机械原理二哈工大.docx
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机械原理二哈工大.docx
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机械原理二哈工大
设计
一.设计要求
如图所示的直动从动件盘形凸轮机构,其原始参数见表,据此设计该凸轮机构。
序号
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(︒)
16
70
90
正弦加速度
30
80
3-4-5多项式
70
95
95
二.确定凸轮推杆升程,回程运动方程,并绘制推杆位移、速度、加速度线图。
(设定
)
正弦加速度运动规律
推程
3-4-5多项式运动规律
回程
Matlab编程
x1=0:
pi/1800:
pi/2;
x2=pi/2:
pi/1800:
37*pi/36;
x3=37*pi/36:
pi/1800:
53*pi/36;
x4=53*pi/36:
pi/1800:
2*pi;
w1=1;
s1=70*[2*x1/pi-1/(2*pi)*sin(4*x1)];
v1=70*w1/(pi/2)*[1-cos(4*x1)];
a1=560/pi*sin(4*x1);
s2=70;
v2=0;
a2=0;
T=(x3-37/36*pi)/(4/9*pi);
s3=70*[1-(10*T.^3-15*T.^4+6*T.^5)];
v3=-30*70*w1*T.^2.*(1-2*T+T.^2)/(4*pi/9);
a3=-60*70*T.*(1-3*T+2*T.^2)/[(4*pi/9)]^2;
s4=0;
v4=0;
a4=0;
figure
(1)
plot(x1,s1,x2,s2,'r',x3,s3,x4,s4,'r')
title('推杆线位移图')
xlabel('φ(rad)')
ylabel('S(mm)')
gridon
set(gca,'yTick',-20:
20:
120);
holdoff
figure
(2)
plot(x1,v1,x2,v2,'r',x3,v3,x4,v4,'r')
title('推杆速度图')
xlabel('φ(rad)')
ylabel('v(mm/s)')
set(gca,'yTick',-150:
50:
250);
holdoff
gridon
figure(3)
plot(x1,a1,x2,a2,'r',x3,a3,x4,a4,'r')
title('推杆加速度图')
xlabel('φ(rad)')
ylabel('a(mm/s^2')
set(gca,'yTick',-800:
200:
800);
holdoff
gridon
三.绘制凸轮机构的
线图
因为
用matlab编程可得
x1=0:
pi/1800:
pi/2;
x2=pi/2:
pi/1800:
37*pi/36;
x3=37*pi/36:
pi/1800:
53*pi/36;
x4=53*pi/36:
pi/1800:
2*pi;
w1=1;
s1=70*[2*x1/pi-1/(2*pi)*sin(4*x1)];
v1=70*w1/(pi/2)*[1-cos(4*x1)];
s2=70;
v2=0;
T=(x3-37/36*pi)/(4/9*pi);
s3=70*[1-(10*T.^3-15*T.^4+6*T.^5)];
v3=-30*70*w1*T.^2.*(1-2*T+T.^2)/(4*pi/9);
s4=0;
v4=0;
figure
(1)
plot(v1,s1,v2,s2,'r',v3,s3,v4,s4,'r')
axis([-150150-2080]);
title('ds/d¦Õ-s')
xlabel('ds/d¦Õ')
ylabel('s')
set(gca,'yTick',-10:
10:
80);
holdoff
gridon
四.确定凸轮基圆半径和偏距
确定凸轮轴心的公共许用区域。
推程许用压力角为30度,回程许用压力角为70度,分析得可以选取轴心坐标(50,-100)
确定最小曲率半径
v=[];
symsx1x2x3x4
s0=100;
e=50;
s1=70*[2*x1/pi-1/(2*pi)*sin(4*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);
forxx1=0:
(pi/100):
(pi/2);
k1=subs(abs((tx1*yxx1-txx1*yx1)/(tx1^2+yx1^2)^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);
forxx2=(pi/2):
(pi/100):
(37*pi/36);
k2=subs(abs((tx2*yxx2-txx2*yx2)/(tx2^2+yx2^2)^1.5),{x2},{xx2});
v=[v,1/k2];
end
T=(x3-37/36*pi)/(4/9*pi);
s3=70*[1-(10*T.^3-15*T.^4+6*T.^5)];
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);
forxx3=37*pi/36:
pi/1800:
53*pi/36;
k3=subs(abs((tx3*yxx3-txx3*yx3)/(tx3^2+yx3^2)^1.5),{x3},{xx3});
v=[v,1/k3];
end
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);
forxx4=53*pi/36:
pi/1800:
2*pi;
k4=subs(abs((tx4*yxx4-txx4*yx4)/(tx4^2+yx4^2)^1.5),{x4},{xx4});
v=[v,1/k4];
end
min(v)
ans=76.8927
理论轮廓曲线
x1=0:
pi/1800:
pi/2;
x2=pi/2:
pi/1800:
37*pi/36;
x3=37*pi/36:
pi/1800:
53*pi/36;
x4=53*pi/36:
pi/1800:
2*pi;
x=0:
pi/1800:
2*pi;
s1=70*[2*x1/pi-1/(2*pi)*sin(4*x1)];
v1=70*w1/(pi/2)*[1-cos(4*x1)];
T=(x3-37/36*pi)/(4/9*pi);
s3=70*[1-(10*T.^3-15*T.^4+6*T.^5)];
s4=0;
s0=100;
e=50;
r=(s0^2+e^2)^(1/2);
rx1=(s0+s1).*cos(x1)-e.*sin(x1);
rx2=(s0+s2).*cos(x2)-e.*sin(x2);
rx3=(s0+s3).*cos(x3)-e.*sin(x3);
rx4=(s0+s4).*cos(x4)-e.*sin(x4);
ry1=(s0+s1).*sin(x1)+e.*cos(x1);
ry2=(s0+s2).*sin(x2)+e.*cos(x2);
ry3=(s0+s3).*sin(x3)+e.*cos(x3);
ry4=(s0+s4).*sin(x4)+e.*cos(x4);
plot(r*cos(x),r*sin(x),'y',rx1,ry1,'b',rx2,ry2,'r',rx3,ry3,'b',rx4,ry4,'g');
set(gca,'yTick',-200:
50:
250);
set(gca,'xTick',-200:
50:
250);
xlabel('x/mm');
ylabel('y/mm');
title('理论轮廓曲线&&基圆');
绘制凸轮轮廓曲线。
这里滚子半径选取为38mm进行实际轮廓线的绘制。
则凸轮的工作轮廓方程为:
symsx1x2x3x4;
s1=70*[2*x1/pi-1/(2*pi)*sin(4*x1)];
s2=70;
T=(x3-37/36*pi)/(4/9*pi);
s3=70*[1-(10*T.^3-15*T.^4+6*T.^5)];
s4=0;
s0=100;
e=50;
R=38;
rx1=(s0+s1).*cos(x1)-e.*sin(x1);
rx2=(s0+s2).*cos(x2)-e.*sin(x2);
rx3=(s0+s3).*cos(x3)-e.*sin(x3);
rx4=(s0+s4).*cos(x4)-e.*sin(x4);
ry1=(s0+s1).*sin(x1)+e.*cos(x1);
ry2=(s0+s2).*sin(x2)+e.*cos(x2);
ry3=(s0+s3).*sin(x3)+e.*cos(x3);
ry4=(s0+s4).*sin(x4)+e.*cos(x4);
dy1=diff(ry1,x1,1);
dy2=diff(ry2,x2,1);
dy3=diff(ry3,x3,1);
dy4=diff(ry4,x4,1);
dx1=diff(rx1,x1,1);
dx2=diff(rx2,x2,1);
dx3=diff(rx3,x3,1);
dx4=diff(rx4,x4,1);
X1=rx1-R*dy1/((dx1)^2+(dy1)^2)^(1/2);
X2=rx2-R*dy2/((dx2)^2+(dy2)^2)^(1/2);
X3=rx3-R*dy3/((dx3)^2+(dy3)^2)^(1/2);
X4=rx4-R*dy4/((dx4)^2+(dy4)^2)^(1/2);
Y1=ry1+R*dx1/((dx1)^2+(dy1)^2)^(1/2);
Y2=ry2+R*dx2/((dx2)^2+(dy2)^2)^(1/2);
Y3=ry3+R*dx3/((dx3)^2+(dy3)^2)^(1/2);
Y4=ry4+R*dx4/((dx4)^2+(dy4)^2)^(1/2);
%绘制内包络线%
ezplot(X1,Y1,[0,pi/2]);
holdon
ezplot(X2,Y2,[pi/2,37*pi/36]);
holdon
ezplot(X3,Y3,[37*pi/36,53*pi/36]);
holdon
ezplot(X4,Y4,[53*pi/36,2*pi]);
holdon
%外包络线%
X11=rx1+R*dy1/((dx1)^2+(dy1)^2)^(1/2);
X21=rx2+R*dy2/((dx2)^2+(dy2)^2)^(1/2);
X31=rx3+R*dy3/((dx3)^2+(dy3)^2)^(1/2);
X41=rx4+R*dy4/((dx4)^2+(dy4)^2)^(1/2);
Y11=ry1-R*dx1/((dx1)^2+(dy1)^2)^(1/2);
Y21=ry2-R*dx2/((dx2)^2+(dy2)^2)^(1/2);
Y31=ry3-R*dx3/((dx3)^2+(dy3)^2)^(1/2);
Y41=ry4-R*dx4/((dx4)^2+(dy4)^2)^(1/2);
ezplot(X11,Y11,[0,pi/2]);
axis([-150150-200250]);
set(gca,'yTick',-200:
50:
250);
holdon
ezplot(X21,Y21,[pi/2,10*pi/9]);
holdon
ezplot(X31,Y31,[10*pi/9,14*pi/9]);
holdon
ezplot(X41,Y41,[14*pi/9,2*pi]);
holdon
gridon
title('内包络线,外包络线图');
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