Experimental Correlation of an N-Dimensional Load Transducer by Finite Element Analysis. Tim Hunter, Ph.D., P.E. Wolf Star Technologies, LLC

Transcription

1 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

2 What are the loads?

3 Linear Systems and Loads In other words F = K x εc = F

4 Back to the Blackboard

5 A closer look [m x n] [n x m] [m x m] [ε1,1 ε1,2 ε1,3 ε1,4 1,1 C 1,2 C 1,3 C ε 2,1 ε 2,2 ε 2,3 ε 2,1 C 2,2 C 2,3 2,4 C ε 3,1 ε 3,2 ε 3,3 ε 3,1 C 3,2 C 3,3 3,4][C C 4,1 C 4,2 C 4,3]= [F F F 3] Strain locations gauges m = # of load cases (e.g. 3) n = # of gauges (e.g. 4) n m

6 A closer look Strain signature due to load case 1 turned on [ε1,1 ε1,2 ε1,3 ε1,4 1,1 C 1,2 C 1,3 C ε 2,1 ε 2,2 ε 2,3 ε 2,1 C 2,2 C 2,3 2,4 C ε 3,1 ε 3,2 ε 3,3 ε 3,1 C 3,2 C 3,3 3,4][C C 4,1 C 4,2 C 4,3]= [F F F 3] Strain locations gauges

7 A closer look Strain signature due to load case 2 turned on [ε1,1 ε1,2 ε1,3 ε1,4 1,1 C 1,2 C 1,3 C ε 2,1 ε 2,2 ε 2,3 ε 2,1 C 2,2 C 2,3 2,4 C ε 3,1 ε 3,2 ε 3,3 ε 3,1 C 3,2 C 3,3 3,4][C C 4,1 C 4,2 C 4,3]= [F F F 3] Strain locations gauges

8 A closer look Strain signature due to load case 3 turned on [ε1,1 ε1,2 ε1,3 ε1,4 1,1 C 1,2 C 1,3 C ε 2,1 ε 2,2 ε 2,3 ε 2,1 C 2,2 C 2,3 2,4 C ε 3,1 ε 3,2 ε 3,3 ε 3,1 C 3,2 C 3,3 3,4][C C 4,1 C 4,2 C 4,3]= [F F F 3] Strain locations gauges

9 The Big Unknown From εc= F How do we find C? Let F = I, then εc= I Perform a psuedo-inverse εc= I ε T εc= ε T I [ε T ε] 1 [ε T ε]c= [ε T ε] 1 ε T I C= [ε T ε] 1 ε T

10 The Big Unknown From εc= F How do we find C? Let F = I, then εc= I Perform a psuedo-inverse εc= I ε T εc= ε T I [ε T ε] 1 [ε T ε]c= [ε T ε] 1 ε T I C= [ε T ε] 1 ε T

11 The Big Unknown From εc= F How do we find C? Let F = I, then εc= I Perform a psuedo-inverse εc= I ε T εc= ε T I [ε T ε] 1 [ε T ε]c= [ε T ε] 1 ε T I C= [ε T ε] 1 ε T

12 The Big Unknown From εc= F How do we find C? Let F = I, then εc= I Perform a psuedo-inverse εc= I ε T εc= ε T I [ε T ε] 1 [ε T ε]c= [ε T ε] 1 ε T I C= [ε T ε] 1 ε T

13 The Big Unknown From εc= F How do we find C? Let F = I, then εc= I Perform a psuedo-inverse εc= I ε T εc= ε T I [ε T ε] 1 [ε T ε]c= [ε T ε] 1 ε T I C= [ε T ε] 1 ε T Can be derived from FEA model

14 Seeing [C] An extremely large number of strain locations and orientations exist. Which ones are best? C= [ε T ε] 1 ε T The optimal strains locations are found when ε T ε max Search is done via a Galil-Kiefer D-Optimal search algorithm

15 Hangman Structure

16 Static Test Setup 16

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: 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 17

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 18

19 Static Load Application cont. 45 o 60 o 45 o Lat/Long 45 o Lat/Vert 60 o Long/Vert 45 o 19

20 Data Manipulation 0 lbs 5 lbs 10.2 lbs 15.4 lbs 25.2 lbs 0 lbs Data Extraction & Decimation (using Glyhworks) Reduction from 60,000 to 150 datapoints 20

21 Post-Test GUI Load Pre-Test Setup Load strain data Create report & load scales 21

22 Lateral Static Load Load Factors should be: Lateral = 1 Longitudinal = 0 Vertical = 0 22

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 23

24 Longitudinal Static Load Load Factors should be: Lateral = 0 Longitudinal = 1 Vertical = 0 24

25 Longitudinal Static Load G2: 15.7% Error G3: 2.1% Error G1: 9.6% Error G4: 0.3% Error G5: 7.2% Error G6: 0.1% Error Note: very noisy, < 20 25

26 Vertical Static Load Load Factors should be: Lateral = 0 Longitudinal = 0 Vertical = 1 26

27 Vertical Static Load G3: 11.2% Error G1: 0.0% Error G2: 0.3% Error G4: 1.6% Error G6: 2.4% Error G5: 0.3% Error Note: very noisy, < 20 27

28 Lat/Long 45 degrees Load Factors should be: Lateral = Longitudinal = Vertical = 0 28

29 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 29

30 Lat/Vert 60 degrees Load Factors should be: Lateral = Longitudinal = 0 Vertical =

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 31

32 Long/Vert 45 degrees Load Factors should be: Lateral = 0 Longitudinal = Vertical =

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 33

34 Static Load Summary Predicted Theoretical Lateral Long. Vert lb Load Application Direction Lat/Long Lat/Vert Long/Vert 45 o 60 o 45 o Lateral Load Scale Factor Long. Vertical Magnitude Angle b/w ideal and predicted 0.39 o 4.67 o 1.47 o 3.79 o 0.74 o 2.91 o Angle calculated as: 1 AB cos AB 34

35 Static Load % Error < 5% 5% - 10% > 10% Lateral Long. Vert. Load Application Direction Lat/Long Lat/Vert Long/Vert 45 o 60 o 45 o Lateral Load Scale Factor Error (%) Long Vertical Magnitude Mag. Angle Offset (degrees) 0.39 o 4.67 o 1.47 o 3.79 o 0.74 o 2.91 o 35

36 Proving Ground Loads

37 Proving Ground Vert Long Lat

38 Force Correlation Measured Force F= m ẍ Test strains From FEA Force from strain gauges

39 Strain Correlation

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41 Come visit us at the Safe Technology booth

42 Special thanks to Mark Fischer Harley-Davidson Motor Company, Inc

43 Questions?