哈工大机械原理大作业 凸轮机构 32

1、Harbin Institute of Technology凸轮机构设计说明书课程名称：机械原理 设计题目：凸轮机构设计（32） 院 系：能源科学与工程学院班 级：1302403 设 计 者：刘远华 学 号：1130240333 指导教师：焦映厚 陈照波 设计时间：2015年6月 哈尔滨工业大学凸轮机构设计一、设计题目行程/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/。50603-4-5多项式3080简-直-简60100120二、凸轮升程、回程运动方程及推杆位移、速度、加速度线图1、运动规律(1)推程规律方程（3-4-5多项

2、式）位移方程S=h10*(/0)3-15*(/0)4+6*(/0)5S=5010*(3/)3-15*(3/)4+6*(3/)5速度方程V=h1/030*(/0)2-60*(/0)3+30*(/0)4V=1501/30*(3/)2-60*(3/)3+30*(/)4加速度方程a=h(1)2/(0)260*(/0) -180*(/0)2+120*(/0)3a=450(1)2/260*(3/) -180*(3/)2+120*(3/)3（2）回程运动规律方程（简-直-简）位移方程S=h-2h/4+(n-2) 1-cosn(-0-s速度方程加速度方程2、编程及代码位移、速度、加速度MATLAB代码clea

3、r,clc%推程运动规律方程h = 50;omega1 = 10;PHI0 = pi/3;phi1 = 0:pi/1000:PHI0;s1 = h*(10*(phi1/PHI0).3 - 15*(phi1/PHI0).4 + 6*(phi1/PHI0).5);nu1 = (h*omega1)/PHI0)*(30*(phi1/PHI0).2 - 60*(phi1/PHI0).3 + 30*(phi1/PHI0).4);a1 = (h*omega12)/PHI02)*(60*(phi1/PHI0) - 180*(phi1/PHI0).2 + 120*(phi1/PHI0).3);%远休止行程PHI

4、s = 5*pi/9;phi2 = PHI0,PHI0+PHIs;s2 = s1(end),s1(end);nu2 = 0,0;a2 = 0,0;%回程运动规律方程（简-直-简）n = 3;PHI00 =4*pi/9;phi3 = (PHI0 + PHIs):pi/1000:(PHI0 + PHIs + PHI00/n); phi4 = (PHI0 + PHIs + PHI00/n):pi/1000:(PHI0 + PHIs + PHI00*(n - 1)/n); phi5 = (PHI0 + PHIs + PHI00*(n - 1)/n):pi/1000:(PHI0 +PHIs + PHI0

5、0); s3 = h - (2*h/(4 + (n - 2)*pi)*(1 - cos(n*pi*(phi3 - PHI0 - PHIs)/(2*PHI00);s4 = h - (h/(4 + (n - 2)*pi)*(n*pi*(phi4 - PHI0 - PHIs)/PHI00 - pi + 2);s5 = (2*h/(4 + (n - 2)*pi)*(1 + cos(n*pi*(phi5 - PHI0 - PHIs)/(2*PHI00) - (n - 2)*pi/2);nu3 = -(h*n*pi*omega1/(4 + (n - 2)*pi)*PHI00)*sin(n*pi*(phi3

6、 - PHI0 - PHIs)/(2*PHI00);nu4 = -h*n*pi*omega1/(4 + (n - 2)*pi)*PHI00) + zeros(size(phi4);nu5 = -(h*n*pi*omega1/(4 + (n - 2)*pi)*PHI00)*sin(n*pi*(phi5 - PHI0 - PHIs)/(2*PHI00) - (n - 2)*pi/2); a3 = -(h*n2*pi2*omega12/(2*(4 + (n - 2)*pi)*PHI002)*cos(n*pi*(phi3 - PHI0 - PHIs)/(2*PHI00);a4 = 0;a5 = -(h

7、*n2*pi2*omega12/(2*(4 + (n - 2)*pi)*PHI002)*cos(n*pi*(phi5 - PHI0 - PHIs)/(2*PHI00) - (n - 2)*pi/2);%近休止行程phi6 = PHI0 + PHIs + PHI00,2*pi;s6 = 0 0;nu6 = 0 0;a6 = 0 0;plot(phi1,s1,phi2,s2,phi3,s3,phi4,s4,phi5,s5,phi6,s6);axis(0 7 0 60);title('位移');plot(phi1,nu1,phi2,nu2,phi3,nu3,phi4,nu4,phi5

8、,nu5,phi6,nu6);title('速度');plot(phi1,a1,phi2,a2,phi3,a3,phi4,a4,phi5,a5,phi6,a6);title('加速度');三、凸轮机构的线图，并依次确定凸轮的基圆半径和偏距MATLAB代码clear,clc%ÍƳÌÔ˶¯¹æÂÉ·½³Ìh = 50;omega1 = 10;PHI0 = pi/3;n = 3;PHI00 =4*pi/9;

9、PHIs = 5*pi/9;syms phi1phi3phi4phi5s1 = h*(10*(phi1/PHI0).3 - 15*(phi1/PHI0).4 + 6*(phi1/PHI0).5);s11 = diff(s1,phi1);%»Ø³ÌÔ˶¯¹æÂÉ·½³Ì£¨¼ò-Ö±-¼ò£©s3 = h - (2*h/(4 + (n -

10、 2)*pi)*(1 - cos(n*pi*(phi3 - PHI0 - PHIs)/(2*PHI00);s4 = h - (h/(4 + (n - 2)*pi)*(n*pi*(phi4 - PHI0 - PHIs)/PHI00 - pi + 2);s5 = (2*h/(4 + (n - 2)*pi)*(1 + cos(n*pi*(phi5 - PHI0 - PHIs)/(2*PHI00) - (n - 2)*pi/2);s33 = diff(s3,phi3);s44 = diff(s4,phi4);s55 = diff(s5,phi5);phi1 = 0:pi/1000:PHI0;phi3

11、= (PHI0 + PHIs):pi/1000:(PHI0 + PHIs + PHI00/n); phi4 = (PHI0 + PHIs + PHI00/n):pi/1000:(PHI0 + PHIs + PHI00*(n - 1)/n); phi5 = (PHI0 + PHIs + PHI00*(n - 1)/n):pi/1000:(PHI0 +PHIs + PHI00); plot(subs(s11),subs(s1),subs(s33),subs(s3),subs(s44),subs(s4),subs(s55),subs(s5);axis(-100 100 -100 100)axis s

12、quaregrid onhold on%xÊÇs11(ds/dphi)µÄ¾ßÌåÊý¾Ý yÊÇsµÄ¾ßÌåÊý¾Ýphi1 = ;phi1 = 0:pi/2000:PHI0;k = sqrt(3);x = eval(s11);p = length(x);xx = x(1:(p + 1)/2);y = eval(s1);yy = y(1:(p + 1)/

13、2);K = diff(yy)./diff(xx); %ÇúÏßÉϼÆËã³öµÄбÂÊdelta = abs(K- k);deltamin = min(delta);Ifindu = find(delta = deltamin);X = xx(Ifindu); %ÕÒµÄÇеãY = yy(Ifindu);%XX = -100:1

14、00;YY = k*(XX - X) + Y;plot(XX,YY)phi5 = ;phi5 = (PHI0 + PHIs + PHI00*(n - 1)/n):pi/2000:(PHI0 +PHIs + PHI00);k1 = tan(5*pi/6);xx1 = eval(s55);yy1 = eval(s5);K1 = diff(yy1)./diff(xx1); %ÇúÏßÉϼÆËã³öµÄбÂÊdelta1

15、 = abs(K1 - k1);deltamin1 = min(delta1);Ifindu1 = find(delta1 = deltamin1);X1 = xx1(Ifindu1); %ÕÒµÄÇеãY1 = yy1(Ifindu1);XX1 = -100:100;YY1 = k1*(XX1 - X1) + Y1;plot(XX1,YY1)k2 = tan(2*pi/3);XX2 = 0:100;YY2 = k2*XX2;plot(XX2,YY2)图作出如上图所示的曲线，因凸轮机构压力角，式中，右侧为升程，作

16、与s轴夹角等于升程许用压力角30°的切界线，则在直线上或其右下方取凸轮轴心时，可使，同理左侧回程，作与s轴夹角等于回程许用压力角60°的切界线，则在直线上或其左下方取凸轮轴心时，可使。在升程起始点，有，为保证此时，作直线与纵坐标夹角为°，凸轮轴心只能在其线上或左下方选取。三条限制线围成的下方阴影角区域为满足的凸轮轴心的公共许用区域。在许用区域内取满足上述条件的一点，取偏距e = 40mm 基圆半径r0 =90mm绘制凸轮理论轮廓上的压力角线图和曲率半径线图压力角：，此时由上知e = 40mm，可由如此公式求压力角。曲率半径：凸轮逆时针转动，从动件导路偏置于凸轮轴心

17、右侧，凸轮理论轮廓线方程为：，在参数方程下确定凸轮轮廓线的曲率半径。MATLAB 代码clear,clcr0 = 90;e = 40;s0 = sqrt(r02 - e2);h = 50;PHI0 = pi/3;n = 3;PHI00 =4*pi/9;PHIs = 5*pi/9;rr = 10;syms phi1phi2phi3phi4phi5phi6s1 = h*(10*(phi1/PHI0).3 - 15*(phi1/PHI0).4 + 6*(phi1/PHI0).5);s2 = h*(10 - 15 + 6);s3 = h - (2*h/(4 + (n - 2)*pi)*(1 - cos

18、(n*pi*(phi3 - PHI0 - PHIs)/(2*PHI00);s4 = h - (h/(4 + (n - 2)*pi)*(n*pi*(phi4 - PHI0 - PHIs)/PHI00 - pi + 2);s5 = (2*h/(4 + (n - 2)*pi)*(1 + cos(n*pi*(phi5 - PHI0 - PHIs)/(2*PHI00) - (n - 2)*pi/2);s6 = 0;x1 = -(s0 + s1)*sin(phi1) - e*cos(phi1); %ÀíÂÛÂÖÀªy1 = (

19、s0 + s1)*cos(phi1) - e*sin(phi1);x2 = -(s0 + s2)*sin(phi2) - e*cos(phi2); %ÀíÂÛÂÖÀªy2 = (s0 + s2)*cos(phi2) - e*sin(phi2);x3 = -(s0 + s3)*sin(phi3) - e*cos(phi3); %ÀíÂÛÂÖÀªy3 = (s0 + s3)*cos(phi3) - e*sin(phi3);x4 = -(s0

20、 + s4)*sin(phi4) - e*cos(phi4); %ÀíÂÛÂÖÀªy4 = (s0 + s4)*cos(phi4) - e*sin(phi4);x5 = -(s0 + s5)*sin(phi5) - e*cos(phi5); %ÀíÂÛÂÖÀªy5 = (s0 + s5)*cos(phi5) - e*sin(phi5);x6 = -(s0 + s6)*sin(phi6) - e*cos(phi6); %À

21、37;ÂÛÂÖÀªy6 = (s0 + s6)*cos(phi6) - e*sin(phi6);dy1 = diff(y1,phi1);dx1 = diff(x1,phi1);dy2 = diff(y2,phi2);dx2 = diff(x2,phi2);dy3 = diff(y3,phi3);dx3 = diff(x3,phi3);dy4 = diff(y4,phi4);dx4 = diff(x4,phi4);dy5 = diff(y5,phi5);dx5 = diff(x5,phi5);dy6 = diff(y6,phi6);dx

22、6 = diff(x6,phi6);ds1 = diff(s1,phi1);ds2 = diff(s2,phi2);ds3 = diff(s3,phi3);ds4 = diff(s4,phi4);ds5 = diff(s5,phi5);ds6 = diff(s6,phi6);alpha1 = atan(abs(ds1 - e)/(s0 + s1);alpha2 = atan(abs(ds2 - e)/(s0 + s2);alpha3 = atan(abs(ds3 - e)/(s0 + s3);alpha4 = atan(abs(ds4 - e)/(s0 + s4);alpha5 = atan(

23、abs(ds5 - e)/(s0 + s5);alpha6 = atan(abs(ds6 - e)/(s0 + s6);dx11 = diff(dx1,phi1);dy11 = diff(dy1,phi1);dx22 = diff(dx2,phi2);dy22 = diff(dy2,phi2);dx33 = diff(dx3,phi3);dy33 = diff(dy3,phi3);dx44 = diff(dx4,phi4);dy44 = diff(dy4,phi4);dx55 = diff(dx5,phi5);dy55 = diff(dy5,phi5);dx66 = diff(dx6,phi6

24、);dy66 = diff(dy6,phi6);rou1 = abs(dx12 + dy12)1.5)/(dx1*dy11 - dx11*dy1);rou2 = abs(dx22 + dy22)1.5)/(dx2*dy22 - dx22*dy2);rou3 = abs(dx32 + dy32)1.5)/(dx3*dy33 - dx33*dy3);rou4 = abs(dx42 + dy42)1.5)/(dx4*dy44 - dx44*dy4);rou5 = abs(dx52 + dy52)1.5)/(dx5*dy55 - dx55*dy5);rou6 = abs(dx62 + dy62)1.5

25、)/(dx6*dy66 - dx66*dy6);phi1 = 0:pi/1000:PHI0;phi2 = PHI0:pi/1000:PHI0+PHIs;phi3 = (PHI0 + PHIs):pi/1000:(PHI0 + PHIs + PHI00/n); phi4 = (PHI0 + PHIs + PHI00/n):pi/1000:(PHI0 + PHIs + PHI00*(n - 1)/n); phi5 = (PHI0 + PHIs + PHI00*(n - 1)/n):pi/1000:(PHI0 +PHIs + PHI00); phi6 = (PHI0 + PHIs + PHI00):

26、pi/1000:2*pi;plot(phi1,subs(alpha1), phi2,subs(alpha2),phi3,subs(alpha3),phi4,subs(alpha4),phi5,subs(alpha5),phi6,subs(alpha6)plot(phi1,subs(rou1), phi2,subs(rou2),phi3,subs(rou3),phi4,subs(rou4),phi5,subs(rou5),phi6,subs(rou6)压力角线图曲率半径线图3、 确定滚子半径，绘制凸轮理论轮廓和实际轮廓凸轮逆时针转动，从动件导路偏置于凸轮轴心右侧，凸轮理论轮廓线方程为：，逐段代入

27、位移表达式则可求凸轮理论轮廓线方程，用Matlab编写程序绘制如图所示。逐段求出最小值得，取滚子半径rr=10mm，以理论轮廓上各点为圆心、以滚子半径为半径作出的滚子圆族包络线即为滚子从动件盘形凸轮的工作轮廓，其方程为：，MATLAB代码clear,clcr0 = 90;e = 40;s0 = sqrt(r02 - e2);h = 50;PHI0 = pi/3;n = 3;PHI00 =4*pi/9;PHIs = 5*pi/9;rr = 10;syms phi1phi2phi3phi4phi5phi6s1 = h*(10*(phi1/PHI0).3 - 15*(phi1/PHI0).4 + 6

28、*(phi1/PHI0).5);s2 = h*(10 - 15 + 6);s3 = h - (2*h/(4 + (n - 2)*pi)*(1 - cos(n*pi*(phi3 - PHI0 - PHIs)/(2*PHI00);s4 = h - (h/(4 + (n - 2)*pi)*(n*pi*(phi4 - PHI0 - PHIs)/PHI00 - pi + 2);s5 = (2*h/(4 + (n - 2)*pi)*(1 + cos(n*pi*(phi5 - PHI0 - PHIs)/(2*PHI00) - (n - 2)*pi/2);s6 = 0;x1 = -(s0 + s1)*sin(

29、phi1) - e*cos(phi1); %ÀíÂÛÂÖÀªy1 = (s0 + s1)*cos(phi1) - e*sin(phi1);x2 = -(s0 + s2)*sin(phi2) - e*cos(phi2); %ÀíÂÛÂÖÀªy2 = (s0 + s2)*cos(phi2) - e*sin(phi2);x3 = -(s0 + s3)*sin(phi3) - e*cos(phi3); %ÀíÂ&#

30、219;ÂÖÀªy3 = (s0 + s3)*cos(phi3) - e*sin(phi3);x4 = -(s0 + s4)*sin(phi4) - e*cos(phi4); %ÀíÂÛÂÖÀªy4 = (s0 + s4)*cos(phi4) - e*sin(phi4);x5 = -(s0 + s5)*sin(phi5) - e*cos(phi5); %ÀíÂÛÂÖÀªy5 = (s0 + s5)

31、*cos(phi5) - e*sin(phi5);x6 = -(s0 + s6)*sin(phi6) - e*cos(phi6); %ÀíÂÛÂÖÀªy6 = (s0 + s6)*cos(phi6) - e*sin(phi6);dy1 = diff(y1,phi1);dx1 = diff(x1,phi1);dy2 = diff(y2,phi2);dx2 = diff(x2,phi2);dy3 = diff(y3,phi3);dx3 = diff(x3,phi3);dy4 = diff(y4,phi4);dx4 = diff(x4,phi4);dy5 = diff(y5,phi5);dx5 = diff(x5,phi5);dy6 = diff(y6,phi6);dx6 = diff(x6,phi6);X1 = x1 - rr*dy1/sqrt(dx12 + dy12); %ʵ¼ÊÂÖÀªY1 = y1 + rr*dx1/sqrt(dx12 + dy12);X2 = x2 - rr*dy2/sqrt(dx22 + dy22);