1、哈工大机械原理大作业2机械原理大作业二课程名称: 机械原理 设计题目: 凸轮结构设计 学 院: 机电工程学院 班 级: 设 计 者: 学 号: 指导教师: 林琳 刘福利 设计时间: 哈尔滨工业大学一、设计题目(1)凸轮机构运动简图:(2)凸轮机构的原始参数序号升程升程运动角升程运动规律升程许用压力角回程运动角回程运动规律回程许用压力角远休止角近休止角1490120余弦加速度35903-4-5多项式658070(1) 推杆升程、回程运动方程如下:A.推杆升程方程:设为升程位移为: 升程速度为: 升程加速度为: B.推杆回程方程:回程位移为: 回程速度为: 回程加速度为: 其中: (2) 利用Ma
2、tlab绘制推杆位移、速度、加速度线图A.推杆位移线图clcclearx1=linspace(0,2*pi/3,300);x2=linspace(2*pi/3,10*pi/9,300);x3=linspace(10*pi/9,29*pi/18,300);x4=linspace(29*pi/18,2*pi,300);T1=(x3-10*pi/9)/(pi/2);s1=45*(1-cos(1.5*x1)s2=90;s3=90*(1-(10*T1.3-15*T1.4+6*T1.5);s4=0;plot(x1,s1,r,x2,s2,r,x3,s3,r,x4,s4,r) xlabel(角度/rad);y
3、label(位移s/mm)title(推杆位移线图)gridaxis(0,7,-10,100)得到推杆位移线图:B.推杆速度线图clcclearx1=linspace(0,2*pi/3,300);x2=linspace(2*pi/3,10*pi/9,300);x3=linspace(10*pi/9,29*pi/18,300);x4=linspace(29*pi/18,2*pi,300);T1=(x3-10*pi/9)/(pi/2);v1=67.5*1*sin(1.5*x1);v2=0;v3=-30*90*1*T1.2/(pi/2).*(1-2*T1+T1.2);v4=0;plot(x1,v1,
4、r,x2,v2,r,x3,v3,r,x4,v4,r)xlabel(角度/rad);ylabel(速度v/(mm/s)title(推杆速度线图)Grid得到推杆速度线图:C.推杆加速度线图clcclearx1=linspace(0,2*pi/3,300);x2=linspace(2*pi/3,10*pi/9,300);x3=linspace(10*pi/9,29*pi/18,300);x4=linspace(29*pi/18,2*pi,300);T1=(x3-10*pi/9)/(pi/2);a1=101.25*1.2.*cos(1.5*x1);a2=0;a3=-60.*90.*T1./(pi/2
5、).2).*(1-3*T1+2*T1.2);a4=0;plot(x1,a1,r,x2,a2,r,x3,a3,r,x4,a4,r)xlabel(角度/rad);ylabel(加速度a/)title(推杆加速度线图)Grid得到推杆加速度线图:三、凸轮机构的ds/d-s线图,并依次确定凸轮的基圆半径和偏距.1、凸轮机构的ds/d-s线图:x1=linspace(0,2*pi/3,300);x2=linspace(2*pi/3,10*pi/9,300);x3=linspace(10*pi/9,29*pi/18,300);x4=linspace(29*pi/18,2*pi,300);T1=(x3-10
6、*pi/9)/(pi/2);s1=45*(1-cos(1.5*x1)s2=90;s3=90*(1-(10*T1.3-15*T1.4+6*T1.5);s4=0;v1=67.5*1*sin(1.5*x1);v2=0;v3=-30*90*1*T1.2/(pi/2).*(1-2*T1+T1.2);v4=0;plot(v1,s1,r,v2,s2,r,v3,s3,r,v4,s4,r)xlabel(ds/d);ylabel(位移s/mm)title(ds/ds曲线)gridaxis(-120,80,-10,100)得到ds/ds曲线:2、确定凸轮的基圆半径和偏距:在线图中,右侧曲线为升程阶段的类速度-位移图
7、,作直线Dtdt与其相切,且与位移轴正方向呈夹角1=350, 故该直线斜率:通过编程求其角度。% 求升程切点位置转角f=sym(tan(55/180*pi)*3*cos(3*k/2)-2*sin(3*k/2)=0);k=solve(f);pretty(k);x=67.5*sin(3*k)/2);y=45*(1-cos(3/2*k);求的转角近似值k= 0.7560(rad)进而求的切点坐标(x,y)=( 61.1625,25.9633 )左侧曲线为回程阶段的类速度-位移图,作直线Dtdt与其相切,它与位移轴正方向的夹角为2=65, 故该直线斜率tan(-25)令 则。通过编程求其角度。% 求回
8、程切点位置转角f=sym(tan(25/180*pi)*2/pi*(2-6*(2*k/pi-20/9)+4*(2*k/pi-20/9)2)+(2*k/pi-20/9)-2*(2*k/pi-20/9)2+(2*k/pi-20/9)3)=0);k=solve(f);pretty(k);x=-90*2/pi*(10*3*(2*k/pi-20/9).2-15*4*(2*k/pi-20/9).3+6*5*(2*k/pi-20/9).4);y=90*(1-(10*(2*k/pi-20/9).3-15*(2*k/pi-20/9).4+6*(2*k/pi-20/9).5);求得转角近似值k=4.5627,切点
9、为(-80.7164,16.8313)因此:直线Dtdt: y -25.9633 =tan(55/180*pi)*(x-61.1625); 直线Dtdt: y-16.8313=-tan(25/180*pi)*(x+80.7164);又因为,在从动件推程起始点,s=0,且时,有,为保证此时的,作直线与纵坐标交角为,凸轮轴心只能在线上或在其左下方选取。易求直线:y=-tan(55/180*pi)*x;编程如下:x1=linspace(0,2*pi/3,300);x2=linspace(2*pi/3,10*pi/9,300);x3=linspace(10*pi/9,29*pi/18,300);x4=
10、linspace(29*pi/18,2*pi,300);T1=(x3-10*pi/9)/(pi/2);s1=45*(1-cos(1.5*x1)s2=90;s3=90*(1-(10*T1.3-15*T1.4+6*T1.5);s4=0;v1=67.5*1*sin(1.5*x1);v2=0;v3=-30*90*1*T1.2/(pi/2).*(1-2*T1+T1.2);v4=0;plot(v1,s1,r,v2,s2,r,v3,s3,r,v4,s4,r)xlabel(ds/d);ylabel(位移s/mm)title(ds/ds曲线)gridaxis(-120,80,-10,100)hold onx=l
11、inspace(-120,80,300);x1=linspace(0,80,300);y1=tan(55/180*pi)*(x-61.1625)+25.9633;y2=-tan(25/180*pi)*(x+80.7164)+16.8313;y3=-tan(55/180*pi)*x1;plot(x,y1,g,x,y2,g,x1,y3,g)axis(-120,80,-100,120)hold onplot(25,-75,*r)gridaxis equal在轴心公共许用区内取轴心位置,能够满足压力角要求,由于三条直线近似交于一点,现取直线Dtdt 与直线Dtdt的交点为轴心位置,通过解二元一次方组:
12、可以求得:最小基圆对应的轴心坐标大致为(21.4196,-30.7955)为方便可取:偏距e=20mm, ,。下图红点所在位置即设为轴心位置。四、滚子半径的确定及凸轮理论轮廓和实际轮廓的绘制.小滚子半径的确定的MATLAB程序:%确定最小曲率半径clcclearv=;syms x1 x2 x3 x4 x5s0=75;e=20;s1=45*(1-cos(1.5*x1);t1=(s1+s0).*cos(x1)-e*sin(x1);y1=(s0+s1).*sin(x1)-e*cos(x1);tx1=diff(t1,x1);txx1=diff(t1,x1,2);yx1=diff(y1,x1);yxx1
13、=diff(y1,x1,2);for xx1=0:(pi/100):(2*pi/3); k1=subs(abs(tx1*yxx1-txx1*yx1)/(tx12+yx12)1.5),x1,xx1); v=v,1/k1;ends2=90;t2=(s2+s0).*cos(x2)-e*sin(x2);y2=(s0+s2).*sin(x2)-e*cos(x2);tx2=diff(t2,x2);txx2=diff(t2,x2,2);yx2=diff(y2,x2);yxx2=diff(y2,x2,2);for xx2=(2*pi/3):(pi/100):(10*pi/9); k2=subs(abs(tx2
14、*yxx2-txx2*yx2)/(tx22+yx22)1.5),x2,xx2); v=v,1/k2;endT1=(x3-10*pi/9)/(pi/2);s3=90*(1-(10*T1.3-15*T1.4+6*T1.5);t3=(s3+s0).*cos(x3)-e*sin(x3);y3=(s0+s3).*sin(x3)-e*cos(x3);tx3=diff(t3,x3);txx3=diff(t3,x3,2);yx3=diff(y3,x3);yxx3=diff(y3,x3,2);for xx3=(10*pi/9):(pi/100):(29*pi/18); k3=subs(abs(tx3*yxx3-
15、txx3*yx3)/(tx32+yx32)1.5),x3,xx3); v=v,1/k3;ends4=0;t4=(s4+s0).*cos(x4)-e*sin(x4);y4=(s0+s4).*sin(x4)-e*cos(x4);tx4=diff(t4,x4);txx4=diff(t4,x4,2);yx4=diff(y4,x4);yxx4=diff(y4,x4,2);for xx4=(29*pi/18):(pi/100):(2*pi); k4=subs(abs(tx4*yxx4-txx4*yx4)/(tx42+yx42)1.5),x4,xx4); v=v,1/k4;endmin(v)运行程序得:。即
16、,又对重载凸轮,可取,不妨最终设定滚子半径为12mm,这时滚子与凸轮间接触应力最小,可提高凸轮寿命。凸轮轮廓线绘制的MATLAB程序:clcclearh=90;w=1;e=20;rr=12;s0=75;q=120*pi/180;qs=200*pi/180;q1=290*pi/180;for i=1:1:120 qq(i)=i*pi/180.0; s1=h/2.*(1-cos(pi/q*qq(i); v1=pi*h*w/(2*q)*sin(pi/q*qq(i);x(i)=(s0+s1)*sin(qq(i)+e*cos(qq(i);y(i)=(s0+s1)*cos(qq(i)-e*sin(qq(i
17、); a(i)=(s0+s1)*cos(qq(i)-e*sin(qq(i)+v1/w*sin(qq(i);b(i)=-(s0+s1)*sin(qq(i)-e*cos(qq(i)+v1/w*cos(qq(i); xx(i)=x(i)+rr*b(i)/sqrt(a(i)*a(i)+b(i)*b(i);yy(i)=y(i)-rr*a(i)/sqrt(a(i)*a(i)+b(i)*b(i);end for i=120:1:200 qq(i)=i*pi/180; s2=h;v2=0;x(i)=(s0+s2)*sin(qq(i)+e*cos(qq(i);y(i)=(s0+s2)*cos(qq(i)-e*s
18、in(qq(i);a(i)=(s0+s2)*cos(qq(i)-e*sin(qq(i)+v2/w*sin(qq(i);b(i)=-(s0+s2)*sin(qq(i)-e*cos(qq(i)+v2/w*cos(qq(i); xx(i)=x(i)+rr*b(i)/sqrt(a(i)*a(i)+b(i)*b(i);yy(i)=y(i)-rr*a(i)/sqrt(a(i)*a(i)+b(i)*b(i);end for i=201:1:290 qq(i)=i*pi/180; T2=(qq(i)-qs)/pi*2; s3=h.*(1-(10*T2.3-15*T2.4+6*T2.5);v=-30*h*w/p
19、i*2.*T2.2.*(1-2*T2+T2.2);v3=-w*h/(q1-qs);x(i)=(s0+s3)*sin(qq(i)+e*cos(qq(i);y(i)=(s0+s3)*cos(qq(i)-e*sin(qq(i);a(i)=(s0+s3)*cos(qq(i)-e*sin(qq(i)+v3/w*sin(qq(i);b(i)=-(s0+s3)*sin(qq(i)-e*cos(qq(i)+v3/w*cos(qq(i);xx(i)=x(i)+rr*b(i)/sqrt(a(i)*a(i)+b(i)*b(i);yy(i)=y(i)-rr*a(i)/sqrt(a(i)*a(i)+b(i)*b(i);
20、endfor i=291:1:360 qq(i)=i*pi/180;x(i)=(s0+0)*sin(qq(i)+e*cos(qq(i);y(i)=(s0+0)*cos(qq(i)-e*sin(qq(i);a(i)=(s0+0)*cos(qq(i)-e*sin(qq(i);b(i)=-(s0+0)*sin(qq(i)-e*cos(qq(i);xx(i)=x(i)+rr*b(i)/sqrt(a(i)*a(i)+b(i)*b(i);yy(i)=y(i)-rr*a(i)/sqrt(a(i)*a(i)+b(i)*b(i);end plot(x,y,r,xx,yy,b)text(-40,-140,实际轮廓
21、线)text(100,80,理论轮廓线)text(-10,-60,基圆)text(-20,40,偏距圆)hold on for i=1:3:360 for j=1:1:360 xxx(j)=x(i)+rr*cos(j*pi/180); yyy(j)=y(i)+rr*sin(j*pi/180); end plot(xxx,yyy,g) hold onendplot(0,0,*r)hold onfor i=1:1:360 m(i)=79.0569*cos(i*pi/180); n(i)=79.0569*sin(i*pi/180); endfor i=1:1:360 z(i)=25*cos(i*pi/180); l(i)=25*sin(i*pi/180); endplot(m,n,-r,z,l,-r) xlabel(y); ylabel(x); title(凸轮轮廓曲线); axis equal; axis(-175,200,-225,100);得到轮廓线图:
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