support.m

转子动力学研究中完整的支承松动数值仿真程序

完整的支承松动数值仿真程序
%运动微分方程

function d=fun(t,y,w)

N=length(y);
w=2100;
m1=4;%两端滑动轴承处等效集中质量
m2=32.1; %转子圆盘等效集中质量
m3=50.0;%轴承支座处等效集中质量
g=9.81;
e=0.00005; %偏心距
k=2.5e7;%弹性轴刚度
delta2=0.6e-3;%初始间隙
c1=1050;%转子圆盘处阻尼系数
c2=2100;%转子在轴承处阻尼系数
k1=7.5e7;
k2=2.5e9;
cb1=350;
cb2=500;

ox1=y(1);%未松动端竖直方向位移x1
oy1=y(2);%未松动端竖直方向位移y1
odx1=y(8);
ody1=y(9);

ox2=y(3);%圆盘位移x2
oy2=y(4);%圆盘位移y2
odx2=y(10);
ody2=y(11);

ox3=y(5);%松动端轴心位移x3
oy3=y(6);%松动端轴心位移y3
odx3=y(12);
ody3=y(13);

oy4=y(7);%质量m3在竖直方向位移y4
ody4=y(14);

if oy4<0
    cb=cb2;
    kb=k2;
elseif  (oy4>=0)&(oy4<=delta2)
        cb=0;
        kb=0;
    else
         cb=cb1;
         kb=k1;
end

M=[  m1   0     0    0    0     0    0;
     0    m1    0    0    0     0    0;
     0    0     m2   0    0     0    0;
     0    0     0    m2   0     0    0;
     0    0     0    0    m1    0    0;
     0    0     0    0    0     m1   0;
     0    0     0    0    0     0    m3;];

C=[  c1   0     0    0    0     0    0;
     0    c1    0    0    0     0    0;
     0    0     c2   0    0     0    0;
     0    0     0    c2   0     0    0;
     0    0     0    0    c1    0    0;
     0    0     0    0    0     c1   0;
     0    0     0    0    0     0    cb;];
  
K=[  k   0     -k    0    0     0    0;
     0    k    0    -k    0     0    0;
     -k   0    2*k    0    -k    0    0;
     0    -k   0    2*k    0    -k    0;
     0    0    -k    0     k    0    0;
     0    0    0    -k     0    k    0;
     0    0    0     0     0    0    kb;];

fx=oilx( ox1, oy1, odx1, ody1, w);
fy=oily( ox1, oy1, odx1, ody1, w);
fx1=oilx( ox3,oy3-oy4,odx3,ody3-ody4,w);
fy1=oily( ox3,oy3-oy4,odx3,ody3-ody4,w);



F=[   fx;
      fy-m1*g;
      m2*e*w^2*cos(t);
      m2*e*w^2*sin(t)-m2*g;
      fx1;
      fy1-m1*g;
      -fy1-m3*g ];
   
C=C/w;
K=K/w^2;
F=F/c/w^2;

for i=1:1:N/2
    y1(i,1)=y(i);
    y2(i,1)=y(i+N/2);
end


yy2=inv(M)*(F-C*y2-K*y1);

d=zeros(N,1);

for i=1:1:N/2
    d(i)=y2(i,1);
    d(i+N/2)=yy2(i,1);
end


%x方向油膜力

function oilforce=oilx(x,y,dx,dy,wi)

R=0.025; L=0.012; miu=0.018;  dfai=1; dert=0.00011;

e=sqrt(x*x+y*y);
delta=miu*wi*R*L*(R/dert)*(R/dert)*(L/2.0/R)*(L/2.0/R);
ppp1=(y+2.0*dx)/(x-2.0*dy);
sign1=sign(ppp1);
        
ppp2=y+2.0*dx;
sign2=sign(ppp2);

alpha=atan(ppp1)-pi/2.0*(sign1+sign2);
alphaa=atan((y*cos(alpha)-x*sin(alpha))/sqrt(abs(1.0-abs(x*x)-abs(y*y))));
fg=2.0*(pi/2.0+alphaa)/sqrt(abs(1.0-abs(x*x)-abs(y*y)));
fv=(2.0+(y*cos(alpha)-x*sin(alpha))*fg)/(1.0-abs(x*x)-abs(y*y));
fs=(x*cos(alpha)+y*sin(alpha))/(1.0-abs((x*cos(alpha)+y*sin(alpha))*(x*cos(alpha)+y*sin(alpha))));

f1=sqrt(abs(abs((x-2.0*dy)*(x-2.0*dy))+abs((y+2.0*dx)*(y+2.0*dx))))/(1.0-abs(x*x)-abs(y*y));

fx=-1.0*f1*(3.0*x*fv-sin(alpha)*fg-2.0*cos(alpha)*fs);
fy=-1.0*f1*(3.0*y*fv+cos(alpha)*fg-2.0*sin(alpha)*fs);

oilforce=fx*delta;



%y方向油膜力

function oilforce=oily(x,y,dx,dy,wi)

R=0.025; L=0.012; miu=0.018;  dfai=1; dert=0.00011;

e=sqrt(x*x+y*y);
delta=miu*wi*R*L*(R/dert)*(R/dert)*(L/2.0/R)*(L/2.0/R);
ppp1=(y+2.0*dx)/(x-2.0*dy);
sign1=sign(ppp1);
       
ppp2=y+2.0*dx;
sign2=sign(ppp2);

alpha=atan(ppp1)-pi/2.0*(sign1+sign2);
alphaa=atan((y*cos(alpha)-x*sin(alpha))/sqrt(abs(1.0-abs(x*x)-abs(y*y))));
fg=2.0*(pi/2.0+alphaa)/sqrt(abs(1.0-abs(x*x)-abs(y*y)));
fv=(2.0+(y*cos(alpha)-x*sin(alpha))*fg)/(1.0-abs(x*x)-abs(y*y));
fs=(x*cos(alpha)+y*sin(alpha))/(1.0-abs((x*cos(alpha)+y*sin(alpha))*(x*cos(alpha)+y*sin(alpha))));

f1=sqrt(abs(abs((x-2.0*dy)*(x-2.0*dy))+abs((y+2.0*dx)*(y+2.0*dx))))/(1.0-abs(x*x)-abs(y*y));

fx=-1.0*f1*(3.0*x*fv-sin(alpha)*fg-2.0*cos(alpha)*fs);
fy=-1.0*f1*(3.0*y*fv+cos(alpha)*fg-2.0*sin(alpha)*fs);

oilforce=fy*delta;



%主分析程序

clear all
h=pi/256;
w=2100;
tf=300000*2*pi/w;
tspan=0:h:tf;
y0=[0.05,0.5,0.05,0.5,0.05,0.5,0.05,0.5,0.05,0.5,0.05,0.5,0.05,0.5];
options=odeset('RelTol',10^-6,'AbsTol',10^-6);  
[t,y]=ode45(@fun,tspan,y0);

figure(1)
subplot(2,2,1);
plot(t,y(:,1),'r',t,y(:,2),'b')
title('未松动端位移响应');xlabel('t');ylabel('x1-red,y1-blue');
subplot(2,2,2);
plot(t,y(:,3),'r',t,y(:,4),'b')
title('圆盘位移响应');xlabel('t');ylabel('x2-red,y2-blue');
subplot(2,2,3);
plot(t,y(:,5),'r',t,y(:,6),'b')
title('松动端轴心位移响应');xlabel('t');ylabel('x3-red,y4-blue');
subplot(2,2,4);
plot(t,y(:,7),'b')
title('m3在竖直方向位移响应');xlabel('t');ylabel('y4');

figure(2)
subplot(2,2,1);
plot(y(:,1),y(:,2))
title('未松动端轴心轨迹');xlabel('x1');ylabel('y1');
subplot(2,2,2);
plot(y(:,5),y(:,6))
title('松动端轴心轨迹');xlabel('x3');ylabel('y3');

yy1=sqrt(y(:,1).^2+y(:,2).^2);%yy1=sqrt(x1^2+y1^2) 
yy2=sqrt(y(:,5).^2+y(:,6).^2);%yy2=sqrt(x3^2+y3^2) 
N1=256;fs=1024;stepf=fs/N1;k=pi*2/882.5056;%882.5056转子固有频率sqrt(k/m2)
n=0:stepf*k:(fs/2-stepf)*k;
YY1=abs(fft(yy1));
YY2=abs(fft(yy2));
figure(3)
plot(n,abs(YY1(1:N1/2)));grid on;
title('未松动情况下幅值谱');xlabel('频率比');ylabel('FFT幅值');
figure(4)
plot(n,abs(YY2(1:N1/2)));grid on;
title('松动情况下幅值谱');xlabel('频率比');ylabel('FFT幅值');
      
fclose('all');