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.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
|α|>[α1]?
开始
读入:
r0,Δr0,rt,h或(φ),e或(lAB、lOA)
δ1,δ2,δ3,δ4,[α1],[α2],[ρamin],N
计算:
s0
I=1
计算:
s,x,y,ds/dδ,dx/dδ,dy/dδ,x′,y′
计算:
α
r0=r0+Δr0
r0=r0=Δr0
是回程?
|α|>[α2]?
选出α1max及相应的凸轮转角δ1
选出α2max及相应的凸轮转角δ2
计算:
ρ
ρ<0?
|ρ|-rt≥[ρamin]?
计算ρa选出|ρamin|及相应的凸轮转角δamin
I=I+1
I≤N?
打印:
x,y,x′,y′,ρamin,δamin,α1max,δ1max,α2max,δ2max,r0,δ,s
结束
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(paa C1=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
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