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1、Harbin Institute of TechnologyHarbin Institute of Technology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：直动从动件盘型凸轮机构设计院系：姓名：学号：班级：指导教师：1.1.题目题目设计直动从动件盘形凸轮机构，其原始参数见表1表一升程升程运升程运升程许回程运回程运回程许远休止近休止（mm)动角动规律用压力动角动规律用压力角角（）角（）（）角（）（）（）3070等加等减速3070正弦加速度601001202.2.凸轮推杆运动规律凸轮推杆运动规律（1）推程运动规律（等加速等减速运动）推程0 350推程350 700（2）回程
2、运动规律（正弦加速度）回程1 700 2 400式中开始输入初始参数运行各部分程序输出 1从动件位移、速度、加速度曲线输出 4绘制理论轮廓线和实际轮廓线输出 2ds/d-s 曲线，确定基圆半径和偏距输出 3理论轮廓线上的压力角和曲率半径图结束3.3.运动线图及凸轮运动线图及凸轮ds s线图线图d采用采用 MatlabMatlab 编程，其所有源程序见附页：编程，其所有源程序见附页：令可得运动规律图如下：1.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
3、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大约为（20，-35）经计算取偏距 e=20mm，r0=40.3mm.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：曲率半径数学模型：(dx/d)2(dy/d)23/2(dx/d)(d2y/d2)(dy/d)(d2x/d2)其中：d2x/d22(ds/d)N1N2ecos(N1)(d2s/d2)s0ssin(N1)d2y/d2 2(ds/d)N1N2esin（N1）(d2s/d2)s0scos(N2)3.
4、凸轮理论廓线和实际廓线理论廓线数学模型：x (s0s)sinecosy (s0s)cosesin凸轮实际廓线坐标方程式：x xrt(dx/d)(dx/d)2(dy/d)2(dy/d)(dx/d)2(dy/d)2y y rt其中 rt 为确定的滚子半径。根据上面公式，利用 matlab 编程求解，其代码如下：令 rt=10mm得图如下：相关程序代码：相关程序代码：（1）位移曲线phi1=linspace(0,70/2/180*pi);%推程phi2=linspace(70/2/180*pi,70/180*pi);phi0=70/180*pi;h=30;s1=2*h*(phi1/phi0).2;s
5、2=h-2*h*(phi0-phi2).2/(phi0).2;plot(phi1,s1)hold onplot(phi2,s2)hold onphi3=linspace(deg2rad(70),deg2rad(170),1000);%远休程s3=h;plot(phi3,s3,-b)hold onphi4=linspace(deg2rad(170),deg2rad(240);%回程s4=h*(1-(phi4-phi0-deg2rad(100)/deg2rad(70)+1/2/pi*sin(2*pi*(phi4-phi0-deg2rad(100)/deg2rad(70);plot(phi4,s4)
6、hold onphi5=linspace(deg2rad(240),deg2rad(360),1000);%近休程s5=0;plot(phi5,s5,-b)axis(0,4/3*deg2rad(360),0,0+3/2*h);grid onylabel(位移/mm);xlabel(凸轮转角/rad);（2）速度曲线phi0=deg2rad(70);%推程phi1=linspace(0,deg2rad(70/2);h=30;n=1;w=2*pi*n/60;v1=4*h*w/(deg2rad(70)2*phi1;plot(phi1,v1)hold onphi2=linspace(deg2rad(7
7、0/2),deg2rad(70);v2=4*h*w*(phi0-phi2)/(deg2rad(70)2;plot(phi2,v2)hold onphi3=linspace(deg2rad(70),deg2rad(170),1000);%远休程v3=0;plot(phi3,v3,-b)hold onphi4=linspace(deg2rad(170),deg2rad(240);%回程v4=-h*w/deg2rad(70)*(1-cos(2*pi/deg2rad(70)*(phi4-deg2rad(70)-deg2rad(100);plot(phi4,v4)hold onphi5=linspace
8、(deg2rad(240),deg2rad(360),1000);%近休程v5=0;plot(phi5,v5,-b)grid onylabel(速度/mm/s);xlabel(凸轮转角/rad);（3）加速度曲线phi0=deg2rad(70);phi1=linspace(0,deg2rad(70/2),103);h=30;n=1;w=2*pi*n/60;a1=4*h*w2/(phi0)2;plot(phi1,a1,-b)hold onphi2=linspace(deg2rad(70/2),deg2rad(70),103);a2=-4*h*w2/(phi0)2;plot(phi2,a2,-b)
9、hold onphi3=linspace(deg2rad(70),deg2rad(170),1000);a3=0;plot(phi3,a3,-b)hold onphi4=linspace(deg2rad(170),deg2rad(240);a4=-2*pi*h*w2/(deg2rad(70)2*sin(2*pi/deg2rad(70)*(phi4-deg2rad(70)-deg2rad(100);plot(phi4,a4)hold onphi5=linspace(deg2rad(240),deg2rad(360),1000);a5=0;plot(phi5,a5,-b)hold onphi6=d
10、eg2rad(35),deg2rad(35);a6=4*h*w2/(phi0)2,-4*h*w2/(phi0)2;plot(phi6,a6)grid onylabel(加速度/mm/s2);xlabel(凸轮转角/rad);（4）曲线phi1=linspace(0,70/2/180*pi,1000);phi2=linspace(70/2/180*pi,70/180*pi,1000);phi0=70/180*pi;h=30;s01=2*h*(phi1/phi0).2;s02=h-2*h*(phi0-phi2).2/(phi0).2;phi3=linspace(deg2rad(70),deg2ra
11、d(170),1000);s03=h;phi4=linspace(deg2rad(170),deg2rad(240);s04=h*(1-(phi4-phi0-deg2rad(100)/deg2rad(70)+1/2/pi*sin(2*pi*(phi4-phi0-deg2rad(100)/deg2rad(70);phi5=linspace(deg2rad(240),deg2rad(360),1000)s05=0;%ds/fs1=4*h*phi1/(phi0)2;s2=4*h*(phi0-phi2)/(phi0).2;s3=0;s4=h*(-1/deg2rad(70)+1/deg2rad(70)*
12、cos(2*pi*(phi4-phi0-deg2rad(100)/deg2rad(70);s5=0;x=s1,s2,s3,s4,s5;y=s01,s02,s03,s04,s05;plot(x,y)hold on%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;y1s=min(y1);y2s=min(y2);x=linspace(-50,50,1000);d1=k1*x+y1s;d2=k2*x+y2s;x0=linspace(0,60,200);d0=-k1*x0;plot(x,d1)ho
13、ld onplot(x,d2)hold onplot(x0,d0)grid onaxis(-55,55,-80,40)axis equal%由图像得r0=40.3,e=20 xlabel(ds/d)ylabel(s/mm)（5）压力角曲线h=30;r0=40.3;e=20;N1=1;%凸轮逆时针转N2=1;%偏距为正n=1;omiga=2*pi*n/60;s0=sqrt(r02-e2);phi1=linspace(0,70/2/180*pi);phi2=linspace(70/2/180*pi,70/180*pi);phi0=70/180*pi;s1=2*h*(phi1/phi0).2;s20
14、=h-2*h*(phi0-phi2).2/(phi0).2;v1=4*h*omiga/(deg2rad(70)2*phi1;v2=4*h*omiga*(phi0-phi2)/(deg2rad(70)2;phi3=linspace(deg2rad(70),deg2rad(170),1000);s3=h;phi4=linspace(deg2rad(170),deg2rad(240);s40=h*(1-(phi4-phi0-deg2rad(100)/deg2rad(70)+1/2/pi*sin(2*pi*(phi4-phi0-deg2rad(100)/deg2rad(70);v4=-h*omiga/
15、deg2rad(70)*(1-cos(2*pi/deg2rad(70)*(phi4-deg2rad(70)-deg2rad(100);phi5=linspace(deg2rad(240),deg2rad(360),1000);s5=0;%计算压力角DsDphi1=v1./omiga;rs1=s0+s1;ang1=abs(atan(DsDphi1-N1*N2*e)./rs1)*180/pi;%ang1：推程压力角DsDphi2=v2./omiga;rs3=s0+s20;ang2=abs(atan(DsDphi2-N1*N2*e)./rs3)*180/pi;%ang3：推程压力角DsDphi3=v
16、4./omiga;rs5=s0+s40ang4=abs(atan(DsDphi3-N1*N2*e)./rs5)*180/pi;%ang5：回程压力角rs2=(s0+h)*ones(1,size(s3,2);rs4=s0*ones(1,size(s5,2);ang3=abs(atan(-N1*N2*e)./rs2)*180/pi+0*phi3;%ang2：远休止压力角ang5=abs(atan(-N1*N2*e)./rs4)*180/pi+0*phi5;%ang4：近休止压力角ang=ang1,ang2,ang3,ang4,ang5;phi=phi1,phi2,phi3,phi4,phi5;pl
17、ot(phi,ang)grid onylabel(压力角/);xlabel(凸轮转角/rad);title(压力角曲线)（6）曲率半径曲线h=30;r0=40.3;e=20;N1=1;%凸轮逆时针转N2=1;%偏距为正rt=10;%滚子半径n=1;M=-1;omiga=2*pi*n/60;s0=sqrt(r02-e2);phi1=linspace(0,70/2/180*pi);phi2=linspace(70/2/180*pi,70/180*pi);phi0=70/180*pi;s1=2*h*(phi1/phi0).2;s2=h-2*h*(phi0-phi2).2/(phi0).2;v1=4*
18、h*omiga/(deg2rad(70)2*phi1;a1=4*h*omiga2/(phi0)2+0*phi1;v2=4*h*omiga*(phi0-phi2)/(deg2rad(70)2;a2=-4*h*omiga2/(phi0)2+0*phi2;phi3=linspace(deg2rad(70),deg2rad(170);s3=h+0*phi3;v3=0+0*phi3;a3=0+0*phi3;phi4=linspace(deg2rad(170),deg2rad(240);s4=h*(1-(phi4-phi0-deg2rad(100)/deg2rad(70)+1/2/pi*sin(2*pi*
19、(phi4-phi0-deg2rad(100)/deg2rad(70);v4=-h*omiga/deg2rad(70)*(1-cos(2*pi/deg2rad(70)*(phi4-deg2rad(70)-deg2rad(100);a4=-2*pi*h*omiga2/(deg2rad(70)2*sin(2*pi/deg2rad(70)*(phi4-deg2rad(70)-deg2rad(100);phi5=linspace(deg2rad(240),deg2rad(360);%s5=0+0*phi5;v5=0+0*phi5;a5=0+0*phi5;phi=phi1,phi2,phi3,phi4,
20、phi5;s=s1,s2,s3,s4,s5;v=v1,v2,v3,v4,v5;a=a1,a2,a3,a4,a5;Dx0Dphi=(v./omiga-N2*N1*e).*sin(N1*phi.*pi/180)+N1*(s0+s).*cos(N1*phi.*pi/180);Dy0Dphi=(v./omiga-N2*N1*e).*cos(N1*phi.*pi/180)-N1*(s0+s).*sin(N1*phi.*pi/180);phi=phi1,phi2,phi3,phi4,phi5;s=s1,s2,s3,s4,s5;v=v1,v2,v3,v4,v5;a=a1,a2,a3,a4,a5;DsDphi
21、=v./omiga;DDsDphi=(a./omiga2);DDxDphi=(DDsDphi-s0-s).*sin(N1*phi.*pi/180)+(2*DsDphi-N1*N2*e).*N1.*cos(N1*phi.*pi/180);DDyDphi=(DDsDphi-s0-s).*cos(N1*phi.*pi/180)-(2*DsDphi-N1*N2*e).*N1.*sin(N1*phi.*pi/180);A=(Dx0Dphi.2+Dy0Dphi.2).1.5;B=Dx0Dphi.*DDyDphi-Dy0Dphi.*DDxDphi;rou=A./B;%理论轮廓曲率半径rou0=abs(rou
22、+M*rt);%实际轮廓曲率半径plot(phi,rou0)axis(1,7,0,100)xlabel(凸轮转角/rad)ylabel(曲率半径/mm)grid ontitle(曲率半径曲线)（7）轮廓线h=30;r0=40.3;e=20;N1=1;%凸轮逆时针转N2=1;%偏距为正rt=10;%滚子半径n=1;M=-1;omiga=2*pi*n/60;s0=sqrt(r02-e2);phi1=linspace(0,70/2/180*pi);%推程phi2=linspace(70/2/180*pi,70/180*pi);phi0=70/180*pi;s1=2*h*(phi1/phi0).2;s
23、2=h-2*h*(phi0-phi2).2/(phi0).2;v1=4*h*omiga/(deg2rad(70)2*phi1;a1=4*h*omiga2/(phi0)2+0*phi1;v2=4*h*omiga*(phi0-phi2)/(deg2rad(70)2;a2=-4*h*omiga2/(phi0)2+0*phi2;phi3=linspace(deg2rad(70),deg2rad(170);%远休程s3=h+0*phi3;v3=0+0*phi3;a3=0+0*phi3;phi4=linspace(deg2rad(170),deg2rad(240);%回程s4=h*(1-(phi4-phi
24、0-deg2rad(100)/deg2rad(70)+1/2/pi*sin(2*pi*(phi4-phi0-deg2rad(100)/deg2rad(70);v4=-h*omiga/deg2rad(70)*(1-cos(2*pi/deg2rad(70)*(phi4-deg2rad(70)-deg2rad(100);a4=-2*pi*h*omiga2/(deg2rad(70)2*sin(2*pi/deg2rad(70)*(phi4-deg2rad(70)-deg2rad(100);phi5=linspace(deg2rad(240),deg2rad(360);%近休程s5=0+0*phi5;v5
25、=0+0*phi5;a5=0+0*phi5;phi=phi1,phi2,phi3,phi4,phi5;s=s1,s2,s3,s4,s5;v=v1,v2,v3,v4,v5;a=a1,a2,a3,a4,a5;%理论轮廓线x0=(s0+s).*sin(N1*phi)+N2*e.*cos(N1*phi);y0=(s0+s).*cos(N1*phi)-N2*e.*sin(N1*phi);plot(x0,y0,-g)hold on%计算实际轮廓线Dx0Dphi=(v./omiga-N2*N1*e).*sin(N1*phi)+N1*(s0+s).*cos(N1*phi);Dy0Dphi=(v./omiga-
26、N2*N1*e).*cos(N1*phi)-N1*(s0+s).*sin(N1*phi);if rt=0 x1=x0;y1=y0;else A=sqrt(Dx0Dphi.2+Dy0Dphi.2);x1=x0-N1*M*rt*Dy0Dphi./A;y1=y0+N1*M*rt*Dx0Dphi./A;endplot(x1,y1,r)hold onr1=r0;aerf=0:0.01:2*pi;x2=r1*sin(aerf);y2=r1*cos(aerf);plot(x2,y2,-.)grid onxlabel(凸轮转角/rad)ylabel(长度/mm)legend(理论轮廓线,实际轮廓线,基圆)%小滚子%(20,34.99)x4=20+1*sin(aerf);y4=34.99+1*cos(aerf);x5=20+10*sin(aerf);y5=34.99+10*cos(aerf);x6=20;y6=34.99;y7=110;x=x4,x5,x6,x6;y=y4,y5,y6,y7;plot(x,y,k,LineWidth,2)hold onaxis equal