凸轮连杆机构课程设计

1、第1章 固定凸轮连杆机构参数选取1. 确定驱动方案 图1如上图所示，设：与从动杆升程运动相对应的曲柄转角为，即;而与降程运动相对应的曲柄转角为，即,则：（1） 当时，选用曲柄AB拉着BC杆运动的方案。（2） 当时，选用曲柄AB推着BC杆运动的方案。（3） 当时，任选其中一种驱动方案。已知数据，很明显，所以选用方案2。2.确定e直动从动杆，取，取3. 确定h从结构紧凑和减小凸轮压力角考虑，应将h值取小些。但h值愈小，对从动杆驱动力的压力角也愈大。通常取，去4. 确定a若a值过小，会使凸轮压力角明显增大，甚至不能实现预期动动。可取a=0.60.9Sm或a=1.21.8lsin。取a=70mm6、确

2、定其值对凸轮的压力角影响极大，过小，尤其是过大，会使压力角急剧增加。在前述参数确定后，最好将优化，目标函数为 a1m() （a1m）min式中a1m为凸轮的最大压力角。暂时取7. 求算b1、b2须先求算bmax、bmin。依据铰销B、D的坐标，可建立它们之间距离的公式。B的坐标为 D的坐标为 式中 曲柄转角，取升程起始时的 =0°；S 与相对应的从动杆位移，即铰销D至其最低位置的距离。S值分为升程（=01）、最高位置停留（=11+2）、降程（=1+21+2+3）、最低位置停留（=1+2+3360°）四个阶段求算。b值为 b= （1）用matlab编程画出b与曲线图，并算出：

3、clearsm=100;h=120;e=0;a=70;d=8*pi/180;fa1=110*pi/180;fa2=0*pi/180;fa3=150*pi/180;fa4=100*pi/180;fa01=0:0.001:fa1;s=sm/2*(1-cos(pi*fa01/fa1);xb=a*sin(d+fa01);yb=-a*cos(d+fa01);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);plot(fa01,b);max(b)min(b)hold on;fa02=fa1;s=sm;xb=a*sin(d+fa02);yb=-a*cos(d+fa02);xd=e

4、;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);plot(fa02,b,'r-d');max(b)min(b)hold on;fa03=fa1+fa2:0.001:fa1+fa2+fa3;s=sm*(1-(fa03-fa1-fa2)/fa3+1/(2*pi)*sin(2*pi*(fa03-fa1-fa2)/fa3);xb=a*sin(d+fa03);yb=-a*cos(d+fa03);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);plot(fa03,b,'g-');max(b)min(b)hold on;fa

5、04=fa1+fa2+fa3:0.001:fa1+fa2+fa3+fa4;s=0;xb=a*sin(d+fa04);yb=-a*cos(d+fa04);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);plot(fa04,b,'r-');max(b)min(b)xlabel('fa');ylabel('b');title('fa-b');运行结果：ans = 217.0095ans = 189.3564b = 197.0794b = 197.0794ans = 197.0794ans = 94.1923

6、ans = 190.0000ans = 136.7980由以上结果可以看出 并且b取最大值时，fa=1.21.4；b取最小值时，fa=3.53.7（2） 根据计算 解得： b1 =61.4086 b2 =155.60098、设计凸轮廊线固定凸轮的理论廊线就是滚子中心C的运动轨迹线，根据铰销B、D的位置及b1、b2值可确定C的位置。参阅1，令铰销B、D的连线BD与DOD1线（或y轴）的夹角为，BD与CD的夹角为，则 显然，XBXD时为正值，反之则为负值，而始终为正值。这样，铰销C的坐标为 该式对直动和摆动两种从动杆类型都适用，运算符号“+”和“”的确定原则是：令B=bmax 时的为 m， b=b

7、时的为m，则对于AB推动BC的驱动方案（如图4所示），在 = mm区间，取“”号；在 =0 m和 =m360°区间，取“+”对于AB拉动BC的驱动方案，则刚好相反。（1） 用matlab求famax、faminclearsm=100;h=120;e=0;a=70;d=8*pi/180;fa1=110*pi/180;fa2=0*pi/180;fa3=150*pi/180;fa4=100*pi/180;fa01=1.2:0.01:1.4;s=sm/2*(1-cos(pi*fa01/fa1);xb=a*sin(d+fa01);yb=-a*cos(d+fa01);xd=e;yd=h+s;b1

8、=sqrt(xb-xd).2+(yb-yd).2);f=polyval(b1,fa01);fa03=3.5:0.01:3.7;s=sm*(1-(fa03-fa1-fa2)/fa3+1/(2*pi)*sin(2*pi*(fa03-fa1-fa2)/fa3);xb=a*sin(d+fa03);yb=-a*cos(d+fa03);xd=e;yd=h+s;b3=sqrt(xb-xd).2+(yb-yd).2);f=polyval(b3,fa03);运行结果：>> b1b1 = Columns 1 through 13 216.1970 216.3140 216.4223 216.5220

9、216.6128 216.6945 216.7672 216.8306 216.8846 216.9291 216.9639 216.9890 217.0042 Columns 14 through 21 217.0095 217.0046 216.9896 216.9642 216.9284 216.8821 216.8252 216.7575>> fa01fa01 = Columns 1 through 13 1.2000 1.2100 1.2200 1.2300 1.2400 1.2500 1.2600 1.2700 1.2800 1.2900 1.3000 1.3100 1

10、.3200 Columns 14 through 21 1.3300 1.3400 1.3500 1.3600 1.3700 1.3800 1.3900 1.4000>> b3b3 = Columns 1 through 13 94.6116 94.5076 94.4185 94.3443 94.2848 94.2401 94.2101 94.1946 94.1936 94.2070 94.2347 94.2766 94.3325 Columns 14 through 21 94.4023 94.4859 94.5832 94.6940 94.8182 94.9555 95.106

11、0 95.2693>> fa03fa03 = Columns 1 through 13 3.5000 3.5100 3.5200 3.5300 3.5400 3.5500 3.5600 3.5700 3.5800 3.5900 3.6000 3.6100 3.6200 Columns 14 through 213.6300 3.6400 3.6500 3.6600 3.6700 3.6800 3.6900 3.7000由以上数据可以看出： famax=1.33famin=3.58(2) 凸轮的设计clearsm=100;h=120;e=0;a=70;d=8*pi/180;fa1=1

12、10*pi/180;fa2=0*pi/180;fa3=150*pi/180;fa4=100*pi/180;famax=1.33;famin=3.58;b1=61.4086;b2=155.6009;fa01=0:0.002:famax;s=sm/2*(1-cos(pi*fa01/fa1);xb=a*sin(d+fa01);yb=-a*cos(d+fa01);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);theta1=asin(xb-xd)./b);beta1=acos(b.2+b2.2-b1.2)./(2*b*b2);xc=xd+b2*sin(theta1+bet

13、a1);yc=yd-b2*cos(theta1+beta1);plot(xc,yc);hold on;fa02=famax:0.002:fa1;s=sm/2*(1-cos(pi*fa02/fa1);xb=a*sin(d+fa02);yb=-a*cos(d+fa02);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);theta1=asin(xb-xd)./b);beta1=acos(b.2+b2.2-b1.2)./(2*b*b2);xc=xd+b2*sin(theta1-beta1);yc=yd-b2*cos(theta1-beta1);plot(xc,yc,

14、9;r');hold on;fa03=fa1+fa2:0.002:famin;s=sm*(1-(fa03-fa1-fa2)/fa3+1/(2*pi)*sin(2*pi*(fa03-fa1-fa2)/fa3);xb=a*sin(d+fa03);yb=-a*cos(d+fa03);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);theta1=asin(xb-xd)./b);beta1=acos(b.2+b2.2-b1.2)./(2*b*b2);xc=xd+b2*sin(theta1-beta1);yc=yd-b2*cos(theta1-beta1);plot(

15、xc,yc);hold on;fa04=famin:0.002:fa1+fa2+fa3;s=sm*(1-(fa04-fa1-fa2)/fa3+1/(2*pi)*sin(2*pi*(fa04-fa1-fa2)/fa3);xb=a*sin(d+fa04);yb=-a*cos(d+fa04);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);theta1=asin(xb-xd)./b);beta1=acos(b.2+b2.2-b1.2)./(2*b*b2);xc=xd+b2*sin(theta1+beta1);yc=yd-b2*cos(theta1+beta1);plot

16、(xc,yc,'r');hold on;fa05=fa1+fa2+fa3:0.002:fa1+fa2+fa3+fa4;s=0;xb=a*sin(d+fa05);yb=-a*cos(d+fa05);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);theta1=asin(xb-xd)./b);beta1=acos(b.2+b2.2-b1.2)./(2*b*b2);xc=xd+b2*sin(theta1+beta1);yc=yd-b2*cos(theta1+beta1);plot(xc,yc);title('凸轮轮廓曲线'); 9.检验压

17、力角（1）凸轮的压力角1 参阅图1，1为PC和Vc的夹角。PC为驱动铰销运动的力(不考虑摩擦力)，BC重合，vc为铰链C的运动方向,，与C点的凸轮廊线切线重合。用K1、K2分别表示PC、vc的斜率，则K1 = 应保证的最大值不超过许用值，即。可取clearsm=100;h=120;e=0;a=70;d=8*pi/180;fa1=110*pi/180;fa2=0*pi/180;fa3=150*pi/180;fa4=100*pi/180;b1=61.4086;b2=155.6009;famax=1.33;famin=3.58;fa01=0:0.001:famax;s=sm/2*(1-cos(pi*

18、fa01/fa1);xb=a*sin(d+fa01);yb=-a*cos(d+fa01);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);theta1=asin(xb-xd)./b);beta1=acos(b.2+b2.2-b1.2)./(2*b*b2);xc=xd+b2*sin(theta1+beta1);yc=yd-b2*cos(theta1+beta1);k11=(yc-yb)./(xc-xb);for i=2:length(fa01)-1 k21(i)=(yc(i-1)-yc(i+1)./(xc(i-1)-xc(i+1); endk21(1)=k21(2)

19、;for i=2:length(fa01)-1 a1(i)=abs(atan(k21(i)-k11(i)./(1+k11(i)*k21(i)*180/pi;enda1(1)=a1(2);dfa01=fa01(2:length(fa01);plot(dfa01,a1);hold on;fa02=famax:0.002:fa1;s=sm/2*(1-cos(pi*fa02/fa1);xb=a*sin(d+fa02);yb=-a*cos(d+fa02);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);theta1=asin(xb-xd)./b);beta1=acos(b.

20、2+b2.2-b1.2)./(2*b*b2);xc=xd+b2*sin(theta1-beta1);yc=yd-b2*cos(theta1-beta1);k11=(yc-yb)./(xc-xb);for i=2:length(fa02)-1 k21(i)=(yc(i-1)-yc(i+1)./(xc(i-1)-xc(i+1); endk21(1)=k21(2);for i=2:length(fa02)-1 a2(i)=abs(atan(k21(i)-k11(i)./(1+k11(i)*k21(i)*180/pi;enda2(1)=a2(2);dfa02=fa02(2:length(fa02);p

21、lot(dfa02,a2);hold on;fa03=fa1+fa2:0.002:famin;s=sm*(1-(fa03-fa1-fa2)/fa3+1/(2*pi)*sin(2*pi*(fa03-fa1-fa2)/fa3);xb=a*sin(d+fa03);yb=-a*cos(d+fa03);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);theta1=asin(xb-xd)./b);beta1=acos(b.2+b2.2-b1.2)./(2*b*b2);xc=xd+b2*sin(theta1-beta1);yc=yd-b2*cos(theta1-beta1);k

22、11=(yc-yb)./(xc-xb);for i=2:length(fa03)-1 k21(i)=(yc(i-1)-yc(i+1)./(xc(i-1)-xc(i+1); endk21(1)=k21(2);for i=2:length(fa03)-1 a3(i)=abs(atan(k21(i)-k11(i)./(1+k11(i)*k21(i)*180/pi;enda3(1)=a3(2);dfa03=fa03(2:length(fa03);plot(dfa03,a3);hold on;fa04=famin:0.002:fa1+fa2+fa3;s=sm*(1-(fa04-fa1-fa2)/fa3+

23、1/(2*pi)*sin(2*pi*(fa04-fa1-fa2)/fa3);xb=a*sin(d+fa04);yb=-a*cos(d+fa04);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);theta1=asin(xb-xd)./b);beta1=acos(b.2+b2.2-b1.2)./(2*b*b2);xc=xd+b2*sin(theta1+beta1);yc=yd-b2*cos(theta1+beta1);k11=(yc-yb)./(xc-xb);for i=2:length(fa04)-1 k21(i)=(yc(i-1)-yc(i+1)./(xc(i-

24、1)-xc(i+1); endk21(1)=k21(2);for i=2:length(fa04)-1 a4(i)=abs(atan(k21(i)-k11(i)./(1+k11(i)*k21(i)*180/pi;enda4(1)=a4(2);dfa04=fa04(2:length(fa04);plot(dfa04,a4);hold on;fa05=fa1+fa2+fa3:0.002:fa1+fa2+fa3+fa4;s=0;xb=a*sin(d+fa05);yb=-a*cos(d+fa05);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);theta1=asin(x

25、b-xd)./b);beta1=acos(b.2+b2.2-b1.2)./(2*b*b2);xc=xd+b2*sin(theta1+beta1);yc=yd-b2*cos(theta1+beta1);k11=(yc-yb)./(xc-xb);for i=2:length(fa05)-1 k21(i)=(yc(i-1)-yc(i+1)./(xc(i-1)-xc(i+1); endk21(1)=k21(2);for i=2:length(fa05)-1 a5(i)=abs(atan(k21(i)-k11(i)./(1+k11(i)*k21(i)*180/pi;enda5(1)=a5(2);dfa0

26、5=fa05(2:length(fa05);plot(dfa05,a5);hold on;xlabel('fa');ylabel('a');title('凸轮压力角'); 由上图可知，满足许用值。（2） 从动杆的压力角 为CD杆对铰销D的驱动力（不考虑摩擦力）与D的运动方向的夹角。对于直动从动杆，显然 对于AB推动BC的驱动方案，在区间取“”号，其它区间取“+”号；而对于AB拉动BC的驱动方案，刚好相反。clearsm=100;h=120;e=0;a=70;d=8*pi/180;fa1=110*pi/180;fa2=0*pi/180;fa3=15

27、0*pi/180;fa4=100*pi/180;b1=61.4086;b2=155.6009;famax=1.33;famin=3.58;fa01=0:0.001:famax;s=sm/2*(1-cos(pi*fa01/fa1);xb=a*sin(d+fa01);yb=-a*cos(d+fa01);xd=e;yd=h+s;b=sqrt(xb-xd).2+(yb-yd).2);theta1=asin(xb-xd)./b);beta1=acos(b.2+b2.2-b1.2)./(2*b*b2);afa=abs(theta1+beta1);plot(fa01,afa);hold on; fa02=famax:0.002:fa1;s=sm/2*(1-cos(pi*fa02/fa1);xb=a*sin(d+fa02);yb=-a*cos(d+fa02);xd=e;yd=h+s;b