哈工大机械原理大作业2-31.doc

哈尔滨工业大学机械原理课程设计Harbin Institute of Technology大作业设计说明书课程名称： 机械原理 设计题目： 凸轮机构 院 系： 机电学院 班 级： 姓 名： 学 号： 指导教师： 丁刚 设计时间： 2014.5.29 哈尔滨工业大学1. 设计题目第31题：升程/mm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/。15090等加等减速4080余弦加速度70401502.运动方程式及运动线图由题目要求凸轮逆时针旋转（1）确定凸轮机构推杆升程、回程运动方程，并绘制推杆位移、速度、加速度线图。升程第一段：（ 0 pi /4）0=pi/2;s1 = 73*2;v1=146*w*;a1 = 146*w2;升程第二段：（pi/4 pi /2） s2 =90-73*(pi/2-)2;v2=146*w*( pi/2-);a2 =-146*w.2;远休止程： （pi/2 10*pi/9)s3 = 90;v3 = 0;a3 = 0;回程： (10*pi/9) ( 14*pi/9)s4 =45*(1+cos(9/4*(-10*pi/9);v4 =-101.25*w*sin(9/4*(-10*pi/9) ;a4 =-227.8*w2* cos(9/4*(-10*pi/9);近休止程： (14*pi/9) =-1.733 & k1=-1.733 & k2=0.363 & k3=0.365) y2=k3*(x2-ds4(i)+s4(i); plot (x2,y2,r); endendhold ony3=-1.732*(x2-ds1(251)+s1(251);plot(x2,y3,r)text(-50,-100,O点（-50，-100）)3.确定滚子半径（1）先求凸轮理论轮廓曲线，程序如下：Clc；clear;w = input(请输入w=);s0 = 100;s = 90;e = 50;x = 0:(pi/100):(pi/4);x1 = (s + s0)*cos(x)-e*sin(x);y1 = (s0 + s)*sin(x) - e*cos(x);y = (pi/4):(pi/100):(pi/2);x2 = (s + s0)*cos(y)-e*sin(y);y2 = (s0 + s)*sin(y) - e*cos(y);z = (pi/2 ):(pi/100):(10*pi/9);x3 = (s + s0)*cos(z)-e*sin(z);y3 = (s0 + s)*sin(z) - e*cos(z);c = (10*pi/9):(pi/1000):( 14*pi/9);x4 = (s + s0)*cos(c)-e*sin(c);y4 = (s0 + s)*sin(c) - e*cos(c);d=(14*pi/9):(pi/1000):( 2*pi);x5 = (s + s0)*cos(d)-e*sin(d);y5 = (s0 + s)*sin(d) - e*cos(d);plot(x1,y1,b,x2,y2,b,x3,y3,b,x4,y4,b,x5,y5,b);xlabel(x/mm)ylabel(y/mm)title(理论轮廓曲线)grid on（2）理论轮廓线最小曲率半径编程代码：由下程序结果可知pmin =81.6667这里滚子半径为 rr pmin- =35mm；取rr=10mm;clear;clc;v=;syms x1 x2 x3 x4 x5 s0 = 100; e = 50; s1 = 73*x1.2;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=diff(y1,x1,2);for xx1= 0:(pi/100):(pi/4); k1=subs(abs(tx1*yxx1-txx1*yx1)/(tx12+yx12)1.5),x1,xx1); v=v,1/k1;end s2 =90-73*(pi/2-x2).2;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=(pi/4):(pi/100):(pi/2); k2=subs(abs(tx2*yxx2-txx2*yx2)/(tx22+yx22)1.5),x2,xx2); v=v,1/k2;end s3 = 90;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=(pi/2 ):(pi/100):(10*pi/9); k3=subs(abs(tx3*yxx3-txx3*yx3)/(tx32+yx32)1.5),x3,xx3); v=v,1/k3;end s4 =45*(1+cos(9/4*(x4-10*pi/9);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=(10*pi/9):(pi/100):( 4*pi/3); k4=subs(abs(tx4*yxx4-txx4*yx4)/(tx42+yx42)1.5),x4,xx4); v=v,1/k4;end s5 =0;t5 = (s5 + s0)*cos(x5)-e*sin(x5); y5 = (s0 + s5)*sin(x5) - e*cos(x5); tx5=diff(t5,x5); txx5=diff(t5,x5,2); yx5=diff(y5,x5); yxx5=diff(y5,x5,2);for xx5=(10*pi/9):(pi/100):( 4*pi/3); k5=subs(abs(tx5*yxx5-txx5*yx5)/(tx52+yx52)1.5),x5,xx5); v=v,1/k5;endpmin=min(v)4.绘制凸轮轮廓曲线clear ;clc;syms x y z c d w= input(请输入w=);s0= 100;e = 50;r = 10;xx =0:(pi/100):(pi/4);s1 = 73*x.2;x1 = (s1 + s0).*cos(x) - e*sin(x);y1 = (s0 + s1).*sin(x) - e*cos(x);n1 = diff (x1);m1 = diff(y1);xt1 = subs(x1+(r*m1)./(sqrt(n1.2+m1.2),x,xx);yt1 = subs(y1 - (r*n1)./sqrt(m1.2 +n1.2),x,xx);yy = (pi/4):(pi/100):(pi/2);s2 = 90-73*(pi/2-y).2;x2 = (s2 + s0).*cos(y)-e*sin(y);y2 = (s0 + s2).*sin(y) - e*cos(y);n2 = diff(x2);m2 = diff(y2);xt2 = subs(x2 + (r*m2)./sqrt(m2.2+n2.2),y,yy);yt2 = subs(y2 - (r*n2)./sqrt(m2.2+n2.2),y,yy);zz = (pi/2 ):(pi/100):(10*pi/9);s3 = 90;x3 = (s3 + s0).*cos(z)-e*sin(z);y3 = (s0 + s3).*sin(z) - e*cos(z);n3 = diff(x3);m3 = diff(y3);xt3= subs(x3 + (r*m3)./sqrt(m3.2+n3.2),z,zz);yt3 = subs(y3 - (r*n3)./sqrt(m3.2+n3.2),z,zz);cc= (10*pi/9):(pi/1000):( 14*pi/9);s4 =45*(1+cos(9/4*(c-10*pi/9);x4 = (s4 + s0).*cos(c)-e*sin(c);y4 = (s0 +s4).*sin(c) - e*cos(c);n4 = diff(x4);m4 = diff(y4);xt4= subs(x4 + (r*m4)./sqrt(m4.2+n4.2),c,cc);yt4 =subs( y4 - (r*n4)./sqrt(m4.2+n4.2),c,cc);dd=(14*pi/9):(pi/1000):( 2*pi);s5 =0;x5 = (s5 + s0).*cos(d)-e*sin(d);y5 = (s0 +s5).*sin(d) - e*cos(d);n5 = diff(x5);m5 = diff(y5);xt5= subs(x5 + (r*m5)./sqrt(m5.2+n5.2),d,dd);yt5 =subs( y5 - (r*n5)./sqrt(m5.2+n5.2),d,dd);plot(xt1,yt1,b,xt2,yt2,b,xt3,yt3,b,xt4,yt4,b,xt5,yt5,b);hold onxlabel(x/mm)ylabel(y/mm)title(凸轮工作曲线)grid on由于分步程序有很多重复，所以采用条件判断语句，求出分段的位移，速度，加速度表达式。总程序：clc,clear;w=1;%给定角速度yy0=(0:0.1:360);%转角yy=pi/180*yy0;%变为弧度h=90;%推程高度y0=90*pi/180;%推程运动角ys=110*pi/180;%远休止角y01=80/180*pi;%回程运动角ys1=80/180 *pi;%近休止角s=ones(1,3601);%单位矩阵v=ones(1,3601);%单位矩阵a=ones(1,3601);%单位矩阵aa1=30/180*pi;%升程许用压力角aa2=70/180*pi;%回程许用压力角for i=1:3601 if yy(1,i)y0/2 & yy(1,i)=y0 & yy(1,i)=y0+ys & yy(1,i)=y0+ys+y01 & yy(1,i)=360 s(1,i)=0; v(1,i)=0; a(1,i)=0; endendsubplot(2,3,1) ;plot(yy,s);grid on;%推杆的位移图像xlabel(转角/rad);ylabel(位移/mm);title(推杆的位移图像)subplot(2,3,2) ;plot(yy,v);grid on;%推杆的速度图像xlabel(转角/rad);ylabel(速度/mm);title(推杆的速度图像)subplot(2,3,3) ;plot(yy,a);grid on;%推杆的加速度图像xlabel(转角/rad);ylabel(加速度/mm);title(推杆的加速度图像)sy=v/w;%类速度ds/sysubplot(2,3,4);plot(-sy,s);grid on;%推杆ds/d-ds图像xlabel(ds/d);ylabel(ds);title(推杆ds/d-ds图像)r0=120;%基圆半径r0x=r0*cos(yy);r0y=r0*sin(yy);ee=22;%偏心距eex=ee*cos(yy);eey=ee*sin(yy);s0=sqrt(r02+ee2)*ones(1,3601);x=(s0+s).*cos(yy)-ee*sin(yy);%理论廓线x坐标y=(s0+s).*sin(yy)+ee*cos(yy);%理论廓线y坐标rr=10;