7.10. Example: Harmonic Response to Unbalanced Force using Component Mode Synthesis (CMS)

The following example shows a harmonic analysis with unbalanced force using the component mode synthesis (CMS) procedure on a rotating part. It illustrates the use of the SYNCHRO command and whirl animation using the ANHARM command during postprocessing.

The structure is a two-spool rotor on symmetric bearings as shown in Figure 7.17: Multi-Spool Rotor Model (Full and CMS Model). The outer spool rotates at up to 5000 RPM and the inner spool rotates about twice as fast.

This model is also used in Example Unbalance Harmonic Analysis in the Advanced Analysis Guide. In the following example, however, the inner spool is reduced to a CMS superelement.

7.10.1. Problem Specifications

An unbalanced force is applied at a node on the outer spool and the harmonic response is calculated.

7.10.2. Input for the Analysis

/out,
/com, ******************************************
/com, Multi-Spool CMS Model
/com, ******************************************
/out,scratch
/filname,cms_model
/prep7
et,1,281
type,1
sectype,1,shell
secdata,0.05/2,1,0,3

mp,ex,1,2.0e11
mp,dens,1,7800
mp,nuxy,1,0.3
mat,1

k,1,0,0.15,0
k,2,0,0.20,0
k,3,3,0.20,0
k,4,3,0.15,0

k,5,0,0,0
k,6,10,0,0

a,1,2,3,4

vrotat,1,,,,,,5,6,360

lsel,s,line,,2,8,2
lsel,a,line,,22,24,2
lsel,a,line,,14,16,2
lesize,all,,,6
lsel,all

lsel,s,line,,9,12,1
lsel,a,line,,17,20,1
lsel,a,line,,25,32,1
lesize,all,,,4
lsel,all

lsel,s,line,,1,7,2
lsel,a,line,,13,15,2
lsel,a,line,,21,23,2
lesize,all,,,1
lsel,all

amesh,all
allsel,all

et,3,281
type,3
secnum,3
mat,1
sectype,3,shell
secdata,0.05/2,1,0,7

k,35,7,0.20,0
k,36,7,0.15,0
k,37,10,0.15,0
k,38,10,0.20,0

a,35,36,37,38

vrotat,21,,,,,,5,6,360

lsel,s,line,,34,40,2
lsel,a,line,,54,56,2
lsel,a,line,,46,48,2
lesize,all,,,6
lsel,all

lsel,s,line,,57,64,1
lsel,a,line,,41,44,1
lsel,a,line,,49,52,1
lesize,all,,,4
lsel,all

lsel,s,line,,33,39,2
lsel,a,line,,45,47,2
lsel,a,line,,53,55,2
lesize,all,,,1
lsel,all

amesh,21,40,1
allsel,all

nummrg,node
nummrg,kp

numstr,node,3000
numstr,elem,3000

et,2,281
mp,ex,2,2.0e11
mp,dens,2,7800
mp,nuxy,2,0.3
mp,alpd,2,1e-3                  ! Material damping
mp,betd,2,1e-4
type,2
secnum,2
mat,2
sectype,2,shell
secdata,0.1/2,1,0,5

k,39,3,0.20,0
k,40,3,0.30,0
k,41,7,0.30,0
k,42,7,0.20,0

a,39,40,41,42

vrotat,41,,,,,,5,6,360

lsel,s,line,,66,72,2
lsel,a,line,,78,80,2
lsel,a,line,,86,88,2
lesize,all,,,8

lsel,s,line,,89,96,1
lsel,a,line,,81,84,1
lsel,a,line,,73,76,1
lesize,all,,,4

lsel,s,line,,65,71,2
lsel,a,line,,77,79,2
lsel,a,line,,85,87,2
lesize,all,,,1

amesh,41,60,1
allsel,all

cpintf,all

et,4,214
keyopt,4,2,1
keyopt,4,3,0
real,4
r,4,1.0e6,1.4e5,,,10,10
rmore,,,,

n,10000,5,0.22,0

type,4
real,4
e,node(5,0.20,0),10000
allsel,all

esel,s,type,,1
cm,comp1,elem
esel,all

esel,s,type,,2
cm,comp2,elem
esel,all

esel,s,type,,3
cm,comp3,elem
esel,all

nsel,s,loc,x,0
nsel,a,loc,x,10
d,all,all,0
nsel,all

d,10000,all,0

nsel,s,loc,x,0
cm,interface1,node
allsel,all,all

nsel,s,loc,x,3
cm,interface2,node
allsel,all,all

nsel,s,loc,x,7
cm,interface3,node
allsel,all,all

nsel,s,loc,x,10
cm,interface4,node
allsel,all,all

save
fini

/clear,nostart

/filname,model
/prep7
et,1,281
type,1
sectype,1,shell
secdata,0.05/2,1,0,3

mp,ex,1,2.0e11
mp,dens,1,7800
mp,nuxy,1,0.3

k,1,0,0.15,0
k,2,0,0.20,0
k,3,3,0.20,0
k,4,3,0.15,0

k,5,0,0,0
k,6,10,0,0

a,1,2,3,4

vrotat,1,,,,,,5,6,360

lsel,s,line,,2,8,2
lsel,a,line,,22,24,2
lsel,a,line,,14,16,2
lesize,all,,,6
lsel,all

lsel,s,line,,9,12,1
lsel,a,line,,17,20,1
lsel,a,line,,25,32,1
lesize,all,,,4
lsel,all

lsel,s,line,,1,7,2
lsel,a,line,,13,15,2
lsel,a,line,,21,23,2
lesize,all,,,1
lsel,all

amesh,all
allsel,all

et,3,281
type,3
secnum,3
mat,1
sectype,3,shell
secdata,0.05/2,1,0,7

k,35,7,0.20,0
k,36,7,0.15,0
k,37,10,0.15,0
k,38,10,0.20,0

a,35,36,37,38

vrotat,21,,,,,,5,6,360

lsel,s,line,,34,40,2
lsel,a,line,,54,56,2
lsel,a,line,,46,48,2
lesize,all,,,6
lsel,all

lsel,s,line,,57,64,1
lsel,a,line,,41,44,1
lsel,a,line,,49,52,1
lesize,all,,,4
lsel,all

lsel,s,line,,33,39,2
lsel,a,line,,45,47,2
lsel,a,line,,53,55,2
lesize,all,,,1
lsel,all

amesh,21,40,1
allsel,all

nummrg,kp
nummrg,node

esel,s,type,,1
cm,comp1,elem
esel,all

esel,s,type,,2
cm,comp2,elem
esel,all

esel,s,type,,3
cm,comp3,elem
esel,all

nsel,s,loc,x,0
cm,interface1,node
allsel,all,all

nsel,s,loc,x,3
cm,interface2,node
allsel,all,all

nsel,s,loc,x,7
cm,interface3,node
allsel,all,all

nsel,s,loc,x,10
cm,interface4,node
allsel,all,all

save
fini
!generation pass

/filname,part1
/sol
antype,substr
seopt,part1,3,1
cmsopt,fix,10

cmomega,comp1,1
coriolis,on,,,on                ! Coriolis on in a stationary reference frame

cmsel,s,comp1
cmsel,s,interface2
m,all,all
nsle

cmsel,s,interface1
m,all,all
nsle

solve
allsel,all,all
fini
save

/filname,part2
/sol
antype,substr
seopt,part2,3,1
cmsopt,fix,10

cmomega,comp3,1
coriolis,on,,,on                ! Coriolis on in a stationary reference frame

cmsel,s,comp3
cmsel,s,interface3
m,all,all
nsle

cmsel,s,interface4
m,all,all
nsle

solve
fini
save

!use pass

/clear,nostart
/filname,use
!/out,
/prep7
et,1,matrix50
type,1
se,part1
se,part2

numstr,node,3000
numstr,elem,3000

et,2,281
sectype,2,shell
secdata,0.1/2,1,0,5

mp,ex,1,2.0e11
mp,dens,1,7800
mp,nuxy,1,0.3
mp,alpd,1,1e-3                  ! Material damping
mp,betd,1,1e-4

type,2
mat,1
secnum,2

k,5,0,0,0
k,6,10,0,0

k,19,3,0.20,0
k,20,3,0.30,0
k,21,7,0.30,0
k,22,7,0.20,0

a,19,20,21,22

vrotat,1,,,,,,5,6,360

lsel,s,line,,2,8,2
lsel,a,line,,14,16,2
lsel,a,line,,22,24,2
lesize,all,,,8
lsel,all

lsel,s,line,,9,12,1
lsel,a,line,,17,20,1
lsel,a,line,,25,32,1
lesize,all,,,4
lsel,all

lsel,s,line,,1,7,2
lsel,a,line,,13,15,2
lsel,a,line,,21,23,2
lesize,all,,,1
lsel,all
nummrg,kp
amesh,1,20,1
allsel,all

nsel,s,loc,x,3
nsel,a,loc,x,7
cpintf,all
allse,all,all

et,4,214
keyopt,4,2,1
keyopt,4,3,0
real,4
r,4,1.0e6,1.4e5,,,10,10
rmore,,,,

n,10000,5,0.22,0

type,4
real,4
e,node(5,0.20,0),10000
allsel,all

nsel,s,loc,x,0
nsel,a,loc,x,10
d,all,all,0
nsel,all

d,10000,all,0

esel,s,type,,1
cm,comp1,elem
allsel,all,all

esel,s,type,,2
cm,comp2,elem
allsel,all,all

save
fini
/com, ******************************************
/com, Solution Controls for Full Harmonic Solve
/com, ******************************************
/solu
antype,harmic                   ! Perform Harmonic analysis
hropt,full

F0 = 1.0e-4                     ! Unbalance Force
n3 = node(5.0,-0.29424,0.58527e-1)

f,n3,fy,-F0                     ! Real FY component at node 'nodeUnb'
f,n3,fz,,F0                     ! Imaginary FZ component at node 'nodeUnb'

cmomega,comp1,1000
cmomega,comp2,500
coriolis,on,,,on                ! Coriolis on in a stationary reference frame

synchro,,comp2

dmprat,0.02                     ! Global damping ratio

spinRpm1 = 0
spinRpm2 = 7200
begin_freq = spinRpm1/60        ! Begin frequency of excitation
end_freq = spinRpm2/60          ! End frequency of excitation
harfrq,begin_freq,end_freq
nsubs,120

kbc,1
solve
finish

/post1
file,use,rst

set,last
/show,jpeg
/graphics,power
/eshape,1
plnsol,u,sum
*get,umax,plnsol,0,max
/show,close
/out,
*stat,umax
/out,scratch
fini

!expansion pass

/clear,nostart
/filname,part1
resume,part1,db
/solu
expass,on
seexp,part1,use
numexp,all,,,yes
solve
fini

/clear,nostart
/filname,part2
resume,part2,db
/solu
expass,on
seexp,part2,use
numexp,all,,,yes
solve
fini

/inquire,test,exist,final,rst
*if,test,eq,1,then
/delete,final,rst
*endif

/clear,nostart
resume,cms_model,db

/post1
*do,j,1,120
file,part1                      ! generation pass 1 rst file
append,1,j
file,part2                      ! generation pass 1 rst file
append,1,j
file,use                        ! generation pass 1 rst file
append,1,j
reswrite,final,,,,1
file,part1                      ! generation pass 1 rst file
append,1,j,,1
file,part2                      ! generation pass 1 rst file
append,1,j,,1
file,use                        ! generation pass 1 rst file
append,1,j,,1

reswrite,final,,,,1
*enddo
fini

/post1
file,final,rst

set,last
/show,jpeg
/graphics,power
/eshape,1
plnsol,u,sum
*get,umax,plnsol,0,max
plesol,s,eqv
*get,smax,plnsol,0,max
plesol,epel,eqv
*get,emax,plnsol,0,max
/show,close
/out,
*stat,umax
*stat,smax
*stat,emax
/out,scratch

plnsol,u,sum
anharm,12,0.1,,,3,              ! Full Harmonic

fini

/post26
file,final,rst

n1 = node(5.0,0.58527e-1,0.29424)
n2 = node(5.0,0.29424,-0.58527e-1)

/com ************************************************************************
/com, Output: Amplitude at nodes %n1% and %n2% as a function of the frequency
/com ************************************************************************

nsol,2,n1,U,Y,UY
nsol,3,n1,U,Z,UZ
realvar,4,2,,,UYR
realvar,5,3,,,UZR
prod,6,4,4,,UYR_2
prod,7,5,5,,UZR_2
sqrt,9,8,,,AMPL%n1%

extreme

nsol,2,n2,U,Y,UY
nsol,3,n2,U,Z,UZ
realvar,4,2,,,UYR
realvar,5,3,,,UZR
prod,6,4,4,,UYR_2
prod,7,5,5,,UZR_2
sqrt,10,8,,,AMPL%n2%

extreme
/com *****************
/com, Graphics display
/com *****************
/gropt,logy,1
/show,jpeg
/title,'Unbalance Response Analysis using CMS Model'
!/yrange,1.0e-5,1.0e+2
/out,
plvar,9,10                      ! Displays variables in the form of a graph
/show,close
!prvar,9,10
finish

/exit,nosave

7.10.3. Output for the Analysis

The results of the unbalanced response analysis, postprocessed in /POST26, are shown in Figure 7.18: Unbalanced Response Using CMS Model and Figure 7.19: Unbalanced Response Using Full Model. The logarithmic plots show the variation of the displacement amplitudes of two selected nodes with respect to the frequency of excitation.

The animation of the whirls is shown below.