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.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
1424.947931297293835.833579542701846.633166412887357.323071617132667.879859130593578.280303424130088.501415783110898.5204708048515108.315033160764117.862984704875127.142552005136136.132********6144.811332419744153.158********5161.155********0168.780264525614176.015193958402182.841407726263189.240951783976195.196492695966200.691351943287205.709540955551210.235796832989214.255618712129217.755304716715220.721989423648223.143681761924225.009303250807226.308726472013227.032813659341
2推程加速阶段Y坐标
209.532813659341208.532370629552206.998924199561204.935879972465202.347567871334199.239236813805195.617049448531191.488076931747186.860293712014181.742572281261176.144677840557.0772********163.551861181761156.580882432274149.177********6141.356170650697133.131********3124.519659744732115.537106908501106.20142493273596.530940065577186.544783981666976.262880575977765.705931370278654.8953994088027.853*********32.603138828747321.16797538678679.57231483194954-2.158********948-14.0000000000000
3推程减速阶段X坐标
227.032813659341227.134********6226.568905051752225.331644205755223.421214513810220.838411540547217.586454974950213.670985176905209.100050353069203.884084407342.0358********191.570525763878184.505401336072176.860074548737168.656256843411159.917723656843150.670231233150140.941425726738130.760744942876120.159********3109.16982895446697.826447900194786.164658186856474.221152038085562.033691978864049.640972945904837.082480700921024.398347089867511.6292027035831-1.183********846-14.0000000000000
4推程减速阶段Y坐标
-14.0000000000000-25.9228338599749-37.8904674143353-49.8635381159681-61.8024134893063-73.6673405558026-85.4185959941913-97.0166364509177-108.422248415730-119.596697079292-130.501873593764-141.100440163605-151.355972402351-161.233098401750-170.697633972432-179.716713530067-188.258916117849-196.294386074865-203.794947880574-210.734214728044.0876********-222.832864069368-227.949297596606-232.418705078147-236.225024238547-239.354479443456-241.795636066125-243.539445995213-244.579284102998-244.910975527746-244.532813659341
5远休阶段X坐标
-14.0000000000000-26.7786721222032-39.4839457654822-52.0809966579133-64.5352971586108-76.8127108955902-88.8795863311907-100.702848998602-112.250092156677-123.489665614559-134.390762482652-144.923503612169-155.059019491793-164.769529377011.028*********-182.810305697758.0911********-198.848174053764-206.060195464824-212.707420203182-218.771628687875-224.236199344965-229.086154166116-233.308199762282
6远休阶段Y坐标
-244.532813659341-243.464986549453-241.729838834477-239.332126433691-236.278421310122-232.577093457254-228.238287957455-223.273897175014-217.697528159994-211.524465352257-204.771628687875-197.457527222762-189.602208400634-181.227203104369-172.355466641343-163.011315824535-153.220362321829-143.009442456216-132.406543649295-121.440727709697-110.142051176688-98.5414829372844-86.6708193426842-74.5625970566802
7减速阶段X坐标
-234.573962542258-237.924423961410-240.528414701632-242.301034179885-243.179109387654-243.122053300159-242.111828793401-240.152********3-237.266657296952-233.497236106624-228.900808808014-223.546496133102-217.512199933386-210.881086014932-203.738039329490-196.166********2-188.243792502170.0410********-171.618025436311.022*********-154.287835944964-145.434490148429-136.467891333878-127.380539946257-118.153********9-108.759487623767-99.1655915087568
8减速阶段Y坐标
-70.4794512845940-58.1011116825609-45.5418784536957-32.8365161989020-20.0390090002643-7.216945791302505.5538022556637218.194003075560030.625487498405742.774993163817654.577361065243365.978032703814576.934811779208287.418870572067797.4149974868349106.921098432862115.946980634777124.512462892978132.644871079527140.375991577690147.73856828721215
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