experimental correlation of an n-dimensional load transducer by finite …€¦ · ·...
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Wolf Star Technologies, LLCA Simulia Alliance Partner
Experimental Correlation of an N-Dimensional Load Transducer by Finite Element Analysis
Tim Hunter, Ph.D., P.E.Wolf Star Technologies, LLC
- or -Getting analysis to match test
Wolf Star Technologies, LLCA Simulia Alliance Partner
Linear Systems and Loads
F= K xεC= F
In other words
Wolf Star Technologies, LLCA Simulia Alliance Partner
A closer look
[ε1,1 ε1,2 ε1,3 ε1,4
ε2,1 ε2,2 ε2,3 ε2,4
ε3,1 ε3,2 ε3,3 ε3,4][
C1,1 C1,2 C1,3
C 2,1 C 2,2 C2,3
C 3,1 C3,2 C3,3
C 4,1 C 4,2 C 4,3
]= [F 1 0 0
0 F 2 0
0 0 F 3]
Strain locations“gauges”
[m x n] [n x m] [m x m]
m = # of load cases (e.g. 3)n = # of gauges (e.g. 4)
n ≥ m
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A closer look
[ε1,1 ε1,2 ε1,3 ε1,4
ε2,1 ε2,2 ε2,3 ε2,4
ε3,1 ε3,2 ε3,3 ε3,4][
C1,1 C1,2 C1,3
C 2,1 C 2,2 C2,3
C 3,1 C3,2 C3,3
C 4,1 C 4,2 C 4,3
]= [F 1 0 0
0 F 2 0
0 0 F 3]
Strain locations“gauges”
Strain “signature” due to load case 1 turned on
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A closer look
[ε1,1 ε1,2 ε1,3 ε1,4
ε2,1 ε2,2 ε2,3 ε2,4
ε3,1 ε3,2 ε3,3 ε3,4][
C1,1 C1,2 C1,3
C 2,1 C 2,2 C2,3
C 3,1 C3,2 C3,3
C 4,1 C 4,2 C 4,3
]= [F 1 0 0
0 F 2 0
0 0 F 3]
Strain locations“gauges”
Strain “signature” due to load case 2 turned on
Wolf Star Technologies, LLCA Simulia Alliance Partner
A closer look
[ε1,1 ε1,2 ε1,3 ε1,4
ε2,1 ε2,2 ε2,3 ε2,4
ε3,1 ε3,2 ε3,3 ε3,4][
C1,1 C1,2 C1,3
C 2,1 C 2,2 C2,3
C 3,1 C3,2 C3,3
C 4,1 C 4,2 C 4,3
]= [F 1 0 0
0 F 2 0
0 0 F 3]
Strain locations“gauges”
Strain “signature” due to load case 3 turned on
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The Big Unknown
εC= FFrom How do we find C ?
Let F = I, then εC= I
Perform a psuedo-inverse
εC= I
εTεC= ε
TI
[εTε]
− 1[ε
Tε]C= [ε
Tε]
− 1ε
TI
C= [εTε]
− 1ε
T
Wolf Star Technologies, LLCA Simulia Alliance Partner
The Big Unknown
εC= FFrom How do we find C ?
Let F = I, then εC= I
Perform a psuedo-inverse
εC= I
εTεC= ε
TI
[εTε]
− 1[ε
Tε]C= [ε
Tε]
− 1ε
TI
C= [εTε]
− 1ε
T
Wolf Star Technologies, LLCA Simulia Alliance Partner
The Big Unknown
εC= FFrom How do we find C ?
Let F = I, then εC= I
Perform a psuedo-inverse
εC= I
εTεC= ε
TI
[εTε]
− 1[ε
Tε]C= [ε
Tε]
− 1ε
TI
C= [εTε]
− 1ε
T
Wolf Star Technologies, LLCA Simulia Alliance Partner
The Big Unknown
εC= FFrom How do we find C ?
Let F = I, then εC= I
Perform a psuedo-inverse
εC= I
εTεC= ε
TI
[εTε]
− 1[ε
Tε]C= [ε
Tε]
− 1ε
TI
C= [εTε]
− 1ε
T
Wolf Star Technologies, LLCA Simulia Alliance Partner
The Big Unknown
εC= FFrom How do we find C ?
Let F = I, then εC= I
Perform a psuedo-inverse
εC= I
εTεC= ε
TI
[εTε]
− 1[ε
Tε]C= [ε
Tε]
− 1ε
TI
C= [εTε]
− 1ε
T
Can be derived from FEA model
Wolf Star Technologies, LLCA Simulia Alliance Partner
Seeing [C]
C= [εTε]
− 1ε
T
An extremely large number of strain locations and orientations exist.
Which ones are best?
The optimal strains locations are found when
∣εTε∣→max
Search is done via a Galil-Kiefer D-Optimal search algorithm
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17
Procedure
1. Clamp fixture in vise in varying orientations (6)
2. Load fixture with various static load magnitudes (4) and
collect strain data (increase load in steps: 5 10.2 15.4
25.2 lbs)
3. Perform preliminary static load strain correlation between
test and analysis at all gauge locations
4. Manipulate strain data to reduce point count
5. Use strain data in WST/True Load Post-Test to predict
loads
6. Compare predicted loads to known loads
7. Compare replicated strain time histories to measured time
histories
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18
Static Load Application
Load was applied with shot bags weighing 5, 5.2, 5.2, 9.8 lbs (in that order)
Load was applied in 6 directions (see below)
Lateral Longitudinal Vertical
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19
Static Load Application cont.
Lat/Long 45o Lat/Vert 60o Long/Vert 45o
45o
60o
45o
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Data Manipulation
Data Extraction & Decimation (using Glyhworks)
Reduction from ≈ 60,000 to ≈ 150 datapoints
0 lbs
5 lbs10.2 lbs 15.4 lbs 25.2 lbs
0 lbs
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21
Post-Test GUI
Load Pre-Test Setup
Load strain data
Create report & load scales
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22
Lateral Static Load
Load Factors should be:
• Lateral = 1
• Longitudinal = 0
• Vertical = 0
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23
Lateral Static Load
G1: 2.8% Error G2: 0.3% Error G3: 5.2% Error
G4: 3.7% Error G5: 0.2% Error G6: 5.6% Error
Note: very noisy, < 20
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24
Longitudinal Static Load
Load Factors should be:
• Lateral = 0
• Longitudinal = 1
• Vertical = 0
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25
Longitudinal Static Load
G1: 9.6% Error
G2: 15.7% Error G3: 2.1% Error
G4: 0.3% Error G5: 7.2% Error G6: 0.1% Error
Note: very noisy, < 20
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26
Vertical Static Load
Load Factors should be:
• Lateral = 0
• Longitudinal = 0
• Vertical = 1
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27
Vertical Static Load
G1: 0.0% Error G2: 0.3% Error
G3: 11.2% Error
G4: 1.6% Error
G5: 0.3% Error
G6: 2.4% Error
Note: very noisy, < 20
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28
Lat/Long 45 degrees
Load Factors should be:
• Lateral = 0.707
• Longitudinal = 0.707
• Vertical = 0
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Lat/Long 45 degrees
G1: 4.7% Error G2: 0.3% Error G3: 0.8% Error
G4: 0.0% Error G5: 0.2% Error G6: 0.1% Error
Note: very noisy, < 20
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30
Lat/Vert 60 degrees
Load Factors should be:
• Lateral = 0.866
• Longitudinal = 0
• Vertical = -0.5
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31
Lat/Vert 60 degrees
G1: 0.4% Error G2: 0.3% Error G3: 15.8% Error
G4: 3.8% Error G5: 0.2% Error G6: 11.2% Error
Note: very noisy, < 20
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32
Long/Vert 45 degrees
Load Factors should be:
• Lateral = 0
• Longitudinal = 0.707
• Vertical = -0.707
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33
Long/Vert 45 degrees
G1: 0.3% Error G2: 0.9% Error G3: 2.6% Error
G4: 0.3% Error G5: 0.7% Error G6: 0.1% Error
Note: good strain replication on all gauges – great correlation
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34
Static Load Summary
Predicted
Theoretical
25.2 lb Load Application Direction
Lateral Long. Vert.Lat/Long
45o
Lat/Vert 60o
Long/Vert 45o
Load Scale Factor
Lateral1.068
1
0.073
0
0.006
0
0.809
0.707
0.937
0.866
0.047
0
Long.0.004
0
1.019
1
0.026
0
0.714
0.707
-0.526
-0.5
0.751
0.707
Vertical-0.006
0
0.040
0
1.039
1
0.024
0
0.005
0
-0.717
-0.707
Magnitude1.068
1
1.022
1
1.039
1
1.079
1
1.075
1
1.039
1
Angle b/w ideal and predicted†
0.39o 4.67o 1.47o 3.79o 0.74o 2.91o
† Angle calculated as:
AB
BA1cos
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Static Load % Error
Load Application Direction
Lateral Long. Vert.Lat/Long
45o
Lat/Vert 60o
Long/Vert 45o
Load Scale Factor Error (%)
Lateral 6.8 7.3 0.6 14.4 9.0 4.7
Long. 0.4 1.9 2.6 1.0 5.2 6.2
Vertical 0.6 0.4 3.9 2.4 0.5 1.4
Magnitude 6.8 2.2 3.9 7.9 7.5 3.9
Mag. Angle Offset (degrees)
0.39o 4.67o 1.47o 3.79o 0.74o 2.91o
< 5%
5% - 10%
> 10%
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Force Correlation
F= m x
Measured Force
Force from strain gauges
Test strains
From FEA
Wolf Star Technologies, LLCA Simulia Alliance Partner
Special thanks toMark Fischer
Harley-Davidson Motor Company, Inc