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
CAEfatigue
Established 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 VIBRATION
Or 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
2

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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
fa
fa
fa
fa
ii
Amplitudes - squared
5
Deterministic
(time)
a1, f1,ϕ1
a2, f2,ϕ2
a3, f3,ϕ3
a4, f4,ϕ4
.
ai, fi,ϕi
.
a40, f40,ϕ40
=
Why Work In Frequency Domain?
frequency
time
Windspeed
PSDStress
PSD
frequency
time
HubStress
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
SOL112SOL103
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
9
Nastran
(or other)
Random
Response
Static
Stress File
Dynamic
Stress File
CFV should be considered as an output request for the stress solver
User
Interface
(in V3.0)
•  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
CAEfatigue
Vibration
Response
Statistics – FEF,
CSV, H3D
Fatigue Data -
Hyperview H3D,
Comma Separated CSV
input
Control
Control
File input
10
•  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)
Nastran
(or other)
Random
Response
Static
Stress File
Dynamic
Stress File

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11
•  Very easy template system
•  Ideal for batch and solver integration
•  easy pre processing of loads
User
Interface
(in V3.0)
Expert System
CAEfatigue
Vibration
Response
Statistics – FEF,
CSV, H3D
Fatigue Data -
Hyperview H3D,
Comma Separated CSV
input
Control
Control
File input
11
Nastran
(or other)
Random
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)
User
Interface
(in V3.0)
Expert System
CAEfatigue
Vibration
Response
Statistics – FEF,
CSV, H3D
Fatigue Data -
Hyperview H3D,
Comma Separated CSV
input
Control
Control
File input
12
Nastran
(or other)
Random
Response
Static
Stress File
Dynamic
Stress File

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13
•  “Running Sum” moment technology
•  Fast OP2 stress file interrogation
•  1000+GB results files easily processed
User
Interface
(in V3.0)
Expert System
CAEfatigue
Vibration
Response
Statistics – FEF,
CSV, H3D
Fatigue Data -
Hyperview H3D,
Comma Separated CSV
input
Control
Control
File input
13
Nastran
(or other)
Random
Response
Static
Stress File
Dynamic
Stress File
Expert System
14
•  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
User
Interface
(in V3.0)
CAEfatigue
Vibration
Response
Statistics – FEF,
CSV, H3D
Fatigue Data -
Hyperview H3D,
Comma Separated CSV
input
Control
Control
File input
14
Nastran
(or other)
Random
Response
Static
Stress File
Dynamic
Stress File

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Expert System
15
•  Multiple correlated loads
(eg 100 inputs)
User
Interface
(in V3.0)
CAEfatigue
Vibration
Response
Statistics – FEF,
CSV, H3D
Fatigue Data -
Hyperview H3D,
Comma Separated CSV
input
Control
Control
File input
15
Nastran
(or other)
Random
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 6Time signals for event 6
event 6 loading
Complete duty cycle
Complete duty cycle
PSD Matrix Event 1
152 seconds
PSD Matrix Event 2
42 seconds
PSD Matrix Event 3
18 seconds
PSD Matrix Event 4
18 seconds
PSD Matrix Event 5
480 seconds
PSD Matrix Event 6
1682 seconds
PSD Matrix Event 7
378 seconds
PSD Matrix Event 8
18 seconds
PSD Matrix Event 9
18 seconds
PSD Matrix Event 10
68 seconds
16

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Expert System
17
Linked to any 3rd party optimisation code (eg
Mode Frontier) which connects ascii Control
file input (Nastran and/or CFV) to ascii CSV
output
User
Interface
(in V3.0)
CAEfatigue
Vibration
Response
Statistics – FEF,
CSV, H3D
Fatigue Data -
Hyperview H3D,
Comma Separated CSV
input
Control
Control
File input
17
Nastran
(or other)
Random
Response
Static
Stress File
Dynamic
Stress File
Expert System
18
TIME2PSD Expert System will make
conversion of test data to PSD format easier,
more accurate, and less prone to user
errors
User
Interface
(in V3.0)
CAEfatigue
Vibration
Response
Statistics – FEF,
CSV, H3D
Fatigue Data -
Hyperview H3D,
Comma Separated CSV
input
Control
Control
File input
18
Nastran
(or other)
Random
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
User
Interface
(in V3.0)
CAEfatigue VIBRATION (CFV) Concept at High Level
CAEfatigue
Vibration
Response
Statistics – FEF,
CSV, H3D
Fatigue Data -
Hyperview H3D,
Comma Separated CSV
input
Control
Control
File input
22
Nastran
(or other)
Random
Response
Static
Stress File
Dynamic
Stress File
CFV Process Is Defined Using “Control File”

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vibfat 777 csvfefetnastran center 0 Results56
vftgdef 777 Dirlik 100 60 16 99.9 16 64
elset 1 632 2 631 3 633
4 631 5
include Sets/1_40k_yield.txt
include Sets/2_50k_yield.txt
include Sets/3_A6_cab.txt
include Sets/4_A6_doors.txt
include Sets/5_glass_windshield.txt
vftgparm777 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 810 701
vftgload801 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.txt
vftgload701 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
25
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 38.0
02-EGV1 14.0
03-ER20 6.0
04-ER30 6.0
05-LP10 96.0
06-LP12 58.0
07-LP14 54.0
08-LR20 6.0
09-LR30 6.0
10-LS20 34.0
Overall
stdRatStd stdRatMin stdRatMax kurtStd kurtMin kurtMean kurtMax
0.127 0.684 1.333 0.636 2.132 2.921 5.646
0.255 0.573 1.521 1.426 2.186 3.725 8.732
0.172 0.665 1.141 1.488 1.800 3.707 6.372
0.120 0.811 1.179 0.980 2.841 3.651 5.427
0.216 0.124 1.749 0.821 1.883 2.873 8.608
0.156 0.580 1.430 0.457 2.053 2.780 4.674
0.155 0.658 1.473 0.428 2.106 2.776 4.484
0.033 0.899 1.015 1.567 2.494 3.974 7.196
0.040 0.853 0.987 0.421 3.518 4.263 4.830
0.297 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
36
TIME2PSD Expert System will make
conversion of test data to PSD format easier,
more accurate, and less prone to user
errors
User
Interface
(in V3.0)
CAEfatigue
Vibration
Response
Statistics – FEF,
CSV, H3D
Fatigue Data -
Hyperview H3D,
Comma Separated CSV
input
Control
Control
File input
36
Nastran
(or other)
Random
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
X time histories
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
38
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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39
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.

10/05/15%
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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
number of blocks determined by integer((Ttotal/(T-δ)) +1
SAE575 example
T
- δ
number of blocks determined by integer((Ttotal/(T-δ)) +1
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!

Time v Frequency Domain Analysis For Large Automotive Systems

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Time v Frequency Domain Analysis For Large Automotive Systems