1、哈工大机械原理大作业二凸轮设计4题Harbin Institute of Technology大作业设计说明书课程名称: 机械原理 设计题目: 凸轮机构设计 4 院 系: 能源科学与技术学院 班 级: 设 计 者: 学 号: 指导教师: 丁 刚 陈 明 设计时间: 2014.06.08 哈尔滨工业大学一、 设计题目序号(4)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/。回程运动规律回城许用压力角/。远休止角/。近休止角/。6090等加等减速4080正弦加速度7045145二、 运动方程式及运动线图本实验假设凸轮逆时针旋转。(1)设定角速度为1=2/3。确定凸轮机构推杆升程
2、、回程运动方程,并绘制推杆位移、速度、加速度线图。升程:为等加速等减速( 0/2)在/4之前,由公式得到在/4到/2由公式可得s=60-(480/pi2)*(pi/2-)2v=((960*w)/(pi2)*(pi/2-)a=-1840/pi2*w2回程:为正弦加速度(3/443/36)由公式 s = h1 T/ + 1/2sin(2T/);v = - h/1 cos(2T/);a = -2h sin(2T/) ; T = () 得到s=60*(43/16-(9*)/(4*)+1/(2*)*sin((9/2)*- 27*/8);v=-(135/)*1*(1-cos(9/2)*-27*/8);a
3、= -607.5*12/*sin(9*/2-27*/8);由上述公式通过编程得到位移、速度、加速度曲线如下:matlab代码w = 2*pi/3x = 0:(pi/100):(pi/4);s1 = (480/pi.2) * x.2v1=(960/(pi.2)*w.*x;a1 =97.4*w.2;t =(pi/4):(pi/100):(pi/2);s11 = 60-(480/pi.2)*(pi/2-t).2;v11 = (960*w)/(pi.2)*(pi/2-t);a11=-(1840/pi.2)*w.2;y = (pi/2):(pi/1000):(3*pi/4);s2 =60;v2=0;a2
4、 = 0;z = (3*pi/4 ):(pi/1000):(43*pi/36);s3 = 60*(43/16 - (9*z)/(4*pi) + 1/(2*pi).*sin (9/2)*z - 27* pi/8);v3 = -135/pi * w .* (1 - cos(9/2)*z - 27*pi/8);a3 = -(607.5 * w.2)/pi) .*sin(9*z/2 - 27*pi/8);c = (43*pi/36):(pi/100):( 2*pi);s4 = 0;v4 = 0;a4 = 0;plot(x,s1,b,t,s11,b,y,s2,b,z,s3,b,c,s4,b)plot(x
5、,v1,g,t,v11,g,y,v2,g,z,v3,g ,c,v4,g)plot(x,a1,r,t,a11,r,y,a2,r,z,a3,r ,c,a4,r)xlabel(转角/rad)ylabel(位移/(m/s)title(位移与转角曲线)三、 凸轮轮廓绘制1、 凸轮机构的线图及基圆半径和偏距的确定凸轮机构的线图如下图所示Matlab代码x = 0:(pi/100):(pi/4);s1 = (480/pi.2) * x.2news1 = 2*(480/pi.2) * xt =(pi/4):(pi/100):(pi/2);s11 = 60-(480/pi.2)*(pi/2-t).2;new11
6、=2*(480/pi.2)*(pi/2-t);y = (pi/2):(pi/1000):(3*pi/4);s2 = 60;news2 = 0;z = (3*pi/4 ):(pi/1000):(43*pi/36);s3 = 60*(43/16 - (9*z)/(4*pi) + 1/(2*pi).*sin (9/2)*z - 27* pi/8);news3 = 60*( - 9/(4*pi) + 9/(4*pi).*cos (9/2)*z - 27* pi/8);c = (43*pi/36):(pi/100):( 2*pi);s4 = 0;news4 = 0; plot(news1,s1,b,ne
7、w11,s11,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)grid设凸轮顺时针旋转,所以右侧是推程,左侧是回程。得到取旋转轴心的区域(划线部分)取O(10,-120)偏距e=10基圆半径r0=1202、 滚子半径的确定及凸轮理论廓线和实际廓线的绘制理论轮廓线理论轮廓线和实际轮廓线(内层为实际轮廓,外层为理论轮廓)Matlab代码s0 =120;e =10;x = 0:(pi/1000):(pi/4);s = (480/pi.2) * x.2;x1 = (s + s0).*c
8、os(x)-e*sin(x);y1 = (s0 + s).*sin(x) +e*cos(x);t =(pi/4):(pi/1000):(pi/2);s= 60-(480/pi.2)*(pi/2-t).2;x11 = (s + s0).*cos(t)-e*sin(t);y11 = (s0 + s).*sin(t) + e*cos(t);y = (pi/2):(pi/1000):(3*pi/4);s =60;x2 = (s + s0).*cos(y)-e*sin(y);y2 = (s0 + s).*sin(y) + e*cos(y);z = (3*pi/4):(pi/1000):(43*pi/36
9、);s = 60*(43/16 - (9*z)/(4*pi) + 1/(2*pi).*sin (9/2)*z - 27* pi/8);x3 = (s + s0).*cos(z)-e*sin(z);y3 = (s0 + s).*sin(z) + e*cos(z);c = (43*pi/36):(pi/1000):( 2*pi);s = 0;x4 = (s + s0).*cos(c)-e*sin(c);y4 = (s0 + s).*sin(c) + e*cos(c);plot(x1,y1,b,x11,y11,b,x2,y2,b,x3,y3,b,x4,y4,b);xlabel(x/mm)ylabel
10、(y/mm)title(理轮轮曲线)3、凸轮轮廓绘制取滚子半径为r=10mm得到的内包络线图为:得到的外包络线图为:Matlab代码w = 2*pi/3;s0 = 120;e = 10;r = 10;x = 0:(pi/1000):(pi/4);s1 = (480/pi.2) * x.2;x1 = (s1 + s0).*cos(x) - e*sin(x);y1 = (s0 + s1).*sin(x) + e*cos(x);n1 = -(s1 + s0).*sin(x)+(2*(480/pi.2) * x).*cos(x) -e*cos(x);m1 = (s0 + s1).*cos(x)+(2*
11、(480/pi.2) * x).*sin(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);yw1 = y1 + (r*n1)./sqrt(m1.2 +n1.2);t =(pi/4):(pi/100):(pi/2);s11 = 60-(480/pi.2)*(pi/2-t).2;x11 = (s11 + s0).*cos(t) - e*sin(t);y11 = (s0 + s11).*sin(t) + e*c
12、os(t);n11= -(s11 + s0).*sin(t)+(2*(480/pi.2)*(pi/2-t).*cos(t) -e*cos(t);m11 = (s0 + s11).*cos(t)+(2*(480/pi.2)*(pi/2-t).*sin(t) - e*sin(t);xt11 = x11+(r*m11)./(sqrt(n11.2+m11.2);yt11 = y11 - (r*n11)./sqrt(m11.2 +n11.2);xw11 = x11 - (r*m11)./sqrt(m11.2 +n11.2);yw11 = y11 + (r*n11)./sqrt(m11.2 +n11.2)
13、;y = (pi/2):(pi/1000):(3*pi/4);s2 = 60;x2 = (s2 + s0).*cos(y)-e*sin(y);y2 = (s0 + s2).*sin(y) + e*cos(y);n2 = -(s2+s0).*sin(y)-e*cos(y);m2 = (s2+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.
14、2+n2.2);z = (3*pi/4 ):(pi/1000):(43*pi/36);s3 = 60*(43/16 - (9*z)/(4*pi) + 1/(2*pi).*sin (9/2)*z - 27* pi/8);x3 = (s3 + s0).*cos(z)-e*sin(z);y3 = (s0 + s3).*sin(z) + e*cos(z);n3 = -( s3 + s0).*sin(z)+(60*( - 9/(4*pi) + 9/(4*pi).*cos (9/2)*z - 27* pi/8).*cos(z)-e*cos(z);m3 = (s0 + s3).*cos(z)+(60*( -
15、 9/(4*pi) + 9/(4*pi).*cos (9/2)*z - 27* pi/8).*sin(z) - e*sin(z);xt3= x3 + (r*m3)./sqrt(m3.2+n3.2);yt3 = y3 - (r*n3)./sqrt(m3.2+n3.2);xw3 = x3 -(r* m3)./sqrt(n3.2+m3.2);yw3 = y3 + (r*n3)./sqrt(n3.2+m3.2);c = (43*pi/36):(pi/100):( 2*pi);s4 = 0;x4 = (s4 + s0).*cos(c)-e*sin(c);y4 = s0 .*sin(c) + e*cos(
16、c);n4 = -( s4+s0).*sin(c)-e*cos(c);m4 = (s0+s4 ).*cos(c) - e*sin(c);xt4= x4 + (r*m4)./sqrt(m4.2+n4.2);yt4 = y4 - (r*n4)./sqrt(m4.2+n4.2);xw4 = x4 - (r*m4)./sqrt(n4.2+m4.2);yw4 = y4 + (r*n4)./sqrt(n4.2+m4.2);plot(xt1,yt1,b,xt11,yt11,b,xt2,yt2,b,xt3,yt3,b,xt4,yt4,b);xlabel(x/mm)ylabel(y/mm)title(凸轮工作曲线)grid将以上程序的plot(xt1,yt1,b,xt11,yt11,b,xt2,yt2,b,xt3,yt3,b,xt4,yt4,b);改为plot(xw1,yw1,b,xw11,yw11,b,xw2,yw2,b,xw3,yw3,b,xw4,yw4,b);得到内包络线。
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