Transient unbalance shifts were determined not to excite a rotor instability in the high pressure turbomachinery of the Space Shuttle Main Engine using the current rotor dynamic models. Sudden unbalance changes of relatively small magnitudes during fast-speed ramps showed stable nonsynchronous motion depending on the resultant unbalance distribution at subsequent high speed dwells. Transient moment unbalance may initiate a limit cycle subsynchronous response that shortly decays, but a persistent subsynchronous with large amplitudes was never achieved. These limit cycle subsynchronous amplitudes appear to be minimized with lower unbalance magnitudes, which indicates improved rotor balancing would sustain synchronous motion only. The transient unbalance phenomenon was determined to be an explanation for synchronous response shifts often observed during engine tests

Beatty, R. F.

Hine, M. J.

Landis, C. E.

English

NASA Technical Reports Server

ROTOR RESPONSE FOR TRANSIENT UNBALANCE CHANGES 
IN A NONLINEAR SIMULATION 
M. J. Hine, C. E. Landis, 
and R. F. Beatty 
Abstract 
Synchronous rotor response varies significantly 
with transient unbalance distribution and speed simul- 
taneously. In addition to this response variation, 
the complexity of a nonlinear rotor system can alter 
the response and produce nonsynchronous motion. A 
transient unbalance phenomena created a concern about 
a perturbation source for unstable operation. As an 
outgrowth of the Dynamic Balance Improvement Study 
Phase I1 contract with NASAIMSFC, transient unbalance 
shifts have been determined not to excite a rotor in- 
stability in the high pressure turbomachinery of the 
Space Shuttle Main Engine using the current rotor- 
dynamic models. Sudden unbalance changes of relatively 
small magnitudes during fast-speed ramps have shown 
stable nonsynchronous motion depending on the resultant 
unbalance distribution at subsequent high speed dwells. 
Transient moment unbalance may initiate a limit cycle 
subsynchronous response that shortly decays, but a 
persistent subsynchronous with large amplitudes was 
never achieved. These limit cycle subsynchronous am- 
plitudes appear to be minimized with lower unbalance 
magnitudes, which indicates improved rotor balancing 
would sustain synchronous motion only. The transient 
unbalance phenomenon was determined to be an explana- 
tion for synchronous response shifts often observed 
during engine tests. 
Introduction 
Throttleable pump-fed liquid rocket engines re- 
quire variable speed turbopumps capable of fast-speed 
ramp rates. A high rate of change in the applied 
torque may cause rotor components to reposition and 
alter the rotor mass unbalance. This concern, along 
with other possible unbalance changing mechanisms, 
https://ntrs.nasa.gov/search.jsp?R=19850018581 2020-03-20T19:06:54+00:00Z
was expressed as a self-enhanced unbalance concern by 
NASA. It was suggested t h a t  t r a n s i e n t  unbalance 
changes could i n i t i a t e  an  asynchronous r o t o r  i n s t a b i l -  
i t y  c l o s e  t o  t h e  s p i n  frequency. The focus of concern 
was wi th  t h e  h igh  performance turbopumps of t h e  Space 
S h u t t l e  Main Engine (SSME). The SSME powerhead wi th  
t h e  main combustion elements and a t t ached  turbopumps 
i s  shown i n  Fig.  1. The t h r o t t l e a b l e  SSME has  high 
Fig.  I. SSME Powerhead Component Arrangement 
p re s su re  l i q u i d  oxygen and l i q u i d  hydrogen turbopumps, 
which have had s t a b i l i t y  problems i n  t h e  p a s t ,  and 
t h i s  t r a n s i e n t  unbalance mechanism was i n v e s t i g a t e d  a s  
a technology item. The primary concern f o r  t h i s  phen- 
omenon w a s  an i n i t i a t i o n  mechanism f o r  a roughly 90 
percent  of speed subsynchronous w h i r l  on t h e  high 
p re s su re  oxygen turbopump. Tes t  d a t a  would normally 
i n d i c a t e  t h i s  subsynchronous response a t  t h e  maximum 
s h a f t  speed, o r  d i r e c t l y  a f t e r  a speed ramp, as shown 
i n  the  example frequency ve r sus  time d a t a  p l o t  of 
F i g .  2. 
To perform t h i s  complex t r a n s i e n t  a n a l y s i s ,  non- 
l i n e a r  models were requi red  and included such e f f e c t s  
provided t h e  capab 
e n t  unbalance a n a l  
ance magnitudes on ad jacent  t u r b i n e  d i s k s  form a 
v a r i a b l e  couple.  These condi t ions  r e q u i r e  unique 
simulation. programming and would gene ra l ly  c r e a t e  a 
l a r g e  computer c o s t .  However, hybr id  computer usage 
made i t  p o s s i b l e  t o  perform t h e  a n a l y s i s  f o r  a mini- 
mal c o s t  and s i g n i f i c a n t  time savings.  
Survey Turbopumps 
The e x i s t i n g  nonl inear  s imula t ion  models of t h e  
h igh  p re s su re  oxygen turbopump (HPOTP) and high pres- 
s u r e  f u e l  ( l i q u i d  hydrogen) turbopump (HPFTP) were 
used t o  perform t h e  a n a l y s i s .  The fol lowing is  a 
b r i e f  d e s c r i p t i o n  of t hese  turbopumps. 
The high pressure oxidizer turbopump is shown in 
Fig. 3 and a summary of its performance characteristics 
are provided in Table 1. Basically, the high pressure 
oxidizer  turbopump cons i s t s  of a double-entry cen t r i -  
fuga l  impeller  supplying l i q u i d  oxygen t o  t h e  main 
chamber. A por t ion  of t h i s  discharge flow i s  diver ted  
t o  a  smaller  cen t r i fuga l  impelle 
s h a f t  t h a t  suppl ies  l i q u i d  oxyge 
e r i s t i c s  i s  
pump driven by a two-stage turbine  t o  d e l i v e r  the  en- 
gine coolant.  The turbopump operates from 27,000 t o  
approximately 37,000 rpm. Two p a i r s  of duplex angular 
Fig. 4. SSME High Presure Fuel Turbopump 
Table 2. SSME HPFTP Performance Data 
PUMP DISCHARGE PRESSURE, PSlA 
TURBINE EFFICIENCY 
contact ball bearings support the rotor radially and 
a thrust bearing is provided for start and shutdown 
axial positioning. A balance piston built into the 
third-stage impeller reacts the axial thrust during 
steady-state operation. Straight smooth annular 
seals between the impeller stages ensure the rotor 
stability. 
ous- 
ings for the high pressure oxidizer and fuel turbo- 
pumps have been verified by years of empirical corre- 
lation and are generally accepted as producing the 
correct trends. The rotors are constructed of beam 
finite elements and the load line diagrams are shown 
in Fig. 5 and 6 for the high pressure oxidizer and 
fuel turbopumps, respectively, The high pressure oxi- 
dizer turbopump housing model, shown in Fig. 7, is 
constructed of plate elements and equivalent support 
beams that tie the housing to the engine chamber 
ground. The high pressure fuel turbopump housing 
model, shown in Fig. 8, is of beam and empirically 
sized spring construction, which is also tied to the 
engine chamber ground. The coupled system was analy- 
zed using modal synthesis techniques that combine 
substructures of the rotor and housing-to-engine 
- 
NODAL PLACEMENT 
0.00 P 
AXIAL COORDINATES 23.32'' 
Fig. 5. SSME HPOTP Rotating Assembly 
Finite Element Model 
NODAL PLACEMENT 
c AXIAL COOROINATES 28.29" 
Fig. 6. SSME IjIPFTP Rotating Assembly 
Finite Element Model 
support structure coupled through nonlinear bearings, 
hydrostatic seals, impeller-diffuser interaction, 
turbine aerodynamic cross-coupling, bearing damping, 
and fixed radial loads. Output capabilities include 
the ability to predict bearing loads, rotor displace- 
ments, and housing accelerations as a function of 
time and speed, and determine the response spectra. 
Fig. 7. SSME HPOTP Housing Finite Element Model 
Fig, 8. SSME HPFTP Housing Model 
The high pressure oxidizer turbopump operates be- 
tween its first and second rotor critical speeds at 
approximately 12,000 and 32,500 rpm, respectively. 
The lowest rotor critical speed is the turbine over- 
'hang mode and is shown in Fig. 9. The higher rotor 
critical speed is the main impeller mode and is shown 
Fig. 9. SSME HPOTP Lowest Rotor Critical 
Turbine Overhang Mode 
in Fig. 10. The high prsssure fuel turbopump operates 
above its first rotor critical speed at about 17,000 
rpm, but the second critical is in the speed range at 
approximately 32,000 rpm. The lower rotor mode has 
its maximum relative deflection approximately halfway 
between the bearing span and is shown in Fig. 11. The 
high pressure fuel turbopump 32,000 rpm rotor mode 
shown in Fig. 12 is highly damped by the straight 
smooth impeller interstage seals. 
FIRST 
STAGE 
AT 32500 RPM 
STATION 1 ORBIT - FORWARD PRECESSION 
IMPELLER 
Fig. 10. SSME HPOTP Higher Rotor Critical 
Main Impeller Mode 
/PUMP BEARING 
TURBINE 
BEARINGS. 
AT 17000 RPM 
STATION 1 ORBIT - FORWARD PRECESSION 
Fig. 11. SSME HPFTP Lowest Rotor Critical 
Skip Rope Mode 
PUMP BEARINGS 
TURBINE THIRD IMPELLER 
BEARINGS 
AT 32000 RPM 
CW - FORWARD PRECESSION 
Fig. 12. SSME HPFTP Higher Rotor Mode 
Node at Third Impeller 
Hybrid Model 
These nonlinear rotordynamics models mechanized 
on an AD10 hybrid computer were used to study the 
transient unbalance changes. The hybrid computer 
allows the complete interactive operation of the model 
during these parametric studies. 
Location, magnitude, and rate of change of the 
unbalances can be changed on-line and the resulting 
bearing loads and housing acceleration can be moni- 
tored on time-history brush charts. If, for example, 
an undesirable unbalance was used, the analysis could 
be terminated immediately and new unbalance values en- 
tered for a repeat case. The time-history data from 
the hybrid model is digitally stored for post-process- 
ing to obtain spectral information. 
A slight model modification had to be made to 
model time and speed varying unbalances since these 
variables were not normal parametric options of the 
model. To the best of our knowledge, Rocketdyne has 
the only time and speed variable unbalance analysis 
capability anywhere. To acquire this capability, an 
existing program option to simulate step unbalances 
at a discrete time was modified. This is mechanized 
as : 
U = U if time < t I U 
U = U + U if time 2 t I s u 
where 
U = effective unbalance 
UI = constant unbalance 
Us = 
increase in unbalance at time t 
u 
t = time the step unbalance occurs 
U 
Graphically, this would look like Fig. 13. 
W 
0 
z u 4 
3 "I 
Z 
3 
TIME 
Fig. 13. Step Unbalance With Time 
To simulate time and speed varying mechanisms, 
this was modified to: 
U = U if time < t 
1 .  U 
U = U + U (time - tU) if tU 5 time <_ t I s S 
where 
fi = rate of unbalance change, gm-in./sec 
s 
ts = time the unbalance stops changing 
Graphically, this appears as Fig. 14. 
u ts 
TIME. 
Fig. 14. Ramp Unbalance With Time 
This mechanization permits complete flexibility 
in specifying the transient unbalance and also main- 
tains the capability for simulating step unbalances. 
Response Results 
The initial state of balance in these simulations 
was established at all the major disks along both 
rotors based on build tolerances. Nominal state of 
balance conditions for the high pressure oxidizer and 
fuel turbopumps are shown in Fig. 15 and 16. It was 
determined for all self-enhanced unbalance mechanisms 
proposed that a significant unbalance change was not 
possible with the SSME turbopumps because splines, 
pilots, and normality tolerances were sufficient for 
maintaining rotor positioning. However, to study the 
PREBURNER IMPELLER 
0.5 GM-IN. 
MAIN IMPELLER 
4.0 GM-IN. 
TURBINE STAGES 
5.0 GM-IN. 
0 
@ 120 POUNDS SlDELOAD AT 29,450 RPM PROPORTIONAL TO SPEED SQUARED 
@ 1500 POUNDS SlDELOAD AT 29,450 RPM PROPORTIONAL TO SPEED SQUARED 
@ 230 POUNDS SlDELOAD AT 29,450 RPM PROPORTIONAL TO SPEED 
Fig. 15. HPOTP Model Initial Conditions 
SECOND STAGE TURBINE 
FIRST STAGE IMPELLER ~ ~ ~ ~ ~ , " ~ S  5'25 GM-lN' 
3.95 GM-IN. FIRST STAGE TURBINE 4.05 GM-IN. 
PUMP BEARINGS 
0.0 
I I 200 POUNDS SIDELOAD 
6.13 GM-IN. 
A 
STAGE IMPELLER THIRD STAGE IMPELLER 
6.68 GM-IN. 
Fig. 16. HPFTP Model Initial Conditions 
effect of changing unbalance for information only, 
it was arbitrarily decided to vary the unbalance 
magnitude by a factor of two over the speed ramp. 
Numerous simulations were performed with typically 
stable and well behaved synchronous only results. 
Some of the more interesting results will now be 
discussed. 
HF'FTP Time-Varying Unbalance 
The unbalance at the first stage impeller was 
varied above and below the maximum anticipated 
unbalance during an increasing speed ramp as in Fig. 
17. The resultant acceleration response at the pump 
flange is shown in Fig. 18. All response parameters 
showed stable behavior following the ramp, Since the 
rotor unbalance distribution is altered, the rotor 
displacement constantly varies along the rotor length. 
3.96 RUN NO. 2 h, 
I I 
0.0 
0.0 0.6 1.7 2.2 
TIME, SECONDS 
Fig. 17. HPFTP Computer (AD-10) Model Input for 
Time-Dependent Unbalance Increase and 
Decrease Applied at the First Impeller 
HPFTP Time-Varying Moment 
A transient moment was simulated by varying op- 
posing unbalances at the first- and second-stage tur- 
bine disks above and below the maximum anticipated 
values during a speed ramp as in Fig. 19 and 20. The 
resultant acceleration response of the pump flange is 
shown in Fig. 21. 
The pump appears to be basically unaffected by 
the moment changes themselves after the speed ramp. 
Following the speed ramp, for both increasing and de- 
creasing turbine moment unbalance cases, a limit cycle 
subsynchronous response is present as shown in exam- 
ples (Fig. 22 and 23) for a turbine bearing load and 
Fig. 18. I-TPFTP Housing Acceleration Response to 
Unbalance Changes at First Impeller 
TIME, SECONDS 
I 
5.25 
TIME, SECONDS 
"U"  
TIME, SECONDS 
Fig. 19 ,  HPFTP Computer (AD-10) Model Input for 
Time-Dependent Moment Unbalance Increase 
TIME. SECONDS 
TIME, SECONDS 
- 0  
t; 2 f -2.025 1 I 
O C % &  0 0.5 1.7 
l~ 0 Q TIME, SECONDS 
Fig.  20. NPFTP Computer (AD-10) Model Input for 
Time-Dependent Moment Unbalance Decrease 
TIME- 
Fig.  21. NPFTP Housing Acceleration Response to 
Varying Moment Unbalance at Turbine 
FREQUENCY, HZ (X 1000) 
Fig. 22. HPFTP Spectra at 37,200 rpm with 
Increasing Moment Unbalance 
FREQUENCY, HZ (X 1000) 
Fig. 23. HPFTP Spectra at 37,200 rpm with 
Increasing Moment Unbalance 
t u rb ine  i n t e r s t a g e  s e a l  displacement wi th  an inc reas ing  
moment unbalance. This lowest r o t o r  mode subsynchron- 
ous response i s  a t t r i b u t e d  t o  t h e  changes during t h e  
ramp s i n c e  during normal opera t ion  at  h igh  speeds,  the  
subsynchronous response i s  not  p re sen t  i n  t h e  simula- 
t i o n s .  This l e v e l  of subsynchronous response i n  t h e  308 
Hz range is  t y p i c a l l y  no t  experienced wi th  a  s t r a i g h t  
smooth impel le r  i n t e r s t a g e  s e a l  conf igura t ion  high pres-  
s u r e  f u e l  tu rbopmp during engine h o t - f i r e  t e s t i n g .  
For normal s t eady- s t a t e  unbalance d i s t r i b u t i o n s  and 
high-speed dwell  condi t ions ,  t h e  t y p i c a l  response spec- 
t ra  is shown i n  Fig.  2 4 ,  which t h e  d a t a  represented  i n  
Fig.  22 and 23 even tua l ly  decays t o  r e f l e c t .  Sens i t iv -  
i t y  t o  t h e  i n i t i a l  condi t ions  i s  t y p i c a l  i n  nonl inear  
s imula t ion  work. 
x 10-3 
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 
FREQUENCY, HZ (X 10001 
Fig.  24 .  Typical  HPFTP Response Spectra  
a t  37,200 rpm 
HPOTP Time-Varying Unbalance 
The e f f e c t  on t h e  r o t o r  response of a  time-vary- 
ing  unbalance during a speed ramp was s tud ied  wi th  
t h e  unbalance occurr ing  s e p a r a t e l y  on t h e  t u r b i n e  and 
main impel le r .  Both inc reas ing  and decreasing unbal- 
ances were s tud ied  dur ing  a  speed inc reas ing  ramp a s  
shown in Fig. 25 and 26. The acceleration of the hous- 
ing flange is shown in Fig. 27 for the unbalance 
changes occurring at the main impeller. As expected, 
the increasing unbalance case produced larger residual 
response magnitudes than the decreasing case. The pump 
housing acceleration response to unbalance changes at 
the turbine is shown in Fig. 28. 
The steady-state pump response was determined by 
the final unbalance magnitude and speed for the main 
impeller unbalance case. Variations in the response 
were observed during the speed ramp for the two analy- 
sis conditions where resonant activity was observed 
near the rotor critical speed and housing resonances. 
The pump was dwelled at high speed for both un- 
balance conditions with subsynchronous activity at 
one-half synchronous speed, or the lowest rotor mode 
in the spectral displacement data at the turbine 
stages which was not present in the bearing loads 
or housing accelerations. 
1----- R A W  1 
AT - 1.7 
Fig. 25. HPOTP Computer (AD-10) Model Input for 
Time-Dependent Unbalance Increase 
Y 
V 
2.2 TIME, SECONDS 
Fig. 26. HFOTP Computer (AD-10) Model Output for 
Time-Dependent Unbalance Decrease 
TIME - 
Fig. 27. HPOTP Housing Acceleration Response 
to Varying Unbalance at Main 
Impeller 
- c c c c c w - c k - - H - t u - e ~ ~ ! ~ ! : : : : ! : ! : ! : ! ! ! ! : : ~ ~ +  
TIME- 
Fig.  28. HPOTP Housing Accelera t ion  Response t o  
Varying Unbalance a t  Turbine 
Turbine response i s  shown i n  Fig.  29 and 30 f o r  
t h e  increased  and decreased main impe l l e r  unbalances,  
r e spec t ive ly .  Of no te  he re  i s  t h a t  t h e  subsynchron- 
ous amplitudes a f t e r  an unbalance inc rease  were h ighe r  
than  those  a f t e r  an unbalance decrease.  This subsyn- 
engine h o t - f i r e  t e s t  and is  a r e f l e c t i o n  of t h e  bear- 
rbng loads .  
FI
RS
T S
TA
GE
 T
UR
BI
NE
 D
IS
PL
AC
EM
EN
T,
 IN
CH
ES
 
FI
RS
T 
ST
AG
E 
TU
RB
IN
E 
DI
SP
LA
CE
M
EN
T,
 IN
CH
ES
 
FREQUENCY. HZ (X 1000) 
Fig. 31. HPOTP Response Spectra  a t  33,000 rpm 
Turbine Unbalance Increase  
FREQUENCY, HZ (X 1000) 
Fig. 32. HPOTP Response Spect ra  a t  33,000 rpm 
Turbine Unbalance Decrease 
Fig. 33. Typical HPOTP Response Spectra at 
33,000 rpm With Modified Turbine 
Interstage Seal 
Conclusions 
Numerous transient unbalance cases were perfoned 
on speed ramps and a divergent rotor instability, or 
nonsynchronous motion close to the operating speed, 
was never achieved. Unbalance changes in excess of 
reasonable analytically predicted magnitudes caused 
significant synchronous response variation due to the 
resulting unbalance distribution exciting different 
system modes. The limit cycle subsynchronous rotor 
motion detected for both turbopumps was always at the 
lowest rotor mode frequency, never at a higher rotor 
mode frequency. The lower rotor mode stability for 
either turbopump has not been a problem since well 
before the first Shuttle launch. The high pressure 
fuel turbopump subsynchronous rotor mode response was 
shown at a speed slightly above the maximum operating 
speed and has not been experienced during hot-fire 
testing since the conversion to straight smooth im- 
peller interstage seals. The high pressure oxidizer 
turbopump lowest rotor mode subsynchronous response is 
not present at speeds up to a maximum operating speed 
of 30,000 rpm and the low levels shown at 33,000 rpm 
can be suppressed with a turbine interstage seal modi- 
fication currently in the development stages. 
Lower transient unbalance magnitude shifts may ex- 
plain some of the synchronous response variation occa- 
sionally seen during engine test or the "haystack" 
phenomenon observed in flight, which was a gradual in- 
crease in high pressure oxidizer turbopump synchronous 
response followed by a short decrease to the original 
levels. However, as a result of this study, a tran- 
sient unbalance mechanism cannot explain, or be de- 
scribed as, the trigger for 90 percent of speed subsyn- 
chronous whirl on the high pressure oxidizer turbopump. 


Rotor response for transient unbalance changes in a nonlinear simulation

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