1、90等加等减速30504-5-6-7多项式60100120二.凸轮推杆运动规律(1)推程运动规律(等加速等减速运动) 推程 F0=901 位移方程如下:2 速度方程如下: 3 加速度方程如下:(2)回程运动规律(4-5-6-7多项式) 回程 ,F0=90,Fs=100,F0=50其中回程过程的位移方程,速度方程,加速度方程如下:三.运动线图及凸轮线图本题目采用Matlab编程,写出凸轮每一段的运动方程,运用Matlab模拟将凸轮的运动曲线以及凸轮形状表现出来。代码见报告的结尾。1、程序流程框图开始输入凸轮推程回程的运动方程输入凸轮基圆偏距等基本参数输出压力角、曲率半径图像输出ds,dv,da图
2、像结束输出凸轮的构件形状2、运动规律ds图像如下:速度规律dv图像如下:加速度da规律如下图:3.凸轮的基圆半径和偏距 以ds/df-s图为基础,可分别作出三条限制线(推程许用压力角的切界限Dtdt,回程许用压力角的限制线Dtdt,起始点压力角许用线B0d),以这三条线可确定最小基圆半径及所对应的偏距e,在其下方选择一合适点,即可满足压力角的限制条件。得图如下:得最小基圆对应的坐标位置O点坐标大约为(13,-50)经计算取偏距e=13mm,r0=51.67mm.2.绘制理论轮廓线上的压力角曲线和曲率半径曲线针对凸轮转向及推杆偏置,令N1=1凸轮逆时针转;N2=1偏距为正。压力角数学模型:曲率半
3、径数学模型:其中:曲率半径以及压力角的图像如下图:压力角图像:曲率半径图像:3.凸轮理论廓线和实际廓线理论廓线数学模型:凸轮实际廓线坐标方程式:其中R0为确定的滚子半径,令R0=15mm利用Matlab程序写出凸轮的理论廓线和实际廓线以及基圆、偏距圆的曲线方程,并且进行模拟 ,可以得出如下凸轮图像:*附页相关程序代码:1 位移曲线phi1=linspace(0,90/2/180*pi); %phi2=linspace(90/2/180*pi,90/180*pi);phi0=90/180*pi;h=40;s1=2*h*(phi1/phi0).2;s2=h-2*h*(phi0-phi2).2/(p
4、hi0).2;plot(phi1,s1)hold onplot(phi2,s2)phi3=linspace(deg2rad(90),deg2rad(190),1000); %s3=h;plot(phi3,s3,-bphi4=linspace(deg2rad(190),deg2rad(240); %s4=h*(1-35*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).4+84*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).5-70*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).6
5、+20*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).7);plot(phi4,s4)phi5=linspace(deg2rad(240),deg2rad(360),1000); %s5=0;plot(phi5,s5,axis(0,0+11/10*deg2rad(360),0,0+11/10*h);grid onylabel(位移/mm);xlabel(凸轮转角 /rad 速度曲线phi0=deg2rad(90);phi1=linspace(0,deg2rad(90/2);n=1;w=2*pi*n/60;v1=4*h*w/(deg2rad(90).2*p
6、hi1;phi2=linspace(deg2rad(90/2),deg2rad(90);v2=4*h*w*(phi0-phi2)/(deg2rad(90).2;v3=0;v4=-h*w/deg2rad(50)*140*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).3-420*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).4+420*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).5-140*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).6
7、;v5=0;plot(phi1,v1)plot(phi2,v2)plot(phi3,v3,plot(phi4,v4)plot(phi5,v5,速度 /mm凸轮转角/rad加速度曲线phi1=linspace(0,deg2rad(90/2),10.3);a1=4*h*w.2/(phi0).2;phi2=linspace(deg2rad(90/2),deg2rad(90),10.3);a2=-4*h*w.2/(phi0).2;a3=0;a4=-(h*w.2/(deg2rad(50).2)*420*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).2-1680*(
8、phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).3+2100*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).4-840*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).5;a5=0;phi6=deg2rad(45),deg2rad(45);a6=4*h*w.2/(phi0).2,-4*h*w.2/(phi0).2;plot(phi1,a1,plot(phi2,a2,plot(phi3,a3,plot(phi4,a4)plot(phi5,a5)plot(phi6,a6)加速度/mm3
9、、 曲线 %ds/f-sphi1=linspace(0,90/2/180*pi,1000);phi2=linspace(90/2/180*pi,90/180*pi,1000);s01=2*h*(phi1/phi0).2;s02=h-2*h*(phi0-phi2).2/(phi0).2;s03=h;s04=h*(1-35*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).4+84*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).5-70*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).
10、6+20*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).7);phi5=linspace(deg2rad(240),deg2rad(360),1000) s05=0;%ds/fs1=4*h/(deg2rad(90)2*phi1;s2=4*h*(phi0-phi2)/(deg2rad(90)2;s3=0;s4=-h/deg2rad(50)*140*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).3-420*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).4+420*(phi4-de
11、g2rad(90)-deg2rad(100)/deg2rad(50).5-140*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).6;x=s1,s2,s3,s4,s5;y=s01,s02,s03,s04,s05;plot(x,y)%确定凸轮半径和偏距k1=tan(pi/2-30/180*pi);k2=-tan(pi/2-60/180*pi);y1=-k1*x+y;y2=-k2*x+y;y11=min(y1);y22=min(y2);x1=linspace(-5,50,10000);x2=linspace(-95,55,10000);d1=k1*x1+y11
12、;d2=k2*x2+y22;x3=linspace(0,45,500);x3=12;y3=-48;plot(line(0,x3,0,y3)plot(line(x3,x3,0,y3)plot(line(0,x3,y3,y3)plot(x1,d1)plot(x2,d2)axis(-110,60,-100,50)%选取O点x4=13;y4=-50;plot(line(0,x4,0,y4)plot(line(x4,x4,0,y4),kplot(line(0,x4,y4,y4),压力角曲线,曲率半径曲线xo=13;yo=50;%题目2铰链O点取值e=xo;r0=sqrt(xo2+yo2);%基圆半径与偏
13、距取值N1=1;N2=2;R0=15;%小滚子半径n=2;omiga=2*pi*n/60;w=omiga;phi4=linspace(deg2rad(190),deg2rad(240),1000);%推程s1=2*h*(phi1/phi0).2+0*phi1;v1=4*h*w/(deg2rad(90).2*phi1+0*phi1;a1=4*h*w.2/(phi0).2+0*phi1;s2=h-2*h*(phi0-phi2).2/(phi0).2+phi2*0;v2=4*h*w*(phi0-phi2)/(deg2rad(90).2+phi2*0;a2=-4*h*w.2/(phi0).2+phi2
14、*0;%远休程s3=h+phi3*0;v3=0+phi3*0;a3=0+phi3*0;%回程s4=h*(1-35*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).4+84*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).5-70*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).6+20*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).7)+phi4*0;v4=-h*w/deg2rad(50)*140*(phi4-deg2rad(90)-deg2
15、rad(100)/deg2rad(50).3-420*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).4+420*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).5-140*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).6+phi4*0;a4=-(h*w.2/(deg2rad(50).2)*420*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).2-1680*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50)
16、.3+2100*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).4-840*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).5+phi4*0;%近休程s5=0+phi5*0;v5=0+phi5*0;a5=0+phi5*0;%全部运动过程s=s1,s2,s3,s4,s5;v=v1,v2,v3,v4,v5;a=a1,a2,a3,a4,a5;phi=phi1,phi2,phi3,phi4,phi5;%初始推程s0,起点坐标x0,y0%理论廓线s0=sqrt(r02-e2);x0=(s0+s).*sin(N1*phi)+N2*
17、e.*cos(N1*phi);y0=(s0+s).*cos(N1*phi)-N2*e.*sin(N1*phi);LXphi=(v./omiga-N1*N2*e).*sin(N1*phi.*pi/180)+N1*(s0+s).*cos(N1*phi.*pi/180);LYphi=(v./omiga-N1*N2*e).*cos(N1*phi.*pi/180)-N1*(s0+s).*sin(N1*phi.*pi/180);%计算压力角%推程压力角r1=s0+s1;ang1=abs(atan(v1/omiga-N1*N2*e)./r1)*180/pi;r2=s0+s2;ang2=abs(atan(v2
18、/omiga-N1*N2*e)./r2)*180/pi;%回程压力角r4=s0+s4;ang4=abs(atan(v4/omiga-N1*N2*e)./r4)*180/pi;%远休程压力角r3=(s0+h)*ones(1,size(s3,5);ang3=abs(atan(-N1*N2*e)./r3)*180/pi+0*phi3;%近休程压力角r5=s0*ones(1,size(s5,5);ang5=abs(atan(-N1*N2*e)./r5)*180/pi+0*phi5;%凸轮的曲率半径LLXphi=(a./omiga2.-s0-s).*sin(N1*phi.*pi/180)+(2*v./o
19、miga-N1*N2*e).*N1.*cos(N1*phi.*pi/180);LLYphi=(a./omiga2.-s0-s).*cos(N1*phi.*pi/180)-(2*v./omiga-N1*N2*e).*N1.*sin(N1*phi.*pi/180);A=(LXphi.2+LYphi.2).1.5;B=-LXphi.*LLYphi+LYphi.*LLXphi;rou=A./B;M=-1;rou0=abs(rou+M*R0);plot(phi,rou0)axis(0,6,10,100)长度/mmangle=ang1,ang2,ang3,ang4,ang5;plot(phi,angle)
20、axis(0,6,0,100)4、 理论轮廓线和实际轮廓线yo=-50; %题目2铰链O点取值 %基圆半径与偏距取值N2=1; %小滚子半径%回程s4=h*(1-35*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).4+84*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).5-70*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).6+20*(phi4-deg2rad(90)-deg2rad(100)/deg2rad(50).7)+phi4*0;%初始推程s0,起点坐标x0,y0 L
21、X=(v./omiga-N1*N2*e).*sin(N1*phi)+N1*(s0+s).*cos(N1*phi);LY=(v./omiga-N1*N2*e).*cos(N1*phi)-N1*(s0+s).*sin(N1*phi);plot(x0,y0,R,linewidth,2)axis equal%实际廓线M=-1;if R0=0 Sx=x0;Sy=y0;else H=sqrt(LX.2+LY.2); Sx=x0-N1*M*R0*LY./H; Sy=y0+N1*M*R0*LX./H;endplot(Sx,Sy)%画出基圆r1=r0;k=0:0.005:2*pi;x2=r1*sin(k);y2=r1*cos(k);plot(x2,y2,-.%画出偏距圆r2=e;k1=0:0.001:x3=r2*sin(k1);y3
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