机械原理大作业二.docx

1、机械原理大作业二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：速度方程：加速度方程： 2.2 回程运动规律方程（抛物线

2、-直线-抛物线）位移方程： 速度方程：加速度方程：式中，-推程运动角； -远休止角； -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：;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：实际轮廓线数学模型：其中为选定的滚子半径，3. 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fa

3、i0_=pi/2;%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=f

4、ai0+fais+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

5、-1)*(n/fai0_*(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)*one

6、s(1,length(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(从动件位

7、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;hold 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 s

8、t1 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=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-

9、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);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

10、+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(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

11、(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_=25-25*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

12、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)=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 a

13、lpha_0=Alpha1,Alpha5,Alpha2,Alpha3,Alpha4,Alpha6;figure(5);plot(t,alpha_0,r);title(压力角变化曲线);xlabel(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

14、i=1:88 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(fai

15、3(i);endfor 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)+

16、(s0+s2p2(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

17、 s2y6 s2x6;%二阶导数syms rou1 rou2 rou3 rou4 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*

18、sin(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*s

19、2y1-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=

20、diff(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);s2

21、x5=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

22、,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(s

23、ubs(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;endfor j=1:95

24、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;endf

25、or 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*l5x; Y5(j)=c5y(j)-r0*l5y;endfor j=1:210 l6x=eval(subs(s1y6/sqrt(s1x62+s1y62),fai,fai6(j); l6y=eval(subs(s1x6/sqrt(s1x62+s1y62),fai,fai6(j); X6(j)=c6x(j)+r0*l6x; Y6(j)=c6y(j)

26、-r0*l6y;endfigure(6);X=X1,X5,X2,X3,X4,X6;Y=Y1,Y5,Y2,Y3,Y4,Y6;plot(X,Y,r);hold on;5计算结果分析5.1计算结果5.1.1从动件的位移速度加速度线图图3. 从动件的位移图线图4. 从动件的速度图线图5. 从动件的加速度图线5.1.2 凸轮机构线图图6. 凸轮机构线图5.1.3 凸轮的理论轮廓上的曲率半径线图图7. 理论轮廓上曲率半径5.1.3 凸轮的理论轮廓上的压力角线图图8. 理论轮廓上的压力角5.1.4 凸轮的理论轮廓与实际轮廓图9. 凸轮的理论轮廓与实际轮廓5.2计算结果分析通过编程得到的图像与任务书上图像吻合，说明计算及编程无误。通过分别观察从动件的位移、速度和加速度随凸轮转过角度的变化图线，可以发现直动从动件盘形凸轮机构在回程运动规律分为三段。通过绘制凸轮机构的ds/d-s线图及计算凸轮机构的曲率半径，得出滚子的半径取10mm。利用凸轮的理论轮廓和滚子半径可以通过计算编程得到凸轮的实际轮廓。最终将二者显示在图9当中。