机械原理课程设计偏置直动滚子推杆盘形凸轮.docx
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机械原理课程设计偏置直动滚子推杆盘形凸轮
凸轮大作业
选题:
凸轮5-C
一:
题目及原始数据:
利用计算机辅助设计完成偏置直动滚子推杆盘形凸轮机构的设计,已知数据如下所示,凸轮沿逆时针方向做匀速运动。
具体要求如下:
1.推程运动规律为等加速等减速运动,回程运动规律为五次多项式运动;
2.近休凸轮转角为0°-30°;推程凸轮转角30°-210°;远休凸轮转角210°-280°;回程凸轮转角280°-360。
°
3.初选基圆半径为22mm;
4.偏距为+14mm
5.滚子半径为18mm
6.推杆行程为35mm
7.许用压力角为α1=35°,α2=65°。
8.最小曲率半径为0.35rr
9.计算点数取120.
二:
推杆运动规律及凸轮轮廓线方程
1.推程加速阶段:
s1=70.*a1.*a1/pi/pi;
x1=(s0+s1).*sin(a1)+e*cos(a1);
y1=(s0+s1).*cos(a1)-e*sin(a1);
k1=140*a1/pi^2;
i1=[(k1-e).*sin(a1)+(s0+s1).*cos(a1)].*[(k1-e).*(k1-e)+(s0+s1).*(s0+s1)].^(-1/2);
j1=[-(k1-e).*cos(a1)+(s0+s1).*sin(a1)].*[(k1-e).*(k1-e)+(s0+s1).*(s0+s1)].^(-1/2);
x10=x1-18*j1;
y10=y1-18*i1;
2.推程减速阶段:
s11=35-70.*(pi-a11).*(pi-a11)/pi/pi;
x11=(s0+s11).*sin(a11)+e*cos(a11);
y11=(s0+s11).*cos(a11)-e*sin(a11);
k11=140.*(pi-a1)/pi^2;
i11=[(k11-e).*sin(a11)+(s0+s11).*cos(a11)].*[(k11-e).*(k11-e)+(s0+s11).*(s0+s11)].^(-1/2);
j11=[-(k11-e).*cos(a11)+(s0+s11).*sin(a11)].*[(k11-e).*(k11-e)+(s0+s11).*(s0+s11)].^(-1/2);
x101=x11-18*j11;
y101=y11-18*i11;
3.远休阶段:
x2=(s0+s2).*sin(a2)+e*cos(a2);
y2=(s0+s2).*cos(a2)-e*sin(a2);
k2=0;
i2=[(k2-e).*sin(a2)+(s0+s2).*cos(a2)].*[(k2-e).*(k2-e)+(s0+s2).*(s0+s2)].^(-1/2);
j2=[-(k2-e).*cos(a2)+(s0+s2).*sin(a2)].*[(k2-e).*(k2-e)+(s0+s2).*(s0+s2)].^(-1/2);
x20=x2-18*j2;
y20=y2-18*i2;
4.回程阶段:
a30=33*pi/18-a3;
s3=(350.*a30.*a30.*a30/(4*pi/9)^3-525.*a30.*a30.*a30.*a30/(4*pi/9)^4+210.*a30.*a30.*a30.*a30.*a30/(4*pi/9)^5);
x3=(s0+s3).*sin(a3)+e*cos(a3);
y3=(s0+s3).*cos(a3)-e*sin(a3);
k3=-1050.*a30.*a30/(4*pi/9)^3+2100.*a30.*a30.*a30/(4*pi/9)^4-1050.*a30.*a30.*a30.*a30/(4*pi/9)^5;
i3=[(k3-e).*sin(a3)+(s0+s3).*cos(a3)].*[(k3-e).*(k3-e)+(s0+s3).*(s0+s3)].^(-1/2);
j3=[-(k3-e).*cos(a3)+(s0+s3).*sin(a3)].*[(k3-e).*(k3-e)+(s0+s3).*(s0+s3)].^(-1/2);
x30=x3-18*j3;
y30=y3-18*i3;
5.近休阶段:
s4=0;
x4=(s0+s4).*sin(a4)+e*cos(a4);
y4=(s0+s4).*cos(a4)-e*sin(a4);
k4=0;
i4=[(k4-e).*sin(a4)+(s0+s4).*cos(a4)].*[(k4-e).*(k4-e)+(s0+s4).*(s0+s4)].^(-1/2);
j4=[-(k4-e).*cos(a4)+(s0+s4).*sin(a4)].*[(k4-e).*(k4-e)+(s0+s4).*(s0+s4)].^(-1/2);
x40=x4-18*j4;
y40=y4-18*i4;
三:
matlab计算程序
e=14;
r0=22
s0=sqrt(r0^2-e^2);
c111=1;
c3=1;
for(i=1:
0.1:
200)%由压力角条件循环求合适基圆半径
if(c111<35/180)&&(c3<65/180)%判断条件
elsea1=0:
pi/60:
pi/2;%推程加速阶段
s1=70.*a1.*a1/pi/pi;
x1=(s0+s1).*sin(a1)+e*cos(a1);
y1=(s0+s1).*cos(a1)-e*sin(a1);
k1=140*a1/pi^2;%对s1求导
i1=[(k1-e).*sin(a1)+(s0+s1).*cos(a1)].*[(k1-e).*(k1-e)+(s0+s1).*(s0+s1)].^(-1/2);
j1=[-(k1-e).*cos(a1)+(s0+s1).*sin(a1)].*[(k1-e).*(k1-e)+(s0+s1).*(s0+s1)].^(-1/2);
x10=x1-18*j1;
y10=y1-18*i1;
a11=pi/2:
pi/60:
pi;%推程减速阶段
s11=35-70.*(pi-a11).*(pi-a11)/pi/pi;
x11=(s0+s11).*sin(a11)+e*cos(a11);
y11=(s0+s11).*cos(a11)-e*sin(a11);
k11=140.*(pi-a1)/pi^2;
i11=[(k11-e).*sin(a11)+(s0+s11).*cos(a11)].*[(k11-e).*(k11-e)+(s0+s11).*(s0+s11)].^(-1/2);
j11=[-(k11-e).*cos(a11)+(s0+s11).*sin(a11)].*[(k11-e).*(k11-e)+(s0+s11).*(s0+s11)].^(-1/2);
x101=x11-18*j11;
y101=y11-18*i11;
a2=pi:
pi/60:
25*pi/18;%凸轮远休阶段s2=35;%推杆行程
x2=(s0+s2).*sin(a2)+e*cos(a2);
y2=(s0+s2).*cos(a2)-e*sin(a2);
k2=0;
i2=[(k2-e).*sin(a2)+(s0+s2).*cos(a2)].*[(k2-e).*(k2-e)+(s0+s2).*(s0+s2)].^(-1/2);
j2=[-(k2-e).*cos(a2)+(s0+s2).*sin(a2)].*[(k2-e).*(k2-e)+(s0+s2).*(s0+s2)].^(-1/2);
x20=x2-18*j2;
y20=y2-18*i2;
a3=25*pi/18:
pi/60:
33*pi/18;%推杆回程阶段
a30=33*pi/18-a3;
s3=(350.*a30.*a30.*a30/(4*pi/9)^3-525.*a30.*a30.*a30.*a30/(4*pi/9)^4+210.*a30.*a30.*a30.*a30.*a30/(4*pi/9)^5);
x3=(s0+s3).*sin(a3)+e*cos(a3);
y3=(s0+s3).*cos(a3)-e*sin(a3);
k3=-1050.*a30.*a30/(4*pi/9)^3+2100.*a30.*a30.*a30/(4*pi/9)^4-1050.*a30.*a30.*a30.*a30/(4*pi/9)^5;
i3=[(k3-e).*sin(a3)+(s0+s3).*cos(a3)].*[(k3-e).*(k3-e)+(s0+s3).*(s0+s3)].^(-1/2);
j3=[-(k3-e).*cos(a3)+(s0+s3).*sin(a3)].*[(k3-e).*(k3-e)+(s0+s3).*(s0+s3)].^(-1/2);
x30=x3-18*j3;
y30=y3-18*i3;
a4=33*pi/18:
pi/60:
2*pi;%推杆近休阶段
s4=0;
x4=(s0+s4).*sin(a4)+e*cos(a4);
y4=(s0+s4).*cos(a4)-e*sin(a4);
k4=0;
i4=[(k4-e).*sin(a4)+(s0+s4).*cos(a4)].*[(k4-e).*(k4-e)+(s0+s4).*(s0+s4)].^(-1/2);
j4=[-(k4-e).*cos(a4)+(s0+s4).*sin(a4)].*[(k4-e).*(k4-e)+(s0+s4).*(s0+s4)].^(-1/2);
x40=x4-18*j4;
y40=y4-18*i4;
plot(x10,y10,'-g*',x101,y101,'-g+',x20,y20,'-r*',x30,y30,'-b*',x40,y40,'-k*',x1,y1,'-g*',x11,y11,'-g+',x2,y2,'-r*',x3,y3,'-b*',x4,y4,'-k*')
%凸轮轮廓曲线绘制
title(‘凸轮轮廓曲线绘制');
xlabel('VariableX');%X轴
ylabel('VariableY');%Y轴
text(-250,-200,'工作廓线')%文字标注
text(100,-100,'理论廓线');
gridon%加网格
axisequal%坐标相等
a1=0:
pi/60:
pi/2;%压力角计算
force1=abs(atan((k1).*(s0+s1).^-1));
c1=max(force1);
a11=pi/2:
pi/60:
pi;
force11=abs(atan((k11).*(s0+s11).^-1));
c11=max(force11);
c111=max(c1,c11);
a2=pi:
pi/60:
25*pi/18;
force2=abs(atan((k2).*(s0+s2).^-1));
c2=max(force2);
a3=25*pi/18:
pi/60:
33*pi/18;
force3=abs(atan((k3).*(s0+s3).^-1));
c3=max(force3);
a4=33*pi/18:
pi/60:
2*pi;
force4=abs(atan((k4).*(s0+s4).^-1));
c4=max(force4);
r0=r0+1;%每循环一次基圆半径+1
s0=sqrt(r0^2-e^2);
end
end
%求最大压力角位置c111
c3
[m1,n1]=sort(force1);
bend1=n1(end-1+1:
end)
jiaodu1=(bend1(end)-1)*3
[m11,n11]=sort(force11);
bend11=n11(end-1+1:
end)
jiaodu11=(bend11(end)-1)*3+90
[m3,n3]=sort(force3);
bend3=n3(end-1+1:
end)
jiaodu=(bend3(end)-1)*3+250
vv=i1./j1;
vv1=diff(vv);
vv2=diff(vv,2);
vv22=[0,vv2];
p=(1+vv1.^2).^(3/2)./vv22;
g=min(p)
vv1=i11./j11;
vv11=diff(vv1);
vv21=diff(vv1,2);
vv221=[0,vv21];
p1=(1+vv11.^2).^(3/2)./vv221;
g1=min(p1)
vv2=i2./j2;
vv222=diff(vv2);
vv223=diff(vv2,2);
vv2211=[0,vv223];
p2=(1+vv222.^2).^(3/2)./vv2211;
g2=min(p2)
vv=i3./j3;
vv1=diff(vv);
vv2=diff(vv,2);
vv22=[0,vv2];
p=(1+vv1.^2).^(3/2)./vv22;
g3=min(p)
vv=i4./j4;
vv1=diff(vv);
vv2=diff(vv,2);
vv22=[0,vv2];
p=(1+vv1.^2).^(3/2)./vv22;
g4=min(p)
)
ro=sqrt(s0^2+e^2)%求合适基圆半径
x1
y1
x11
y11
x2
y2
x3
y3
x4
y4
x10
y10
x101
y101
x20
y20
x30
y30
x40
y40
force1
force11
force2
force3
force4
c111
c3
jiaodu11
jiaodu3
四:
计算结果及分析:
(1)工作廓线坐标:
1;推程加速阶段X坐标
1424.3835.1846.7357.2667.3578.0088.0898.15108.4117.5127.6136.6144.4153.5161.0168.4176.2182.3189.6195.6200.7205.1210.9214.9217.5220.8223.4225.7226.3227.1
2推程加速阶段Y坐标
209.1208.2206.1204.5202.4199.5195.1191.7186.4181.1176.7170.0163.1156.4149.6141.7133.3124.2115.1106.596.7186.6976.7765.8654.2743.5632.7321.679.954-2.948-14.00
3推程减速阶段X坐标
227.1227.6226.2225.5223.0220.7217.0213.5209.9203.2198.0191.8184.2176.7168.1159.3150.0140.8130.6120.3109.697.4786.6474.5562.4049.4837.1024.7511.31-1.846-14.00
4推程减速阶段Y坐标
-14.00-25.49-37.53-49.81-61.63-73.26-85.13-97.77-108.0-119.2-130.4-141.5-151.1-161.0-170.2-179.7-188.9-196.5-203.4-210.4-217.9-222.8-227.6-232.7-236.7-239.6-241.5-243.3-244.8-244.6-244.1
5远休阶段X坐标
-14.00-26.32-39.22-52.33-64.08-76.02-88.07-100.2-112.7-123.9-134.2-144.9-155.3-164.1-174.6-182.8-191.1-198.4-206.4-212.2-218.5-224.5-229.6-233.2
6远休阶段Y坐标
-244.1-243.3-241.7-239.1-236.2-232.4-228.5-223.4-217.4-211.7-204.5-197.2-189.4-181.9-172.3-163.5-153.9-143.6-132.5-121.7-110.8-98.44-86.42-74.02
7减速阶段X坐标
-234.8-237.0-240.2-242.5-243.4-243.9-242.1-240.3-237.2-233.4-228.4-223.2-217.6-210.2-203.0-196.2-188.0-180.9-171.1-163.9-154.4-145.9-136.8-127.7-118.9-108.7-99.68
8减速阶段Y坐标
-70.40-58.09-45.57-32.20-20.43-7.2505.37218.0030.5742.7654.3365.4576.8287.7797.49106.2115.7124.8132.7140.0147.2154.0161.8167.9173.4179.2185.1
9近休X坐标
-92.81-82.02-72.10-62.45-51.31-40.80-29.29-18.15-7.2643.77613.99
10近休Y坐标
1188.0193.2197.5200.0203.3206.7207.6209.8209.2209.5209.1
(2)理论廓线坐标;
推程加速阶段X坐标
12.0022.8432.2642.6652.7762.4271.1881.6490.9299.81108.7116.4125.1133.8140.0148.9155.9161.8168.9174.3179.9184.9189.0193.9197.2200.4203.3205.1207.8208.8209.7
推程加速阶段Y坐标
191.6190.3189.1187.5184.2182.9178.8174.8170.7165.7160.9155.2149.9142.1136.8128.2121.3113.4104.296.9187.9078.6068.3159.7649.5538.5528.0717.457.054-3.310-14.81
推程减速阶段X坐标
209.0209.9208.7207.1205.0203.4199.7196.8191.2187.6181.2175.8169.0161.6154.5146.2137.2128.5119.4109.799.9788.7677.0266.6355.9144.6932.9620.159.487-2.737-14.15
推程减速阶段Y坐标
-16.14-27.33-38.05-49.38-60.04-71.76-81.88-92.41-102.8-113.4-123.4-132.7-142.3-151.3-159.2-168.1-175.9-183.9-190.4-196.9-202.9-207.9-211.1-215.5-219.5-222.2-224.6-225.3-226.3-226.7-226.5
远休阶段X坐标
-12.74-24.44-36.88-48.94-59.36-71.91-82.89-93.01-104.9-114.7-124.4-134.4-143.3-152.4-161.6-169.2-177.8-184.2-190.6-197.3-202.1-207.0-212.2-216.4远休阶段Y坐标
-226.5-225.5-223.9-221.4-218.1-215.4-211.4-206.5-201.4-195.5-189.3-182.6-175.4-167.4-159.4-151.4-141.1-132.7-122.2-112.2-102.1-91.10-80.69-69.97回程阶段X坐标
-217.4-220.3-222.2-224.3-225.5-225.5-224.0-222.9-219.4-216.9-212.3-207.4-202.0-195.1-189.3-182.7-174.4-167.3-159.1-151.5-142.3-134.1-125.9-117.6-108.7-99.37-90.00
回程阶段Y坐标
-65.52-53.96-42.26-30.33-19.38-7.8053.33914.7425.1436.6847.8857.5267.2177.4586.7095.27103.1111.3119.6126.5133.9140.6146.9153.7158.2164.9169.3
近休阶段X坐标
-84.20-75.30-66.83-56.50-47.71-37.59-27.78-17.93-7.9562.96712.00
近休阶段Y坐标
172.1176.7180.2183.2186.4188.5190.9191.2191.8191.2191.6
凸轮压力角
00.0.0.743390.241860.179030.475370.808280.214470.173310.624600.464810.166590.275080.651490.456750.995420.671040.436690.258220.240840.200710.591830.822590.116060.181120.068860.687940.544470.355570.26052
0.67510.72700.25070.16040.56280.71410.34300.60410.03370.97890.06420.34660.88850.55390.89990.10030.89570.61950