A rotating shaft is supported by two symmetric bearings and a foundation structure. This foundation is reduced to a Component Mode Synthesis (CMS) superelement. A Campbell diagram analysis is performed on the model.
Problem Specifications:
| Shaft length | = 0.595 m |
| Shaft diameter | = 0.015 m |
| Support block length | = 0.79 m |
| Support block height | = 0.25 m |
| Support block width | = 0.154 m |
| Support block thickness | = 0.025 m |
| Bearing stiffness | = 5E+07 N/m |
The inertia properties of the disks are:
| Disc No | Mass [kg] | Ixx [kg-m2] | Iyy [kg-m2] | Izz [kg-m2] |
| 1 | 0.334 | 2.688e-4 | 2.688e-4 | 1.360e-4 |
| 2 | 0.782 | 7.02e-4 | 7.020e-4 | 4.310e-4 |
| 3 | 4.390 | 1.39e-2 | 1.194e-2 | 8.809e-3 |
The material properties for this analysis are:
| Structure | Material | Young's modulus [N/m2] | Density [kg/m3] | Poisson's ratio |
| Shaft | Steel | 2 E+11 | 7850 | 0.3 |
| Support | Aluminum | 7 E+10 | 2710 | 0.3 |
!** parameters
fl=0.79 ! foundation length
fw=0.154 ! foundation width
ft=0.025 ! foundation thickness
ex_f=70e9 ! foundation young's modulus
dens_f=2710 ! foundation density
fsh=0.25 ! support height
fst=0.025 ! support thickness
sch=0.2 ! shaft centre height
bor=0.025 ! bearing or =0.025 m
bs=5e7 ! bearing stiffness n/m
!** disc 1
m1=0.334
j1=2.688e-4
i1=1.36e-4
!** disc 2
m2=0.782
j2=7.02e-4
i2=4.31e-4
!** disc 3
m3=4.39
ix3=1.39e-2
iy3=1.194e-2
iz3=8.809e-3
ex_s=200e9
dens_s=7850
s_or=0.015
/prep7
!** foundation
block,0,fw,0,ft,0,fl
block,0,fw,0,fsh,(0.23-fst/2),(0.23+fst/2)
block,0,fw,0,fsh,(0.668-fst/2),(0.668+fst/2)
wpcsys,-1,0
wpoff,fw/2,sch
cswpla,11,1,1,1,
cyl4, , ,bor, , , ,fl
vsbv,2,4,,,keep
vsbv,3,4,
vovlap,all
wpcsys,-1,0
csys,0
n,1,fw/2,0.2,0.073
n,2,fw/2,0.2,0.23
n,3,fw/2,0.2,0.23+0.147
n,4,fw/2,0.2,0.23+0.147+0.179
n,5,fw/2,0.2,0.23+0.147+0.179+0.112
!** shaft
et,1,188
keyopt,1,3,3
sectype,1,beam,csolid,shaft, 0
secoffset,cent
secdata,s_or
ex,1,ex_s
nuxy,1,0.3
dens,1,dens_s
r,1,
e,1,2
*repeat,4,1,1
et,2,21
r,2,m1,m1,m1,j1,i1,i1
r,3,m2,m2,m2,j3,i2,i2
r,4,m3,m3,m3,ix3,iy3,iz3
type,2 ! motor
real,4
e,1
real,2 ! disc 1
e,3
real,3 ! disc 2
e,4
et,5,185
keyopt,5,2,3
ex,5,ex_f
nuxy,5,0.3
dens,5,dens_f
r,5
type,5
mat,5
real,5
csys,11
lsel,s,loc,x,0.025
lesize,all,,,4
csys,0
lsel,s,loc,y,0.1*ft,0.9*ft
lesize,all,,,2
lsel,s,loc,z,(0.23-fst/3),(0.23+fst/3)
lesize,all,,,2,,1
lsel,s,loc,z,(0.668-fst/3),(0.668+fst/3)
lesize,all,,,2,,1
allsel
esize,0.05
vsweep,all
*get,maxnode,node,,num,max
!** bearings radial stiffness modeling
et,7,14
r,7,bs/4
type,7
real,7
csys,11
nsel,s,loc,x,0,bor
nsel,r,loc,z,0.23
e,2,node(bor,0,0.23)
e,2,node(bor,45,0.23)
e,2,node(bor,90,0.23)
e,2,node(bor,135,0.23)
e,2,node(bor,180,0.23)
e,2,node(bor,225,0.23)
e,2,node(bor,270,0.23)
e,2,node(bor,315,0.23)
nsel,s,loc,x,0,bor
nsel,r,loc,z,0.668
e,5,node(bor,0,0.668)
e,5,node(bor,45,0.668)
e,5,node(bor,90,0.668)
e,5,node(bor,135,0.668)
e,5,node(bor,180,0.668)
e,5,node(bor,225,0.668)
e,5,node(bor,270,0.668)
e,5,node(bor,315,0.668)
allsel
!** components
esel,s,ename,,188
esel,a,ename,,21
cm,rotor,elem ! rotating parts
esel,a,ename,,14
nsle,s,1
cm,rotor_bear,elem ! rotor+bearings (non se)
esel,inve
cm,support,elem ! foundation (se)
allsel
save,rotor_supp_full,db
finish
!***************************
! superelement generation
!***************************
/filname,support
/solu
antype,substr
ematwrite,yes
seopt,support,2,
cmsopt,fix,4
nsel,s,loc,x,bor
m,all,all
csys,0 ! fix bottom of the support structure
nsel,s,loc,y,0
d,all,all
cmsel,s,support,elem
nsle,s
solve ! generate superelement "support.sub"
fini
save
!**********************************************
! rotor+bearings+superelement modal analysis
!**********************************************
/clear, nostart
/filname, rotor_use
resume, rotor_supp_full,db ! resume original assembly model
/prep7
vclear,all ! delete foundation elements to be replaced by superelement
et,10,matrix50
type,10
se,support ! read in superelement from file "support.sub"
allsel
/solu
pi=acos(-1)
rpmtorps=2*pi/60
antype,modal
modopt, qrdamp,6,1,0,1,on
mxpand,6, , ,1
coriolis,on,,,on
beta,1e-6
cmomega,rotor,0*rpmtorps,,,fw/2,sch,0.073,fw/2,sch,0.668
solve
cmomega,rotor,1000*rpmtorps,,,fw/2,sch,0.073,fw/2,sch,0.668
solve
cmomega,rotor,5000*rpmtorps,,,fw/2,sch,0.073,fw/2,sch,0.668
solve
cmomega,rotor,10000*rpmtorps,,,fw/2,sch,0.073,fw/2,sch,0.668
solve
save, rotor_use,db
finish
! **********************************
! expand results for superelement
! **********************************
/clear, nostart
/filname, support
resume, support,db
/solu
expass,on
seexp, support, rotor_use,
numexp,all, , , yes
solve
finish
! **********************
! review the results
! **********************
/clear, nostart
resume, rotor_use,db
/post1
cmsfile,clear
file, rotor_use,rst
/gropt,divx,5
/gropt,divy,5
/yrange,0,500,1
/show,jpeg
plcamp,on,1,rpm,,rotor ! plot campbell diagram with 1st order excitation
prcamp,on,1,rpm,,rotor
/noerase
plcamp,on,2,rpm,,rotor ! plot campbell diagram with 2nd order excitation
prcamp,on,2,rpm,,rotor
plcamp,on,3,rpm,,rotor ! plot campbell diagram with 3rd order excitation
prcamp,on,3,rpm,,rotor
plcamp,on,4,rpm,,rotor ! plot campbell diagram with 4th order excitation
prcamp,on,4,rpm,,rotor
/show,close
/erase
fini
!** combined results of foundation and rotor
/clear, nostart
/verify
resume, rotor_use,db
/post1
/eshape,1
cmsfile,clear
file, rotor_use,rst
set,3,2
/show,jpeg
plnsol,u,sum,2
*get, umax,plnsol,0,max
*stat,umax
/show,close
cmsfile,add,support.rst
set,last
esel,s,ename,,185
/show,jpeg
plnsol,u,sum,2
*get, umax,plnsol,0,max
*stat,umax
/show,close
finish
