課程設(shè)計(jì)牛頭刨床的運(yùn)動(dòng)分析—Matlab程序

1、牛頭刨床的運(yùn)動(dòng)分析Matlab程序摘要：文中建立了用解析法作牛頭刨床的運(yùn)動(dòng)分析，基于機(jī)構(gòu)的位置方程式，將位置方程對(duì)時(shí)間求一次和二次倒數(shù)，得到機(jī)構(gòu)的速度和加速的方程，然后就得到位移、速度、加速度，并通過復(fù)數(shù)矢量法和矩陣法，并且借助Matlab等軟件對(duì)牛頭刨床進(jìn)行運(yùn)動(dòng)分析，并對(duì)牛頭刨床的運(yùn)動(dòng)學(xué)規(guī)律進(jìn)行了仿真，為該機(jī)床的優(yōu)化設(shè)計(jì)提供了理論支撐。Abstract:This paper establishes the analytical method used for shaping motion analysis, based on the position of the mechanism equ

2、ations, the position equation on time and one of the first and two countdown, be the velocity and acceleration equations of displacement, velocity, and then get, acceleration, and by complex number vector method and matrix method, and with the aid of Matlab software shaper motion analysis, and the s

3、haper of the kinematics of the machine tool for simulation, optimization design has provided the theory support.1.引言： 對(duì)牛頭刨床進(jìn)行運(yùn)動(dòng)分析的任務(wù)是在已知機(jī)構(gòu)尺寸及原動(dòng)件運(yùn)動(dòng)規(guī)律的情況下，確定機(jī)構(gòu)中其他構(gòu)件上某些點(diǎn)的軌跡、位移、速度、加速度和構(gòu)件的角位移、角速度及角加速度。而這些內(nèi)容，不論是設(shè)計(jì)新的機(jī)器，還是為了了解現(xiàn)有機(jī)械的運(yùn)動(dòng)性能，都是十分必要的，而且它還是研究機(jī)械動(dòng)力性能的必要基礎(chǔ)和前提。對(duì)于牛頭刨床來說，其刨刀在有效工作行程中應(yīng)該接近等速運(yùn)動(dòng)，而回程速度卻應(yīng)高于前者速度

4、，從而提高效率。為了確定牛頭刨床的設(shè)計(jì)是否滿足要求，就必須對(duì)其進(jìn)行運(yùn)動(dòng)分析。本文建立了牛頭刨床的力學(xué)模型，并推導(dǎo)了其運(yùn)動(dòng)微分方程，通過數(shù)值方法求得了牛頭刨床的運(yùn)動(dòng)學(xué)規(guī)律并開發(fā)了一款用于牛頭刨床的通用運(yùn)動(dòng)學(xué)分析軟件。2.機(jī)構(gòu)結(jié)構(gòu)分析： 1.自由度計(jì)算：F=3n-2-F=5*3-7*2=1 2.結(jié)構(gòu)分析： 5個(gè)可動(dòng)構(gòu)件，兩個(gè)二級(jí)桿組組成，5個(gè)轉(zhuǎn)動(dòng)副2個(gè)移 動(dòng)副， 為二級(jí)機(jī)構(gòu)。3.機(jī)構(gòu)運(yùn)動(dòng)分及程序設(shè)計(jì)1.如圖先建立坐標(biāo)系，已知=125mm, =600mm，=150mm,原動(dòng)件1的方位角和等角速度=1 rad/s 如圖所示：解：1.位置分析：由于有四個(gè)位置量，為了求解需要建立兩個(gè)封閉矢量方程。有圖形A

5、BCA可寫出矢量方程:可變?yōu)椋海?）由封閉圖形CDEGC可寫出矢量方程：（2）得到方程：由上式可得：2.速度和加速度分析式(1)和(2)對(duì)時(shí)間取一次二次導(dǎo)數(shù)寫成矩陣形式，即得一下速度方程： =加速度方程=+二、matlab源程序： 程序1clear all;clc;w1=1;l1=0.125;l3=0.600;l4=0.150;l6=0.275;l61=0.575;for m=1:3601o1(m)=pi*(m-1)/1800;o31(m)=atan(l6+l1*sin(o1(m)/(l1*cos(o1(m);if o31(m)>=0 o3(m)=o31(m);else o3(m)=pi

6、+o31(m);end;s3(m)=(l1*cos(o1(m)/cos(o3(m);o4(m)=pi-asin(l61-l3*sin(o3(m)/l4);se(m)=l3*cos(o3(m)+l4*cos(o4(m);if o1(m)=pi/2 o3(m)=pi/2; s3(m)=l1+l6; endif o1(m)=3*pi/2 o3(m)=pi/2; s3(m)=l6-l1; endA1=cos(o3(m),-s3(m)*sin(o3(m),0,0;sin(o3(m),s3(m)*cos(o3(m),0,0;0,-l3*sin(o3(m),-l4*sin(o4(m),-1;0,l3*cos

7、(o3(m),l4*cos(o4(m),0;B1=w1*-l1*sin(o1(m);l1*cos(o1(m);0;0;D1=A1B1;E1(:,m)=D1;ds(m)=D1(1);w3(m)=D1(2);w4(m)=D1(3);ve(m)=D1(4);A2=cos(o3(m),-s3(m)*sin(o3(m),0,0;sin(o3(m),s3(m)*cos(o3(m),0,0;0,-l3*sin(o3(m),-l4*sin(o4(m),-1;0,l3*cos(o3(m),l4*cos(o4(m),0;B2=-w3(m)*sin(o3(m),(-ds(m)*sin(o3(m)-s3(m)*w3(

8、m)*cos(o3(m),0,0;w3(m)*cos(o3(m),(ds(m)*cos(o3(m)-s3(m)*w3(m)*sin(o3(m),0,0;0,-l3*w3(m)*cos(o3(m),-l4*w4(m)*cos(o4(m),0;0,-l3*w3(m)*sin(o3(m),-l4*w4(m)*sin(o4(m),0*ds(m);w3(m);w4(m);ve(m);C2=w1*-l1*w1*cos(o1(m);-l1*w1*sin(o1(m);0;0;B=B2+C2;D2=A2B;E2(:,m)=D2;dds(m)=D2(1);a3(m)=D2(2);a4(m)=D2(3);ae(m)

9、=D2(4);end;o11=o1*180/pi;y=o3*180/pi;o4*180/pi;w=w3;w4;a=a3;a4;figure;subplot(221);h1=plotyy(o11,y,o11, se); axis equal;title('位置線圖');xlabel('ittheta1');ylabel('ittheta3,theta4,Se');subplot(222);h2=plotyy(o11,w,o11,ve);title('速度線圖');xlabel('ittheta1');ylabel(&

10、#39;itomega3,omega4,Ve');subplot(212);h3=plotyy(o11,a,o11,ae); title('加速度線圖');xlabel('ittheta1');ylabel('italpha3,alpha4,alphaE');F=o11;o3./pi*180;o4./pi*180;se;w3;w4;ve;a3;a4;ae'G=F(1:100:3601,:)5.程序運(yùn)行結(jié)果：6.SAM61 仿真結(jié)果：Result listing SAM 6.1.46 . Mechanism: noname_Nr:T

11、imeVx(5)Ax(5)x(5)-sm/sm/s2m 00.0000.045-9.9970.279 10.028-0.206-8.0660.277 20.056-0.405-6.3350.268 30.083-0.560-4.9020.254 40.111-0.680-3.7750.237 50.139-0.772-2.9120.217 60.167-0.844-2.2530.194 70.194-0.899-1.7370.170 80.222-0.941-1.3080.145 90.250-0.972-0.9190.118 100.278-0.992-0.5340.091 110.306-

12、1.001-0.1270.063 120.333-0.9990.3190.035 130.361-0.9830.8120.008 140.389-0.9531.351-0.019 150.417-0.9081.929-0.045 160.444-0.8462.534-0.070 170.472-0.7673.155-0.092 180.500-0.6713.789-0.112 190.528-0.5564.445-0.129 200.556-0.4235.162-0.143 210.583-0.2686.028-0.152 220.611-0.0867.189-0.157 230.6390.1

13、368.830-0.157 240.6670.41111.054-0.149 250.6940.75313.598-0.133 260.7221.16015.465-0.107 270.7501.58914.869-0.069 280.7781.94810.292-0.019 290.8062.1302.4400.038 300.8332.082-5.6040.097 310.8611.842-11.1810.152 320.8891.489-13.8350.198 330.9171.093-14.3380.234 340.9440.704-13.5060.259 350.9720.350-1

14、1.9190.274 361.0000.045-9.9990.2796.結(jié)論經(jīng)過仿真數(shù)據(jù)結(jié)果還算合理：部分偏差由于仿真軟件畫法漏洞引起 桿長設(shè)置不精確。經(jīng)驗(yàn)證解析法的正確性，以解析法分析的牛頭刨床的運(yùn)動(dòng)特性符合實(shí)際。程序2l1=0.125;l3=0.6;l4=0.15;l6=0.275;l61=0.575;omega1=1;alpha1=0;hd=pi/180;du=180/pi;for n1=1:459;theta1(n1)=-2*pi+5.8119+(n1-1)*hd;ll=l1,l3,l4,l6,l61;theta,omega,alpha=six_ bar(theta1(n1),omeg

15、a1,alpha1,ll);s3(n1)=theta(1);theta3(n1)=theta(2);theta4(n1)=theta(3);sE(n1)=theta(4);v2(n1)=omega(1);omega3(n1)=omega(2);omega4(n1)=omega(3);vE(n1)=omega(4);a2(n1)=alpha(1);alopha3(n1)=alpha(2);alpha4(n1)=alpha(3);aE(n1)=alpha(4);endfigure(3);n1=1:459;t=(n1-1)*2*pi/360; subplot(2,2,1);plot(t,theta3

16、*du,'r-.');grid on;hold on;axis auto;haxes,hlin1,hline2=plotyy(t,theta4*du,t,sE);grid on;hold on;xlabel(時(shí)間/s')axes(haxes(1);ylabel(角位移/circ')axes(haxes(2);ylabel('位移/m')hold on;grid on;text(1.15,-0.65,'theta_3')text(3.4,0.27,'theta_4')text(2.25,-0.15,'s_E&

17、#39;)subplot(2,2,2);plot(t,omega3,'r-.');grid on;hold on;axis auto;haxes,hline1,hline2=plotyy(t,omega4,t,vE);grid on;hold on;xlabel('時(shí)間/s')axes(haxes(1);xlabel('角速度/radcdots-1')axes(haxes(2);ylabel('速度/mcdots-1')grid on;hold on;text(3.1,0.35,'omega_3')text(2.1

18、,0.1,'omega_4')text(5.5,0.45,'v_E')subplot(2,2,3);plot(t,alpha3,'r-.');grid on;hold on;axis auto;haxes,hline1,hline2=plotyy(t,alpha4,t,aE);grid on;hold on;xlabel('時(shí)間/s')axes(haxes(1);ylabel('角加速度/radcdots-2')axes(haxes(2);ylabel('加速度/mcdots-2')grid on;

19、hold on;text(1.5,0.3,'alpha_3')text(3.5,0.51,alpha_4')text(1.5,-0.11,'a_E')subplot(2,2,4);n1=20;x(1)=0;y(1)=0;x(2)=(s3(n1)*1000-50)*cos(theta3(n1);y(2)=(s3(n1)*1000-50)*sin(theta3(n1);x(3)=0;y(3)=l6*1000;x(4)=l1*1000*cos(thetal(n1)y(4)=s3(n1)*1000*sin(theta3(n1);x(5)=(s3(n1)*1000

20、*50*cos(theta3(n1);y(5)=(s3(n1)*1000*50*sin(theta3(n1);x(6)=l3*1000*cos(theta3(n1);y(6)=l3*1000*sin(theta3(n1);x(7)=l3*1000*cos(theta3(n1)*14*1000*cos(theta4(n1);y(7)=l3*1000*sin(theta3(n1)*14*1000*sin(theta4(n1);x(8)=l3*1000*cos(theta3(n1)*14*1000*cos(theta4(n1)-900;y(8)=l61*1000;x(9)=l3*1000*cos(t

21、heta3(n1)*14*1000*cos(theta4(n1)*600;y(9)=l61*1000;x(10)=(s3(n1)*1000-50)*cos(theta3(n1);y(10)=(s3(n1)*1000-50)*sin(theta3(n1);x(11)=x(10)+25*cos(pi/2-theta3(n1);y(11)=y(10)-25*sin(pi/2-theta3(n1);x(12)=x(11)+100*cos(pi/2-theta3(n1);y(12)=y(11)+100*cos(pi/2-theta3(n1);x(13)=x(12)-50*cos(pi/2-theta3(

22、n1);y(13)=y(12)+50*sin(pi/2-theta3(n1);x(14)=x(10)-25*cos(pi/2-theta3(n1);y(14)=y(10)+25sin(pi/2-theta3(n1);x(15)=x(10);y(15)=y(10);x(16)=0;y(16)=0;x(17)=0;y(17)=16*1000;k=1:2;plot(x(k),y(k);hold on;k=3:4;plot(x(k),y(k);hold on;k=5:9;plot(x(k),y(k);hold on;k=10:15;plot(x(k),y(k);hold on;k=16:17;hold

23、 on;plot(x(k),y(k);hold on;grid on;axis(-500 600 0 650);title('牛頭刨床仿真');grid on;xlabel('mm');ylabel('mm');plot(x(1),y(1),'o');plot(x(3),y(3),'o');plot(x(4),y(4),'o');plot(x(6),y(4),'o');plot(x(7),y(7),'o');hold on;grid on;xlabel('mm

24、');ylabel('mm');axis(-400 600 0 650);function theta,omega,alpha=six_ bar(theta1,omega1,alpha1,ll)l1=ll(1);l3=ll(2);l4=ll(3);l6=ll(4);l61=ll(5);s3=sqrt(l1*cos(theta1)*(l1*cos(theta1)+(l6+l1*sin(theta1)*(16+l1*sin(theta1);theta3=acos(11*cos(theta1)/s3);theta4=pi-asin(l61-l3*sin(theta3)/l4)

25、;sE=l3(cos(theta3)+l4*cos(theta4);theta(1)=s3;theta(2)=theta3;theta(3)=theta4;theta(4)=sE;A=sin(theta3),s3*cos(theta3),0,0;-cos(theta3),s3,sin(theta3),0,0;0,l3*cos(theta3),l4*cos(theta4),0;B=l1cos(theta1);l1sin(theta1);0;0;0mega=A(omegal*B);v2=omega(1);omega3=omega(2);omega4=omega(3);vE=omega(4);A=sin(theta3),s3*cos(theta3),0,0;cos(theta3),-s3*sin(theta3),0,0;0,l3*sin(theta3),l4*sin(theta4),1;0,l3*cos(theta3),l4*