哈工大—机械原理凸轮大作业

1、题目要求及机构运动简图如图1所示直动从动件盘形凸轮机构。其原始参数见表1。图一凸轮运动简图表一凸轮原始参数行程（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（）6590余弦加速度3550改进正弦701001201计算流程框图建立数学模型压力角图丄确定轴向1及基圆半径 升程压力角ds/dY-s 曲线+确定滚子半径理论轮廓实际轮廓-co X X sin?说 X)2 n-X cos? X )2 0 “速度方程位移方程加速度方程i速度线图位移线图加速线图回程压力角轮廓图建立数学模型1.从动件运动规律方程首先，由于设计凸轮轮廓与凸

2、轮角速度无关，所以不妨设凸轮运动角速度为w = 1rad/s。(1) 推程运动规律(0 90s=2 X1n hw ,v=2 0?多？a=?2 0式中：h=65mm, 0=n /2(2) 远休程运动规律(90 90 )s = 65mm a = 0(3)回程运动规律 (190 40 ) iA O O -? 0?-? ShS1?= ?h? k?(?( - ? 0? s) sin(4? n?0)0/ (190 96.25 )50hs2?= ?h? 4+n?(2? 0? )s 9?sinG +0-4? n?L0?-? s 3? 0)?(196.25 233.75)hs3?= ?h?(4 +-tA O O

3、 -? 0?-? S(- ? 0? s) sin (4 ?冗？ 0) n ?:0)?(233.75 240)回程运动中的速度和加速度为位移对时间t的倒数:ds dt dv dt(4)近休程运动规律(240 360)s = 02.从动件位移、速度、加速度线图(1)位移线图100150230Z5030035040)转响农/度間 切 如 関 如 讪(2)速度线图100-1Mtoo 150200250300350400050从动件谊用-时酬经圏O-1&0(3) 加速度线图5004033002M1M-1 DO200400乍9EF.茴应/ 一戶300035040050100150200250(4)位移、速

4、度、加速度线图MATLAB源程序%已知条件h = 65; %mm%radphi_O = 90./180* pi;alp ha_up_al = 35./180* pi; %升程许用压力角 phi_OO = 50./180* pi;alp ha_dow n_al = 70./180* pi; % 回程许用压力角phi_s = 100./180*pi;phi_ss = 120./180*pi;w = 1;% 绘制从动件位移、速度、加速度线图% 推程阶段t_up = 0 : 0.5 : 90;t_up1 = t_up./180*pi;syms t_up1 phi_up s_upv_up a_up ph

5、i_up = w.*t_up1;s_up = h./2.*(1 - cos(pi.*phi_up./phi_0);v_up = diff(s_up,t_up1);a_up = diff(v_up,t_up1);s_up1 = double(subs(s_up,t_up./180*pi); v_up1 = double(subs(v_up,t_up./180*pi); a_up1 = double(subs(a_up,t_up./180*pi); % 远休程t_s = 90 : 0.5 : (90+100); t_s1 = t_up./180*pi; s_s(1:201) = h; v_s(1:

6、201) = 0; a_s(1:201) = 0;% 回程阶段 1 t_down1 = (90+100) : 0.5 : (90+100+50/8); t_down11 = t_down1./180*pi;syms t_down11 phi_down1 s_down1 v_down1 a_down1 phi_down1 = w.*t_down11;s_down1 = h - h./(4+pi).*(pi.*(phi_down1 - phi_0 - phi_s)./phi_00 - . sin(4.*pi.*(phi_down1 - phi_0 - phi_s)./phi_00)./4);v_d

7、own1 = diff(s_down1,t_down11); a_down1 = diff(v_down1,t_down11);s_down11 = double(subs(s_down1,t_down1./180*pi);v_down11 = double(subs(v_down1,t_down1./180*pi); a_down11 = double(subs(a_down1,t_down1./180*pi);% 回程阶段 2 t_down2 = (90+100+50/8) : 0.5 : (90+100+7*50/8); t_down22 = t_down2./180*pi;syms t

8、_down22 phi_down2 s_down2 v_down2 a_down2 phi_down2 = w.*t_down22;s_down2 = h - h./(4+pi).*(2+pi.*(phi_down2 - phi_0 - phi_s)./phi_00 - 9.*sin(pi./3 + 4.*pi.*(phi_down2 - phi_0 - phi_s)./(3.*phi_00)./4);v_down2 = diff(s_down2,t_down22);a_down2 = diff(v_down2,t_down22);s_down22 = double(subs(s_down2,

9、t_down2./180*pi);v_down22 = double(subs(v_down2,t_down2./180*pi); a_down22 = double(subs(a_down2,t_down2./180*pi);% 回程阶段 3t_down3 = (90+100+7*50/8) : 0.5 : (90+100+50);t_down33 = t_down3./180*pi;syms t_down33 phi_down3 s_down3 v_down3 a_down3 phi_down3 = w.*t_down33;s_down3 = h - h./(4+pi).*(4+pi.*(

10、phi_down3 - phi_O - phi_s)./phi_OO - sin(4.*pi.*(phi_down3 - phi_0 - phi_s)./phi_00)./4);v_down3 = diff(s_down3,t_down33);a_down3 = diff(v_down3,t_down33);s_down33 = double(subs(s_down3,t_down3./18O*pi);v_down33 = double(subs(v_down3,t_down3./18O*pi);a_down33 = double(subs(a_down3,t_down3./18O*pi);%

11、 近休程t_ss = (90+100+50) : 0.5 : 360;s_ss(1:241) = 0;v_ss(1:241) = 0;a_ss(1:241) = 0;% 绘图位移t = t_up t_s t_down1 t_down2 t_down3 t_ss;phi = w .* t ./ 180 .*pi;s = s_up1 s_s s_down11 s_down22 s_down33 s_ss; v = v_up1 v_s v_down11 v_down22 v_down33 v_ss;a = a_up1 a_s a_down11 a_down22 a_down33 a_ss;figur

12、e(Name,从动件位移-时间线图); plot(t,s,k,linewidth,1.0);grid on;title( 从动件位移 -时间线图 );xIabelC转角 phi / 度)；ylabel(位移 h/mm);% 绘图速度figure(Name,从动件速度-时间线图); plot(t,v,k,linewidth,1.0);grid on;titleC从动件速度-时间线图);xlabelC转角 phi / 度)；ylabelC速度 v/mm*s-1);% 绘图加速度figure(Name,从动件加速度-时间线图); plot(t,a,k,linewidth,1.0);grid on;t

13、itle(从动件加速度-时间线图);xlabelC转角 phi / 度)；ylabel(加速度 a/mm*s-2);3. 绘制ds/d线图并确定基圆半径和偏距(1) 绘制ds/d线图及源程序 MATLAB 源程序：%绘制ds/dphi-s线图，确定基圆半径和偏距 ds_dphi = v ./ w;figure(Name,凸轮 ds/dphi - s线图); plot(ds_dphi,s,k,linewidth,1.5); hold on;axis(-150 150 -70 70);grid on;titleC 凸轮 ds/dphi - s 线图);xlabel(ds/d phi / (mm*s

14、-2);ylabel(s/mm);% 三条临界线 x = linsp ace(-150,150,301);k_up = tan(pi/2 - alp ha_up_al);y_up 二 k_up.*x - 66;plot(x,y_u p,li newidth,1.5);k_dow n = - tan(pi/2 - al pha_dow n_al); y_dow n = k_dow n.*x - 24.7; plot(x,y_dow n,li newidth,1.5); x0 = linsp ace(0,150,151);k0 = - tan(alp ha_up_al);y0 = k0.*x0;p

15、lot(x0,y0,-);%由图像选取凸轮基圆半径为r0 = sqrt(232 + 34八2) = 41 mm偏距e = 23mmp lot(23,-34,or);r0 = 41;e = 23;p lot(li nsp ace(0,23,10),li nsp ace(0,-34,10),r,li nsp ace(0,23,10),li nsp ace(-34,-34,10),r,li nsp ace(23,23,10),li nsp ace(0,-34,10),r,li newidth,1.0);ds/dphii / (mm*/)(2) 确定基圆半径和偏距在凸轮机构的ds/d -s线图里再作斜

16、直线Dt-dt与升程的ds/d -s曲线相 切并使与纵坐标夹角为升程许用压力角a ，则Dt-dt线的右下方为选择凸轮轴 心的许用区。作斜直线Dt-dt与回程的ds/d -s曲线相切，并使与纵坐标夹 角为回程的许用压力角a ，则Dt-dt线的左下方为选择凸轮轴心的许用区。 考虑到升程开始瞬时机构压力角也不超过许用值，自B0点作限制线B0-d0与纵坐标夹角为升程a ，则这三条直线的围成的下方区域为为选取凸轮中心的许用 区。由图可取基圆半径r0= V?0+ ?0=41mm偏距e=23mm s0=34mm4. 绘制凸轮理论轮廓压力角、曲率半径线图(1)压力角、曲率半径数学模型 压力角计算公式：a= a

17、tan?| 竺-e|/(s0 + s)?d 曲率半径计算公式:223/2(dx/d )2 (dy/d )2(dx/d)(d2y/d2) (dy/d )(d2x/d 2)其中:dx/d(ds/d )esi n 佝s)cosdy/d(ds/d )ecos(s0s)sind2x/d2 2(ds/d ) ecos(d2s/d2) s0 ssind2y/d2(ds/d ) esin(d2s/d2) S0 s|cos(2) MATLAB 程序% 凸轮理论轮廓压力角和曲率半径线图r0 = 41;e = 23;s0 = 34;%压力角t = t_up t_s t_dow n1 t_dow n2 t_dow n

18、3 t_ss;al pha = ata n( abs(ds_d phi - e)./(s0 + s) ./ pi.*180;%曲率半径P = (rO + s)A2 + (w.*v)A2)A(3./2) ./ (rO + s).2 + 2.*(w.*v).2 - w.*w.*a.*(r0 + s); %画图figure(Name,凸轮理论轮廓压力角和曲率半径线图)；hAx,hLi ne1,hL in e2 = p lotyy(t ,p ./2,t,al pha);titleC凸轮理论轮廓压力角和曲率半径线图);xIabelC转角 phi / 度)；ylabel(hAx(1),曲率半径 *2 /

19、mm);% left y-axisylabel(hAx(2),压力角 / 度);% right y-axisgrid on;axis(hAx(1),0,360,-20,100);axis(hAx (2),0,360,-20,100);hLi ne1丄i neWidth = 1;hLi ne2丄i neWidth = 1;hLi nel.Color = k;hLi ne2.Color = b;(3) 理论轮廓压力角、曲率半径线图凸轮理论轮廓压力ft和曲率&径纟戈图50100150200转角0/度250300350型一 J H G .二D10005. 确定滚子半径，绘制凸轮理论轮廓与实际轮廓(1)

20、建立数学模型根据曲率半径线图可知，最小曲率半径在30mm附近，防止凸轮工作轮廓出 现尖点或出现相交包络线，选取滚子半径为 rr = 10mm。凸轮理论轮廓曲线方程为：x= (80 + s) cos?- ?y = (80 + s)si n?+ ?(其中 0 ? 2?dy/d?凸轮实际轮廓曲线方程为:X = x+ rrdx/d?V (dx/d?；2 + (dy/d?)2Y= y rr V(dx/d?)2 + (dy/d?)2(其中 0 ? 2?(2)MATLAB 程序%确定滚子半径，绘制凸轮理论轮廓和实际轮廓rr = 10; %滚子半径%理论轮廓x = (s0 + s).*s in(p hi) +

21、 e.*cos( phi);y = (s0 + s).*cos( phi) - e.*s in(p hi);%实际轮廓X = x + rr.*(gradie nt(y)./0.5)./sqrt(gradie nt(x)./0.5).A2 + (gradie nt(y)./0.5).A2);Y = y - rr.*(gradie nt(x)./0.5)./sqrt(gradie nt(x)./0.5)A2 + (gradie nt(y)./0.5)A2);%绘图figure(Name,凸轮轮廓);plot(x,y,k,X,Y,k,linewidth,1.0); % 轮廓hold on;grid on;theta = 0:p i/100:2* pi;pIot(r0.*cos(theta),r0.*s