凸轮机构大作业 西工大机械原理.docx
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凸轮机构大作业西工大机械原理
大作业
(二)
凸轮机构设计
(题号:
4-A)
(一)题目及原始数据···············
(二)推杆运动规律及凸轮廓线方程·········
(三)程序框图·········
(四)计算程序·················
(五)程序计算结果及分析·············
(六)凸轮机构图·················
(七)心得体会··················
(八)参考书···················
一题目及原始数据
试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
(1)推程运动规律为五次多项式运动规律,回程运动规律为余弦加速度运动规律;
(2)打印出原始数据;
(3)打印出理论轮廓和实际轮廓的坐标值;
(4)打印出推程和回程的最大压力角,以及出现最大压力角时凸轮的相应转角;
(5)打印出凸轮实际轮廓曲线的最小曲率半径,以及相应的凸轮转角;
(6)打印最后所确定的凸轮的基圆半径。
表一偏置直动滚子推杆盘形凸轮机构的已知参数
题号
初选的基圆半径R0/mm
偏距
E/mm
滚子半径Rr/mm
推杆行程
h/mm
许用压力角
许用最小曲率半径[ρamin]
[α1]
[α2]
4-A
15
5
10
28
30°
70˚
0.3Rr
计算点数:
N=90
q1=60;近休止角δ1
q2=180;推程运动角δ2
q3=90;远休止角δ3
q4=90;回程运动角δ4
二推杆运动规律及凸轮廓线方程
推杆运动规律:
(1)近休阶段:
0o≤δ<60o
s=0;
ds/dδ=0;
=0;
(2)推程阶段:
60o≤δ<180o
五次多项式运动规律:
Q1=Q-60;
s=10*h*Q1*Q1*Q1/(q2*q2*q2)-15*h*Q1*Q1*Q1*Q1/(q2*q2*q2*q2)+6*h*Q1*Q1*Q1*Q1*Q1/(q2*q2*q2*q2*q2);
ds/dδ=30*h*Q1*Q1*QQ/(q2*q2*q2)-60*h*Q1*Q1*Q1*QQ/(q2*q2*q2*q2)+30*h*Q1*Q1*Q1*Q1*QQ/(q2*q2*q2*q2*q2);
=60*h*Q1*QQ*QQ/(q2*q2*q2)-180*h*Q1*Q1*QQ*QQ/((q2*q2*q2*q2))+120*h*Q1*Q1*Q1*QQ*QQ/((q2*q2*q2*q2*q2));
(3)远休阶段:
180o≤δ<270o
s=h=24;
ds/dδ=0;
=0;
(4)回程阶段:
270≤δ<360
Q2=Q-270;
s=h*(1+cos(2*Q2/QQ))/2;
ds/dδ=-h*sin(2*Q2/QQ);
=-2*h*cos(2*Q2/QQ);
凸轮廓线方程:
(1)理论廓线方程:
s0=sqrt(r02-e2)
x=(s0+s)sinδ+ecosδ
y=(s0+s)cosδ-esinδ
(2)实际廓线方程
先求x,y的一、二阶导数
dx=(ds/dδ-e)*sin(δ)+(s0+s)*cos(δ);
dy=(ds/dδ-e)*cos(δ)-(s0+s)*sin(δ);
dxx=dss*sin(δ)+(ds/dδ-e)*cos(δ)+ds/dδ*cos(δ)-(s0+s)*sin(δ);
dyy=dss*cos(δ)-(ds/dδ-e)*sin(δ)-ds/dδ*sin(δ)-(s0+s)*cos(δ);
x1=x-rr*coso;y1=y-rr*sino;
再求sinθ,cosθ
sinθ=x’/sqrt((x’)2+(y’)2)
cosθ=-y’/sqrt((x’)2+(y’)2)
最后求实际廓线方程
x1=x-rr*cosθ;
y1=y-rr*sinθ;
三程序框图
四计算程序
1.
#include
#include
voidmain(){
doubler0,or,rr,h,e,q1,q2,q3,q4,a,a11,a22,Q,pi,pa,paa,QQ,A1,A2,B1,B2,C1,C2;/*定义变量*/
doublexz[90],yz[90],sz[90],x1z[90],y1z[90],Q1,Q2;
doubles0,s,x,y,y1,x1,dx,dxx,dy,dyy,ds,dss,sino,coso,p;
intN,i,j;
r0=19;e=5;h=28;rr=10;q1=60;q2=120;q3=90;q4=90;a11=30;a22=70;or=1;pi=3.141592653;pa=3;/*给已知量赋值*/
N=90;A1=0;B1=0;C1=1000;
for(;;){
Q=0;
C1=1000;
QQ=180/pi;
r0=r0+or;
s0=sqrt(r0*r0-e*e);
for(i=1,j=0;i<=N;i++,j++){
if(Q<60){/*近休阶段*/
s=0;
ds=0;
dss=0;
a=atan(e/sqrt(r0*r0-e*e));/*求压力角*/
if(a>a11/QQ){
break;
}
else{
if(a>A1)
A1=a;
A2=Q;
}
}
elseif(Q>=60&&Q<180){/*五次多项式运动*/
Q1=Q-60;
s=10*h*Q1*Q1*Q1/(q2*q2*q2)-15*h*Q1*Q1*Q1*Q1/(q2*q2*q2*q2)+6*h*Q1*Q1*Q1*Q1*Q1/(q2*q2*q2*q2*q2);
ds=30*h*Q1*Q1*QQ/(q2*q2*q2)-60*h*Q1*Q1*Q1*QQ/(q2*q2*q2*q2)+30*h*Q1*Q1*Q1*Q1*QQ/(q2*q2*q2*q2*q2);
dss=60*h*Q1*QQ*QQ/(q2*q2*q2)-180*h*Q1*Q1*QQ*QQ/((q2*q2*q2*q2))+120*h*Q1*Q1*Q1*QQ*QQ/((q2*q2*q2*q2*q2));
a=atan(fabs(ds-e)/(sqrt(r0*r0-e*e)+s));
if(a>a11/QQ){
break;
}
else{/*远休阶段*/
if(a>A1)
A1=a;
A2=Q;
}
}
elseif(Q>=180&&Q<270){
s=28;
ds=0;dss=0;
a=atan(fabs(ds-e)/(sqrt(r0*r0-e*e)+s));
if(a>a22/QQ){
break;
}
else{
if(a>B1)
B1=a;
B2=Q;
}
}
elseif(Q>=270&&Q<360){/*余弦加速度运动*/
Q2=Q-270;
s=h*(1+cos(2*Q2/QQ))/2;
ds=-h*sin(2*Q2/QQ);
dss=-2*h*cos(2*Q2/QQ);
a=atan(fabs(ds-e)/(sqrt(r0*r0-e*e)+s));
if(a>a22/QQ){
break;
}
else{
if(a>B1)
B1=a;
B2=Q;
}
}
dx=(ds-e)*sin(Q/QQ)+(s0+s)*cos(Q/QQ);
dy=(ds-e)*cos(Q/QQ)-(s0+s)*sin(Q/QQ);
dxx=dss*sin(Q/QQ)+(ds-e)*cos(Q/QQ)+ds*cos(Q/QQ)-(s0+s)*sin(Q/QQ);
dyy=dss*cos(Q/QQ)-(ds-e)*sin(Q/QQ)-ds*sin(Q/QQ)-(s0+s)*cos(Q/QQ);
sino=dx/(sqrt(dx*dx+dy*dy));
coso=-dy/(sqrt(dx*dx+dy*dy));
x=(s0+s)*sin(Q/QQ)+e*cos(Q/QQ);
y=(s0+s)*cos(Q/QQ)-e*sin(Q/QQ);
x1=x-rr*coso;y1=y-rr*sino;
sz[j]=s;
yz[j]=y;
xz[j]=x;
x1z[j]=x1;
y1z[j]=y1;
p=pow(dx*dx+dy*dy,1.5)/(dx*dyy-dy*dxx);/*求理论轮廓曲率半径*/
if(p<0){
paa=(fabs(p)-rr);
if(paa{break;}
else{
if(paaC1=paa;
C2=Q;
}
}
Q=Q+4;
}
if(i==91){break;}
}
for(j=0;j<90;j++){
printf("第%d组数据",j+1);/*输出数据*/
printf("s=%f",sz[j]);
printf("x=%f,y=%f;",xz[j],yz[j]);
printf("x1=%f,y1=%f\n",x1z[j],y1z[j]);
}
printf("r0=%f\n",r0);
printf("推程最大压力角(弧度)=%f,相应凸轮转角=%f\n",A1,A2-4);
printf("回程最大压力角(弧度)=%f,相应凸轮转角=%f\n",B1,B2-4);
printf("最小曲率半径=%f,相应凸轮转角=%f\n",C1,C2-4);
}
2.matalab绘图
x=[5.0000006.6252418.2182059.77113011.27645112.72683514.11521515.43482716.67924217.84239718.91862619.90268520.78978121.57559022.25628622.82855123.29845923.70661524.09755424.50779924.96374525.48031826.06037926.69483627.36338328.03580028.67371529.23272929.66480129.92076829.95290729.71740629.17665028.30122127.07150725.47886523.52624621.22824518.61055115.70875712.5665649.2333765.7613492.201948-1.397906-5.000000-8.578422-12.115052-15.592657-18.994297-22.303399-25.503841-28.580030-31.516981-34.300384-36.916679-39.353120-41.597836-43.639892-45.469338-47.077263-48.455831-49.598328-50.499187-51.154019-51.559634-51.714055-51.616530-51.233453-50.364513-48.991675-47.144744-44.866118-42.209132-39.235944-36.015085-32.618764-29.120045-25.590019-22.095099-18.694544-15.438322-12.365412-9.502600-6.863834-4.450154-2.250205-0.2413031.6089973.3408955.000000];
y=[23.47338923.06742722.54908221.92088121.18588320.34767019.41032518.37841517.25696716.05144514.76772113.41205111.99103910.5116088.9809657.4065685.8004084.1854212.5724590.957412-0.675351-2.349452-4.092999-5.935252-7.903549-10.020601-12.302228-14.755601-17.378031-20.156343-23.066822-26.075733-29.140389-32.210697-35.231149-38.143149-40.887607-43.407693-45.651627-47.575413-49.145373-50.340385-51.153688-51.594160-51.686950-51.473389-50.999220-50.276588-49.309014-48.101211-46.659063-44.989598-43.100947-41.002313-38.703920-36.216966-33.553566-30.726696-27.750129-24.638366-21.406568-18.070478-14.646352-11.150869-7.601061-4.014222-0.4078253.2005596.79215910.32106513.71568716.90757319.83519722.44627024.69965826.56682228.03272429.09616429.76952030.07792830.05790829.75553529.22419528.52206427.70939126.84572025.98717425.18391224.47787223.90090723.473389];
x1=[2.9166673.8647244.7939535.6998266.5779307.4239878.2338759.0036499.72955810.40806511.03586511.60990012.12737212.58576112.98283413.31665513.63719713.98995414.38521614.84172215.36972415.96191716.59554917.24147417.87162618.46105518.98639119.42387919.74858719.93492319.95801319.79539519.42861218.84439318.03524416.99936915.73998714.26421612.58180210.7039848.6426806.4099754.0176121.476005-1.207747-4.033175-6.919656-9.772424-12.577583-15.321465-17.990702-20.572290-23.053652-25.422699-27.667890-29.778285-31.743603-33.554270-35.201463-36.677159-37.974167-39.086169-40.007747-40.734411-41.262621-41.589804-41.714366-41.635699-41.376364-40.850805-40.008452-38.855049-37.403903-35.676949-33.704972-31.526827-29.187728-26.736824-24.224319-21.698402-19.202199-16.770908-14.429195-12.188866-10.046784-7.982989-5.959305-3.919615-1.7954630.4759892.916667];
y1=[13.69281013.45599913.15363112.78718112.35843211.86947411.32268910.72074210.0665649.3633438.6145047.8236976.9947736.1317715.2388964.3204983.2197081.8218430.191177-1.605194-3.495769-5.415401-7.320538-9.196225-11.051016-12.905780-14.783306-16.701480-18.669812-20.688233-22.747295-24.829259-26.909752-28.959788-30.947932-32.842380-34.612723-36.231183-37.673270-38.917916-39.947376-40.747241-41.306893-41.620545-41.688758-41.520236-41.137755-40.554855-39.774375-38.800119-37.636833-36.290183-34.766732-33.073900-31.219936-29.213872-27.065480-24.785228-22.384225-19.874168-17.267286-14.576280-11.814260-8.994681-6.131282-3.238012-0.3289662.5816835.1075827.2405829.32231811.31463413.17822014.87457416.36849017.63062918.63974919.38430219.86321620.08579920.07080319.84472219.43947218.88962018.22947317.49055716.70048615.88498615.07523114.32007613.692810];
plot(x1,y1,x,y,'r'):
五程序计算结果及分析
基圆半径r0=24.000000
推程最大压力角(弧度)=0.513512,相应凸轮转角=172.000000
回程最大压力角(弧度)=0.766377,相应凸轮转角=352.000000
最小曲率半径=14.000000,相应凸轮转角=340.000000
序号
δ
S
X
Y
X1
Y1
1
0
0.000000
5.000000
23.473389
2.916667
13.692810
2
4
0.000000
6.625241
23.067427
3.864724
13.455999
3
8
0.000000
8.218205
22.549082
4.793953
13.153631
4
12
0.000000
9.771130
21.920881
5.699826
12.787181
5
16
0.000000
11.276451
21.185883
6.577930
12.358432
6
20
0.000000
12.726835
20.347670
7.423987
11.869474
7
24
0.000000
14.115215
19.410325
8.233875
11.322689
8
28
0.000000
15.434827
18.378415
9.003649
10.720742
9
32
0.000000
16.679242
17.256967
9.729558
10.066564
10
36
0.000000
17.842397
16.051445
10.408065
9.363343
11
40
0.000000
18.918626
14.767721
11.035865
8.614504
12
44
0.000000
19.902685
13.412051
11.609900
7.823697
13
48
0.000000
20.789781
11.991039
12.127372
6.994773
14
52
0.000000
21.575590
10.511608
12.585761
6.131771
15
56
0.000000
22.256286
8.980965
12.982834
5.238896
16
60
0.000000
22.828551
7.406568
13.316655
4.320498
17
64
0.009859
23.298459
5.800408
13.637197
3.219708
18
68
0.074888
23.706615
4.185421
13.989954
1.821843
19
72
0.239680
24.097554
2.572459
14.385216
0.191177
20
76
0.538042
24.507799
0.957412
14.841722
-1.605194
21
80
0.993827
24.963745
-0.675351
15.369724
-3.495769
22
84
1.621760
25.480318
-2.349452
15.961917
-5.415401
23
88
2.428271
26.060379
-4.092999
16.595549
-7.320538
24
92
3.412322
26.694836
-5.935252
17.241474
-9.196225
25
96
4.566240
27.363383
-7.903549
17.871626
-11.051016
26
100
5.876543
28.035800
-10.020601
18.461055
-12.905780
27
104
7.324772
28.673715
-12.302228
18.986391
-14.783306
28
108
8.888320
29.232729
-14.755601
19.423879
-16.701480
29
112
10.541260
29.664801
-17.378031
19.748587