Kul Aircraft Structural Design (4 cr) Fatigue Analyses (3/3)

Transcription

1 Kul Aircraft Structural Design (4 cr) (3/3) M Kanerva 016

2 Objective and Contents of the Module The objective of the module is to describe (1) how aircraft fatigue analyses are performed and () how fatigue is controlled during the aircraft service Contents Overview Lessons learned Load spectra Atmospheric turbulence Aircraft response to turbulence Aircraft fatigue loads Fatigue analyses Structural integrity programs & analyses Page

3 Fatigue analyses Overview Lessons learned Load spectra Atmospheric turbulence Aircraft response to turbulence Aircraft fatigue loads Fatigue analyses Structural integrity programs Revision Page 3

4 Atmospheric Turbulence Model Global Turbulence Model 1/5 Global turbulence model for aircraft load analyses is derived by taking into account that an aircraft encounters patches of turbulences Assumptions of the model: 1. In each patch, gust velocity is assumed to be normally distributed and has a specific gust intensity w defined by its rms value: p( y) = 1 1 p s w Ø expœ- Œº 1 y Ł s w ł ø œ œß Page 4

5 Atmospheric Turbulence Model Global Turbulence Model /5 Assumptions of the model (continued):. The patches divide into two groups, one representing mild turbulence (non-storm), the other representing more severe turbulence (storm) 3. Gust intensities in both groups of patches are normally distributed and have specific rms values of the gust intensity (b 1 and b ): p( s w ) = 1 Ø 1 s w expœ- p b1 Œ º Ł b1 ł ø œ œß p( s ) = 1 Ø 1 s w expœ- p b Œ º Ł b Note! The equations take into account that w is always positive w ł ø œ œß Page 5

6 Page 6 Atmospheric Turbulence Model Global Turbulence Model 3/5 Assumptions of the model (continued): 4. For both groups of patches, the rms values b 1 and b of the gust intensity s w depend on the altitude 5. For both groups of patches, there is a specific probability of existence, these probabilities P 1 and P being dependent on the altitude ( ) ( ) ) ( 1 exp 1 ) ( h P P h b h b p w w = œ œ ß ø Œ Œ º Ø ł Ł - = s p s ( ) ( ) ( ) h P P h b h b p w w 1 exp 1 ) ( = œ œ ß ø Œ Œ º Ø ł Ł - = s p s

7 Page 7 Atmospheric Turbulence Model Global Turbulence Model 4/5 Based on the assumptions, the probability density of the gust intensity s w is: where: b1(h) and b(h) are the rms values of the gust intensity s w for the non-storm and storm turbulence patches, respectively P1(h) and P(h) are the fractions of time that the aircraft flies in the non-storm and storm turbulence, respectively œ œ ß ø Œ Œ º Ø ł Ł - + œ œ ß ø Œ Œ º Ø ł Ł - = exp 1 1 exp 1 ) ( b b P b b P p w w w s p s p s

8 Atmospheric Turbulence Model Recommended Values of b 1 and b (CS-5/FAR-5) Altitude [1000 ft[ b 1 and b [ft/s] Page 8

9 Atmospheric Turbulence Model Recommended Values of P 1 and P (CS-5/FAR-5) Altitude [1000 ft[ P 1 and P Page 9

10 Atmospheric Turbulence Model Frequency of Velocity Exceedance 1/ For aircraft load analyses, frequencies of exceeding for different gust velocity levels need to be known For the stationary Gaussian random process, this frequency can be computed with the Rice s equation: N ( y) = N 0 Ø expœ- Œ Œº 1 y Łs y ł ø œ œ œß where No is the number of zero crossings per unit time with positive (or negative) slope Page 10

11 Atmospheric Turbulence Model Frequency of Velocity Exceedance / Term No in the Rice s equation can be thought of as a characteristic frequency No is defined by the equation: N 0 = f 0 F( F( f f ) df ) df 0 According to the definition, No is the radius of gyration of the PSD about zero frequency Page 11

12 Fatigue analyses Overview Lessons learned Load spectra Atmospheric turbulence Aircraft response to turbulence Aircraft fatigue loads Fatigue analyses Structural integrity programs Page 1

13 Aircraft Response to Turbulence Introduction Response to atmospheric turbulence must be determined for each (possibly) fatigue critical detail of an aircraft structure A convenient load measure is used in the analysis, e.g. centre of gravity acceleration bending and torsion moment of a wing cross-section force per unit width of wing skin strain or stress of a wing spar Page 13

14 Aircraft Response to Turbulence Transfer Function 1/ Structure response to turbulence is described by the transfer function that transfers the input PSD into the output PSD: turbulence F o ( f ) = F i ( f ) H ( f ) s i = 0 F i ( f ) df ; s In case of a flexible aircraft, transfer function is specific for each local load of the aircraft o = 0 F o ( f ) df response Page 14

15 Aircraft Response to Turbulence Transfer Function / Typically, response PSD curves have peaks at natural frequencies In the examples beside (related to a specific wing cross-section): 0.3 Hz is the airplane short-period natural frequency 1.5 Hz is the first wing-bending frequency.3 and.7 Hz are the engine frequencies 3.3 Hz is the first fuselage bending frequency Wing bending Wing torsion Page 15

16 Aircraft Response to Turbulence Amplification Coefficient 1/4 Amplification coefficient is further used to describe aircraft response to turbulence It is defined to be the ratio of the output and input intensities: A = s s y w = 0 F y ( w) dw F ( w) dw 0 w w = gust intensity (rms value) y = load intensity (rms value) Page 16

17 Aircraft Response to Turbulence Amplification Coefficient /4 Value of the amplification coefficient must normally be determined for each local load with a dynamical analysis, taking into account important vibration modes In preliminary analyses, the amplification coefficient for vertical gusts can be estimated by assuming a rigid airplane: A = K s rv T C La ( W / S) The gust response factor Ks in the equation can be estimated when aircraft and turbulence characteristics are known Page 17

18 Aircraft Response to Turbulence Amplification Coefficient 3/4 Gust response factor Ks for computing the amplification coefficient of the g-load, rigid airplane Page 18

19 Aircraft Response to Turbulence Amplification Coefficient 4/4 Typical increase in the amplification due to elasticity is of the order Page 19

20 Rice s equation and the amplification coefficient give an equation for computing the number of exceeding of load level y due to turbulence with the gust intensity of s w : Note: N0 is the number of zero crossings for the local load y Aircraft Response to Turbulence Load Level Exceedances 1/8 ( ) œ œ ß ø Œ Œ º Ø - = œ œ ß ø Œ Œ º Ø ł Ł - = œ œ ß ø Œ Œ º Ø ł Ł - = / 1 exp 1 exp 1 exp ) ( w w y A y N A y N y N y N s s s w A s s y = Page 0

21 Aircraft Response to Turbulence Load Level Exceedances /8 The number of zero crossings N 0 must also be determined, as needed, by taking into account flexibility of the aircraft When the vertical motion of the aircraft is only accounted for, and a rigid airplane is assumed, N 0 can be estimated using the equation: N V = p c 0 k 0 The coefficient k 0 in the equation depends on the aircraft and turbulence characteristics Typical increase of N0 due to elasticity is of the order Page 1

22 Aircraft Response to Turbulence Load Level Exceedances 3/8 Coefficient k 0 vs. mass parameter for a rigid aircraft Page

23 Aircraft Response to Turbulence Load Level Exceedances 4/8 In a set of turbulence patches with the gust intensities s wi, the number of exceeding of load level y is: N ( y) Ø 1 expœ - Œº ( y / A) = ti N0 s wi s wi ø œ œß where ti is the fraction of time when s w = s wi Page 3

24 Aircraft Response to Turbulence Load Level Exceedances 5/8 Considering a continuous variation of the gust intensity s w, the summation on the previous slide is replaced by an integral: N( y) = s w ( y / A) Ø 1 N0 exp p( s = 0 s w œ œ ø Œ - Œº ß w ) ds w where the factor with the probability density p(s w )ds w is equivalent to the fraction of time in the numerical summation Page 4

25 Aircraft Response to Turbulence Load Level Exceedances 6/8 With the applied turbulence model (probability density of s w ), the equation for the number of exceeding of load level y becomes: N ( y) N 0 = P1 exp - Ł y / A b 1 + ł P exp - Ł y / A b ł Note! the equation is derived e.g. in the textbook of Hoblit on the semi log plot, each of the two terms represents its own share Page 5

26 Aircraft Response to Turbulence Load Level Exceedances 7/8 The equation for computing the number of load level exceedances is finally modified to the form that takes into account the load level due to the reference flight condition (cruise flight): N( y) = N 0 Ø ŒP1 exp - Œ º Ł y - y 1g b 1 / A + ł P exp - Ł y - y b 1g / A ø œ ł œ ß where y 1g is the load level corresponding to the cruise flight Note: The equation applies for each part of mission or flight with constant b i, and P i per patch Page 6

27 Aircraft Response to Turbulence Design Envelope Analysis 1/ The continuous turbulence model must also be used as a basis for determining limit loads due to gusts The load level due to a gust is: s y ydesign = s y hd = s w hd = = Łs w ł where: h d is the design ratio of peak to rms values Us is the limit turbulence intensity Note! Us is now a true airspeed gust velocity ( As ) w hd = A ( s wh d ) AUs Page 7

28 Aircraft Response to Turbulence Design Envelope Analysis / Us values to be used in load analyses are given by CS-5 in the form: U s = where: U F sref g U ref is the reference turbulence intensity defined with true airspeed (TAS) values as a function of the altitude F g is the flight profile alleviation factor used also in the discrete gust load analysis The equation to be used for computing the limit loads is: P L = PL -1 g U s A where P L-1g is the steady 1g load for the condition Page 8

29 Fatigue analyses Overview Lessons learned Load spectra Atmospheric turbulence Aircraft response to turbulence Aircraft fatigue loads Fatigue analyses Structural integrity programs Reminder Page 9

30 Aircraft Fatigue Loads Modelling of Aircraft Use Ground Loads Significant loads are applied to many structures in landing, the magnitude of loads depending on the vertical velocity in touch down Frequencies of exceeding must be established for vertical landing speeds Vertical velocities greatly depend on the type of the aircraft Measured velocities of similar aircraft can be utilised in the specification of vertical velocities Page 30

31 Aircraft Fatigue Loads Modelling of Aircraft Use GAG-cycle 1/ Ground-Air-Ground cycle (GAG-cycle) is the highest peak-to-peak load cycle encountered by an aircraft structure once per flight When fatigue loads are based on exceedance curves, the GAG-cycle must be extracted from the curves for its analysis Page 31

32 Aircraft Fatigue Loads Modelling of Aircraft Use GAG-cycle / Pressurisation occurs once per flight and can be included in the GAGcycle in load analyses of fuselage structures For a transport aircraft, peak-to-peak GAG-cycle is the most damaging cycle and may account for 90% of the total fatigue life E.g. ESDU (Engineering Sciences Data Unit) gives an approximate method for extracting the GAG-cycle from the aircraft load spectrum Page 3

33 Fatigue analyses Overview Lessons learned Load spectra Atmospheric turbulence Aircraft response to turbulence Aircraft fatigue loads Fatigue analyses Structural integrity programs Reminder Page 33

34 Crack-Free Life 3. The spent life due to the load cycles is estimated to be ni /Ni 4. All load cycles are analysed accordingly 5. The spent life D due to all loads in unit time is computed, which further gives an estimate for the crack-free life T: D = n N ; T = D i i 1 Note! The unit time may be one flight or a set of flights representing the aircraft use as a whole Page 34

35 Crack-Free Life Notes The effect of loading sequence on fatigue life is different with different materials and mean stresses: Page 35

36 Fatigue analyses Overview Lessons learned Load spectra Atmospheric turbulence Aircraft response to turbulence Aircraft fatigue loads Fatigue analyses Structural integrity programs Page 36

37 Structural Integrity Programs Introduction Structural integrity programs have been developed to ensure the safety of aircraft structures The programs define an organised approach for structural integrity actions covering the whole life-cycle of the aircraft The US military standard MIL- STD-1530C Aircraft Structural Integrity Program is an example of a standardised approach Page 37

38 Structural Integrity Programs Civil Aviation Civil transport aircraft are typically used in a similar way by different operators Structure inspections included in the maintenance programme then form a good basis for securing the structural integrity If the actual use differs considerably from the planned use, additional activities are needed (e.g. to take into account high number of GAGcycles for large aircraft used in short routes) As needed, supplemental inspection and maintenance tasks are defined based on experience and further evaluation Page 38

39 Structural Integrity Programs Military Aviation The use of fighters is operator specific and often differs from the planned use Military operators therefore define their own structural integrity programs based on actual use Actual use, in terms of the Fatigue Life Expended (FLE), is monitored for each aircraft Fleet leaders, analyses and data gathered from other operators are used to foresee actions needed to secure structural integrity and the targeted lifetime The fleet is used so that individual aircraft consume their fatigue lives with (closely) the same rate Page 39

40 Structural Integrity Programs Procedure Task I Design Data Task II Analysis and development testing Task III Certification testing Note! The procedure assumes that the design and certification data are available For more information, see e.g. the MSc thesis of T. Hukkanen (TKK 008) Task IV Development and certification of a structural integrity program Task V Structural integrity actions Page 40

41 Structural Integrity Programs FLE Estimate Based on Measured Load Data Load data measured with strain gauges can be used to evaluate FLE of a fatigue critical structure detail: Strain data is recorded Transfer functions are developed for computing load spectrum of the hot spot Measured load spectrum is transformed to load cycles Applicable fatigue analysis software is used to evaluate: (1) the crack nucleation time and () the crack propagation rate Figure: T. Hukkanen MSc Thesis Page 41

42 Structural Integrity Programs FLE Estimate Based on Flight Parameter Data An alternative method for the evaluation of FLE is to derive structure loads from flight parameter data: Flight parameter data and strain data are recorded Load analysis method based on flight parameter data is developed (neural network) Applicable fatigue analysis software is used to evaluate crack nucleation time and crack propagation rate MU & SAFE -Data Interpolation & smoothing Inverse Simulation S/G Data (HOLM) Flight parameter based F-18 fatigue life analysis Pre-processing of Data s [Mpa] 0.5 s FFT & Filtering s glob (t) = f (Flight Params(t)) x 1 x x y 1 3 Figure: T. Salonen MSc Thesis x n Neural Network Training Data y y 3 Page 4

43 Structural Integrity Programs FLE Estimate Based on Analysis Data Third method for the evaluation of FLE is to compute structure loads: CFD analysis is used to define aerodynamic load data for different flight conditions Structure loads corresponding to the estimated use are computed with calibrated FE models Applicable fatigue analysis software is used to evaluate crack nucleation time and crack propagation rate Figure: Patria Page 43

44 Structural Integrity Programs Life Extension When a fatigue critical structure is identified early enough, it is often possible to extend its fatigue life Possible means: shot peening of the surface (metallic parts) polishing of the surface (metallic parts) local reinforcement (e.g. composite patch) Figures: J. Linna MSc Thesis Page 44

45 Structural Integrity Programs FINAF F-18 Activities Load Analysis Tools Development and use of flight simulation software Development and use of CFD analysis tools Development and use of FE models: global local structural details Figure: Aalto/AM/AE Figures: Patria Page 45

46 Structural Integrity Programs FINAF F-18 Activities Load Measurement Systems Development and use of the HOLM (Hornet Operational Loads Measurement) system: two F-18C aircraft 6 strain gauges / aircraft strain recording frequency 180/640 Hz additionally, 00 flight parameters recorded at high frequencies Page 46

47 Structural Integrity Programs FINAF F-18 Activities Analysis Systems Development and use of methods for utilising measured data: transfer functions load history analyses Development and use of a flight parameter based load analysis system MU & SAFE -Data Interpolation & smoothing Inverse Simulation Flight parameter based F-18 fatigue life analysis Pre-processing of Data s glob (t) = f (Flight Params(t)) x 1 x y 1 x 3 x n Neural Network y y 3 Development and use of fatigue life analysis systems S/G Data (HOLM) s [Mpa] 0.5 s FFT & Filtering Training Data fatigue crack growth residual strength Page 47

48 Structural Integrity Programs FINAF F-18 Activities Record of Fatigue Critical Areas Upper Outboard Longeron, Y491-Y508 Crease Longeron Dorsal Longeron, Y557.5 Crease Longeron Sivuvakaajan Stub Former Y590.5 Kaaren Y508 takakiinnitystapin alue ILEF pääsalon rystyset Sisäsiiven etusalko Ulkosiiven taittovaihteiston korvakkeet 1,,3,8 ja 9 Ulkosiiven etusalon pystyjäykiste X w =0 in Aft Shear Tie Figure: Patria Ulkosiiven Rib, Missile Support TEF:n ja Aileronin saranakorvakkeet + TEF:n Formerit 5 & 6 Page 48

49 Structural Integrity Programs FINAF F-18 Activities Inspection Method Development Development and use of methods for inspecting structures: ultrasonics thermographics X-ray Page 49

50 Structural Integrity Programs FINAF F-18 Activities Fatigue Testing Analyses on parameter effects on material fatigue: Chemical surface treatments Mechanical surface working methods (shot peening, polishing) Cold-working of hole edges Fatigue testing of joints Figure: J. Linna MSc thesis Page 50

51 Structural Integrity Programs FINAF F-18 Activities Repair Technique Development Surface working methods Geometry modifications Part/fastener (and material) replacements Reinforcements, e.g. composite patches Page 51

52 Structural Integrity Programs Fatigue Analysis of OH-KOG 1/4 The remaining fatigue life of the DHC-6 Twin Otter Series 300 OH-KOG aircraft wing was evaluated due to the modifications and exceptional use of the aircraft: Entry into service in 1979 The aircraft has been used mainly for geographical surveying In 007, the OH-KOG had gathered FH Fatigue life of FH has been verified for the wing in the normal use Figure: M. Anttila MSc thesis Page 5

53 Structural Integrity Programs Fatigue Analysis of OH-KOG /4 Specific features of OH-KOG: Pods for measuring devices at the wing tips (several modifications during the operational use) Measuring flights at low altitude ( ft) Figures: M. Anttila MSc thesis Note! The pods at wing tips have a significant effect on aeroelastic properties of the wing Page 53

54 Structural Integrity Programs Fatigue Analysis of OH-KOG 3/4 Tasks: 1. Creation and verification of the wing FE model (original and modified wings). Evaluation of the original load spectrum 3. Reference fatigue analysis -> stress levels on the wing to obtain the certified fatigue life 4. Creation of the actual load spectrum 5. Palmgren-Miner fatigue analysis corresponding to the actual use Note! Lack of initial data affected the approach making the analysis complicated n G-mittausdataa - Kosovo t (s) Figures: M. Anttila MSc thesis Page 54

55 Structural Integrity Programs Fatigue Analysis of OH-KOG 4/4 Results: Based on the conservative analysis, the actual use has consumed fatigue life faster than the planned use Fatigue life consumption rate highly depends on the measuring area The whole fatigue life has not yet been consumed 1 / FH Kumulatiiviset kuormitukset Dnn Etelä-Suomi Tunturilappi Afrikka Irlanti Kosovo Alkuperäinen Figure: M. Anttila MSc thesis Page 55

56 Structural Integrity Programs Fatigue Analysis of PIK-0 1/3 Different versions of the Finnish PIK-0 glider have originally been certified to 3000 or 4000 FH Many gliders are still in use and several of them have exceeded their certified fatigue life (the continuing use based on structure inspections) A fatigue analysis was made for the wing upper spar cap which is the most fatigue critical structure detail of the glider Page 56

57 Structural Integrity Programs Fatigue Analysis of PIK-0 /3 Tasks: 1. Creation and verification of the wing FE model. Identification of the critical cross-section (based on analysis and original load test results) 3. Creation of load spectra (4 analytic and 3 measured load spectra) 4. Search of the representative SN-data for UD glass/epoxy and carbon/epoxy 5. Palmgren-Miner fatigue analyses Figure: T. Lukkarinen MSc thesis Page 57

58 Structural Integrity Programs Fatigue Analysis of PIK-0 3/3 Conclusions: Very conservative load spectra have been used in the original fatigue life evaluations Conservative analysis predicts that the spar is not fatigue critical even when the glider is partly used for aerobatic flight Figure: T. Lukkarinen MSc thesis Page 58