The document discusses the performance prediction of shafts, particularly focusing on problems related to shaft alignment and whirling vibrations. It emphasizes the impact of bearing stiffness on bearing loads and shaft slopes in marine propulsion systems, with case studies revealing how variations in stiffness affect system performance. Furthermore, the document introduces a study on lateral vibrations and the importance of understanding natural frequencies in the context of maintaining optimal operational conditions.

1. Consequence of detailed modelling into shaft performance prediction
q g p p
Shaft Alignment and Whirling vibration

2. Problem?
A proper Shaft Analysis report issued.
Practical alignment verfication muserments shows a recognaizable variation!
Why ?!
In some of the cases it is subjected to the tools used.
But there is some other reasons!
One of these reasons is the cosequence of the system components stiffness into:
One of these reasons is the cosequence of the system components stiffness into:
1‐Bearing loads and Shaft slope inside propeller bearing
2‐Propeller shaft lateral vibration.
2 Propeller shaft lateral vibration
This will explain some of the other reasons meanwhile it helps to investigate the most
reliable working domain for new projects.
li bl ki d i f j t
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3. Model of the case study
Propeller
ASTB FSTB AGB FGB
ASTB=Aft Sterntube Bearing
FSTB=Fwd Sterntube Bearing
AGB=Aft Gearbox Bearing
FGB=Fwd Gearbox Bearing
GB= Gearbox (OR Main
Engine first
E i fi two bearings).
b i )
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4. Bearing stiffness
External Bearing
E t lB i
Calc. Tool
Shaft
Bearing
Oil Film
Calculation
Bearing
Material
Practical or theoretical
Model assumption
Bearing
Foundation
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5. Part 1‐ Alignment
Case No.1‐ Variation of FSTB Stiffness
Case No 1 Variation of FSTB Stiffness
Working Domain:
‐Variation of Forward Sterntube Bearing
stiffness from 5.0E7 N/m to 5.0E10 N/m.
‐GAP & SAG are kept constant at all analysis
Propeller
points.
GB
ASTB FSTB
‐All other bearings assumed stiffness kept
constant.
‐GB bearings offsets changed at each analysis
point in order to maintain the same GAP‐SAG
figures.
fi
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6. Case No.1‐ Variation of FSTB Stiffness
Results:
A‐ Bearing loads.
FSTB Stiffness variation effect on Bearing Loads
FSTB Stiffness variation effect on Bearing Loads
120
ASTB/10 FSTB AGB FGB
100
80
kN)
60
Load (k
40
20
0
4.00E+07 4.00E+08 4.00E+09 4.00E+10
Stiffness (N/m)
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7. Case No.1‐ Variation of FSTB Stiffness
Results:
B‐ Slope of the shaft inside Aft Sterntube bearing.
FSTB Stiffness variation effect on Shaft Slope at ASTB
FSTB Stiffness variation effect on Shaft Slope at ASTB
0.53
0.525
0.52
0.515
mm/m)
0.51
Shaft Slope at ASTB
p
Slope (m
0.505
0.5
0.495
0.49
4.00E+07 4.00E+08 4.00E+09 4.00E+10
Stiffness (N/m)
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8. Case No.2‐ Variation of ASTB Stiffness
Working Domain:
‐Variation of Aft Sterntube Bearing stiffness
from 3.0E8 N/m to 5.0E10 N/m.
‐GAP & SAG are kept constant at all analysis
Propeller
points.
GB
ASTB FSTB
‐All other bearings assumed stiffness kept
constant.
‐GB bearings offsets changed at each analysis
point in order to maintain the same GAP‐SAG
figures.
fi
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9. Case No.2‐ Variation of ASTB Stiffness
Results:
A‐ Bearing loads.
ASTB Stiffness variation effect on Bearing Loads
ASTB Stiffness variation effect on Bearing Loads
90
ASTB/10 FSTB AGB FGB
80
70
60
Load (kN)
50
40
30
20
10
0
2.00E+08 2.00E+09 2.00E+10
Stiffness (mm/m)
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10. Case No.2‐ Variation of ASTB Stiffness
Results:
B‐ Slope of the shaft inside Aft Sterntube Bearing.
ASTB Stiffness variation effect on Shaft Slope at ASTB
ASTB Stiffness variation effect on Shaft Slope at ASTB
0.75
0.7
0.65
Shaft Slope at ASTB
Slope(mm/m)
0.6
0.55
0.5
0.45
0 45
0.4
2.00E+08 2.00E+09 2.00E+10
Stiffness (N/m)
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11. Case No.3‐ Variation of GB Bearings Stiffness.
(OR Main Engine foundation stiffness)
fo ndation
Working Domain:
‐Variation of Gearbox Bearings stiffness from
2.0E7 N/m to 1.0E11 N/m.
‐GAP & SAG are kept constant at all analysis Propeller
points.
GB
ASTB FSTB
‐All other bearings assumed stiffness kept
constant.
‐GB bearings offsets changed at each analysis
point in order to maintain the same GAP‐SAG
figures.
fi
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12. Case No.3‐ Variation of GB Bearings Stiffness.
(OR Main Engine foundation stiffness)
fo ndation
Results:
A‐ Bearing loads.
GB bearings Stiffness variation effect on Bearing Loads
100
ASTB/10 FSTB AGB FGB
90
80
70
60
Load (kN)
50
L
40
30
20
10
0
2.00E+07 2.00E+08 2.00E+09 2.00E+10
Stiffness (N/m)
Stiffness (N/m)
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13. Case No.3‐ Variation of GB Bearings Stiffness.
(OR Main Engine foundation stiffness)
fo ndation
Results:
B‐ Slope of the shaft inside Aft Sterntube Bearing.
GB bearings Stiffness variation effect on Shaft Slope at ASTB
GB bearings Stiffness variation effect on Shaft Slope at ASTB
0.538
0.536
0.534
Shaft Slope at ASTB
0.532
mm/m)
Slope (m
0.53
0.528
0.526
0.524
1.00E+07 1.00E+08 1.00E+09 1.00E+10 1.00E+11
Stiffness (N/m)
( / )
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14. Discussion of results
A‐ Bearing loads.
A Bearing loads
It is of importance to advice a well reliable stiffness range for the bearings
(Foundation & Material) in order to ensure a more reliable loads into the
bearing.
120 100
90
90
100 80
80
70
70
80
60 60
60 50 50
40 40
40 30 30
20 20
20
10
10
0 0
0
4.00E+07 4.00E+08 4.00E+09 4.00E+10 2.00E+08 2.00E+07 2.00E+08 2.00E+09 2.00E+10
2.00E+09 2.00E+10
Case 1
C Case 2
C Case 3
Variation of FSTB Stiffness Variation of ASTB Stiffness Variation of GB B. Stiffness
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15. Discussion of results
B‐ Slope of the shaft inside propeller bearing.
B Slope of the shaft inside propeller bearing
Is the slope of the shaft inside the propeller bearing (only) is judgeable ?
0.53 0.75 0.538
0.525 0.7 0.536
0.52 Shaft Slope at ASTB
0.65 0.534
0.515
0.6 0.532
0.51
Shaft Slope at ASTB 0.55 0.53
0.505
0.5 0.528
0.5
05 Shaft Slope at ASTB
f
0.495 0.45 0.526
0.49 0.4 0.524
4.00E+07 4.00E+08 4.00E+09 4.00E+10 2.00E+08 2.00E+09 2.00E+10 1.00E+07 1.00E+08 1.00E+09 1.00E+10 1.00E+11
Case 1 Case 2 Case 3
Variation of FSTB Stiffness Variation of ASTB Stiffness Variation of GB B. Stiffness
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16. Discussion of results
B‐ Slope of the shaft inside propeller bearing.
B Slope of the shaft inside propeller bearing
Slope mismatch between the shaft and the bearing is more interesting, So
the slope of the bearing it self is important as well.
BEARING REACTIONS IN VERTICAL - OPERATING CONDITION 1 (GB-COLD-STATIC)
-----------------------------------------------------------------------------------
----
Position Load Pressure Offset Slope
[cm] [kN] [bar] [mm] [mm/m]
Bearing 1 244 182 5 -0 221
0.221 0.669
0 669
Bearing 2 284 129 5 -0.060 0.511
Bearing 3 803 5 0 0.000 -0.163
Bearing 4 1325 78 5 0.719 0.447
Lubricant White metal Bearing 5 1436 59 4 1.223 0.474
238 -1.074 7.340E-004 235233 15 -220
244 -1.036 7.200E-004 246710 16 -221
244 -1.035 7.200E-004 246930 16 -221
249 -1.000 7.050E-004 248883 16 -39
254 -0.964 6.910E-004 250869 16 -40
259 -0.930 6.770E-004 252888 16 -40
264 -0.896
-0 896 6 620E-004
6.620E-004 254940 17 -41
269 -0.863 6.470E-004 257025 17 -42
274 -0.831 6.320E-004 259143 17 -42
279 -0.799 6.170E-004 261294 17 -43
284 -0.769 6.020E-004 263463 17 -44
292 -0.723 5.790E-004 256819 17 84
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17. Discussion of results
B‐ Slope of the shaft inside propeller bearing.
B Slope of the shaft inside propeller bearing
Then a traditional evaluation of the oil fils stiffness can be checked.
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18. Part 2‐Lateral vibration study.
Introduction‐
Introduction Basics
Vibration: Is a harmonic motion.
Vib ti I h i ti
Stiffness: Is the rigidity of an object
Damping: Is the resistance to the motion.
System response: Is the amount of the
object deflection based on stiffness and
damping (Local/Global).
damping (Local/Global)
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19. Part 2‐Lateral vibration study.
Introduction‐ Lateral vibration mode shapes
Introduction Lateral vibration mode shapes Amplitude
and stiffness components.
λ4
λ3
λ2
λ1
λ1 > λ2 > λ3 > λ4 Ω1 < Ω2 < Ω3 < Ω4
wave lengths vibrating frequencies
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20. Part 2‐Lateral vibration study.
Introduction‐ System response amplification factor with related damping.
Introduction System response amplification factor with related damping
5
4 η=0
η=0.1
or
η 0.2
η=0.2
plification facto
η=0.3
3
η=0.4
η=0.5
η=1
Amp
2 η=1.5
η=2
η=7
1
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Ω/Ωn
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21. Part 2‐Lateral vibration study.
Introduction‐ Lateral vibration and whirling.
Introduction Lateral vibration and whirling
Real life whirling case
Real life whirling case Whirling case during test System stiffness diagram in lateral
Whirling case during test System stiffness diagram in lateral
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22. Case study‐ Variation of ASTB Stiffness
Working Domain:
‐Variation of Aft Sterntube bearing stiffness
from 3.0E8 N/m to 5.0E10 N/m.
‐GAP & SAG are kept constant at all analysis
Propeller
points.
GB
ASTB FSTB
‐All other bearings assumed stiffness kept
constant.
‐GB bearings offsets changed at each analysis
point in order to maintain the same GAP‐SAG
figures.
fi
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23. Case study‐ Variation of ASTB Stiffness
Results:
ASTB Stiffness variation effect on
ASTB Stiffness variation effect on ASTB Stiffness variation effect on
ASTB Stiffness variation effect on
Shaft natural frequency (order1) Propeller natural frequency (order4)
800 190
750 180
M)
700 170
Speed (RPM
Speed (RPM)
)
650 160
150
600
Shaft natural frequency (order1) 140
550 Propeller natural frequency (order4)
p q y( )
130
500 120
2.00E+08 2.00E+09 2.00E+10 2.00E+08 2.00E+09 2.00E+10
Stiffness (N/m)
Stiffness (mm/m)
1‐ Lateral vibration 2‐ Lateral vibration
Shaft natural frequency. Propeller blades natural frequency.
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24. 1‐ Lateral vibration, Shaft natural frequency.
How it Built?
What is the Natural frequency and Excitation frequency ?
What is the mode shapes?
Clear mode shapes.
Cl d h Integrated mode shapes.
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25. 1‐ Lateral vibration, Shaft natural frequency
How to handle?
Most determined mode shapes:
Cantliver , First bending.
Direction of the local/global
response.
Damping: Have a slight effect on the
D i H li ht ff t th 5
cantiver mode and almost no effect on 4
the first bending (Global response 3
direction is linear toward the maximum
direction is linear toward the maximum 2
bending without resistance). 1
0
0 0.5 1 1.5
General conclusion: Running
close to reasonance have to
be avoided.
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26. 2‐ Lateral vibration, Propeller blades natural
frequency
How it built?
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27. 2‐ Lateral vibration, Propeller blades natural
frequency
What is the Natural frequency and Excitation frequency ?
What is the mode shapes?
190 Propeller natural frequency (order4)
180
170
160
150
140
130
120
2.00E+08
2 00E+08 2.00E+09
2 00E+09 2.00E+10
2 00E+10
5
4
3
2
1
0
0 0.5 1 1.5
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28. 2‐ Lateral vibration, Propeller blades natural
frequency
How to handle?
How to handle?
Diametrical Damping
2.1) Shaft impact (Direct impact)
Propeller shaft
Most determined mode shapes: response to vibration
Cantliver , First bending.
Cantliver First bending
Direction of the local/global
response.
Propeller damping (Resistance) effect due to this
applied vibration motion have to be considered
5
as it is very effctive (Propeller diametrical
damping). 4
3
So far the damping is effective, then a view
2
of the excitation force is important as well.
f th it ti f i i t t ll
1
The system response of this vibration motion 0
0 0.5 1 1.5
should be followed up as it is an excitation force
should be followed up as it is an excitation force
for another vibration motion‐‐‐‐ >
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29. 2‐ Lateral vibration, Propeller blades natural
frequency
How to handle?
How to handle?
2.2) ASTB impact (indirect impact)
Aft Sterntube bearing vibration,
(Consequence of main propeller
(Consequence of main propeller
viberation).
Bending variation leads to load variation into the
bearing.
bearing
Is the bearing damping able to dominate Bearing Damping
capability.
the new intreduced harmonic load?
Is the viberation motion charctrestics
acceptable ?
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30. Questions and discussion !
BERG PROPULSION PRODUCTION AB
BERG PROPULSION PRODUCTION AB
Mohamed Zeid
Naval Architect ‐ Rotordynamics Specialist
Direct: +46 31 30 10 736
Mobile: +46 761 175 022
E‐mail: mohamed.zeid@bergpropulsion.com
@ gp p
www.bergpropulsion.com
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