凸轮连杆程序

凸轮连杆程序%-- 11-8-14 下午3:20 --%disp ' ******** 偏置移动从动件盘形凸轮设计********'disp '已知条件:'disp ' 凸轮作逆时针方向转动,从动件偏置在凸轮轴心的右边'disp ' 从动件在推程作指定规律运动,在回程作指定规律运动'rb = 90;rt = 30;e = 0;h = 110;ft = 100;fs = 90;fh = 100;alp = 45;L2=447;L3=134;L4=508;L5=92;L6=100;L7=150;zshan=17;z1=22;z2=37; z3=19;z4=80;r=180;xa=-90;ya=500;xe=0;ye=-150;guding=2*pi/3fprintf (1,' 基圆半径rb = %3.4f mm \n',rb) fprintf (1,' 滚子半径rt = %3.4f mm \n',rt) fprintf (1,' 推杆偏距 e = %3.4f mm \n',e) fprintf (1,' 推程升程h = %3.4f mm \n',h) fprintf (1,' 推程运动角ft = %3.4f 度\n',ft) fprintf (1,' 远休止角fs = %3.4f 度\n',fs) fprintf (1,' 回程运动角fh = %3.4f 度\n',fh)fprintf (1,' 推程许用压力角alp = %3.4f 度\n',alp) fprintf (1,' 杆长L2 = %3.4f mm \n',L2) fprintf (1,' 杆长L3 = %3.4f mm \n',L3) fprintf (1,' 杆长L4 = %3.4f mm \n',L4) fprintf (1,' 杆长L5 = %3.4f mm \n',L5) fprintf (1,' 杆长L6 = %3.4f mm \n',L6) fprintf (1,' 杆长L7 = %3.4f mm \n',L7) fprintf (1,' 齿数zshan = %3.4f mm \n',zshan)fprintf (1,' 齿数z1 = %3.4f mm \n',z1) fprintf (1,' 齿数z2 = %3.4f mm \n',z2) fprintf (1,' 齿数z3 = %3.4f mm \n',z3) fprintf (1,' 齿数z4 = %3.4f mm \n',z4) fprintf (1,' 扇齿轮半径r = %3.4f mm \n',r)fprintf (1,' a点横坐标xa = %3.4f mm \n',xa) fprintf (1,' a点纵坐标ya = %3.4f mm \n',ya) fprintf (1,' e点横坐标xe = %3.4f mm \n',xe) fprintf (1,' e点纵坐标ye = %3.4f mm \n',ye) fprintf (1,' gudingjiao guding = %3.4f mm \n',guding)hd= pi / 180;du = 180 / pi;se=sqrt( rb^2 - e^2 );d1 = ft + fs;d2 = ft + fs + fh;disp ' 'disp '计算过程和输出结果:'disp ' 1- 计算凸轮理论轮廓的压力角和曲率半径'disp ' 1-1 推程's = zeros(ft);ds = zeros(ft);d2s = zeros(ft);at = zeros(ft);atd = zeros(ft);pt = zeros(ft);jiao6=zeros(ft);jiaoD=zeros(ft);xc=zeros(ft);yc=zeros(ft);xb=zeros(ft);yb=z eros(ft);xd=zeros(ft);yd=zeros(ft);for f=1: 17 * pi / 18if 1<f<7 * pi / 18s(f)=0;s = s(f);ds(f)=0;ds = ds(f);d2s(f)=0;d2s = d2s(f);elseif 7 * pi / 18 < f < 33 * pi / 72s(f)=2 * h *((f - 7 * pi / 18)/ (5*pi/9)-sin(4*pi*(f-7*pi/18)/(5*pi/9)))/(pi+2);s = s(f);ds(f)=2 * h *(1-cos(4*pi*(f-7*pi/18)/(5*pi/9)))/(pi+2)*(5*pi/9);ds = ds(f);d2s(f)=8*pi * h*sin(4*pi(f-7*pi/18)/(5*pi/9)) /(pi+2)/(5*pi/9)^ 2;d2s = d2s(f);d2s = d2s(f);elseif 33 * pi / 72 <f< 43 * pi / 72% s(f)=2 * h *(4*pi*(f-7*pi/18)^2/(5*pi/9)^2);s = s(f);s(f)=2 * h *((pi^2 - 8)/16/pi-(pi-2)*(f-7*pi/18)/(5*pi/9)+4*pi*(f-7*pi/18)^2/(5*pi/9)^2);s = s(f);% ds(f)= h/(pi+2)/(5*pi/9);ds = ds(f);% d2s(f)=8*pi * h/(5*pi/9)^ 2;d2s = d2s(f);d2s = d2s(f)ds(f)= h *(2-pi+8*pi*(f-7*pi/18)/(5*pi/9))/(pi+2)/(5*pi/9);ds = ds(f);d2s(f)=8*pi * h/(pi+2)/(5*pi/9)^ 2;d2s = d2s(f);d2s = d2s(f)elseif 43 * pi / 72 <f< 53 * pi / 72s(f)=2 * h *((pi+1)*(f-7*pi/18)/(5*pi/9)-pi/4+sin(4*pi*(f-7*pi/18)/(5*pi/9))/4/pi)/( pi+2);s = s(f);ds(f)= 2* h *(pi+1+cos(4*pi*(f-7*pi/18)/(5*pi/9)))/(pi+2)/(5*pi/9);ds = ds(f);d2s(f)=-8*pi * h*sin(4*pi*(f-7*pi/18)/(5*pi/9))/(pi+2)/(5*pi/9)^2;d2s =d2s(f);elseif 53 * pi / 72 <f< 63 * pi / 72s(f)= h *((8-33*pi^2)/16/pi+(7*pi+2)*(f-7*pi/18)/(5*pi/9)-4*pi*(f-7*pi/18)^2/(5 *pi/9)^2)/(pi+2);s = s(f);ds(f)= h *(7*pi+2-8*pi*(f-7*pi/18)/(5*pi/9))/(pi+2)/(5*pi/9);ds = ds(f);d2s(f)=-8*pi * h/(pi+2)/(5*pi/9)^2;d2s = d2s(f);elseif 63 * pi / 72 <f< 17 * pi / 18s(f)= 2*h *(pi/2+(f-7*pi/18)/(5*pi/9)-sin(4*pi*(f-7*pi/18)/(5*pi/9))/4/pi)/(pi+2);s = s(f);ds(f)= 2*h *(1-cos(4*pi*(f-7*pi/18)/(5*pi/9)))/(pi+2)/(5*pi/9);ds = ds(f); d2s(f)=-8*pi * h*sin(4*pi*(f-7*pi/18)/(5*pi/9))/(pi+2)/(5*pi/9)^2;d2s = d2s(f);% 求压力角endjiao6=s/r*(z2/z3*(z1/zshan))xd=L6*cos(0+s/r*(z2/z3*(z1/zshan)))+xeyd=L6*sin(0+s/r*(z2/z3*(z1/zshan)))+yejiaoD=acos((L5^2+xd^2+yd^2-L3^2)/2*L5*(xd^2+yd^2)^(1/2))+acos((L6^ 2+xd^2+yd^2-L7^2)/2*L6*(xd^2+yd^2)^(1/2))+0+s/r*(z2/z3*(z1/zshan)) xc=L5*cos(jiaoD)+xdyc=L5*sin(jiaoD)+yda=((xa-xc)^2+(ya-yc)^2)^(1/2)at(f)=atan((a*cos(acos((L2^2+a^2-rb^2)/(2*a*L2))+s)-L2*(1-ds))/(a*sin(acos((L 2^2+a^2-rb^2)/(2*a*L2))+s)));atd(f) = at(f) * du;p1=(a^2+L2^2*(1-ds)^2-2*a*L2*(1-ds)*cos(acos((L2^2+a^2-rb^2)/(2*a* L2))+s))^1.5;p2=a^2+L2^2*(1-ds)^3-L2*a*(d2s*sin(acos((L2^2+a^2-rb^2)/(2*a*L2))+s)+(1 -ds)*(2-ds)*cos(acos((L2^2+a^2-rb^2)/(2*a*L2))-s));pt(f)= p1 /p2;p = pt(f);endatm = 0;% ftm=0for f=1: 17 * pi / 18if atd(f) > atmatm = atd(f);endendfprintf (1,' 最大压力角atm = %3.4f 度\n',atm)for f=1: 17 * pi / 18if abs(atd(f) - atm) < 0.1ftm = f;breakendendfprintf (1,' 对应的位置角ftm = %3.4f 度\n',ftm)if atm > alpfprintf (1,' * 凸轮推程压力角超过许用值,需要增大基圆!\n')endptn = rb + h;for f=1: 17 * pi / 18if pt(f) < ptnptn = pt(f);endendfprintf (1,' 轮廓最小曲率半径ptn = %3.4f mm\n',ptn)for f=1: 17 * pi / 18if abs(pt(f) - ptn) < 0.1ftn = f;breakendendfprintf (1,' 对应的位置角ftn = %3.4f 度\n',ftn)if ptn < rt+ 5fprintf (1,' * 凸轮推程轮廓曲率半径小于许用值,需要增大基圆或减小滚子!\n')enddisp ' 1-2 回程(余弦加速度运动)'s = zeros(fh);ds = zeros(fh);d2s = zeros(fh);ah = zeros(fh);ahd = zeros(fh);ph = zeros(fh);for f = 17 * pi / 18 : 2 * piif 17*pi/18<f<73*pi/72s(f)= 2*h *(pi/2+(27*pi/18-f)/(5*pi/9)-sin(4*pi*(27*pi/18-f)/(5*pi/9))/4/pi)/(pi+2) ;s = s(f);i / 18 : 2 * piif abs(ph(f) - phn) < 0.1fhn = f;breakendendfprintf (1,' 对应的位置角fhn = %3.4f 度\n',fhn)if phn < rt + 5fprintf (1,' * 凸轮回程轮廓曲率半径小于许用值,需要增大基圆或减小滚子!\n')enddisp ' 2- 计算凸轮理论廓线与实际廓线的直角坐标'n = 360;s = zeros(n);ds = zeros(n);r = zeros(n);rp = zeros(n);x = zeros(n);y = zeros(n);dx = zeros(n);dy = zeros(n);xx = zeros(n);yy = zeros(n);xp = zeros(n);yp = zeros(n);xxp = zeros(n);yyp = zeros(n);for f = 1 : nif 1<f<7 * pi / 18s(f)=0;s = s(f);ds(f)=0;ds = ds(f);d2s(f)=0;d2s = d2s(f);elseif 7 * pi / 18 < f < 33 * pi / 72s(f)=2 * h *((f - 7 * pi / 18)/ (5*pi/9)-sin(4*pi*(f-7*pi/18)/(5*pi/9)))/(pi+2);s = s(f);ds(f)=2 * h *(1-cos(4*pi*(f-7*pi/18)/(5*pi/9)))/(pi+2)*(5*pi/9);ds = ds(f); d2s(f)=8*pi * h*sin(4*pi(f-7*pi/18)/(5*pi/9)) /(pi+2)/(5*pi/9)^ 2;d2s = d2s(f);d2s = d2s(f);elseif 33 * pi / 72 <f< 43 * pi / 72s(f)=2 * h *((pi^2 - 8)/16/pi-(pi-2)(f-7*pi/18)/ (5*pi/9)+4*pi*(f-7*pi/18)^2/(5*pi/9)^2);s = s(f);ds(f)= h *(2-pi+8*pi*(f-7*pi/18)/(5*pi/9))/(pi+2)/(5*pi/9);ds = ds(f);d2s(f)=8*pi * h/(pi+2)/(5*pi/9)^ 2;d2s = d2s(f);d2s = d2s(f)elseif 43 * pi / 72 <f< 53 * pi / 72s(f)=2 * h *((pi+1)*(f-7*pi/18)/(5*pi/9)-pi/4+sin(4*pi*(f-7*pi/18)/(5*pi/9))/4/pi)/( pi+2);s = s(f);ds(f)= 2* h *(pi+1+cos(4*pi*(f-7*pi/18)/(5*pi/9)))/(pi+2)/(5*pi/9);ds = ds(f);d2s(f)=-8*pi * h*sin(4*pi*(f-7*pi/18)/(5*pi/9))/(pi+2)/(5*pi/9)^2;d2s = d2s(f);elseif 53 * pi / 72 <f< 63 * pi / 72s(f)= h *((8-33*pi^2)/16/pi+(7*pi+2)*(f-7*pi/18)/(5*pi/9)-4*pi*(f-7*pi/18)^2/(5 *pi/9)^2)/(pi+2);s = s(f);ds(f)= h *(7*pi+2-8*pi*(f-7*pi/18)/(5*pi/9))/(pi+2)/(5*pi/9);ds = ds(f);d2s(f)=-8*pi * h/(pi+2)/(5*pi/9)^2;d2s = d2s(f);elseif 63 * pi / 72 <f< 17 * pi / 18s(f)= 2*h *(pi/2+(f-7*pi/18)/(5*pi/9)-sin(4*pi*(f-7*pi/18)/(5*pi/9))/4/pi)/(pi+2);s = s(f);ds(f)= 2*h *(1-cos(4*pi*(f-7*pi/18)/(5*pi/9)))/(pi+2)/(5*pi/9);ds = ds(f); d2s(f)=-8*pi * h*sin(4*pi*(f-7pi/18)/(5*pi/9))/(pi+2)/(5*pi/9)^2;d2s = d2s(f);elseif 17*pi/18<f<73*pi/72s(f)= 2*h *(pi/2+(27*pi/18-f)/(5*pi/9)-sin(4*pi*(27*pi/18-f)/(5*pi/9))/4/pi)/(pi+2);s = s(f);ds(f)= 2*h *(-1+cos(4*pi*(27*pi/18-f)/(5*pi/9)))/(pi+2)/(5*pi/9);ds = ds(f);d2s(f)=8*pi * h*sin(4*pi*(27pi/18-f)/(5*pi/9))/(pi+2)/(5*pi/9)^2;d2s = d2s(f);elseif 73 * pi / 72 <f< 83 * pi / 72s(f)= h *((8-33*pi^2)/16/pi+(7*pi+2)*(27*pi/18-f)/(5*pi/9)-4*pi*(27*pi/18-f)^2/(5*pi/9)^2)/(pi+2 );s = s(f);ds(f)= h *(-7*pi-2+8*pi*(27*pi/18-f)/(5*pi/9))/(pi+2)/(5*pi/9);ds = ds(f); d2s(f)=8*pi * h/(pi+2)/(5*pi/9)^2;d2s = d2s(f);elseif 83 * pi / 72 <f< 93 * pi / 72s(f)=2 * h *((pi+1)*(27*pi/18-f)/(5*pi/9)-pi/4+sin(4*pi*(27*pi/18-f)/(5*pi/9))/4/pi) /(pi+2);s = s(f);ds(f)= 2* h *(-pi-1-cos(4*pi*(27*pi/18-f)/(5*pi/9)))/(pi+2)/(5*pi/9);ds = ds(f);d2s(f)=8*pi * h*sin(4*pi*(27*pi/18-f)/(5*pi/9))/(pi+2)/(5*pi/9)^2;d2s = d2s(f);elseif 93 * pi / 72 <f< 103 * pi / 72s(f)=2 * h *((pi^2 - 8)/16/pi-(pi-2)(27*pi/18-f)/ (5*pi/9)+4*pi*(27*pi/18-f)^2/(5*pi/9)^2);s = s(f);ds(f)= h *(-2+pi-8*pi*(27*pi/18-f)/(5*pi/9))/(pi+2)/(5*pi/9);ds = ds(f);d2s(f)=-8*pi * h/(pi+2)/(5*pi/9)^ 2;d2s = d2s(f);d2s = d2s(f);elseif 103 * pi / 72 < f < 3 * pi / 2s(f)=2 * h *((27 * pi / 18-f)/ (5*pi/9)-sin(4*pi*(27*pi/18-f)/(5*pi/9)))/(pi+2);s = s(f);ds(f)=2 * h *(-1+cos(4*pi*(27*pi/18-f)/(5*pi/9)))/(pi+2)*(5*pi/9);ds = ds(f);d2s(f)=-8*pi * h*sin(4*pi(27*pi/18-f)/(5*pi/9)) /(pi+2)/(5*pi/9)^ 2;d2s = d2s(f);d2s = d2s(f);elseif 3 * pi / 2< f <2*pis(f)=0;s = s(f);ds(f)=0;ds = ds(f);d2s(f)=0;d2s = d2s(f);endxd=L6*cos(0+s/r*(z2*z1/z3/zshan)+pi)+xeyd=L6*cos(0+s/r*(z2*z1/z3/zshan)+pi)+yejiaoD=acos((L5^2+xd^2+yd^2-L3^2)/2*L5*(xd^2+yd^2)^(1/2))+acos((L6^ 2+xd^2+yd^2-L7^2)/2*L6*(xd^2+yd^2)^(1/2))+0+s/r*(z2/z3*(z1/zshan))xc=L5*cos(jiaoD)+xdyc=L5*sin(jiaoD)+yda=((xa-xc)^2+(ya-yc)^2)^(1/2)baijiao=acos(L2^2+a^2-(xa-xc-L2*cos(guding-pi+jiaoD))^2+(yz-yc-L2*sin( guding-pi+jiaoD))^2)^0.5)/(2*L2*a)xb=a*sin(f)-L2*sin(f+baijiao); xb = xx(f);yb=a*cos(f)-L2*cos(f+baijiao); yb = yy(f);% dx(f) = (ds - e) * sin(f * hd) + (se + s) * cos(f * hd); dx = dx(f);% dy(f) = (ds - e) * cos(f * hd) - (se + s) * sin(f * hd); dy = dy(f);% xp(f) = x + rt * dy / sqrt(dx ^ 2 + dy ^ 2);xxp = xp(f);% yp(f) = y - rt * dx / sqrt(dx ^ 2 + dy ^ 2);yyp = yp(f);% r(f) = sqrt (x ^2 + y ^2 );% rp(f) = sqrt (xxp ^2 + yyp ^2 );enddisp ' 2-1 推程(等加速/等减速运动)'disp ' 凸轮转角理论x 理论y 实际x 实际y'for f = 10 : 10 :ftnu = [f xx(f) yy(f) xp(f) yp(f)];disp(nu)enddisp ' 2-2 回程(余弦加速度运动)'disp ' 凸轮转角理论x 理论y 实际x 实际y'for f = d1 : 10 : d2nu = [f xx(f) yy(f) xp(f) yp(f)];disp(nu)enddisp ' 2-3 凸轮轮廓向径'disp ' 凸轮转角理论r 实际r'for f = 10 : 10 : nnu = [f r(f) rp(f)];disp(nu)enddisp '绘制凸轮的理论轮廓和实际轮廓:'plot(xx,yy,'r-.') % 理论轮廓(红色,点划线)axis ([-(rb+h-10) (rb+h+10) -(rb+h+10) (rb+rt+10)]) % 横轴和纵轴的下限和上限axis equal % 横轴和纵轴的尺度比例相同text(rb+h+3,0,'X') % 标注横轴text(0,rb+rt+3,'Y') % 标注纵轴text(-5,5,'O') % 标注直角坐标系原点title('偏置移动从动件盘形凸轮设计') % 标注图形标题hold on; % 保持图形plot([-(rb+h) (rb+h)],[0 0],'k') % 横轴(黑色)plot([0 0],[-(rb+h) (rb+rt)],'k') % 纵轴(黑色)plot([e e],[0 (rb+rt)],'k--') % 初始偏置位置(黑色,虚线)ct = linspace(0,2*pi); % 画圆的极角变化范围plot(rb*cos(ct),rb*sin(ct),'g') % 基圆(绿色)plot(e*cos(ct),e*sin(ct),'c--') % 偏距圆(蓝绿色,虚线)plot(e + rt*cos(ct),se + rt*sin(ct),'y') % 滚子圆(黄色)plot(xp,yp,'b') % 实际轮廓(蓝色)。