哈工大机械原理大作业2.docx
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哈工大机械原理大作业2.docx
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哈工大机械原理大作业2
1.原题如下:
设计直动从动件盘形凸轮机构,其原始参数见表1
表一:
凸轮机构原始参数
升程(mm)
升程运动角(º)
升程运动规律
升程许用压力角(º)
回程运动角(º)
回程运动规律
回程许用压力角(º)
远休止角
(º)
近休止角
(º)
140
150
正弦加速度
30
100
等减等加速
60
35
75
解答如下:
1.凸轮推杆运动规律
(1)推程运动规律
推程
式中
且
(2)回程运动规律
回程
式中
3.运动线图及凸轮
线图
采用Matlab编程,其源程序如下:
clear
clc
x1=linspace(0,5*pi/6,300);
x2=linspace(5*pi/6,43*pi/36,300);
x3=linspace(43*pi/36,7*pi/4,300);
x4=linspace(7*pi/4,2*pi,300);
t1=x1/(5*pi/6)
s1=140*(10*t1.^3-15*t1.^4+6*t1.^5);
s2=140;
t2=9*x3/(5*pi)-43/20;
s3=140*(1-(10*t2.^3-15*t2.^4+6*t2.^5));
s4=0;
plot(x1,s1,'k',x2,s2,'k',x3,s3,'k',x4,s4,'k');
xlabel('角度/rad');
ylabel('位移s/mm');
grid;
clear
clc
x1=linspace(0,5*pi/6,300);
x2=linspace(5*pi/6,43*pi/36,300);
x3=linspace(43*pi/36,7*pi/4,300);
x4=linspace(7*pi/4,2*pi,300);
f1=5*pi/6;
t1=x1/f1;
f2=5*pi/9;
t2=(x3-43*pi/36)*9/(5*pi);
v1=(t1.^2-2*t1.^3+t1.^4)*4200/f1;
v2=0;
v3=-30*140*(t2.^2-2*t2.^3+t2.^4)/f2;
v4=0;
plot(x1,v1,'k',x2,v2,'k',x3,v3,'k',x4,v4,'k')
xlabel('角度/rad');
ylabel('速度v/(mm/s)');
grid;
clear
clc
x1=linspace(0,5*pi/6,300);
x2=linspace(5*pi/6,43*pi/36,300);
x3=linspace(43*pi/36,7*pi/4,300);
x4=linspace(7*pi/4,2*pi,300);
f1=5*pi/6;
t1=x1/f1;
f2=5*pi/9;
t2=(x3-43*pi/36)/f2;
a1=60*140*(t1-3*t1.^2+2*t1.^3)/f1^2;
a2=0;
a3=-60*140*(t2-3*t2.^2+2*t2.^3)/f2^2;
a4=0;
plot(x1,a1,'k',x2,a2,'k',x3,a3,'k',x4,a4,'k')
xlabel('角度/rad');
ylabel('加速度a/');
grid;
可得运动规律图如下:
推杆位移:
推杆速度;
推杆加速度:
3、
凸轮机构的
-s线图,并依次确定凸轮的基圆半径和偏距
(1)凸轮机构的
-s线图:
Clear
clc
x1=linspace(0,5*pi/6,300);
x2=linspace(5*pi/6,43*pi/36,300);
x3=linspace(43*pi/36,7*pi/4,300);
x4=linspace(7*pi/4,2*pi,300);
f1=5*pi/6;
t1=x1/f1;
f2=5*pi/9;
t2=(x3-43*pi/36)/f2;
s1=140*(10*t1.^3-15*t1.^4+6*t1.^5);
s2=140;
t2=9*x3/(5*pi)-43/20;
s3=140*(1-(10*t2.^3-15*t2.^4+6*t2.^5));
s4=0;
v1=(t1.^2-2*t1.^3+t1.^4)*4200/f1;
v2=0;
v3=-30*140*(t2.^2-2*t2.^3+t2.^4)/f2;
v4=0;
plot(v1,s1,'r',v2,s2,'r',v3,s3,'r',v4,s4,'r');
xlabel('ds/dψ');
ylabel('位移s/mm');
grid;如图:
2)确定凸轮的基圆半径和偏距:
clear
clc
x1=linspace(0,5*pi/6,300);
x2=linspace(5*pi/6,43*pi/36,300);
x3=linspace(43*pi/36,7*pi/4,300);
x4=linspace(7*pi/4,2*pi,300);
f1=5*pi/6;
t1=x1/f1;
f2=5*pi/9;
t2=(x3-43*pi/36)/f2;
s1=140*(10*t1.^3-15*t1.^4+6*t1.^5);
s2=140;
t2=9*x3/(5*pi)-43/20;
s3=140*(1-(10*t2.^3-15*t2.^4+6*t2.^5));
s4=0;
v1=(t1.^2-2*t1.^3+t1.^4)*4200/f1;
v2=0;
v3=-30*140*(t2.^2-2*t2.^3+t2.^4)/f2;
v4=0;
k1=tan(pi/2-40*pi/180);k2=-tan(pi/6);
f=sym('-k1*(2*k/f1^3-6*k^2/f1^4+4*k^3/f1^5)+k^2/f1^3-2*k^3/f1^4+k^4/f1^5=0');
k=solve(f);
t01=k/f1;
s01=140*(10*t01.^3-15*t01.^4+6*t01.^5);
v01=(t01.^2-2*t01.^3+t01.^4)*4200/f1;
c=87.5056;
d=37.7790;%求出推程切点坐标
x=-200:
1:
200;
y5=k1*(x-c)+d;
f2=5*pi/9;
k2=-tan(pi/6);
f=sym('-k2*(-2*(k*9/(5*pi)-43/20)*9/(5*pi)+6*(k*9/(5*pi)-43/20)^2*9/(5*pi)-4*(k*9/(5*pi)-43/20)^3*9/(5*pi))-(k*9/(5*pi)-43/20)^2+2*(k*9/(5*pi)-43/20)^3-(k*9/(5*pi)-43/20)^4=0');
k=solve(f);
t02=k*9/(5*pi)-43/20;
s02=140*(1-(10*t02.^3-15*t02.^4+6*t02.^5));
v02=-30*140*(t02.^2-2*t02.^3+t02.^4)/f2;
o=29.1715;
p=-118.4712;%求出回程切点坐标
y6=k2*(x-p)+o;
y7=x*-k1;
plot(v1,s1,v2,s2,v3,s3,v4,s4,x,y5,x,y6,x,y7);
xlabel('ds/dψ');
ylabel('位移s/mm');
grid;
如图:
由图确定回转中心所在的区域,取偏距e=20mm,
mm,
则
mm。
四、滚子半径的确定及凸轮理论轮廓和实际轮廓的绘制.
(1)确定滚子半径
clear
clc
s0=80;e=20;r0=sqrt(s0^2+e^2);
forx1=0:
0.01:
5*pi/6;
t1=x1/(5*pi/6);
s1=140*(10*t1.^3-15*t1.^4+6*t1.^5);
xx1=(s0+s1)*cos(x1)-e*sin(x1);
y1=(s0+s1)*sin(x1)+e*cos(x1);
dxx1=-(s0+s1)*sin(x1)-e*cos(x1);
dy1=(s0+s1)*cos(x1)-e*sin(x1);
d2xx1=-(s0+s1)*cos(x1)+e*sin(x1);
d2y1=-(s0+s1)*sin(x1)-e*cos(x1);
p1=(dxx1^2+dy1^2)^1.5/(dxx1*d2y1-d2xx1*dy1);
plot(x1,p1);
holdon;
end
forx2=5*pi/6:
0.01:
43*pi/36;
s2=140;
xx2=(s0+s2)*cos(x2)-e*sin(x2);
y2=(s0+s2)*sin(x2)+e*cos(x2);
dxx2=-(s0+s2)*sin(x2)-e*cos(x2);
dy2=(s0+s2)*cos(x2)-e*sin(x2);
d2xx2=-(s0+s2)*cos(x2)+e*sin(x2);
d2y2=-(s0+s2)*sin(x2)-e*cos(x2);
p2=(dxx2^2+dy2^2)^1.5/(dxx2*d2y2-d2xx2*dy2);
plot(x2,p2);
holdon;
end
forx3=43*pi/36:
0.01:
7*pi/4;
t2=9*x3/(5*pi)-43/20;
s3=140*(1-(10*t2.^3-15*t2.^4+6*t2.^5));
xx3=(s0+s3)*cos(x3)-e*sin(x3);
y3=(s0+s3)*sin(x3)+e*cos(x3);
dxx3=-(s0+s3)*sin(x3)-e*cos(x3);
dy3=(s0+s3)*cos(x3)-e*sin(x3);
d2xx3=-(s0+s3)*cos(x3)+e*sin(x3);
d2y3=-(s0+s3)*sin(x3)-e*cos(x3);
p3=(dxx3^2+dy3^2)^1.5/(dxx3*d2y3-d2xx3*dy3);
plot(x3,p3);
holdon;
end
forx4=7*pi/4:
0.01:
2*pi;
s4=0;
xx4=(s0+s4)*cos(x4)-e*sin(x4);
y4=(s0+s4)*sin(x4)+e*cos(x4);
dxx4=-(s0+s4)*sin(x4)-e*cos(x4);
dy4=(s0+s4)*cos(x4)-e*sin(x4);
d2xx4=-(s0+s4)*cos(x4)+e*sin(x4);
d2y4=-(s0+s4)*sin(x4)-e*cos(x4);
p4=(dxx4^2+dy4^2)^1.5/(dxx4*d2y4-d2xx4*dy4);
plot(x4,p4);
holdon;
end
grid;
如图:
可知最小曲率半径为
所以,小滚子
取小滚子曲率半径
mm
(2)确定凸轮理论廓线,基元及实际廓线。
clear
clc
s0=80;e=20;r0=sqrt(s0^2+e^2);
forx1=0:
0.001:
5*pi/6;
t1=x1/(5*pi/6);
s1=140*(10*t1.^3-15*t1.^4+6*t1.^5);
xx1=(s0+s1)*cos(x1)-e*sin(x1);
y1=(s0+s1)*sin(x1)+e*cos(x1);
plot(xx1,y1);
holdon;
end
forx2=5*pi/6:
0.001:
43*pi/36;
s2=140;
xx2=(s0+s2)*cos(x2)-e*sin(x2);
y2=(s0+s2)*sin(x2)+e*cos(x2);
plot(xx2,y2);
holdon;
end
forx3=43*pi/36:
0.001:
7*pi/4;
t2=9*x3/(5*pi)-43/20;
s3=140*(1-(10*t2.^3-15*t2.^4+6*t2.^5));
xx3=(s0+s3)*cos(x3)-e*sin(x3);
y3=(s0+s3)*sin(x3)+e*cos(x3);
plot(xx3,y3);
holdon;
end
forx4=7*pi/4:
0.001:
2*pi;
s4=0;
xx4=(s0+s4)*cos(x4)-e*sin(x4);
y4=(s0+s4)*sin(x4)+e*cos(x4);
plot(xx4,y4);
holdon;
end
grid;
s0=80;e=20;r0=sqrt(s0^2+e^2);
forfai=0:
0.01:
2*pi;
a=r0*cos(fai);
b=r0*sin(fai);
plot(a,b);
holdon;
end
forx1=0:
0.05:
5*pi/6;
t1=x1/(5*pi/6);
s1=140*(10*t1.^3-15*t1.^4+6*t1.^5);
xx1=(s0+s1)*cos(x1)-e*sin(x1);
y1=(s0+s1)*sin(x1)+e*cos(x1);
plot(xx1,y1);
holdon;
forfai=0:
0.1:
2*pi;
a=xx1+15*cos(fai);
b=y1+15*sin(fai);
plot(a,b);
holdon;
end
end
forx2=5*pi/6:
0.05:
43*pi/36;
s2=140;
xx2=(s0+s2)*cos(x2)-e*sin(x2);
y2=(s0+s2)*sin(x2)+e*cos(x2);
plot(xx2,y2);
holdon;
forfai=0:
0.1:
2*pi;
a=xx2+15*cos(fai);
b=y2+15*sin(fai);
plot(a,b);
holdon;
end
end
forx3=43*pi/36:
0.05:
7*pi/4;
t2=9*x3/(5*pi)-43/20;
s3=140*(1-(10*t2.^3-15*t2.^4+6*t2.^5));
xx3=(s0+s3)*cos(x3)-e*sin(x3);
y3=(s0+s3)*sin(x3)+e*cos(x3);
plot(xx3,y3);
holdon;
forfai=0:
0.1:
2*pi;
a=xx3+15*cos(fai);
b=y3+15*sin(fai);
plot(a,b);
holdon;
end
end
forx4=7*pi/4:
0.05:
2*pi;
s4=0;
xx4=(s0+s4)*cos(x4)-e*sin(x4);
y4=(s0+s4)*sin(x4)+e*cos(x4);
plot(xx4,y4);
holdon;
forfai=0:
0.1:
2*pi;
a=xx4+15*cos(fai);
b=y4+15*sin(fai);
plot(a,b);
holdon;
end
end
gridon;
结果如图所示:
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