Hyperloop Accelerator Design Review

TA: Benjamin Cahill ECE 445 February 25, 2015

Mohammad Jaber Michael Eraci Shivam Sharma

Group #24

Table of Contents

1.0 Introduction...... 3 1.1 Statement of Purpose...... 3 1.2 Objectives...... 3 1.2.1 Benefits ...... 3 1.2.2 Features ...... 3

2.0 Design...... 4 2.1 Block Diagram ...... 4 2.2 Block Descriptions...... 5

3.0 Schematics and Simulation ...... 6 3.1 Circuit Diagram ...... 6 3.2 Control Flow Diagram ...... 7 3.3 Simulations ...... 7

4.0 Requirements and Verification ...... 10 4.1 Tolerance Analysis ...... 11

5.0 Cost and Schedule ...... 12 5.1 Cost Analysis ...... 12 5.1.1 Labor Cost ...... 12 5.1.2 Parts...... 12 5.1.3 Total Cost ...... 13 5.2 Schedule ...... 13

6.0 Mathematical Theory and Calculations ...... 15 6.1 Coil Gun Theory and Equations ...... 15 6.1.1 Introduction ...... 15 6.1.2 Equations ...... 16

7.0 Safety Statement ...... 18 7.1 Ethics with Reference to IEE Code of Ethics ...... 18

8.0 References ...... 21

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1.0 INTRODUCTION 1.1 Statement of Purpose

The Hyperloop was an idea put forth by Elon Musk as a less expensive alternative to maglev trains. The goal of this project is to assist a Mechanical Engineering team finish the prototype that has been started but is not yet working. Our prototype Hyperloop will be a proof of concept and a starting point for future students to improve and refine. We will also act as consultants for all the electrical aspects of the Hyperloop design.

1.2 Objectives

1.2.1 Goals The goal of our project is to help a Mechanical Engineering senior design team create a working prototype Hyperloop Accelerator (Tubular Induction Motor). The previous mechanical engineering team acquired most of the parts for the project and partially assembled the linear induction motor.

1.2.2 Functions Our objective is to review and improve on the current motor design and assemble a functioning capsule accelerator. The accelerator should be able to propel a capsule around a loop of partial vacuum tubing.

1.2.3 Benefits ● A working prototype will provide a proof of concept for the Hyperloop ● A completed working prototype can serve as a foundation for future Hyperloop projects where further improvement can be made on the design by future teams

1.2.4 Features ● Sensors for average speed ● Sensors for power consumption ● Linear motion via tubular Induction Motor ● Stop/Start Capability

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2.0 DESIGN 2.1 Block Diagram While getting the tubular induction motor to work is the central aim of this project, there are other supporting modules we can use to reduce power consumption by only turning on the motor when the travelling capsule reaches the accelerating strip.

Figure 1: The induction motor receives inputs whether directly or indirectly from four other modules.

As shown in Figure 1, the induction motor is the terminal module with inputs from other modules used to turn it on/off to save on power consumption.

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2.2 Block Description

2.2.1 Sensors Module This module detects whether or not the moving capsule is inside the stretch of tube located inside the induction motor. We will probably use two IR sensors to detect when the capsule enters the tubular induction motor and when it leaves. 2.2.2 Control This module will use a microcontroller such as an Arduino Uno to accept input from the sensors and determine a control signal telling the power when to turn on or off the induction motor. 2.2.3 DC Power Source This module accepts the 120V RMS value AC output of the AC power module and creates a 5 V DC voltage +/- 0.5 V for use for logic operations and sensors. 2.2.4 AC Power Module This module provides a 120V RMS output to the AC to DC converter and a modulated signal to the tubular linear induction motor (on when the car is in the accelerator and off when the car is travelling through the rest of the loop. 2.2.5 Tubular Linear Induction Motor This module uses Faraday’s law to accelerate a capsule along a straight length of tube whenever the capsule completes one lap of the loop.

The motor consists of: a. Stator: 35 turns of copper winding linearly arranged along the straight length PVC pipe using wooden and aluminum supports. Serves as an induction coil b. Rotor (capsule): An iron core

Three phase AC current is passed through the coils in the stator to induce a magnetic field in them. The changing direction of the current at periodic intervals leads to a changing magnetic field in the stator in turn inducing a field in the rotor. The alternating polarity of magnetic fields between stator and motor provides linear motion.

5 3.0 Schematics and Simulations

3.1 Circuit Diagram

Figure 2: Diagram for the operation of a single coil

This circuit will be built for each of the 36 coils. The charging and discharging of the coils will be controlled by the Arduino through the use of thyristors.

Part Part number Thyristor BT 139-600 Bridge Rectifier 583-MP154 (Mouser) Capacitor 667-EET-HC2E1220A

6 3.2 Control Flow Diagram

Figure 3: Flow chart describing the eventual control structure

3.3 Simulations

Figure 4: Schematic used for the PSPICE simulation of the charging up and discharge of the 1.2 mF capacitor.

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Figure 5: It takes about 0.2 seconds to charge to capacitor to 63% of the maximal charge. Therefore the time constant is about 0.2 seconds. We will define the time to charge a capacitor as 5 time constants. As such, the capacitor charges in 1 second.

Figure 6: This is the current passing through the coil. If one were to use a 250 VAC source instead of the 50 VAC source from the simulation, the current would be 25 A. This is less than the 50 A maximum so the thyristor should not have a problem with managing that current.

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Figure 7: This shows the current leaving the bridge rectifier. If one were to use a 250 VAC source instead of the 50 VAC source from the simulation, the maximum current would be 2.25 A. This is less than the 15 A maximum so the bridge circuit should not have a problem with managing that current.

Figure 8: Velocity as a function of capsule mass Assuming that the coefficient of energy transfer from the coils to the capsule is independent of the capsule’s mass, lighter capsules would have higher velocities after leaving the coil.

9 4.0 REQUIREMENTS AND VERIFICATION

Requirement Verification Points

1. Induction Motor:

a. The motor should be able to a. Detach straight length tube 40 make the capsule move the from apparatus. Turn on length of the motor, which is 0.9 accelerator and verify that meters. the capsule is ejected out b. The motor should be able to of the end of the tube. 10 accelerate the capsule b. Dedicate a control LED for continuously without need to displaying when the restart the system. capsule passes by a sensor. Verify that the LED flashes no less than 2 times within a 30 second interval of the hyperloop being turned on.

2. Sensors:

a. There are two sensors used to a. When the capsule is 20 detect entry and exit of the directly under each sensor capsule (rotor). Sensors an output LED from the detecting white (no capsule) microcontroller should be output a high voltage. The on and when the capsule capsule is dark in color. When is not the LED output the capsule enters or exits the should be off. motor, the sensors detect black and output a low voltage.

3. The AC Power Source:

10 a. An oscilloscope trace of 20 a. Should be able to turn on and off the capacitor voltage will the motor based off of the output show the capacitor voltage of the control unit. This 150 ms before and 150 ms mechanism will employ thyristors after the pulse signal is as electrical switches. activated. The voltage before must be 200 V DC +/- 100 V DC. The voltage after must be -150 V DC +/- 150 VDC.

4. DC Power Source: 10

a. DC voltage from AC to DC a. Use oscilloscope to converter is 13V +/- 7 V (voltage measure voltage over 2 input limits for arduino). seconds and verify that the output voltage is always between 6V and 20V.

4.1 Tolerance Analysis Many of tolerances for the project are included above as part of the requirements and verifications. There are other tolerances talked about with the mechanical engineering team that have not yet been finalized.

The diameter of the core has to be half the diameter of the pipe in order for the capsule to smoothly navigate the turns and to have minimal air resistance. This was told to us as a qualification by the mechanical engineering team. Half the diameter of the pipe is 1.5” and we need to be able to increase this in order to maximize flux linkage. Through experimentation we need to find a value between 1.5” and 3.”

Currently the mechanical engineering team is working on tolerances for the velocity necessary for the capsule to minimally get around the loop and the maximum velocity we can achieve.

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5.0 COST AND SCHEDULE

5.1 Cost Analysis

5.1.1 Labor Cost

Name Hourly Rate Total Hours Total labor Cost = Hourly Invested Rate x 1.5 x Total Hours Invested

Mohammad Jaber $30 160 $7200

Michael Eraci $30 160 $7200

Shivam Sharma $30 160 $7200

Total $ 21,800

5.1.2 Parts

Item Quantity Cost Availability

Additional copper wire (for 10m (approx) $5 Yes replacement of conducting coils) 18AWG

Bridge Rectifier 40 $6.49 Order pending arrival

Step up/Step down transformer 1 $25 Not ordered yet

Magnetic sensors 12 $30 Not ordered yet

Arduino Board 1 $20 Yes

Connecting wires 20-30 $15 Yes

Total $91.49 * Since the motor is already partially assembled we will mostly be working with the parts at our disposal.

12 5.1.3 Total Cost

Section Total

Labor $21,800

Parts $75

Total $21,875

5.2 Schedule

Week Task Responsibility

2/9 Finish and submit proposal Michael

Begin working on design and prepare for mock design review Mohammad

Arrange a meeting with Prof. Haran Shivam

2/16 Prepare for mock design review and design review Michael

Initial Calculations Shivam

Proposal Corrections Mohammad

Individually complete Eagle assignment Individual

2/23 Finalize specifications for motor Shivam

Ordering parts and testing of preliminary model Mohammad

Make sure everything is ready for design review Michael

3/2 Repair of broken coils in induction motor begin design of PCB Michael

Begin work on power source Shivam

receive parts and begin work on controls Mohammad

3/9 continue work on controls Mohammad

Continue design and order of PCB Michael

Finish power source Shivam

3/16 Touch base with MechE team Michael

13 finish with controls and work with sensors Mohammad

continue motor assembly Shivam

3/23 Spring break

3/30 Individual Progress Reports All team members

Begin testing controls with motor and power source Mohammad

receive PCB and begin assembly Michael

Finish motor assembly Shivam

4/6 Consult With MechE team and test motor with hyperloop Mohammad apparatus.

Mock Demo Shivam

Make sure everything is working and finalize testing Michael

4/13 Sign up for Demonstration Michael

Final hyperloop test Demo with MechE team Shivam

4/20 Final Demonstration Michael

4/27 Final paper Mohammad

5/4 Final paper submission Michael

14 6.0 Mathematical Calculations 6.1 COIL GUN THEORY, EQUATIONS AND DESIGN TRADE-OFFS 6.1.1 INTRODUCTION

In order to linearly accelerate the capsule, the design focus shifted from a pure linear induction motor to a multi-stage coil gun due to budget constraints and the simplicity of design.

A coil gun is essential is similar to an induction motor, except instead electromagnetic induction, the concept of coil guns relies fundamentally on the magneto-static interaction between magnets (or magnetic materials)

Consider a circular coil of winding with “N” turns. When we pass a current (“I”) through the coil, given ampere’s law, magnetic flux (“ϕ”) is established in the area encompassed by the coil. This magnetic field is strongest at the center of the coil and decreases axially. The coil is now essentially a temporary magnet with the north pole at the face through which magnetic flux lines come out and the other face the south pole.

A ferromagnetic material in the vicinity of the coil (temporary magnet) will get magnetized. The surface of the material facing a particular pole of the coil is magnetized as an opposite pole. Magnetic dipoles within the ferromagnetic material will align themselves so that the material is attracted to the magnetic field.

In this way the ferromagnetic cylinder will experience an attractive force due to the magnetic field and get accelerated towards the coil.

In a multi-stage coil, coils are placed next to each other and once the cylinder has passed completely through one coil, the current through it is turned off (if the current remained on then once the ferromagnetic material was on the other side it would experience attractive force in the direction it just came from) and the current in the coil next to it is turned on. This way the ferromagnetic material continues to experience attractive forces in the same direction and can be linearly accelerated.

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6.2.2) EQUATIONS

Figure 9. Interaction between a coil winding and cylindrical iron core

a) Magnetic Field Intensity and Force for a single coil

Consider the diagram above, with a coil and solid iron cylinder.

i = Current through the coil N = number of turns L= length of winding Rcoil = Radius of the coil A = Area of the face of the iron cylinder

Consistent with Ampere’s Law. The magnetic flux density (B) through a coil with current (i) flowing in it is maximum at the center of the coil and decreases axially.

The magnetic field intensity H is given by :

퐵 퐻 = (1) µ0

µ0=permeability of free air

At the center of the coil,

퐻(푥 = 0) = 푖/2푅 (2)

16 The axial field is much more complicated to calculate. Referring to a research paper* that adopts a linear model for calculating H, the axial magnetic field intensity can be approximated by the following formula,

(3)

As seen above, the axial field is a function of distance (x) and is maximum at the center of the coil.

The force experienced by a ferromagnetic material interacting with this field can then be approximated by the following formula:

(4) Where, Χx = linear magnetic susceptibility as function of x.

These equations are too complex to solve for H or F. Plotting these equation within a particular interval for x gives us a good idea of what H and F look like as the position of the iron cylinder changes with respect to the coil.

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Figure 10. Magnetic Field Intensity vs Position

Figure 11. Magnetic Force on cylinder vs position

Taking x=0 for as center of the coil. As mentioned in the introduction the field intensity is maximum at the center of the coil and decreases axially. Also, the direction of force reverses once the cylinder crosses the center of the coil.

18 Conclusion: the coil must be turned off before the cylinder reaches the center of the coil and the next coil in the multi-stage coil gun must be turned on to continue the acceleration process b) Magnetizing Current The current “i” through the coil sets up the magnetic flux in the coil. Hence, it is called the magnetizing current. The magnetic flux that links with iron core depends on the reluctance of the core. Assuming perfect flux lines, the relation between the magnetizing current and the flux linked to the iron core is given by:

푁푖 휙 = (5) 푐표푟푒 푅 Assuming, perfect flux lines Where, 푙 푅 = 푅푒푙푢푐푡푎푛푐푒 = ( 푐 ) (6) µ푚퐴 Where, µm = magnetic permeability of the iron used lc = length of the iron core Now, Φcore = µ0*H(x)*A Therefore we get,

µ 퐻(0)푙 푖 = 0 푐 (7) (µ푚 푁)

Conclusion: The magnetizing current must be kept as small as possible to prevent reverse inductance in the coil. From the above equation it is evident that in order to do this we need an iron core with short length and very high magnetic permeability. At the same time, the diameter of the cylinder must be as large as possible to maximize the flux linkage. The above formulas are useful for a long finite length solenoid. In order to get values corresponding to our design we need to do a finite element analysis of our flux boundary value problem to get a good expression to approximate the flux linkage.

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c) Magnetic Saturation

Hysteresis of ferromagnetic materials is an important phenomenon, in that it defines the maximum magnetic field intensity that can be applied to a ferromagnetic material to provide useful for work. At a particular value of applied H, B in the material saturates and this is the maximum field that can be set up in the material to do useful work. Applying H, beyond saturation limit only leads to heat losses.

Figure 12. Magnetic Hysterisis Curve

The saturation capability of an iron core is directly related to its dimension. For, our design while it preferable to have the cylinder as small as possible to maximize exit velocity, a smaller cylinder will saturate at a much lower field than a larger one.

Conclusion: Thus, from electromagnetic perspective, the dimension of the cylinder should be as large as possible both to maximize the flux linkage and maximum saturation field. Typically for iron, the maximum saturation field is much higher as compared to the magnetic force that we can apply.

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d) Calculation: Theoretical maximum recharge time for proof of concept accelerator.

Assume 30% energy transferred from coil to capsule. The mass of the iron capsule is roughly 0.1 Kg, the capacitance we of the coil’s capacitor is 1200 mcF, and the voltage on the capacitor is will be 200V when the pulse occurs.

The energy stored in the capacitor would be ½ C V^2 = ½ (1200 mcF) (200V)^2= 24J. After transferring 30% of that energy to the capsule we will have 7.2J of energy in the capsule. The velocity of the capsule is related to the capsule energy as E=1/2 m v^2. Therefore v=sqrt(2 E/m)=sqrt(2*7.2/0.1)= 12 m/s (~39 ft/s).

As such our theoretical nozzle velocity for the proof of concept accelerator loop is 39 ft/s. The period of oscillation would be 50ft / 39(ft/s) = 1.3 seconds. As such our accelerator should recharge in a time period shorter than about 1 second just to be sure that it can accelerate the tube again as it passes by.

21 7.0 Safety Statement

Electrical Safety: This project does involve AC and DC voltages at 240 V. Dry human skin can insulate against voltages below 50 V, but can not once a voltage is above 50 V. As such one would need to show caution in interacting with the circuit and ensure that all capacitors involved are discharged before usage. One way to do such a discharge would be to use a screwdriver to touch each terminal of the capacitors.

Mechanical Safety: The capsule that we are accelerating could reach speeds of 20 m/s. If the capsule were to break out of the tube, it would continue outwards and potentially injure any observer. As such, all observers must be on the inner portion of the loop whenever the capsule is in motion.

22 7.1 Ethics with Regards to IEEE Code of Ethics

1. To accept responsibility in making decisions consistent with the safety, health, and welfare of the public, and to disclose promptly factors that might endanger the public or the environment.

We will choose parts and make our calculations always with safety in mind. We will make sure and safety concerns are made visible.

2. To avoid real or perceived conflicts of interest whenever possible, and to disclose them to affected parties when they do exist.

While working with the Mechanical Engineering team we will work in tandem to achieve the goals of both parties.

3. To be honest and realistic in stating claims or estimates based on available data.

We will make sure that any claims we make in our design are fully backed by our research and testing.

4. To reject bribery in all its forms.

As a group we probably will not come across this but we will maintain our integrity as a group.

5. To improve the understanding of technology, its appropriate application, and potential consequences.

We will make sure that our process and research are fully recorded so that people in the future can understand and replicate our work.

6. To maintain and improve our technical competence and to undertake technological tasks for others only if qualified by training or experience, or after full disclosure of pertinent limitations.

During this project we hope to learn more about the mechanics of the tubular induction motor and use the resources the ECE department has to offer to help us understand more.

23 7. To seek, accept, and offer honest criticism of technical work, to acknowledge and correct errors, and to credit properly the contributions of others.

During reviews and talks with our TA we will take criticisms and converse on how to solve the issue in a respectful manner.

8. To treat fairly all persons and to not engage in acts of discrimination based on race, religion, gender, disability, age, national origin, sexual orientation, gender identity, or gender expression.

We will work together as a group and use our collective knowledge and experience to reach our goals. We will treat each other fairly.

9. To avoid injuring others, their property, reputation, or employment by false or malicious action.

We will follow proper lab procedure and safety techniques in order to keep everyone safe.

10. To assist colleagues and co-workers in their professional development and to support them in following this code of ethics.

We will continue to help each other grow as engineering and to not ridicule each other for the questions asked.

24 8.0 References

[1] Thyristor (BT 139-600) datasheet http://www.farnell.com/datasheets/1758085.pdf

[2] Bridge Rectifier (583-MP154) datasheet http://www.mouser.com/ds/2/345/mp1505-1510-14294.pdf

[3] Capacitor (667-EET-HC2E1220A) datasheet http://www.farnell.com/datasheets/1758085.pdf

[4] *Jeff Holzgrafe, Nathan Lintz, Nick Eyre, & Jay Patterson, Effect of Projectile Design on Coil Gun Performance ,Franklin W. Olin College of Engineering, December 14, 2012; http://www.nickeyre.com/images/coilgun.pdf

[5]https://www.ndeed.org/EducationResources/CommunityCollege/MagParticle/Physics/ HysteresisLoop.htm

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