機械原理大作業(yè)二(共15頁)

1、機械原理(yunl)大作業(yè)二課程名稱： 機械(jxi)原理(yunl) 設計題目：直動從動件盤形凸輪機構(gòu)(13) 院 系： 英才學院 班 級： 完 成 者： 學 號： 指導教師： 林琳 設計時間： 2015.5.13 哈爾濱工業(yè)大學設計(shj)題目(tm) 設計(shj)如圖1所示的直動從動件盤形凸輪機構(gòu)，其原始參數(shù)見表1圖1行程（mm）升程運動角（度）升程運動規(guī)律升程許用應力角（度）回程運動角（度）回程運動規(guī)律回程許用應力角（度）遠休程角（度）近休程角（度）4550余弦加速度3590拋-直-拋70100120表1凸輪輪廓設計計算數(shù)學模型2.1推程運動規(guī)律方程位移方程：s=h21-cos(0

2、) , 00速度方程：v=h120sin0 , 00加速度方程： a=2h2202cos0 , 002.2 回程運動規(guī)律方程（拋物線-直線-拋物線）位移方程： s=h-hn22n-102-0-s2 , 0+s 0+s+0n s=h-hn-1n0-0-s-12 , 0+s+0n 0+s +0(n-1)n s=hn22n-1(1-0-s0)2 , 0+s +0(n-1)n 0+s +0速度(sd)方程(fngchng)：v=-hn21n-102-0-s , 0+s 0+s+0n v=-hn1n-10 , 0+s+0n 0+s +0(n-1)nv=-hn21n-1021-0-s0 , 0+s +0(

3、n-1)n 0+s +0加速度方程(fngchng)：a=-hn212n-102 , 0+s 0+s+0n a=0 , 0+s+0n 0+s +0(n-1)na=-hn212n-102 , 0+s +0(n-1)n 0+s +0 式中，0-推程運動角； s-遠休止角； 0-回程運動角2.3滾子半徑及凸輪的理論廓線和實際廓線為求滾子許用半徑，須確定最小曲率半徑，以防止凸輪工作輪廓出現(xiàn)尖點或出現(xiàn)相交包絡線，確定最小曲率半徑數(shù)學模型如下：=dxd2+(dyd)232dxdd2yd2-(dyd)(d2xd2);利用上面的公式可以求得曲率半徑的最小值，而后可以確定實際輪廓曲線。理論輪廓線數(shù)學模型：x=s

4、0+ssin+ecosy=s0+scos-esin實際輪廓線數(shù)學模型：x=x+r0dxddxd2+dyd2y=y+r0dyddxd2+dyd2其中(qzhng)r0為選定(xun dn)的滾子半徑，s0=r02-e2計算(j sun)流程圖圖2. 計算流程圖計算(j sun)程序清單編程語言為ATLAB，編程環(huán)境(hunjng)為MATLAB R2014a，具體解釋(jish)見備注clc;clear;h=50;%行程ds=pi/180;fai0=50*ds;%升程運動角fai0_=pi/2;%回程運動角fais=100*ds;%遠休止角fais_=120*ds;%近休止角alpha1=35*

5、ds;%升程許用應力角alpha2=70*ds;%回程許用應力角n=5;%給定初始值5w=5;%角速度 fai1=0:0.01:fai0;fai2=fai0+fais:0.01:fai0+fais+fai0_/n;fai3=fai0+fais+fai0_/n:0.01:fai0+fais+fai0_*(n-1)/n;fai4=fai0+fais+fai0_*(n-1)/n:0.01:fai0+fais+fai0_;fai5=fai0:0.01:fai0+fais;fai6=fai0+fais+fai0_:0.01:2*pi;%推程s1=h/2*(1-cos(pi/fai0*fai1);v1=p

6、i*h*w/(2*fai0)*sin(pi/fai0*fai1);a1=pi2*h*w2/(2*fai02)*cos(pi/fai0*fai1);%回程拋物線一s2p1=h-h*n2/(2*(n-1)*fai0_2)*power(fai2-fai0-fais,2);v2p1=-h*n2*w/(n-1)*fai0_2)*(fai2-fai0-fais);a2p1=-h*n2*w2/(n-1)*fai0_2)*ones(1,length(fai2);%回程直線s2l=h-h/(n-1)*(n/fai0_*(fai3-fai0-fais)-1/2);v2l=-h*n*w/(n-1)*fai0_)*o

7、nes(1,length(fai3);a2l=zeros(1,length(fai3);%回程拋物線二s2p2=h*n2/(2*(n-1)*power(1-(fai4-fai0-fais)/fai0_),2);v2p2=-h*n2*w/(n-1)*fai0_)*(1-(fai4-fai0-fais)/fai0_);a2p2=h*n2*w2/(n-1)*fai0_2)*ones(1,length(fai4);%遠休程s3=h/2*(1-cos(pi/fai0*fai0)*ones(1,length(fai5);v3=zeros(1,length(fai5);a3=zeros(1,length(f

8、ai5);%近休程s4=h*n2/(2*(n-1)*power(1-(fai0_)/fai0_),2)*ones(1,length(fai6);v4=zeros(1,length(fai6);a4=zeros(1,length(fai6);%從動件位移(wiy)、速度(sd)、加速度圖線figure(1);s=s1,s3,s2p1,s2l,s2p2,s4;t=fai1,fai5,fai2,fai3,fai4,fai6;plot(t,s,r);grid on;hold on;title(從動件位移(wiy)圖線);xlabel(凸輪轉(zhuǎn)過的角度);ylabel(從動件位移);hold on; fi

9、gure(2);v=v1,v3,v2p1,v2l,v2p2,v4;plot(t,v,r);grid on;hold on;title(從動件速度圖線);xlabel(凸輪轉(zhuǎn)過的角度);ylabel(從動件速度);hold on; figure(3);a=a1,a3,a2p1,a2l,a2p2,a4;plot(t,a,r);grid on;hold on;title(從動件加速度圖線);xlabel(凸輪轉(zhuǎn)過的角度);ylabel(從動件加速度);hold on; %畫ds/d-s圖像syms fai st1 st2 st3 st4 diff1 diff2 diff3 diff4;st1=h/2

10、*(1-cos(pi/fai0*fai);diff1=diff(st1,fai);k1=0:0.01:fai0;dif1=eval(subs(diff1,fai,k1);st2=h-h*n2/(2*(n-1)*fai0_2)*power(fai-fai0-fais,2);diff2=diff(st2,fai);k2=fai0+fais:0.01:fai0+fais+fai0_/n;dif2=eval(subs(diff2,fai,k2);st3=h-h/(n-1)*(n/fai0_*(fai-fai0-fais)-1/2);diff3=diff(st3,fai);k3=fai0+fais+fa

11、i0_/n:0.01:fai0+fais+fai0_*(n-1)/n;dif3=ones(1,length(k3)*eval(diff3);st4=h*n2/(2*(n-1)*power(1-(fai-fai0-fais)/fai0_),2);diff4=diff(st4,fai);k4=fai0+fais+fai0_*(n-1)/n:0.01:fai0+fais+fai0_;dif4=eval(subs(diff4,fai,k4);k5=fai0:0.01:fai0+fais;k6=fai0+fais+fai0_:0.01:2*pi;dif5=zeros(1,length(k5);dif6=

12、zeros(1,length(k6); dif=dif1,dif5,dif2,dif3,dif4,dif6;figure(4);plot(dif,s,k);grid on; hold on;title(凸輪(tln)機構(gòu)(jgu)ds/d-s圖線);xlabel(ds/d);ylabel(s);hold on;%確定(qudng)凸輪基圓半徑和偏距%先畫過原點的直線，該直線與縱坐標軸的夾角為 alpha1x=0:0.01:90;y=-tan(alpha1)*x;plot(x,y,r);hold on;%畫兩條邊界切線 x0=90*sin(18*0.398/5);y0=25-25*cos(18*

13、0.398/5);x=0:0.01:90;y=tan(pi/2-alpha1)*(x-x0)+y0;plot(x,y,r);hold on;x0_=90*sin(18*2.177/5);y0_=25-25*cos(18*2.177/5);x_=-50:0.01:90;y_=tan(pi/2+alpha2)*(x_+x0_)+y0_;plot(x_,y_,r)hold on;%凸輪實際輪廓cx=50;cy=-45;%基圓圓心坐標e=50;r=sqrt(cx2+cy2);s0=sqrt(r2-e2); %凸輪(tln)壓力(yl)角圖線for i=1:88 Alpha1(i)=atan(abs(d

14、if1(i)-e)/(s0+s1(i);endfor i=1:32 Alpha2(i)=atan(abs(dif2(i)-e)/(s0+s2p1(i);endfor i=1:95 Alpha3(i)=atan(abs(dif3(i)-e)/(s0+s2l(i);endfor i=1:32 Alpha4(i)=atan(abs(dif4(i)-e)/(s0+s2p2(i);endfor i=1:175 Alpha5(i)=atan(e/(s0+s1(88);endfor i=1:210 Alpha6(i)=atan(e/(s0+s2p2(32);end alpha_0=Alpha1,Alpha5

15、,Alpha2,Alpha3,Alpha4,Alpha6;figure(5);plot(t,alpha_0,r);title(壓力(yl)角變化曲線);xlabel(轉(zhuǎn)過的角度);ylabel(壓力角);grid on;hold on;figure(6);m=0:0.01:2*pi;x=r*cos(m);y=r*sin(m);xe=e*cos(m);ye=e*sin(m);plot(x,y,k);hold on;plot(xe,ye,k);title(凸輪的理論輪廓與實際輪廓);axis equal;grid on; hold on;%滾子(n z)的理論(lln)輪廓圖線for i=1:88

16、 c1x(i)=e*cos(fai1(i)+(s0+s1(i)*sin(fai1(i); c1y(i)=-e*sin(fai1(i)+(s0+s1(i)*cos(fai1(i);endfor i=1:32 c2x(i)=e*cos(fai2(i)+(s0+s2p1(i)*sin(fai2(i); c2y(i)=-e*sin(fai2(i)+(s0+s2p1(i)*cos(fai2(i);endfor i=1:95 c3x(i)=e*cos(fai3(i)+(s0+s2l(i)*sin(fai3(i); c3y(i)=-e*sin(fai3(i)+(s0+s2l(i)*cos(fai3(i);e

17、ndfor i=1:32 c4x(i)=e*cos(fai4(i)+(s0+s2p2(i)*sin(fai4(i); c4y(i)=-e*sin(fai4(i)+(s0+s2p2(i)*cos(fai4(i);endfor i=1:175 c5x(i)=e*cos(fai5(i)+(s0+s1(88)*sin(fai5(i); c5y(i)=-e*sin(fai5(i)+(s0+s1(88)*cos(fai5(i);endfor i=1:210 c6x(i)=e*cos(fai6(i)+(s0+s2p2(32)*sin(fai6(i); c6y(i)=-e*sin(fai6(i)+(s0+s2

18、p2(32)*cos(fai6(i);endcpx=c1x,c5x,c2x,c3x,c4x,c6x;cpy=c1y,c5y,c2y,c3y,c4y,c6y;plot(cpx,cpy,r);hold on; %凸輪(tln)的滾子半徑及其實際輪廓syms sx1 sx2 sx3 sx4 sy1 sy2 sy3 sy4 sx5 sx6 sy5 sy6;syms s1x1 s1x2 s1x3 s1x4 s1y1 s1y2 s1y3 s1y4 s1x5 s1y5 s1y6 s1x6;%一階導數(shù)syms s2x1 s2x2 s2x3 s2x4 s2y1 s2y2 s2y3 s2y3 s2x5 s2y5

19、s2y6 s2x6;%二階導數(shù)syms rou1 rou2 rou3 rou4 rou5 rou6;%曲率半徑表達式sx1=e*cos(fai)+(s0+st1)*sin(fai);sy1=-e*sin(fai)+(s0+st1)*cos(fai);sx2=e*cos(fai)+(s0+st2)*sin(fai);sy2=-e*sin(fai)+(s0+st2)*cos(fai);sx3=e*cos(fai)+(s0+st3)*sin(fai);sy3=-e*sin(fai)+(s0+st3)*cos(fai);sx4=e*cos(fai)+(s0+st4)*sin(fai);sy4=-e*s

20、in(fai)+(s0+st4)*cos(fai);sx5=e*cos(fai)+(s0+s1(88)*sin(fai);sy5=-e*sin(fai)+(s0+s1(88)*cos(fai);sx6=e*cos(fai)+(s0+s2p2(32)*sin(fai);sy6=-e*sin(fai)+(s0+s2p2(32)*cos(fai);s1x1=diff(sx1,fai);s1y1=diff(sy1,fai);s2x1=diff(sx1,fai,2);s2y1=diff(sy1,fai,2);n1=0:0.01:fai0;rou1=abs(s1x12+s1y12)1.5/(s1x1*s2

21、y1-s2x1*s1y1);rou_1=eval(subs(rou1,fai,n1);s1x2=diff(sx2,fai);s1y2=diff(sy2,fai);s2x2=diff(sx2,fai,2);s2y2=diff(sy2,fai,2);n2=fai0+fais:0.01:fai0+fais+fai0_/n;rou2=abs(s1x22+s1y22)1.5/(s1x2*s2y2-s2x2*s1y2);rou_2=eval(subs(rou2,fai,n2);s1x3=diff(sx3,fai);s1y3=diff(sy3,fai);s2x3=diff(sx3,fai,2);s2y3=d

22、iff(sy3,fai,2);n3=fai0+fais+fai0_/n:0.01:fai0+fais+fai0_*(n-1)/n;rou3=abs(s1x32+s1y32)1.5/(s1x3*s2y3-s2x3*s1y3);rou_3=eval(subs(rou3,fai,n3);s1x4=diff(sx4,fai);s1y4=diff(sy4,fai);s2x4=diff(sx4,fai,2);s2y4=diff(sy4,fai,2);s1y5=diff(sy5,fai);s1x5=diff(sx5,fai);s1x6=diff(sx6,fai);s1y6=diff(sy6,fai);s2x

23、5=diff(sx5,fai,2);s2y5=diff(sy5,fai,2);s2y6=diff(sy6,fai,2);s2x6=diff(sx6,fai,2);n4=fai0+fais+fai0_*(n-1)/n:0.01:fai0+fais+fai0_;rou4=abs(s1x42+s1y42)1.5/(s1x4*s2y4-s2x4*s1y4);rou_4=eval(subs(rou4,fai,n4);n5=fai0:0.01:fai0+fais;rou5=abs(s1x52+s1y52)1.5/(s1x5*s2y5-s2x5*s1y5);rou_5=eval(subs(rou5,fai,

24、n5);n6=fai0+fais+fai0_:0.01:2*pi;rou6=abs(s1x62+s1y62)1.5/(s1x6*s2y6-s2x6*s1y6);rou_6=eval(subs(rou6,fai,n6);rou=rou_1,rou_5,rou_2,rou_3,rou_4,rou_6;n_=n1,n5,n2,n3,n4,n6;figure(7);plot(n_,rou,b);axis(0 4.5 0 100)title(曲率(ql)半徑(bnjng)變化曲線);grid on; hold on;rou_min=min(rou);r0=9;%凸輪(tln)的實際輪廓曲線 for j=

25、1:88 l1x=eval(subs(s1y1/sqrt(s1x12+s1y12),fai,fai1(j); l1y=eval(subs(s1x1/sqrt(s1x12+s1y12),fai,fai1(j); X1(j)=c1x(j)+r0*l1x; Y1(j)=c1y(j)-r0*l1y;endfor j=1:32 l2x=eval(subs(s1y2/sqrt(s1x22+s1y22),fai,fai2(j); l2y=eval(subs(s1x2/sqrt(s1x22+s1y22),fai,fai2(j); X2(j)=c2x(j)+r0*l2x; Y2(j)=c2y(j)-r0*l2y

26、;endfor j=1:95 l3x=eval(subs(s1y3/sqrt(s1x32+s1y32),fai,fai3(j); l3y=eval(subs(s1x3/sqrt(s1x32+s1y32),fai,fai3(j); X3(j)=c3x(j)+r0*l3x; Y3(j)=c3y(j)-r0*l3y;endfor j=1:32 l4x=eval(subs(s1y4/sqrt(s1x42+s1y42),fai,fai4(j); l4y=eval(subs(s1x4/sqrt(s1x42+s1y42),fai,fai4(j); X4(j)=c4x(j)+r0*l4x; Y4(j)=c4y(j)-r0*l4y;endfor j=1:175 l5x=eval(subs(s1y5/sqrt(s1x52+s1y52),fai,fai5(j); l5y=eval(subs(s1x5/sqrt(s1x52+s1y52),fai,fai5(j); X5(j)=c5x(j)+r0