基于MATLAB的凸轮设计

1、 中国地质大学（武汉）1. 凸轮要求 设计一对心直动滚子推杆盘形凸轮机构，滚子半径rr=10mm，凸轮以等角速度逆时针回转。凸轮转角=0120 时，推杆等速上升20mm；=120180时，推杆远休止；=180270时，推杆等加速等减速下降20mm；=270360时，推杆近休止。要求推程的最大压力角<=30，试选取合适的基圆半径，并绘制凸轮的廓线。问此凸轮是否有缺陷，应如何补救。2列出凸轮运动方程S=30*V=30a=0 0<<2/3 S=20V=0a=0 2/3<< S=-140+320*-1602*2V=320-3202*a=-320/2 <<54

2、S=360-480*+1602*2V=-480-3202*a=-320/2 5/4<<32 S=0V=0a=0 2/3<<23. 由方程写MATLAB源程序%1.已知参数clear;r0=50; %基圆半径rr=10; %滚子半径h=20; %行程delta01=120;%推程运动角delta02=60; % 远休角delta03=90;%回程运动角 hd=pi/180;du=180/pi;n1=delta01+delta02;n2=delta01+delta02+delta03; %2凸轮曲线设计n=360;for i=1:360 %计算推杆运动规律 if i<

3、=delta01 s(i)=30/pi*(i*hd); ds(i)=30/pi; ds=ds(i); elseif i>delta01 && i<=n1; s(i)=h; ds(i)=0; ds=ds(i); elseif i>n1 && i<=(n1+delta03/2) s(i)=-140+320/pi*(i*hd)-160/pi2*(i*hd)2; ds(i)=320/pi-320/pi2*(i*hd); ds=ds(i); elseif i>(n1+delta03/2) && i<=n2 s(i)=36

4、0-480/pi*(i*hd)+160/pi2*(i*hd)2; ds(i)=-480/pi+320/pi2*(i*hd); ds=ds(i); elseif i>n2 && i<=n s(i)=0; ds=0; end %计算凸轮轨迹曲线xx(i)=(r0+s(i)*sin(i*hd);%计算理论轮廓曲线 yy(i)=(r0+s(i)*cos(i*hd); dx(i)=ds*sin(i*hd)+(r0+s(i)*cos(i*hd);%计算导数 dy(i)=ds*cos(i*hd)-(r0+s(i)*sin(i*hd); xp(i)=xx(i)+rr*dy(i)/s

5、qrt(dx(i)2+dy(i)2); yp(i)=yy(i)-rr*dx(i)/sqrt(dx(i)2+dy(i)2);end %3.输出凸轮轮廓曲线figure(1);hold on;grid on;axis equal;axis(-(r0+h-30) (r0+h+10) -(r0+h+10) (r0+rr+10);text(r0+h+3,4,'X');text(3,r0+rr+3,'Y');text(-6,4,'O');title('对心直动滚子推杆盘形凸轮设计');xlabel('x/mm');ylabel

6、('y/mm');plot(-(r0+h-40) (r0+h),0 0,'k');plot(0 0,-(r0+h) (r0+rr),'k');plot(xx,yy,'r-');%»绘凸轮实际轮廓曲线ct=linspace(0,2*pi);plot(r0*cos(ct),r0*sin(ct),'g');%绘凸轮基圆plot(rr*cos(ct),r0+rr*sin(ct),'k');%绘滚子圆plot(0,r0,'o');%滚子圆中心plot(0 0,r0 r0+30,

7、9;k');plot(xp,yp,'b'); %绘凸轮实际轮廓曲线 %4. 凸轮机构运动仿真%计算凸轮滚子转角xp0=0;yp0=r0-rr;dss=sqrt(diff(xp).2+diff(yp).2);%对轮廓曲线进行差分计算ss(1)=sqrt(xp(1)-xp0)2+(xp(1)-yp0)2);%轮廓曲线第一点长度for i=1:359 ss(i+1)=ss(i)+dss(i);%计算实际廓曲线长度endphi=ss/rr;%计算滚子转角%运动仿真开始figure(2);m=moviein(20);j=0;for i=1:360 j=j+1; delta(i)=

8、i*hd;%凸轮转角 xy=xp',yp'%凸轮实际轮廓曲线坐标 A1=cos(delta(i),sin(delta(i);%凸轮坐标旋转矩阵 -sin(delta(i),cos(delta(i); xy=xy*A1;%旋转后实际凸轮曲线坐标 clf; %绘凸轮 plot(xy(:,1),xy(:,2); hold on;axis equal; axis(-(120) (470) -(100) (140); plot(-(r0+h-40) (r0+h),0,'k');%绘凸轮水平轴 plot(0 0,-(r0+h) (r0+rr),'k');%绘

9、凸轮垂直轴 plot(r0*cos(ct),r0*sin(ct),'g');%绘基圆 plot(rr*cos(ct),r0+s(i)+rr*sin(ct),'k');绘滚子圆 plot(0 rr*cos(-phi(i),r0+s(i) r0+s(i)+rr*sin(-phi(i),'k'); % 绘滚子圆标线 plot(0 0,r0+s(i) r0+s(i)+40,'k');%绘推杆 %绘推杆曲线 plot(1:360+r0+h,s+r0); plot(r0+h) (r0+h+360),r0 r0,'k'); pl

10、ot(r0+h) (r0+h),r0 r0+h,'k'); plot(i+r0+h,s(i)+r0,'*'); title('对心直动滚子推杆盘形凸轮设计'); xlabel('x/mm'); ylable('y/mm'); m(j)=getframe;endmovie(m);4.运动仿真结果在MATLAB中可以看出轮廓曲线有一处缺口。应用圆弧连接起来。5.计算结果由于数据太多，只等间隔取了三十六组数据Xx8.9718 18.2411 27.5000 36.4246 44.6859 51.9615 57.9477

11、62.3712 65.0000 65.6539 64.2123 60.6218 53.6231 44.9951 35.0000 23.9414 12.1554 0.0000 -12.0696 -23.2658 -32.7778 -39.9163 -44.3549 -47.1503 -48.8408 -49.7267 -50.0000 -49.2404 -46.9846 -43.3013 -38.3022 -32.1394 -25.0000 -17.1010 -8.6824 -0.0000Yy50.8817 50.1169 47.6314 43.4092 37.4959 30.0000 21.0

12、912 10.9977 0.0000 -11.5765 - 23.3714 -35.0000 -44.9951 -53.6231 -60.6218 -65.7785 -68.9365-70.0000 -68.4502 -63.9223 -56.7728 -47.5704 -37.2182 -27.2222 -17.7766 -8.7682 -0.0000 8.6824 17.1010 25.0000 32.1394 38.3022 43.3013 46.9846 49.2404 50.0000Dx52.5400 53.3830 52.4060 49.5474 44.8111 38.2699 3

13、0.0646 20.4019 9.5493 -2.1723 -14.3980 -26.7301 -44.9951 -53.6231 -60.6218 -65.7785 -68.9365- 70.0000 -67.4676 -60.0514 -48.2845 -33.0207 -19.8785 -12.5201 -7.1415 -3.1953 0.0000 8.6824 17.1010 25.0000 32.1394 38.3022 43.3013 46.984649.2404 50.0000Dy0.4324 -9.2677 -19.2301 -29.1094 -38.5478 -47.1869 -54.6817 -60.7129 -65.0000 -67.3121 -67.4