Lebensdaueranalysen im Zeitbzw. Frequenzbereich

Transcription

1 Lebensdaueranalysen im Zeitbzw. Frequenzbereich Axel Werkhausen (ECS), erhard Spindelberger (ECS) ECS / Disclosure or duplication without consent is prohibited

2 ECS - Historical Overview 1899 J. PUCH Erste Steierm. Fahrrad-Fabriks A raz 1914 PUCHWERKE A 1928 AUSTRO-DAIMLER- PUCHWERKE A 1957 TORONTO CANADA 1899 Österr. DAIMLER Motorenges. Wr. Neustadt 1934 STEYR-DAIMLER-PUCH A 1864 J. & F. Werndl & Coomp. STEYR 1926 STEYR-WERKE A Truck Division of SDP acquired by MAN 1995 Engineering Center Steyr Date: March 2013 Author: W. Dantendorfer ECS / Disclosure or duplication without consent is prohibited 2

3 ECS - Location / Area Proving round Office Building Production, Engine- & Drivetrain Testing Fatigue Lab Chassis Dyno Date: March 2013 Author: W. Dantendorfer ECS / Disclosure or duplication without consent is prohibited 3

4 Testing Services Date: March 2013 Author: W. Dantendorfer ECS / Disclosure or duplication without consent is prohibited 4

5 Fatigue Testing & Measurement Engineering Component Testing Axle Testing Sensor Development Servo-hydraulic Fatigue Test Road simulators up to 24 channels Axel test benches up to 12 channels Component test benches Test bench development & consulting Measurement data logging and processing Fatigue relevant data Engine relating data Bogie Suspension test 18 Channel Suspension & Chassis Test Date: March 2013 Author: W. Dantendorfer ECS / Disclosure or duplication without consent is prohibited 5

6 Simulation Services Multi-Body-Simulation Vehicle Thermal Simulation CFD Simul. E-Motor Cooling Cost Management by using Design for Manufacture & Assembly (DFMA) Methodology and Tool Multi-Body-Simulation (MBS) for load and comfort Finite Element Analysis on fatigue, vibration and acoustics Simulation and optimization of the vehicle thermal & energy management Driving simulation determines driving performance parameters (consumption, losses, emissions,...) Fluid flow calculation (CFD) Product & Engineering Data Management (PDM / EDM) PLM / SAP services (EIB) CAD based Dip-Coating simulation Dip Paint Process Simulation Finite Element Analysis on Fatigue - Housing Date: March 2013 Author: W. Dantendorfer ECS / Disclosure or duplication without consent is prohibited 6

7 ECS Software Products >> Dip Paint Simulation >> PLM data exchange and integration platform >> Sub-model analysis and data mapping >> Operational strength analysis based on FEM results >> Automatic calibration of engine control units >> Optimization of energy management for vehicles >> Non-linear joints for multi-body simulations >> Journal bearing model for multi-body simulations >> Automatic meshing >> NC programming system for turning, drilling and milling >> Pre- and post-processing of acoustic analysis on a modal basis Date: March 2013 Author: W. Dantendorfer ECS / Disclosure or duplication without consent is prohibited 7

8 Finite Element Methode Fatigue basic plast break heat Load Time FT 2 Load - PSD Frequency 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 8

9 How to use FEMFAT MAX in Time Domain? WHEN??? Direction of Principle Stresses are permanently altering Direction and location of forces and boundary conditions are constant Existing Load Histories More than one channel, which are generally not in phase IMPORT One stress result for each channel (e.g. for unit load) One load history for each channel channel max EXAMPLEs Chassis parts like: Knuckles, subframes, H-Arms,... Body in White Crankshaft with modal approach 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 9

10 FEMFAT in the Frequency Domain WHEN??? Load definition is a PSD random characteristic signals multiple axis can be combined IMPORT stresses from modal frequency response analysis PSD for load spectra per axis Probability model (Dirlik, Rayleigh, ) FEMFAT SPOT EXAMPLE engine firing exitations (high frequencies) Buildings (wind exitations) electronics (frequencies) comparison with shaker tests in laboratories 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 10

11 Local Stress Concept Crack Initiation Influences in FEMFAT Stress Tensors Stress radient Mean Stress Influence MultiAXial Load Temperature Influence PLASTic Deformations etc. Stress Amplitude UCS Stress Amplitude Mean Stress Specimen Material Data Stress Amplitude UTS Load cycles Load cycles UCS Mean Stress UTS Finally : Component S/N curve including all influences FOR EACH NODE & for each RFM entry 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 11

12 Local Stress Concept Crack Initiation Analyzed S/N Curve at a FE-Node by FEMFAT... A... for a certain survival probability in% Amplitude stress A N 1 N (log) Analysed S/N Curve at a FE-Node by FEMFAT n 1 Damage d 1 = n 1 N 1 Endurance A SF A = Endurance A N (log) Endurance safety factor / damage (fatigue limit) 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 12

13 Data Processing in Fatigue Analysis FE- Data Nodes & Elements Physical Properties roup Data Stress Result Data Amplitude Stress Mean Stress Constant Stress Fatigue Influences Load Spectra Rainflow Stepped Synthetic Finite F Element E M Method for Fatigue Specimen Material Data RESULTS Damage Values, Life Endurance Safety Factors, Analysis Report 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 13

14 Motivation for Fatigue Analysis in Frequency Domain Signals with random characteristics! Road excitation Acceleration excitation Excitation examples: High frequency vibration of firing excitation Shaker tests (electronic devices, automotive components) Turbulence (aerospace) Wind/wave excitation (buildings) Side force excitation ECS / Disclosure or duplication without consent is prohibited 14

15 Frequency Domain Fourier Transformation Load FT 2 Load - PSD Time Frequency Power Spectral Density (PSD) = Square of Fourier Transformed Signal = Mean Value of Power of the signal ECS / Disclosure or duplication without consent is prohibited 16

16 Linear Time-Invariant (LTI) Systems f u( t) (t) h( t)* f ( t) h( t)... Impulse- Response (System- Property) Linear Time-Invariant System u ( t) h( t ) f ( ) d Output-Signal = Superposition of time- shifted Impulse-Response - Functions Fourier-transformation: Convolution in time-domain => Multiplication in frequency-domain U( ) H( ) F( ) Advantage: Simple multiplication in frequency-domain ECS / Disclosure or duplication without consent is prohibited 17

17 ECS / Disclosure or duplication without consent is prohibited 18 The Equation of Motion for Linear Elastic Mechanical Systems 18 ) ( ) ( ) ( ) ( ) ( 2 F U Z F U K V i M Dynamic Stiffness Matrix Z: Transfer Matrix H: ) ( ) ( ) ( ) ( 1 F H F Z U Output = Structural Response Dynamic Transfer Behavior of System Input = Excitation Frequency Domain!?

18 Time Domain 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 19

19 Analysis Technique in Time Domain Structural Analysis: Load - Time - History Load Time Modal Transient Response Analysis Stress- tensor - Time - History Stress Time ECS / Disclosure or duplication without consent is prohibited 20

20 Multiaxial-Input-Data / Structural Analysis Modal Frequency Response Property of Mechanical System Modal Stresses Unit Load Case 1 Modal Transfer Functions Unit Load Case 1 x Stress Scaling Unit Stresses 1 Unit Load Case 2 Modal Transfer Functions Unit Load Case 2 x Stress Scaling Unit Stresses 2 Unit Load Case N Modal Transfer Functions Unit Load Case N x Stress Scaling Unit Stresses N ECS / Disclosure or duplication without consent is prohibited 21

21 Hybrid Models FE + MBS + FEMFAT ChannelMax Component Modes 1 2 n MBS and (E)HD (Co - Simulation) Modal Coordinates Channel 1 FEMFAT q 1(t) q1(t) 1 q 2(t) Channel 2 q n(t) q 2(t) 2 Fatigue FE Channel n n q n(t) Modal Stresses 1 2 n Lifetime prediction of dynamic loaded parts considering dynamic effects due to natural vibrations Additional Load Cases (Bolts,...) Date: August 2013 Author: FEFMAT SUPPORT ECS / Disclosure or duplication without consent is prohibited 22

22 Analysis Technique in Time Domain Structural Analysis: Load - Time - History Load Time Modal Transient Response Analysis Stress- tensor - Time - History Stress Time Fatigue Analysis: Cutting Plane Method ECS / Disclosure or duplication without consent is prohibited 23

23 Cutting Plane Criteria Current Cutting Plane depending on and a e 2 a n alt, TC alt 2 2 a m 2 m e sign m n m n m Yield 2 2 Yield.. a m n a n A a e ( ) - M m e ( ) + M 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 24

24 Critical Cutting Plane Criteria m HAIH diagram and loading points are calculated for all cutting planes a m n a n A a e crit a endu - M + M Criteria (m=const) for critical loading point: a endu a e crit Min 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 25

25 Analysis Technique in Time Domain Structural Analysis: Load - Time - History Load Time Modal Transient Response Analysis Stress- tensor - Time - History Stress Time Fatigue Analysis: Rain Flow Matrix Cutting Plane Method ECS / Disclosure or duplication without consent is prohibited 26

26 Rainflow Counting of Closed Hysteresis Loops Rainflow time 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 27

27 Classes Stress / Classes Rainflow Counting: Principle I Closed Hysteresis Points Classes Time t Strain Rainflowcounting Pictures from Radaj: Ermüdungsfestigkeitsnachweis 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 28

28 Classes Stress / Classes Rainflow Counting: Principle I Closed Hysteresis Points Classes Time t Strain Rainflowcounting 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 29

29 Force [N] Moment [Nmm] RainflowMatrix for Time-Domain Rainflow Matrix / Load History Time Load History Moments Moment Mx My Mz time [sec] Force Force Fx Fy Fz time [sec] 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 30

30 Analysis Technique in Time Domain Structural Analysis: Load - Time - History Load Time Modal Transient Response Analysis Stress- tensor - Time - History Stress Time Fatigue Analysis: S-N-Line DAMAE S N Rain Flow Matrix Cutting Plane Method ECS / Disclosure or duplication without consent is prohibited 31

31 MINER Rule in FEMFAT Load spectrum entry A 1, M 1, n 1 Analyzed S/N Curve at a FE-Node by FEMFAT... A 1... for a certain survival probability in% - + MEAN N 1 N (log) n 1 Damage d 1 = n 1 N 1 Crack is initiated at d total = 1 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 32

32 Linear Damage Accumulation by Palmgren Miner A 3 M 3 n 3 A 2 M 2 n 2 A 1 M 1 n 1 A 1 Analysed S/N Curves at a FE-Node by FEMFAT - + MEAN A 2 A 3 N 1 N 2 N 3 S/N 1 S/N 2 S/N 3 N (log) n 1 n 2 n 3 d i = n i N i Total Damage: D = d i = d 1 + d 2 + d d n 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 33

33 The Frequency Domain 6/18/2014 Author: FEMFAT Support ECS / Disclosure or duplication without consent is prohibited 34

34 Analysis Technique in Frequency Domain Structural Analysis: Load in Frequency Domain Load -PSD Frequency Modal Frequency Response Analysis Stress-tensor in Frequency Domain Stress-PSD Frequency Fatigue Analysis: DAMAE S S-N-Line N Probability Density Function p S Cutting Plane Method PDF: Dirlik, Rayleigh ECS / Disclosure or duplication without consent is prohibited 35

35 Multiaxial Load Cases / Frequency Domain Structural Analysis: Frequency Response Auto -PSD 1,1 DAMAE Analysis: Unit Load Case1 F Unit Load Case 2 Frequency Response Frequency Response FE Solver Unit Stresses1 Unit Stresses 2 x Auto -PSD 2,2 x Cross -PSD 1,2 Stress - PSD Multiaxial Fatigue - Analysis x Half width Damping 2 Damage Frequency Response 3 Mode System frequency range < modal base spectral resolution damping ECS / Disclosure or duplication without consent is prohibited 36

36 Input - Power Spectrum / Fatigue Analysis PSD Input Matrix Unit Stresses 2 Unit Stresses 1 Unit Stresses 3 Unit Stresses 1 Auto - PSD 1,1 Cross - PSD 1,2 Cross - PSD 1,3 Unit Stresses 2 Cross- PSD 2,1 Auto - PSD 2,2 Cross - PSD 2,3 Unit Stresses 3 Cross - PSD 3,1 Cross - PSD 3,2 Auto - PSD 3,3 ECS / Disclosure or duplication without consent is prohibited 37

37 Method of Modal Reduction (to Reduce Size of Equation System) Modal Stresses - FILE.OP2 78 Hz 156 Hz 187 Hz Modal Transfer Functions - FILE.PCH Unit Load Case 1 Unit Load Case 2 Unit Load Case 3 ECS / Disclosure or duplication without consent is prohibited 38

38 Stress PSD Matrix Cutting Plane Method xx yy zz xy xz yz xx xx xx xx xx xx xx yy zz xy xz yz yy yy yy yy yy yy xx yy zz xy xz yz zz zz zz zz zz zz xx yy zz xy xz yz xy xy xy xy xy xy xx yy zz xy xz yz xz xz xz xz xz xz xx yy zz xy xz yz yz yz yz yz yz yz 6 x 6 Stress PSD n ( ) a a 2 S i j i equi j i, ji S n (t) Cutting - Plane. (t) n, ( t) S n n ECS / Disclosure or duplication without consent is prohibited 39

39 Equivalent Stress Methods Supported Methods: von Mises Stress eq Normal Stress in Critical Plane Equivalent Stress in Critical Plane Modified Equivalent Stress in Critical Plane Automatic (brittle ductile materials) eq na 2 eq na eq k k a k 4 k 1 na a k 2 According to FKM-uideline, values for shear fatigue strength factor k are: Steel: k = 1.73 Nodular cast iron: k = 1.54 Cast aluminum alloys: k = 1.33 ray cast iron: k = 1.18 FEMFAT SPECTRAL uses statistically correct equivalent stress PSDs! ECS / Disclosure or duplication without consent is prohibited 40

40 Probability Model and Damage Analysis Aim: Estimation of stochastic Amplitude-Stress-Distribution from PSD p(s) Dirlik PROBABILITY MODEL p(s) Rayleigh m m m 1 i 0 2 [0, [... Area i ( ) d m... Center of Area PSD i-th Order Moment of Density:... eometric Moment of Inertia Rayleigh -> narrow band signals D total 0 PDF Dirlik -> broad band signals p( a) D( a) d a ECS / Disclosure or duplication without consent is prohibited 41

41 Example: Battery-Carrier Date: D R A F T Author: tbd ECS / Disclosure or duplication without consent is prohibited 42

42 Supported Influence Factors Probability model (Dirlik, Rayleigh) Stress radient (endurance limit, slope/cycle limit) Surface Roughness Constant Stress (bolt pre-tension) Modified Haigh Diagram (ultimate tensile strength) Size Influence Statistical Influence Isothermal Temperature Rotating Principal Stresses Influence ECS / Disclosure or duplication without consent is prohibited 43

43 Summary Advantages: Fast method (structural analysis, fatigue analysis) Load-case superposition (very flexible) Simple combination of different load situations Simple simulation chain (no multi-body simulation, reverse FFT not required) Disadvantages: Linear elastic behavior assumed/required (superposition) Less accuracy compared to time domain (no rainflow-counting; statistics) Conclusions: FEMFAT SPECTRAL is a reliable and effective tool for damage analysis of multi-axially stochastically loaded systems. ECS / Disclosure or duplication without consent is prohibited 44

44 The future is ours to make. Date: D R A F T Author: tbd ECS / Disclosure or duplication without consent is prohibited 45