2),amount);w52=repmat(w51,1,step);h52=repmat(h51,1,step);theta2=repmat(theta,amount,1);x52=(h52-R).*sin(theta2)+(R.*theta2-w52).*cos(theta2);y52=(R.*theta2-w52).*sin

11、(theta2)+(R-h52).*cos(theta2);theta53=(w51-h51/tan(alpha3)/R;x53=sin(theta53).*(h51-R)+cos(theta53).*(R.*theta53-w51);y53=sin(theta53).*(R*theta53-w51)+cos(theta53).*(R-h51);%-全刀齒-w6=w21;w31;w41;w11;w51;h6=h21;h31;h41;h11;h51;w6=flipud(w6);h6=flipud(h6);w6=w6;-flipud(w6);h6=h6;flipud(h6);w62=w6;h62=

12、h6;for i=2:N w62=w6+(i-1)*P;w62; h62=h6;h62;endtheta6=repmat(theta,5*amount*2*N,1);w62=repmat(w62,1,step);h62=repmat(h62,1,step);x62=(h62-R).*sin(theta6)+(R.*theta6-w62).*cos(theta6);y62=(R.*theta6-w62).*sin(theta6)+(R-h62).*cos(theta6);%-figure;plot(x12,y12);hold on;grid on;axis equal;plot(x22,y22)

13、;plot(x32,y32);plot(x42,y42);plot(x52,y52);figure;plot(x12,y12);hold on;grid on;axis equal;plot(x22,y22);plot(x32,y32);plot(x42,y42);plot(x52,y52);figure;plot(x13,y13);hold on;grid on;axis equal;plot(x23,y23,o);plot(x33,y33,*);plot(x43,y43,.);plot(x53,y53,+);figureplot(x12,y12);hold on;grid on;axis

14、equal;plot(x22,y22);plot(x32,y32);plot(x42,y42);plot(x52,y52);plot(x13,y13,*);plot(x23,y23,*);plot(x33,y33,*);plot(x43,y43,*);plot(x53,y53,*);figureplot(w62,h62);hold on;grid on;axis equal;figureplot(x62,y62);hold on;grid on;axis equal;以下為角度轉化為弧度的子程序function rad=deg2rad(deg)rad=deg./180.*pi;以下為計算最小圓弧半徑的子程序function x,y,r=threepointcircle(x1,y1,x2,y2,x3,y3)k12=(x2-x1)/(y1-y2);k23=(x3-x2)/(y2-y3);x=(y2+y3-y1-y2)/2+k12*(x1+x2)/2-k23*(x2+x3)/2)/(k12-k