凸轮机构大作业.docx
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凸轮机构大作业
机械原理大作业
凸轮机构设计
(题号:
4-A)
班级
学号
姓名
成绩
同组者
2016年5月14日
目录
(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
程序
#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
数据
第1组数据s=0.000000x=5.000000,y=23.473389;x1=2.916667,y1=13.692810
第2组数据s=0.000000x=6.625241,y=23.067427;x1=3.864724,y1=13.455999
第3组数据s=0.000000x=8.218205,y=22.549082;x1=4.793953,y1=13.153631
第4组数据s=0.000000x=9.771130,y=21.920881;x1=5.699826,y1=12.787181
第5组数据s=0.000000x=11.276451,y=21.185883;x1=6.577930,y1=12.358432
第6组数据s=0.000000x=12.726835,y=20.347670;x1=7.423987,y1=11.869474
第7组数据s=0.000000x=14.115215,y=19.410325;x1=8.233875,y1=11.322689
第8组数据s=0.000000x=15.434827,y=18.378415;x1=9.003649,y1=10.720742
第9组数据s=0.000000x=16.679242,y=17.256967;x1=9.729558,y1=10.066564
第10组数据s=0.000000x=17.842397,y=16.051445;x1=10.408065,y1=9.363343
第11组数据s=0.000000x=18.918626,y=14.767721;x1=11.035865,y1=8.614504
第12组数据s=0.000000x=19.902685,y=13.412051;x1=11.609900,y1=7.823697
第13组数据s=0.000000x=20.789781,y=11.991039;x1=12.127372,y1=6.994773
第14组数据s=0.000000x=21.575590,y=10.511608;x1=12.585761,y1=6.131771
第15组数据s=0.000000x=22.256286,y=8.980965;x1=12.982834,y1=5.238896
第16组数据s=0.000000x=22.828551,y=7.406568;x1=13.316655,y1=4.320498
第17组数据s=0.009859x=23.298459,y=5.800408;x1=13.637197,y1=3.219708
第18组数据s=0.074888x=23.706615,y=4.185421;x1=13.989954,y1=1.821843
第19组数据s=0.239680x=24.097554,y=2.572459;x1=14.385216,y1=0.191177
第20组数据s=0.538042x=24.507799,y=0.957412;x1=14.841722,y1=-1.605194
第21组数据s=0.993827x=24.963745,y=-0.675351;x1=15.369724,y1=-3.495769
第22组数据s=1.621760x=25.480318,y=-2.349452;x1=15.961917,y1=-5.415401
第23组数据s=2.428271x=26.060379,y=-4.092999;x1=16.595549,y1=-7.320538
第24组数据s=3.412322x=26.694836,y=-5.935252;x1=17.241474,y1=-9.196225
第25组数据s=4.566240x=27.363383,y=-7.903549;x1=17.871626,y1=-11.051016
第26组数据s=5.876543x=28.03