哈工大机械原理大作业凸轮机构32

1、凸轮机构设计说明书课程名称：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：学 号：1130240333指导教师：设计时间：2015年6月哈尔滨工业大学凸轮机构设计、设计题目 止T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601001201、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多项式)位移方程S=h10*( #0八3-15*( 0 奶)八4+6*(外)八

2、5S=5010*(3 /t)a3-15*(3 / n )八4+6*(3 / 沪5速度方程V=h3/ 30*( /M)o)A2-6O*( / 3)八3+30*( (/ 研4V=150 31/ 30*(3 (/ 沪2-60*(3 (/ 沪3+30*(/沪出加速度方程a=h( 3)A2/( 0)A260*( (/ Q) -180*( / 研2+120*( (/ 3)八3 a=450( 3A2/ n 八260*(3冗(-180*(3 /n )八2+120*(3/n)八3（ 2）回程运动规律方程（简 -直-简） 位移方程S=h-2h/4+（n-2） n1- cosn n -协 &速度方程加速度方程2、编

3、程及代码位移、速度、加速度 MATLAB 代码 clear,clc%推程运动规律方程h = 50;omega1 = 10;PHI0 = pi/3;phi1 = 0:pi/1000:PHI0;si = h*(10*(phi1/PHI0)A3 - 15*(phi1/PHI0).A4 + 6*(phi1/PHI0).A5);nu1 =(h*omega1)/PHI0)*(30*(phi1/PHI0)A2-60*(phii/PHI0).A3 30*(phi1/PHI0).A4);a1 =(h*omega1A2)/PHI0A2)*(60*(phi1/PHI0)-180*(phi1/PHI0).A2 120

4、*(phi1/PHI0).A3);%远休止行程PHIs = 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)

5、:pi/1000:(PHI0 +PHIs + PHI00);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)

6、*pi)*PHI00)*sin(n*pi*(phi3 - 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* nA2*piA2*omegaM2/(2*(4 + (n - 2)*pi)*PHI00T)*cos( n*pi*(phi3 - PHIO - PH

7、Is)/(2*PHI00);a4 = 0;a5 = -(h* nA2*piA2*omegaM2/(2*(4 + (n - 2)*pi)*PHI00A2)*cos( n*pi*(phi5 - PHIO - 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,

8、nu2,phi3,nu3,phi4,nu4,phi5,nu5,phi6,nu6); title(速度);plot(phi1,a1,phi2,a2,phi3,a3,phi4,a4,phi5,a5,phi6,a6);title(加速度);1M/1-11 厂岸1514i4 r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%i?3 ? ?1?e ?3 ih = 50; omega1 = 10;PHI0 = pi/3;n = 3;PHI00 =4*pi/9;PHIs = 5*pi/9;syms phi1phi3phi4phi5 si = h*(10*(phi1/P

9、HI0)A3 - 15*(phi1/PHI0).A4 + 6*(phi1/PHI0).A5);s11 = diff(s1,phi1);%?3 ? ?1? e ?3 ? o-? 土？ b垃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 - PHI

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

11、0);plot(subs(s11),subs(s1),subs(s33),subs(s3),subs(s44),subs(s4),subs(s55),subs(s5); axis(-100 100 -100 100)axis squaregrid onhold on%xe?s11(ds/dphi) ? ?ey?Y y e?s 卩?？ ?ey?Yphi1 = ;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)/2);K =

12、diff(yy)./diff(xx); %? ? e? ?3? p?D ? e delta = abs(K- k);deltamin = min(delta);Ifindu = find(delta = deltamin);X = xx(Ifindu);%?o?D ?Y = yy(Ifindu);%XX = -100:100;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

13、(s55);yy1 = eval(s5);K1 = diff(yy1)./diff(xx1);%?u ? e? ?3? p?D ? edelta1 = abs(K1 - k1);deltamin1 = min(delta1);Ifindu1 = find(delta1 = deltamin1);X1 = xx1(Ifindul);%?o?D ?Y1 = 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

14、)作出如上图所示的ds/d -s曲线，因凸轮机构压力角tan二ds d -e，式So+S中，So=“o2-e2，右侧为升程，作与s轴夹角等于升程许用压力角30 的切界线Dtdt，则在直线上或其右下方取凸轮轴心时，可使=arctan dS d -e，同理左侧回程，作与S轴夹角等于回程许用压So+S力角60的切界线Dtdt，则在直线上或其左下方取凸轮轴心时，可使二arctane。在升程起始点，有 tan =工，为保证此时So + SSo，作直线Bodo与纵坐标夹角为30 ，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

15、一点，取偏距e = 40mm基圆半径厂心;冷葆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：=arctands d e，此时由上知e = 40mm，可由如此公式求So+S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右侧， 凸轮理论轮廓线方程为：x=(S0+s)sin +ecos，(02 )，在参数方程y=(s0+s)cos -esin3(x2+y2)2F确定凸轮轮廓线的曲率半径x y -x yMATLAB代码clear,clcr0 = 90;e = 40;s0 = sqrt(r0A2 - eA2);h = 50;PHI0 = pi/3;n = 3;PHI00 =4*pi/9;

16、PHIs = 5*pi/9;rr = 10;syms phi1phi2phi3phi4phi5phi6 si = h*(10*(phi1/PHI0).A3 - 15*(phi1/PHI0).A4 + 6*(phi1/PHI0).A5);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/

17、(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); y1 = (s0 + s1)*cos(phi1) - e*sin(phi1);x2 = -(s0 + s2)*sin(phi2) - e*cos(phi2); y2 = (s0 + s2)*cos(phi2) - e*sin(phi2);x3 = -(s0 + s3)*sin(phi3) - e*cos(phi3); y3 = (s0 + s3)

18、*cos(phi3) - e*sin(phi3);x4 = -(s0 + s4)*sin(phi4) - e*cos(phi4); y4 = (s0 + s4)*cos(phi4) - e*sin(phi4);x5 = -(s0 + s5)*sin(phi5) - e*cos(phi5); y5 = (s0 + s5)*cos(phi5) - e*sin(phi5);x6 = -(s0 + s6)*sin(phi6) - e*cos(phi6); y6 = (s0 + s6)*cos(phi6) - e*sin(phi6);%a ? aa%a ? aa%a ? aa%a ?aa%a ?aa%a

19、 ?aady1 = 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);ds1 = diff(s1,phi1);ds2 = diff(s2,phi2);ds3 = diff(s3,ph

20、i3); 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(abs(ds5 - e)/(s0 + s5); alpha6 = atan(abs(ds6 - e)/(s0 + s6);dx11 = d

21、iff(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); dy66 = diff(dy6,phi6);roul = abs(dxM2 + dy1A2)A1.5)/(dx1*

22、dy11 - dx11*dy1); rou2 = abs(dx2A2 + dy2A2F1.5)/(dx2*dy22 - dx22*dy2); rou3 = abs(dx3A2 + dy3A2)A1.5)/(dx3*dy33 - dx33*dy3); rou4 = abs(dx4A2 + dy4A2)A1.5)/(dx4*dy44 - dx44*dy4); rou5 = abs(dx5A2 + dy5A2)A1.5)/(dx5*dy55 - dx55*dy5); rou6 = abs(dx6A2 + dy6A2)A1.5)/(dx6*dy66 - dx66*dy6);phi1 = 0:pi/10

23、00: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):pi/1000:2*pi;plot(phi1,subs(alpha1), phi2

24、,subs(alpha2),phi3,subs(alpha3),phi4,subs(alpha4),phi5,subs(alpha5),phi6,subs(al pha6)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三、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：x=(s0+s)s in +ecosy=(s+爲s -esin，(2)逐段代入位移表达式则可求

25、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pmin= 407?m,取滚子半径= lomm，以理论dy d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：X =x+rrJ(dxd )2+(dy；d )200、/dx dY=y-rrJ(dxd )2+(dy;d )2MATLAB代码clear,clcr0 = 90;e = 40;s0 = sqrt(r0A2 - eA2);h = 50;PHI0 = pi/3;n = 3;PHI00 =4*pi/9;PHIs = 5*pi/9;rr = 10;syms phi1phi2

26、phi3phi4phi5phi6 si = h*(10*(phi1/PHI0).A3 - 15*(phi1/PHI0).A4 + 6*(phi1/PHI0).A5);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*(phi

27、5 - PHI0 - PHIs)/(2*PHI00) - (n - 2)*pi/2);s6 = 0;x1 = -(s0 + s1)*sin(phi1) - e*cos(phi1); % ? aayi = (s0 + si)*cos(phii) - e*si n( ph ii);x2 = -(sO + s2)*sin(phi2) - e*cos(phi2);%a ? aay2 = (s0 + s2)*cos(phi2) - e*sin(phi2);x3 = -(sO + s3)*si n( phi3) - e*cos(phi3);%a ? aay3 = (sO + s3)*cos(phi3) -

28、 e*sin(phi3);x4 = -(sO + s4)*si n( phi4) - e*cos(phi4);%a ? aay4 = (sO + s4)*cos(phi4) - e*sin(phi4);x5 = -(sO + s5)*sin(phi5) - e*cos(phi5);%a ?aay5 = (sO + s5)*cos(phi5) - e*sin(phi5);x6 = -(sO + s6)*sin(phi6) - e*cos(phi6);%a ?aay6 = (sO + 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(dx1A2 + dy1A2);%e p?e? aaY1 = y1 + rr*dx1/sqrt(dx1A