LIFE CALCULATION OF FIRST STAGE COMPRESSOR BLADE OF A AIRCRAFT

Transcription

1 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, Gdansk, Poland Ryszard Szczepanik Air Force Institute of Technology Warsaw, Poland

2 Outline Background Unsteady forced acting on blades I Compressor stage rotor blade Life estimation Conclusions

3 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.

4 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 , Gdańsk 2009, Advances in Vibration Engineering, 11(2), , 2012.

5 5

6 Blade failure SO-3 engine

7 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

8 Tip-timing, I stage SO-3 compressor big 120x100x20 mm SO-3 engine (ISKRA)

9 Tip-timing, I stage S0-3 compressor medium -100x80x30mm SO-3 engine (ISKRA)

10 Tip-timing, I stage S0-3 compressor small - 60x50x20mm. SO-3 engine (ISKRA)

11 Sensors used during tests 1 per rev TE1 Sleeve

12 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

13 First day, Test run -10:20 10:26

14 First day, Test run -10:27 10:28

15 First day, Test run -10:30 10:31

16 1st day, 10-32

17 Campbell diagram of the first stage of the rotor blade of the SO-3 engine 3114 Hz 3227 Hz 1847 Hz 1919 Hz 1342 Hz 1568 Hz 341Hz rpm EO 572 Hz

18 Stress distribution in rotor blade in time domain 110 MPa

19 FE-blade models Model I Model II

20 Modal stress at 337 Hz model I

21 Modal stress at 341 Hz model II

22 Modal stress at 1342 Hz

23 FE rotor model

24 Modes shapes Hz

25 Modes shapes Hz

26 Modes shapes -rotor SO Hz

27 (min) (min) Total engine working time during tests. Total engine work time work time with blocks First day Second day Third day Fourth day Fifth day Sixth day 18 Total 1121 (18h 41min) 835 (13h 55min)

28 The first day of the experiment

29 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 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

30 Campbell diagram of the first stage of the rotor blade of the SO-3 engine 3114 Hz 3227 Hz 1847 Hz 1919 Hz 1342 Hz 1568 Hz 341Hz EO 572 Hz rpm

31 Growth of blade #3 crack.

32 The fourth day of the experiment

33 The frequency of a blade no. 3 without a crack is 520 Hz, whereas blade no.3 with a crack is 463 Hz 3

34 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 mm (420 Hz)

35 The last day of the experiment

36 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)

37 CFD model of an SO-3 engine first stage compressor

38 Nominal State Time domain analysis Frequency domain analysis 34 blades (1 st stage stator) 44 blades (inlet stator) -- 3 rd revolution -- 4 th revolution 38

39 The axial force for nominal state (red) and for a single blocked inlet segment (green). Nominal Low frequencies excitations

40 Partially blocked inlet Cartesian system Cylindrical system Sudden fluctuations Fx, Fy, Fz Axial, Radial, Circumferential 40

41 Comparison amplitude 61% increase! 31 [N] (nominal state) Nominal state 50 [N] Blocked inlet It explains the sudden rise in blade vibration amplitude 41

42 Comparison spectrum (blade) 34 blades (1 st stage stator) Blocked inlet 44 blades (inlet stator) Nominal state 42

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

44 Worst case of loading one block two blocks Two Blockoposite three blocks four blocks five blocks Crosssection F x F y F x F y F x F y F x F y F x F y F x F y [N] [N] [N] [N] [N] [N] [N] [N] [N] [N] [N] [N] 1 0, , ,2126 0,4214 0,5683 1,084 0,3585 0,8675 0,6006 1,371 0,6809 2, , , ,1955 0,3545 0,5133 0,8921 0,3259 0,7266 0,5656 1,302 0,566 1, , , ,2045 0,3417 0,5383 0,8633 0,3509 0,721 0,5692 1,258 0,4508 1, , , ,214 0,3272 0,5761 0,8664 0,3729 0,7029 0,5228 1,126 0,3446 1, , , ,2268 0,3209 0,6195 0,8787 0,372 0,6341 0,4565 0,944 0,2788 0, , , ,2386 0,3214 0,6516 0,8703 0,3596 0,5497 0,4426 0,831 0,3172 0, , , ,2415 0,3058 0,7117 0,9094 0,3585 0,496 0,4318 0,676 0,429 0, , , ,2227 0,2606 0,7865 0,9745 0,3614 0,4506 0,3405 0,440 0,452 0, , , ,224 0,2323 0,6713 0,8194 0,3781 0,4067 0,0571 0,0283 0,936 0, , , ,2357 0,2119 0,2448 0,3243 0,4232 0,3771 0,4024 0,2913 1,340 1,169

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

46 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.

47 MATERIAL (HYSTERESIS) DAMPING Total damping energy D 0 (Nm) in entire volume of the body: Loss factor D 0 v Ddv 0 W 0 is the total strain energy D 0 2 W 0

48 MATERIAL (HYSTERESIS) DAMPING Equivalent Viscous Damping C K C the natural frequency (rad/s) and K is the modal stiffness (N/m). Loss factor D 0 2 W 0

49 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 C e at various strain amplitudes as given below. Rao and Saldanha ' 2 ' ' ' ' W D F W W F 2 2 ' 2 ' F Km C F K C e n e

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

51 Nonlinear Damping in first mode of the blade The material properties are taken as J = 16, n = 2.3 and s e = N/cm 2

52 Mean stress at the operating speed The mean stress at this location is 268 MPa

53 ALTERNATING STRESS The resonant stress is then determined by multiplying with the quality factor 1 2

54 Resonant stress at critical speed at element 13893

55 Resonant stress for different block segments 1 block segment, damping , stress 46.7 MPa 2 block segments, damping , stress 129 MPa 2 block segments in opposit direction, damping , stress 292 MPa

56 Resonant stress for different block segments 3 block segments, damping , stress 183 MPa 4 block segments, damping , stress 342 MPa 5 block segments, damping , 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

57 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 K t = 2.1 The fatigue reduction factor is estimated to be Modified endurance limit 300 MPa

58 LIFE The estimated Life at RPM (Goodman) is given as 4-5 blocked segments 1.37 min (5.91 min exp) 3 blocked segments 182 min (99 min exp) s a s ' e (1 s t m K s u )

59 Crack propagation -experiment Two segments blocked 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

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

61 Crack propagation Conversion between stress intensity factor range and nominal stress range Ds is given by DK a 1.12Ds a T k f 2 b, a/b k

62 Crack propagation life A crack initiated propagates when the stress range exceeds the threshold value given above following Paris law (NASGRO) da dn C DK m microns/cy cle where C = 4.88 x10-6 and m=3.2 Paris material constants

63 NASGRO

64 Crack propagation life For the initial crack length (semi elliptic crack) Da f = 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 MPa Life estimation with crack propagation to 1cm at RPM and a 2EO equalled cycles. Thus life for Hz : / (501.84) = sec =3.705 min.

65 Crack propagation life Life estimation with crack propagation to 1cm at RPM and a 2EO equalled cycles. Thus life for Hz : / (501.84) = sec =3.705 min. In experiment crack propagation lasted 55.7 min.

66 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.