LIFE CALCULATION OF FIRST STAGE COMPRESSOR BLADE OF A AIRCRAFT

Romuald Rządkowski, Marcin Drewczyński, Marek Soliński,

The Szewalski Institute of Fluid Flow Machinery, Fiszera 14,

80-952 Gdansk, Poland

Ryszard Szczepanik

Air Force Institute of Technology Warsaw, Poland

Outline

• Background

• Unsteady forced acting on blades

• I Compressor stage rotor blade

• Life estimation

• Conclusions

Literature -Foreign object ingestion into aircraft

engines

• Storace et al 1984 developed a computer program to predict structural response due to soft body impact

• Rao and Srinivas 2003 used LS Dyna for impact of fan blades by bird

• Bianchi 2009 used RADIOSS for a bird strike onto a helicopter blade and onto a rotor control chain

• Heidari, Carlson and Yantis 1995 developed rotor dynamics as a nonlinear transient analysis for a propulsion system during the fan blade loss event from a bird strike.

Literature -Foreign object ingestion into aircraft

engines –CFD calculations

• Rao and Saravana Kumar 2008 simulated the steady state operation of a two stage pump to study the resulting unsteady pressure field from nozzle excitation. Here the bird strike is simulated by blockage of inlet struts that results in unsteady pressure field on the first stage compressor blade.

• Rządkowski R., Soliński M., Szczepanik R., 2009 The Unsteady Low-Frequency Aerodynamic Forces Acting on the Rotor Blade in the First Stage of an Jet Engine Axial Compressor,

in book ed. R. Rzadkowski, Dynamics of Steam and Gas Turbines, Proceedings of IFToMM International Symposium on Dynamics of Steam and Gas Turbines,1-3 Dec. 2009, p. 201-212, Gdańsk 2009,

Advances in Vibration Engineering, 11(2), 171-183, 2012.

5

Blade failure SO-3 engine

• An experiment was carried out (2007) on a first stage rotor blade in the compressor of an SO-3 engine at the Air Force Institute of Technology in Warsaw to initiate a crack, which in real life could be caused by birds engulfed in the engine, by placing rectangular blocks on the stator blades

• Tip-timing , I stage SO-3 compressor

SO-3 engine (ISKRA)

big – 120x100x20 mm

• Tip-timing , I stage S0-3 compressor

SO-3 engine (ISKRA)

medium -100x80x30mm

• Tip-timing , I stage S0-3 compressor

SO-3 engine (ISKRA)

small - 60x50x20mm.

Sensors used during tests 1 per rev

TE1

Sleeve

First day

• Tests 10:20 – 10:32, 11:22-11:35 – no blocker

• Tests 16:17 – 16:32, 18:25-19:45 – big blocker

• Tests 20:30 – 21:30

• – medium blocker

First day, Test run -10:20 – 10:26

First day, Test run -10:27 – 10:28

First day, Test run -10:30 – 10:31

1st day, 10-32

Campbell diagram of the first stage of the rotor

blade of the SO-3 engine

EO

341Hz 572 Hz

1342 Hz 1568 Hz

1847 Hz 1919 Hz

3114 Hz 3227 Hz

rpm

Stress distribution in rotor blade in time domain

110 MPa

FE-blade models

Model I

Model II

Modal stress at 337 Hz –model I

Modal stress at 341 Hz –model II

Modal stress at 1342 Hz

FE rotor model

Modes shapes

238.21 Hz

Modes shapes

407.56 Hz

Modes shapes -rotor –SO-3

461.05 Hz

Total engine working time during tests.

__________________ Total engine work time work time with blocks _______________________________(min)__________________(min)______________________

First day 286 165 Second day 208 199 Third day 231 216 Fourth day 190 129 Fifth day 188 126

Sixth day 18 Total 1121 (18h 41min) 835 (13h 55min)

The first day of the experiment

• On the fourth day, after 669min (11h 9min) of work with the blocks and approximately 143min of work with a resonance of 572,25 Hz at 15600 rpm,

• a crack indication was found on the blade no. 3 in the middle of the root area on the suction side.

• The length of the crack was estimated to be 2-3 mm

Campbell diagram of the first stage of the rotor

blade of the SO-3 engine

EO

341Hz 572 Hz

1342 Hz 1568 Hz

1847 Hz 1919 Hz

3114 Hz 3227 Hz

rpm

Growth of blade #3 crack.

The fourth day of the experiment

• The frequency of a blade no. 3 without a crack is

520 Hz, whereas blade no.3 with a crack is 463 Hz

3

• On the fifth day (169 min of work with a

resonance and with the blocks) the blade no. 3 crack increased to 5-7 mm and on the sixth day to 10-12 mm (420 Hz)

The last day of the experiment

• In addition, on the sixth day, using the eddy current

inspection technique, crack indications were found

on four more blades (12, 14, 17 and 24).

3

12 14 17 24

CFD model of an SO-3 engine first stage compressor

Nominal State

Time domain analysis Frequency domain analysis

38 -- 3rd revolution -- 4th revolution

34 blades (1st stage

stator)

44 blades (inlet stator)

The axial force for nominal state (red) and for a single blocked inlet segment (green).

Nominal

Low frequencies excitations

Partially blocked inlet

Cartesian system Cylindrical system

40 Axial, Radial, Circumferential Fx, Fy, Fz

Sudden fluctuations

Comparison – amplitude

41

Nominal state

Blocked inlet

31 [N] (nominal state)

50 [N]

It explains the sudden rise in blade vibration amplitude

61% increase!

Comparison – spectrum (blade)

42 Nominal state

Blocked inlet

34 blades (1st stage stator)

44 blades (inlet stator)

Axial force for nominal state (red), for single blocked inlet segment (green) and for four blocked segments

(blue).

Worst case of loading

one block two blocks

Two Block-

oposite

three blocks four blocks five blocks

Cross-

section Fx Fy Fx Fy Fx Fy Fx Fy Fx Fy Fx Fy

[N] [N] [N] [N] [N] [N] [N] [N] [N] [N] [N] [N]

1 0,05221 0,11822 0,2126 0,4214 0,5683 1,084 0,3585 0,8675 0,6006 1,371 0,6809 2,2532

2 0,04979 0,09890 0,1955 0,3545 0,5133 0,8921 0,3259 0,7266 0,5656 1,302 0,566 1,9475

3 0,05204 0,09328 0,2045 0,3417 0,5383 0,8633 0,3509 0,721 0,5692 1,258 0,4508 1,5147

4 0,05341 0,08622 0,214 0,3272 0,5761 0,8664 0,3729 0,7029 0,5228 1,126 0,3446 1,1499

5 0,05429 0,07809 0,2268 0,3209 0,6195 0,8787 0,372 0,6341 0,4565 0,944 0,2788 0,9324

6 0,05625 0,07064 0,2386 0,3214 0,6516 0,8703 0,3596 0,5497 0,4426 0,831 0,3172 0,8339

7 0,05915 0,06337 0,2415 0,3058 0,7117 0,9094 0,3585 0,496 0,4318 0,676 0,429 0,8237

8 0,06382 0,05788 0,2227 0,2606 0,7865 0,9745 0,3614 0,4506 0,3405 0,440 0,452 0,7025

9 0,07051 0,05459 0,224 0,2323 0,6713 0,8194 0,3781 0,4067 0,0571 0,0283 0,936 0,908

10 0,07785 0,05235 0,2357 0,2119 0,2448 0,3243 0,4232 0,3771 0,4024 0,2913 1,340 1,169

Campbell diagram for first stage compressor rotor blade of SO-3 engine

rpm

MATERIAL (HYSTERESIS) DAMPING

• Lazan 1968 conducted systematic and extensive measurements on hysteresis in simple tension and defined the loss of energy per cycle D under a stress amplitude s by

D = J (s / s e )n

J and n are material properties and s e is endurance limit.

MATERIAL (HYSTERESIS) DAMPING • Total damping energy D0 (Nm) in entire volume of

the body:

Loss factor

W0 is the total strain energy

v

DdvD0

0

0

0

2 W

D

MATERIAL (HYSTERESIS) DAMPING • Equivalent Viscous Damping C

the natural frequency (rad/s) and K is the modal stiffness (N/m).

Loss factor

0

0

2 W

D

KC

MATERIAL (HYSTERESIS) DAMPING • For increased (or decreased) strain amplitudes,

the orthonormal reference strain amplitudes, stress and strain energy are multiplied by a factor F to obtain the equivalent viscous damping Ce at various strain amplitudes as given below. Rao and Saldanha 2003.

'2

''

'

'

0

0

2

00

W

D

FWW

F

2

2'

2

'

FKm

C

FK

C

e

n

e

Campbell diagram for first stage compressor rotor blade of SO-3 engine

rpm

Nonlinear Damping in first mode of the blade

The material properties are taken as J = 16, n = 2.3 and s e = 63000 N/cm2

Mean stress at the operating speed

The mean stress at this location is 268 MPa

ALTERNATING STRESS

• The resonant stress is then determined by multiplying with the quality factor

2

1

Resonant stress at critical speed at element 13893

Resonant stress for different block segments

• 1 block segment, damping 0.0049 , stress 46.7 MPa

• 2 block segments, damping 0.0069 , stress 129 MPa

• 2 block segments in opposit direction, damping 0.0087 , stress 292 MPa

Resonant stress for different block segments

• 3 block segments, damping 0.00754 , stress 183 MPa

• 4 block segments, damping 0.0097 , stress 342 MPa

• 5 block segments, damping 0.0091 , stress 337 MPa

The damping ratio obtained from the non-rotating single blade experiment at the Air Force Institute of Technology was in the region of 0.0065-0.0075

FATIGUE MODIFICATION FOR THE BLADE

• The endurance limit of the material needs to be updated for the component taking into account various factors. The following fatigue material data is assumed in updating the endurance limit

• s u = 1100 MPa

• s e = 630 MPa (experimental)

• Fatigue stress concentration factor Kt = 2.1

• The fatigue reduction factor is estimated to be 0.476.

• Modified endurance limit 300 MPa

LIFE

• The estimated Life at 15000 RPM (Goodman) is given as

• 4-5 blocked segments 1.37 min (5.91 min exp)

• 3 blocked segments 182 min (99 min exp)

)1('

ut

mea

K s

sss

Crack propagation -experiment

• Two segments blocked 129.6 MPa

55.7 min, 5-7 mm crack

• Next the block segments were removed (35 MPa) but crack propagation continued for 17,91 min to reach 9-10 mm

Crack propagation

• Crack propagation was simulated for semi - elliptical crack, with initial crack length: 0.015 mm

Crack propagation

• Conversion between stress intensity factor range and nominal stress range Ds is given by

,2

12.1 s fb

ak

TaK

DD

2.55 1 2.2 0.9

1.91 0.8 1.69 0.7 1.5 0.6

1.35 0.5 1.22 0.4 1.15 0.3 1.07 0.2 1.03 0.1

k a/b

Crack propagation life

• A crack initiated propagates when the stress range exceeds the threshold value given above following Paris law (NASGRO)

• where C = 4.88 x10-6 and m=3.2 Paris material constants

clemicrons/cy mKCdN

daD

NASGRO

Crack propagation life • For the initial crack length (semi elliptic crack)

Daf= 0.015 mm, the notch radius r= 2.64 mm measured from model.

• In considered notch geometry a/b is taken as 0.5, K(a/b) = 1.35 and = 0.5 from Fig 10. The mean stress is 268 MPa and amplitude of alternating is 129.6 MPa

• Life estimation with crack propagation to 1cm at 15000 RPM and a 2EO equalled 111514 cycles.

• Thus life for 501.84 Hz : 111514 / (501.84) = 222.32 sec =3.705 min.

Crack propagation life

• Life estimation with crack propagation to 1cm at 15000 RPM and a 2EO equalled 111514 cycles.

• Thus life for 501.84 Hz : 111514 / (501.84) = 222.32 sec =3.705 min.

• In experiment crack propagation lasted 55.7 min.

Conclusions

• A bird impact is modeled as a block in the flow path that generates transient high pressure distribution on the first compressor rotor as a shock for 123 min to crack initiaton and 73.61min to 12 mm crack length propagation.

• The blade material data was verified experimentally. Several excitation harmonics of unsteady forces acting on a rotor blade (blocked by one to five block segments) were found using the FFT. A nonlinear damping model with an iteration procedure to obtain the alternating stress field was used in five cases.

• To determine resonant stress, only hysteresis damping was considered here, since at high operational speeds, friction can be neglected. The material damping is determined in the I mode of vibration as a function of reference strain amplitude at the operating speed. This nonlinear damping model is used by an iteration procedure to obtain the resonant stress.

• The life estimation up to crack initiation was calculated numerically and compared with the experiment. The results obtained from numerical analysis were shorter than the experimental ones.