Characterization of Elastomeric Isolators for Shock of Elastomeric Isolators for Shock - Vol. 2 - May 1, 2009 . Team Nick Haupt Matt Hildebrand Jim Holmberg Brian Kornis . ... shock

Vol. 2 ME 4054

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Characterization of Elastomeric

Isolators for Shock

- Vol. 2 -

May 1, 2009

Team Nick Haupt Matt Hildebrand Jim Holmberg Brian Kornis Sam Newbauer

Advisors Jim Wieczorek Ed Alexander

Client

Vol. 2 Table of Contents

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Table of Contents

1 Problem Definition Supporting Documents ............................................................................. 4

1.1 Annotated Bibliography ........................................................................................................ 4

1.2 User Needs ............................................................................................................................ 7

1.3 Concept Alternatives ........................................................................................................... 12

1.3.1 Test Procedures ............................................................................................................ 12

1.3.2 Isolators ........................................................................................................................ 14

1.3.3 Fixtures ......................................................................................................................... 17

1.4 Concept Selection ................................................................................................................ 20

1.4.1 Test Procedures ............................................................................................................ 20

1.4.2 Isolators ........................................................................................................................ 21

1.4.3 Fixtures ......................................................................................................................... 23

1.5 Damping Modes in Ansys .................................................................................................... 26

2 Design Description Supporting Documents ............................................................................. 28

2.1 Drawings ............................................................................................................................. 28

2.1.1 Drop Test Fixture Drawings .......................................................................................... 28

2.1.2 MTS Test Fixture Drawings ........................................................................................... 31

2.2 Bill of Materials ................................................................................................................... 36

3 Evaluation Supporting Documents .......................................................................................... 37

3.1 Evaluation Reports ............................................................................................................. 37

3.1.1 Isolator Stiffness ........................................................................................................... 37

3.1.2 Isolator Damping .......................................................................................................... 47

3.1.3 MTS Test Fixture ........................................................................................................... 61

Vol. 2 Table of Contents

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3.1.4 Drop Test Fixture .......................................................................................................... 68

3.1.5 Ansys Correlation ......................................................................................................... 77

3.2 Cost Analysis ........................................................................................................................ 90

3.3 Environmental Impact Statement ....................................................................................... 91

3.4 Regulatory and Safety Considerations ................................................................................ 93

4 Additional Materials ................................................................................................................ 94

4.1 Data Analysis ....................................................................................................................... 94

4.2 MatLab Code ..................................................................................................................... 100

4.2.1 Step Displacement Code ............................................................................................. 100

4.2.2 Ramp Displacement Code………………………………………………………………………………………112

4.2.3 Drop Test Displacement Code………………………………………………………………………………..123

4.3 ANSYS Code ....................................................................................................................... 141

4.4 Simulink Model ................................................................................................................. 144

4.4.1 Simulink Code ............................................................................................................. 144

4.4.2 Simulink Block Diagram….……………………………………………………………………………………..145

Vol. 2 1.1 Annotated Bibliography

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1 Problem Definition Supporting Documents

1.1 Annotated Bibliography

The research that was executed for this project included: different mathematical models of polymers, diverse testing to find dynamic damping, effects of viscoelasticity, different damping theories, and searches on different data acquisition equipment. Most of the research and testing in the field of shock absorbers are related to shock absorbers in automobiles. The testing on automobiles is related more to vibration dependent variables due to road conditions rather than shock events related to close proximity underwater explosions. The research that was performed aided in the project by: mathematically modeling the isolator, finding successful testing of shock absorbers, knowing the limits and specifications of testing equipment, and knowing how polymers behave differently than metal-based components. 1. McCrum, N. G. and Buckley, C. P. and Bucknall, C.B. 1997, “Principles of Polymer Engineering” Oxford University Press, Oxford, Great Britain, Vol. 2 How to engineer polymers, does not apply to project. 2. Viscoelasticity 1-2 from Professor Ramalingam, Course ME 5223 Article describes what viscoelasticity is and the effects it has on a system. Discusses creep and stress relaxation. Also explains different rubber models (Maxwell, Kelvin-Voigt, and SLS) and the advantages and disadvantages of each. 3. PractDesignViscoelasticity from Professor Ramalingam, Course ME 5223 Overestimating parameters to allow for a conservative design in polymers, does not apply to project. 4. Basso, R. 1998, “Experimental Characterization of Damping Force in Shock Absorbers with Constant Velocity Excitation” Vehicle System Dynamics, 30, pp.431-442 Article describes how/why they used force versus velocity-displaced curves to find damping force in shock absorber. 5. Kowalski, D. and Rao, M. D. and Gruenberg, S. 2002 “Dynamic Testing of Shock Absorbers Under Non-Sinusoidal Conditions” Proceedings of the Institution of Mechanical Engineers 216, pp.373-384 The research is to develop a test and analysis methodology to obtain dynamic properties of a shock absorber. Testing involves using sine-on-sine testing instead of a swept sine wave.


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6. Inman, D. J. Mechanical Engineering at Virginia Tech, Virginia Tech Power Point The notes are a vibration response lecture. They describe the difference between a vibration and shock response. 7. Dall’Asta, A. and Ragni L. 2006 “Experimental Tests and Analytical Model of High Damping Rubber Dissipating Devices” ScienceDirect, pp.1874-1884 The report discusses shear cyclic testing in rubber materials, does not apply to project. 8. Adhiakri, S. 1999 “Rates of Change of Eigenvalues and Eigenvectors in Damped Dynamic System” AIAA Journal 39 Theory that mathematically derives changes in eigenvalues and eigenvectors in a dynamic damped system, does not apply to project. 9. Bloss, B. and Rao, M. D. “Measurement of Damping in Structures by the Power Input Method” Michigan Technological University Paper explains how to measure the damping in structures using a power loss method. 10. Damping theory Chapter discusses different damping (viscous, hysteristic, and coulomb) and how to measure damping. 11. Haupt, P. and Sedlan, K. 2001 “Viscoplasticity of Elastomeric Materials: Experimental Facts and Constitutive Modeling” Archive of Applied Mechanics 71, 89-109 Tests were performed to measure the finite elasticity, rate-dependence, and viscoelasticity of rubber materials. 12. Lin, T. R. and Farag, N. H. and Pan, J. 2004 “Evaluation of Frequency Dependent Rubber Mount Stiffness and Damping by Impact Test” Applied Acoustics 66, pp.829-844 An impact test was performed on a rubber mount to determine stiffness and damping. The impact test results were then verified with vibration results by using a mechanical shaker. 13. Roylance, D. 2000 “The Kinematic Equations” Department of Materials Science and Engineering, Massachusetts Institute of Technology Paper discussing the theory of kinematic equations regarding elasticity, does not apply to project. 14. http://www.novotechnik.com/products/linear/linear_non-contact.html Website on displacement sensor.

http://www.novotechnik.com/products/linear/linear_non-contact.html�


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15. Rao, M. D. and Gruenberg, S. 2002 “Measurement of Equivalent Stiffness and Damping of Shock Absorbers” Experimental Techniques, pp.39-42 Electrodynamic shakers and hydraulic actuators were used to test the shock absorbers and obtain the stiffness and damping, does not apply to project. 16. Military Specifications 1989 Shock Tests High Impact MIL-S-901D (Navy) Military standards that full-scale shock tests must meet. 17. http://www.mts.com/stellent/groups/public/documents/library/dev_004324.pdf Data pertaining to the specifications of an MTS tensile test machine. 18. Hanson, D. E. and Hawley, M. and Houlton, R. 2005 “A Mechanism for the Mullins Effect” Condensed Matter, Materials Science, and Chemistry Article discusses the mullins effect. The mullins effect says that the each test on a rubber material will lead to different results due to internal effects. 19. Paige, R. E. and Mars, W. V. 2004 “Implications of the Mullins Effect on the Stiffness of a Pre-loaded Rubber Component” ABAQUS Users’ Conference Experiment that was performed to determine results in the mullins effect on a rubber material. Experiment describes the mullins effect as a dependence on the hyperelastic response on the maximum deformation previously experienced. 20. Gaberson, H. 2007 “Shock Analysis Using the Pseudo Velocity Shock Spectrum-Part 1” Shock and Vibration Symposium Paper describes how to mathematically calculate the effects a shock would have on a system. 21. Gaberson, H. 2007 “Shock Analysis Using the Pseudo Velocity Shock Spectrum-Part 2” Shock and Vibration Symposium Paper is part two of reference 20. This paper focuses more empirical data than mathematical calculations. 22. Marano, G. C. and Greco, R. 2004 “A Performance-Reliability-Based Criterion for the Optimum Design of Bridge Isolators” Journal of Earthquake Technology 41, pp. 261-276 Report that determines earthquake effects on bridge isolators, does not apply to project.

http://www.mts.com/stellent/groups/public/documents/library/dev_004324.pdf�


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23. Bhuiyan, A.R. and Okui, Y. and Mitamura, H. and Imai, T. 2009, “A Rheology Model of High Damping Rubber Bearings for Seismic Analysis: Identification of Nonlinear Viscosity” International Journal of Solids 46, pp. 1778-1792 Experiment uses three different tests to find the nonlinear damping of high damping rubber bearings. 24. Mactoce, P. “Viscoelastic Damping 101” Roush Industries, pp. 10-12 Article that discusses the difference of elastic, viscous, and viscoelastic materials.

1.2 User Needs

The focus of this project is developing a shock test that can fully characterize an

elastomeric shock isolator. Another part of this project is developing a finite element analysis

model based on the data collected from the drop test. A product design specification was

developed based upon well thought-out customer needs. These needs were determined based

on previous experiences with measurement laboratories and discussion/approval with our

advisor. The user needs are split up into two sections, one for the shock test/data acquisition

and one for the finite element modeling. Each need is given a rank of importance from 1-5

where 5 is most important and 1 is least important. While each needs should be taken into

consideration it is the higher ranking needs that need to be addressed first. Some of the high

importance needs include test repeatability, test uses BAE machinery, and the shock test

characterizes spring and damping forces. It was initially conceived that our group would do

testing on the University campus. However, it is important that the test be done at BAE

because they do not have access to University of Minnesota machines. The test needs to be

repeatable so that BAE may perform the test multiple times on different isolators and get

accurate data each time. Finally, spring and damping forces must be characterizes if an

accurate model can be developed.

Vol. 2 1.2 User Needs

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Product Design Specification

Customer Needs Driving Product Specification

# Need Importance

Shock Test/Data Acquisition Needs

1 Shock test does not damage isolators 5

2 Shock test will mount variously sized and shaped isolators 4

3 Shock test is safe 3

4 Shock test is repeatable 4

5 Shock test is easy to reproduce 2

6 Shock test is easy to load 2

7 Shock test is inexpensive 1

8 Shock test has limited DOF 2

9 Shock test loads isolator in tension 4

10 Shock test loads isolator in compression 4

11 Shock test loads isolator in shear 4

12 Shock test implements existing test machinery @ BAE 5

13 Shock test fixture is easy to set up 2

14 Analysis of shock test data can be done at BAE 5

15 Shock test has controlled velocity input 4

16 Shock test has controlled acceleration 2

17 Shock test has controlled frequency 2

18 Shock test has controlled amplitude 3

19 Shock test has controlled deflection 5

20 Shock test can easily mount an isolator 2

21 Shock test characterizes nonlinear spring constant 5


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All of these user needs were then used to determine a product specification for both the

shock test and the FEA model. Every user need must be categorized to a design specification,

but it is acceptable to use several needs for one specification. Each metric is categorized by

importance and give a set of units. The marginal value is the lowest value acceptable for the

22 Shock test characterizes nonlinear damping constant 5

23 Data from shock test can be related to manufacturer specs

24 Shock test is rugged/durable, does not break after use 3

25 Shock test is time efficient 1

26 Shock test can scale to higher loads 4

27 Shock test can find failure point of isolator in tension 4

28 Shock test can find failure point of isolator in compression 4

29 Shock test can find failure point of isolator in shear 4

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FEA Design Needs

1 Isolator model improves upon previous models 5

2 Isolator model incorporates spring and damper 4

3 Isolator model correlates with test data 3

4 Isolator model can be used in system level analysis 3

5 FEA model uses a minimum number of nodes 5

6 FEA analysis takes a minimum amount of time to complete 2

7 FEA analysis can be easily imported and edited

8 FEA defines loads

9 FEA analysis has sufficient resolution

10 Accounts for tension, compression and shear loading


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need and the ideal value is the goal. For example, a controlled isolator deflection of 2 inches is

ideal, but a 0.3 inch deflection is acceptable. These needs and specifications were determined

based on previous laboratory testing knowledge.

Corresponding PDS

# Need #'s Metric Importance Units Marginal Value Ideal Value

Shock Test/Data Acquisition Metrics

1 1,3,12,15,26 Load 3 Kg 20 65

2 1, 3, 12, 15 Test Velocity 5 Ft/s 4 12

3 1, 3, 12, 16 Test Acceleration 3 G 30 50

4 17 Frequency Control 2 Hz 3 10

5 18,19 Amplitude Control 5 in 0.3 1

6 2 Fixture Capacity: height 3 in 3 7

7 2 Fixture Capacity: width 3 in 3 6

8 2 Fixture Capacity: depth 3 in 3 6

9 4,5,6,7,13,20,25 Set Up Time 3 min 45 15

10 7 Cost 2 $ $1,100 <$100

11 4, 5 Time to analyze shock test data 3 hrs 8 2

12 19 Deflection Control 3 in 0.3 2

13 4, 21 Confidence of calculated spring constant 3 % 75 95

14 4, 22 Confidence of calculated damping constant 3 % 75 95

15 5 Time to make custom fixture 2 hrs 6 1

16 5, 14 Data analysis is performed with MS Excel 2 Binary No Yes

17 4, 3 Fixture displacement under max load 4 in 0.05 0.01

18 4, 5 Stress relaxation while measuring static load 4 % 10 5

19 8,9,10,11 Degrees of Freedom due to mounting 4 Quantity 1 1

20 2,20

Number of different isolators the fixture is

compatible with 2 Quantity 1 >2

21 27,28,29 Failure point of isolator (deflection) 3 in 0.5 >.5


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22 27,28,29 Failure point of isolator (load) 3 kg 20 >65

23 23

Relate shock test results to manufacture spec (if

available) 2 Binary No Yes

24 6,7,13,20,25 Number of operators for shock test 2 Quantity 3 1

25 4,24 Fixture operating life 3

No.

operations 50 >1000

FEA Metrics

1 1,2,3 FEA model correlates with test data 4 Binary No Yes

2 4,6 FEA Analysis Run Time 2 min 3 0.5

3 4,5 Nodes in FEA Model 5 Quantity 100 10

4 1,2,3 Spring constant varies with displacement 5 Binary No Yes

5 1,2,3

Damping coefficient varies with displacement and

velocity 4 Binary No Yes

6 7 ANSYS code length 2 # of Lines 500 <500

7 8 Applied load 4 kg 20 65

8 9 Number of Time Steps 3 Quantity 200 500

9 9 Smallest Time Step 3 sec 0.0001 1x10-6

10 9 Number of Elements Quantity 1 5

11 1,3,10 Number of Dimensions Quantity 1 3

Vol.2 1.3 Concept Alternatives

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1.3 Concept Alternatives

The following sections discuss alternative models that were discussed for this project. The

alternatives include: test procedures, different isolators, and other fixture apparatuses.

1.3.1 Test Procedure Alternatives

Only a few test options were available for us to choose from. Among these include MTS

tensile test machine, BAE drop test, student made drop test, and hammer test. Ultimately, the

two tests that were chosen were the MTS tensile test machine and the MTS drop test machine.

This section of the report will discuss the other two options and why they were not chosen.

The student made drop test would entail creating a small drop test device and

measuring deflection by means of high speed video recording. The test could be made from a

large PVC pipe mounted to a wooden or metal base. Known weights, such as lead or metal,

would be dropped from the top of the pipe and would impact on an isolator.

Vol. 2 1.3.1 Test Procedure Alternatives

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High speed video would record the impact and deflection/velocity would be measured

using the necessary software needed to analyze the video. There are many weaknesses to this

idea. First, there would be no way to ensure that the dropped weight stays vertical and lands

perfectly on the isolator. The weight could easily strike the sides of the pipe and rotate while

falling. In addition, the only means of data acquisition would be the high speed video. Using

accelerometers was an initial thought but did not receive enough thought to become viable.

Ultimately this idea was thrown out after it was discovered that BAE Systems had a MTS

Monterey Impac drop test machine. The BAE drop test machine would provide more accurate

velocity and data acquisition.

The hammer test involved a platform and large hammer.

A mass would be mounted on top of the isolator(s) and could also be attached on the

side to provide shear. The hammer would swing and strike the platform from underneath. The

resulting impact would cause the mass to accelerate upwards while being damped by the

isolators. An accelerometer would be attached to this mass in order to measure the

accelerations due to the hammer impact and isolator damping. The advantages of this test was

the ease of multidirectional testing (tension/shear/compression) and the fact that shear and

Vol. 2 1.3.1 Test Procedure Alternatives

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tension could be tested at the same time using multiple isolators. The disadvantages of this

test were the large amount of expected noise to the impact of a large hammer on a surface. In

addition, the only feasible means of data acquisition is using an accelerometer, which alone

would not be enough to fully characterize an isolator.

1.3.2 Isolator Alternatives

The isolator that BAE will end up testing is different than the isolator chosen for student

testing. The isolator that BAE will be using was on back order at the beginning of this project

and was unavailable for immediate testing. One of the first tasks for the group was to find an

isolator that would be suitable for testing. There were several criterions that the isolators

would be compared against. This criterion included deflection, load, design symmetry and cost.

These criterions were compared with the isolator that BAE would be using. The idea is to get a

similar isolator for a much lower cost. Cost is an issue because several isolators will be

destroyed in order to develop failure criteria. The total budget for the project is $1000, and it is

difficult to determine initially how much money would be needed for other parts of the project

(fixture designs). Design symmetry simply means that the isolator is symmetric. An asymmetric

isolator is much more difficult to model in finite element analysis and the BAE chosen isolator is

symmetric.

The BAE chosen isolator is the GB-330 from Barry Controls.

It is rated to 2 inches of deflection and between 2 and 4 kilo-Newtons of force.

Vol. 2 1.3.2 Isolator Alternatives

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The first isolator alternative was the VHC-3A from Barry Controls.

This isolator is rated to 145 pounds of force and 2 inches of deflection. The load and deflection

rating alone make this a good choice as it is similar to the BAE isolator. However, the high cost

of $175 each and awkward symmetry make it difficult to meet budget and FEA requirements.

At least four isolators are needed to fully characterize failure criteria, which would run over

$500. While this is within budget, it can be hard to plan where the rest of the money may need

to go, and it is recommended to find a less expensive isolator.

Another isolator alternative is the Machinery Mount 633a from Barry Controls.

This isolator is rated to 135 pounds of force and 0.5 inches of deflection. The cost of the

isolator is $35. The advantages of this isolator are the low cost and acceptable deflection/force

rating. However, the asymmetry of the design would make it difficult to model. A circular

isolator like the GB-530 is required to create an accurate symmetric 3-D model.

The isolator that was chosen was the McMaster 6962K45 isolator.

Vol. 2 1.3.2 Isolator Alternatives

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This isolator is rated to 135 pounds and 0.5 inches of deflection. The cost of the isolator

is $24 dollars. This isolator was chosen because of the acceptable force/deflection rating, the

inexpensive cost and the cylindrical symmetrical shape. This isolator was inexpensive enough

that 7 isolators were purchased. 0.5 inches is enough of a deflection to take enough data

points using both the MTS 810 and Monterey Impac drop tests.

1.3.3 Test Fixture Alternatives

1.3.3.1 MTS 810 Test Fixtures

A test fixture was required to attach the isolator to the MTS 810 tensile test machine.

The MTS machine has two hydraulic grips that can be used to securely grip metal rods or

sheets. An isolator alone cannot be directly connected to the grips and needs a fixture for

connection. In addition, a fixture is needed to facilitate testing in the shear direction. An initial

idea for a test fixture involved thin aluminum sheet metal that was bent and welded to form an

L-angel with supporting side panels.

Vol. 2 1.3.3 Test Fixture Alternatives

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Another idea was constructing a similar L-angle piece by bolting together two pieces of

metal. Two other pieces of metal would be bolted on the L-angle to provide additional support.

This idea was well supported, but when it came time to construct the fixture available materials

from the UMN student machine shop allowed for a 1-piece L-angle. 2 side bars were still

constructed for side support. As an afterthought, an additional aluminum block is needed for

the shear test to stabilize the hydraulic grips.


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1.3.3.2 Drop Test Fixture Alternatives

A drop test fixture is needed to protect the isolator and data acquisition devices from

damage due to the high acceleration impacts. Two different cases are considered based on

how the isolator mounts to either the floor or a fixture. In Case I the isolator is fixed to the

fixture. In this case the entire fixture cannot deflect more than 0.005” (2 orders of magnitude

under isolator deflection 0.5”)during the initial isolator deflection. The advantages of case I is

ease of fabrication and a much lower G force.

In case II the isolator is fixed to the ground through the rubber. The fixture would not

be connected to the isolator in anyway, so it can be certain that the initial 0.5 inches of

deflection represents characteristics of the isolator alone. In this setup, the fixture is free to

deflect any amount given that it is still able to protect the isolator and absorb enough impact to

protect the data acquisition equipment. The advantages of case II are that the isolator is fixed

to ground, which ensures that the initial isolator deflection is accurate.


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Ultimately, case I was chosen because it was seemingly impossible to mount the isolator

to the ground. If BAE finds it more appropriate in the future to use case II, they are free to drill

into the ground mount and assemble this fixture idea. Another reason why case I was chosen

was due to the much lower G force. The fixture in case 1 includes a larger base plate and is

capable of absorbing much more of the impact. We wanted to be absolutely sure that our

testing did not destroy any BAE equipment and found the fixture deflection acceptable.

1.4 Concept Selection

In this section, concept selection will be discussed and the reasons for choosing each

concept will be analyzed. This will supplement the information in section 1.4 and repeat some

of the reasoning discussed there.

Vol. 2 1.4.1 Test Procedures

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1.4.1 Test Procedures

The main focus of this project was to develop a shock test that accurately characterizes

elastomeric isolators. The data taken from this test will be used to develop a finite element

analysis model. Several different testing methods became available to us after some periods of

research and prior methods of testing. An MTS tensile test machine was the first test

conceived, as everyone in the group has had experience using one while at the University.

Research revealed the idea of a drop test and we began thinking of ways our group could

fabricate a test device. Discussion and advice from Jim Wieczorek lead to the introduction of

the BAE hammer test and drop test. Four potential tests were considered and below is the

generated concept selection chart directly comparing all four tests.

Test Methods

MTS Test Drop Test (BAE) Drop Test (Fabricated) Hammer Test

Selection Criteria Weight Rating

Weighted

Score Rating

Weighted

Score Rating

Weighted

Score Rating

Weighted

Score

Test will not damage

isolators (unless desired) 15% 5 0.75 2 0.3 3 0.45 2 0.3

Test is repeatable 30% 5 1.5 3 0.9 3 0.9 3 0.9

Test obtains the required

test velocity (or can be scaled) 20% 2 0.4 4 0.8 4 0.8 3 0.6

Test can find failure points 10% 3 0.3 2 0.2 1 0.1 1 0.1

Test has controlled velocity,

acceleration and deflection 15% 4 0.6 3 0.45 2 0.3 3 0.45

Ease of operation (time included) 10% 4 0.4 3 0.3 3 0.3 2 0.2

Total

Score 3.95 2.95 2.85 2.55

Rank 1 2 3 4

Continue? Yes Probably Maybe Probably not

The main criterion that the test must meet is repeatability. If the test is not repeatable

then BAE will not be able to acquire future data using different isolators. Obtaining the

Vol. 2 1.4.1 Test Procedures

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required velocity is also important, but not necessarily needed if the velocity can be scaled. The

test must not damage the isolator and should have controlled and measureable velocity,

deflection and acceleration. Finally, the test needs to be able to give failure criteria (able to fail

the isolator by applying too much deflection/force) and the test needs to be easy to operate

(for example a test that requires 4 technicians is not easy to operate.) Each selection criterion

is given a weight percentage. Each test is then given a rating (1 through 5) on how that test

performs with respect to the given criterion. A weighted score is determined by multiplying the

rating and weighted percentage. The total score is then summed and compared with other test

methods. A rank and decision on whether or not to continue is developed based on the total

score.

Ultimately, the MTS and Drop Test were chosen. These tests offered better

repeatability and more accurate measurements than the hammer test or fabricated drop test,

in addition to other advantages seen in the chart.

1.4.2 Isolator Selection

There are many different shock isolators that can be used for many different purposes.

BAE has a specific isolator that they plan on using for Naval purposes; however, that isolator is

unavailable to us because of cost and wait time. BAE will not receive this particular isolator

until after the design project is already complete. In addition, there particular isolator costs

around $1,000 and they would like to test less expensive isolators to ensure test repeatability

and safety. One of the first goals of our design team was to select an appropriate isolator for

our testing. Many isolators were viewed from many different vendors. The concept selection

chart below lists the top three choices.

Isolators

6962K45 VHC-3A MM 633A

Selection Criteria Weight Rating Weighted Score Rating Weighted Score Rating Weighted Score

Cost 20% 5 1 2 0.4 5 1

Vol. 2 1.4.2 Isolator Selection

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Max Load 30% 4 1.2 5 1.5 4 1.2

Form

Factor/Design 20% 5 1 3 0.6 3 0.6

Max Deflection 30% 4 1.2 5 1.5 4 1.2

Total

Score 4.4 4 4

Rank 1 3 3

Purchase? Yes No No

The four criterion that were considered when selecting an appropriate isolator were

cost, load, form factor (symmetry for FEA modeling), and deflection. Ideally, we want an

isolator that is similar to the GB-330 series, but in actuality any isolator that has a large enough

deflection to acquire a significant amount of data points is acceptable. As a guideline, our

advisor suggested that the isolator needs to deflect enough to absorb an impact at 12 ft/s and

50 G’s (acceleration due to gravity.) Using kinematics it can be found that the stopping distance

required for 12 ft/s at 50 G’s is 0.537 inches.

This means we want an isolator that can deflect at least 0.5 inches. Ultimately, the

McMaster isolator (6962k45) was chosen for its cost and symmetry in three dimensions. The

other two isolators were shaped differently than the BAE isolator and the odd design would

make it difficult to model in finite element analysis programs.

Vol. 2 1.4.3 Fixture Selection

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1.4.3 Fixture Selection

1.4.3.1 MTS Fixture Selection

A fixture was needed in order to connect the isolator to the MTS 810 tensile test

machine. The MTS machine has two hydraulic grips that are used to secure test specimens.

Due to the form of shock isolators these hydraulic grips cannot simply latch onto the isolator.

For tension and compression a few simple bolts could suffice as a fixture; however, shear

testing must also be done. In order to fabricate a fixture that facilitates testing in shear as well

as tension/compression an L shaped bracket is needed. The two fixtures seen in the chart

below are both similar in shape. The main difference between the two is how they are

fabricated. One idea involved using thin aluminum sheet metal with bending and welding to

form the desired L-shape.

The second idea invloved using 4 pieces of steel, 2 large pieces that would bolt together

to form the L and 2 smaller pieces that would connect on the sides to give additional support.

Fixture Concepts

4 Piece Steel L (bolts)

1 Piece Sheet Metal L with tabs

(weld)


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Selection Criteria Weight

Ratin

g

Weighted

Score Rating Weighted Score

Ease of Installation (on test machine) 15% 4 0.6 4 0.6

Allows load in

shear/tension/compression 30% 4 1.2 4 1.2

Mounts several different Isolators 5% 3 0.15 3 0.15

Cost 5% 5 0.25 4 0.2

Ease of Manufacture 25% 5 1.25 4 1

Durability 10% 4 0.4 4 0.4

Portability 10% 5 0.5 5 0.5

Total

Score 4.35 4.05

Rank 1 2

Continue

? yes no

The selection criterion used for this concept selection included ease of installation (time

it takes and how many people are needed to install the fixture), fixture allows

shear/tension/compression, the fixture mounts several different isolators, cost, ease of

manufacture, durability and portability. It is important to take into consideration all of these

requirements when designing a new product. Ultimately, due to time and cost constraints our

team ended up constructing a different fixture based on available materials. The final design

was a pre-bent L-angle made out of aluminum. Two side bars were also fabricated (see

previous section for graphic.)

1.4.3.2 Drop Test Fixture

The drop test involves dropping a 170 pound mass on top of a shock isolator and

measuring deflection, force and acceleration. A mass this large will create a sizeable impact, so

the concern is for the safety of the test equipment and the shock isolator. A drop test fixture is

required to protect not only the isolator being tested but also the accelerometers being used

for data acquisition. Two different cases are presented (as seen in design alternatives.) Case 1


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involves fixing the isolator to the fixture base plate while case 2 involves fixing the isolator to

the ground. The selection criterion used in this selection is G force (how much the fixture

reduces the force due to gravity upon impact), material required and cost (this includes ease of

manufacture), and acquired accurate data acquisition. It was determined that case 1 reduces

the G force impact more because the entire fixture absorbs most of the impact. In case 2, since

the isolator is fixed to ground it is believed that the impact will produce much higher G forces.

The main reason why case I was chosen over case II was because it would be difficult to mount

the fixture to the ground. Mounting the fixture to the ground would involve drilling into the

concrete base of the drop test.

Fixture Concepts

Case I Isolator Fixed to steel/rubber

plate Case II Isolator Fixed to Ground

Selection Criteria Weight Rating Weighted Score Rating Weighted Score

G Force: accelerometer is

safe 30% 5 1.5 3 0.9

Material required, cost 20% 3 0.6 5 1

Accurate data acquisition 50% 4 2 4 1.5

Total

Score 4.1 3.9

Rank 1 2

Continue? Yes No

Ultimately, the fixture chosen was fabricated and used for testing. This design was

considered a success because it successfully protected the isolator and accelerometers being

tested. In addition, accurate test data was taken and validated by comparing it with MTS 810


26

ramp data. Since a metal base was used, it would be easy for BAE to drill new holes to mount

different isolators.

1.5 Damping Modes in Ansys

Most damping in ANSYS is approximated as a form of viscous damping. The most common form of viscous damping is the Rayleigh-type damping given by:

Equation 1: Rayleigh-type damping

The C matrix in ANSYS is created using the following form.

Equation 2: ANSYS Damping

where Alpha damping (Viscous)

Beta damping (Viscous)

Material dependent beta damping

Element damping matrices Frequency-dependent damping matrix

For the isolator model, the system damping can be simplified using only element damping matrices. Thus, Equation 2 reduces to the equation shown below.

Equation 3: ANSYS Damping Using Only Element Damping Matrices The Combination Element COMBIN37 shown in Figure 2 accounts for the nonlinearities in the damping constants of the isolator. Complex system models are created by attaching multiple elements in parallel. Each element can be turned on or off using control nodes.

Vol. 2 1.5 Damping Modes in Ansys

27

Figure 1: COMBIN37 Element Pictorial Diagram [3]

Frictional damping can be added by using the FSLIDE component in the COMBIN37 element. The FSLIDE values specify the absolute force that must be exceeded before sliding occurs at a given displacement. Structural damping is accounted for in the non-linear spring element, COMBIN39. The element uses a force defection table created using empirical data to model the spring. The hysteresis is modeled by controlling whether the spring retraction follows the extension path or returns on a separate force-displacement retraction path. Together, the COMBIN37 and COMBIN39 allow for a one dimensional model with nonlinearity in the spring-damper system to be constructed. Since the isolator model is comprised of an initial velocity shock event and does not have sustaining oscillation, structural damping can be ignored.

Vol. 2 2.1.1 Drop Test Fixture Drawings

28

2 Design Description Supporting Documents

The following sections are documents that support the design process of this project.

2.1 Drawings

The following sections are line drawings of the two fixtures. The drawings include individual

drawings of each important component along with assembly drawings.

2.1.1 Drop Test Fixture Drawings

Drop Test Fixture Drawings

The following images are drawings of the drop test fixture used in the drop test. The fixture

consists of two side plates, a bulk aluminum piece that the isolator is placed on top of (the

aluminum piece will be referred to as ground), and the assembly of the fixture with the isolator

in place. Dimensions are given for the drawings of the side plates and ground piece. All

dimensions are in inches.


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The ground piece holds the isolator. This part is directly under the mass during the drop test.

The side plates connect to the ground and are shown in the next figure.

The side plates keep the isolator from failing during the drop test. The side plates are taller

than the ground piece, thus once the isolator deflects the allowable limit the rest of the mass

hits the side plates. The side plates then absorb the rest of the impact.


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The complete assembly is shown above. The fixture sits on a rubber mat to reduce the amount

of g’s the accelerometers will experience. This fixture only allows the isolator to deflect 0.75

inches.

Fixture

Rubber Mat

Isolator

Vol. 2 2.1.2 MTS Fixture Drawings

31

2.1.2 MTS Fixture Drawings

The following drawings represent the MTS test fixture used in this project. These

drawings were created using Pro Engineer Wildfire 4.0. All dimensions are in inches.

This is the L-bracket component. The particular bracket used in this test was made of

aluminum, but a steel bracket could provide more support if higher forces are required.


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This is the support beam which appears on each side of the L-bracket to give additional

support. Again, this was made from aluminum but could be made out of steel for more support

at higher loads.


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This shear paddle is connected to the isolator and a separate threaded rod is used to connect to

the MTS machine (see assembly fixture drawing below.)


34

This shear moment block provides additional support on the bottom hydraulic grip and

prevents the entire fixture from rotating due a moment force.


35

These are assembly drawings showing how to assemble the fixture for different testing

configurations. Notice how the shear configuration requires extra support to prevent fixture

motion and deflection.

Vol. 2 2.2 Bill of Materials

36

2.2 Bill of Materials (Component List)

In this section a table is given which includes every item used to create the fixtures needed to

run the test procedures. Notice that there are two columns for cost; projected and actual.

Projected cost would be how much the items would cost if the test was repeated. Actual cost

was what we paid during this project. Several of the materials and components were taken for

free as scrap from the University of Minnesota student machine shop.

MTS 810 Test Fixture

Description Qty Vendor

Projected

Cost

Actual

Cost

Neoprene Shock Isolator 7 McMaster $164.78 $164.78

Aluminum L-Angle 6"x6"x.375" 4" Long 1 UMN/Discount Steel $14.55 $0

Aluminum Support Bar .5"x.5"x 8.5" 2 UMN/Discount Steel $5.68 $0

SHCS 1/4-20 x .5" 4 McMaster/UMN $0.58 $0

SHCS 3/8-24 x .5" 2 McMaster/UMN $1.59 $0

Nut 3/8-24 2 McMaster/UMN $0.25 $0

Threaded rod 3/8-24 x 4" 1 McMaster/UMN $2.30 $0

Drop Test Fixture

Description Qty Vendor

Projected

Cost

Actual

Cost

Aluminum Flat Bar 1"x4" Length 36" 1 Discount Steel $53.86 $53.86

Aluminum Flat Bar 3"x5" Length 8.125" 1 Discount Steel $53.82 $53.82

Natural Gum Rubber Mat 12"x12"x1" 1 McMaster $35.01 $35.01

SHCS 1/2-20 x 1.25" 8 McMaster/UMN $8.57 $0.00

Total (Projected, Paid) $336.85 $307.47

Vol. 2 3.1 Evaluation Reports

37

3 Evaluation Supporting Documents

3.1 Evaluation Reports

The five design requirements are evaluated in the 5 corresponding reports below.

3.1.1 Design Requirement 1: Evaluation of Isolator Stiffness

Introduction

The dynamic characteristics of a shock isolator must be known before a finite element analysis can be performed on a shock isolation system. In order to fully understand isolator characteristics both spring and damping coefficients must be identified. The mathematical model of the isolator is shown in Equation 1. (1)

Stiffness is a static property of the isolator, where damping is a dynamic property. In this report, static analyses will be performed on the isolator to examine the stiffness. An additional report will dynamically load the isolator to examine the damping force. For static conditions, the stiffness is defined by the following equation.

(2)

The stiffness of the isolator is expected to be dependent on the loading direction (tension, compression, and shear) and displacement. The following test method establishes how to find the displacement dependant stiffness of the isolator in each loading direction.

Equipment The following equipment is required to perform the isolator stiffness test:

• MTS Tensile Test Machine – 810 Load Frame

Vol. 2 3.1.1 Evaluation of Isolator Stiffness

38

• MTS Side-Loading Hydraulic Wedge Grips – Model # 647.10

• MTS Test Fixture (see MTS Test Fixture Report – Section 4.2)

• Shock Isolator- McMaster-Carr part number 6562K45, Max Displacement 0.5” at 135 lbf

• 2 Bolts (size of the bolts based on the size of the connection holes in the isolator)

• 4 Threaded Rods (size of thread based on the size of the threaded hole in the isolator)

• 1 Washer (size based on face of isolator and threaded hole size of isolator)

• 1 Shear Adaptor (see MTS Test Fixture Report)

• 5 Nuts (size based on size of threaded rods and size of bolts used)

• 1 Connection Adaptor (see MTS Test Fixture Report)

Methods The following methods outline how to determine the stiffness of an isolator. The methods explain the setup of the fixture in compression, tension, and shear, and the testing procedure.

Compression/Tension Test Setup Bolt the shorter threaded rod to the bottom of the MTS test fixture, make sure the rod does not extend too far above the fixture as this will cause disturbances when the isolator is tested in compression. Next, bolt the isolator to the MTS test fixture. A washer is placed on the face of the isolator; the washer must cover the entire face of the isolator. Connect the threaded rod to the top of the isolator; make sure the rod does not extend past the threads of the isolator as this will cause disturbances when the isolator is tested in compression. Bolt the rod and washer in place. Connect the bottom of the test fixture to the non-moving grips of the MTS tensile test machine. Connect the thread that is extended from the top of the isolator to the moving grips of the MTS tensile test machine. The entire assembly of the isolator to the test fixture and the connection of the fixture to the MTS tensile test machine are shown in Figure 1.


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Figure 2 - Fixture Setup for the MTS Tensile Test Machine in Tension/Compression

To Moveable Grips

To Stable Grips

Washer Must Cover Entire Surface


40

Shear Test Setup Bolt the shear adaptor to the isolator. Bolt the isolator to the side of the MTS test fixture. Next, secure the connection adaptor to the bottom of the fixture. Fasten the longer threaded rod to the shear adaptor. Connect the bottom of the test fixture to the non-moving grips of the MTS tensile test machine. Connect the thread that is extended from the shear adaptor to the moving grips of the MTS tensile test machine. The entire assembly of the isolator to the test fixture and the connection of the fixture to the MTS tensile test machine are shown in Figure 2.

Figure 3 - Fixture Setup for the MTS Tensile Test Machine in Shear

Test Procedure

The first step is to condition the isolator. Input a signal to the isolator with amplitude at the rated deflection of the isolator (if the isolator has a rated deflection of two inches, the amplitude of the signal would be a deflection of two inches) and a frequency of 0.2 hertz. Let the signal run for 15 seconds. Conditioning only needs to be performed before the first test and only if the isolator has not been conditioned/tested for 30 minutes. After conditioning the tests can be performed. Set the sampling rate of the MTS tensile test machine to the highest

Shear Adaptor

Connection Adaptor

To Stable Grips

To Moveable Grips

Shear Adaptor (Only one side shown for clarity)


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value. The variables to be recorded are time, displacement, and force. Have a program that displaces the isolator to a certain value, holds the isolator at that displacement for one second, and then returns the isolator to the zero position.

Tension Testing There will be ten displacement tests in tension. The displacements will be determined by the rated displacement of the isolator. Tables 1 and 2 show the displacements of each test for an isolator at a rated deflection. Run the program with the deflection of the isolator set to the corresponding value in test 1. Save the results. Set the displacement to the corresponding value in test 2. Do not run the test until the force on the isolator is less than one pound.

Table 1: Test displacement values for tests 1-5

Rated Displacement of Isolator (inches)

Displacement of Test 1 (inches)





1 0.1 0.2 0.3 0.4 0.5

1.5 0.15 0.3 0.45 0.6 0.75

2 0.2 0.4 0.6 0.8 1

2.5 0.25 0.5 0.75 1 1.25

3 0.3 0.6 0.9 1.2 1.5

3.5 0.35 0.7 1.05 1.4 1.75

4 0.4 0.8 1.2 1.6 2

Table 2: Test Displacement values for tests 6-10

Rated Displacement of Isolator (inches)






1 0.6 0.7 0.8 0.9 1

1.5 0.9 1.05 1.2 1.35 1.5

2 1.2 1.4 1.6 1.8 2

2.5 1.5 1.75 2 2.25 2.5

3 1.8 2.1 2.4 2.7 3

3.5 2.1 2.45 2.8 3.15 3.5

4 2.4 2.8 3.2 3.6 4


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To lessen the amount of time it takes for the load on the isolator to be reduced to less than one pound, displace the isolator 0.1 inches in compression (-0.1 inches in tension), hold the isolator at 0.1 inches of displacement for 5 seconds and then return the isolator to the zero position. Repeat the process for each of the ten tests. Make sure to save all results with a descriptive name of what was performed. Before beginning any test make sure the force on the isolator is less than one pound. Compression Testing The compression testing procedure is the same as the tension procedure except the displacement values will be negative. Follow the same procedure for the tension testing. To lessen the amount of time it takes for the load on the isolator to be reduced to less than one pound displace the isolator 0.1 inches in tension (+0.1 inches) hold the isolator at 0.1 inches of displacement for 5 seconds and then return the isolator to the zero position. Make sure to save all results with a descriptive name of what was performed. Before beginning any test make sure the force on the isolator is less than one pound. Shear Testing The shear testing procedure is the same as the tension procedure except the shear setup is used. Follow the same procedure for the tension testing. The isolator is axisymmetric, so the shear stiffness will be the same in every angular direction. To lessen the amount of time it takes for the load on the isolator to be reduced to less than one pound displace the isolator in the opposite direction the results are being recorded in to 0.1 inches, hold the isolator at 0.1 inches of displacement for 5 seconds and then return the isolator to the zero position. Make sure to save all results with a descriptive name of what was performed. Before beginning any test make sure the force on the isolator is less than one pound.


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Data Analysis Matlab was used for the data analysis – See section 4.2 for further discussion of analysis and source code of Matlab scripts.

I. Import data file II. Filter noise from position and force data sets III. Use equation (2) to calculate stiffness as function of time IV. Find location where stiffness stabilizes within certain criteria V. Find average stiffness of N data points after spring coefficient stabilizes VI. Repeat steps I-V for each data file VII. Perform regression analysis on stiffness for each loading direction

Results

The isolator stiffness test was performed for many loading configurations; for conciseness, the results of a single test will be shown here. Below is a plot showing the displacement as a function of time.

Figure 4 - Displacement during 0.5" Compression Test


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Below is a plot showing measured force with respect to time.

Figure 5 - Force during 0.5" Compression Test

From Figure 4, it can be seen that the raw force data (red line) contains high-frequency noise and is oscillatory after the displacement stabilizes at 0.5 inches. To remove this noise, the raw force and position data were filtered with a low-pass FIR filter to attenuate frequencies above 200 Hz.

Another important observation from figure 4 is that the force decays slightly between 0.1 and 0.2 seconds. Since the isolator is made of neoprene rubber, the isolator has viscoelastic (time-dependent) properties. Consequently, the time at which the force is calculated will affect the corresponding stiffness. Since the stiffness is to be implemented in a dynamic analysis, the stiffness should be measured as close to the time when the displacement stabilizes at 0.5” as possible. Also, the calculated stiffness from the raw data should be allowed to stabilize within certain criteria. This prevents the choice of filter from influencing the results.

The plot below shows the stiffness as a function of time. The yellow line is the stiffness calculated from the original force and the filtered position. The red line is the stiffness calculated from the low-pass (600 Hz) filtered force and the filtered position. The black line is the stiffness calculated from the low-pass (200 Hz) filtered force and the filtered position. The


45

two vertical blue lines between 0.1 and 0.2 seconds show the region where the stiffness met the necessary criteria to calculate the stiffness. The stiffness used in future analyses was filtered with the 200 Hz low-pass filter.

Figure 6 - Stiffness during 0.5” Compression Test

Step VI in the data analysis procedure says to analyze all the data files corresponding to the displacements from tables 1 and 2. The following plot shows the calculated stiffness from each of these displacements. A regression analysis was performed on the stiffness results. By looking at the stiffness results, it was determined that a linear model was sufficient for the compression loading direction. For the tension and shear loading conditions, a 3rd order polynomial model was used to fit the stiffness results. An uncertainty analyses was performed on the results of the regression analysis and can be seen with the red lines showing the 95% confidence interval for the mean response.


46

Figure 7 – Regression Analysis of Stiffness for Tension and Compression

Figure 8 - Regression Analysis of Stiffness for Shear


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Discussion The experiment succeeded in determining the stiffness of the isolator over its rated deflection. One weakness of this experiment was that multiple isolators were not tested. Due to time constraints only one isolator was tested over its full rated deflection, a second isolator was tested, but only at three displacements. The group determined that with the given time, that testing one isolator was reasonable because the second isolator was within five pounds of force of the first isolator at its three tested positions. For future tests multiple isolators should be tested and then a statistical test should be performed to know the error in the measured results. The strengths of the test include: BAE is able to replicate the test, a technician can perform the test in a relatively short amount of time, and the test proved to be an accurate way of finding the stiffness. BAE is able to replicate the test because the test was performed at BAE. They have all the equipment needed to perform this test on future isolators. The tests took about an hour to obtain all the data points needed to analyze the isolator in tension and compression. During the drop test (see damping report) the data that was measured was graphed with the stiffness of the isolator. The difference in force from the measured data and the data obtained from the stiffness of the isolator (which is the damping force, see damping report) is 11 percent in compression. The group was able to acquire the stiffness of the isolator which allowed the group to proceed on to finding the damping coefficient in the isolator (see damping report).

3.1.2 Design Requirement 2: Evaluation of Isolator Damping

Introduction The dynamic characteristics of a shock isolator must be known before a finite element analysis can be performed on a shock isolation system. In order to fully understand isolator characteristics both stiffness and damping components must be evaluated. Since stiffness was discussed previously, the focus of this evaluation report is isolator damping. Damping is the energy dissipation mechanism that causes vibratory motion to slow down and stop over time. The damping force is a function of displacement and velocity and varies based on the isolator’s material and shape. A suitable testing procedure must be developed and carried out to determine the damping characteristics of isolators. This testing procedure must evaluate damping up to velocities of 12 feet per second, per BAE request.

Vol. 2 3.1.2 Evaluation of Isolator Damping

48

The damping of an isolator can only be determined once the stiffness (spring coefficient) is calculated. This evaluation report assumes that the stiffness of the isolator being tested has already been calculated based on the previous stiffness report. Two test methods were developed to evaluate the damping of the isolator. A tight correlation between the two tests is desired to demonstrate repeatability and validity.

1. This test uses a tensile test machine to displace the isolator at a specified velocity.

This test will measure force, position, and time. The test will be applied for a range of low velocities (0.4 to 4.5 ft/s) to evaluate the relationship of damping to displacement and displacement velocity.

2. This test uses a drop test machine provided by BAE Systems to evaluate damping of the isolator at high velocities (2 ft/s to 13 ft/s). A large weight is dropped from a specified height and allowed to collide with the isolator. The acceleration and position of the mass will be measured while the weight deflects the isolator.

Equipment Shock Isolator – McMaster-Carr part number 6562K45, neoprene isolator rated to 0.5 inches of

deflection and 135 pounds of force. MTS Monterey Impac (Drop Test) – 170 pound weight constrained to vertical direction by

means of two 16 foot cylindrical rods. Microtron Accelerometer 7290A-10 – Variable Capacitance, Range: 10 g’s, Sensitivity: 200 mV/g String Potentiometer PV-75A-100G – (Serial #: 9622-18619), Sensitivity: 13.2 mV/V/in, Range: 70” Drop Test Fixture – Student fabricated fixture provides the necessary strength and durability to

absorb the kinetic energy of the weight and protect the isolator. The fixture has two aluminum plates bolted to a 3 inch thick aluminum base. The isolator is fixed to the aluminum base and extends vertically 0.75 inches above the two side plates. This design restricts the isolator deflection to 0.75


49

inches. See theory section and appendix 3.3.4 for more information on the design. See appendix 2.1.1 for engineering drawings.

Rubber Mat – Thickness: 1 inch, Dimensions: 4.5” x 8”, Material: Natural rubber, Supplier:

McMaster-Carr, Part #:8633K63, Used to prevent damage to accelerometers when drop weight and fixture collide.

Nicolet Odyssey Data Acquisition – Sample Rate: 50 KHz, Low Pass Filter: 12.5 KHz, Used to

acquire data from the linear transducer and accelerometer.

Photron Fastcam SA1.1 675K-M1 – Frame Rate: 3000 Hz, High-speed camera used to view

deflection of isolator during drop test. MTS 810 Tensile Test Machine – different load cells are compatible with this machine, for this

test a 500 pound load cell was used. MTS Fixture – Student fabricated fixture, allows isolator mounting for compression, tension and

shear. MTS Fixture Shear Adapter – Aluminum plate to connect the isolator and MTS grip for shear

testing. See appendix 2.1.2 for engineering drawings.

Methods Damping Theory The motion of the drop weight can be expressed by the following equation. The isolator has two contributions to this equation: the stiffness force ( ) and the damping force.


50

(3) Where m = mass of drop weight, g = gravity, and k = isolator stiffness. Since the stiffness was determined in the previous experiments, damping force can be calculated by knowing the free fall acceleration (gravity), acceleration of weight, and deflection of the isolator. For the test using the tensile test machine, the damping will be evaluated with the following equation. (4) Impact Theory It is assumed that the impact of the weight to the isolator will be perfectly inelastic (the two weights will stick together). This assumption can be numerically analyzed by considering the kinetic energy of the weight before and after the collision. A perfectly inelastic collision does not dissipate energy. Since the velocity of the isolator and weight will be the same after the impact, the following analysis shows the inelasticity of the collision.

Fixture Design Shock isolators have a usable range and can be damaged if the displacement is outside of this range. Accelerometers also have a usable acceleration range and can be destroyed if the acceleration is outside of this usable range. To prevent damage to equipment, a test fixture was developed to limit the peak acceleration as well as protect the isolator. The design of the fixture is outlined further in appendix 3.3.4. Velocity of Weight To meet the design requirement for this test, the damping of the isolator must be evaluated at velocities up to 12 ft/s. The following energy equations were used to determine the height of the drop test to achieve the desired velocity.

(5)


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(6)

(7)

Simplifying and solving for velocity yields the final equation for impact velocity.

(8)

Drop Test Procedure The following procedure was used to perform the drop test on the shock isolator. The test was performed at twenty different heights, corresponding to equally spaced velocities between 2 ft/s and 13 ft/s. I. Setup

a. Install accelerometer to designated location atop the drop weight.

b. Attach the string from the position transducer to screw located on the drop weight. c. Connect both accelerometer and linear transducer to the Odyssey data acquisition

computer system. d. Setup high-speed video recording device including computer system, lighting and

recording device.


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e. Setup the drop test fixture i. Lift drop weight to an appropriate height using drop test controller

ii. Bolt isolator to the base of the fixture iii. Lay rubber mat down under drop weight location iv. Lay drop test fixture on top of rubber mat v. Center the test fixture so that the isolator is directly below the center of the drop

weight

II. Execution a. Zero the linear motion transducer

i. Lift drop weight using drop test controller and slowly lower weight until the bottom of the weight is approximately 0.05 inches above the top of the isolator

ii. Use feeler gauge to measure gap between isolator and drop weight. iii. Using the Odyssey data acquisition system, set the displacement output equal to

the measured gap. b. Calculate height for desired velocity

c. Lift drop weight, using drop test controller, to the calculated height d. Set activation switch (activation switch is connected to the left 16 foot tall rod. The

switch needle must be in contact with the drop weight otherwise the drop test controller will not respond to a drop request.)

e. Alert nearby patrons of the test and give a short countdown f. Using the drop test controller, drop the weight g. After the weight/fixture/isolator have reached equilibrium and the weight is resting on

the isolator, lift the weight to an appropriate height to readjust and inspect the fixture h. Tighten any loose bolts i. Re-center the fixture j. Inspect data on Odyssey data acquisition system

i. Save data as text file and send to floppy disk k. Repeat steps a-j for each desired velocity

III. Analysis

a. Matlab usage for data analysis – See Section 4.2 for further discussion of analysis and source code of Matlab scripts. i. Import data files

ii. Filter high frequency noise from position and acceleration data sets iii. Import regression analysis of isolator stiffness iv. Use equation (1) to calculate the damping force as function of displacement


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v. Repeat steps i-iv for each data file corresponding to each desired velocity vi. Analyze 3-dimensional plot of damping force, displacement, and velocity to

determine dependence of damping force on displacement and velocity. MTS Tensile Test Procedure

The following procedure was used to perform the ramp test on the shock isolator. The test was performed at 10 different velocities from 0.45 ft/s to 4.5 ft/s based on the capabilities of the MTS machine. VIII. Setup

a. Attach isolator to MTS fixture and shear plate if needed b. Attach fixture to MTS bottom grip c. Apply washer to top of isolator d. Attach threaded rod with washer and nut to top MTS grip e. Condition Isolator (only needed before first test and only if the isolator has not been

conditioned or tested for 30 minutes) i. Input a signal to the isolator with amplitude at the rated deflection of

the isolator and a frequency of 0.2 hertz ii. Let signal run for 15 seconds

IX. Execution

a. Properly input desired velocity into the ramp input function of the MTS software b. Use software to perform a test c. Repeat from step a) for next desired velocity d. Repeat from step a) for shear and tension (assuming compression was first)

X. Analysis a. Matlab usage for data analysis – See section 4.1 for further discussion of analysis and

source code of Matlab scripts. i. Import data files

ii. Filter high frequency noise from position and acceleration data sets iii. Import regression analysis of isolator stiffness iv. Use equation (2) to calculate the damping force as function of displacement v. Repeat steps i-iv for each data file corresponding to each desired velocity

vi. Analyze 3-dimensional plot of damping force, displacement, and velocity to determine dependence of damping force on displacement and velocity.


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Results Ramp Displacement Test Analysis from this test was dependent on a constant ramp deflection of the isolator. Given the limited deflection range for the isolator (0.5 inches), the 810 MTS machine was not able to sustain a constant velocity input at velocities above 1.8 ft/s. Consequently, the data analysis was limited to five or less data sets in each of the loading configurations. Below is a plot showing the input velocity as a function of time. The red line is the “original” or raw velocity data. The black line is the “filtered” velocity with the high frequency noise removed. For this particular test, the velocity remained constant for most of the displacement range, since the input velocity was small relative to some of the other tests.

Figure 9 – Velocity Data for 0.45 ft/s Ramp Displacement Test

The following plots show the damping force as a function of displacement for two different velocity tests.


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Figure 10 - Velocity Data for 0.45 ft/s Ramp Displacement Test

Figure 11 - Velocity Data for 0.9 ft/s Ramp Displacement Test


56

The damping force given by figures 2 and 3 is very similar. They both show the damping force increase with deflection. As the deflection nears 0.45 inches, the damping force approaches 20 lbf. The damping force found in shear is shown in Figure 4. The damping force that was found was negligible.

Figure 4 - Velocity Data for 0.45 ft/s Ramp Displacement Test in Shear

Drop Test Analysis of damping was restricted to 0.5 inches of deflection because isolator stiffness was analyzed up to 0.5 inches of deflection. Below are plots showing the acceleration as a function of displacement. The green line is the “original” or raw acceleration data. The black line is the “filtered” acceleration with the high frequency noise removed. The red line is the “spring” acceleration that would result if the isolator were a perfect spring; this acceleration was calculated using the regression analysis of the isolator stiffness. The accelerometer reads -1 G for a freefall condition.


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Figure 5 – Acceleration Data for Impact Velocity of 2 ft/s

Figure 6 – Acceleration Data for Impact Velocity of 11 ft/s


58

At impact, the acceleration briefly spikes, but stabilizes shortly thereafter. The amplitude of this acceleration spike increases with impact velocity. For all velocities tested, the acceleration stabilized within 0.4 inches of isolator deflection, thus allowing 0.1 inches of displacement to analyze isolator damping. Using equation 1, the difference in acceleration between the “spring” and “filtered” acceleration can be transferred into a damping force. The following plots show the calculated damping force. The displacement region with the initial acceleration spike was removed. An uncertainty analysis was performed on the damping force and is shown with the red lines in the plots below. The error analysis uses the largest error contributions, the error from the regression analysis of the stiffness and the uncertainty in the zero displacement position (± 0.010 inches) during the drop test. Each red line is two standard errors from the mean damping force, which corresponds to a 95% confidence interval.

Figure 7– Damping Force for Impact Velocity of 2 ft/s


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Figure 8 – Damping Force for Impact Velocity of 11 ft/s

The damping force given by figures 7 and 8 is very similar. For deflections between 0 and 0.3 inches, the damping force is below 10 lbf. As the deflection nears 0.5 inches, the damping force approaches 20 lbf. It can be seen that the damping force becomes erratic at high velocities, but the damping force follows the same trend as the low velocity test.

Discussion The two experiments to determine isolator damping provided similar quantitative and qualitative results. It can be seen from figures 5, 6, 7, and 8 that the damping force demonstrated a consistent relationship with respect to displacement. An uncertainty analysis was performed on the experiments to construct a confidence interval for the results. Consequently, the damping force results should be considered valid within the corresponding confidence interval. The damping force from the drop test was shown for just two velocities, 2 ft/s and 11 ft/s, but these results are representative of the results at all other velocities that were tested. From figures 6 and 7, the damping force is nearly the same for impact velocities of 2 ft/s and 11 ft/s. Consequently, it can be said that the damping force is independent of velocity and is solely based on displacement. This conclusion is valid for the range of velocities that were tested in these experiments.


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The tests described in this report have several benefits for evaluating damping.

• Easy evaluation of damping force over large range of velocities. • Efficient and effective Matlab programs can be utilized to analyze data. • High speed video gives visual feedback to assess the test setup.

The tests described in this report have several weaknesses for evaluating damping.

• Fixtures must be fabricated to protect the isolator and data acquisition equipment. • Noise in data from collision during drop test. • The drop test experiment can currently be used for compression only. • A series of tests are required to calculate damping (stiffness tests over range of

displacements then dynamic tests as described in this report) The design of this test procedure should ultimately be considered a success. A drop test has never been used at BAE for shock isolator characterization so revolutionary new results can be given. The two largest weaknesses for the test, that is the large amount of noise and failure to test in tension and shear, can be rectified through proper Matlab programming and the design of a new test fixture. For the first time ever using the drop test for shock characterization, getting accurate and quantifiable data is a success. Compression results from this test can be compared to that of the ramp MTS tests and used to validate both procedures. Once validated, this test can be used to determine how a given isolator will behave under high impact velocities, up to 13 feet per second. The design requirement of characterizing damping and reaching 12 feet per second impact velocities was met by doing several tests on two different test machines. Lower velocity ramp tests were determined using the MTS 810 tensile test machine. These lower velocity results were directly compared to the lower impact velocities of the Monterey Impac drop test. Since the drop test covered a wide range of impact velocities, a comparison of damping force with different velocities was issued. It was seen that damping force is independent of velocity. The fact that similar damping results were seen across the wide range of velocities and the two different test machines validates the results. Ultimately, the design requirement is fully met.

Vol. 2 3.1.3 Evaluation of MTS Fixture Displacement

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3.1.3 Design Requirement 3: MTS Test Fixture Deflection

Introduction

Finite Element Analysis (FEA) was utilized to help confirm that our third design requirement is met. The requirement states that our MTS test fixture will not deflect more than 0.005 inches (0.000127 m) under peak leading conditions of 2.5kN in shear. A model of the test fixture was constructed using Pro/E, a solid modeling program, and imported into ANSYS classic as an IGES geometry file. The model was then tested to demonstrate the maximum deflection of our fixture design.

Performing a FEA calculation demands a careful and methodical attention to the units that are used. Checks must be performed at each step to verify the units in ANSYS. A calculation is only valid if all units used are consistent and the end result makes sense when compared with hand calculations.

Numerous assumptions and approximations of the fixtures load conditions were needed to create a model. Conservative estimations of the force inputs and loading conditions were used to present two different cases for the fixture: one with side bars and one without side bars.

The methods section will show a step by step progression to our solution while documenting the assumptions utilized along the way. The results section will detail our final output and demonstrate that the design meets our design requirement.

Equipment

The following programs were used to create the solid model and perform the Transient FEA calculation.

• ANSYS classic 11.0 release (Student Edition) • Pro/E Wildfire 4.0

Methods

Creating a valid FEA calculation is dependent on using a consistent set of units. The Units that are defined in a Pro/E model are exported to ANSYS in a 1 to 1 form when using an IGES file. This means that ANSYS will interpret the units of a model using 1 mm as a unit less 1. It will


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then be the user’s responsibility to use the correct units throughout ANSYS for the solution to be valid. For this purpose, the bracket design and calculation were all completed using the SI units of m and N.

Hand calculations and measurements of the constructed bracket were the first step in creating a model and determining the loads. Figure 1 shows a sample of my hand calculations used to determine the loads and moments that would be affecting the bracket. Figure 1 also shows an earlier model that was not used after examining how the moments in the bracket would be transmitted to the lower grip of the MTS machine. A single bolt design to constrain movement of the fixture was found to not meet our requirements for deflection. Therefore a larger block was envisioned that could attach to the middle of the isolator and help provide a better constraint in the MTS grips.


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Figure 1: Sample hand calculations from design notebook for a 500 lb shear load.

The ANSYS geometry was confirmed by using the modeling tool that allows the user to measure the distance between two surfaces. In figure 2, the distances between two known surfaces confirmed that the model geometry was in meters.


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The preprocessing, solution, and post processing of the bracket was complete using a Cornell University ANSYS short course tutorial [1].

The first step is to select the type of analysis to be completed under Main menu Preferences structural. In order to mesh the solid, the element types should be picked. This simulation used a Solid Brick 8node45 element and a Mesh Facet 200 to help define the mesh.

The Material properties of the aluminum we set as a structural Linear Elastic Isotropic. The Young’s modulus set at and the Poisson’s ratio was set to 0.30.

The mesh can now be established using the mesh tool. The smart size control was set to produce a fine mesh of the fixture. The mesh developed for our model can be seen in figure 2.

Figure 2: Complete mesh and point loads.

Each node is constrained for all DOF on the small plate.

1115 N loads in the positive y-direction

3460 N loads in the X-direction to account for the isolator moment


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The loads and deflections were added as appropriate. A simplifying assumption is that constrained plate on the bottom is a part of the fixture. This simplified constraining the surface. In reality the plate is pretension against the fixture due to the bolts holding it in place.

In figure 3, the fixture was tested for performance without side bars. The resulting displacement vector sum showed a maximum deflection of 0.0010 m. This does not meet the design requirement of less than 0.000127 m.

Figure 3: Fixture displacement with our side arms.

The addition of the fixture arms was a more difficult problem. Given a small amount of previous work with ANSYS, the team was unable to create a pin joint connection between the arms and the ends of the fixture. To compromise, the bars were assumed to be directly attached; the surrounding nodes were checked for excessive stress in the post processing. It did not appear that small amount of deflection caused an issue in the validity of the solution.


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Figures 4 and 5 show that the solution with the side arms did meet the design requirement and only deflected less than the maximum of 0.00013 m

Figure 4: Final solution with side arms.

Results

As shown in Figures 4 and 5, the fixture meets the criteria for the maximum loading case in shear. The hand calculations, the FEA solution, and our observation during our test with the actual fixture lend to the validity of this maximum deflection of 0.00013 m result.


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Figure 5: Final solution

Discussion

One of the groups’ concerns for the model was that the bolted fixture arms would have too much play to help reduce some of the loading. This was likely that case in our actual test where our maximum shear force peaked around 250N or an order of magnitude lower than our FEA model. In the case that there was more than 1 mm of play in loose fitting bolts, then the arms would not have been under tension in the test. For our load of 250N, over deflection was most likely not a problem since likely deflection of the fixture without side arms would have been reduced by an order of magnitude as well.

In future tests, that approach maximum load capacity of the fixture it would be worth looking into using a welded triangular aluminum plate to add extra rigidity to the fixture.

Vol. 2 3.1.4 Evaluation of Drop Test Fixture Stiffness

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3.1.4 Design Requirement 4: Drop Test Fixture Stiffness

Introduction To evaluate the damping of the shock isolator, an experiment will be performed where a large mass (170 lbs) is dropped onto the shock isolator. The manufacturer of the shock isolator certifies the isolator up to 0.75 inches of deflection. Past this deflection, the isolator may begin to wear or even catastrophically fail. The analysis below shows that a fixture is required to limit the deflection of the isolator.

With the 170 lb mass falling at 12 ft/s, the kinetic energy of the mass is given by the

equation Joules. If the isolator is considered a perfect spring, the stored energy is

given by the equation . For the isolator to be tested, the maximum rated displacement is

0.75 inches. The spring coefficient (k) was found during the stiffness tests; k is approximately 460 lbf/in. Thus, the maximum energy that can be stored in the isolator is 15 Joules. Consequently, a fixture is required to limit the isolator deflection to 0.75 inches and store/dissipate the remaining kinetic energy of the mass.

Now that a fixture is required, a few requirements must be put forth to design against. The data analysis for the drop test will use position as an independent variable. Consequently, the accuracy of the position measurement is extremely important. The drop test will have two time periods, the isolator deflection period and the post-fixture impact period. During the isolator deflection period, the fixture must not deflect more than .005 inches. This requirement stems from the data analysis of the drop test. The maximum expected load during the isolator deflection period is 300 lbs. Consequently, this puts a lower bound on the stiffness of the fixture.

(9)

Another critical measurement during the drop test is acceleration. The range of expected acceleration during the isolator deflection period is ± 2 G’s. However, when the drop mass impacts the fixture, a large, impulsive acceleration will occur. This large acceleration may damage accelerometers meant to measure small accelerations. BAE Systems has a variable capacitance accelerometer with a measuring range of ± 10 G’s that can withstand a peak acceleration without damage of 6000 G’s. Consequently, the upper bound on the fixture stiffness is due to the restriction on maximum acceleration. The tolerance bound on the


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stiffness is asymmetrical to minimize the risk of breaking equipment by minimizing the peak acceleration.

Methods Two methods were used to validate the design of the drop test fixture. First, theoretical calculations were used to design the fixture and for initial validation. Second, the drop test was performed to verify the final design.

Theoretical Analysis

The following analysis was used to determine the dimensions and materials to use in designing the fixture. Consider a rod of cross-sectional area, A, and elastic modulus, E, in uniaxial compression.

Figure 12 - Stiffness Analysis of Elastic Body

Using Hooke’s law on the rod shown in figure 1, the following equations can be derived.

(1)

(2)


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At impact, the kinetic energy of the drop mass will be converted to potential (strain) energy in the fixture. The worst case scenario is that no energy is dissipated during the collision. The following equations assume no energy dissipation and relate the kinetic energy of the drop mass to deflection and stiffness of the fixture.

(6)

(7)

The peak force acting on the fixture and drop mass is related to the fixture deflection and stiffness by Hooke’s law. The peak acceleration on the drop mass is related to the peak force by Newton’s 2nd law of motion.

(8)

(9)

Using equations 2, 6, and 10 as criteria for design, it was determined that an all-metal fixture would not meet the requirements. An all-metal fixture (aluminum or steel) easily met the stiffness criteria. However, from equation 2, it was determined that the max stress in the fixture was above the yield stress for steel. Also, the peak acceleration ranged from 30000 G’s to 10000 G’s, depending on the design.

Now consider two springs in series; the springs can be replaced by an equivalent spring that matches the overall stiffness of the spring system. The following equation can be used to find the equivalent stiffness of two springs in series.

(3)

(4)

(5)


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(10)

This equation was developed so a less-stiff mat could be placed underneath the stiff metal fixture. With this design, an acceptable design was found with an equivalent stiffness of

65.2 that limited the peak acceleration to 1500 G’s.

Final Design

• Metal Fixture – See section 4.2 for dimensions 1. Material: 6061 Aluminum 2. Stiffness: 58000

The image below shows the final design of the drop test fixture from the 3D CAD package Pro/Engineer. See the caption below the image for a legend to decipher the color coding of parts in assembly.

Figure 13 – 3D CAD Image of Drop Test Fixture, Side Plates – Grey, Base – Green, Rubber – Blue

• Mat

1. Material: Natural Rubber 2. Dimensions: 4.5”x8”x1” 3. Stiffness: 65.2


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Experimental Validation

The fixture design was evaluated by examining the two sub-requirements that constrained the stiffness of the fixture.

1. The fixture does not deflect more than 0.005 inches during the isolator deflection period. This sub-requirement was evaluated by examining the high-speed video of the drop test.

2. The peak acceleration of the drop mass is less than 6000 G’s. This sub-requirement was evaluated by an accelerometer mounted to the drop mass.

See appendix 3.3.2 for drop test procedure.

Equipment

MTS Monterey Impac (Drop Test) – 170 pound mass constrained to vertical direction by means of two 16 foot cylindrical rods.

PCB Piezotronics Accelerometer – Model #: 305A05, Serial #: 8699, Nominal Range: 2500 G’s

Nicolet Odyssey Data Acquisition – Sample Rate: 50 KHz, Low Pass Filter: 12.5 KHz, Used to acquire data from accelerometer.

Photron Fastcam SA1.1 675K-M1 – Frame Rate: 3000 Hz, High-speed camera used to view deflection of fixture during drop test.


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Experimental Results

The deflection of the fixture during the isolator deflection period was evaluated using software (Photron Fastcam Viewer) provided by the manufacturer of the high-speed camera. The position of a single pixel on the fixture was followed during the isolator deflection period to determine if the fixture deflected more than 0.005”. Below are pictures of the fixture before impact and during the isolator deflection period.

Figure 14 - Drop Test Fixture and Drop Mass before 13 ft/s Impact


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Figure 15 - Drop Test Fixture and Drop Mass after 13 ft/s Impact

From the Photron software program, it was determined that 1 inch on the fixture was equal to 54 pixels (a position resolution of 0.0185”). By analyzing figures 3 and 4, the fixture deflected the width of one pixel (0.0185 ± 0.009”) with an impact velocity of 13 ft/s. However, this measurement is very imprecise considering the measuring increment is nearly four times the deflection requirement.

An alternative method to analyzing the deflection of the drop test fixture was done by performing the drop test with and without the fixture. This test was allowed by BAE test technicians, despite our concern of breaking equipment. The technicians wanted to test the accelerometers to their fullest, and this was a great chance to do so. The test was setup following the normal procedure, but with the isolator sitting on the ground, not on the fixture. Comparing the results of this test with the results of another test at the same velocity allows one to decipher any effect the fixture has on the results. The calculated damping forces for tests with and without the fixture are shown below.


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Figure 16 - Damping Force for Drop Test at 13 ft/s

The damping forces from figure 5 show that the results are very consistent. This consistency shows that the drop test fixture does not significantly deflect.

The peak acceleration acting on the drop mass was measured by an accelerometer mounted to the top of the drop mass. The measured acceleration for a 13 ft/s impact is shown in the following plot.


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Figure 17 - Acceleration of Drop Mass during 13 ft/s Impact

From figure 6, it can be seen that the peak acceleration is very close to the theoretical peak acceleration of 1500 G’s.

Discussion

The drop test fixture was designed with theoretical calculations to ensure certain requirements were met. The predicted peak acceleration of the drop mass was 1484 g’s. The experimental validation of this requirement found the peak acceleration to be slightly less than the predicted acceleration and well less than the upper limit on acceleration. The predicted deflection of the fixture was 0.0046”. Using the high-speed camera, the measured fixture deflection was more than the required deflection. However, the large uncertainty in this measurement supersedes any pass/fail indication that this measurement provide. A more precise measurement of fixture deflection is required to validate this requirement. The test results for tests with and without the drop test fixture were within 1 lbs of each (once the impact oscillations stabilized), which shows the fixture likely meets the stiffness requirement. Also, by looking at the correlation of isolator damping between the MTS ramp and drop tests, it appears that the fixture deflection had little influence on the results of the tests. Consequently, the drop test fixture meets the stiffness criteria for this design.

Vol. 2 3.1.5 Evaluation of Ansys Isolator Model

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3.1.5 Design Requirement 5: ANSYS Isolator Model - Drop Test

Simulation

Introduction Transient Finite Element Analysis (FEA) can model a shock isolation system once the dynamic characteristics of a shock isolator are known. A FEA model that is built using empirical test data will be valid within the range of displacements and velocities for which the test data was collected on the isolator. The model can be extrapolated outside this empirical data range; however, the results may not be valid. In order to characterize an isolator using transient FEA, a number of simplifying assumptions should be made. The FEA model built by the shock team was comprised of uncoupled 1-D approximations of the isolators. A 1-D tension and compression model was constructed first. A second model for the isolator in shear was also created. The system was modeled using ANSYS classic and comprised of spring and damper elements. The model was successfully constructed and tested using the empirical results of the MTS and Drop test. In a test comparison between the MTS data and an ANSYS generated model generally fits within 95% prediction interval of the MTS data as shown in figure 12.

Equipment The following programs were used to analyze data or perform the Transient FEA calculation.

• ANSYS classic 11.0 release (Student Edition) • Matlab 7.6.0 (R2008a) • Microsoft Excel 2008

Methods The following methods outline how an ANSYS model is constructed after empirical data is collected. This section will cover empirical data conversion, element types, configuring the model, solving the model, confirming the solution, and shock event modeling.

Converting empirical data:

The test data generated by Matlab program will produce the outputs needed to create and specify the constants for the ANSYS model. The first task in processing the data is to decide which units you will use in ANSYS and convert all data into these. ANSYS classic does not keep


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track of the units you are using. This means that the user must keep track of all units though all modeling. Careful documentation of your input values and units though out building the model are very important when justifying that the solution at the end is valid. To simplify this job, the SHOCK team elected to convert the empirical data to all SI units.

The first set of data to consider is the spring-constant –deflection curve table. The data set should be converted into a force- deflection table with the relationship shown in equation 1.

Equation 1: Spring force is a function of the spring constant time displacement.

The next data sets to consider are the damping force outputs. With all of the damping values the various constant velocities and displacements, an understanding to the prominent type of damping should be inferred. As stated in volume 1 of the report in section 3.2.2, the main types of damping are viscous, frictional, and structural damping. Each damping type takes a different form. In viscous damping, the damping force is velocity dependent. The damping force in a nonlinear form is listed in equation 2.

Equation 2: Nonlinear viscous damping force.

Frictional damping is velocity independent and can be a function of displacement. Frictional damping can be found in the form shown in equation 3.

Equation 3: Damping as a function of displacement.

Hysteretic damping is a frequency domain phenomenon. In shock event modeling we have assumed that frequency dependent damping is unimportant since we are most concerned with modeling the damping of a shock event. Under this assumption, we opted not to test the isolator in the frequency domain. My results do not include this type of damping. However, if this mode of damping was deemed important, the COMBIN39 element listed in the elements section could model the damping force.

After the damping data is analyzed a number of analytical functions should be created to model the damping. In the SHOCK groups’ case, the damping was demonstrated to be entirely caused by frictional damping.

In compression, the damping was found to have a linear relationship with displacement. The damping in tension was accurately fit with a third order polynomial. The third order polynomial


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was then broken into three parts. Each part was then modeled with a linear approximations as shown in figures 1 and 2.

Figure 1: Frictional Damping in compression as a function of displacement with Excel linear regression line of best fit.

Figure 2: Frictional Damping in tension as a function of displacement approximated by three linear functions.

y = 4831.1x - 25.482R² = 0.974

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-80

-70

-60

-50

-40

-30

-20

-10

0

-0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0

Forc

e (N

)

Displacement (m)

Frictional damping in compression

Damping force

Linear (Damping force)

y = 10331x - 31.222R² = 0.9875

y = -4262.5x + 66.337R² = 0.9939

y = -1347x + 43.683R² = 0.8584

0

5

10

15

20

25

30

35

40

0 0.002 0.004 0.006 0.008 0.01 0.012

Forc

e (N

)

Displacement (m)

Frictional damping in tension

Damping part1

Damping part 2

Damping part 3

Linear (Damping part1)

Linear (Damping part 2)

Linear (Damping part 3)


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Element selection

There are many types of elements available in ANSYS transient analysis. The SHOCK team model used the combination class of elements which are the spring and damper elements and a mass element for modeling a shock event.

1. In order to access these elements you must first select the type of modeling. Under the ANSYS main menu Preferences Check the structural and h-method boxes.

2. In the Main menu open Preprocesser Element Type Add Select COMBIN39, COMBIN37, and MASS21 elements.

3. With the element types selected, the next step is to specify the key options and the real constants. These options are how the spring and damping forces adjusted to approximate the empirical data.

Summary of the COMBIN39, COMBIN37, and MASS21 and their respective options and examples from our data analysis will be given in the next section.

COMBIN37 element: Non linear damping.

Figure 3: Pictorial representation of the COMBIN37 element.

The nonlinear damping can be added to the element COMBIN37 as a function of the displacement, the velocity and the acceleration. Equation 4 is used at each time step to calculate the damping coefficient.

Equation 4: function that recalculates RVMOD at each subset.

Where RVMOD is the modified value of an input real constant (a real constant could be the damping coefficient or sliding force in our case as shown in K9 in figure 4) value


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RVAL (the initial condition), C1 through C4 are other real constants, and CPAR is the control parameter. (Note that the COMBIN37 can be used for temp and rotational systems as in the example below.) CPAR can be defined as the difference between nodes, the first time derivative, second time derivative, etc.

The COMBIN37 element is a one Degree Of Freedom (DOF) model. This will limit our ability to tie in the shear model in x-direction and build a two DOF model. The COMBIN37 element is still functional because it will give us the greatest ability to model all types of damping as a function of displacement and/or velocity. Other benefits are that you can turn the elements on and off depending on the position of node 2. This allows a piece wise addition of elements and allows for a complex modeling of the damping force.


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Figure 4: COMBIN37 key options.

Figure 5: COMBIN37 real constants.

COMBIN39 Element: Non linear spring

The COMBIN39 allows for twenty data points of force – deflection information to be entered by selecting K6 in the key options box to reference a “Force-delf table” shown in Figure 5. The Force deflection table the Shock team was defined in the real constant section and is shown in Figure 6. The COMBIN39 element also allows for the possibility of hysteresis modeling through the use of key options K1 and K2. The hysteresis is modeled by declaring whether the spring is conservative, i.e. returns on the same force-deflection path of the extension or non-conservative, meaning it follows a separate force-deflection path during the return to zero deflection.


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Figure 5: COMBIN39 key options.

Figure 6: SHOCK group example of the COMBIN39 real constant force deflection table. Units for deflection and force are (m) and (N) respectively.


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Mass21 element:

The MASS21 element is only necessary when conducting shock event simulations. The mass is assigned to a node and given a scalar value. The mass the team has selected to use is the MASS21 element. Figures 7 and 8 show the Shock groups mass configuration.

Figure 7: MASS21 key options.

Figure 8: MASS21 Real constants.


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Modeling and defining nodes:

The nodes of the system must be added to the system for the elements to be added between them. To add nodes: Go to the ANSYS main menu Preprocessor Modeling Create Nodes.

The 1-D model will require two nodes to be placed. For visual purposes the nodes have been placed with node two vertically higher then node 1. The node, elements and constraints have been added figure 9 as a representation of the model on the ANSYS classic screen. In the actual model, nodes 1 and 2 are modeled to be coincident for simplicity. In figure 9, node 2 is constrained in the x direction but is free to move in vertical direction.

Figure 9: Element representation in ANSYS with DOF constraints.

Once a model is created, an important step is to verify that all of the information about the elements, nodes, displacements, and initial conditions are properly set. This check will allow for verification of the constants used in the simulations and hopefully lead you to identify issues with your models before the simulations are run and diagnose problems that appear after. Figure 10 is a common list command that lists the element number, the type of element, the associated real constants, and nodes. Using this information, the SHOCK team was able to confirm the elements were properly set. Elements 1 - 6 were COMBIN37 damping elements. Element 7 was a COMBIN39 nonlinear spring. Element 8 was a MASS21 element.

MASS21 element

Node 2

Node 1

1 – COMBIN39 element

5 – COMBIN37 elements

X-direction constraints

Y-direction constraints


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Figure 10: Listing of element information from the ELIST command.

Solution Controls

After you model is confirmed, it can be solved. A panel under the ANSYS main menu Solution Sol’n Controls allows you can define the length of time for the analysis and the number of time steps to be preformed. The SHOCK team analysis commonly specified 300 substeps to be used. At each substep, information on the system is recorded to a data file. In our analysis, three hundred substeps has been a fair balance between the number of data points and the length of time needed to generate a solution.

To begin the solution click on SolveCurrent LS. A normal solution will take between two and ten minutes for our simplified model.


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Once the solution is complete a time analysis can be used to visualize the data collected and export it as a comma separated data text file. The data files can then be imported to Matlab and analyzed for how well they conform to the empirical results. If the ANSYS model is not in compliance with the empirical data, changes to the models constants should be iterated until the model successfully models the isolators characteristics over the range of data collected.

Confirming the solution

The first step in confirming your solution is to prove that elements you have defined in your model are functioning as expected. This is necessary to show that each element is producing the value specified. A number of issues can arise from using non-linear elements. When an element also has the ability to turn on and off, it is important to confirm that a mistake in the on and off values did not occur. In the SHOCK teams’ model, the damping was tested in from the upper to lower deflection limits of 0.012 m (0.5 in) and -0.012 m (-0.5 in). Figure 11 shows the results of the test that was completed in both directions. The graph shows the displacement dependent damping caused by the COMBIN37 elements.

Figure 11: Damping element performance test. Green line goes from -0.012 to 0.012 m.

Displacement (m)

Force (N)


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Shock event modeling

Modeling a shock event is possible once the model is confirmed to function properly. An initial velocity input or a forcing function can be defined and be applied to the mass at node two. Once the system is solved, the velocities and displacements should be checked to verify that the model stayed within the range of empirically collected data. The model should then be able to show the acceleration of node two and the eventual dissipation of movement by the damping forces.

Results

The result of our model and our procedure can be confirmed for the test case of constant velocity inputs. The ANSYS generated model conforms to within the 95% confidence interval of the empirically MTS force data. This result was found using the iterative method of changing the ANSYS model to fit the Empirical data sets with higher accuracy. Figure 12 shows the test case for tension and compression and how the ANSYS model conformed within the 95% confidence interval of the MTS test.

Figure 12: Empirical MTS data vs. ANSYS data with check 95% confidence interval check.

-0.01 -0.005 0 0.005 0.01

-1000

-500

0

500

Displacement (m)

Forc

e (N

)

Empirical Data vs. ANSYS model results constructed using Empirical Data: Test at a constant velocity of 0.27 m/s (0.9 ft/s)

Empirical MTS dataEmpirical MTS dataANSYS solution95% confidence interval of MTS data95% confidence interval of MTS data95% confidence interval of MTS data95% confidence interval of MTS data


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A further test of a shock event simulation demonstrates that our simulations are limited to within the range of tested velocities. Since a drop test fixture was not developed to test in the 1-4 m/s range, we do not have the proper data validate a model at full speed in tension. A valid shock event model for the tension and compression of the isolator is valid below velocities of 1 m/s and within the test deflection range. A valid test would have to vary the mass attached to node two and the initial velocity to stay within these ranges.

Discussion

The inability for our shock event model to be valid in high velocity tension events is not a downfall of this report. The methods outlined in our project demonstrate the viability of extracting spring and damping constants using a drop test apparatuses. In our design selection, various methods and fixture concepts to test isolator damping properties in tension using a drop test were developed. Due to time constraints the SHOCK team focused on proving that accurate and meaningful damping properties could be extracted. BAE would be tasked with creating a drop test that functions in tension and shear.

This knowledge in hand that the drop test is a viable option, another group or BAE engineer could be tasked with creating a fixture that could be used to collect the high velocity tension damping.

The use of ANSYS to solve transient models came with its share of difficulties. Entering in the information using ANSYS classic demanded the attention of a SHOCK team group member for a majority of the semester. The difficulty in constructing a model that functions correctly lead to difficult attempt to ascend the ANSYS learning curve by building a model and learning along the way.

In the end, the use of a transient FEA code is necessary to model a larger, more complex systems built of many isolators to demonstrate the larger effect. As computer power continues to increase it is important to understand both the ability of a FEA modeling to approximate a real events while also accounting for the inherent limitations imposed by the model.


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3.2 Cost Analysis

This section of the report will describe the cost of our project. The bill of materials from

the previous section totals the projected cost for materials only. In this section, other factors

will be considered including labor and cost analysis.

The MTS 810 tensile test machine test procedure takes between 1-3 hours depending

on how many different test runs are desired. For this test procedure only one technician needs

to be present and zero engineers need to be present. The MTS Monterey Impac Drop test takes

between 1-3 hours depending on how many different velocities are tested and how many trials

are desired. For this procedure 2 technicians need to be present and 1 engineer needs to be

present. The engineer needs to be present to qualify and verify the safety of each test trial. 2

technicians are needed if high speed video is desired, otherwise only 1 technician is needed to

operate the Odyssey data acquisition device and the Monterey Impac Drop test.

Below is a table listing the total cost of each test including parts and labor. In terms of

labor costs it is assumed that technicians get paid $24 per hour and engineers get paid $50 per

hour. This can be altered once actual salaries are known, but for the purposes for this cost

analysis these numbers are sufficient.

MTS 810 Tensile Test Monterey Impac Drop Test

Cost of Test Fixture $24.95 $151.25

Technicians needed 1 2

Engineers needed 0 1

Time needed (hours) 3 3

Cost of Labor $72 $194

Total Cost for Test $96.95 345.25

The numbers given for the total cost should be perceived as a rough estimate. While

the cost of the test fixture is accurate to what was paid, the given salaries for technicians and

Vol. 2 3.2 Cost Analysis

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engineers could be false. In addition, the time needed to run each test is vastly proportional to

the amount of data that is desired. Many tests could be run and multiple isolators that would

increase the time needed to over 40 hours. The purpose of the above chart is to compare the

costs of the MTS 810 and the Monterey Impac test procedures.

Sales potential is not applicable for this subject; however, cost analysis can be used to

explain how money is saved by doing these tests. The purpose of these tests is to generate

sufficient data to accurately characterize an elastomeric isolator for the purpose of generating a

finite element analysis model. Once enough testing has been done a particular series of

isolators, an accurate model is created and future testing can be done computationally. By

doing several tests on a particular series of an isolator the company is saving money by avoiding

the need to individually test every isolator they use. Further testing can be done solely by one

engineer by means of the finite element analysis model instead of using several technicians

spending countless hours individually testing every isolator.

Ultimately, generating finite element analysis models of elastomeric isolators will be

beneficial to the company because it prevents the need to spend time and money on testing

each isolator individually.

3.3 Environmental Impact Statement

Purpose

The end product of the SHOCK teams’ effort was a laboratory procedure to determine

the stiffness and damping of a shock isolator. The value added by our procedure is the accurate

model of an isolator that can be built and tested using Finite Element Analysis (FEA) computer

simulations. The accurate model of the isolator in a FEA code means that a subassembly

comprised of many isolators can be designed, tested, and analyzed in a computer. Performing

an accurate computer simulation will save on development time and materials. Only a final test

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will be needed to confirm the computer models results. This will lead to a direct savings in

materials that would be used in an iterative design and testing scenario.

Impact on the environment

The design will have environmental impact in two main ways. The first will be that the

isolators and the systems they are protecting will survive large shock events, leading to an

increased life expectancy of the isolator and the equipment. The second will be by reducing the

amount of testing needed to fulfill the Military shock test specification: MIL-S-901D for navel

applications.

Within the test document, a large structure shock event test for components of 7500 lb

weight and larger must be certified using heavy weight test using a floating shock platform.

Reducing the number of explosive shots will provide a direct impact on the water quality and

marine life living in the blast area.

Alternatives to design

An alternative to the current testing of full scale components using heavy weight test

would be to test subassemblies using medium and light weight drop hammers. The hammers

are much better from a cost and environmental point of view. This will lead to a near guarantee

of success on the first attempt using a heavy shock test.

Since our design is a unique set of fixtures that are made of aluminum and rubber, our

direct impact on the environment is by utilizing two types of machines that are already owned

by BAE systems: a MTS machine and Drop test hammer. We are therefore making the best use

of equipment available to design a test procedure that will require minimum capital investment

to gain results.

Discussion

The greatest cost and time savings in designing a complex system can be realized by

creating a comprehensive model of the assembly. As new computer simulation programs

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become available and processing power a large shift in resources to comprehensive computer

past analysis will be demanded. Providing an accurate way to pass in the boundary conditions

of the materials will provide the more accurate results.

3.4 Regulatory and Safety Considerations

This section of the report will cover the regulations and safety procedures that need to

be considered when performing the two shock tests. During the MTS 810 shock test two safety

hazards were addressed. First, everyone in the lab is required to wear safety glasses. OSHA has

regulations that state that it is the employer’s responsibility to ensure that all employees have

access to and are using safety glasses. This regulation is held at BAE. There are many locations

throughout the facility that provide new protective safety glasses. In addition, there are signs

and warning labels stating which areas in the facility require which personal protective

equipment. An employee is not allowed to be in a designated area without the proper safety

equipment. For full OSHA regulations see OSHA 1910.133. The second safety concern that was

addressed in the MTS 810 lab was protection against flying objects. A protective clear barrier

was placed in front of the MTS 810 machine prior to testing. This barrier would protect anyone

in the lab incase a failure occurs and small bits of metal go flying.

For the Monterey Impac drop test there were several different safety precautions. First,

the drop test was located in an area which required steel-toed shoes, safety glasses and hearing

protection (ear plugs and sound protective headphones.) OSHA regulation 1910.132 states that

“The employer shall assess the workplace to determine if hazards are present, or are likely to

be present, which necessitate the use of personal protective equipment (PPE). If such hazards

are present, or likely to be present, the employer shall: Select, and have each affected

employee use, the types of PPE that will protect the affected employee from the hazards

identified in the hazard assessment.” This includes the use of steel-toed shoes. Again, BAE

follows these regulations by providing its employees with steel-toe shoe covers. A qualified

safety engineer was also present during the testing to ensure that everyone was wearing the

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proper protective gear. Finally, a similar clear barricade was placed in front of the drop test to

prevent projectiles from striking anyone nearby.

4 Additional Material

4.1 Data Analysis

Introduction This paper will fully explain the data analysis methods for three tests: MTS stiffness, MTS damping, and the drop test. An overview of filtering will first be presented, since this technique is implemented in the data analysis for each of the tests. The data was filtered to remove unwanted noise and correspondingly, simplify the data analysis. The first attempt at filtering the data was with IIR (infinite impulse response) filters. These filters were quickly abandoned, because the amount of phase delay (or time delay in the time domain) was dependent on the frequency of the input signal. Most of the data from these experiments contain noise, and the frequency of this noise varies with time. Consequently, the phase delay from the IIR filter may, unknowingly, vary along the length of the data set. To solve the phase delay problem, the filter type was changed from IIR to FIR (finite impulse response). A major consequence of this change was that the filter order had to increase from one or two for the IIR filter to 20+ for the FIR filter. Filter Design Steps

1. Examine the data and calculate the noise frequencies you would like to remove. 2. Calculate the filter coefficients

a. Use Matlab’s “Filter Design Toolbox” b. Use the Java Applet on the following website

http://www.dsptutor.freeuk.com/FIRFilterDesign/FIRFilterDesign.html 3. Implement filter into Matlab script

a. Define array (call array ‘b’)with all of the filter coefficients b. filtered_data = filter(b,1,data);

Comments: With FIR filters, the filter is entirely forward looking (no feedback) and so the number “1” in the above function makes this designation.

http://www.dsptutor.freeuk.com/FIRFilterDesign/FIRFilterDesign.html�

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4. Since the filter delays the data, the filtered data arrays must be realigned with their previous values. This is accomplished by shifting the cells in the array until the filtered data is aligned with the original data.

5. Examine the filtered data and decide if the filter removed the intended noise. Make sure to inspect the data closely. The filtered data should be centered on the original data, if not, the cutoff frequency should be increased or the filter order decreased.

6. If filtered data passes step 5, continue with data analysis, otherwise see step 2.

MTS Stiffness Test 1. Open and run the Matlab script “Step_Displacement_Main.m” – this script is called the

“step_main” function hereafter. 2. A prompt will ask the user if they want to analyze a data file or a folder of data files. If

“Single File” go to 3. If “Entire Folder” go to 4. 3. If a single file is analyzed

a. A prompt will ask user to select a data file to analyze. i. The program currently looks for “.dat” files. The file type can be changed

in the Matlab script if necessary. b. A plot will appear, similar to the one shown below. The green vertical lines show

the region where the stiffness coefficient was calculated. The region is selected by looking at the peak-to-peak value of the stiffness and finding where the value drops below a specific criterion. The criterion can be changed in the heading of the step_main function.

Figure 18 – Step Displacement – Plot from Analyzing a Single File


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c. A dialog will ask the user to select “OK” when they are done looking at the plot. d. A prompt will appear, asking the user if they want to analyze another file. If

“Yes” go to 3a. If “No” go to 3e. e. A prompt will appear, asking the user if they want to save the analysis results of

the last file. 4. If a folder of files is analyzed

a. A prompt will ask user to select a folder to analyze. i. The program currently looks for “.dat” files. The file type can be changed

in the Matlab script if necessary. b. A prompt will appear, asking the user if they want to save the analysis results. c. After several seconds, a plot will appear, similar to the plot below.

Figure 19 – Step Displacement – Plot from Analyzing an Entire Folder

MTS Ramp Test 1. Open and run the Matlab script “Ramp_Displacement_Main.m” – this script is called the

“ramp_main” function hereafter. 2. A prompt will ask the user if they want to analyze a data file or a folder of data files. If

“Single File” go to 3. If “Entire Folder” go to 4. 3. If a single file is analyzed

a. A prompt will ask user to select an analysis file from the step displacement (stiffness) test. This is the analysis file that was created when an entire folder was analyzed.

b. A prompt will ask user to select a data file to analyze.


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i. The program currently looks for “.dat” files. The file type can be changed in the Matlab script if necessary.

c. A plot will appear, similar to the one shown below. The blue vertical lines show the region where the damping force was calculated. The region is selected by looking at the magnitudes of the velocity and acceleration and finding where their values drop below specific criterion. The criterion can be changed in the heading of the ramp_main function.

Figure 20 – Ramp Displacement – Plot from Analyzing a Single File

d. A dialog will ask the user to select “OK” when they are done looking at the plot. e. A prompt will appear, asking the user if they want to analyze another file. If

“Yes” go to 3a. If “No” go to 3e. f. A prompt will appear, asking the user if they want to save the analysis results of



b. A prompt will ask user to select a folder to analyze. i. The program currently looks for “.dat” files. The file type can be changed

in the Matlab script if necessary. c. After several seconds, a prompt will appear, asking the user if they want to save

the analysis results.


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d. A 3-dimensional plot will appear. The damping force will be plotted against displacement and input velocity. This plot is useful for examining the relationship between damping force and the two independent variables.

Drop Test

1. Open and run the Matlab script “Drop_Test_Main.m” – this script is called the “drop_main” function hereafter.

2. A prompt will ask the user if they want to analyze a data file or a folder of data files. If “Single File” go to 3. If “Entire Folder” go to 4.

3. If a single file is analyzed a. A prompt will ask user to select an analysis file from the step displacement

(stiffness) test. This is the analysis file that was created when an entire folder was analyzed.

b. A prompt will ask user to select a data file to analyze. i. The program currently looks for “.csv” files. The file type can be changed

in the Matlab script if necessary. c. A plot will appear, similar to the one shown below. The damping force is

calculated in the displacement region shown by the bottom graph. The settings for this can be changed in the heading of the drop_main function. The error bars shown on the damping force have an extra contribution than the previous analyses. The value that controls this extra uncertainty is can be controlled in the heading of the drop_main function.


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Figure 21 –Drop Test – Plot from Analyzing a Single File

d. A dialog will ask the user to select “OK” when they are done looking at the plot. e. A prompt will appear, asking the user if they want to analyze another file. If

“Yes” go to 3a. If “No” go to 3e. f. A prompt will appear, asking the user if they want to save the analysis results of



b. A prompt will ask user to select a folder to analyze. i. The program currently looks for “.csv” files. The file type can be changed

in the Matlab script if necessary. c. After several seconds, a prompt will appear, asking the user if they want to save

the analysis results. d. A 3-dimensional plot will appear. The damping force will be plotted against

displacement and input velocity. This plot is useful for examining the relationship between damping force and the two independent variables.

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4.2 MatLab Code

The following sections show the code used in the data analysis. The code is the analysis of the step displacement, ramp displacement, and drop test.

4.2.1 Step Displacement Code

clear close all % The variables below are declared in this main function and are used by % many different functions. It was helpful to have them as global % variables to reduce the number variables sent to a function. global x_mean k_mean time force position d N; %%% Important parameters for the calculation of the spring coefficient %%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Calculate spring constant after the average peak to peak spring % coefficient drops below this threshold ratio. % Ratio = delta(P2P)/range(p2p) start = 0.03; % Calculate spring coefficient with a specific number of samples n_sample = 180; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This program is separated into two sections by this IF statement. The % user can choose to process a single file or folder. % This button prompts the user to choose to process a single file or folder button = questdlg('Do you want to process a single file or entire folder?','Data Analysis','Single File','Folder','Cancel','Single File'); if strcmp(button,'Folder') % Locate the directory to import files directory = uigetdir('C:\Documents and Settings\Jim\My Documents\School\Senior Year\Spring 09\ME4054 - Senior Design\MTS Tests\Step Displacement Data'); % IF statement to see if user cancels "folder select" prompt if ~directory == 0 % Get the names of all DAT files in directory dirListing = dir(strcat(directory,'/*.dat'));

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% Initialize arrays to place spring coefficient calculated from each file k_mean = zeros(length(dirListing),1); x_mean = zeros(length(dirListing),1); % Loop through the files, open files, and analyze each one for d = 1:length(dirListing) % Check if file is actually a folder if ~dirListing(d).isdir % Use full path filename = fullfile(directory,dirListing(d).name); files(d) = cellstr(dirListing(d).name); % Retrieve information about file and place information in struct array struct = importdata(filename,'\t',5); % Place data from file in arrays time = struct.data(:,1); position = struct.data(:,2); force = struct.data(:,3); % Remove these variables to free memory. clear filename struct name path; % Find length of data arrays N = length(time); % Filter position and force data to remove high frequency % noise. See function for cutoff frequencies. filter_data(force,position,N); % This function finds the location where the data meets % stabilization criteria and then calculates spring % coefficient. k_spring_calc(start,n_sample); % Uncomment the following 3 lines of code to show plots for % each file in the folder. The "close all" command will % clear the plots after the "OK" button is pressed. %plot_data(force,position,time) %pause %close all end % if - (to check if file is actually a folder) end % for-loop (to cycle through all files in folder) % Sort spring coefficients calculated from all files in folder % The names of the files is also sorted in case this information % would like to be output to a text file. [x_mean,k_mean,files] = sort_xk(x_mean,k_mean,files);


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% Prompt for name and path to save analysis file. The file will % contain the spring coefficent and filename for each steady state position. [save_name,save_path] = uiputfile('*.txt','Save Step Displacement Analysis?','Step_Analysis.txt'); if ~save_name == 0 fid = fopen(fullfile(save_path,save_name), 'wt'); fprintf(fid,'Position(in)\tSpring_Coefficient(lbs/ft)\tFilename\n'); for i = 1:length(x_mean) y = [x_mean' ; k_mean']; fprintf(fid, ['%4f\t%4f\t"' char(files(i)) '"\n'],x_mean(i)',k_mean(i)'); end fclose(fid); end % Perform regression analysis on the calculated spring % coefficients. Compression uses linear fit. Tension and shear % use 3rd order polynomial fit. regress(x_mean,k_mean); end % if - (to check if folder select window is canceled) end % if - (to analyze data if 'folder' is selected) if strcmp(button,'Single File') % Put code in WHILE loop so user can analyze several files. % Initialize quit to 1, so WHILE loop runs at least once. quit = 1; while quit == 1; % Prompt user to select data file they would like to analyze. [name,path] = uigetfile('*.dat','Select Data File','C:\Documents and Settings\Jim\My Documents\School\Senior Year\Spring 09\ME4054 - Senior Design\MTS Tests\Step Displacement Data'); if ~name == 0 % Initialize counter variable to 1. This counter is only used % when an entire folder is processed. So the counter acts as a % dummy variable in this section of code. d = 1; % Retrieve information about file and place information in struct array filename = fullfile(path,name); struct = importdata(filename,'\t',5); files(d) = cellstr(name); % Place data from file in arrays


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time = struct.data(:,1); position = struct.data(:,2); force = struct.data(:,3); % Remove these variables to free memory. clear struct; % Find length of data arrays N = length(time); %Perform Fast-Fourier-Transform on data to find relative %magnitudes of noise frequencies %fft_data(force,N) % Filter position and force data to remove high frequency % noise. See function for cutoff frequencies. filter_data(force,position,N); % This function finds the location where the data meets % stabilization criteria and then calculates spring % coefficient. k_spring_calc(start,n_sample); % Plot data. plot_data(force,position,time,name) % This warning dialog is used to delay the question dialog % "questdlg". Warning dialogs are non-nodal windows, which % means the user can examine other windows without returning a % value to the dialog. uiwait(warndlg('Press "OK" when you are done')) % This dialog asks the user if they want to analyze another file. % The dialog is nodal, which means the user must answer "Yes" or % "No" before the window can be closed or another window can be % viewed. answer = questdlg('Analyze Another File?','Continue Analysis?','Yes','No','No'); if strcmp(answer,'No') quit = 0; end end end % Prompt for name and path to save analysis file. if ~name == 0 [save_name,save_path] = uiputfile('*.txt','Save Step Displacement Analysis?',['Analysis_', strrep(name,'.dat',''),'.txt']); if ~save_name == 0 fid = fopen(fullfile(save_path,save_name), 'wt'); y = [x_mean' ; k_mean']; fprintf(fid,'Position(in)\tForce(lbs)\n'); fprintf(fid, '%4f\t%4f\n', y); fclose(fid); end end


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end

function [x_mean,k_mean,files] = sort_xk(x_mean,k_mean,files) for i = 1:length(files) - 1 for j = i+1:length(files) if x_mean(i) > x_mean(j) temp_x = x_mean(i); x_mean(i) = x_mean(j); x_mean(j) = temp_x; temp_k = k_mean(i); k_mean(i) = k_mean(j); k_mean(j) = temp_k; temp_f = files(i); files(i) = files(j); files(j) = temp_f; end end end function regress(x_mean,k_mean) j = 0; k = 0; for i = 1:length(x_mean) if x_mean(i) < 0 j = j + 1; x_mean_comp(j) = x_mean(i); k_mean_comp(j) = k_mean(i); end if x_mean(i) > 0 k = k + 1; x_mean_tens(k) = x_mean(i); k_mean_tens(k) = k_mean(i); end end % Find range of spring coefficient data to scale plot k_upper = max(k_mean)*1.1; k_lower = min(k_mean)*0.9; % Find range of step displacements to scale plot x_upper = max(x_mean)*1.1; x_lower = min(x_mean)*0.9; figure if ~j==0


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[poly_comp,se_comp] = polyfit(x_mean_comp,k_mean_comp,1); [k_comp,sd_comp] = polyval(poly_comp,x_mean_comp,se_comp); k_comp_upper = k_comp + 1.96*sd_comp; k_comp_lower = k_comp - 1.96*sd_comp; plot(x_mean_comp,k_comp,'-k.','LineWidth',3) hold; plot(x_mean_comp,k_comp_lower,'--r',x_mean_comp,k_comp_upper,'--r') end if ~k==0 [poly_tens,se_tens] = polyfit(x_mean_tens,k_mean_tens,3); [k_tens,sd_tens] = polyval(poly_tens,x_mean_tens,se_tens); k_tens_upper = k_tens + 1.96*sd_tens; k_tens_lower = k_tens - 1.96*sd_tens; plot(x_mean_tens,k_tens,'-k.','LineWidth',3) if j==0 hold; end plot(x_mean_tens,k_tens_lower,'--r',x_mean_tens,k_tens_upper,'--r') end axis([x_lower x_upper k_lower k_upper]) xlabel('Displacement (inches)') ylabel('Stiffness (lbs/ft)') grid

function plot_data(force,position,time,name) global filtered_force_all filtered_position filtered_k_spring_all filtered_k_spring_high i_high i_low; N = length(time); % Find range of position data to scale plot x_upper = filtered_position(round(N*.6))*1.1; x_lower = filtered_position(round(N*.6))*0.9; if x_upper < x_lower temp = x_upper; x_upper = x_lower; x_lower = temp; end % Find range of force data to scale plot f_upper = filtered_force_all(round(N*.6))*1.1; f_lower = filtered_force_all(round(N*.6))*0.9; if f_upper < f_lower temp = f_upper;


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f_upper = f_lower; f_lower = temp; end % Find range of spring coefficient data to scale plot k_upper = filtered_k_spring_all(round(N*.6))*1.1; k_lower = filtered_k_spring_all(round(N*.6))*0.9; % Plot data figure subplot(3,1,1) plot(time,position,'r') hold; plot(time,filtered_position,'k','LineWidth',3); axis([0 1 x_lower x_upper]) xlabel('Time (seconds)') ylabel('Distance (inches)') legend('Original Position','Filtered Position') title(['File Name: ',name]) line([time(i_low) time(i_low)],[x_lower x_upper],'Color',[0 1 0],'LineWidth',3) line([time(i_high) time(i_high)],[x_lower x_upper],'Color',[0 1 0],'LineWidth',3) grid subplot(3,1,2) plot(time,force,'r'); hold; plot(time,filtered_force_all,'k','LineWidth',3); axis([0 1 f_lower f_upper]) xlabel('Time (seconds)') ylabel('Force (lbf)') legend('Original Force','Filtered Force') line([time(i_low) time(i_low)],[f_lower f_upper],'Color',[0 1 0],'LineWidth',3) line([time(i_high) time(i_high)],[f_lower f_upper],'Color',[0 1 0],'LineWidth',3) grid subplot(3,1,3) plot(time,filtered_k_spring_high,'r') hold; plot(time,filtered_k_spring_all,'k','LineWidth',3); axis([0.1 1 k_lower k_upper]) grid xlabel('Time (seconds)') ylabel('Stiffness (lbf/ft)') legend('60 Hz Cutoff Filtered Stiffness','10 Hz Cutoff Filtered Stiffness') line([time(i_low) time(i_low)],[k_lower k_upper],'Color',[0 1 0],'LineWidth',3) line([time(i_high) time(i_high)],[k_lower k_upper],'Color',[0 1 0],'LineWidth',3)

function k_spring_calc(start,n_sample)


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global x_mean k_mean N d force position filtered_force_high filtered_force_all filtered_position k_spring filtered_k_spring_all filtered_k_spring_high p2p_high i_high i_low; % Calculate spring coefficient from measured data. (lbs/ft) k_spring = 12.*force./position; % Calculate spring coefficient from filtered data. (lbs/ft) filtered_k_spring_high = 12.*filtered_force_high./filtered_position; filtered_k_spring_all = 12.*filtered_force_all./filtered_position; % Variables for max and min of sample. Initialize for use in WHILE loop p2p_high = 100*ones(N,1); % Initialize variables for use WHILE loop i = 2; % Start at 2 because loop uses previous data point in calculation temp_1 = zeros(n_sample,1); temp_3 = 0; temp_4 = 0; % Loop to calculate peak to peak of spring coefficient data as function of % time. Variable "start" is used as criteria for starting to calculate % spring coefficient. The calculation find the average from a series of % "n_sample" spring coefficients while ((p2p_high(i - 1) > start && i <= N - n_sample - 1) ) % Look ahead n_sample counter positions from counter i to calculate peak to peak for j = 1:n_sample temp_1(j) = filtered_k_spring_high(i + j - 2); end % Find max and min from the sample k_max_high = max(temp_1); k_min_high = min(temp_1); % Calculate the peak to peak of the sample then normalize by average % spring coefficient during the sample p2p_high(i) = abs(2*(k_max_high - k_min_high)/(k_max_high + k_min_high)); i = i + 1; end i_low = i - 1; i_high = (i - 1 + n_sample); % The following code simply calculated the average spring coefficient and % position, then outputs it to the array k_mean and x_mean for j = i_low:i_high; temp_3 = temp_3 + filtered_k_spring_all(j); temp_4 = temp_4 + filtered_position(j); end


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k_mean(d) = temp_3/n_sample; x_mean(d) = temp_4/n_sample;

function filter_data(force,position,N) global filtered_force_high filtered_force_all filtered_position; %FIR Filter %30 order, Passband = (0 to 50Hz), Stopband Attenuation = 21db, Transition %Bandwidth = 245 Hz. %See http://www.dsptutor.freeuk.com/FIRFilterDesign/FIRFilterDesign.html b(1)=.0181; b(2)=.0205; b(3)=.0229; b(4)=.0252; b(5)=.0275; b(6)=.0296; b(7)=.0316; b(8)=.0335; b(9)=.0352; b(10)=.0367; b(11)=.038; b(12)=.0391; b(13)=.04; b(14)=.0406; b(15)=.041; b(16)=.0411; b(17)=.041; b(18)=.0406; b(19)=.04; b(20)=.0391; b(21)=.038; b(22)=.0367; b(23)=.0352; b(24)=.0335; b(25)=.0316; b(26)=.0296; b(27)=.0275; b(28)=.0252; b(29)=.0229; b(30)=.0205; b(31)=.0181; %FIR Filter %200 order, Passband = (0 to 10Hz), Stopband Attenuation = 21db, Transition %Bandwidth = 37 Hz. %See http://www.dsptutor.freeuk.com/FIRFilterDesign/FIRFilterDesign.html c(1)=.0023; c(2)=.0024; c(3)=.0024; c(4)=.0025; c(5)=.0026; c(6)=.0026; c(7)=.0027; c(8)=.0028;


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c(9)=.0028; c(10)=.0029; c(11)=.003; c(12)=.003; c(13)=.0031; c(14)=.0031; c(15)=.0032; c(16)=.0033; c(17)=.0033; c(18)=.0034; c(19)=.0035; c(20)=.0035; c(21)=.0036; c(22)=.0036; c(23)=.0037; c(24)=.0038; c(25)=.0038; c(26)=.0039; c(27)=.004; c(28)=.004; c(29)=.0041; c(30)=.0041; c(31)=.0042; c(32)=.0043; c(33)=.0043; c(34)=.0044; c(35)=.0044; c(36)=.0045; c(37)=.0045; c(38)=.0046; c(39)=.0047; c(40)=.0047; c(41)=.0048; c(42)=.0048; c(43)=.0049; c(44)=.0049; c(45)=.005; c(46)=.005; c(47)=.0051; c(48)=.0051; c(49)=.0052; c(50)=.0052; c(51)=.0053; c(52)=.0053; c(53)=.0054; c(54)=.0054; c(55)=.0055; c(56)=.0055; c(57)=.0055; c(58)=.0056; c(59)=.0056; c(60)=.0057; c(61)=.0057; c(62)=.0058; c(63)=.0058; c(64)=.0058; c(65)=.0059;


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c(180)=.0036; c(181)=.0036; c(182)=.0035; c(183)=.0035; c(184)=.0034; c(185)=.0033; c(186)=.0033; c(187)=.0032; c(188)=.0031; c(189)=.0031; c(190)=.003; c(191)=.003; c(192)=.0029; c(193)=.0028; c(194)=.0028; c(195)=.0027; c(196)=.0026; c(197)=.0026; c(198)=.0025; c(199)=.0024; c(200)=.0024; c(201)=.0023; % Remove high-frequency noise from position and force data. filtered_position = filter(b,1,position); filtered_force_high = filter(b,1,force); % Remove oscillatory frequencies above 10 Hz from force data. filtered_force_all = filter(c,1,force); % FIR filters delay data by a fixed, calcuable time. The delay depends on % the filter order. High order filters delay signal more than low order % filters. offset_1 = round((length(c)-1)/(2)); offset_2 = round((length(b)-1)/(2)); % Modify position and force data to account for this time offset. for i = 1:N-offset_2 filtered_position(i) = filtered_position(i+offset_2); filtered_force_high(i) = filtered_force_high(i+offset_2); end for i = 1:N-offset_1 filtered_force_all(i) = filtered_force_all(i+offset_1); end function fft_data(force,N) % Create array for FFT. Ignore initial transient period of displacement force_fft_array = zeros(N-1000,1); for i = 1:N-1000 force_fft_array(i) = force(i + 800); end


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% Perform FFT on measured force data force_fft = abs(fft(force_fft_array,N-1000)); frequency = 0 : N - 1001; figure plot(frequency,force_fft,'k'); axis([0 1000 0 100]) xlabel('Frequency (Hz)') ylabel('Signal Amplitude')

4.2.2 Ramp Displacement Code

clear close all % The variables below are declared in this main function and are used by % many different functions. It was helpful to have them as global % variables to reduce the number variables sent to a function. global button force position time N analysis_path analysis_name; %%%%%% Important parameters for the calculation of the damping force %%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This variable sets the maximum acceleration (ft/sec^2) for which to allow % calculation of damping force. a_max = 5; % The velocity must be within this percentage of the maximum sample velocity % for which to allow calculation of damping force. v_min = 5; % The number of samples that meet the above criteria must be larger than the % following variable. n_min = 10; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This program is separated into two sections by this IF statement. The % user can choose to process a single file or folder. % This button prompts the user to choose to process a single file or folder button = questdlg('Do you want to process a single file or entire folder?','Data Analysis','Single File','Folder','Cancel','Single File'); if ~strcmp(button,'Cancel') [analysis_name,analysis_path] = uigetfile('*.txt','Select Step Displacement Analysis File'); if ~analysis_name==0 if strcmp(button,'Folder') %Locate the directory to import files directory = uigetdir;

Vol. 2 4.2.2 Ramp Displacement MatLab Code

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% IF statement to see if user cancels "folder select" prompt if ~directory == 0 % Get the names of all DAT files in directory dirListing = dir(strcat(directory,'/*.dat')); % Initialize array to place important data related to the % damping force. Damping data for each file in the folder % will be placed in this array. damping = zeros(1,4); % This variable is used to initialize concatenation of data % to be placed in "damping" array. state = 1; % Loop through the files, open files, and analyze each one for d = 1:length(dirListing) %msgbox(['Processing file ',num2str(d),' of ', num2str(length(dirListing))],'replace') % Check if file is actually a folder if ~dirListing(d).isdir % Use full path filename = fullfile(directory,dirListing(d).name); files(d) = cellstr(dirListing(d).name); % Retrieve information about file and place information in struct array struct = importdata(filename,'\t',5); % Place data from file in arrays time = struct.data(:,1); position = struct.data(:,2); force = struct.data(:,3); % Find length of data arrays N = length(time); % Filter position and force data to remove high frequency % noise. See function for cutoff frequencies. filter_ramp_data(N); % This function calculates the damping force. The % variables passed to this function are used as % criteria for the function to converge on a % solution. damp_temp = damping_calc(a_max,v_min,n_min); % The function "vertcat" does not work for empty % arrays, so the variable "state" is used to


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% reserve the concatenation of new data only if the % "damping" array has already been filled with % data. if length(damp_temp) >= n_min % Enter this IF statement to fill "damping" % with data for the first time. if state == 1 damping = damp_temp; state = 0; end % Enter this IF statement if "damping" already % has data in it if ~state == 1 damping = vertcat(damping,damp_temp); end end % IF - (to fill "damping" array) end % IF - (to check if file is actually a folder) end % FOR-loop (to cycle through all files in folder) % Create a 3D plot of damping force with respect to % deflection and velocity plot3(damping(:,1),damping(:,2),damping(:,3),'*') xlabel('Position (inches)') ylabel('Velocity (ft/sec)') zlabel('Damping Force (lbf)') grid % Prompt for name and path to save analysis file. The file will % contain the damping force, postion, velocity and filename % for each file that converges on a damping force solution. [save_name,save_path] = uiputfile('*.txt','Save Ramp Analysis?','Ramp_Analysis.txt'); if ~save_name == 0 fid = fopen(fullfile(save_path,save_name), 'wt'); fprintf(fid, 'Position(in)\tVelocity(ft/s)\tDamping_Force(lbf)\tUncertainty_Damping_Force(lbf)\n'); fprintf(fid, '%4f\t%4f\t%4f\t%4f\n' , damping'); fclose(fid); end end % if - (to check if folder select window is canceled) end % if - (to analyze data if 'folder' is selected) if strcmp(button,'Single File') quit = 1; while quit == 1; [name,path] = uigetfile('*.dat','Select Data File'); if ~name == 0


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% Initialize counter variable to 1. This counter is only used % when an entire folder is processed. So the counter acts as a % dummy variable in this section of code. d = 1; % Retrieve information about file and place information in struct array filename = fullfile(path,name); struct = importdata(filename,'\t',5); files(d) = cellstr(name); % Place data from file in arrays time = struct.data(:,1); position = struct.data(:,2); force = struct.data(:,3); % Find length of data arrays N = length(time); % Filter position and force data to remove high frequency % noise. See function for cutoff frequencies. filter_ramp_data(N); % This function calculates the damping force. The % variables passed to this function are used as % criteria for the function to converge on a % solution. [damping] = damping_calc(a_max,v_min,n_min); % Plot position, velocity, and force. These plots % allow user to visualize regions where damping is % calculated. plot_ramp_data(d,files) uiwait(warndlg('Press "OK" when you are done')) % This dialog asks the user if they want to analyze another file. % The dialog is nodal, which means the user must answer "Yes" or % "No" before the window can be closed or another window can be % viewed. answer = questdlg('Analyze Another File?','Continue Analysis?','Yes','No','No'); if strcmp(answer,'No') quit = 0; end end % IF - (to check if file select dialog is canceled) end % WHILE - (to check if user wants to continue analyzing single files) % Prompt for name and path to save analysis file. if ~name == 0


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[save_name,save_path] = uiputfile('*.txt','Save Ramp Analysis?',['Analysis_', strrep(name,'.dat',''),'.txt']); if ~save_name == 0 fid = fopen(fullfile(save_path,save_name), 'wt'); fprintf(fid, 'Position(in)\tVelocity(ft/s)\tDamping_Force(lbf)\tUncertainty_Damping_Force(lbf)\n'); fprintf(fid, '%4f\t%4f\t%4f\t%4f\n' , damping'); fclose(fid); end end end % IF (to check if "Single File" is selected) end % IF - (to check if folder select dialog is canceled) end % IF - (to check if "Single File or Folder" dialog is canceled)

function [f_spring,m_spring] = regress_ramp(x_array) global analysis_path analysis_name; % Retrieve information about file and place information in struct array analysis_file = fullfile(analysis_path,analysis_name); struct = importdata(analysis_file,'\t'); % Place data from file in arrays x_mean = struct(:,1); k_mean = struct(:,2); j = 0; k = 0; for i = 1:length(x_mean) if x_mean(i) < 0 j = j + 1; x_mean_comp(j) = x_mean(i); k_mean_comp(j) = k_mean(i); end if x_mean(i) > 0 k = k + 1; x_mean_tens(k) = x_mean(i); k_mean_tens(k) = k_mean(i); end end if ~j == 0 [poly_comp,se_comp] = polyfit(x_mean_comp,k_mean_comp,1); end if ~k == 0 [poly_tens,se_tens] = polyfit(x_mean_tens,k_mean_tens,3);


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end if mean(x_array) > 0 [k_tens,sd_tens] = polyval(poly_tens,x_array,se_tens); f_spring = k_tens.*x_array./12; m_spring = 1.96*sd_tens.*x_array./12; else [k_comp,sd_comp] = polyval(poly_comp,x_array,se_comp); f_spring = k_comp.*x_array./12; m_spring = 1.96*sd_comp.*x_array./12; end function plot_ramp_data(d,files) global force position time velocity filtered_velocity acceleration filtered_force filtered_position filtered_acceleration i_low i_high; % Find range of position data to scale plot x_upper = max(filtered_position); x_lower = min(filtered_position); if x_upper < 0 x_upper = x_upper*.9; else x_upper = x_upper*1.1; end if x_lower < 0 x_lower = x_lower*1.1; else x_lower = x_lower*0.9; end % % Find range of force data to scale plot f_upper = max(filtered_force); f_lower = min(filtered_force); if f_upper < 0 f_upper = f_upper*.9; else f_upper = f_upper*1.1; end if f_lower < 0 f_lower = f_lower*1.1; else f_lower = f_lower*0.9; end % Find range of velcoity data to scale plot v_upper = max(filtered_velocity); v_lower = min(filtered_velocity); if v_upper < 0


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v_upper = v_upper*.9; else v_upper = v_upper*1.1; end if v_lower < 0 v_lower = v_lower*1.1; else v_lower = v_lower*0.9; end % Find range of acceleration data to scale plot a_upper = max(filtered_acceleration); a_lower = min(filtered_acceleration); if a_upper < 0 a_upper = a_upper*.9; else a_upper = a_upper*1.1; end if a_lower < 0 a_lower = a_lower*1.1; else a_lower = a_lower*0.9; end % Plot data subplot(4,2,2) plot(time,position,'r',time,filtered_position,'k'); axis([0 0.2 x_lower x_upper]) xlabel('Time (seconds)') ylabel('Distance (inches)') legend('Original Position','Filtered Position',4) line([time(i_low) time(i_low)],[x_lower x_upper],'LineWidth',2) line([time(i_high) time(i_high)],[x_lower x_upper],'LineWidth',2) title(['Name of data file: ' files(d)]) subplot(4,2,4) plot(time,force,'r',time,filtered_force,'k'); axis([0 0.2 f_lower f_upper]) xlabel('Time (seconds)') ylabel('Force (lbf)') grid legend('Original Force','Filtered Force',4) line([time(i_low) time(i_low)],[f_lower f_upper],'LineWidth',2) line([time(i_high) time(i_high)],[f_lower f_upper],'LineWidth',2) subplot(4,2,6) plot(time,velocity,'r',time,filtered_velocity,'k'); axis([0 0.2 v_lower v_upper]) grid xlabel('Time (seconds)') ylabel('Velocity (ft/sec)') legend('Original Velocity','Filtered Velocity',4)


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line([time(i_low) time(i_low)],[v_lower v_upper],'LineWidth',2) line([time(i_high) time(i_high)],[v_lower v_upper],'LineWidth',2) subplot(4,2,8) plot(time,acceleration,'y',time,filtered_acceleration,'k'); axis([0 0.2 a_lower a_upper]) grid xlabel('Time (seconds)') ylabel('Acceleration(ft/sec^2)') legend('Original Acceleration','Filtered Acceleration',4) line([time(i_low) time(i_low)],[a_lower a_upper],'LineWidth',2) line([time(i_high) time(i_high)],[a_lower a_upper],'LineWidth',2) function filter_ramp_data(N) global velocity filtered_velocity filtered_position filtered_force time position force acceleration filtered_acceleration; % Initialize velocity and acceleration arrays. velocity = zeros(N,1); acceleration = zeros(N,1); %FIR Filter %30 order, Passband = (0 to 50Hz), Stopband Attenuation = 21db, Transition %Bandwidth = 245 Hz. %See http://www.dsptutor.freeuk.com/FIRFilterDesign/FIRFilterDesign.html b(1)=.0181; b(2)=.0205; b(3)=.0229; b(4)=.0252; b(5)=.0275; b(6)=.0296; b(7)=.0316; b(8)=.0335; b(9)=.0352; b(10)=.0367; b(11)=.038; b(12)=.0391; b(13)=.04; b(14)=.0406; b(15)=.041; b(16)=.0411; b(17)=.041; b(18)=.0406; b(19)=.04; b(20)=.0391; b(21)=.038; b(22)=.0367; b(23)=.0352; b(24)=.0335; b(25)=.0316; b(26)=.0296; b(27)=.0275; b(28)=.0252; b(29)=.0229; b(30)=.0205;


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b(31)=.0181; %FIR Filter %20 order, Passband = (0 to 300Hz), Stopband Attenuation = 21db, Transition %Bandwidth = 368 Hz. %See http://www.dsptutor.freeuk.com/FIRFilterDesign/FIRFilterDesign.html c(1) = -0.01740681; c(2) = -0.008708606; c(3) = 0.0035628849; c(4) = 0.018759178; c(5) = 0.035896298; c(6) = 0.053738404; c(7) = 0.070911326; c(8) = 0.08603425; c(9) = 0.09785556; c(10) = 0.10537791; c(11) = 0.107959226; c(12) = 0.10537791; c(13) = 0.09785556; c(14) = 0.08603425; c(15) = 0.070911326; c(16) = 0.053738404; c(17) = 0.035896298; c(18) = 0.018759178; c(19) = 0.0035628849; c(20) = -0.008708606; c(21) = -0.01740681; % Calculate velocity and acceleration from position array. Use finite % difference equations to approximate these quantities. for i = 3:N velocity(i) = (position(i)-position(i-1))/(12*(time(i)-time(i-1))); acceleration(i) = (velocity(i)-velocity(i-1))/((time(i)-time(i-2))); end % Acceleration array is very noisy, so filter B is used with a cutoff % frequency of 50 Hz. filtered_acceleration = filter(b,1,acceleration); % Filter C is used for remainder of array, cutoff frequency of 300 Hz. filtered_position = filter(c,1,position); filtered_force = filter(c,1,force); filtered_velocity = filter(c,1,velocity); % FIR filters delay data by a fixed, calcuable time. The delay depends on % the filter order. High order filters delay signal more than low order % filters. offset_1 =round((length(b)-1)/(2)); offset_2 =round((length(c)-1)/(2)); % Modify position and force data to account for this time offset. for i = 1:N-offset_1 filtered_acceleration(i) = filtered_acceleration(i+offset_1); filtered_position(i) = filtered_position(i+offset_2); filtered_velocity(i)= filtered_velocity(i+offset_2); filtered_force(i) = filtered_force(i+offset_2);


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end function damping = damping_calc(a_max,v_min,n_min) global button filtered_position filtered_force filtered_acceleration filtered_velocity time i_high i_low N; % This variable is used to count the number of data points that meet the % criteria for calculating the damping force. n_sample = 0; % This variable is used as a place keeper to remember the largest number of % data points that meet the damping force calculation criteria. n_max = 1; % Initialize this variable to 0. This function will return this value if % the data does not converge to a solution for damping force. damping = 0; i_low = 1; i_high = 1; % Determine if the test is compression or tension. The sign of the maximum % velocity is determined by this IF statement. if filtered_position(round(N*.8))>0 v_max = max(filtered_velocity); else v_max = min(filtered_velocity); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Loop through data to find region where data meets certain criteria. The % criteria are as follows: % 1. The velocity must be within v_min percent of the maximum velocity for % the data. This criteron was established so the loop would not % prematurely converge on a region that did not match the desired % velocity. % 2. The acceleration must be within a_max of 0 ft/s^2. This % criterion prevents inertial effects from influencing the damping force % calculation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i = 1:N while (abs(filtered_acceleration(i + n_sample)) < a_max && 100*abs((v_max-filtered_velocity(i + n_sample))/v_max) < v_min) n_sample = n_sample + 1; if i + n_sample == N break end end % This IF statement checks to see if the region that meets the % calculation criteria is the largest region found thus far. The % variables n_max and i_max are used as place keepers to track location % of largest region that meets the calculation criteria. if (n_sample >= n_min && n_sample > n_max) n_max = n_sample;


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i_max = i; else n_sample = 0; end end % This IF statement checks if data converged on a damping force solution. if n_max >= n_min % Initialize arrays to store position, velocity, and force from region % that met calculation criteria damp_pos = zeros(n_max,1); temp_1 = zeros(n_max,1); damp_vel = zeros(n_max,1); temp_2 = zeros(n_max,1); i_low = i_max; i_high = i_max + n_max - 1; % Loop through arrays to store position, velocity, and force data for j = 1:n_max damp_pos(j) = filtered_position(i_max + j - 1); temp_1(j) = filtered_force(i_max + j - 1); damp_vel(j) = filtered_velocity(i_max + j - 1); temp_2(j) = time(i_max + j - 1); end % Calculate spring force from stiffness regression analysis [spring_force,m_spring_force] = regress_ramp(damp_pos); % Calculate damping force damp_force = temp_1 - spring_force; % Calculate uncertainty in damping force damp_force_up = temp_1 - spring_force + m_spring_force; damp_force_low = temp_1 - spring_force - m_spring_force; % Send damping information back to Main function damping = [damp_pos,damp_vel,damp_force,m_spring_force]; % IF statement to plot damping force results only if "single file" is % selected if strcmp(button,'Single File') figure subplot(4,2,[1 3]) plot(damp_pos,temp_1,'.k-',damp_pos,spring_force,'.g-') xlabel('Deflection (inches)') ylabel('Force (lbf)') grid legend('Measured Force','Regression Spring Force',4) subplot(4,2,[5 7]) plot(damp_pos,damp_force,'k.-',damp_pos,damp_force_up,'r--',damp_pos,damp_force_low,'r--') xlabel('Deflection (inches)')


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ylabel('Force (lbf)') grid legend('Damping Force',4) end end

4.2.3 Drop Test Code clear close all % The variables below are declared in this main function and are used by % many different functions. It was helpful to have them as global % variables to reduce the number variables sent to a function. global d N button analysis_path analysis_name time m_position acceleration; %%%%%% Important parameters for the calculation of the damping force %%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Uncertainty (+/-) in zero displacement position. This value will be used % for an uncertainty analysis that will produce a confidence interval for % the damping force. m_position = 0.01; %(inches) % Evaluate uncertainty in 0 displacement position at the following position. Avoid evaluating % uncertainty at 0 displacement position because of spike in acceleration % that occurs from collision. The evaluation position should be in the % displacement region where the data analysis will occur. eval_m_position = -0.45; %(inches) % The following variables specify the position range for which all the other % data is trimmed from. Allow positions above impact displacement to allow % free fall acceleration and velocity to be calculated. Also filters % require several data points to initialize themselves before they output % data correctly. x_start = 0.3; x_end = -0.65; % The following variables specify the position range for which the damping % force is calculated. To reduce the amount of junk data output to text % files, these variables are used to limit the output data to a certain % range. damping_x_start = -0.1; damping_x_end = -0.5; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This program is separated into two sections by this IF statement. The % user can choose to process a single file or folder. % This button prompts the user to choose to process a single file or folder button = questdlg('Do you want to process a single file or entire folder?','Data Analysis','Single File','Folder','Cancel','Single File'); if ~strcmp(button,'Cancel')

Vol. 2 4.2.3 Drop Test MatLab Code

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% The damping force calculation requires an analysis file that contains % the spring coefficient (lbf/ft) as a function of displacement. The % user is prompted to select this file with the following line of code. [analysis_name,analysis_path] = uigetfile('*.txt','Select Step Displacement Analysis File'); if ~analysis_name==0 if strcmp(button,'Folder') %Locate the directory to import files directory = uigetdir; if ~directory == 0 % Get the names of all DAT files in directory dirListing = dir(strcat(directory,'/*.csv')); % Initialize array to place important data related to the % damping force. Damping data for each file in the folder % will be placed in this array. damping = zeros(1,4); % This variable is used to initialize concatenation of data % to be placed in "damping" array. state = 1; % Loop through the files, open files, and analyze each one for d = 1:length(dirListing) % Check if file is actually a folder if ~dirListing(d).isdir % Use full path filename = fullfile(directory,dirListing(d).name); files(d) = cellstr(dirListing(d).name); % Retrieve information about file and place information in struct array struct = importdata(filename,',',6); % Place data from file in arrays. It is assumed % that time is in the first column in the data % file, acceleration in the second column, and % position in the fourth column. time = struct.data(:,1); acceleration = struct.data(:,2); position = struct.data(:,4); clear struct; % The data acquisition for the drop test uses a % high sampling rate, so the data files are very % large. The following function is called to trim % the data file to the pertinent range of data.


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% The range is determined by the expected % displacements. See the function for more % information on setting the minimum and maximum % position range to include. [time,acceleration,position] = trim_data(time,acceleration,position,x_start,x_end); % Find length of data arrays N = length(time); % Filter position and acceleration data to remove high frequency % noise. See function for cutoff frequencies. filter_drop_data(time,acceleration,position,N); % The following function will calculate the damping % force. The regression analysis from the % stiffness tests is used in this calculation. damp_temp = damp_force_calc(damping_x_start,damping_x_end,m_position,eval_m_position); % Enter this IF statement to fill "damping" % with data for the first time. if state == 1 damping = damp_temp; state = 0; end % Enter this IF statement if "damping" already % has data in it if ~state == 1 damping = vertcat(damping,damp_temp); end end % if - (to check if file is actually a folder) end % for-loop (to cycle through all files in folder) % Create a 3D plot of damping force with respect to % deflection and velocity plot3(damping(:,1),damping(:,2),damping(:,3),'*');%,damping(:,1),damping(:,2),damping(:,3)+damping(:,4),'r.',damping(:,1),damping(:,2),damping(:,3)-damping(:,4),'r.') xlabel('Position (inches)') ylabel('Velocity (ft/sec)') zlabel('Damping Force (lbf)') grid % Prompt for name and path to save analysis file. The file will % contain the damping force, postion, velocity and filename % for each file that converges on a damping force solution.


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[save_name,save_path] = uiputfile('*.txt','Save Drop Test Analysis?','Drop_Analysis.txt'); if ~save_name == 0 fid = fopen(fullfile(save_path,save_name), 'wt'); fprintf(fid, 'Position(in)\tVelocity(ft/s)\tDamping_Force(lbf)\tUncertainty_Damping_Force(lbf)\n'); fprintf(fid, '%4f\t%4f\t%4f\t%4f\n' , damping'); fclose(fid); end end % if - (to check if folder select window is canceled) end % if - (to analyze data if 'folder' is selected) if strcmp(button,'Single File') quit = 1; while quit == 1; [name,path] = uigetfile('*.csv','Select Data File'); if ~name == 0 %This is the counter variable for case where a folder %is analyzed. It is initialized here because some %functions require this variable. d = 1; % Retrieve information about file and place information in struct array filename = fullfile(path,name); struct = importdata(filename,',',6); % Place data from file in arrays. It is assumed % that time is in the first column in the data % file, acceleration in the second column, and % position in the fourth column. time = struct.data(:,1); acceleration = struct.data(:,2); position = struct.data(:,4); clear struct; % The data acquisition for the drop test uses a % high sampling rate, so the data files are very % large. The following function is called to trim % the data file to the pertinent range of data. % The range is determined by the expected % displacements. See the function for more % information on setting the minimum and maximum % position range to include. [time,acceleration,position] = trim_data(time,acceleration,position,x_start,x_end); % Find length of data arrays


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N = length(time); % Filter position and acceleration data to remove high frequency % noise. See function for cutoff frequencies. filter_drop_data(time,acceleration,position,N); % The following function will calculate the damping % force. The regression analysis from the % stiffness tests is used in this calculation. damping = damp_force_calc(damping_x_start,damping_x_end,m_position,eval_m_position); % Plot position, acceleration, and damping force. These plots % allow the user to visualize regions where damping is % calculated. plot_drop_data(time,acceleration,damping) uiwait(warndlg('Press "OK" when you are done')) % This dialog asks the user if they want to analyze another file. % The dialog is nodal, which means the user must answer "Yes" or % "No" before the window can be closed or another window can be % viewed. answer = questdlg('Analyze Another File?','Continue Analysis?','Yes','No','No'); if strcmp(answer,'No') quit = 0; end end end % Prompt for name and path to save analysis file. if ~name == 0 [save_name,save_path] = uiputfile('*.txt','Save Ramp Analysis?',['Analysis_', strrep(name,'.csv',''),'.txt']); if ~save_name == 0 fid = fopen(fullfile(save_path,save_name), 'wt'); fprintf(fid, 'Position(in)\tVelocity(ft/s)\tDamping_Force(lbf)\tUncertainty_Damping_Force(lbf)\n'); fprintf(fid, '%4f\t%4f\t%4f\t%4f\n' , damping'); fclose(fid); end end end end end function [time_trim,acceleration_trim,position_trim] = trim_data(time,acceleration,position,x_start,x_end)


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% Use states to identify different regions in data. Initialize to state 1 % until position is less than the x_start. Then set state to 2. Once % position drops below x_end, the state is set to 0. All data outside of % state 2 is erased. state = 1; for i = 1:length(time) if (state == 1 && position(i) < x_start) start = i; state = 2; end if position(i) < x_end && state == 2 i_min = i; state = 0; end end % Now initialize arrays for trimmed data sets to be output. N = i_min - start + 1; time_trim = zeros(N,1); acceleration_trim = zeros(N,1); position_trim = zeros(N,1); % Write trimmed data sets from original data. for i = 1:N time_trim(i) = time(i+start); acceleration_trim(i) = acceleration(i+start); position_trim(i) = position(i+start); end function [x_mean,k_mean,files] = sort_xk(x_mean,k_mean,files) for i = 1:length(files) - 1 for j = i+1:length(files) if x_mean(i) > x_mean(j) temp_x = x_mean(i); x_mean(i) = x_mean(j); x_mean(j) = temp_x; temp_k = k_mean(i); k_mean(i) = k_mean(j); k_mean(j) = temp_k; temp_f = files(i); files(i) = files(j); files(j) = temp_f; end end end function [f_spring,m_spring] = regress_spring(x_array)


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global analysis_path analysis_name; % Retrieve information about file and place information in struct array analysis_file = fullfile(analysis_path,analysis_name); struct = importdata(analysis_file,'\t'); % Place data from file in arrays x_mean = struct(:,1); k_mean = struct(:,2); j = 0; k = 0; for i = 1:length(x_mean) if x_mean(i) < 0 j = j + 1; x_mean_comp(j) = x_mean(i); k_mean_comp(j) = k_mean(i); end end [poly_comp,sd_comp] = polyfit(x_mean_comp,k_mean_comp,1); [k_comp,se_comp] = polyval(poly_comp,x_array,sd_comp); f_spring = k_comp.*x_array./12; m_spring = 1.96*se_comp.*x_array./12; function regress(x_mean,k_mean) j = 0; k = 0; for i = 1:length(x_mean) if x_mean(i) < 0 j = j + 1; x_mean_comp(j) = x_mean(i); k_mean_comp(j) = k_mean(i); end if x_mean(i) > 0 k = k + 1; x_mean_tens(k) = x_mean(i); k_mean_tens(k) = k_mean(i); end end % Find range of spring coefficient data to scale plot k_upper = max(k_mean)*1.1; k_lower = min(k_mean)*0.9; % Find range of step displacements to scale plot x_upper = max(x_mean)*1.1; x_lower = min(x_mean)*0.9;


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figure if ~j==0 [poly_comp,se_comp] = polyfit(x_mean_comp,k_mean_comp,1); [k_comp,sd_comp] = polyval(poly_comp,x_mean_comp,se_comp); k_comp_upper = k_comp + 1.96*sd_comp; k_comp_lower = k_comp - 1.96*sd_comp; plot(x_mean_comp,k_comp,'-k.',x_mean_comp,k_comp_lower,'--r',x_mean_comp,k_comp_upper,'--r') hold; end if ~k==0 [poly_tens,se_tens] = polyfit(x_mean_tens,k_mean_tens,3); [k_tens,sd_tens] = polyval(poly_tens,x_mean_tens,se_tens); k_tens_upper = k_tens + 1.96*sd_tens; k_tens_lower = k_tens - 1.96*sd_tens; plot(x_mean_tens,k_tens,'-k.',x_mean_tens,k_tens_lower,'--r',x_mean_tens,k_tens_upper,'--r') end axis([x_lower x_upper k_lower k_upper]) title('Spring Coefficient for Step Displacement') xlabel('Displacement (inches)') ylabel('Spring Coefficient (lbs/ft)') function plot_drop_data(time,acceleration,damping) global filtered_acceleration filtered_position d button damp_force spring_acceleration free_acceleration; %Formatting of plots is different for entire folder and single file %analyses if strcmp(button,'Folder') if d == 1; subplot(2,1,1) plot(filtered_position,filtered_acceleration,'k',filtered_position,spring_acceleration,'r'); xlabel('Distance (inches)') ylabel('Acceleration (Gs)') axis([-.55 0 -1.2 2]) grid hold


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subplot(2,1,2) plot(filtered_position,damp_force,'k'); xlabel('Distance (inches)') ylabel('Damping Force (lbs)') axis([-.55 0 0 100]) grid hold else subplot(2,1,1) plot(filtered_position,filtered_acceleration,'g'); xlabel('Distance (inches)') ylabel('Acceleration (Gs)') legend('Acceleration Data 1','Spring Acceleration','Acceleration Data 2') axis([-.55 0 -1.2 2]) subplot(2,1,2) plot(filtered_position,damp_force,'r'); xlabel('Distance (inches)') ylabel('Damping Force (lbs)') legend('Data set 1','Data set 2') axis([-.55 0 0 60]) end else figure subplot(3,1,1) plot(time,acceleration,'g',time,filtered_acceleration,'k'); %axis([0 1 x_lower x_upper]) xlabel('Time (seconds)') ylabel('Acceleration (Gs)') legend('Original Acceleration','Filtered Acceleration') title(['Impact velocity = ',num2str(min(damping(:,2))),' ft/sec']) grid subplot(3,1,2) plot(filtered_position,acceleration,'g',filtered_position,filtered_acceleration,'k',damping(:,1),spring_acceleration,'r'); xlabel('Distance (inches)') ylabel('Acceleration (Gs)') legend('Original Acceleration','Filtered Acceleration','Spring Acceleration') axis([-.55 0 -1.2 2]) grid title(['Free Fall Acceleration = ',num2str(free_acceleration),' Gs']) subplot(3,1,3) plot(damping(:,1),damping(:,3),damping(:,1),damping(:,3)-damping(:,4),'r-',damping(:,1),damping(:,3)+damping(:,4),'r-'); xlabel('Distance (inches)') ylabel('Damping Force (lbs)')


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axis([-.55 0 0 60]) grid end function k_spring_calc(start,n_sample) global x_mean k_mean N d force position filtered_force_high filtered_force_all filtered_position k_spring filtered_k_spring_all filtered_k_spring_high p2p_high p2p_all i_high i_low; % Calculate spring coefficient from measured data. (lbs/ft) k_spring = 12.*force./position; % Calculate spring coefficient from filtered data. (lbs/ft) filtered_k_spring_high = 12.*filtered_force_high./filtered_position; filtered_k_spring_all = 12.*filtered_force_all./filtered_position; % Variables for max and min of sample. Initialize for use in "while" loop p2p_high = 100*ones(N,1); p2p_all = 100*ones(N,1); % Initialize variables for use in "while" loop. i = 2; temp_1 = zeros(n_sample,1); temp_2 = zeros(n_sample,1); temp_3 = 0; temp_4 = 0; % Loop to calculate peak to peak of spring coefficient as function of % time. The high-frequency filtered spring coefficient is used for the convergence % criteria. This spring coefficient more accurately models the transient % spring/displacement data than the low-frequency spring coefficient. while ((p2p_high(i - 1) > start && i <= N - n_sample - 1) ) % Look ahead n_sample data points and fill temporary arrays. for j = 1:n_sample temp_1(j) = filtered_k_spring_high(i + j - 2); temp_2(j) = filtered_k_spring_all(i + j - 2); end % Find max and min of temporary arrays. k_max_high = max(temp_1); k_min_high = min(temp_1); k_max_all = max(temp_2); k_min_all = min(temp_2); % Calculate peak-to-peak values of data in temporary arrays. p2p_high(i) = abs(2*(k_max_high - k_min_high)/(k_max_high + k_min_high)); p2p_all(i) = abs(2*(k_max_all - k_min_all)/(k_max_all + k_min_all)); i = i + 1; end % This variable marks the position where the spring coefficient calculation


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% starts. i_low = (i - 1); % This variable marks the position where the spring coefficient calculation % ends. i_high = (i - 1 + n_sample); % The following lines of code calculate the average spring coefficient over % the range defined by i_low and i_high. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for j = i_low:i_high; temp_3 = temp_3 + filtered_k_spring_all(j); temp_4 = temp_4 + filtered_position(j); end k_mean(d) = temp_3/n_sample; x_mean(d) = temp_4/n_sample; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function filter_drop_data(time,acceleration,position,N) global filtered_acceleration filtered_position filtered_velocity; %FIR Filter %40 order, Passband = (0 to 200Hz), Stopband Attenuation = 21db, Transition %Bandwidth = 184 Hz. %See http://www.dsptutor.freeuk.com/FIRFilterDesign/FIRFilterDesign.html b(1)=-.0152; b(2)=-.0151; b(3)=-.0142; b(4)=-.0124; b(5)=-.0096; b(6)=-.006; b(7)=-.0015; b(8)=.0038; b(9)=.0097; b(10)=.0161; b(11)=.0229; b(12)=.0299; b(13)=.0369; b(14)=.0437; b(15)=.05; b(16)=.0557; b(17)=.0607; b(18)=.0647; b(19)=.0677; b(20)=.0695; b(21)=.0701; b(22)=.0695; b(23)=.0677; b(24)=.0647; b(25)=.0607; b(26)=.0557; b(27)=.05; b(28)=.0437; b(29)=.0369;


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b(30)=.0299; b(31)=.0229; b(32)=.0161; b(33)=.0097; b(34)=.0038; b(35)=-.0015; b(36)=-.006; b(37)=-.0096; b(38)=-.0124; b(39)=-.0142; b(40)=-.0151; b(41)=-.0152; %FIR Filter %200 order, Passband = (0 to 10Hz), Stopband Attenuation = 21db, Transition %Bandwidth = 37 Hz. %See http://www.dsptutor.freeuk.com/FIRFilterDesign/FIRFilterDesign.html c(1)=.0023; c(2)=.0024; c(3)=.0024; c(4)=.0025; c(5)=.0026; c(6)=.0026; c(7)=.0027; c(8)=.0028; c(9)=.0028; c(10)=.0029; c(11)=.003; c(12)=.003; c(13)=.0031; c(14)=.0031; c(15)=.0032; c(16)=.0033; c(17)=.0033; c(18)=.0034; c(19)=.0035; c(20)=.0035; c(21)=.0036; c(22)=.0036; c(23)=.0037; c(24)=.0038; c(25)=.0038; c(26)=.0039; c(27)=.004; c(28)=.004; c(29)=.0041; c(30)=.0041; c(31)=.0042; c(32)=.0043; c(33)=.0043; c(34)=.0044; c(35)=.0044; c(36)=.0045; c(37)=.0045; c(38)=.0046; c(39)=.0047; c(40)=.0047;


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c(155)=.0051; c(156)=.005; c(157)=.005; c(158)=.0049; c(159)=.0049; c(160)=.0048; c(161)=.0048; c(162)=.0047; c(163)=.0047; c(164)=.0046; c(165)=.0045; c(166)=.0045; c(167)=.0044; c(168)=.0044; c(169)=.0043; c(170)=.0043; c(171)=.0042; c(172)=.0041; c(173)=.0041; c(174)=.004; c(175)=.004; c(176)=.0039; c(177)=.0038; c(178)=.0038; c(179)=.0037; c(180)=.0036; c(181)=.0036; c(182)=.0035; c(183)=.0035; c(184)=.0034; c(185)=.0033; c(186)=.0033; c(187)=.0032; c(188)=.0031; c(189)=.0031; c(190)=.003; c(191)=.003; c(192)=.0029; c(193)=.0028; c(194)=.0028; c(195)=.0027; c(196)=.0026; c(197)=.0026; c(198)=.0025; c(199)=.0024; c(200)=.0024; c(201)=.0023; % Calculate velocity of drop weight using finite difference approximation. velocity = zeros(N,1); for i = 2:N velocity(i) = (position(i)-position(i-1))/(12*(time(i)-time(i-1))); end % Filter velocity data with low pass filter (cutoff frequency = 10 Hz). filtered_velocity = filter(c,1,velocity);


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% Filter data with low pass filter (cutoff frequency = 200 Hz). filtered_position = filter(b,1,position); filtered_acceleration = filter(b,1,acceleration); % FIR filters delay data by a fixed, calcuable time. The delay depends on % the filter order. High order filters delay signal more than low order % filters. offset_1 = round((length(b)-1)/(2)); offset_2 = round((length(c)-1)/(2)); % Modify position and force data to account for this time offset. for i = 1:N-offset_1 filtered_position(i) = filtered_position(i+offset_1); filtered_acceleration(i) = filtered_acceleration(i+offset_1); filtered_velocity(i) = filtered_velocity(i+offset_1); end for i = 1:N-offset_2 filtered_velocity(i) = filtered_velocity(i+offset_2); end function [damping] = damp_force_calc(damping_x_start,damping_x_end,m_position,eval_m_position) global acceleration filtered_position filtered_acceleration filtered_velocity spring_acceleration free_acceleration; N = length(filtered_position); % The following variables are used help calculate the free-fall % acceleration of the weight. a_start_x = 0.2; a_end_x = -0.05; temp_sum = 0; n_samples = 80; min_sum = 1000; % Use states to ascertain where the WHILE loop is in the data array. state = 1; i = 0; % This loop is used to calculate uncertainty in acceleration due to % uncertaintiy in the zero displacement position. Also, the free_fall % acceleration is calculated. while (~state == 0 && i <= N) i = i + 1; % The following branch of IF statements finds the freefall acceleration % by averaging n_samples. if (i + n_samples < N) if (filtered_position(i + n_samples) < a_start_x && filtered_position(i + n_samples) > a_end_x) for k = 0:n_samples - 1 temp_sum = temp_sum + acceleration(k + i);


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end if temp_sum < min_sum min_sum = temp_sum; j = i + k; end end temp_sum = 0; end % IF statements to find "i" where position drops below uncertainty in % position at evaluation points. The acceleration at these points are % then used in the uncertainty analysis. if (state == 1 && filtered_position(i) < m_position + eval_m_position) temp_low = filtered_acceleration(i); state = 2; end if (filtered_position(i) < m_position && state == 2) temp_zero = filtered_acceleration(i); state = 3; end if (filtered_position(i) < eval_m_position - m_position && state == 3) temp_high = filtered_acceleration(i); state = 0; end end % Calculate free fall acceleration free_acceleration = min_sum/n_samples; % Calculate uncertainties in acceleration at eval_m_position a_high = temp_high - temp_zero; a_low = temp_zero - temp_low; % Calculate largest uncertainity in acceleration at eval_m_position. Use % this value for the remainder of the analysis. a_max = max(a_high,a_low); % Trim data sets so damping force is analyzed only in the necessary region. [temp_acceleration,temp_velocity,temp_position] = trim_data(filtered_acceleration,filtered_velocity,filtered_position,damping_x_start,damping_x_end); % Retrieve regression analysis on stiffness (spring force). [f_spring,m_spring] = regress_spring(temp_position); % The following is the measured weight of the drop weight. weight = 170; %(lbf) % Use the stiffness regression results and free fall acceleration to % predict the acceleration of the weight from an isolator without damping. spring_acceleration = free_acceleration - f_spring./weight; m_spring_acceleration = m_spring./weight;


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% Subtract stiffness force from measured force to calculate damping force. damp_force = 170.*(temp_acceleration - spring_acceleration); m_damp_force = 170.*(m_spring_acceleration - a_max); % Return damping data to MAIN function damping = [temp_position,temp_velocity,damp_force,m_damp_force]; 4.3 Ansys Code /FILNAME,4_5_09,1 /BATCH /COM,ANSYS RELEASE 11.0SP1 UP20070830 15:24:32 04/18/2009 /input,menust,tmp,'',,,,,,,,,,,,,,,,1 /GRA,POWER /GST,ON /PLO,INFO,3 /GRO,CURL,ON /CPLANE,1 /REPLOT,RESIZE WPSTYLE,,,,,,,,0 /FILNAME,BAE,0 /CWD,'C:\temp\nick4_18_09' /PREP7 !* ET,1,COMBIN37 !* /REPLOT,RESIZE KEYOPT,1,1,0 KEYOPT,1,2,2 KEYOPT,1,3,2 KEYOPT,1,4,0 KEYOPT,1,5,0 KEYOPT,1,6,4 KEYOPT,1,9,0 !* R,1, ,100,0, , , , RMORE, , , , , , , RMORE, , !* R,1,0,100,0,0,0,0, RMORE,0,0,0,0,0,0, RMORE,0, !* N,1,0,0,0,,,, N,2,0,0.05,0,,,, TYPE, 1 MAT, REAL, 1 ESYS, 0 SECNUM, TSHAP,LINE !*

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FLST,2,2,1 FITEM,2,1 FITEM,2,2 E,P51X N,3,0,0.0,0,,,, N,4,0,0.05,0,,,, N,4,0,0.05,0,,,, TYPE, 1 MAT, REAL, 1 ESYS, 0 SECNUM, TSHAP,LINE !* !* /NOPR /PMETH,OFF,0 KEYW,PR_SET,1 KEYW,PR_STRUC,1 KEYW,PR_THERM,0 KEYW,PR_FLUID,0 KEYW,PR_ELMAG,0 KEYW,MAGNOD,0 KEYW,MAGEDG,0 KEYW,MAGHFE,0 KEYW,MAGELC,0 KEYW,PR_MULTI,0 KEYW,PR_CFD,0 /GO !* /COM, /COM,Preferences for GUI filtering have been set to display: /COM, Structural !* !* ANTYPE,4 !* TRNOPT,FULL LUMPM,0 !* FLST,2,1,1,ORDE,1 FITEM,2,1 !* /GO D,P51X, , , , , ,ALL, , , , , R,1,0,100,0,0,0,0, RMORE,0,0,0,0,0,0, RMORE,0, !* R,1,0,100,0,0,0,0, RMORE,0,0,0,0,0,0, RMORE,0, !* elist,all,,,0,1 FINISH /SOL DELTIM,0.001,0.001,0.01

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OUTRES,ERASE OUTRES,ALL,4 TIME,1.0 FLST,2,1,1,ORDE,1 FITEM,2,2 IC,P51X,UY, ,-1.0, /STATUS,SOLU SOLVE FINISH /POST26 FINISH /CLEAR /COM,ANSYS RELEASE 11.0SP1 UP20070830 16:29:13 04/18/2009 /input,start110,ans,'T:\Program Files\ANSYS Inc\v110\ANSYS\apdl\',,,,,,,,,,,,,,,,1 /POST1 INRES,BASIC FILE,'BAE','rst','.' SET,LAST FINISH /POST26 FILE,'BAE','rst','.' /UI,COLL,1 NUMVAR,200 SOLU,191,NCMIT STORE,MERGE FILLDATA,191,,,,1,1 REALVAR,191,191 !* RFORCE,2,1,F,Y, FY_2 STORE,MERGE !* NSOL,3,2,U,Y, UY_3 STORE,MERGE XVAR,1 PLVAR,2, XVAR,1 PLVAR,3, NLIST,ALL, , , ,NODE,NODE,NODE !* !* ICLIST,ALL ICLIST,ALL,,,VELO !* /REPLOT FINISH /PREP7 FINISH /CLEAR,START

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4.4 Simulink The following section shows the simulink model and code that was used in the drop test simulation. 4.4.1 Simulink Code gravity = -32.2; %gravity (ft/sec^2) m = 170/gravity; %mass of drop machine (slugs) k = 5500; %nominal spring coefficient in compression(lbf/ft) t_end = 0.005; %end time of simulation (seconds) t_step = 0.00005; %max time step of simulation (seconds) psi = 0.05; %damping ratio of neoprene rubber wn = (k/m)^0.5; %natural frequency (rad/sec) b = 10; %damping coefficient (lbf*sec/ft) b0 = b; %Define b0 so damping can be varied v0 = -12; %Initial velocity (ft/sec) offset = 5/m; %Initialize value for coulomb friction gain = b/m; %Initialize value for viscous damping sim('Drop_Test_Simulation'); %run simulation for nominal damping coefficient f = m*(fb + fk); %fb and fk are forces per unit mass in simulink inch = 12*x; %convert position data to inches acc_g = a/abs(g); %convert acceleration data to units of gravity subplot(4,1,1); plot(t,inch,'k') title({'Drop Simulation with Initial Velocity = 12 ft/sec';'Black = Nominal Damping, Green = 110% of Nominal Damping, Red = 90% of Nominal Damping'}); grid on hold on ylabel('Position (inches)') subplot(4,1,2) plot(t,v,'k') grid on hold on ylabel('Velocity (ft/sec)') subplot(4,1,3) plot(t,acc_g,'k') grid on hold on ylabel('Acceleration (Gs)') subplot(4,1,4) plot(t,f,'k') grid on xlabel('Time (seconds)') ylabel('Force on Isolator (lbf)') clear x v a; b = b0*.9; %run simulation for 20% less than nominal damping gain = b/m; sim('Drop_Test_Simulation'); f = m*(fb + fk); %f = m*fb; inch = 12*x; acc_g = a/32.2; subplot(4,1,1); plot(t,inch,'r') ylabel('Position (inches)') subplot(4,1,2)

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plot(t,v,'r') ylabel('Velocity (ft/sec)') subplot(4,1,3) plot(t,acc_g,'r') ylabel('Acceleration (Gs)') subplot(4,1,4) plot(t,f,'r') xlabel('Time (seconds)') ylabel('Force on Isolator (lbf)') clear x v a ; b = b0*1.2; %run simulation for 20% more than nominal damping gain = b/m; sim('Drop_Test_Simulation'); f = m*(fb + fk); %f = m*fb; inch = 12*x; acc_g = a/32.2; subplot(4,1,1); plot(t,inch,'g') ylabel('Position (inches)') subplot(4,1,2) plot(t,v,'g') ylabel('Velocity (ft/sec)') subplot(4,1,3) plot(t,acc_g,'g') ylabel('Acceleration (Gs)') subplot(4,1,4) plot(t,f,'g') xlabel('Time (seconds)') ylabel('Force on Isolator (lbf)') clear x v a b; 4.4.2 Simulink Block Diagram