机械原理大作业凸轮机构22号

1、大作业2 凸轮机构设计1设计题目，包括机构运动简图和凸轮机构的原始参数；如图2-1所示直动从动件盘形凸轮机构，其原始参数见表2-1。从表2-1中选择一组凸轮机构的原始参数，据此设计该凸轮机构。图2-1表2-1 凸轮机构原始参数升程（mm）升程运动角（°）升程运动规律升程许用压力角（°）回程运动角（°）回程运动规律回程许用压力角（°）远休止角（°）近休止角（°）12090等加等减速4080等减等加速70701202.凸轮推杆升程、回程运动方程及推杆位移、速度、加速度线图（1）升程当0xpi/4时由公式 带入得s1=2*h*x12/(pi

2、/2)2v1=4*h*w*x1/(pi/2)2a1=4*h*w2/(pi/2)2当pi/4<xpi/2时由公式 带入得s2=h-2*h*(pi/2-x2)2/(pi/2)2v2=4*h*w*(pi/2-x2)/(pi/2)2a2=-4*h*w2/(pi/2)2（2）近休止当pi/2<xpi8/9时s3=hv3=0a3=0（3）回程当pi8/9<x10pi/9时由公式s=h-2h0'2-(0+s)2 v=-4hw0'2-(0+s) a=-4hw20'2带入得s4=h-2*h*(x4-8*pi/9)2/(4*pi/9)2v4=-4*h*w*(x4-8*pi

3、/9)/(4*pi/9)2a4=-4*h*w2/(4*pi/9)2当10pi/9<x4pi/3时由公式s=2h0'20+s+0'-2 v=-4hw0'20+s+0'- a=4hw20'2带入得s5=2*h*(12*pi/9-x5)2/(4*pi/9)2v5=-4*h*w*(12*pi/9-x5)/(4*pi/9)2a5=4*h*w2/(4*pi/9)2（4）远休止当pi*4/3<x2*pi时由公式s6=0v6=0a6=0位移与转角曲线速度与转角曲线加速度与转角曲线3凸轮机构的线图，并依次确定凸轮的基圆半径和偏距；ds/ d与s曲线确定凸轮的基

4、圆半径和偏距根据此图，可以取基圆半径r0=120mm，偏距e=30mm4滚子半径的确定及凸轮理论廓线和实际廓线的绘制凸轮理论轮廓 x=S0+S*sinx+e*cosx y=(S0+S)*cosx-e*sin(x)式中， 滚子半径的确定用matlab求得凸轮最小曲率半径求得最小曲率半径99.83mm 取滚子半径r=10mm则求得凸轮理论轮廓用matlab求得凸轮工作轮廓凸轮工作轮廓曲线附录1.推杆位移、速度、加速度线图matlab程序clc;clear;global w h w=pi;h=120;%升程1x1=0:(0.0001*pi):(pi/4);s1=2.*h.*x1.2./(pi./2)

5、.2;v1=4*h*w*x1/(pi/2)2;a1=4*h*w2/(pi/2)2;%升程2x2=(pi/4):(0.0001*pi):(pi/2);s2=h-2.*h.*(pi./2-x2).2/(pi./2).2;v2=4*h*w*(pi/2-x2)/(pi/2)2;a2=-4*h*w2/(pi/2)2;%近休止x3=(pi/2):(0.0001*pi):(pi*8/9);s3=h;v3=0;a3=0;%回程1x4=(pi*8/9):(pi*0.0001):(pi*10/9);s4=h-2.*h.*(x4-8.*pi./9).2/(4.*pi./9).2;v4=-4*h*w*(x4-8*pi

6、/9)/(4*pi/9)2;a4=-4*h*w2/(4*pi/9)2;%回程2x5=(pi*10/9):(pi*0.0001):(4*pi/3);s5=2.*h.*(12.*pi./9-x5).2/(4.*pi./9).2;v5=-4*h*w*(12*pi/9-x5)/(4*pi/9)2;a5=4*h*w2/(4*pi/9)2;%远休止x6=(4*pi/3):(pi*0.0001):(2*pi);s6=0;v6=0;a6=0; subplot(2,2,1);plot(x1,s1,'g.',x2,s2,'g.',x3,s3,'g.',x4,s4,&

7、#39;g.',x5,s5,'g.',x6,s6,'g.');xlabel('转角/rad')ylabel('位移/mm')title('位移与转角曲线') subplot(2,2,2);plot(x1,v1,'g.',x2,v2,'g.',x3,v3,'g.',x4,v4,'g.',x5,v5,'g.',x6,v6,'g.');xlabel('转角/rad')ylabel('速度/ m/

8、s')title('速度与转角曲线') subplot(2,2,3);plot(x1,a1,'g.',x2,a2,'g.',x3,a3,'g.',x4,a4,'g.',x5,a5,'g.',x6,a6,'g.');xlabel('转角/rad')ylabel('加速度/ m/s2')title('加速度与转角曲线')2.图matlab程序clc;clear;global w h w=pi;h=120;%升程1x1=0:(0.00

9、01*pi):(pi/4);s1=2.*h.*x1.2./(pi./2).2;s11=4.*h.*x1./(pi./2).2;%升程2x2=(pi/4):(0.0001*pi):(pi/2);s2=h-2.*h.*(pi./2-x2).2/(pi./2).2;s22=4.*h.*(pi./2-x2)./(pi./2).2;%近休止x3=(pi/2):(0.0001*pi):(pi*8/9);s3=h;s33=0%回程1x4=(pi*8/9):(pi*0.0001):(pi*10/9);s4=h-2.*h.*(x4-8.*pi./9).2/(4.*pi./9).2;s44=-4.*h.*(x4-

10、8.*pi./9)./(4.*pi./9).2;%回程2x5=(pi*10/9):(pi*0.0001):(4*pi/3);s5=2.*h.*(12.*pi./9-x5).2/(4.*pi./9).2;s55=-4.*h.*(12.*pi./9-x5)./(4.*pi./9).2;%远休止x6=(4*pi/3):(pi*0.0001):(2*pi);s6=0;s66=0; plot(s11,s1,'g.',s22,s2,'g.',s33,s3,'g.',s44,s4,'g.',s55,s5,'g.',s66,s6,

11、'g.');xlabel('ds/d')ylabel('s/mm')title('ds/ d与s曲线')3.滚子最小曲率半径计算Matlab程序clc;clear;global r0 e hr0=120;e=30;s0=sqrt(r02-e2);h=120;syms x1 x2 x3 x4 x5 x6v=; s1=2.*h.*x1.2./(pi./2).2;b1=(s0+s1).*cos(x1)-e*sin(x1);a1=(s0+s1).*sin(x1)+e*cos(x1);ta1=diff(a1,x1);ta11=diff(a1

12、,x1,2);tb1=diff(b1,x1);tb11=diff(b1,x1,2);for x11=0:(pi/100):(pi/4); c1=subs(abs(ta1*tb11-ta11*tb1)/(ta12+tb12)1.5),x1,x11); v=v,1/c1;end s2=h-2.*h.*(pi./2-x2).2/(pi./2).2;b2=(s0+s2).*cos(x2)-e*sin(x2);a2=(s0+s2).*sin(x2)+e*cos(x2);ta2=diff(a2,x2);ta22=diff(a2,x2,2);tb2=diff(b2,x2);tb22=diff(b2,x2,2

13、);for x22=(pi/4):(pi/100):(pi/2); c2=subs(abs(ta2*tb22-ta22*tb2)/(ta22+tb22)1.5),x2,x22); v=v,1/c2;end s3=h;b3=(s0+s3).*cos(x3)-e*sin(x3);a3=(s0+s3).*sin(x3)+e*cos(x3);ta3=diff(a3,x3);ta33=diff(a3,x3,2);tb3=diff(b3,x3);tb33=diff(b3,x3,2);for x33=(pi/2):(pi/100):(pi8/9); c3=subs(abs(ta3*tb33-ta33*tb3

14、)/(ta32+tb32)1.5),x3,x33); v=v,1/c3;end s4=h-2.*h.*(x4-8.*pi./9).2/(4.*pi./9).2;b4=(s0+s4).*cos(x4)-e*sin(x4);a4=(s0+s4).*sin(x4)+e*cos(x4);ta4=diff(a4,x4);ta44=diff(a4,x4,2);tb4=diff(b4,x4);tb44=diff(b4,x4,2);for x44=(pi*8/9):(pi/100):(pi/9*10); c4=subs(abs(ta4*tb44-ta44*tb4)/(ta42+tb42)1.5),x4,x44

15、); v=v,1/c4;end s5=2.*h.*(12.*pi./9-x5).2/(4.*pi./9).2;b5=(s0+s5).*cos(x5)-e*sin(x5);a5=(s0+s5).*sin(x5)+e*cos(x5);ta5=diff(a5,x5);ta55=diff(a5,x5,2);tb5=diff(b5,x5);tb55=diff(b5,x5,2);for x55=(pi*10/9):(pi/100):(pi/3*4); c5=subs(abs(ta5*tb55-ta55*tb5)/(ta52+tb52)1.5),x5,x55); v=v,1/c5;end s6=0;b6=(

16、s0+s6).*cos(x6)-e*sin(x6);a6=(s0+s6).*sin(x6)+e*cos(x6);ta6=diff(a6,x6);ta66=diff(a6,x6,2);tb6=diff(b6,x6);tb66=diff(b6,x6,2);for x66=(pi*4/3):(pi/100):(pi*2); c6=subs(abs(ta6*tb66-ta66*tb6)/(ta62+tb62)1.5),x6,x66); v=v,1/c6;endmin(v)4.凸轮理论轮廓曲线图Matlab程序clc;clear;global r0 e hr0=120;e=30;s0=sqrt(r02-

17、e2);h=120;x1=0:(0.0001*pi):(pi/4);s1=2.*h.*x1.2./(pi./2).2;b1=(s0+s1).*cos(x1)-e*sin(x1);a1=(s0+s1).*sin(x1)+e*cos(x1);x2=(pi/4):(0.0001*pi):(pi/2);s2=h-2.*h.*(pi./2-x2).2/(pi./2).2;b2=(s0+s2).*cos(x2)-e*sin(x2);a2=(s0+s2).*sin(x2)+e*cos(x2);x3=(pi/2):(0.0001*pi):(pi*8/9);s3=h;b3=(s0+s3).*cos(x3)-e*

18、sin(x3);a3=(s0+s3).*sin(x3)+e*cos(x3);x4=(pi*8/9):(pi*0.0001):(pi*10/9);s4=h-2.*h.*(x4-8.*pi./9).2/(4.*pi./9).2;b4=(s0+s4).*cos(x4)-e*sin(x4);x5=(pi*10/9):(pi*0.0001):(4*pi/3);s5=2.*h.*(12.*pi./9-x5).2/(4.*pi./9).2;b5=(s0+s5).*cos(x5)-e*sin(x5);a5=(s0+s5).*sin(x5)+e*cos(x5);x6=(4*pi/3):(pi*0.0001):(

19、2*pi);s6=0;b6=(s0+s6).*cos(x6)-e*sin(x6);a6=(s0+s6).*sin(x6)+e*cos(x6); plot(a1,b1,'g.',a2,b2,'g.',a3,b3,'g.',a4,b4,'g.',a5,b5,'g.',a6,b6,'g.');axis equalxlabel('x/mm')ylabel('y/mm')title('凸轮理论轮廓曲线')5.凸轮工作轮廓内外包络曲线Matlab程序clc;cle

20、ar;global r0 e h r w s0r0=120;e=30;s0=sqrt(r02-e2);h=120;r=10;w=pi; x1=0:(0.0001*pi):(pi/4);s1=2.*h.*x1.2./(pi./2).2;v1=4*h*w*x1/(pi/2)2;b1=(s0+s1).*cos(x1)-e*sin(x1);a1=(s0+s1).*sin(x1)+e*cos(x1);n1=v1.*cos(x1)-(s1+s0).*cos(x1)-e*sin(x1);m1=v1.*cos(x1)-(s1+s0).*sin(x1)-e*cos(x1);xt1=a1+(r*m1)./(sqr

21、t(n1.2+m1.2);yt1=b1-(r*n1)./(sqrt(m1.2+n1.2);xw1=a1-(r*m1)./(sqrt(m1.2+n1.2);yw1=b1+(r*n1)./(sqrt(m1.2+n1.2); x2=(pi/4):(0.0001*pi):(pi/2);s2=h-2.*h.*(pi./2-x2).2/(pi./2).2;v2=4*h*w*(pi/2-x2)/(pi/2)2;b2=(s0+s2).*cos(x2)-e*sin(x2);a2=(s0+s2).*sin(x2)+e*cos(x2);n2=v2.*cos(x2)-(s2+s0).*cos(x2)-e*sin(x2

22、);m2=v2.*cos(x2)-(s2+s0).*sin(x2)-e*cos(x2);xt2=a2+(r*m2)./(sqrt(n2.2+m2.2);yt2=b2-(r*n2)./(sqrt(m2.2+n2.2);xw2=a2-(r*m2)./(sqrt(m2.2+n2.2);yw2=b2+(r*n2)./(sqrt(m2.2+n2.2); x3=(pi/2):(0.0001*pi):(pi*8/9);s3=h;v3=0;b3=(s0+s3).*cos(x3)-e*sin(x3);a3=(s0+s3).*sin(x3)+e*cos(x3);n3=v3.*cos(x3)-(s3+s0).*co

23、s(x3)-e*sin(x3);m3=v3.*cos(x3)-(s3+s0).*sin(x3)-e*cos(x3);xt3=a3+(r*m3)./(sqrt(n3.2+m3.2);yt3=b3-(r*n3)./(sqrt(m3.2+n3.2);xw3=a3-(r*m3)./(sqrt(m3.2+n3.2);yw3=b3+(r*n3)./(sqrt(m3.2+n3.2); x4=(pi*8/9):(pi*0.0001):(pi*10/9);s4=h-2.*h.*(x4-8.*pi./9).2/(4.*pi./9).2;v4=-4*h*w*(x4-8*pi/9)/(4*pi/9)2;b4=(s0+

24、s4).*cos(x4)-e*sin(x4);a4=(s0+s4).*sin(x4)+e*cos(x4);n4=v4.*cos(x4)-(s4+s0).*cos(x4)-e*sin(x4);m4=v4.*cos(x4)-(s4+s0).*sin(x4)-e*cos(x4);xt4=a4+(r*m4)./(sqrt(n4.2+m4.2);yt4=b4-(r*n4)./(sqrt(m4.2+n4.2);xw4=a4-(r*m4)./(sqrt(m4.2+n4.2);yw4=b4+(r*n4)./(sqrt(m4.2+n4.2); x5=(pi*10/9):(pi*0.0001):(4*pi/3);s5=2.*h.*(12.*pi./9-x5).2/(4.*pi./9).2;v5=-4*h*w*(12*pi/9-x5)/(4*pi