AssignmentVehicle system dynamics simulation学院：机电学院专业：机械工程及自动化姓名：指导教师：The model we are going to analys:The FBD of the suspension system is shown as follow:According to the New's second Law, we can get the equation:2)()(221211mgz z c z z k z m --+-=∙∙∙∙221212)()(z k mg z z c z z k z m w +-----=∙∙∙∙0)()()()(222111222111=-++--+-++--+∙∙∙∙∙∙∙∙w w w w z L z k z L z k z L z c z L z c z m χχχχ0)()()()(2222111122221111=-++----++---∙∙∙∙∙∙∙∙w w w w z L z L k z L z L k z L z L c z L z L c J χχχχχd w w w w Q z L z k z L z c z m ,111111111)()(-=------∙∙∙∙∙χχd w w w w Q z L z k z L z c z m ,222222222)()(-=-+--+-∙∙∙∙∙χχWhen there is no excitation we can get the equation:2)()(221211mg z z c z z k z m --+-=∙∙∙∙221212)()(z k mg z z c z z k z m w +-----=∙∙∙∙Then we substitude the data into the equation, we write a procedure to simulate the system:Date:⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧==⋅==⋅===MN/m0.10km 25.1s/m kN 0.20MN/m 0.1m kg 3020kg2100kg 3250w 2l c k I m m by w bProgram :1.For the no excitation situation.Buid a file named rigid1.mfunction dy=rigid1(t,y)dy=zeros(4,1);dy(1)=y(2);dy(3)=y(4);dy(2)=-(615.38*y(1)-615.38*y(3)+12.31*dy(1)-12.31*dy(3)-9.81);dy(4)=-(5238.1*y(3)-476.19*y(1)+9.52*dy(3)-9.52*dy(1)-9.81);Buid an other file named test1.m[T,Y]=ode45('rigid1',[0 1.5],[0 0 0 0]);figure (1)plot(T,Y(:,1))gridon,xlabel('time(sec)'),ylabel('displayment(m)'),title('displayment of boge')figure (2)plot(T,Y(:,2))grid on,xlabel('time(sec)'),ylabel('velocity(m/s)'),title('velocity of boge')figure (3)plot(T,Y(:,3))gridon,xlabel('time(sec)'),ylabel('displayment(m)'),title('displayment of wheel')figure (4)plot(T,Y(:,4))grid on,xlabel('time(sec)'),ylabel('velocity(m/s)'),title('velocity of wheel')We can get the figures as follows: The velocity of m1:Dumping, then it goes to zero. The velocity of m2 and m3:Dumping, then goes to zero.The displacement of m1:Dump to a constant.The displacement of m2 and m3:Dump to a constant.When there are excitations, according to Newton's second Law and momentum equation we can get0)()()()(32321=-++--+-++--+∙∙∙∙∙∙∙∙z l z k z l z k z l z c z l z c z m χχχχ0)()()()(3232=-++----++---∙∙∙∙∙∙∙∙z l z kl z l z kl z l z cl z l z l c J χχχχχd Q z l z k z l z c z m ,222)()(22-=------∙∙∙∙∙χχd Q z l z k z l z c z m ,33333)()(-=-+--+-∙∙∙∙∙χχ )(22,2x z k Q w d -= )(33,3x z k Q w d -=There are four excitations, each wheel set get one excitation. X1=0.005sin(4πt) X2=0.005sin(8πt) X1 and X2 act on boge 1 X3=0.005sin(4πt) X4=0.005sin(6πt) X1 and X2 act on boge 2Program:Mw=2100;%wheel massMb=3250;%boge massMc=0;%car body massKw=1.0e7;%wheel elastic coeffetionKs=0e6;%secendary suspension coeffetionKp=1.0e6;%primery suspension coeffetionCs=1;%secendary dump coeffetionCp=5.0e4;%primery suspension coeffetionlc=0;%car body lenthlt=1.25;%boge lenthic=1;%car body inertiaib=3020;%boge inertiaA=[-(Kp+Cp+Kw+Mw),0,0,0,(Kp+Cp),0,0,-lt*(Kp+Cp),0,0;0,-(Kp+Cp+Kw+Mw),0,0,(Kp+Cp),0,0,-lt*(Kp+Cp),0,0;0,0,-(Kp+Cp+Kw+Mw),0,0,(Kp+Cp),0,0,-lt*(Kp+Cp),0;0,0,0,-(Kp+Cp+Kw+Mw),0,(Kp+Cp),0,0,-lt*(Kp+Cp),0;(Kp+Cp),(Kp+Cp),0,0,-(Ks+Cs+2*Kp+2*Cp+Mb),0,(Ks+Cs),0,0,-lc*(Ks+Cs) ;0,0,(Kp+Cp),(Kp+Cp),0,-(Ks+Cs+2*Kp+2*Cp+Mb),(Ks+Cs),0,0,-lc*(Ks+Cs) ;0,0,0,0,(Ks+Cs),(Ks+Cs),-(2*Ks+2*Cs+Mc),0,0,0;lt*(Kp+Cp),-lt*(Kp+Cp),0,0,0,0,0,(2*lt^2*(Kp+Cp)-ib),0,0;0,0,(lt*Kp+lt*Cp),-(lt*Kp+lt*Cp),0,0,0,0,(2*lt^2*(Kp+Cp)-ib),0;0,0,0,0,(lc*Ks+lc*Cs),-(lc*Ks+lc*Cs),0,0,0,(2*lc^2*(Ks+Cs)-ic)];B=[-(2*Mw+Cp),0,0,0,Cp,0,0,-Cp*lt,0,0;0,-(2*Mw+Cp),0,0,Cp,0,0,Cp*lt,0,0;0,0,-(2*Mw+Cp),0,0,Cp,0,0,-Cp*lt,0;0,0,0,-(2*Mw+Cp),0,Cp,0,0,Cp*lt,0;Cp,Cp,0,0,-(Cs+2*Cp+2*Mb),0,Cs,0,0,-Cs*lc;0,0,Cp,Cp,0,-(Cs+2*Cp+2*Mb),Cs,0,0,-Cs*lc;0,0,0,0,Cs,Cs,-(2*Mc+2*Cs),0,0,0;lt*Cp,-lt*Cp,0,0,0,0,0,(2*lt^2*Cp-2*ib),0,0;0,0,lt*Cp,-lt*Cp,0,0,0,0,(2*lt^2*Cp-2*ib),0;0,0,0,0,lc*Cs,-lc*Cs,0,0,0,(2*lc^2*Cs-2*ic)];C=diag([Mw,Mw,Mw,Mw,Mb,Mb,Mc,ib,ib,ic]);D=9.8*[Mw,Mw,Mw,Mw,Mb,Mb,Mc,0,0,0]';Ts=0.001;%seperate 10s into 10000 partst=0:Ts:10;x1=0.05*sin(4*pi*t); %the excitation of wheel 1x2=0.05*sin(8*pi*t); %the excitation of wheel 2x3=0.05*sin(4*pi*t); %the excitation of wheel 3x4=0.05*sin(6*pi*t); %the excitation of wheel 4N=4000;YY=zeros(10,2);VV=zeros(10,2);AA=zeros(10,2);for j=3:NXn=Kw*[x1(j-2);x2(j-2);x3(j-2);x4(j-2);0;0;0;0;0;0];YY(:,j)=A\B*YY(:,j-1)+A\C*YY(:,j-2)-A\Xn-A\D; %displayment matrixVV(:,j)=YY(:,j)-YY(:,j-1); %speed matrixAA(:,j)=VV(:,j)-VV(:,j-1); %acceleration matrixendi=3:N;figure(1)plot(i,YY(1,i))gridon,xlabel('time(Ts)'),ylabel('displayment(m)'),title('displayment of wheel 1');figure(2)plot(i,YY(2,i))gridon,xlabel('time(Ts)'),ylabel('displayment(m)'),title('displayment of wheel 2');figure(3)plot(i,YY(3,i))gridon,xlabel('time(Ts)'),ylabel('displayment(m)'),title('displayment of wheel 3');figure(4)plot(i,YY(4,i))gridon,xlabel('time(Ts)'),ylabel('displayment(m)'),title('displayment of wheel 4');figure(5)plot(i,YY(5,i))gridon,xlabel('time(Ts)'),ylabel('displayment(m)'),title('displayment of boge 1');figure(6)plot(i,YY(6,i))gridon,xlabel('time(Ts)'),ylabel('displayment(m)'),title('displayment of boge 2');figure(7)plot(i,YY(8,i))grid on,xlabel('time(Ts)'),ylabel('angulardisplayment(m)'),title('angular displayment of boge 1');figure(8)plot(i,YY(9,i))grid on,xlabel('time(Ts)'),ylabel('angulardisplayment(m)'),title('angular displayment of boge 2');figure(9)plot(i,VV(1,i))grid on,xlabel('time(Ts)'),ylabel('velocity(m/s)'),title('velocity of wheel 1');figure(10)plot(i,VV(2,i))grid on,xlabel('time(Ts)'),ylabel('velocity(m/s)'),title('velocity of wheel 2');figure(11)plot(i,VV(3,i))grid on,xlabel('time(Ts)'),ylabel('velocity(m/s)'),title('velocity of wheel 3');figure(12)plot(i,VV(4,i))grid on,xlabel('time(Ts)'),ylabel('velocity(m/s)'),title('velocity of wheel 4');figure(13)plot(i,VV(5,i))grid on,xlabel('time(Ts)'),ylabel('velocity(m/s)'),title('velocity of boge 1');figure(14)plot(i,VV(6,i))grid on,xlabel('time(Ts)'),ylabel('velocity(m/s)'),title('velocity of boge 2');figure(15)plot(i,VV(8,i))grid on,xlabel('time(Ts)'),ylabel('angulervelocity(rad/s)'),title('angular velocity of boge 1');figure(16)plot(i,VV(9,i))grid on,xlabel('time(Ts)'),ylabel('angulervelocity(rad/s)'),title('angular velocity of boge 2');figure(17)plot(i,AA(1,i))gridon,xlabel('time(Ts)'),ylabel('acceleration(m/s2)'),title('accelerat ion of wheel 1');figure(18)plot(i,AA(2,i))gridon,xlabel('time(Ts)'),ylabel('acceleration(m/s2)'),title('accelerat ion of wheel 2');figure(19)plot(i,AA(3,i))gridon,xlabel('time(Ts)'),ylabel('acceleration(m/s2)'),title('accelerat ion of wheel 3');figure(20)plot(i,AA(4,i))gridon,xlabel('time(Ts)'),ylabel('acceleration(m/s2)'),title('accelerat ion of wheel 4');figure(21)plot(i,AA(5,i))gridon,xlabel('time(Ts)'),ylabel('acceleration(m/s2)'),title('accelerat ion of boge 1');figure(22)plot(i,AA(6,i))gridon,xlabel('time(Ts)'),ylabel('acceleration(m/s2)'),title('accelerat ion of boge 2');For the excitation X1 and X2.We can get the figure as follow:The displacement of boge 1:Inertialy goes to stable.The displacement of wheel 1 and wheel 2:The displayment of wheels it with the excitation.The velocity of boge 1:It has a big implus at the very first time, then it goes to a stady state.The velocity of wheel 1 and wheel 2:After the big implus at the very first time, the velocity goes to a stady state.The acceleration of boge 1:It has a bige acceleration at first, but quickly goes to a stady state. The acceleration of wheel 1 and wheel 2:It has a bige acceleration at first, but quickly goes to a stady state.The angular displayment and angular velocity of boge 1:The pitch of the boge inetialy goes to stady state. For the excitation X3 and X4.We can get the figure as follow:The displacement of boge 2:Inertialy goes to stable.The displacement of wheel 3 and wheel 4:The displayment of wheels it with the excitation.The velocity of boge 2:It has a big implus at the very first time, then it goes to a stady state.The velocity of wheel 3 and wheel 4:After the big implus at the very first time, the velocity goes to a stady state. The acceleration of boge 2:It has a bige acceleration at first, but quickly goes to a stady state.The acceleration of wheel 3 and wheel 4:It has a bige acceleration at first, but quickly goes to a stady state. The angular displayment and angular velocity of boge 2:The pitch of the boge inetialy goes to stady state.Analys for the result:When there is no excitation, the amplitude of boge’s acceleration is incresed with time untill it goes to zero. The displament and the velocity of car body are the same tendency as the acceleration, but the displament is dumped to 0.0196m.When there are some ecitation occurs at the rail, the response of the boge is decreased after the excitation passes the primery suspention.The displament, velocity and acceleration of boge are all smaller than wheel sets. That’s the function of the suspention.。