Experimental Correlation of an N-Dimensional Load Transducer by Finite …€¦ · · 2012-09-05Experimental Correlation of an N-Dimensional Load Transducer by Finite Element Analysis

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


What are the loads?


Linear Systems and Loads

F= K xεC= F

In other words


Back to the Blackboard


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


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 “signature” due to load case 1 turned on


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]




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]




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


The Big Unknown




εC= I

εTεC= ε

TI

[εTε]

− 1[ε

Tε]C= [ε

Tε]

− 1ε

TI

C= [εTε]

− 1ε

T


The Big Unknown




εC= I

εTεC= ε

TI

[εTε]

− 1[ε

Tε]C= [ε

Tε]

− 1ε

TI

C= [εTε]

− 1ε

T


The Big Unknown




εC= I

εTεC= ε

TI

[εTε]

− 1[ε

Tε]C= [ε

Tε]

− 1ε

TI

C= [εTε]

− 1ε

T


The Big Unknown




εC= I

εTεC= ε

TI

[εTε]

− 1[ε

Tε]C= [ε

Tε]

− 1ε

TI

C= [εTε]

− 1ε

T

Can be derived from FEA model


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


“Hangman” Structure


16

Static Test Setup


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


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


19

Static Load Application cont.

Lat/Long 45o Lat/Vert 60o Long/Vert 45o

45o

60o

45o


20

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


21

Post-Test GUI

Load Pre-Test Setup

Load strain data

Create report & load scales


22

Lateral Static Load

Load Factors should be:

• Lateral = 1

• Longitudinal = 0

• Vertical = 0


23

Lateral Static Load

G1: 2.8% Error G2: 0.3% Error G3: 5.2% Error


Note: very noisy, < 20


24

Longitudinal Static Load


• Lateral = 0


• Vertical = 0


25

Longitudinal Static Load

G1: 9.6% Error

G2: 15.7% Error G3: 2.1% Error




26

Vertical Static Load


• Lateral = 0


• Vertical = 1


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



28

Lat/Long 45 degrees


• Lateral = 0.707

• Longitudinal = 0.707

• Vertical = 0


29

Lat/Long 45 degrees





30

Lat/Vert 60 degrees


• Lateral = 0.866


• Vertical = -0.5


31

Lat/Vert 60 degrees





32

Long/Vert 45 degrees


• Lateral = 0

• Longitudinal = 0.707

• Vertical = -0.707


33

Long/Vert 45 degrees



Note: good strain replication on all gauges – great correlation


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


35

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%


Proving Ground Loads


Proving Ground

Long Lat

Vert


Force Correlation

F= m x

Measured Force

Force from strain gauges

Test strains

From FEA


Strain Correlation



Come visit us at theSafe Technology booth


Special thanks toMark Fischer

Harley-Davidson Motor Company, Inc


Questions?

Documents

Experimental Correlation of an N-Dimensional Load Transducer by Finite …€¦ · · 2012-09-05Experimental Correlation of an N-Dimensional Load Transducer by Finite Element Analysis