EML 4905 Senior Design Project

A B.S. THESIS

PREPARED IN PARTIAL FULFILLMENT OF THE

REQUIREMENT FOR THE DEGREE OF

BACHELOR OF SCIENCE

IN

MECHANICAL ENGINEERING

SMA HYSTERETIC SHOCK ABSORBER

100% REPORT

TEAM VIBRANIUM

Harold Hastings

Alexander Zuleta

Advisor: Dr. Norman Munroe

November 21, 2013

This B.S. thesis is written in partial fulfillment of the requirements in EML 4905.

The contents represent the opinion of the authors and not the Department of

Mechanical and Materials Engineering.

i

Ethics Statement & Signatures

The work submitted in this B.S. thesis is solely prepared by a team consisting of Harold

Hastings and Alexander Zuleta and it is original. Excerpts from others’ work have been clearly

identified, their work acknowledged within the text and listed in the list of references. All of the

engineering drawings, computer programs, formulations, design work, prototype development

and testing reported in this document are also original and prepared by the same team of

students.

Harold Hastings Team Leader

Alexander Zuleta Team Member

Dr. Norman Munroe

Faculty Advisor

ii

Table of Contents

Ethics Statement & Signatures .................................................................................................... i

Table of Contents ....................................................................................................................... ii

List of Figures .............................................................................................................................v

List of Tables ........................................................................................................................... vii

Abstract ......................................................................................................................................1

Introduction ................................................................................................................................2

Problem Statement...................................................................................................................2

Motivation ...............................................................................................................................2

Literature Survey .....................................................................................................................3

History & Background Information ......................................................................................3

Applications .........................................................................................................................3

Material & SMA Properties..................................................................................................4

Project Formulation .................................................................................................................5

Overview .................................................................................................................................5

Project Objectives ....................................................................................................................5

Design Specifications & Other Considerations .........................................................................6

Design Alternatives .....................................................................................................................6

Overview of Conceptual Designs Developed ...........................................................................6

Spring Design 1 .......................................................................................................................7

Spring Design 2 .......................................................................................................................8

iii

Spring Design 3 .......................................................................................................................9

Prototype Design 1 ................................................................................................................ 10

Prototype Design 2 ................................................................................................................ 14

Prototype Design 3 ................................................................................................................ 15

Other Considerations ............................................................................................................. 16

Feasibility Assessment........................................................................................................... 17

Project Management.................................................................................................................. 18

Overview ............................................................................................................................... 18

Division of Labor .................................................................................................................. 18

Organization of Work & Timeline ......................................................................................... 19

Engineering Design & Analyses ................................................................................................ 19

Overview ............................................................................................................................... 19

Stress Analysis & Finite Elemental Analysis ......................................................................... 20

Structural Design ................................................................................................................... 22

DSC (Differential Scanning Calorimetry) Analysis ................................................................ 26

Thermal Control System ........................................................................................................ 29

Pulse Width Modulation Power Control ................................................................................. 31

Thermal Analysis .................................................................................................................. 32

Transient thermal analysis ..................................................................................................... 33

Nitinol Spring Design Making ............................................................................................... 34

iv

Design Overview ................................................................................................................... 39

Cost Analysis ........................................................................................................................ 40

Prototype Construction .............................................................................................................. 40

Parts List ............................................................................................................................... 40

Construction .......................................................................................................................... 42

Spring Fabrication .............................................................................................................. 42

Thermal Delivery System ................................................................................................... 45

Prototype Assembly ........................................................................................................... 45

Testing & Evaluation ................................................................................................................ 46

Overview ............................................................................................................................... 46

Design of Experiment ............................................................................................................ 46

Data & Data Analysis ............................................................................................................ 47

Full Martensitic experiment ............................................................................................... 47

Full Austenitic experiment ................................................................................................. 49

Design Considerations............................................................................................................... 53

Assembly and Disassembly ................................................................................................... 53

Maintenance of the System .................................................................................................... 55

Regular Maintenance ......................................................................................................... 55

Major Maintenance ............................................................................................................ 55

Environmental Impact ........................................................................................................... 55

Conclusion ................................................................................................................................ 56

v

Conclusion & Discussion ....................................................................................................... 56

Recommendations & Future Work ......................................................................................... 57

References ................................................................................................................................ 58

Appendix A: Experimental Equipment ...................................................................................... 61

Appendix B: Technical Drawings .............................................................................................. 65

Shock Absorber Prototype Technical Drawing ....................................................................... 65

Constant Pitch Compression Spring Technical Drawing ........................................................ 66

Test Fixture Technical Drawing ............................................................................................. 67

Test Fixture Assembly Technical Drawing ............................................................................ 68

List of Figures

Figure 1 VPC Spring [5] .............................................................................................................8

Figure 2 Flat Spring [4] ...............................................................................................................9

Figure 3 Compression Spring .................................................................................................... 10

Figure 4 Shock Absorber Housing ............................................................................................. 11

Figure 5 Spring Housing ........................................................................................................... 11

Figure 6 Ni-Ti Shock Absorber Assembly ................................................................................. 12

Figure 7 Ni-Ti Shock Absorber Assembly Section View ........................................................... 13

Figure 8 SMA Shock Absorber Concept .................................................................................... 14

Figure 9 - Shock Absorber Digital Prototype ............................................................................. 15

Figure 10- Cross Section of Assembly ....................................................................................... 16

Figure 11 Spring Force Diagram ............................................................................................... 20

vi

Figure 12 Unloaded Nitinol Spring ............................................................................................ 21

Figure 13 Loaded Nitinol Spring ............................................................................................... 21

Figure 14 Shock Absorber Assembly Section View ................................................................... 22

Figure 15 Internal Spring Configuration .................................................................................... 23

Figure 16 Austenite Final Temperature vs. Annealing Temperature........................................... 27

Figure 17 Energy Absorbed during Phase Transformation NiTi 460 .......................................... 28

Figure 18Energy Absorbed during Phase Transformation NiTi 510 ........................................... 28

Figure 19Energy Absorbed during Phase Transformation NiTi 560 ........................................... 29

Figure 20 - Values for different wire diameters ......................................................................... 30

Figure 21-Aproximate electrical current per .1 mm increment in the wire diameter ................... 31

Figure 22 - Duty Cycle .............................................................................................................. 32

Figure 23 - PWM Power Controller Shell - B001 ...................................................................... 32

Figure 24-Transient Heat over 600s – ABS – Plastic ................................................................. 33

Figure 25-Temperature Distribution at 600s – ABS plastic ........................................................ 34

Figure 26 spring working Diagram ............................................................................................ 36

Figure 27 Inventor Working Diagram ........................................................................................ 38

Figure 28 Spring Fixtures .......................................................................................................... 43

Figure 29 Spring Fixtures .......................................................................................................... 43

Figure 30 Method to measure Logarithmic Decrement .............................................................. 47

Figure 31 Damping ratio formulas for underdamped systems .................................................... 48

Figure 32 Time to reach equilibrium (Full Martensite) .............................................................. 49

Figure 33 Full Austenite Response Time ................................................................................... 50

Figure 34 Resonance Frequency (Hz) vs. Spring Rate (N/m) ..................................................... 51

vii

Figure 35 Duty Cycle 1 Temperature vs. Time .......................................................................... 51

Figure 36 Duty Cycle 0.75 Temperature vs. Time ..................................................................... 52

Figure 37 Duty Cycle 0.5 Temperature vs. Time ....................................................................... 52

Figure 38 Cool Down Temperature vs. Time ............................................................................. 53

Figure 39 Lip Feature and Threads on Top and Bottom Shells ................................................... 54

Figure 40 Threading on Top and Bottom Lids ........................................................................... 55

Figure 41 Isolated Scale ............................................................................................................ 64

Figure 42 DSC Apparatus ......................................................................................................... 64

List of Tables

Table 1 Material Selection Analysis .......................................................................................... 17

Table 2 Division of Labor ......................................................................................................... 18

Table 3 Project Timeline ........................................................................................................... 19

Table 4 Spring Constant with Varying Wire Diameter and Fixed Spring Diameter .................... 24

Table 5 Variable Pitch and Fixed Wire Diameter and Number of Coils ..................................... 24

Table 6 Variable Number of Coils and Fixed Wire Diameter and Pitch ..................................... 25

Table 7 Variable Wire Diameter and Fixed Pitch and Number of Coils ..................................... 25

Table 8 Transformation Temperature vs. Annealing Temperature ............................................. 27

Table 9 - Nitinol Surface Tension for Bending .......................................................................... 34

Table 10 Inventor Spring Load .................................................................................................. 37

Table 11 Inventor Spring Dimensions ....................................................................................... 37

Table 12 Inventor Spring Coils .................................................................................................. 37

Table 13 Inventor Assembly Dimensions .................................................................................. 37

viii

Table 14 Inventor Spring Material ............................................................................................. 38

Table 15 Inventor Results .......................................................................................................... 38

Table 16 Team Vibranium’s Spring Design Table ..................................................................... 39

Table 17 Cost Analysis Table .................................................................................................... 40

Table 18 Spring Components .................................................................................................... 44

Table 19 Annealing Kiln ........................................................................................................... 44

Table 20 Kiln with Annealing Fixture ....................................................................................... 44

Table 21 Circuit Diagram .......................................................................................................... 45

Table 22 Full Martensitic Experiment Variables ........................................................................ 48

Table 23 Full Austenitic Experiment Variables ......................................................................... 49

Table 24 Damping ratio results .................................................................................................. 50

1

Abstract

A prototype of passive-damping shock absorber intended for the Florida International

University (FIU), Formula Society of Automotive Engineers (SAE). This shock absorber was

motivated by the idea of an adjustable long-life shock absorber with limited to no moving parts

and/or working fluid. Due to the simplicity of the mechanism, with respect to its moving

components, it was anticipated that a highly reliable weight optimized prototype could be

realized for Formula SAE. Additional considerations for use earthquake damping systems were

discussed, but due to time constraints it was not pursued.

Due to the exotic material properties as well as compatibility considerations with existing

hardware this project was divided into the following four phases: Phase I: Material Selection,

Phase II: Design, Phase III: Analysis and Phase IV: Manufacture. In Phase I a rough estimate of

the working load was established and specific material properties of current automotive springs

were analyzed (i.e. Young’s modulus and yield strength of SAE 9254) and based on the resultant

data an alloy of Nitinol™ (binary or ternary alloy has yet to be determined at this time) was

chosen that had similar properties. During Phase II the geometry of a standard MacPherson Strut

was analyzed and an initial concept for a design that would be compatible with existing

automotive was explored. After the problem was well defined and constrained several rough

sketches were conceived. Subsequently an appropriate design of the spring which was to be the

focus of the shock absorber will be decided upon. SolidWorks® will be utilized as the primary

design software package. At Phase III analysis of the Nitinol™ springs was performed as well as

the shock absorber as a system to ensure that proper standards and proof of concept was

achieved. SolidWorks® and AutoDesk Inventor will be the primary software packages used in

2

Phase III. Phase IV the majority of the prototype was outsourced, however, all of the springs,

electronics, and test fixture were manufactured by Team Vibranium.

Introduction

Problem Statement

The purpose of this senior project was to design and fabricate a prototype of a suspension

system which would not rely on a strut-type damper, due to reduction of components with

moving parts the system would have offer a longer useful life, as well as provide flexibility by

adjusting the stiffness and damping of the suspension.

Motivation

The design project was motivated by Alexander Zuleta’s previous experience working

with Nitinol™ and his desire to continue using this exotic material. Harold Hastings suggested

that the material’s property would be well suited for damping vibrations. This initially prompted

a discussion about an isolation table and that discussion eventually guided them to a fluid less

passive damping shock absorber. Subsequently the question of “a need” was posited and

determined that high-end racing car suspensions were in need of a highly reliable adjustable

light-weight suspension system and could positively benefit from such a product.

Once the concept was visualized and a need was determined research on the material and

concept to confirm the feasibility of the conceptual design was executed. Hence, Team

Vibranium was established and following a consultation with their advisor, Dr. Norman Munroe,

project planning and literature survey was initiated.

3

Literature Survey

History & Background Information

Nitinol™ is a popular metal alloy that belongs to the small group of the SMA class. Its

crystalline configuration allows it behave in two ways: superplastic and “smart” in the sense that

it can return to shape after being excessively deformed without experiencing plasticity. Its

properties reside in the material response to heat or mechanical deformation which causes a

variation in its Young’s modulus and phase transformation.

It was discovered in the 1960’s as part of a Naval Ordinance Lab project, and gained

popularity for its high biocompatibility and the high recovery forces that can be generated when

the material is properly constrained during phase transformation. Such interesting behavior

drives research and enthusiasts to innovate into new applications every day.

Applications

Nitinol™ has been extensively used in medical applications due to its high

biocompatibility, flexibility, and desirable surface finish which protected the material from

environmental factors and made it practical for use in the human body; Stents are the typical type

of medical devices that make use of the SMA’s super elastic properties to expand clogged

arteries or serve to support the vein walls.

Yet another application that has become popular is the fabrication of Ni-Ti Actuators that

make use of the shape memory property by producing work when passing electric current

through it which produces heat initiating the phase change which allows it to act as a switch or

tendon.

4

Material & SMA Properties

Standard binary Ni-Ti Alloys are made out of Nickel and Titanium at approximately a

50%-50% concentration with slight variations. Ternary elements can be also added to extend the

material properties and create new alloys that fit specific applications. Some examples of ternary

alloys are: Ni-Ti-Co (Cobalt alloy), Ni-Ti-Cu (Copper Alloy), Ni-Ti-Fe (Iron Alloy), and others.

The internal atomic arrangement of Nitinol can be present in two phases as martensite

and austenite. Both phases have different properties and the material can jump from one phase to

another depending on the stress or temperature applied. The transformation temperature can vary

in materials with different concentrations and compositions. By heat treating the SMA the

transformation temperature can be altered and “re-trained” into a new shape. The addition of

ternary elements to the material could change the temperature transformation in both directions.

When fully austenitic phase is present the material behaves as super elastic with a higher

young modulus and with the ability to fully recover after excessive deformation. Super elastic

alloys are also characterized for having low transformation temperatures and being already

austenite at ambient conditions. On the other hand Shape memory alloys have a high

transformation temperature and require extra power to initiate a phase change. Such

characteristics make it useful for making actuators that can be turn on by just running current

through the material.

Ni-Ti alloy’s response to loading and temperature change is nonlinear and special

simulation models should be used to predict the behavior. There are several Finite Elemental

Analysis (FEA) software packages on the market that can simulate Nitinol™ including

SolidWorks® which has an SMA model included in the customs materials section. By utilizing

5

FEA stress and fatigue analysis, one could aid in the development and optimization of innovative

and reliable products.

The demand of Nitinol has increase globally along with the competition for better quality

and price. The material has also been recognized by the FDA (Food and Drug Administration) as

a safe material. Nitinol is sold in wire, sheet, rod, or billet form with a variety of diameters and

sizes.

Project Formulation

Overview

The design of a Nitinol–based suspension was conceptualized as a way to use the

material’s damping properties and its strong response to heat to have a variable system that could

outperformed in different situations. By constructing martensitic- Nitinol springs and controlling

its phase transformation, the system response can be manipulated since the martensitic phase

shows stronger damping ratios than austenitic.

Project Objectives

To Prototype a variable damping ratio shock absorber with the use of Nitinol as active

material.

To control the characteristics of the suspension by using an electrically controlled heating

source.

To effectively damp high amplitude inputs.

6

Design Specifications & Other Considerations

The design should incorporate both the hysteretic damping and superelastic properties of

Nitinol. Team Vibranium will design a prototype that will be suitable for testing and direct

implementation in the field. At the highest spring coefficient “setting” the prototype should be

able to withstand a 20 lbf load.

The scope of this project was not overwhelming, however, there were very few off-the-

shelf components that were suitable for the structure of the prototype. Additionally, consisting

of only two members, Team Vibranium was not able to effectively distribute areas of expertise

efficiently (i.e. Mechanical Engineer, Electrical Engineer, Systems Engineer, Material Science

Engineer, etc.). Additionally, there were so many unknowns due to the non-linear response of

Nitinol it was difficult to use traditional models for analysis. It should be reaffirmed that this

project was to design a prototype for testing as there are currently no other hysteretic dampers

that also take advantage of the superelastic properties of Nitinol.

Design Alternatives

Overview of Conceptual Designs Developed

As previously described, reference Motivation, the need and feasibility of a fluid less

passive damping shock absorber was determined to be adequate in order to proceed with the

conceptual design. With the intention of narrowing the scope of the project the following

constraints were posited: Ni-Ti Shape Memory Alloy (SMA) that would allow the user to control

the transformation temperature, spring design that will effectively use the tubular housing that

will contain it, utilize existing hardware (shock absorber tubular housing and mounting points)

7

for backwards compatibility and for reference geometry, multiple Ni-Ti alloy compression

springs and mounting plate that will dissipate the energy stored in the coil spring, and a thermal

delivery system that will regulate the temperature of the SMA which will allow the user to

control the phase of the SMA.

Due to the standardized nature of shock absorber housing the subsequent design

alternatives were focused on the design springs because the design problem is well defined and

constrained.

Spring Design 1

A Variable Pitch Cylindrical Spring (VPC Spring, See Figure 1) was the initial design

that was chosen for the springs. This was due to the non-linear load vs. deflection curve that

minimized resonant surging and vibration [9]. Because Ni-Ti alloys have a much smaller

Young’s Modulus than standard cylindrical springs are not suitable as the size and pitch of the

spring necessary to dampen vibrations through a vehicle would be cost prohibitive and too bulky

for the housing. It should be possible through careful calculations, to design a spring such that

the work generated by the spring would be greater than or equal to the work done the on vehicle

through vibrations. However, due to the cost prohibitive machining cost it was decided that

another alternative would be best.

8

Figure 1 VPC Spring [5]

Spring Design 2

A Flat Spring (See Figure 2) was the next obvious alternative for the reason that this

particular variation of the spring provides more travel for the spring which is ideal for a design

with limited space. The difficulty with this design is reducing the buckling of the spring in such

a relatively large volume. There is also a concern of if a spring of suitable strength could be

produced with the combination of this type of spring and material.

9

Figure 2 Flat Spring [4]

Spring Design 3

A Constant Pitch Compression Spring (See Figure 3) was ultimately chosen as the spring

for this project. The symmetry of the spring substantially reduced machining costs as this was a

“one off” design. In order to offset the reduced Modulus of Elasticity as compared to spring

steel a high pitch, approximately 18 mm, was selected to obtain the necessary spring rate (See

Structural Design). As an added benefit, this simplified the design process as the formulas for

constant pitch springs are well established and were much easier to iterate in order to satisfy

multiple conditions i.e. spring rate, coil diameter, and free length. This would have been

extremely difficult to achieve if the variable pitch spring was chosen.

10

Figure 3 Compression Spring

Prototype Design 1

Based on the constraints of the standard shock absorber, the shock damping apparatus

must fit within the standard housing (See Figure 3). Using this as a geometric parameter there

would be a total of eight Ni-Ti springs will be attached to the spring housing (See Figure 4).

Four of the springs would be superelastic (austenitic) and the other four would be SMA

(martensitic) with an easily attainable transition temperature (less than 100° C).

The spring housing will be free to slide within the lower blue (See Figure 3) tube and will

be constrained by the lower guide rods which will also prevent buckling of the lower springs

(See Figure 6). The lower guide rods will be concentric and fit within the hollow inner diameter

of the upper guide rods. The eight springs, four on each side attached at the nipples, will be

11

fixed to the interior of the extreme ends of the shock absorber housing. The assembly (See

Figure 5 and Figure 6) is anticipated to appear and operate as a standard shock absorber.

Figure 4 Shock Absorber Housing

Figure 5 Spring Housing

12

Figure 6 Ni-Ti Shock Absorber Assembly

13

Figure 7 Ni-Ti Shock Absorber Assembly Section View

14

Prototype Design 2

This design was conceptualized thinking about how to maximize the damping ratio in

both directions. The assembly uses eight Ni-Ti springs (See Figure 7), four superelastic

(austenitic) and four SMA (martensitic). The black plate is free to slide and able compress the

top and bottom springs. The springs are fixed to the black plate and the frame. The red ends are

tightened with screws to the shafts.

Figure 8 SMA Shock Absorber Concept

15

Prototype Design 3

This design draws heavily from Prototype Design 1 and incorporates a more robust

geometry with more consideration of the dynamic interaction of the parts. The end caps were

modeled with a feature for mounting and the top shell features air vents to avoid excessive heat

accumulation and with the compression decompression cycle will act like a self-powered forced

convection.

Figure 9 - Shock Absorber Digital Prototype

16

Figure 10- Cross Section of Assembly

Other Considerations

Due to the nature of the project, the utmost importance and meticulous deliberation must

be afforded to the alloys under consideration. The binary Ni-Ti alloy was the primary

consideration for the springs, but there was some concern that these alloys would not be stiff

enough in the martensitic phase which is the phase that performs most of the damping by

converting potential energy into strain and ultimately heat. This also suggested that the

temperature of the alloy would need to be regulated in order to control the phase distribution

within the alloy. The real possibility of a binary Ni-Ti alloy that was not sufficiently strong has

guided Team Vibranium to explore the ternary alloys. A Ni-Ti-Co composition has shown initial

promise, but the control of the phase transformation appears to be well below expected operating

temperatures and therefore difficult to control.

The thermal delivery system was treated as a separate, yet necessary system and as such

will not be fully integrated into the final prototype design. However, Team Vibranium has

developed a thermal delivery system that will be used during the experimentation for proof of

17

concept. This system utilizes an electric current that will passed through the Nitinol springs,

which subsequently will experience an increase in temperature through the mechanism of

resistive heating. This process will be controlled by a micro-controller and Pulse Width

Modulation (PWM) controller in order to regulate the material’s temperature at a desired level.

In order to accurately gauge the amount of power the system consumed a shunt and ammeter was

integrated as the maximum amperage was on the order of 96 amps which was rated almost one

order of magnitude greater than the multi-meters in possession of Team Vibranium.

Feasibility Assessment

The feasibility of the aforementioned design alternatives initially appears simple and

achievable. However, upon further inspection into the problem it is clear that the material must

first be selected in order to properly choose the correct spring. By this logic and by comparing

currently/historically used automotive spring materials and comparing the Modulus of

Resilience, it is immediately apparent that binary Ni-Ti would be suitable. In the interest of

thoroughness, vendors that produce the ternary alloys have been contacted and Team Vibranium

was informed material properties were proprietary information (See Table 1). Assuming that

binary Ni-Ti alloy is a suitable material there are already Ni-Ti springs available on the market,

which suggests that the manufacturability is only a matter of price.

Table 1 Material Selection Analysis

Alloy Modulus of Elasticity (N/m^2) Shear Modulus (N/m^2) Yield Strength (N/m^2) Modulus of Reslience (N/m^2) Range of Er +/-10%

SAE9254 2.000E+11 7.800E+10 1.034E+09 2.673E+06 2.406E+06

SAE9260 2.000E+11 8.000E+10 1.149E+09 3.301E+06 1.058E+07

Ti-6Al-4V 1.200E+11 4.500E+10 8.850E+08 3.263E+06

 Ti-10Fe-2Mo-3Al  1.070E+11 4.210E+10 1.200E+09 6.729E+06

 Ti-4.5Fe-6.8Mo-1.5Al  1.170E+11 4.300E+10 1.500E+09 9.615E+06

Ni-Ti (Martensitic) 4.100E+10 2.880E+10 5.600E+08 3.824E+06

Ni-Ti-Ta 3.700E+10

Ni-Ti-Nb

Ni-Ti-Co

Ni-Ti-Mo

18

Spring Design 3, the constant pitch compression spring, was not the ideal choice for the

performance of the system, but when one factors in cost, manufacturability, and complexity of

design then it was the most suitable selection.

Prototype Design 1 & 2 were concepts that were developed early in the development

process and did not satisfy essential requirements such as: ease of assembly, minimization of

cost, material selection, and machinability. Moreover, a grave oversight was the lack of

consideration of how to mount the damper to a component and/or system. Therefore, Prototype

Design 3 was created by using Prototype Design 1 and implementing all the parameters that were

lacking. Hence, Prototype Design 3 was selected.

Project Management

Overview

Drawing on each other’s experience and strengths the breakdown of work into specific

tasks (See Table 2) was devised. Despite being limited to only two people tasks were assigned

uniformly based on estimated time to complete and intensity of labor.

Division of Labor

Table 2 Division of Labor

Pro

ject

Fo

rmu

lati

on

Des

ign

Alt

ern

ativ

es

Pro

po

sed

Des

ign

Solid

Wo

rks

An

alys

is

AN

SYS

An

alys

is

Par

t Li

st/C

ost

An

alys

is

Pro

toty

pe

Co

nst

ruct

ion

Pro

toty

pe

Test

ing

Pro

toty

pe

Org

aniz

atio

n

Rep

ort

Pre

par

atio

n

Harold Hastings

Alexander Zuleta

19

Organization of Work & Timeline

Table 3 Project Timeline

Feb

Mar

Ap

r

May

Jun

Jul

Au

g

Sep

Oct

No

v

Dec

Project Formulation

Design Alternatives

Proposed Design

CAD Modeling

SolidWorks Analysis

ANSYS Analysis

Part List/Cost Analysis

Prototype Construction

Prototype Testing

Team Poster

Protoype Organization

Report Preparation

Final Presentation

Engineering Design & Analyses

Overview

In order to analyze and predict the behavior of Nitinol springs a FEA analysis was

proposed as a starting point. The SolidworksTM

CAD package already includes a non-linear

model for simulating Nitinol shape memory alloys and which can be calibrated to the specific

alloy in use. The results are then compared to some theoretical data which has been prepared

using a tabulated spring formula spreadsheets in order to identify the maximum and minimum

spring rates and deflection for given temperature and forces.

20

Figure 11 Spring Force Diagram

Stress Analysis & Finite Elemental Analysis

Nitinol is a material that experiences very large strains compared to other metals and in

order to simulate such material properties, a specialized FEA non-linear algorithm must be

applied. The SolidworksTM

simulation package powered by D'assault Systemes includes a SMA

Nitinol Material model that is of easy configuration and which also provides results for stress

concentration and cyclic loading test. The following figures show a simulation performed over a

4mm wire diameter spring using the SMA model. It is immediately apparent that there is a slight

buckling. This buckling is the primary reason that most springs are manufactured as “closed and

ground” which means that last two coils at the end of the spring are touching, and the top and

bottom are ground so that the spring sits flat. This same phenomenon presented itself during

experimentation of the apparatus and would consistently contact the guide rod and created

“noise” in the signal of the accelerometer.

21

Figure 12 Unloaded Nitinol Spring

Figure 13 Loaded Nitinol Spring

22

Structural Design

It was proposed that the shock absorber should contain all the moving parts enclosed by

two relative moving shells (See Figure 12) which resembles that of a strut type damper. In the

interior, the white plate moves relative to the red guide rods while the orange guide rods slide

inside of the red guide rods. Additionally, eight springs total, four superelastic (austentic) and

four SMA (martensitic), are used in both sides to capture motion in all directions; the springs

were fixed to the red plate and end caps by an epoxy. The assembly was intended for ease of

assembly/disassembly and was not intended for high load bearing duties.

Figure 14 Shock Absorber Assembly Section View

23

Figure 15 Internal Spring Configuration

To select the appropriate dimension of the spring dimension a tabulated table was

prepared by using the following material formula to determine the spring constant:

The shear modulus was a function of temperature since the young modulus varies

throughout the phase transformation from martensitic to austenitic and which range is between

40 and 70 GPa for standard binary Ni-Ti alloys.

Due to the close proximity of the guide rods to the springs’ temperature, lubricity and

rigidity were the main concerns during the material selection process. Ultimately, Copolymer

Acetal was chosen due to the low coefficient of friction, on the order of .06 to 0.41, maximum

continuous temperature use of 207-284 °F, and a Young’s Modulus of 1.4-3.0 GPa.[16]

The assembly was manufactured by CNC with ABS Plastic material. Due to the quantity

of surface features on the assembly it was apparent that rapid prototyping was be an option, as

well as CNC. Because the apparatus would be exposed to temperatures hovering around 70° C

PLA could become pliable and demonstrate excessive deformation, and the choice was made to

24

use ABS material and outsourcing the manufacturing to China was the quickest and most cost-

effective avenue.

Table 4 Spring Constant with Varying Wire Diameter and Fixed Spring Diameter

Youngs Modulus 40000000000 INPUTS

Poisson's ratio 0.33 OUTPUTs

Shear Modulus 29850746269

Number of coils 6

Spring diameter 22.9

Wire Diameter (mm )Spring Diameter (mm) Spring rate ( N/mm) lb/in

0.1 22.9 0.0000 0.0000

0.2 22.9 0.0001 0.0005

0.3 22.9 0.0004 0.0024

0.4 22.9 0.0013 0.0076

0.5 22.9 0.0032 0.0185

0.6 22.9 0.0067 0.0383

0.7 22.9 0.0124 0.0710

0.8 22.9 0.0212 0.1211

0.9 22.9 0.0340 0.1940

1 22.9 0.0518 0.2957

1.5 22.9 0.2622 1.4970

1.6 22.9 0.3394 1.9379

1.7 22.9 0.4325 2.4697

1.8 22.9 0.5436 3.1042

1.9 22.9 0.6749 3.8536

2 22.9 0.8286 4.7312

The total sliding travel of the system is determined by the geometry constraints of the

spring which embraces solid height, free length and spring diameter as shown in the following

tables in which some parameters vary and other held fixed.

Table 5 Variable Pitch and Fixed Wire Diameter and Number of Coils

25

SPRING DESIGN

Given (p) and (d) and (Na) (mm)

Pitch(p) 19

Wire diameter (d) 1.9

Number of coils (Na) 6

Pitch(p) Wire diameter (d) Coils (Na) Free Length (L0) Solid Length (Ls) Travel

1 1.9 6 7.9 13.3 -5.4

5 1.9 6 31.9 13.3 18.6

10 1.9 6 61.9 13.3 48.6

15 1.9 6 91.9 13.3 78.6

16 1.9 6 97.9 13.3 84.6

17 1.9 6 103.9 13.3 90.6

18 1.9 6 109.9 13.3 96.6

19 1.9 6 115.9 13.3 102.6

20 1.9 6 121.9 13.3 108.6

25 1.9 6 151.9 13.3 138.6

Helical Compression Plain

Table 6 Variable Number of Coils and Fixed Wire Diameter and Pitch

Pitch(p) Wire diameter (d) Coils (Na) Free Length (L0) Solid Length (Ls) Travel

19 1.9 6 115.9 13.3 102.6

19 1.9 7 134.9 15.2 119.7

19 1.9 8 153.9 17.1 136.8

19 1.9 9 172.9 19 153.9

19 1.9 10 191.9 20.9 171

19 1.9 11 210.9 22.8 188.1

19 1.9 12 229.9 24.7 205.2

19 1.9 13 248.9 26.6 222.3

19 1.9 14 267.9 28.5 239.4

19 1.9 15 286.9 30.4 256.5

Table 7 Variable Wire Diameter and Fixed Pitch and Number of Coils

26

Pitch(p) Wire diameter (d) Coils (Na) Free Length (L0) Solid Length (Ls) Travel

19 1 6 115 7 108

19 2 6 116 14 102

19 3 6 117 21 96

19 4 6 118 28 90

19 5 6 119 35 84

19 6 6 120 42 78

19 7 6 121 49 72

19 8 6 122 56 66

19 9 6 123 63 60

19 10 6 124 70 54

DSC (Differential Scanning Calorimetry) Analysis

The most important element in the Nitinol Shock Absorber project design is the spring

calculation and fabrication. Nitinol is known for changing its internal structure as a function of

temperature .This phenomenon is due to a phase transformation where material can undergo

limited deformation without breaking atomic bonds.

Phase transformation temperature is determined by the alloy recipe and the process used

to train the material; training is done by annealing the Nitinol constrained to a fixture at specific

temperature for 15-20 min or more depending on wanted properties.

In order determine the right temperature at which the material should be annealed, 3

specimens were heat treated at 460 C, 510 C, and 560.Each sample was tested using the a DSC

instrument in order to determine the heat flow (energy absorbed) during the phase transition. The

transformation temperature shifts up and down at different annealing temperatures; and based on

the design intent the annealing the temperature was chosen to be 560 C.

27

Table 8 Transformation Temperature vs. Annealing Temperature

Annealing Temp. ( C ) Transformation Temp. ( C )

460 66.81

510 73.55

560 68.37

Figure 16 Austenite Final Temperature vs. Annealing Temperature

28

Figure 17 Energy Absorbed during Phase Transformation NiTi 460

Figure 18Energy Absorbed during Phase Transformation NiTi 510

29

Figure 19Energy Absorbed during Phase Transformation NiTi 560

Thermal Control System

Nitinol Properties are greatly influenced by the temperature since its internal structure

passes through a solid state phase transformation when heated; during such transition the

material becomes stiffer as the temperature increases. As this is a diffusionless transformation, it

is time independent and is solely a function of temperature.

Nitinol has a high resistivity compared to common materials such as copper or

aluminum; this property can be used to generate internal heat using electricity, commonly known

as resistive heating, and since Nitinol is a metal alloy it can conduct high currents and at the

same time be able to produce enough heat to force itself into a solid state phase transformation.

30

For the design of a thermally controlled shock absorber, it was ideal to utilize a

microcontroller powered control system to provide such power generation in a quantitative

manner in order to study its behavior under different configurations. A power control using

PWM (Pulse Width Modulation) was chosen as the method by using an Arduino microcontroller

and a MOSFET power controller shell that is capable of switching large currents over high

frequencies.

Since both resistivity and design geometry are known, the material resistance formula can

be used to generate a table with theoretical values of how much current would pass through the

wire if it were put into a short circuit.

Figure 20 - Values for different wire diameters

31

Figure 21-Aproximate electrical current per .1 mm increment in the wire diameter

Pulse Width Modulation Power Control

A Pulse width modulation control works by changing the duty cycle of a signal in order

to vary the power input to the load. PWM can be easily achieved with a custom designed circuit,

an LM555 timer, or through a prototyping platform such the Arduino which has a dedicated

function to generate a signal.

The Arduino UNO® was selected for simplicity of use and programmability which will

allow for a more dynamic control of the signal through programming. Since the power rating of

the Arduino is limited to small currents, A PWM Power Controlled Shell ( reference as B001 )

will be in interface with the Arduino in order to handle the load; Each of the two embedded

32

MOSFET embedded are rated to 52 Amperes in a continuously load or pulsed currents up to 310

Amperes.

Figure 22 - Duty Cycle

Figure 23 - PWM Power Controller Shell - B001

Thermal Analysis

The Nitinol based shock absorber will experience high stress due to the carried weight,

the temperature generated by the spring and the input signal strength. In order to perform a

33

material selection FEA and dynamic simulation had to be performed in order to detect weak

points and friction within the parts.

Transient thermal analysis

Since the Nitinol requires temperatures above 50⁰ C in order to go into a phase

transformation, FEA transient thermal analysis has to be perform to obtain a the heat distribution

over a working time. The following is a simulation of the end cap made out of ABS resin with

heat generation where the spring is to be bonded or anchored; the simulation run over 10 minutes

with a heat source of 55⁰ C.

Figure 24-Transient Heat over 600s – ABS – Plastic

34

Figure 25-Temperature Distribution at 600s – ABS plastic

Nitinol Spring Design Making

To ensure the springs were designed properly the following table was used to estimate the

approximate surface tension when the wire was bent at a known radius. If the tension becomes

greater than 10% the material could go into plastic deformation or possibly have a surface

rupture.

Table 9 - Nitinol Surface Tension for Bending

Outer Fiber Strain Ratio of Bend Diameter to

Wire Diameter/Thickness

Ratio of Bend Radius to

Wire Diameter/Thickness

1% 100.0 to 1 50.0 to 1

2% 48.9 to 1 24.4 to 1

35

3% 32.2 to 1 16.1 to 1

4% 23.9 to 1 11.9 to 1

5% 18.9 to 1 9.44 to 1

6% 15.5 to 1 7.74 to 1

7% 13.1 to 1 6.56 to 1

8% 11.3 to 1 5.64 to 1

9% 10.0 to 1 5.00 to 1

10% 8.83 to 1 4.41 to 1

20% 3.95 to 1 1.97 to 1

30% 2.33 to 1 1.16 to 1

40% 1.49 to 1 0.74 to 1

50% 0.99 to 1 0.50 to 1

60% 0.65 to 1 0.33 to 1

70% 0.42 to 1 0.21 to 1

80% 0.25 to 1 0.13 to 1

To use the above referenced numbers; divide the bend diameter by the wire diameter

in question. Find the closest value in the middle column and read the corresponding value in the

first column. For example, for a 1 mm diameter wire being bent around a rod with a diameter of

10 mm, the ratio of bend diameter to wire diameter is 10 to 1, which represents approximately

9% strain on the surface of the wire. In simple bending, this strain will be in tension along the

outer surface of the wire and in compression on the inner surface of the wire. The interior of the

wire will see smaller strain magnitudes with strain of approximately 0% near the midline of the

wire (neutral axis).

36

The maximum recoverable strain limits for both Superelastic and shape memory NiTi is

about 6 to 8%. However, 3 to 4% is the recommended limit for product design. The ductility of

NiTi wire which has been cold worked and heat treated is typically 10 to 20% in tension. Fully

annealed NiTi wire has a ductility limit of about 60 to 70%.

Note: The numbers in the above table are approximate values based on general beam theory

calculations for all materials. They have not been specifically calculated for NiTi alloys.[17]

The following tables were created with Autodesk Inventor. Based on geometric and

material properties that were input into the software package the following values were

generated.

Figure 26 spring working Diagram

37

Table 10 Inventor Spring Load

Min. Load F1 7.340 N

Max. Load F8 44.482 N

Working Load F 44.482 N

Table 11 Inventor Spring Dimensions

Loose Spring Length L0 114.000 mm

Wire Diameter d 1.900 mm

Pitch of Free Spring t 19.683 mm

Outside Spring Diameter D1 24.800 mm

Mean Spring Diameter D 22.900 mm

Inside Spring Diameter D2 21.000 mm

Spring Index c 12.053 ul

Table 12 Inventor Spring Coils

Active Coils n 5.695 ul

Coil Direction right

Spring Ends

Params Start End

Closed End Coils nz1 1.000 ul nz2 1.000 ul

Transition Coils nt1 1.000 ul nt2 1.000 ul

Ground Coils zo1 1.000 ul zo2 1.000 ul

Table 13 Inventor Assembly Dimensions

38

Min. Load Length L1 103.640 mm

Max. Load Length L8 51.213 mm

Working Stroke H 52.427 mm

Working Load Length Lw 51.213 mm

Installed Length L 114.000 mm

Table 14 Inventor Spring Material

User material

Ultimate Tensile Stress σult 1102.400 MPa

Allowable Torsional Stress τA 600.000 MPa

Modulus of Elasticity in Shear G 29745.000 MPa

Density ρ 6550 kg/m^3

Utilization Factor of Spring Material us 0.900 ul

Figure 27 Inventor Working Diagram

Table 15 Inventor Results

Space between Coils of Free Spring a 17.783 mm

Pitch of Free Spring t 19.683 mm

Stress Concentration Factor Kw 1.000 ul

Spring Constant k 0.708 N/mm

Min. Load Spring Deflection s1 10.360 mm

Total Spring Deflection s8 62.787 mm

Limit Spring Deflection s9 101.279 mm

Limit Test Length of Spring Lminf 17.229 mm

Theoretic Limit Length of Spring L9 12.721 mm

Spring Limit Force F9 71.752 N

Min. Load Stress τ1 62.400 MPa

Max. Load Stress τ8 378.182 MPa

Solid Length Stress τ9 610.031 MPa

39

Critical Speed of Spring v 11.745 mps

Natural Frequency of Spring Surge f 152.567 Hz

Deformation Energy W8 1.396 J

Wire Length l 563.909 mm

Spring Mass m 0.010 kg

Spring Check Result Positive

Team Vibranium created their own table :

Table 16 Team Vibranium’s Spring Design Table

ksi Mpa lbs N

0.080 Force 2.004 8.916

5781 39859 0.060

2589 17853 0.040

4314 29745

1932 13323 in mm

0.7480 19.000

100 689 0.0748 1.900

20 140 0.9016 22.900

130 896 12.053 12.053

35 241

55 379 in mm in mm in mm in mm

87 601 4.563 115.900 5.236 133.000 4.713 119.700 4.638 117.800

0.524 13.300 0.524 13.300 0.598 15.200 0.598 15.200

4.039 102.600 4.713 119.700 4.114 104.500 4.039 102.600

lbf N

2.004 8.916

0.898 3.993

ksi MPa

13.572 60.372 12 81

6.079 27.042 4.92

35 242.93071 1.00

7.788 34.644 16 108.81269

3.488 15.518 in mm 2.21

5.784 25.728 1 13

2.591 11.524 1 30

ksi Mpa lbf/in N/m lbf/in N/m

16 109 3.840 672.486 7.680 1344.971

43 295 1.720 301.217 5.560 973.703

Pure Austenite

PureMartensite

Free Length (L0)

Curvature Correction Factor (Kc)

Bergstrasser Facor (Kb)

Wahl Factor (Kw)

Martensite

Martensite

Austenite

Austenite

2.000

8.000

2.000

8.000

0.000

6.000

1.000

7.000

Physical Properties of Spring

Spring Index ( C )

Overall Spring Constant (k)

Torsional Modulus of Rupture

Transformation Strain

Single cycle

100 cycles

100,000 cycles

Shear Modulus

Mean Shear Stress (τm)

Alternating Shear Stress (τa)

Poison's Ratio

Spring Design Helical Compression Plain

Spring Design

Pitch (p)

Wire diameter (d)

Austenite

Martensite

Yield Strength

Austenite

Martensite

Plain Plain & Ground

Martensite

Martensite

Austenite

Alternating Fatigue Force (Fa)

Martensite

Martensite

Installation Preload (Fmin)

Fatigue Loading Considerations

Austenite

Austenite

Mean Fatigue Force (Fm)

Martensite

Austenite

Force Developed (Fmax)

Shear Stress (τ)

Stress

Allowable Stress

Martensite

Austenite

Spring Constant (k)

Spring Deflection (y)

Ultimate Strength

Alternating Strength

Mean Strength

Material Properties

Property

Young's Modulus

Austenite

Martensite

Transformation Properties

Hysteresis

1.119

1.111

1.066

1.041

Squared or Closed Squared & Ground

Concentration Factors

Shear Stress Correction Factor (Ks)

Spring Diameter (D)

Static Load

0.33

Austenite

Austenite

Static

Fatigue

Factor of Safety

Number of End Coils (Ne)

Number of Coils (Na)

Travel

Solid Length (Ls)

Total Number of Coils (Nt)

6.000

Design Overview

As previously mentioned, the final design has a robust geometry that will easily handle a

maximum desired load of 20 lb. The changes in the overall spring constant were greater than the

changes in damping ratios. The heat delivery was able precisely control the heat over to the

desire range of temperatures. Heating response was notices to be faster than cooling response

and dependent of current density.

40

Cost Analysis

The cost analysis that has been provided (See Table 9) has been based off of costs

provided by the vendors, and an estimate of machining time was based on complexity of parts at

a rate of $50.00 per hour. Due to the complexity of the selected prototype, it was determined

that rapid prototyping (3D printing) was the most cost effective, and outsourcing the work to

China was the cheapest option.

Table 17 Cost Analysis Table

Item Quantity Expected Cost Actual Cost Expected Maching Cost Actual Machining Cost Material Vendor

Annealing Fixture 2 $40.00 $55.00 $50.00 30+25 Brass C360 eBay

Vibration Data Logger 1 $200.00 $342.52 $0.00 $0.00 N/A Convergence Instruments

Temperature Data Logger 1 $100.00 $125.99 $0.00 $0.00 N/A Amazon

5 Minute Epoxy 1 $20.00 $9.97 $0.00 $0.00 2-part Expoxy DevCon

Springs 8 $128.40 $157.37 $150.00 $0.00 Ni-Ti NDC

Guide Rods (Set) 8 $30.00 $67.10 $5.00 $0.00 Acetal Amazon

Upper Housing 1 $100.00 $200.00 $50.00 $0.00 ABS Plastic Industri-Man (China)

Lower Housing 1 $100.00 $200.00 $100.00 $0.00 ABS Plastic Industri-Man (China)

Spring Plate 1 $200.00 $40.00 $0.00 $0.00 ABS Plastic Industri-Man (China)

Upper Endcap 1 $100.00 $100.00 $75.00 $0.00 ABS Plastic Industri-Man (China)

Lower Endcap 1 $100.00 $100.00 $75.00 $0.00 ABS Plastic Industri-Man (China)

MOSFET PWM Controller 1 $20.00 $35.67 $0.00 $0.00 N/A eBay

Arduino Uno 1 $20.00 $20.00 $0.00 $0.00 N/A eBay

Shunt & Ammeter 1 $20.00 $18.90 $0.00 $0.00 Various Amazon

Misc Electronics $25.00 $80.00 $0.00 $0.00 Various Multiple

Multi-meter 1 $50.00 $50.00 $0.00 $0.00 Various Sears

Thermocouple 1 $20.00 $16.00 $0.00 $0.00 Iron-Constantan Omega

Thermocouple to Digital Converter 1 $50.00 $20.45 $0.00 $0.00 Various eBay

Test Fixture 1 $50.00 $120.00 $0.00 $0.00 Various Multiple

Engineering Hours (x2 engineers) 200 (hrs) $6,000.00 (salary) $0.00 $0.00

$7,373.40 $1,758.97 $505.00 $0.00

($2400.00 per month salary per engineer)

Subtotal

Estimated Total Cost

Actual Cost to Date

$7,878.40

$1,758.97

Prototype Construction

Parts List

1. Peg Board 4 sq. ft.

2. 3/8” Wooden Dowel x 3 ft

41

3. ¾” Plywood

4. SMA NiTi Springs x 4

5. Superelastic NiTi Springs x 4

6. Upper Shell Half x 2

7. Lower Shell Half x 2

8. Upper Guide Rod x 4

9. Lower Guide Rod x 4

10. Upper Lid

11. Lower Lid

12. Slider

13. M10 x 100 Carraige Bolt x 3

14. 10mm galvanized washers x 50

15. 10mm nylon washers x 6

16. 5 minute epoxy 25 ml

17. Wood epoxy 100 ml

18. 12 AWG X 14 ft

19. Arduino Uno Controller

42

20. Type J Thermocouple

21. Digital to Analog Thermocouple converter

22. PWM Power Controller Shell

23. 100 Watt Shunt Ammeter combination

24. Power Resistor 0.25Ω - 1Ω x 2

25. Various Electrical Connectors

Construction

Spring Fabrication

Once the DSC analysis is performed and the annealing temperature determined, the next

step is to constrain the material into shape using a metal fixture. The fixtures were fabricated

using solid brass rods with the spring form embossed. The wire is coiled up to the rod and fixed

from the ends using a pair of hose clamps. To accomplish the correct sizing taking into

consideration the material springback, two fixtures were made with 10% and 20% diameter

compensation in order to compare different results; based on some tests made the springback

compensation was estimated to be negative 10% for the spring diameter and positive 20% for the

its free length, therefore the final revision of the fixture was made longer with a smaller

diameter. The pitch was unaffected after heat treatment.

43

Figure 28 Spring Fixtures

Figure 29 Spring Fixtures

44

The Nitinol material was acquired in wire form and in order to shape it into a spring coil,

heat treatment must be carried out.

The temperature for annealing was selected to be 560° C based on the DSC analysis. The

loaded fixture placed in the oven for 20 minutes based on common practices used to train

Nitinol, and which and later should be quenched in water at room temperature.

Table 18 Spring Components

Material Behavior Count Annealing Temp. (C) Transformation Temp.(C) Diameter

Superelastic Nitinol Alloy Elastic 4 560 Not tested 1.9 mm

SMA Ni51Ti49 Plastic and Elastic 4 560 68 1.9 mm

Table 19 Annealing Kiln

Table 20 Kiln with Annealing Fixture

45

Thermal Delivery System

The thermal delivery system in the SMA Shock Absorber is founded on resistive heating

to raise the material temperature by passing current through and which consequently induces a

non-diffusive phase transformation that causes a response. The Young’s modulus changes as a

function of temperatures which can be control quantitatively by taking feedback from a

thermocouple.

Table 21 Circuit Diagram

Prototype Assembly

When all of the components and hardware had been manufactured and/or accumulated

46

Testing & Evaluation

Overview

Insofar as the testing of the system, Team Vibranium currently plans to manufacture a

specialized testing rig that can introduce a controlled frequency of varying force and amplitude

into the system. The response of the system will then be measured. The data collected will be

analyzed, subsequently a transfer function will be created, and a ratio of the input/output

frequencies and amplitudes will be generated which will determine the effectiveness of the

system.

Design of Experiment

In order to ensure accurate results it was determined that digital test equipment was

dictated by the required resolution and dynamic response of the system. A wood frame was

created to mount the shock absorber on. A three axis Micro Electro Mechanical System

(MEMS) accelerometer (See Appendix A) was mounted to the shock absorber housing and an

infrared thermometer data logger (See Appendix A) was used to record the data. The system

was tested by preloading the system, perturbing it, and measuring the dynamic response

(specifically the time it took the system to reach equilibrium). This rudimentary experiment was

initially performed with the springs at ambient temperature. Subsequently the experiment was

performed with varying PWM settings to alter the temperature of the springs while keeping the

compression distance of the springs constant. Several iterations of the aforementioned procedure

were performed and the resultant data was be recorded and tabulated. The resultant data allowed

for Team Vibranium to determine if there was any significant response in damping. The

47

following second order ordinary differential equation is well established with a known solution.

The damping coefficient could be attained by solving the subsequent equation.

Data & Data Analysis

Full Martensitic experiment

By using the acceleration sensor the system response could be graphed and the time taken

to damp the perturbation could be easily measured. This test was performed at ambient

temperature when all springs where at their martensitic state. During both martensitic and

austenitic phase the system behaves under-damped. During the martensitic phase the system

shows a higher damping ratio than in austenitic phase.

Figure 30 Method to measure Logarithmic Decrement

48

The following formulas we used to determine the damping ratio based on the information

obtained from the data acquisition system.

Figure 31 Damping ratio formulas for underdamped systems

Mass Ambient Temeprature Wire Temperature Time to equilibrum X1 (g) X2(mg)

5 lbf 26°C 25°C 440ms 1.18164 134

Martensitic Phase

Table 22 Full Martensitic Experiment Variables

49

Figure 32 Time to reach equilibrium (Full Martensite)

Full Austenitic experiment

Mass Ambient Temeprature Wire Temperature Time to equilibrum X1 (mG) X2(mG)

15 lbf 26°C 70°C 840ms 386.422 57.6172

Austenitic Phase

Table 23 Full Austenitic Experiment Variables

50

Figure 33 Full Austenite Response Time

Phase Dampin Ratio

Martensitic 0.30

Austenitic 0.23

Table 24 Damping ratio results

The experiments showed that it was possible to vary the damping ratio over a small range by

changing the phase from martensitic to austenitic. The K equivalent spring constant was also

greatly increased when in austenitic phase.

The following was obtained over different duty cycles in order to determine how fast the system

heated up to the desire austenitic phase temperature.

51

Figure 34 Resonance Frequency (Hz) vs. Spring Rate (N/m)

Figure 35 Duty Cycle 1 Temperature vs. Time

52

Figure 36 Duty Cycle 0.75 Temperature vs. Time

Figure 37 Duty Cycle 0.5 Temperature vs. Time

53

Figure 38 Cool Down Temperature vs. Time

Design Considerations

Assembly and Disassembly

During the design process it was determined that a lip feature would be integrated on

both the top and shells (See Figure 33).

54

Figure 39 Lip Feature and Threads on Top and Bottom Shells

Additionally, the top and bottom lids were threaded, as well as the upper and lower shells that

they were mated to (See Figure 34). This was to ensure easy removal of the top and bottom

shells, which was paramount for access of instrumentation during the experimentation process.

Additionally, it served as a visual confirmation that the components were operating as expected.

Initially the idea was to use an adhesive to join the respective halves of the upper and lower

shells permanently, but that would not have allowed for complete disassembly. Ultimately, only

the upper and lower guide rods were epoxied to their respective lids and the springs were

epoxied to both the lid and slider. This constituted a sub-assembly that could not be

disassembled any further.

55

Figure 40 Threading on Top and Bottom Lids

Maintenance of the System

Regular Maintenance

One of the goals for this design was to make a low maintenance suspension system. The

only regular maintenance would be to ensure that any dirt and debris has been removed from the

path of any moving parts.

Major Maintenance

At this time no major maintenance can be recommended without further long-term

testing.

Environmental Impact

Although Titanium, one of the two elements of Nitinol, is the ninth most abundant

element in the Earth’s crust.[18]

“There is not much information available on the effects of nickel

56

upon organisms other than humans. We do know that high nickel concentrations on sandy soils

can clearly damage plants and high nickel concentrations in surface waters can diminish the

growth rates of algae. Micro organisms can also suffer from growth decline due to the presence

of nickel, but they usually develop resistance to nickel after a while.

For animals nickel is an essential foodstuff in small amounts. But nickel is not only

favorable as an essential element; it can also be dangerous when the maximum tolerable amounts

are exceeded. This can cause various kinds of cancer on different sites within the bodies of

animals, mainly of those that live near refineries. Nickel is not known to accumulate in plants or

animals. As a result nickel will not bio magnify up the food chain.” [18]

Conclusion

Conclusion & Discussion

As is evidenced by the above graphs, the fully martensitic configuration reaches

equilibrium 0.440 ms and the fully austenitic configuration reaches equilibrium in 840ms. Using

logarithmic decrement it was found that the damping ratio was 0.32 for the fully austenitic

configuration. For the fully martensitic configuration logarithmic decrement determined the

damping ratio to be 0.23. This illustrates a conclusive advantage to damping in the martensitic

phase. Due to the complexity of the phase change being coupled with temperature more

equipment, time, and analytical models will be needed to accurately provide usable data.

57

Recommendations & Future Work

In order to proceed with further studies more specialized equipment should be used. The

composition of the material is a key factor in determining the material properties since minor

changes in composition could lead to big changes in transformation temperatures, therefore the

right composition should be studies as well. Also, a better testing fixture should be developed in

order to avoid undesired vibrations.

58

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59

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Appendix A: Experimental Equipment

1. Convergence Instruments | Vibration Sentry RT 128 | 3-axis ± 16g MEMS accelerometer

2. Omega | BARE-20-J-12 | Bare Wire Type-J Thermocouple

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3. DROK | DC Digital Electric Meter 0 to 100A Ammeter LED Tester Blue + Shunt

4. Craftsman | Model 82139 | Multimeter

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5. Schumacher | XP500 | Jump Starter

6. DSC courtesy of Florida International University Department of Mechanical & Materials

Engineering

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Figure 41 Isolated Scale

Figure 42 DSC Apparatus

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Appendix B: Technical Drawings

Shock Absorber Prototype Technical Drawing

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Constant Pitch Compression Spring Technical Drawing

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Test Fixture Technical Drawing

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Test Fixture Assembly Technical Drawing