Practical Problems Of Modal Analysis Of Aero Engine Blades
Strain Posavljak
“ORAO” a.d.
Sabackih djaka bb, 76300 Bijeljina, Bosnia and Herzegovina
strain.posavljak@orao.aero
ABSTRACT
In this paper the results of application of modal analysis of aero engine blades are presented. Three practical problems were
taken in account. The first problem is connected with overhaul technology requirements. The second is connected with control
of blades on fatigue while the third problem connected with blade fractures. In the first two cases the results obtained by
experiment and results obtained by the finite element method are compared. In the third case using the finite element method
it is shown that fracture of one blade is result of fatigue on the third bending shape of oscillating.
Introduction
The most loaded parts of aero engines are the compressor and turbine rotor blades. During the engine exploitation they are
subjected to disturbing forces of aerodynamic or mechanical nature. These forces provoke oscillating of blades. Condition for
appearing of dangerous resonant regimes is the coincidence of frequencies of disturbing forces and dynamical frequencies of
concrete rotor blade, that dependent on its eigenfrequency and rotational frequency. For safe exploitation of engines it is need
that rotor blades work out of resonant regimes.
Consequence of oscillating of aero engine blades is oscillation fatigue. Therefore the studying of blade oscillations is
exceptionally important. It includes experimental and numerical modal analysis. The firms that work in area of maintenance,
repair and overhaul of aero engines, for experimental modal analysis of blades, use different types of shakers. As numerical
method of modal analysis, modal analysis by the finite element method (FEM modal analysis) today has active role. More
about oscillating of rotor blades it can find in references [1-3].
Experimental And FEM Modal Analysis
For some of the aero engine blades, overhaul technology requires testing of their modal shapes of oscillating and
corresponding eigenfrequencies. Arrangement of blades on disk according to eigenfrequencies can be the first reason. The
second reason can be fatigue control or endurance testing which is carried out on the shaker. In order to help to operator on
the shaker in searching of eigenfrequencies, it is good to use the finite element method. For example, for compressor rotor
blade 2nd stage of R25-300 aero engine [3-5], here marked with B1, experimental modal analysis was realized using Brüel &
Kjaer’s shaker (B&K shaker). The same is presented in Figure 1.
Figure 1. Photography and scheme of B&K shaker with used components
By tightening tool fastened with shaker head, blade B1 was tightened in the root. Blade plume was free. Before testing, on the
concave blade plume surface, the emulsion of kerosene and corundum sand was deposited. Electro dynamical force of shaker
was generated by exciter control via power amplifier. The feed-back was established by accelerometer with conditioning
amplifier. Frequency of electro dynamical force was adapted from zero up to value of some eigenfrequincy of blade B1. In the
moment of equalizing of electro dynamical force frequency and some eigenfrequency of blade B1, corresponding modal
shapes of oscillating ware provoked. Modal shapes were discovered by technique known as technique of sand figures. At all
modal shapes of oscillating corundum sand was heaped along nodal lines (zero displacement lines).
FEM modal analysis, using I-DEAS software package and technique of Guyan reduction, was carried out parallel with
experimental modal analysis. Simplified discretized calculation model of blade B1 is shown in Figure 2. Because the blade B1
was made of stainless steel, the standard steel properties: modulus elasticity E = 206800.0 MPa, Poisson’s ratio ν = 0.29,
mass density ρ = 7820.0 kg/m3 and shear modulus G = 80155.04 MPa, were assigned to discretized calculation model.
Figure 2. Simplified discretized calculation model of blade B1
Modal shapes of blade B1 determined using B&K shaker supported by technique of sand figures and using FEM are
presented in Figure 3. The values of eigenfrequencies are included in Table 1. In that table the data about deviations are also
included.
Figure 3. Modal shapes of oscillating of blade B1 determined using B&K shaker supported by
technique of sand figures (a) and using FEM (b)
Table 1. Eigenfrequencies of blade B1
MODAL
SHAPES
1st
nd
3rd
th
th
2
4
5
Values in Hz
Determined using
B&K shaker
232.5
Determined using
FEM
Deviation [%]
232.90
+ 0.172
901.2
886.70
- 1.609
1099.0
1147.97
+4.456
2315.0
2240.28
-3.228
2620.0
2759.65
+5.330
Although instead of complete blade B1, the blade plume was taken for generating of discretized calculation model, deviations
of experimental and FEM modal analysis results are satisfying.
Control Of Aero Engine Blades On Fatigue
Procedure of control of aero engine blades on fatigue is consisted in looking for an answer on the question, can the blades
endure defined number of cycles on defined stress level. Random sample of produced series is subjected to control. The
series is possible to accept if it shows that the answer on the given question is positive. If it not so, it is need to take the
measures which will remove defects of manufacture process. It is usually that fatigue control is performed at the first bending
shape of oscillating. In order to realize fatigue control it is need to carry out preparation with next activities:
−
−
−
To conduct test determining of eigenfrequency at the first bending shape of oscillating,
To determine the place and direction of maximum oscillation stresses,
To prescribe the control way of defined stress level and defined number of cycles.
All this it will be illustrated using blades, here observed as blades type B2 (stainless steel blades) [6]. Preparation of their
control on fatigue was carried out using three blades marked with B2-1, B2-2 and B2-3. The test determining of
eigenfrequency at the first bending shape of oscillating, was conducted on blade B2-1. FEM modal analysis, using I-DEAS
software package and Lanczos technique, was applied. Simplified discretized calculation model of blade B2-1 and its the first
bending shape of oscillating are presented in Figure 4. The steel properties: modulus elasticity E = 200000.0 MPa, Poisson’s
3
ratio ν = 0.29, mass density ρ = 7820.0 kg/m and shear modulus G = 77519.38 MPa, were assigned to discretized calculation
model of blade B2-1.
Figure 4. Simplified discretized calculation model of blade B2-1 and its the first bending shape of oscillating
Experimental modal analysis of blade B2-1 was carried out using Ling Dynamic System’s shaker (LDS shaker). LDS shaker
with used components is shown in Figure 5.
Figure 5. Photography and scheme of LDS shaker with used components
Using tightening tool, similarly as the blade B1, the blade B2-1 was tightened in the root also. LDS shaker was obtained
excitation from sine program controller via power amplifier. The feed-back was established using accelerometer direct
connected with sine program controller. Using motion analyzer and strobe lamp, oscillating of blade was illusory slowed. In that
way, conditions for discovering of the first bending shape of oscillating and conditions for accompanying of blade top oscillating
range by measure microscope were ensured. The results of test determining of blade B2-1 eigenfrequency are contained in
Table 2. Deviation between eigenfrequency determined by FEM and by LDS shaker is insignificant. The data about
eigenfrequency of blade B2-1 was very useful. It was served for easier and faster determining of eigenfrequencies of all the
other blades chosen for control on fatigue.
Table 2. Eigenfrequency of blade B2-1 at the first bending shape of oscillating
Value in Hz
Determined using
LDS shaker
1279.000
Determined using
FEM
1267.655
Deviation [%]
+ 0.895
Except that blade B2-1 was used for test determining of eigenfreuency at the first bending shape of oscillating it was used for
determining of the place and direction of maximum oscillation stress. On this blade the copper coating was deposited. The kind
of blade was subjected to oscillating at the first bending shape with blade top oscillating range 2.5 mm. After of the certain time
at the place of maximum oscillation stress, dark spot was appeared. The spot was expanded with increasing of the number of
cycles. The blade coated with copper without and with enough expanded dark spot is shown in Figure 6. The dark spot was
served for determining of the place and direction of maximum oscillation stress.
Figure 6. Blade B2-1 coated with copper and the same blade with dark spot and determined place
and direction of maximum oscillation stress
For blades of type B2 defined stress level was amounted σ = ±480 MPa. The strain ε = ±2400 µD (1µD = 1 µm/mm)
corresponding to that stress level, was determined by equation
ε =
σ
E ⋅10 6
(1)
in which for modulus of elasticity, the value E = 2⋅105 MPa was taken. Measuring of strains at the place of maximum oscillation
stress was realized by Wheatston’s quarter bridge formed of HBM strain gages LY41 1.5/350 with nominal resistance 350
Ω and factor K = 1.92. Three passive strain gages of the quarter bridge were located on one rejected blade, while the active
strain gage was located on the place of maximum stress of blade B2-2 and B2-3. Quarter bridge was supplied by current of
direct voltage US = 5 V via amplifier RM4220. Voltage measuring signal was conducted via the same amplifier to oscilloscope
HP54501A. Scheme of complete measuring chain, quarter bridge – amplifier – oscilloscope, is presented in Figure 7.
Figure 7. Scheme of measuring chain
Blades B2-2 and B2-3 with strain gages were subjected to oscillating on LDS shaker. For different values of blade top
oscillating ranges, the measuring voltage signals UM were recorded. Blade top oscillating ranges were accompanied by
measure microscope with magnifying 10X. Graphical illustration of blade top oscillating range D versus measuring voltage
signal UM is given in Figure 8.
Figure 8. Blade top oscillating range D vs. voltage measuring signal UM
According to Figure 8, the law of blade top oscillating range D vs. measuring voltage signal UM, is described by linear equation
D = 0.3838 U M
(2)
Before using, the quarter bridge of strain gages was calibrated according to the scheme in Figure 9. Using equation
ε =
1
K
RP
− 1 ⋅ 10 6
R + RP
(3)
from [7], for strain ε = -2400 µD, resistance of strain gages R=R1=R2=R3=R4=350 Ω and factor of strain gages K = 1.92,
resistance value RP = 75605 Ω was obtained. The same was adapted by resistance decade. Voltage value UM = 5.687 V, read
on the oscilloscope, corresponds to adapted resistance RP. For this voltage value, from Eq. (2), the value D = 2.2 mm was
obtained. It is perimeter for indirect control of defined stress level σ = ±480 MPa of blades B2.
Figure 9. Calibration scheme quarter bridge of strain gages
Defined number of cycles, N=2⋅106, of blades B2 can be controlled by measuring of time t in minutes which is computed by
equation
t =
2 ⋅ 10 6
f ⋅ 60
where f = eigenfrequency of sampled blade of produced series.
(4)
Investigation Of Blade Fracture Reasons
In many cases fractures of aero engine blades are result of their oscillating. Material of blades at the place of maximum
oscillation stresses attains fatigue life limit. The cracks initiated at those places fast propagate up to critical size. The fractures
th
as result of oscillating appear in area of blade plumes. In Figure 10 is presented fractured compressor rotor blade 4 stage of
VIPER 632 aero engine. The blade is made of aluminum alloy MSRR 8007. For needs of this paper it is marked with B3. The
results of investigation of fracture reasons of this blade, the first time are presented in this paper.
Figure 10. Fractured blade B3 and magnified view of its fracture
Distance of real fracture position from blade plume root section is ~40 mm. The fracture has two zones, the longer zone of
brittle fracture on the side of trailing edge and the shorter zone of ductile fracture on the side of leading edge. It means that
initiation crack was provoked on the side of trailing edge. In Figure 10 brittle and ductile zone of fracture are marked by roman
numerals I and II. The limit between these zones is shown with two contrary directed arrows.
Because the fracture has position in area of blade plume it was assumed that fracture is result of its oscillating. For that
purpose, FEM modal analysis was realized. Solid and simplified discretized calculation model of blade B3 are presented in
Figure 11. Material properties: modulus elasticity E = 75000.0 MPa, Poisson’s ratio ν = 0.29, mass density ρ = 2600.0 kg/m3
and shear modulus G = 29069.77 MPa, were assigned to discretized calculation model.
Figure 11. Solid and simplified discretized calculation model of blade B3
As in case of blade B1, FEM modal analysis was realized using I-DEAS software package and technique of Guyan reduction.
Five modal shapes of oscillating are presented in Figure 12. The data about eigenfrequencies are contained in Table 3.
Figure 12. Modal shapes of oscillating of blade B3 determined using FEM modal analysis
Table 3. Eigenfrequencies of blade B3
MODAL
SHAPES
1st
Values in [Hz]
1219.370
2nd
4199.662
rd
4762.567
3
th
4
8794.883
5th
10692.920
According to Figure 12, taking into consideration real fracture position, it can conclude that only the 3rd bending shape of
oscillating is the main reason of blade B3 fracture. It is separated and presented in Figure 13. Distance of expected fracture
position, according to this figure, has value 39.1 mm. It can see that expected fracture position has good coincidence with real
fracture position.
Figure 13. Expected fracture position determined by analysis of the third bending shape of oscillating of blade B3
Conclusions
Practical problems of modal analysis of aero engine blades it is need to solve by combination of experimental and FEM modal
analysis. Experimental modal analysis is good base for improvement of FEM modal analysis. On the other hand, FEM modal
analysis can to serve as preliminary modal analysis or as additional tool to experimental modal analysis. Satisfying results of
FEM modal analysis can be obtained when instead of complete blades we take only blade plumes.
Preparation activities for control of aero engine blades on fatigue, explained here, give enough information and thank to those
information, control on fatigue of blade B2 for known customer was realized. In similar or modified way, preparation of the
other blades for control on fatigue can be realized. Prescribed blade top oscillating range “D” for control of defined stress level
and time “t” needed for attaining defined number of cycles, are two measurable perimeters that can use for control of aero
engine blades on fatigue.
Always when the blade fractures appear in area of blade plumes it is need to conduct FEM modal analysis. Obtained modal
shapes individually to analyze, and to discover modal shape that is possible cause of concrete blade fracture.
Acknowledgments
This paper was sponsored by enterprise “ORAO” a.d. I am grateful to Mr. Prica Milan, General manager and to Mr. Kecman
Teodosije, Technical manager, for them understanding.
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