2011 Technology Awareness Days Fatigue Testing and Simulation

Transcription

1 2011 Technology Awareness Days Fatigue Testing and Simulation 2 Seminar Schedule 9:00 9:30 10:30 10:50 11:30 12:00 13:00 14:00 14:30 16:00 Part 1 Introduction Part 2 Proving Ground optimization Morning Coffee Keynote speech Dr. Andrew Blows (Jaguar Land Rover) Part 3 Road Simulation & Component Testing Lunch Part 4 Accelerated Vibration Testing Afternoon Tea Part 5 Virtual CAE Testing Close 1

2 Part 1 Introduction ncode 2006 Slide 4 Fatigue avoidance: CAE centred process Material Test Customer usage CAD Manufacturing Geometry Materials Loads Analysis Test Life Life 2

3 Sources of Vibration Terrain-induced vibration Low frequency (typically 0-32Hz) 4Ground profile 4Tyre (or track) profile 4Wheel imbalance 4Suspension dynamics Powertrain-induced vibration Mid high frequency (typically Hz) 4Gaussian random with superimposed sinusoidal harmonics 4Frequency dependent on engine/road speed Types of test Terrain-induced vibration Proving ground test Road simulator test Component test FEM virtual test Powertrain-induced vibration Dynamometer test Electro-dynamic shaker FEM virtual shaker 3

4 What s a proving ground test all about Proving grounds accelerate damage accumulation by concentrating on the most extreme loading events and then concatenating them one after the other Proving grounds simulate ride and handling characteristics of the real road Typical proving ground surfaces: 4Belgium block 4Highway 4Washboard 4Gravel 4Potholes 4Cross country 4Off-road 4Etc 8 ncode 2006 Slide 8 The proving ground challenge What s the optimum proving ground schedule? 4What surfaces? 4What vehicle weight conditions? 4What road speeds? 4What manoeuvres? What s the ratio of proving ground miles to road miles? How does proving ground A correlate to proving ground B 9 4

5 Road simulator rigs Replay proving ground in the lab Use proving ground optimization to reduce number of surfaces Use additional signal processing to remove non-damaging segments from the drive signal 4-post servo-hydraulic rig 12/16 channel spindle couple rigs 4-channel corner rig Component test Much simpler and cheaper than road simulator Dynamic or quasi-static Uniaxial or multiaxial Constant amplitude test Block load test Peak-valley sequences Transient dynamic 5

6 Powertrain dynamometer test Used to test powertrain structural components Simulate torque and reaction loads on the system FEM used for stress and fatigue analysis of casing and shafts, etc. Fatigue and fretting of gears usually based on simplified fatigue model 44 square test rig for CV joints Electro-dynamic shaker test FRT bracket REAR bracket Life distribution High-frequency vibration qualification tests sine sweep & sine dwell PSD random sine on random Efficient FEM solution for stress and fatigue evaluation Life Distribution (seconds) FRT bracket REAR bracket Log Life Distribution (seconds) 6

7 Conclusion Proving ground test Road simulator test Component test Dynamometer test Electro-dynamic shaker How to optimize the test How to optimize the FEM virtual test Part 2 Proving Ground Optimization ncode 2006 Slide 15 7

8 The proving ground challenge What s the optimum proving ground schedule? 4What surfaces? 4What vehicle weight conditions? 4What road speeds? 4What manoeuvres? What s the ratio of proving ground miles to road miles? How does proving ground A correlate to proving ground B 16 GlyphWorks optimization solution Proving ground data Road data 17 8

9 Contents What to measure? Tips on Data Characterization 4What is characterization 4Converting acceleration to relative displacement 4The effect of signal tapering 4Finding the average surface representation 4Finding the target user How does Proving Ground Optimization analysis work? 4Best fit method 4Track optimized method 18 What to measure Can t correlate every component simultaneously Some components more heavily correlated to road surface than others E.g 4 Steering tie rod strong correlation to lateral loads 4 Trailing arm strong correlation to suspension loads 4 Radiator Strong correlation with powertrain 4 Air filter Strong correlation with engine run up 4 Exhaust muffler Moderate correlation to road load Chassis, steering and suspension Powertrain components Ancillary components High correlation Weaker correlation 19 9

10 What to measure Better to optimize based on generic terrain severity and manoeuvres 4Centre of gravity (C of G) acceleration (with roll, pitch and yaw rates) 4Wheel force transducer (WFT) 4Wheel displacement & steering angle turn the vehicle into a transducer for measuring road profile 4Tri-axial acceleration at spindle 4Strain gauge measurements or load transducers at multiple locations 4CAN bus channels and GPS 20 How to characterize the data? Measured time signals are too long for optimization analysis Need to extract relevant information in a concise and efficient format Multi-channel histogram format is often best 4 Level crossing analysis 4 Time at level histogram 4 Rainflow cycle counting 4 Pseudo damage indices 4 Relative Damage Spectrum (RDS) 4 Fatigue Damage Spectrum (FDS) 4 Power Spectral Density (PSD) 4 Joint statistical distributions 4 Combinations of the above 21 10

11 Converting acceleration to displacement by double-integration Concatenation glyph is used to taper the start and end points of the time signal and avoid filter ringing Double integration to convert acceleration to displacement Use Butterworth high-pass filter to remove DC offset prior to integrating the signal 22 The effect of signal tapering Original acceleration time signal Tapered acceleration time signal Double integration of un tapered signal causes ringing Tapering the signal will significantly reduce the ringing effect 23 11

12 Converting acceleration to displacement by double-integration Concatenation glyph is used to taper the start and end points of the time signal and avoid filter ringing Double integration to convert acceleration to displacement Use Butterworth high-pass filter to remove DC offset prior to integrating the signal 24 Converting acceleration to displacement by double-integration Concatenation glyph is used to taper the start and end points of the time signal and avoid filter ringing Double integration to convert acceleration to displacement Use Butterworth high-pass filter to remove DC offset prior to integrating the signal 25 12

13 Relative Damage Spectrum (RDS) Band-pass Method Acceleration time history on suspension Band-stop Method Double Integrate to convert acceleration to displacement Disp Band-pass Frequency Frequency filter Disp Band-stop Frequency Choose next frequency band Rainflow count filtered signal Damage Hz Frequency Plot damage vs frequency Page 26 Damage Hz Frequency 26 Relative Damage Spectrum (RDS) Band-pass Method Acceleration time history on suspension Band-stop Method Double Integrate to convert acceleration to displacement Disp Band-pass Frequency Frequency filter Disp Band-stop Frequency Choose next frequency band Rainflow count filtered signal Damage Hz Frequency Plot damage vs frequency Page 27 Damage Hz Frequency 27 13

14 Finding the average proving ground surface Record several passes of each proving ground surface Characterize all passes individually Use Schedule Create tool (or ASCII Schedule file) to find average histogram ASCII Schedule File has.ach file extension HistogramScheduleFile, 1 BLOCK(MEAN), 1 RDS_Belgian_p1.s3h, 1 RDS_Belgian_p2.s3h, 1 RDS_Belgian_p3.s3h, 1 ENDBLOCK Type & version number Begin data block Data End data block BLOCK(MAX), m BLOCK(MIN), m BLOCK(SUM), m BLOCK(MEAN), m BLOCK(SD), m BLOCK(MSD, n), m Take maximum envelope of all histograms and multiply it by m Take minimum envelope of all histograms and multiply it by m Take sum of all histograms and multiply it by m Take mean of all histograms and multiply it by m Take standard deviation of all histograms and multiply it by m Take mean of all histograms plus n standard deviations and multiply it by m 28 Building the target customer schedule Trailer A A_Hwy 1 *50 + A_Hwy 2 *100 + A_Hwy 3 *1,000 or Tractor only Event 1 *5% + Event 2 *35% + Event 3 *60% and Trailer B or B_Hwy 1 *50 + B_Hwy 2 *100 + B_Hwy 3 *1,000 etc *10,000 Trailer C C_Hwy 1 *50 + C_Hwy 2 *100 + C_Hwy 3 *1000 *1000 HistogramScheduleFile, 1 BLOCK(SUM), Event1.s3h, 0.05 Event2.s3h, 0.35 Event3.s3h, 0.6 ENDBLOCK BLOCK(MAX), 1000 BLOCK(SUM), 1 A_Hwy1.s3h, 50 A_Hwy2.s3h, 100 A_Hwy3.s3h, 1000 ENDBLOCK BLOCK(SUM), 1 B_Hwy1.s3h, 50 B_Hwy2.s3h, 100 B_Hwy3.s3h, 1000 ENDBLOCK BLOCK(SUM), 1 C_Hwy1.s3h, 50 C_Hwy2.s3h, 100 C_Hwy3.s3h, 1000 ENDBLOCK ENDBLOCK 29 14

15 Rainflow Statistics using the Rainflow tool Rainflow Duration Extrapolation takes From-To rainflow matrix obtained from a short duration event and extrapolated to find the effect of a much longer event 30 Rainflow Statistics using the Rainflow tool Rainflow Percentile Extrapolation takes several From-To rainflow matrices obtained from a sample of users and can be used to find the 95% user 31 15

16 Contents What to measure? Tips on Data Characterization 4What is characterization 4Converting acceleration to relative displacement 4The effect of signal tapering 4Finding the average surface representation 4Finding the target user How does Proving Ground Optimization analysis work? 4Best fit method 4Track optimized method 32 Proving ground optimization method outline Channel 1 Channel 2 Channel 3 1 Belgium 2 Bump 3 City road 4 Paved 5 Round T a s r PG = o g l e t Channel 1 Channel 2 Channel 3 Measure data on each PG surface 4 PG matrix Measure same data on the road 4 Target vector Solution vector = how many repeats of each PG surface [ PG] [ sol] = [ target] 1 [ sol] = [ PG] [ target] BUT Can t invert a non-square matrix! Pseudo matrix inversion could work but gives negative PG repeats you can t have negative damage! ncode 2006 Slide 33 16

17 Best fit optimization Given linear expression: [ PG] [ sol] = [ target] Find solution vector which minimizes the least-square objective function: CUSCOR Linear objective used for acceleration, displacement, etc {([ ] [ ] [ ]) } 2 min PG sol target OR Log objective used for damage related optimization { ([ PG ] [ sol ]) log ([ target ])} min log With simple constraints: [ sol] 0 ncode 2006 Slide 34 Linear vs. Non-linear Best fit Linear Best fit optimization Non-linear Best fit optimization Level crossing count Log damage Target histogram Solution histogram Target histogram Solution histogram Channel 1 Wheel 1 Channel 2 Wheel 2 Channel 3 Wheel 3 Channel 1 Vertical Channel 2 Transverse Channel 3 Longitudinal (a) Level crossing histogram based on wheel displacement (b) Relative Damage Spectrum (RDS) based on spindle acceleration Linear Best fit on displacement, acceleration, load, strain, etc. Non-linear Best fit on damage because damage varies exponentially with amplitude 35 17

18 Track Optimization Given linear expression: [ PG] [ sol] = [ target] Find solution vector which minimizes the number of proving ground repeats: min With non-linear inequality constraints: [ sol] Linear objective used for acceleration, displacement, etc {[ PG] [ sol] [ target] } 0 OR Log objective used for damage related optimization { ([ PG] [ sol] ) ([ target] )} log log 0 ncode 2006 Slide 36 Best fit vs. Track optimized solution Log damage Log damage Target histogram Solution histogram Target histogram Solution histogram Channel 1 Vertical Relative Damage Spectrum (RDS) Channel 2 Transverse Channel 3 Longitudinal Channel 1 Vertical Channel 2 Transverse Channel 3 Longitudinal Relative Damage Spectrum (RDS) based on spindle acceleration Best fit tried to fit best line through histogram Best fit is orthogonal i.e. can reproduce original target mix Relative Damage Spectrum (RDS) based on spindle acceleration Track optimized solution minimizes number of track repeats but maintains at least the same damage 37 18

19 Case Study 1 Method Optimization based on RDS at front left-hand wheel spindle Target consists of random mix from 240 track surfaces scaled to 30,000 tracks to simulate customer usage Solution from 12 track configurations 38 Case Study 1 Results Best fit solution Track optimized solution Track repeats = 1013 Track surfaces required = 9 Track repeats = 347 Track surfaces required =

20 Case Study 1 Results Calculate fatigue damage based on 10 strain gauged components 4Chassis 4Steering 4Suspension Target Best Fit Solution Track Optimized Solution Compare target with optimized solutions All damage within a factor of 2 Track optimized slightly more conservative than Best fit 40 Case Study 1 Results Fatigue Damage Spectra (FDS) Calculate fatigue damage at 6 dashmounted locations (only 2 shown here) Damage presented as FDS plots Compare target with optimized track solutions Excellent correlation on all components across all frequencies Log Damage Log Damage Dash console location 1 Target RDS Best Fit Solution Track Optimized Solution Dash console location

21 Conclusions Brief overview of Proving Ground Optimization Tips on Data Characterization 4What is characterization 4Converting acceleration to relative displacement 4The effect of signal tapering 4Finding the average surface representation 4Finding the target user How does Proving Ground Optimization analysis work? 4Best fit method 4Track optimized method 42 Seminar Schedule 9:00 9:30 10:30 10:50 11:30 12:00 13:00 14:00 14:30 16:00 Part 1 Introduction Part 2 Proving Ground optimization Morning Coffee Keynote speech Dr. Andrew Blows (Jaguar Land Rover) Part 3 Road Simulation & Component Testing Lunch Part 4 Accelerated Vibration Testing Afternoon Tea Part 5 Virtual CAE Testing Close 21

22 Part 3a Road Simulator Testing ncode 2006 Slide 44 Road simulator rigs Replay proving ground in the lab Use proving ground optimization to reduce number of surfaces Use additional signal processing to remove non-damaging segments from the drive signal 4-post servo-hydraulic rig 12/16 channel spindle couple rigs 4-channel corner rig 22

23 Buffered Fatigue Editing 1. Measure time signal on critical components 2. Calculate time correlated fatigue damage 3. Remove non-damaging segments 4. Splice remaining segments together Buffered Fatigue Editing 1. Measure time signal on critical components 2. Calculate time correlated fatigue damage 3. Remove non-damaging segments 4. Splice remaining segments together 23

24 When cycles span multiple buffers time Some cycles may start in one buffer and finish in another Must keep both these buffers in order to maintain the cycle Example shows GAG cycle (Ground-Air-Ground) GAG cycle is usually the largest fatigue cycle for aircraft fuselage. Test must keep buffers with max and min loads in order to keep the fatigue information Fatigue Edit method assigns half damage to start of cycle and half to end Buffered Fatigue Editing 4. Splice remaining segments together Use Linear Overlap method to eliminate impulse and phase transients on the rig 24

25 Load axis elimination Resolve input signals into hyperspherical coordinate system Rainflow count each resolved coordinate Observe axes with low damage correlation Resultant Load Plane Conclusion Buffered fatigue editing removes non-damaging segments from drive signals Best optimization by retaining 90% damage and add additional 10% on repeat count Eliminate axes with low damage correlation using Potential Damage analysis glyph 25

26 Part 3b Simple Component Testing ncode 2006 Slide 55 Component test Much simpler and cheaper than road simulator Dynamic or quasi-static Uniaxial or multiaxial Constant amplitude test Block load test Peak-valley sequences Transient dynamic 26

27 Constant amplitude test NC1 Stress Range UTS Number of Cycles to Failure Original Range Const. Amplitude Constant amplitude Sine wave Cycle between max and min of recorded event Use SN curve to find target cycle count Need confidence in fatigue model Uniaxial only Quasi-static response Block load sequence reduction Convert random load sequence into discrete blocks Uses Rainflow cycle counting Does not rely on a fatigue model Uniaxial only Quasi-static response 27

28 Peak-valley signal reduction Decimates data Gate small cycles Does not rely on a fatigue model Uniaxial or Multiaxial* Quasi-static response 360 Points 36 Points Multi-axial considerations in Peak Valley reduction If there s a peak/valley in any channel then keep the same time point in all the other channels Maintains phase relationship between multiple channels X = Unit Amplitude Y = Unit Amplitude *Special case for sinusoidal waves multiaxial amplitudes are NOT maintained X + Y = 2 Amplitude 28

29 Conclusions Tests Time Domain Cycle Domain Dynamic Quasi-static Multiaxial Uniaxial Buffered Fatigue Editing Road simulator Proving Ground Peak-valley Extraction* Compressed Time Testing Load Scaling Block Load Sequence Constant amplitude Seminar Schedule 9:00 9:30 10:30 10:50 11:30 12:00 13:00 14:00 14:30 16:00 Part 1 Introduction Part 2 Proving Ground optimization Morning Coffee Keynote speech Dr. Andrew Blows (Jaguar Land Rover) Part 3 Road Simulation & Component Testing Lunch Part 4 Accelerated Vibration Testing Afternoon Tea Part 5 Virtual CAE Testing Close 29

30 Part 4 Accelerated Vibration Test ncode 2006 Slide 67 Electro-dynamic shaker test FRT bracket REAR bracket Life distribution High-frequency vibration qualification tests sine sweep & sine dwell PSD random sine on random Efficient FEM solution for stress and fatigue evaluation Life Distribution (seconds) FRT bracket REAR bracket Log Life Distribution (seconds) 30

31 Why are Acceleration and Frequency both important? M Acceleration g Time Freq. Acceleration Velocity Displacement 1 Hz 10 g 15.6 m/s 2.48 m 10 Hz 10 g 1.56 m/s 24.8 mm 100 Hz 10 g m/s mm Strain on spine Strain energy Acceleration Displacement = ( 2π f ) 2 Natural frequency effect Frequency Hz Strain reducing with f 2 Review of Theory Fatigue Damage Spectrum (FDS) Damage vs. Frequency plot FDS steadily builds through exposure to vibration Shock Response Spectrum (SRS) Peak shock vs. Frequency plot SRS sensitive to extreme amplitude peaks Flight load data Sine-on-random qualification Flight load data Sine-on-random qualification 31

32 Review of Theory Shock Response Spectrum (SRS) Fatigue Damage Spectrum (FDS) Developed by US engineer Biot in 1934 Used to describe frequency and amplitude content of transient events Originally developed for earthquake design of buildings Used extensively for shock and vibration in aircraft components, missiles and ground vehicle industry Developed in 1980 s by French Ministry of Defence Based on principle of SRS Implemented in French Defence standard GAM-EG-13 since 2000 Used extensively in aerospace and ground vehicle industry Relative Damage Spectrum (RDS) vs. Fatigue Damage Spectrum (FDS) RDS Acceleration time history on suspension Lalanne/Fatigue Damage Spectrum (FDS) Accel, g Frequency Band-pass Single Degree of Freedom Frequency filter Accel, g Δf Frequency Choose next frequency band Rainflow count filtered signal Increment filter by Δf Damage Hz Frequency Plot damage vs frequency Log Damage Frequency 72 Page 72 32

33 Fatigue Damage Spectrum (FDS) & Shock Response Spectrum (SRS) Acceleration time history on suspension Lalanne/Fatigue Damage Spectrum (FDS) Frequency filter Single Degree of Freedom Accel, g Δf Frequency Shock Response Spectrum (SRS) Rainflow count filtered signal Increment filter by Δf Peak amplitude of filtered signal Plot damage vs frequency Log Damage Peak value Frequency Frequency 73 Page 73 Shaker optimization Fatigue Damage Spectrum (FDS) plots damage vs. frequency Shaker optimization calculates PSD with same FDS over shorter test time 33

34 Case Study 1 Muffler Create accelerated random PSD test for muffler Acceleration data taken from Belgian Block and Cross Country proving ground surfaces Target Duty schedule provided by OEM (53 days continuous PG use) Front Chassis Bracket Rear Chassis Bracket Accelerated test 72 hours per axis (x, y & z) Case Study 1 Muffler Base acceleration input for 6 proving ground events: Belgian block and Cross country Curb weight and GVW conditions x, y & z vibration loading For each event, calculate: Fatigue Damage Spectrum (FDS) Shock Response Spectrum (SRS) 34

35 Case Study 1 Muffler In Fatigue Damage Domain: 1. sum Fatigue Damage Spectra (FDS) over the design life of the vehicle (Mission FDS) 1875 laps Belgian block Plus 806 laps Cross Country GlyphWorks Schedule Create module 2. envelope Shock Response Spectra (SRS) to establish critical Mission loads (Mission SRS) Case Study 1 Muffler Test Synthesis Synthesize Test Input Mission FDS 53 days Synthesize PSD Test 72 hours Validate Test Calculate SRS of accelerated test Compare SRS with Mission SRS. Optimize fit by adjusting test duration Validation 35

36 Case Study 1 Muffler Accelerated PSD, 72 hours per axis (x, y & z) x axis y axis z axis Test amplitude exceeds mission at ~14Hz Test amplitude < mission in other cases Test ERS Mission ERS Test ERS Mission ERS Test ERS Mission ERS x axis y axis z axis Case Study 1 Muffler FRT bracket REAR bracket Life distribution Test carried through to failure Failure occurs in mounting brackets Fatigue results are commercially sensitive Prediction and test results within a factor of 2! Life Distribution (seconds) FRT bracket REAR bracket Log Life Distribution (seconds) 36

37 Case Study 2 Automotive Transmission Automotive transmission system specified with a swept sine endurance test. OEM replaced it with a new PSD based test. New test showed significantly less damage even though RMS was the same. FDS analysis showed PSD was more damaging for higher natural frequency responses and significantly less damaging for lower natural frequencies. Fatigue Damage Fatigue Damage Spectrum Damage from Swept Sine Testing Damage from Random PSD Testing Natural Frequency [Hz] Case study 3 Structural Health Monitoring of an army truck 1. Record operational vibration levels Peak Shock Exposure Certified Peak Shock Shock Exposure Limit Acceleration Random PSD (g 2 /Hz) Sinusoidal tones (g) 2.2g 2.2g 2. Onboard analysis (Shock and Fatigue Damage Spectra) 1.1g 1.0g 0.01 Shaker Cumulative Fatigue Exposure Certified Cumulative Endurance Fatigue Limit Exposure MIL-STD-810F vibration test Log frequency Hz 83 37

38 Case Study 4 Engine Management Unit Require single random PSD vibration test for EMU Perform ramped engine test 4Measure acceleration signal 4Measure engine RPM Calculate Waterfall analysis of PSD for each engine RPM band Case Study 4 Engine Management Unit Calculate FDS for each RPM slice Verify ERS from test with ERS envelope from Waterfall analysis Create single PSD test by weighting damage relative to Engine Speed Usage Profile 38

39 Conclusion Fatigue Damage Spectrum (FDS) plots damage vs. frequency Shaker optimization calculates PSD with same FDS over shorter test time Seminar Schedule 9:00 9:30 10:30 10:50 11:30 12:00 13:00 14:00 14:30 16:00 Part 1 Introduction Part 2 Proving Ground optimization Morning Coffee Keynote speech Dr. Andrew Blows (Jaguar Land Rover) Part 3 Road Simulation & Component Testing Lunch Part 4 Accelerated Vibration Testing Afternoon Tea Part 5 Virtual CAE Testing Close 39

40 Part 5 Virtual CAE Testing ncode 2006 Slide 92 A simple process 40

41 5 Box Trick Load history 4Huge effect on fatigue life 4Need to characterize the target customer well Load history Geometry 4Accuracy of surface stresses are critically important ±10% stress ±100% life 4Structural FE modelling is generally to class standards Geometry Fatigue Properties Fatigue Analysis Optimize Fatigue Results Fatigue properties 4Material fatigue properties are relatively inexpensive to obtain 4Materials Assurance Service available from ncode laboratory Understanding Component Loading & Material Performance Yields Most Significant Improvement on Life Assessment Today! 94 What makes a good Fatigue Design Curve? The regression curve represents the life at which 50% of samples have failed. Design curve shown with 95% Certainty of Survival and 95% Confidence The more samples you test the more confident you are about the scatter Compare batch/supplier variability Stress Range S SN Fatigue Test Analysis Supplier A Supplier B Supplier A Test Data Supplier A Regression fit 2 sigma range 2 sigma range Supplier A Design curve Supplier B Test Data Number of Cycles to failure N 95 41

42 What makes a good Fatigue Design Curve? Launch of new Materials Assurance Service 4 Assurance that your material design parameters adequately represent your current material 4 Assurance that a newly sourced material has equivalent fatigue performance to your old material What we need What we do What you get What next? Current material properties Is supplied material representative of supplied properties? If properties are good then continue with confidence A few samples of material to be compared Tensile tests SN/EN fatigue tests Metallographic analysis Statistical analysis Is supplied material at least as good as the supplied properties? If properties cannot be assured with required confidence, then option of full fatigue testing with cost of Assurance Service subtracted from the bill! 96 What makes a good FE-fatigue analysis? Good Surface Stress Results!!! Fatigue cracks usually initiate at free surfaces Fatigue damage increases exponentially with stress 10% error in stress 100% error in life! Shell models Stresses calculated at Gauss points and extrapolated to node Node has separate stress result from each element Most FEA uses average nodal stress FE Accuracy/convergence 1. Nodal displacement 2. Nodal forces & moments 3. Element Gauss point stresses 4. Node at element stresses 5. Nodal averaged stresses Recommendations Low mesh density OK for load path & natural modes High mesh density Required for Fatigue Best stress result = Element Gauss point stresses Recommend using Node at element check for convergence Use nodal averaged only if you are certain of convergence 42

43 What makes a good FE-fatigue analysis? Good Surface Stress Results!!! Fatigue cracks usually initiate at free surfaces Fatigue damage increases exponentially with stress 10% error in stress 100% error in life! Solid models Stresses calculated at Gauss points but Gauss points not on surface! x z Option 1 skim surface with membrane or thin shells Shells resolve stresses to surface plane Use element stresses from the shells as before y Option 2 Use surface node results Transform stresses to surface plane Use Node at element (or Nodal averaged stresses) on surface nodes only Node at element are preferred! Types of FE stress analysis 3 basic types of FE stress analysis 4Linear static superposition 4Time step 4Harmonic response Linear static superposition is most efficient FE analysis technique but is limited Time step is computationally intensive but allows for non-linear analysis and dynamic analysis Harmonic analysis is very efficient for steady state random loading 99 43

44 Linear Static Superposition L 1 =1 C 1 C 1 x Real Load L 1 + C 2 C 2 x L 2 =1 Real Load L 2 = σ A C = FE Stress tensor for Unit Load Cases Stress time signal at element Time Step Procedure Load time signals processed by FE L1 L 1 σ A Stress time signal at element L 2 L 2 Stress for combined loads calculated by FE point by point. For long time histories, issues with solution time and disk space requirements 44

45 Harmonic Response Transfer Function L( f ) = 1 C( f ) C( f ) 2 Real Load L 1 σ A = C(f) = Complex transfer tensor for unit Load Cases L(f) Stress PSD at element L Harmonic Response Transfer Function t C( f ) σ phase offset t amplitude gain L( f ) = 1 Output stress amplitude σ ( f ) = L( f ) gain( f ) Gain Complex transfer function expresses gain and phase in complex number form: ( ) = ( ) ( ) = ( ) gain f C f phase f C f Phase f f Output stress PSD S( f ) = L( f ) C( f )

46 FE Analysis Route Map CAE Analysis Deterministic Random Dynamic Non-linear Linear-static Uniaxial Multiaxial Steady-state Transient Multiaxial Uniaxial Modal reduction Contact nonlinearity? Harmonic Response Analysis Time-step Analysis Linear-static Superposition Deciding between Static and Dynamic Sinusoidal force of amplitude A results in sinusoidal stress of amplitude B Ratio B/A depends on frequency BUT is relatively constant between 0Hz and 1/3 the 1st mode natural frequency PSD frequency Max frequency Static Natural frequency f frequency Dynamic Sinusoidal Force Mass M Stiffness K Damping C Sinusoidal Stress with amplitude B Calculate PSD of input time history. Calculate the 1st mode natural frequency f 1 For Steady-State excitation use modal reduction For non-steady analysis use full transient Rule-of-thumb: if max frequency in PSD < 1/3 f 1 then use static analysis 46

47 Modal Reduction Natural Modes Analysis Eliminate modes outside the bandwidth of the input Modal Transform FE Model with n DOF Output modal stresses to DesignLife ν 1 ν 1 ν 2 ν 2 ν n ν n 1 static stress vector + a few modal participation vectors Time step solution of reduced FE Matrix 1 static + a few dynamic modes DesignLife calculates time step signal based on modal results σ A Stress time signal at element Dealing with contact non-linearity L 2 L 1 Real load L 1 t Non-linear contact modelled as 2 linear static load cases Load cases scaled by real loads +ve loads applied to Load case 1 -ve loads applies to Load case 2 Real load L2 Combined load case t t 47

48 Dealing with rotational symmetry Vertical loading Rotation angle 18 linear static radial load cases Analysis automatically scales vertical loading between radial load cases depending on rotation angle Colour represents load case Dealing with non-linear wind loading Free wind speed driven by pressure systems Mean wind speed variation with height Turbulent wind profile due to obstacles on the ground Gradient height

49 Dealing with non-linear wind loading Calculate damage for each load case and sum damage as a duty cycle 20 m/s 10 years 15 m/s 30 years 10 m/s 50 years 5 m/s 100 years Life 110 Conclusions Accuracy of results depend on good surface stress results: 4Shells element Gauss point stresses. (Node at element used for convergence check) 4Solids Node at element stresses on surface nodes. Transform stresses to the surface plane 3 types of FE analysis 4Linear static superposition 4Time step 4Harmonic response Discussed rule-of-thumb for separating dynamic and quasistatic analyses Discussed modal reduction as a technique for speeding up analysis Discussed techniques for dealing with contact non-linearities Discussed technique for dealing with non-linear wind loads using duty schedules 49

50 Part 5a. Virtual CAE Testing Case Studies Gearbox casing Main shaft ncode 2006 Slide 112 Case Studies Analysis of a Wind Turbine gear box 4Based on a 2 MW turbine 4Back-calculation to determine safety margin for increased loads Identify reserve for future applications Analysis of a main drive shaft 4Duty cycle loading Fast analysis Detailed analysis zoomed in on critical areas Multi-axial considerations 4Selection of critical areas by damage criteria 4Criteria controlled by user to meet demands 50

51 Generalized Gearbox Schematic used to generate FE Model Generalized Gearbox Schematic 1 Ref 1. Improving Wind Turbine Gearbox Reliability W. Musial and S. Butterfield National Renewable Energy Laboratory, B. McNiff McNiff Light Industry Presented at the 2007 European Wind Energy Conference Milan, Italy, May 7 10, 2007 Wind Turbine Gearbox Casing 1 million nodes Linear or quad elements Solids or skim with shells

52 FE Model showing load application elements at bearing positions Typical 2-3MW rated Gearbox >1m diameter Max torque ~<1MNm 750kN reaction / side (1kN nominal applied) Linear Static Superposition unit load results 52

53 Linear Static Superposition constant amplitude Maximum load, 15 active loadcases (bearing reactions) Available loadcases Selected for combination Scale factors Wind Turbine Gearbox Casing fatigue results Stress results Life results Life results Linear elements Quad elements 53

54 Wind Turbine Gearbox Casing fatigue results Fatigue life convergence results at critical node Worst life years Best life years Linear elements with surface shell skim Linear elements with calculated surface vector Quadratic elements with surface shell skim Quadratic elements with calculated surface vector Recommend well refined quadratic mesh (Linear elements converge very slowly and overstiff) Recommend using calculated surface vector instead of shell skim (shell skim helps resolve surface stresses but does not improve accuracy and prevents stress gradient fatigue techniques) Recommend using Node-on-element* fatigue results to determine degree of convergence Expected error range in FE-based Fatigue life estimation FE Predicted life 1000% 300% 200% 100% 50% 33% 10% Best real-world (factor 2) Best possible design correlation (factor 3) Typical design margin (factor 10) 54

55 Part 5b. Virtual CAE Testing Case Studies Gearbox casing Main shaft ncode 2006 Slide 122 Case study 2 Analysis of main drive shaft

56 Wind Turbine Loading the duty cycle Loading defined as a series of events Each event is assigned a duration (hours, days, occurrences etc) Total duration of all the events defines design life, eg 20 years. DesignLife solution: 4Solve each event, calculate damage, multiply by the event duration 4Sum damage from all events 4Present total damage for 20 years DesignLife also considers interaction (sequence effects) 4Peak stresses in one event are matched with peak compressive stresses in a different event and included in the Rainflow count 4Regulatory bodies have shown an interest in this refinement. Wind Turbine Loading the duty cycle How to handle long and complex duty cycles Problems: 4Tracking cycles correctly across events 4Handling complex sequences 4Doing this efficiently Event A Event B 56

57 Independent processing Event 1 * 2 Event 2 * 3 A C D E B Cycle count events independently Result = 2*A, 2*B, 3*C, 3*D, 3*E (Actually we sum the damages) Fast, but can miss the biggest cycle Accurate enough in many cases (where there are no big mean shifts between events) Combined full option Event 1 * 2 Event 2 * 3 A C D E F G B Concatenate events Cycle count the whole history Accurate, but could be very slow (especially in FE applications ) 57

58 Combined fast Event 1 * 2 Event 2 * 3 Residuals A C D E F G B Cycle count each event Factor each closed cycle by repeat count n Concatenate residuals (between events) and cycle count Accurate enough and quite fast (as fast as independent) Captures maximum outer loop FE model and unit loadcases Ansys 11 58

59 ncode DesignLife Demonstration Material Fatigue Data multiple R ratio SN curves 130 Multi-axial peak valley extraction

60 ncode DesignLife Demonstration Combined Damage 132 ncode DesignLife Results in Ansys

61 ncode DesignLife Demonstration Use non-pvx time signal edited for 1 rotation ( 1 wavelength) Also added emergency shutdown event (1 per year) 5 years 10 years 4 years 1 year 20 (in 20 years) Conclusion Use multi-run analysis to: 4Exclude non-fatiguing parts of the model 4Select most appropriate algorithm for the job Learned how duty cycles are used for Mission Profiling in FEbased fatigue analysis Learned how to use buffered fatigue analysis and multiaxial PVX to optimise analysis of a rotating shaft 61

62 Concluding Remark Load history 4Huge effect on fatigue life 4Need to characterize the target customer well Load history Geometry 4Accuracy of surface stresses are critically important ±10% stress ±100% life 4Structural FE modelling is generally to class standards Geometry Fatigue Properties Fatigue Analysis Optimize Fatigue Results Fatigue properties 4Material fatigue properties are relatively inexpensive to obtain 4Materials Assurance Service available from ncode laboratory Understanding Component Loading & Material Performance Yields Most Significant Improvement on Life Assessment Today! 136 Seminar Schedule 9:00 9:30 10:30 10:50 11:30 12:00 13:00 14:00 14:30 16:00 Part 1 Introduction Part 2 Proving Ground optimization Morning Coffee Keynote speech Dr. Andrew Blows (Jaguar Land Rover) Part 3 Road Simulation & Component Testing Lunch Part 4 Accelerated Vibration Testing Afternoon Tea Part 5 Virtual CAE Testing Close 62

63 Thank You Dr. Andrew Halfpenny Chief Technologist HBM ncode Products Tel: UK: +44 (0) North America: +1 (248)