机械原理大作业-凸轮结构20

1、 凸轮机构设计题目要求：试用计算机辅助设计完成下列偏置直动推杆盘形凸轮机构的设计，已知数据如下各表所示。凸轮沿逆时针方向作匀速转动。表一 偏置直动滚子推杆盘形凸轮机构的已知参数升程/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/。70120余弦加速度3590正弦加速度656090要求：1） 确定凸轮推杆的升程、回程运动方程，并绘制推杆位移、速度、加速度线图。2） 绘制凸轮机构的线图；3） 确定凸轮基圆半径和偏距；4） 确定滚子半径；5）绘制凸轮理论廓线和实际廓线。推杆运动规律：（取）1) 推程运动规律：由余弦加速度运动公式可得

2、2) 回程运动规律：正弦加速度运动公式可得试中：T=经带入计算可得：s1 = 0.035*(1 - cos(1.5*x);v1=0.105/2 * w * sin(1.5 * x);a1 = 0.1575/2 * w2 .* cos(1.5*x);s3 = 0.070*(3 - 2*z/pi + 1/(2*pi).*sin (4*z - 4* pi);v3 = -0.140/pi * w .* (1 - cos(4*z - 4* pi);a3 = 0.56 * w2/pi .*sin(4*z - 4* pi);三 计算程序（matlab）（1） 推杆位移、速度、加速度线图编程；a.位移与转角曲

3、线w = 2*pi/3x = 0:(pi/100):(2*pi/3);s1 = 0.035*(1 - cos(1.5*x);v1=0.105/2 * w * sin(1.5 * x);a1 = 0.1575/2 * w2 .* cos(1.5*x);y = (2*pi/3):(pi/100):(pi);s2 = 0.070;v2=0;a2 = 0;z = (pi ):(pi/100):(3*pi/2);s3 = 0.070*(3 - 2*z/pi + 1/(2*pi).*sin (4*z - 4* pi);v3 = -0.140/pi * w .* (1 - cos(4*z - 4* pi);

4、a3 = 0.56 * w2/pi .*sin(4*z - 4* pi);c = (3*pi/2):(pi/100):( 2*pi);s4 = 0;v4 = 0;a4 = 0;plot(x,s1,'b',y,s2,'b',z,s3,'b',c,s4,'b')xlabel('转角/rad')ylabel('位移/m/')title('位移与转角曲线')b.速度与转角曲线w = 2*pi/3x = 0:(pi/100):(2*pi/3);s1 = 0.035*(1 - cos(1.5*x

5、);v1=0.105/2 * w * sin(1.5 * x);a1 = 0.1575/2 * w2 .* cos(1.5*x);y = (2*pi/3):(pi/100):(pi);s2 = 0.070;v2=0;a2 = 0;z = (pi ):(pi/100):(3*pi/2);s3 = 0.07*(3 - 2*z/pi + 1/(2*pi).*sin (4*z - 4* pi);v3 = -0.140/pi * w .* (1 - cos(4*z - 4* pi);a3 = 0.56 * w2/pi .*sin(4*z - 4* pi);c = (3*pi/2):(pi/100):(

6、2*pi);s4 = 0;v4 = 0;a4 = 0;plot(x,v1,'g',y,v2,'g',z,v3,'g ',c,v4,'g')xlabel('转角/rad')ylabel('速度/(m/s)')title('速度与转角曲线')c.加速度与位移转角曲线w = 2*pi/3x = 0:(pi/100):(2*pi/3);s1 = 0.035*(1 - cos(1.5*x);v1=0.105/2 * w * sin(1.5 * x);a1 = 0.1575/2 * w2 .*

7、cos(1.5*x);y = (2*pi/3):(pi/100):(pi);s2 = 0.070;v2=0;a2 = 0;z = (pi):(pi/100):(3*pi/2);s3 = 0.070*(3 - 2*z/pi + 1/(2*pi).*sin (4*z - 4* pi);v3 = -0.140/pi * w .* (1 - cos(4*z - 4* pi);a3 = 0.56 * w2/pi .*sin(4*z - 4* pi);c = (3*pi/2):(pi/100):( 2*pi);s4 = 0;v4 = 0;a4 = 0;plot(x,a1,'r',y,a2,

8、'r',z,a3,'r ',c,a4,'r')xlabel('转角/rad')ylabel('加速度/(m2/s)')title('加速度与转角曲线')（2）凸轮机构的线图编程；w = 2*pi/3x = 0:(pi/100):(2*pi/3);s1 = 35*(1 - cos(1.5*x);news1 = 35*1.5*sin(1.5*x);y = (2*pi/3):(pi/100):(pi);s2 = 70;news2 = 0;z = (pi ):(pi/100):(3*pi/2);s3=70*

9、(3 - 2*z/pi + 1/(2*pi).*sin (4*z - 4* pi);news3 =-140/pi * w .* (1 - cos(4*z - 4* pi);c = (3*pi/2):(pi/100):( 2*pi);s4 = 0;news4 = 0; plot(news1,s1,'b',news2,s2,'b',news3,s3,'b',news4,s4,'b')xlabel('ds/dp');ylabel('(位移s/mm)')title('ds/dp 与位移s曲线'

10、;)grid（3） 确定基圆半径和偏距；（4）经过对凸轮机构的线图分析确定其偏距e=17,s=70,基圆半径r0=32，得s0=50;a.先求凸轮理论轮廓曲线，程序如下：w = 2*pi/3;s0 = 50;s = 70;e = 17;x = 0:(pi/100):(2*pi/3);x1 = (s + s0)*cos(x)-e*sin(x);y1 = (s0 + s)*sin(x) - e*cos(x);y = (2*pi/3):(pi/100):(pi);x2 = (s + s0)*cos(y)-e*sin(y);y2 = (s0 + s)*sin(y) - e*cos(y);z = (pi

11、):(pi/100):(3*pi/2);x3 = (s + s0)*cos(z)-e*sin(z);y3 = (s0 + s)*sin(z) - e*cos(z);c = (3*pi/2):(pi/100):( 2*pi);x4 = (s + s0)*cos(c)-e*sin(c);y4 = (s0 + s)*sin(c) - e*cos(c);plot(x1,y1,'b',x2,y2,'b',x3,y3,'b',x4,y4,'b');xlabel('x/mm')ylabel('y/mm')titl

12、e('理轮轮曲线')b.再通过该廓线求其最小曲率半径，程序如下：v=;syms x1 x2 x3 x4 x5 s0 = 50; e = 20; s1 = 35*(1 - cos(1.5*x1);t1 = (s1 + s0)*cos(x1)-e*sin(x1); y1 = (s0 + s1)*sin(x1) - e*cos(x1); tx1=diff(t1,x1); txx1=diff(t1,x1,2); yx1=diff(y1,x1); yxx1=diff(y1,x1,2);for xx1= 0:(pi/100):(2*pi/3); k1=subs(abs(tx1*yxx1-t

13、xx1*yx1)/(tx12+yx12)1.5),x1,xx1); v=v,1/k1;end s2 = 70;t2 = (s2 + s0)*cos(x2)-e*sin(x2); y2 = (s0 + s2)*sin(x2) - e*cos(x2); tx2=diff(t2,x2); txx2=diff(t2,x2,2); yx2=diff(y2,x2); yxx2=diff(y2,x2,2);for xx2=(2*pi/3):(pi/100):(pi); k2=subs(abs(tx2*yxx2-txx2*yx2)/(tx22+yx22)1.5),x2,xx2); v=v,1/k2;end s

14、3 = 110*(10/3- 2*x3/pi + 1/(2*pi).*sin (4*x3 - 14* pi/3);t3 = (s3 + s0)*cos(x3)-e*sin(x3); y3 = (s0 + s3)*sin(x3) - e*cos(x3); tx3=diff(t3,x3); txx3=diff(t3,x3,2); yx3=diff(y3,x3); yxx3=diff(y3,x3,2);for xx3=(pi):(pi/100):(3*pi/2); k3=subs(abs(tx3*yxx3-txx3*yx3)/(tx32+yx32)1.5),x3,xx3); v=v,1/k3;end

15、 s4 = 0;t4 = (s4 + s0)*cos(x4)-e*sin(x4); y4 = (s0 + s4)*sin(x4) - e*cos(x4); tx4=diff(t4,x4); txx4=diff(t4,x4,2); yx4=diff(y4,x4); yxx4=diff(y4,x4,2);for xx4=(3*pi/2):(pi/100):( 2*pi); k4=subs(abs(tx4*yxx4-txx4*yx4)/(tx42+yx42)1.5),x4,xx4); v=v,1/k4;endmin(v)（3） 凸轮的理论廓线和其包络线；由基圆半径确定其滚子的半径为r=8mm，其他参

16、数保持不变；a.凸轮的理论廓线w = 2*pi/3;s0 = 50;s = 70;e = 17;x = 0:(pi/100):(2*pi/3);x1 = (s + s0)*cos(x)-e*sin(x);y1 = (s0 + s)*sin(x) - e*cos(x);y = (2*pi/3):(pi/100):(pi);x2 = (s + s0)*cos(y)-e*sin(y);y2 = (s0 + s)*sin(y) - e*cos(y);z = (pi ):(pi/100):(3*pi/2);x3 = (s + s0)*cos(z)-e*sin(z);y3 = (s0 + s)*sin(z

17、) - e*cos(z);c = (3*pi/2):(pi/100):( 2*pi);x4 = (s + s0)*cos(c)-e*sin(c);y4 = (s0 + s)*sin(c) - e*cos(c);plot(x1,y1,'b',x2,y2,'b',x3,y3,'b',x4,y4,'b');xlabel('x/mm')ylabel('y/mm')title('理轮轮曲线')b.凸轮的包络线w = 2*pi/3;s0 = 50;e = 17;r = 8;x = 0:(pi/1

18、00):(2*pi/3);s1 = 35*(1 - cos(1.5*x);x1 = (s1 + s0).*cos(x) - e*sin(x);y1 = (s0 + s1).*sin(x) - e*cos(x);n1 = -(35*1.5*sin(x) + s0).*sin(x) -e*cos(x);m1 = (s0 + 35*1.5*sin(x) ).*cos(x) + e*sin(x);xt1 = x1+(r*m1)./(sqrt(n1.2+m1.2);yt1 = y1 - (r*n1)./sqrt(m1.2 +n1.2);xw1 = x1 - (r*m1)./sqrt(m1.2 +n1.2

19、);yw1 = y1 + (r*n1)./sqrt(m1.2 +n1.2);y = (2*pi/3):(pi/100):(pi);s2 = 70;x2 = (s2 + s0).*cos(y)-e*sin(y);y2 = (s0 + s2).*sin(y) - e*cos(y);n2 = -s0.*sin(y)-e*cos(y);m2 = s0 .*cos(y) + e*sin(y);xt2 = x2 + (r*m2)./sqrt(m2.2+n2.2);yt2 = y2 - (r*n2)./sqrt(m2.2+n2.2);xw2 = x2 - (r*m2)./sqrt(m2.2+n2.2);yw2 = y2 + (r*n2)./sqrt(m2.2+n2.2);z = (pi ):(pi/100):(3*pi/2);s3 = 70*(3- 2*z/pi + 1/(2*pi).*sin (4*z - 4* pi);x3 = (s3 + s0).*cos(z)-e*sin(z);y3 = (s0 + s3).*sin(z) - e*cos(z);n3 = -(140/pi *cos(4*z - 4*pi) + s0).*s