STOCHASTIC SIMULATION APPROACH FOR REALISTIC LIFETIME FORECAST AND ASSURANCE OF COMMERCIAL VEHICLE BRAKING SYSTEMS

Transcription

1 Failure Probability F(t) Sensitive Robust Shape parameter b STOCHASTIC SIMULATION APPROACH FOR REALISTIC LIFETIME FORECAST AND ASSURANCE OF COMMERCIAL VEHICLE BRAKING SYSTEMS Virtual Lifetime Determination Technologie Transfer Initiative 12. Weimar Optimization and Stochastic Days 2015 Durability (t-t0) 10 6 LC M. Sc. Martin Dazer Dipl.-Ing. Stefan Kemmler Prof. Dr.-Ing. Bernd Bertsche Dr.-Ing. Tobias Leopold Dipl.-Ing Jens Fricke Institute of Machine Components Reliability Engineering Technology Transfer Initiative Knorr-Bremse Group Systeme für Nutzfahrzeuge GmbH

2 Failure Probability F(t) Sensitive Robust Shape parameter b Research Cooperation Virtual Lifetime Determination Technologie Transfer Initiative Durability (t-t0) 10 6 LC 2

3 Agenda 1. Motivation 2. Application example: brake caliper 3. Simulation process 4. Design of Experiments 5. Result evaluation 6. Summary and Outlook 3

4 Virtual Lifetime Determination of commercial vehicle braking systems 1. MOTIVATION 4

5 1. Motivation Real durability tests t max Identification of specific product properties: t min Systematic and unsystematic scattering of lifetime Failure mechanism Lowest and longest cycle times Failure distribution Control of correct targetengineering by requirements Scattering produces a characteristic lifetime distribution 5

6 F(t) Stress Amplitude (log) Stress Amplitude (log) 1. Motivation 50% Endurable nominal load amplitude in operation Occurring nominal load amplitude on component Motivation: Realistic lifetime prediction through stochastic simulation of stress and strength Load cycles N (log) Nominal load cycles N nom (log) 90% Scatter band of endurable load amplitudes in operation 50% 10% 90% Scatter band of the load amplitudes occur on the component Stochastic Simulation 10% cumulative density Scatter band of load cycles N Source: Bertsche 2004 Load cycles N (log) 6

7 1. Motivation Input Variability Simulation System Output Variability Lifetime Parameter variations of the product lead to variations in product properties as a result of internal correlations. This can cause functional or structural failure and the deterioration of product quality. Aim: Realistic forecast of time to failure 7

8 1. Motivation FEA-Simulation model Mapping of damage-related effects Stress amplitudes Strain amplitudes Parametric CAD-Model Mapping the caliper geometry Changes in the geometry Parameter study Automatic simulation of the established DOE Statistical evaluation Source: Dynardo

9 Virtual Lifetime Determination of commercial vehicle braking systems 2. APPLICATION EXAMPLE BRAKE CALIPER 9

10 Percent 2. Application example Brake caliper Brake caliper Piston Pressure cylinder dummy Piston Have to withstand high loads in case of overload Therefore tested with high loads Failures in Low-Cycle-Fatigue range (LCF) Probability Probability functionplot of lifetime for lifetime Weibull Weibull Full data Full ML-Estimation data - Brake disc Brake pads Percent Statistics Shape 2,89116 Scale 0, A v erage 0, Stdv. 0, Median 0, Application example: Brake caliper ,09 0,1 0,15 0,2 0,3 0,4 Standardized lifetime 0,5 0,6 0,7 0,8 0,9 10

11 Virtual Lifetime Determination of commercial vehicle braking systems 3. SIMULATION PROCESS 11

12 tamplitude Simulation process Tension Pressure Shear Bending Torsion Loadcase simulation Werkstoffcharakterisierung Zyklische Stress Spannungs / Strain Dehnungskurve hysteresis εa ela D Source: maschinenbau-wissen 2015 Definition of claim and the associated amplitudes Load definition Material properties Characterization of the relevant material properties Source: Haibach 2005 The level of deterioration related stress and strain amplitudes Stochastic Simulation Identification and consideration of nonhomogeneous loading states Source: SOFEA 2015 Deterioration σ a P = 10 % 50 % 90 % Lifetime distribution Carrying Capacity Bauteilgeometrie Strength Beanspruchungs- Zeitfunktion for variance determination ε a igkeit ε a Pü = 10 % 50 % 90 % Klassierung des Lastkollekivs Belastungsverteilung FEM-Analyse Dehnungswöhlerlinie F σ A, σ m, ε A Stress / Strain Wöhler curve 12 Sc Schädigungsparamete εa wöhlerlinie Pü = 10 % 50 % 90 % Characterization of the strength model Source: Haibach 2005 N Schädigungsrechnung

13 3. Simulation process load definition Real force flow in the brake caliper Contact surface Clamping force Simulated force flow in the brake caliper Contact surface system boundary Clamping force causes high FE-calculation time System simulation to determine deterioration Same damage state system boundary Bolt pretension for lower FE-calculation time 13

14 3. Simulation process load definition There are variations in the clamping force occuring through hysteresis effects Load spectrum is determined from test reports Best-Fit: Lognormal distribution Probability function for clamping force Probability function of clamping force Lognormal - 95%-KI % KI Densitiy Distribution function of clamping of force force Lognormal Test for goodness of fit Lognormal A D = 0,242 p-value = 0, Shape 0,03424 Scale 0,03219 N 50 Percent Densitiy ,95 1 1,05 1,1 Standardized clamping force Standardized clamping force 1,15 0 0,96 0,99 1,02 1,05 1,08 Standardized clamping force Standardized clamping force 1,11 14

15 tamplitude Simulation process Tension Pressure Shear Bending Torsion Loadcase simulation Werkstoffcharakterisierung Zyklische Stress Spannungs / Strain Dehnungskurve hysteresis εa ela D Source: maschinenbau-wissen 2015 Definition of claim and the associated amplitudes Load definition Material properties Characterization of the relevant material properties Source: Haibach 2005 The level of deterioration related stress and strain amplitudes Stochastic Simulation Identification and consideration of nonhomogeneous loading states Source: SOFEA 2015 Deterioration σ a P = 10 % 50 % 90 % Lifetime distribution Carrying capacity Bauteilgeometrie Strength Beanspruchungs- Zeitfunktion for variance determination ε a igkeit ε a Pü = 10 % 50 % 90 % Klassierung des Lastkollekivs Belastungsverteilung FEM-Analyse Dehnungswöhlerlinie F σ A, σ m, ε A Stress / Strain Wöhler curve 15 Sc Schädigungsparamete εa wöhlerlinie Pü = 10 % 50 % 90 % Characterization of the strength model Source: Haibach 2005 N Schädigungsrechnung

16 Stress σ [Mpa] 3. Simulation process material properties Material behavior GJS Mathematical modeling using Ramberg-Osgood-equation: ε a,t = σ a E + σ a K R e = 370 MPa R e = first load yield strength R e = cyclic yield strength 1 n R e = 500 MPa Significantly higher cyclic yield strength R e Material shows clear solidifying behavior Strain ε [%] Cyclic First load First discharge General Ramberg-Osgoodequation: ε a,t = σ a E + σ a K 1 n Modelling the fist load curve: K = 1160 n = 0,19 Modelling the first discharge curve: K = 1300 n = 0,17 Modelling the cyclic curve: K = 924,9 n = 0,1 Nominal material behavior 16

17 Stress σ [Mpa] 3. Simulation process material properties Material behavior GJS Mathematische Modellierung mit Ramberg-Osgood- Gleichung General Ramberg-Osgoodequation: ε a,t = σ a E + σ a K 1 n R e = 500 MPa R e = 370 MPa R e = zügige Streckgrenze R e = zyklische Streckgrenze Deutlich höhere zyklische How can Streckgrenze the scattering R e behavior mapped Werkstoff zeigt deutliches mathematically? verfestigendes Verhalten Modelling the fist load curve: K = 1160 n = 0,19 Modelling the first discharge curve: K = 1300 n = 0,17 Modelling the cyclic curve: K = 924,9 n = 0, Strain ε [%] First load Nominal material behavior 17

18 Distribution of smallest extreme values 3. Simulation process material properties Only data from the static tensile test available Mathematical derivation of the scattering of n and k σ a R m,max R m 2 Determination of the limits and the distribution of n, and k: R m,min R p0,2;max R p0,2 R p0,2;min 1 Generation of point clouds using monte carlo simulation with m samplings Using two interpolation points solving Ramberg Osgood iteratively for n and k Loop to j, i = m ε 0,2i = R p0,2 i E + R p0,2 i K 1 n ε 0,2,min ε 0,2 ε 0,2,max ε g,min ε g ε g,max ε a Distribution of smallest extreme values ε gj = R m j E + R m j K 1 n 18

19 Density Density Density 3. Simulation process material properties Determination of the variance of K and n using 1000 Monte Carlo Samplings Density Location 164,4 Scale 0,1952 N 1000 Density function of n Density function n Weibull Density Location 389,9 Scale 1174 N 1000 Density function of K Density function K Weibull Best fit for initial loading K and n with Weibull distribution ,1875 0,1890 0,1905 0,1920 0,1935 0,1950 n Location 83,37 Scale 0,1026 N 1000 n Density function of n Density function n' Weibull 0, Location 310,5 Scale 936,2 N K K Density function of K Density function K' Weibull 1180 Density Density Proportionate transfer of variance at K, K, n and n ,0960 0,0976 0,0992 0,1008 0,1024 0,1040 n' Location 143,5 Scale 0,1746 N 1000 n Density function n'' Weibull Density function of n K' Location 435,0 Scale 1326 N 1000 K Density function K'' Weibull Density function of K 940 Density Density ,1665 0,1680 0,1695 0,1710 0,1725 0,1740 0,1755 0,1770 n'' n K'' K

20 tamplitude Simulation process Tension Pressure Shear Bending Torsion Loadcase simulation Werkstoffcharakterisierung Zyklische Stress Spannungs / Strain Dehnungskurve hysteresis εa ela D Source: maschinenbau-wissen 2015 Definition of claim and the associated amplitudes Load definition Material properties Characterization of the relevant material properties Source: Haibach 2005 The level of deterioration related stress and strain amplitudes Stochastic Simulation Identification and consideration of nonhomogeneous loading states Source: SOFEA 2015 Deterioration σ a P = 10 % 50 % 90 % Lifetime distribution Carrying Capacity Bauteilgeometrie Strength Beanspruchungs- Zeitfunktion for variance determination ε a igkeit ε a Pü = 10 % 50 % 90 % Klassierung des Lastkollekivs Belastungsverteilung FEM-Analyse Dehnungswöhlerlinie F σ A, σ m, ε A Stress / Strain Wöhler curve 20 Sc Schädigungsparamete εa wöhlerlinie Pü = 10 % 50 % 90 % Characterization of the strength model Source: Haibach 2005 N Schädigungsrechnung

21 Örtliche Local notch Kerbspannung stress σ [MPa] σ [MPa] 3. Simulation process deterioration First load simulation: ε a,t = σ a E + σ a K 1 n Cyclic operation load simulation: ε a,t = σ a E + σ a K 1 n σ m Correct mapping of the location of the hysteresis Mean stress influence Local notch strain ε [%] Nearly elastic operating load hysteresis Örtliche Kerbdehnung ε [%] Accelerated Representative Simulation Process (ARSP) for deterioration calculation at constant load Formation of residual compressive stress First discharge load simulation - Masing behavior: ε a,t = σ a E + σ a K 1 n Abstract representation 21

22 tamplitude Simulation process Tension Pressure Shear Bending Torsion Loadcase simulation Werkstoffcharakterisierung Zyklische Stress Spannungs / Strain Dehnungskurve hysteresis εa ela D Source: maschinenbau-wissen 2015 Definition of claim and the associated amplitudes Load definition Material properties Characterization of the relevant material properties Source: Haibach 2005 The level of deterioration related stress and strain amplitudes Stochastic Simulation Identification and consideration of nonhomogeneous loading states Source: SOFEA 2015 Deterioration σ a P = 10 % 50 % 90 % Lifetime distribution Carrying Capacity Bauteilgeometrie Strength Beanspruchungs- Zeitfunktion for variance determination ε a igkeit ε a Pü = 10 % 50 % 90 % Klassierung des Lastkollekivs Belastungsverteilung FEM-Analyse Dehnungswöhlerlinie F σ A, σ m, ε A Stress / Strain Wöhler curve 22 Sc Schädigungsparamete εa wöhlerlinie Pü = 10 % 50 % 90 % Characterization of the strength model Source: Haibach 2005 N Schädigungsrechnung

23 3. Simulation process strength Stress Wöhler curve Strain Wöhler curve σ a According to Haibach: modeling of stress levels with normal distribution using Database of FKM ε a ε' f,1 ε' f,2 c 1 c 2 Only 2 nominal literature sources. No large database Stress Level 1 10 % P Failure 50 % 90 % k Scattering of endurance strength N D σ' f,2 /E Uniform Distribution b 2 Stress Level 2 σ' f,1 /E b 1 Endurance Level Modeled with: N = N D σ σ D k Modeled with: ε a = σ f E 2N b + ε f 2N c N N Determination of scattering of k: Monte Carlo Simulation using 3 interpolation points Determination of scattering of σ f, ε f, b and c: Using uniform distribution between σ f1 and ε f1 23

24 Density Density 3. Simulation process strength Result for variance of k and N D of Stress Wöhler curve Density function of k Normal Density function of k Normal Density function of σ f Uniform Density function of sigf Result for variance of σ f, ε f, b and c of Strain Wöhler curve 120 Average -5,456 Stdv 400,3371 N Density ,3-6,0-5,7-5,4 k k -5,1-4,8-4,5 Density Sig(f) σ f Compatibility condition according to Haibach: Already determined Using uniform distribution 100 Density function of N D Normal Density function of ND Normal Average Stdv N 1000 Density function of b Density Uniform function of b n = b c ; k = σ f (ε f ) n Density Density Completely determined ND N D 0-0,0690-0,0684-0,0678-0,0672-0,0666 b b -0,0660-0,

25 X 1 X 3 X 2 Virtual Lifetime Determination of commercial vehicle braking systems 4. DESIGN OF EXPERIMENTS 25

26 4. Design of Experiments Spacefilling latinhypercube sampling Source: Siebertz 2010 Optimal cover of the parameter space Design Parameter Using 3σ Normal Distribution Material Model Using Distribution of smallest extreme values Strength Model Stress: Using Normal Distribution Strain: Using Uniform Distribution Load Spectra Using Lognormal Distribution and ARSP 26

27 Local Örtliche notch Kerbspannung stress σ [MPa] Local Örtliche Kerbspannung notch stress σ [MPa] σ [MPa] 4. Design of Experiments Spacefilling latinhypercube sampling Load Spectra Using Lognormal Distribution and ARSP 10 Distribution Densitiy function of clamping of clamping force force Lognormal Location 0,03424 Scale 0,03219 N 50 Higher compressive residual stress Local notch strain ε [%] 8 Densitiy 6 4 Örtliche Kerbdehnung ε [%] 2 Source: Siebertz ,96 0,99 1,02 1,05 1,08 Standardized clamping force Standardized clamping force 1,11 Optimal cover of the parameter space Integration of the load spectrum through parametric study Örtliche Kerbdehnung ε [%] Local notch strain ε [%] 27

28 Workflow Step 2 4. Design of Experiments Sampling of Design Parameter Material model Workflow Step 1 Sending deterioration outputs from FE-Simulation Workflow Step 2 Sampling of Stress strength model Calculation of lifetime Workflow Step 3 Sending deterioration outputs from FE- Simulation Sampling of Strain strength model Calculation of lifetime Workflow Step 3 Workflow Step 4 Sending back results to Robustness Analysis for Postprocessing 28

29 Virtual Lifetime Determination of commercial vehicle braking systems 5. RESULT EVALUATION 29

30 5. Result Evaluation Probability plot of FKM; PSWT; Real data Weibull Full data - ML-Estimation Percent 99, Variable FKM approx. PSWT approx. Real data 0,1 0,01 0,1 Standardized time to failure 1 30

31 5. Result Evaluation Percent 99, Probability plot of FKM; PSWT; Real data Weibull Full data - ML-Estimation Variable FKM approx. PSWT approx. Real data Very good approximation using stress based FKM algorithm Nearley same Weibull shape parameter b Small deviation in characteristic life time T Larger deviation on upper levels 0,1 0,01 0,1 Standardized time to failure 1 using strain based PSWT Pronounced Differences to conservative side for PSWT Additionally insufficient fit FKM approximation slightly overestimates the real life time Reason for this behavior: Increasing plastic component of strain amplitude 31

32 Virtual Lifetime Determination of commercial vehicle braking systems 6. SUMMARY AND OUTLOOK 32

33 6. Summary and Outlook Mapping of systematic uncertainties of Design Parameter Material model Strength model Load Development of a Accelerated Representative Simulation Process Succesfull development of a virtual lifetime distribution Check of reproducibility Future investigations to the influence of plastic compontents in strain amplitudes for deterioration calculation Investigations to the strain based strength model Increase of maturity level in early design stages! 33

34 THANK YOU FOR YOUR ATTENTION! 34