Time v Frequency Domain Analysis For Large Automotive Systems

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Neil Bishop§, Stuart Kerr§, Paresh Murthy§, and Karl Sweitzer§§ §CAEfatigue Limited, Farnham, Surrey, UK. §§Booz Allen Hamilton, Herndon, VA, USA

Time v Frequency Domain Analysis For Large Automotive Systems

CAEfatigueEstablished in the United Kingdom and focused on frequency domain response and fatigue analysis solutions. CEO of the Company, and others in the company, have been pioneers in the field for 30 years. Dr. Neil Bishop could be considered to be the “inventor” of the 1st generation tools and is very well known in the field.

CAEfatigue VIBRATIONOr CFV for short is a 2nd generation frequency domain random response and fatigue solver - re-engineered from the ground up with all-new algorithms and technology. It uses, as input, system transfer functions from solvers like Nastran, Ansys, Abaqus and Optistruct, and outputs random response and fatigue damage results that can be processed in post processors like Patran or Hyperview.

simple tools advanced features faster solutions!

Frequency Domain Response and Fatigue Analysis Solver

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Summary

Frequency domain is generally better for dynamics. Both quantitative and qualitative advantages are well recognised. Traditional fatigue was born in the time domain (mainly statics) CAEfatigue VIBRATION is a 2nd generation frequency domain random response and fatigue tool based on multiple new technology developments. Presentation Agenda

•  Technology Overview (why we would want to work in the frequency domain)

•  Accuracy •  Improving the Management of Loads in the Frequency Domain

Transition From 1st to 2nd Generation Vibration Fatigue Solvers •  Automotive customers need to be able to apply multiple (eg 100 simultaneous) inputs

(Many automotive OEM’s are very keen to use these methods for large models)

4

NB PSD

Sine waves

Deterministic Components

Random PSD

Combined Loads – Frequency Domain

Stress pdf

Fatigue Damage

Loads have to be combined before calculation of the

stress pdf

Mean Load

Response Parameters (if Needed)

Time Domain

Frequency Domain

1st generation tools do not allow either

•  Aerospace customers need to be able to apply mixed random and deterministic loads (eg sine sweep + mean + random or random + narrow band + mean)

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What Is A PSD (What Is The Frequency Domain) Power Spectral Density (PSD)

Random (time domain)

=

4040

44

33

22

11

,.,.,,,,

fa

fa

fafafafa

ii

Amplitudes - squared

5

Deterministic (time)

a1, f1,ϕ1a2, f2,ϕ2a3, f3,ϕ3a4, f4,ϕ4

.ai, fi,ϕi

.a40, f40,ϕ40

=

Why Work In Frequency Domain?

frequency

time

Win

d sp

eed

PSD

Str

ess

PSD

frequency

time

Hub

Str

ess

Time Domain SOL109 or SOL112

Direct or Modal Transient (loads & system connected)

Frequency Domain SOL108 or SOL111

Direct or Modal FRA (loads & system not connected)

applied to structure

applied to structure

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Mode 1

Mode 2

Mode 200

Mode j

Modes (stress fields) for weight condition i

Example: Modal Transient (Direct Not Possible)

Weight 1

Weight 2

Weight 5

Weight i

Fatigue life calculation for Weight i, and Event k, using 200 Modes (stress fields) and

200 MPF’s (time histories) Sum of all damages

SOL112 SOL103

Event 1

Event 2

Event 40

Event k

PMF 1

MPF 2

MPF 200

MPF l

MPF’s for Weight i and Event k

•  The number of Nastran runs required for the example problem would be 5 x 40 = 200 Nastran runs. •  This example also has 200 modal stress fields for each weight condition, hence 200 x 5 = 1,000 modal

stress fields are required. •  Each modal stress field contains approx 4M x 10 (GID’s) x 1000 = 40,000,000,000 stress components. •  200 x 200 = 40,000 MPF’s have to be generated. If we assume these are 1000 seconds at 2000Hz; then

80,000,000,000 MPF data points have to be managed.

•  4M elements (quads) •  5 Weight Conditions •  40 Events •  200 Modes

Example: Frequency Based (Modal or Direct)

Weight 1

Weight 2

Weight 5

Weight i

Transfer Function 1

Transfer Function 2

Transfer Function i

Transfer Function 5

Nastran SOL111/108 for

frequency j

Nastran SOL103

Nastran Database

Stress recovery module

Event 1

Event 2

Event 200

Event k Fatigue life

calculation for all Events for

Weight i

Sum of all damages

Moment set for

Transfer Function i

Repeat for all transfer functions

Complete Transfer Function (all frequencies)

for weight i written to OP2 file i (for all subcases)

•  In the frequency domain only 5 stress solver runs are needed (in current implementation these can be very large but possibilities exist to minimise or even eliminate these OP2 files)

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User Interface (in V3.0)

CAEfatigue VIBRATION Concept at High Level (a 2nd Generation Frequency Based Fatigue Solver)

CAEfatigue Vibration

Response Statistics – FEF,

CSV, H3D

Fatigue Data - FEF, CSV, H3D Results: Patran FEF,

Hyperview H3D, Comma Separated CSV

input Control

Control File input

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Nastran (or other) Random

Response

Static Stress File

Dynamic Stress File

CFV should be considered as an output request for the stress solver


•  Concept – Random Response AND Fatigue Solver •  Simple Implementation (Easy to Adopt) •  More Robust Solutions •  Suitable for Very Large Models •  More Flexible Loads (Mixed Random & Deterministic) •  Can use Multiple Simultaneous Inputs for both direct

(SOL108) and modal (SOL111) analysis •  Elegant Connections to 3rd Party Optimisation Codes •  Test v Analysis Correlation Made Easier With TIME2PSD

Expert System




CSV, H3D



input Control

Control File input

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•  Non-linear rms strain and max strain •  displacement, velocity and acceleration,

force (R3.0) •  Composite layers (R4) •  Ansys support (R2.1) •  Abaqus support (R2.1)


Response

Static Stress File

Dynamic Stress File

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•  Very easy template system •  Ideal for batch and solver integration •  easy pre processing of loads




Expert System



CSV, H3D



input Control

Control File input

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Response

Static Stress File

Dynamic Stress File


•  Complex principal stress •  Gershgorin Circle Theorem

(eigenvalue extraction) •  Strain-life solver •  Seam welds (R2.1) •  Temp dependant materials (R 2.1) •  Spot welds (R3.0)




Expert System



CSV, H3D



input Control

Control File input

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Response

Static Stress File

Dynamic Stress File

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•  “Running Sum” moment technology •  Fast OP2 stress file interrogation •  1000+GB results files easily processed




Expert System



CSV, H3D



input Control

Control File input

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Response

Static Stress File

Dynamic Stress File



Expert System


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•  Mixed random plus harmonics (MIL-STD-810G)

•  New sine sweep technology •  Unique sine-on-random •  Unique narrow-band-on-random •  Embedding of MMPDS material data




CSV, H3D



input Control

Control File input

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Response

Static Stress File

Dynamic Stress File

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Expert System


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•  Multiple correlated loads (eg 100 inputs)




CSV, H3D



input Control

Control File input

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Response

Static Stress File

Dynamic Stress File

Conversion of Simultaneous Time Histories to PSD Matrix

time signal 1 time signal 2

time signal 3 time signal 4 time signal 5

time signal 6

time signal 7 time signal 8

time signal 9 time signal 10 time signal 11

time signal 12

PSD matrix for event 6 Time signals for event 6

event 6 loading

Complete duty cycle

Complete duty cycle

PSD Matrix Event 1 152 seconds









PSD Matrix Event 10 68 seconds 16

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Expert System


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Linked to any 3rd party optimisation code (eg Mode Frontier) which connects ascii Control file input (Nastran and/or CFV) to ascii CSV output




CSV, H3D



input Control

Control File input

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Response

Static Stress File

Dynamic Stress File



Expert System


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TIME2PSD Expert System will make conversion of test data to PSD format easier, more accurate, and less prone to user errors




CSV, H3D



input Control

Control File input

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Response

Static Stress File

Dynamic Stress File

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Model Used in For Accuracy Assessment. This is a summary of a paper (2015-01-0535) that was presented last week at the SAE2015 Congress. This model contains 91,783 elements, 580,758 DOF, 12 load application points (x, y, z at 4 locations) and 10 events (sets of loads in the form of time histories).

FEM Groups

Steel Cab Frame (critical element

1035259)

Main Cab Shell (critical element

1057009

Doors (critical element 8158502)

Front Strut (critical element 1050094)

Glass Screen (critical element 1068132)

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Statistical Analysis of Input Time Histories

Note that the max kurtosis is 12.438 and the average is 3.948, compared with an idealized Gaussian value of 3.0

www.caefatigue.com


CAEfatigue VIBRATION (CFV) Concept at High Level (a 2nd Generation Frequency Based Fatigue Solver)



CSV, H3D



input Control

Control File input

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Response

Static Stress File

Dynamic Stress File

CFV Process Is Defined Using “Control File”

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vibfat 777 csvfefetnastran center 0 Results56vftgdef 777 Dirlik 100 60 16 99.9 16 64 elset 1 632 2 631 3 633 4 631 5 include Sets/1_40k_yield.txtinclude Sets/2_50k_yield.txtinclude Sets/3_A6_cab.txtinclude Sets/4_A6_doors.txtinclude Sets/5_glass_windshield.txtvftgparm777 sn stress sgvon swt vftgseq 777 0 seconds 2874.0 101 152.0 102 42.0 103 18.0 104 18.0 105 480.0 106 1682.0 107 378.0 108 18.0 109 18.0 110 68.0 vftgevnt101 801 701 . .vftgevnt110 810 701vftgload801 PSD 80001 1.0 multi "OP2_files/Truck_SOL111_cent.op2”include AllEventPSDs/EA10bpsd.txt

. .vftgload810 PSD 80010 1.0 multi "OP2_files/Truck_SOL111_cent.op2”include AllEventPSDs/LS20bpsd.txtvftgload701 static 1.0 1 "OP2_files/truck_sol101_cent.op2”

Control File for CAEfatigue VIBRATION Analysis. Summed Events – LOGLVL=0

Control File for CAEfatigue VIBRATION Analysis. Summed Events – LOGLVL=0

$ Material 1 is Mild Steel EN $------|-----MID--CNVRT2-------|-------|-------|-------|-------|- VMATFTG 631 1.0 $------|--STATIC------YS-----UTS-------E-------|-------|-------|- STATIC 358.5 2.0E5 $------|------EN------Sf-------b------Ef-------c-------K-------n EN 560.8 -0.109 0.065 -0.39 461.7 0.12 $ Material 2 is assumed Manten Steel EN VMATFTG 632 1.0 STATIC 560.0 2.0E5 EN 917.0 -0.095 0.260 -0.470 1103.0 0.19 $ Material 3 is RQC100 Steel SN VMATFTG 633 1.0 STATIC 800.0 2.0E5 $------|------SN----SRI1------B1-----NC1------B2-----NFC------- SN 13240.0 -0.216 1E8 0.0 1E18

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www.caefatigue.com

Fringe Data Output From CFV Analysis?

Response Statistics •  m0, m1, m2, m4 •  Zero crossings •  Peaks per second •  Irregularity factor •  Mean stress •  Mean+P*rms stress •  Mean-P*rms stress •  Mean+P*rms strain •  Mean-P*rms strain •  RMS stress •  RMS strain

Fatigue Results •  Damage •  Log damage •  Life •  Log of life •  Margin of safety

Solids and shells, as well as nodes and elements, all allowed at the same time for specific layer or worst layer

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P is a user definable variable

Fatigue damage (log of damage) contour plot for all events for the steel frame. A maximum of -0.921 means the damage is 0.1200, or the life (in

repeats of the complete duty cycle) is 8.34 repeats

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Fatigue damage (log of damage) contour plot for all events for the cab doors. A maximum of -1.16 means the damage is 0.0692, or the

life (in repeats of the complete duty cycle) is 14.45 repeats

Fatigue damage (log of damage) contour plot for all events for the front strut. A maximum of -0.848 means the damage is 0.142, or

the life (in repeats of the complete duty cycle) is 7.05 repeats

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Event 8: Maximum Root Mean Square strain (rms) = 0.000493

RMS Stress Responses

rms values calculated using CAEfatigue VIBRATION for each event and each critical element

rms values calculated using the SOL112 von-Mises time histories for each event and each critical element

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RMS Stress Response Comparison

Comparison of Damage Results

Fatigue damage increments calculated using the SOL112 von-Mises time histories for each event and each critical element

Fatigue damage increments calculated using CAEfatigue VIBRATION for each event and each critical element

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Comparison of Damage Results

Statistical Analysis of Response (von-Mises) Time Histories

Responses'from'SOL112 Period'(s)01-EA10 38.002-EGV1 14.003-ER20 6.004-ER30 6.005-LP10 96.006-LP12 58.007-LP14 54.008-LR20 6.009-LR30 6.010-LS20 34.0

Overall

stdRatStd stdRatMin stdRatMax kurtStd kurtMin kurtMean kurtMax0.127 0.684 1.333 0.636 2.132 2.921 5.6460.255 0.573 1.521 1.426 2.186 3.725 8.7320.172 0.665 1.141 1.488 1.800 3.707 6.3720.120 0.811 1.179 0.980 2.841 3.651 5.4270.216 0.124 1.749 0.821 1.883 2.873 8.6080.156 0.580 1.430 0.457 2.053 2.780 4.6740.155 0.658 1.473 0.428 2.106 2.776 4.4840.033 0.899 1.015 1.567 2.494 3.974 7.1960.040 0.853 0.987 0.421 3.518 4.263 4.8300.297 0.413 1.644 1.290 1.847 3.300 8.304

0.124 1.749 1.800 3.397 8.732

Note that the max kurtosis has now reduced to 8.732 (from 12.438) and the average has reduced to 3.397 (from 3.948), compared with an idealized Gaussian value of 3.0. This apparent “cleaning” of the data is obviously beneficial

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Comparison of PSD Responses

Event 7: PSD’s calculated using CAEfatigue VIBRATION compared to the PSD’s calculated from the SOL112 von-Mises time histories

Event 8: PSD’s calculated using CAEfatigue VIBRATION compared to the PSD’s calculated from the SOL112 von-Mises time histories



Expert System


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TIME2PSD Expert System will make conversion of test data to PSD format easier, more accurate, and less prone to user errors




CSV, H3D



input Control

Control File input

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Response

Static Stress File

Dynamic Stress File

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New Internal CAEFatigue VIBRATION process Process for N events, each event containing X inputs (time histories)

RPC/text file 1 with X time histories



RPC/text file N with X time histories

TIME2PSD Expert System

PSD matrix file 1

PSD matrix file 2

PSD matrix file 3

PSD matrix file N

TIME2PSD Expert System Control File Entry

means file (optional)

rms scaling file (optional)

•  Basic statistics (min, max, mean, std, skew, kurtosis)

•  Spectral moments •  Time period used in averaging (may

not be the same as the total period) •  Number of averages

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TIME2PSD Control File Entries

SRATE Number of samples in 1 second (real) – then dt = 1/srate. (required). EVIDST Start ID for events (required). TABIDST Start ID for VTABRND tables (required). EVENT_N Number of time history event files (integer > 0) (optional – default = 1). WINDOW Window function to use (optional – choices Hanning or None - default – Hanning).

This is applied to the “block” of date extracted from the total time signal. FORMAT Format of time signal files (RPC or CSV) (optional – default = CSV). MEANS Used to decide if means to be calculated (yes/no) (default = no). Ignored if no

mean stress correction specified. (optional – default = no). MAXF Max frequency in output (used to over ride the Nyquist frequency when outputting

PSD data) (optional - default = Nyquist). “filedir” Used to specify the directory where all relevant time history files (of format RPC,

CSV or TXT are located (required). TS_filedirectory This should correspond to the name of the directory containing the loads. “mapping” Used to specify format and order of channel data. skip Number of header lines to skip in an asci file. (optional – default = 0).

TIME2PSD SRATE EVIDST TABIDST EVENT_N WINDOW FORMAT MEANS MAXF

“filedir” TS_filedirectory

"mapping" skip CHAN_N T_UNITS chan1 chan2 chan3 chan4

chan5 chan6 chan7 chan8 chan9 chan10 chan11 cont

"EV_OPTS" EV_NUM NSI RMSI TSMOOTH SF T δ

Load_name

t1 t2 t3 t4 t5 t6 cont

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TIME2PSD Control File Entries

CHAN_N Number of channels in event file to use. (optional – needed if all channels are not used or if mapping is not 1 to 1 etc).

T_UNITS Time units (optional - default = seconds). chani location in asci input file for channel “i” of data (optional). “EV_OPTS” Optional Event parameters (one set for each Event). EV_NUM Number of this Event. NSI Number of non-stationary intervals for this Event (optional - default = 1). RMSI Number of rms scaling intervals for this Event (optional - default = 1). TSMOOTH Number of adjacent time points to be used for temporal smoothing of response PSD

for this Event (optional – default = 1). SF Scale factor to apply to time signals in this Event before FFT (optional - default = 1). T Length of window function in time for this Event (real) (auto or T). (required). δ Overlap or gap in time between windows for this Event (real) (+ means overlap)

(optional - default = 0). Load_name Name of the loading file used for this event (eg “load.rsp”). ti,tj Used to specify sections (defined by pairs of time values t1-t2, t3-t4, t5-t6, t7-t8) to

delete from Event files before FFT process is applied (optional – default = none).

TIME2PSD SRATE EVIDST TABIDST EVENT_N WINDOW FORMAT MEANS MAXF

“filedir” TS_filedirectory

"mapping" skip CHAN_N T_UNITS chan1 chan2 chan3 chan4

chan5 chan6 chan7 chan8 chan9 chan10 chan11 cont

"EV_OPTS" EV_NUM NSI RMSI TSMOOTH SF T δ

Load_name

t1 t2 t3 t4 t5 t6 cont

t1

t2 t3

t4

t5

t6

T δ

number of blocks determined by integer((Ttotal/(T-δ)) +1

Conventional example

need an automatic way to calculate T If number of stationary intervals is greater than 1 then the original samples would be split into NSI samples and then the whole of the above approach would be applied independently to each sample.

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!200$

!150$

!100$

!50$

0$

50$

100$

150$

200$

1.99$ 2.09$ 2.19$ 2.29$ 2.39$ 2.49$

!200$

!150$

!100$

!50$

0$

50$

100$

150$

200$

1.99$ 2.09$ 2.19$ 2.29$ 2.39$ 2.49$

t1

t2

T - δ


SAE575 example T

- δ


Wrap Up

Frequency domain generally better for dynamics. Both quantitative and qualitative advantages are well recognised, but until now computational and technological limitations have restricted use. New 2nd generation frequency domain random response and fatigue technology now enables the analysis of large automotive systems to be undertaken – with associated qualitative and quantitative performance benefits.

Thank You!