机械原理大作业二

1、机械原理大作业二课程名称： 机械原理 设计题目：直动从动件盘形凸轮机构(13) 院 系： 英才学院 班 级： 完 成 者： 学 号： 指导教师： 林琳 设计时间： 2015.5.13 哈尔滨工业大学1. 设计题目 设计如图1所示的直动从动件盘形凸轮机构，其原始参数见表1图1行程（mm）升程运动角（度）升程运动规律升程许用应力角（度）回程运动角（度）回程运动规律回程许用应力角（度）远休程角（度）近休程角（度）4550余弦加速度3590抛-直-抛70100120表12. 凸轮轮廓设计计算数学模型2.1推程运动规律方程位移方程：s=h21-cos(0) , 00速度方程：v=h120sin0 , 0

2、0加速度方程： a=2h2202cos0 , 002.2 回程运动规律方程（抛物线-直线-抛物线）位移方程： s=h-hn22n-10'2-0-s2 , 0+s 0+s+0'n s=h-hn-1n0'-0-s-12 , 0+s+0'n 0+s +0'(n-1)n s=hn22n-1(1-0-s0')2 , 0+s +0'(n-1)n 0+s +0'速度方程：v=-hn21n-10'2-0-s , 0+s 0+s+0'n v=-hn1n-10' , 0+s+0'n 0+s +0'(n-1)nv

3、=-hn21n-10'21-0-s0' , 0+s +0'(n-1)n 0+s +0'加速度方程：a=-hn212n-10'2 , 0+s 0+s+0'n a=0 , 0+s+0'n 0+s +0'(n-1)na=-hn212n-10'2 , 0+s +0'(n-1)n 0+s +0' 式中，0-推程运动角； s-远休止角； 0'-回程运动角2.3滚子半径及凸轮的理论廓线和实际廓线为求滚子许用半径，须确定最小曲率半径，以防止凸轮工作轮廓出现尖点或出现相交包络线，确定最小曲率半径数学模型如下：=dxd

4、2+(dyd)232dxdd2yd2-(dyd)(d2xd2);利用上面的公式可以求得曲率半径的最小值，而后可以确定实际轮廓曲线。理论轮廓线数学模型：x=s0+ssin+ecosy=s0+scos-esin实际轮廓线数学模型：x'=x+r0dxddxd2+dyd2y'=y+r0dyddxd2+dyd2其中r0为选定的滚子半径，s0=r02-e23. 计算流程图图2. 计算流程图4. 计算程序清单编程语言为ATLAB，编程环境为MATLAB R2014a，具体解释见备注clc;clear;h=50;%行程ds=pi/180;fai0=50*ds;%升程运动角fai0_=pi/2;

5、%回程运动角fais=100*ds;%远休止角fais_=120*ds;%近休止角alpha1=35*ds;%升程许用应力角alpha2=70*ds;%回程许用应力角n=5;%给定初始值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+

6、fai0_:0.01:2*pi;%推程s1=h/2*(1-cos(pi/fai0*fai1);v1=pi*h*w/(2*fai0)*sin(pi/fai0*fai1);a1=pi2*h*w2/(2*fai02)*cos(pi/fai0*fai1);%回程抛物线一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);%回程直线s2l=h-h/(n-1)*(n/fa

7、i0_*(fai3-fai0-fais)-1/2);v2l=-h*n*w/(n-1)*fai0_)*ones(1,length(fai3);a2l=zeros(1,length(fai3);%回程抛物线二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);%远休程s3=h/2*(1-cos(pi/fai0*fai0)*ones(1,lengt

8、h(fai5);v3=zeros(1,length(fai5);a3=zeros(1,length(fai5);%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);%从动件位移、速度、加速度图线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(

9、9;从动件位移图线');xlabel('凸轮转过的角度');ylabel('从动件位移');hold on; figure(2);v=v1,v3,v2p1,v2l,v2p2,v4;plot(t,v,'r');grid on;hold on;title('从动件速度图线');xlabel('凸轮转过的角度');ylabel('从动件速度');hold on; figure(3);a=a1,a3,a2p1,a2l,a2p2,a4;plot(t,a,'r');grid on;hol

10、d on;title('从动件加速度图线');xlabel('凸轮转过的角度');ylabel('从动件加速度');hold on; %画ds/d-s图像syms fai st1 st2 st3 st4 diff1 diff2 diff3 diff4;st1=h/2*(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=d

11、iff(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+fai0_/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);k

12、4=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=zeros(1,length(k6); dif=dif1,dif5,dif2,dif3,dif4,dif6;figure(4);plot(dif,s,'k');grid on; hold on;title('凸轮机构ds/d-s图线');xlabel(&

13、#39;ds/d');ylabel('s');hold on;%确定凸轮基圆半径和偏距%先画过原点的直线，该直线与纵坐标轴的夹角为 alpha1x=0:0.01:90;y=-tan(alpha1)*x;plot(x,y,'r');hold on;%画两条边界切线 x0=90*sin(18*0.398/5);y0=25-25*cos(18*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-

14、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;%凸轮实际轮廓cx=50;cy=-45;%基圆圆心坐标e=50;r=sqrt(cx2+cy2);s0=sqrt(r2-e2); %凸轮压力角图线for i=1:88 Alpha1(i)=atan(abs(dif1(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)

15、=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,Alpha2,Alpha3,Alpha4,Alpha6;figure(5);plot(t,alpha_0,'r');title('压力角变化曲线');xlabel(

16、'转过的角度');ylabel('压力角');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('凸轮的理论轮廓与实际轮廓');axis equal;grid on; hold on;%滚子的理论轮廓图线for i=1:88 c1x(i)=e*cos(fai1(i)+(s0+s1(i)*sin(fai1(i)

17、; 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);endfor i=1:32 c4x(i)=e*cos(fai4(i)+(s0+s2p2(

18、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+s2p2(32)*cos(fai6(i);endcpx=c1x,c5x,c2x,c3x,c

19、4x,c6x;cpy=c1y,c5y,c2y,c3y,c4y,c6y;plot(cpx,cpy,'r');hold on; %凸轮的滚子半径及其实际轮廓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;%一阶导数syms s2x1 s2x2 s2x3 s2x4 s2y1 s2y2 s2y3 s2y3 s2x5 s2y5 s2y6 s2x6;%二阶导数syms rou1 rou2 rou3 rou

20、4 rou5 rou6;%曲率半径表达式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*sin(fai)+(s0+st4)*cos(fai);sx5=e*cos(fa

21、i)+(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*s2y1-s2x1*s1y1);rou_1=eval(subs(rou1,fai

22、,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=diff(sy3,fai,2);n3=fai0+fais+fai0_/n:0.

23、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);s2x5=diff(sx5,fai,2);s2y5=diff(sy5,fai,2)

24、;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,n5);n6=fai0+fais+fai0_:0.01:2*pi;rou6=

25、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('曲率半径变化曲线');grid on; hold on;rou_min=min(rou);r0=9;%凸轮的实际轮廓曲线 for j=1:88 l1x=eval(subs(s1y1/sqrt(s1x12

26、+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;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),f