Download 399 draft.docx - University of Victoria

Project Title: Mass Acceleration
Final Report
Website: http://web.uvic.ca/~cpberg/Site/Welcome.html
by
[Syed Ali; V00137245]
[Chris Burg;V00653139]
Group: #19
Supervisor: [Ashoka K.S. Bhat]
Due: December. 3rd, 2012
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December 3rd, 2012
Ashoka Bhat
Professor of Electrical Engineering
University of Victoria
Dear Dr. Bhat:
Please accept the accompanied ELEC 399 report entitled “Research and design of
prototype electromagnetic mass driver technologies”. This report is the result of work completed
throughout the course of the fall 2012 semester. During this course our group was tasked with
selecting and researching a design project of our choice. We decided on this project based on
the relevant interests of the team and the potential to carry on research into a 499 project.
While working on this report we were afforded the opportunity to learn about the linear
induction motors, electromagnetics, embedded systems and sensors and future applications of
this technology.
We would like to thank you for your time helping and the project proposal which has
served as the basis of our project.
Sincerely,
Chris Berg, Syed Ali
Group # 19
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Table of Contents
1.0 Introduction ................................................................................................................................... 4
2.0 Goals ............................................................................................................................................. 4
3.0 System Design................................................................................................................................ 5
3.1 Electromagnetic Theory ............................................................................................................. 6
3.2 Switching Circuit ........................................................................................................................ 7
3.3 Control System........................................................................................................................... 8
3.4 Track and Projectile.................................................................................................................... 9
4.0 Force Equations ........................................................................................................................... 10
5.0 Controller R&D ............................................................................................................................ 12
6.0 Electromagnet R&D.................................................................................................................. 13
7.0 Summary ..................................................................................................................................... 13
8.0 Future Development .................................................................................................................... 14
9.0 Applications ................................................................................................................................. 14
10.0 References ................................................................................................................................. 15
Research............................................................................................................................................ 15
Appendix I ......................................................................................................................................... 16
Supervisor’s Comments: .................................................................................................................... 18
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1.0 Introduction
In order to facilitate a revolution in space exploration new launch systems must be
considered that dramatically lower the cost of achieving orbit. Electromagnetic catapult launch
systems are a class of potential launch systems that use electromagnetism to accelerate payloads
to high speeds.
The Coilgun (a.k.a. electromagnetic mass driver) is a direct adaptation of a linear
synchronous motor that operates through the inductive reaction between stationary stator coils
and a coaxial conducting armature that is attached to a projectile. It has been shown that with
superconducting materials incorporated into the design, efficiency can reach >= 90%. (1)
With future breakthroughs in high-temperature superconductivity, we believe that
Coilgun technology may offer the cheapest and most economical launch platform for future
space exploration.
2.0 Goals
The intention of our project was to investigate the basic theory surrounding Coil gun
designs and to develop a model for future experimentation. This project analyzed much of the
basic physics involved in linear synchronous motors and electromagnetic and analyzed some
requirements necessary to create such a system. Topics that saw analysis and testing included:
Basic charging circuits, boosters, sensors and embedded control systems.
Additionally this project intended to identify and address any misconceptions regarding
basic Coil gun theory that may not have been specifically addressed in advanced academic
literature. This included testing basic electromagnetic theory and comparing computer modeled
results to experimental results.
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3.0 System Design
A Coil gun consists of magnetic core wrapped with a copper coil (figure 1). The entire
launcher system will have multiple coils setup; each subsequent stage will detect the incoming
velocity and adjust the power applied to the coil. The stages will be arranged in a toroid or
linear setup (figure 2). Once the projectile has reached a desired velocity, the projectile can be
allowed to propel out to a desired location.
Figure 1: Single stage coil system
Figure 2: Two-Stage Toroidal Track
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3.1 Electromagnetic Theory
The cross sectional view of the solenoid (figure 3). The magnetic field lines indicate the
attractive force caused by the solenoid magnet. The projectile should be ferromagnetic to cause
attraction. As the projectile enters the solenoid the flux linkage will begin to increase causing a
back emf to oppose the supply voltage.
Figure 3: Flux Linkage vs Distance
As the object moves closer to the center of the solenoid, the repulsive force (negative
force) will begin to take effect causing the projectile to pull back to the center. In this case, the
solenoid 1 will be turned off, simultaneously turning on the subsequent solenoid to continue the
‘attractive force’ on the projectile.
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Using Maxwell 3D, the above simulation resulted in the field diagram shown in the
figure above. As you can see that there is linkage between the projectile and the right coil, while
very minimal linkage with the left coil; this is due to the opposite rotation of the current density
applied to the cores.
The position and size of the projectile plays an important role in terms of acceleration.
Using a similarly sized projectile and inductor lengths produces maximum efficiency(2).
Figure 4: Work Per Unit Volume vs Projectile Length
3.2 Switching Circuit
There are several methods used to high power switching circuits. The elements range
from transistors such as high power MOSFETs to Thyristors.
MOSFETs are devices used in high power switching and can be used to power the
individual coil stages(figure 5). Additional amplification can be used to achieve higher power.
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Figure 5: Charging Circuit
Thyristors (SCR) can also be used for this application. When a small current is applied
to the gate, the thyristor begins to conduct from anode to cathode (figure 6a). However, the gate
cannot stop the thyristor from continuing to conduct; switching off the current or the supply to
the anode can turn off the thyristor.
Figure 6a: Thyristor
Figure 6b: IGCT
Another device known as the Integrated Gate Commutated Thyristor (IGCT) (figure 6b)
can be used. IBCT has the turn off property via the gate which the regular thyristor does not.
3.3 Control System
Using optical sensors to detect an emitted light source within the track , the velocity of
the projectile can be calculated by determining the time the projectile takes to pass between two
successive light detectors. This information is used to determine when to cut power to the
inductive boosters, as well as providing a closed-loop control method for future development
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(figure 7). The prototype initially will use open-loop control to obtain the maximum stable
velocity the system can obtain.
Figure 7: Velocity Sensing
Equation 1: Velocity
Arduino will be used as a scalable central control system (Figure 8). The system will interface
with both the optical and control the high-power charging circuit.
Figure 8: Arduino Controller
3.4 Track and Projectile
The track will be made of a heat tolerant, non-conductive PVC material shaped into a
toroid (Figure 2). Small insertions in the track will allow the optical emitter and sensor to detect
an object passing between them. A ferromagnetic cylinder with a diameter slightly smaller than
the thickness of the track will be used as a projectile.
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Figure 2: Two-Stage Toroidal Track
4.0 Force Equations
When current is flowing in a multi-turn coil, the magnetic field is produced around the coil
which stores the magnetic energy. The magnetic flux is given by the expression below:
where N is the number of turns, i is the current in amperes, is the the total reluctance of the
system. The flux always follows a path of the least reluctance; the relationship is identical to
Ohms law. The reluctance is defined by the equation:
where A is the cross-sectional area.
The equation for the magnetic stored energy is given by the expression:
From the energy equation, the change in force F with respect to distance x is given by the
expression:
We can now derive the equation further by integrating both sides.
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Figure 9: Equivalent Reluctance circuit model
For simplicity, we will consider the reluctance equivalent circuit shown in figure above. The
total reluctance will be the sum of the reluctances of which the flux penetrates:
We know that from the reluctance definition, the change in total reluctance will be a function of
the change in its length and the area with respect to the moving projectile in the x-direction; this
makes the total reluctance non-linear. It is clear that as you move along the x-axis, the Rg in the
circuit above will begin to fade as no flux will be reaching the Rp. Subsequently, the next stage
coil will be out of phase to attract projectile, continuing to flow the flux in Rp. This cycle will
continue and propel the object forward. In the example above, we have neglected any loss of
energy through hysteresis.
Using Matlab, a force vs. displacement graph was obtained. The parameters used are also noted
in the comments of the Matlab script (see Appendix).
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5.0 Controller R&D
Based on Arduino documentation, input must range from 6v-20v, optimally from 7V-12V.
However, light sensor output ranged from 0V-3V. Two circuits were developed to boost signal
strength.
Transistor amplifier circuit
In order to boost the output signal strength, the amplifier circuit shown below was developed.
This circuit provided the necessary drop in voltage required to detect a break in optical
detection.
Figure 10a: Photodiode Amplifier Circuit
Current Limiting Circuit
A simpler voltage divider circuit was also developed. As seen in the figure below, By using a
larger input voltage we were able to simply get the desired voltage with a limited current.
Figure 10b: Current Limiting Circuit
Both circuits were able to detect an object passing between the light emitter and sensor. The
current limiting circuit suffered from a low tolerance of outside noise, while the signal amplifier
was able to adjust for noise in software. Due to ease of implementation of the current limiting
circuit, as well as the low accuracy requirements of the photodiode we suggest moving forward
with the current limiting circuit in future designs.
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6.0 Electromagnet R&D
Field testing of the electromagnetic inductor was compared to simulated results. With
ferrite core of length = 50 mm, diameter = 42 mm, turns = 80, assumed relative permeability of
312(average), and current 10 A:
Experimental results using Gauss Meter showed an internal magnetic field of 0.087 T. This
result was surprising but could have arisen due to estimations of the permeability of ferrite and
the turns-ratio.
7.0 Summary
Research into basic Coil gun theory presented interesting results and challenges. A
multistage toroidal configuration theoretically should allow for continual increase in the speed
of the projectile until the energy imparted is equal to frictional losses. Experimentation showed
that the magnetic field inside a hollow ferrite solenoid was in disagreement with theory, which
was an unexpected result. This most likely was due to assumptions regarding the relative
permeability of our ferrite core.
The force relationship with the change in reluctance was used to simulate the force vs.
displacement (see Appendix). The relationship graph is plausible as it clearly indicates that the
force will diminish as the distance of the projectile increases. The rate at which the force
diminishes depends on the change in reluctance from the core, the air gap and to the projectile.
Figure 11: Reluctance gap approx.
Figure 11 shows the relationship as the reluctance will change; it is determined by the
hypotenuse of the depiction above.
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Research into Arduino based control systems showed a need for photoreceptor
amplification. This was accomplished by developing and testing two signal amplification
circuits shown in section 6.0. Due to low accuracy requirements, it is expected that using the
simple current limiting circuit (figure 10b) will be acceptable for detecting the projectile.
This report has neglected the electrical, magnetic and mechanical losses and is based on
a lossless system where the input energy applied to the system, is stored as magnetic energy
which is converted to the work applied and hence the force per distance. As better technology
emerges, these losses will need to be minimized to achieve the optimal result.
8.0 Future Development
Theoretical and experimental results must be reconciled with theory before further
development can continue. Resolving the magnetic field discrepancy shown in section 6.5 can
be resolved by calculating the exact relative permeability of the ferrite core and creating a
solenoid with an exact known number of turns.
Further development of the prototype system must include research on track materials,
reducing drag on the payload and development of a physical system.
9.0 Applications
With emerging breakthroughs in materials science and computing, future development
must focus on integration of superconductive materials and quick response control systems.
Improvements in room temperature superconductivity is especially important for earth based
Coil gun launcher systems to be viable. Areas of particular application are space launch,
particle acceleration, space acceleration, transportation and defense and magnetic bearing
design.
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10.0 References
1. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA426465&Location=U2&doc=GetTRDoc.pdf
2.
http://www.coilgun.info/about/home.htm
Research
http://library.utem.edu.my/index2.php?option=com_docman&task=doc_view&gid=5052&Ite
mid=200
http://www.utexas.edu/research/cem/IEEE/PR%20107%20Bresie%20Publications.pdf
http://www.utexas.edu/research/cem/IEEE/PR%20103%20Ingram%20Publications.pdf
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Appendix I
Matlab Force simulation
% Calculating the force as a function of the changing reluctance due to the
% change of projectile x direction
%
|\
%
lg | \ sqrt(lg^2 + x^2)
%
|__\
%
x
% F=-(1/2)*(flux)^2 (dR/dx)
% flux = N*i/R
% F=-(1/2)*(N*i/R)^2 (dR/dx)
% re-arraging
% F=-(1/2)*(N*i)^2 d(1/R)/dx
% Reluctance now becomes a function of lg and x as shown in the depiction
% above.
% R(x) = (1/uo*Ac)*(-x/((lg^2 + x^2)^(3/2))
clear all
%Define variables
uo=1.2566e-6;
lg=.002; %meters
Ac=1.1025e-4; % Area 10.5^2mm^2 For simplicity, the area of airgab is
% used for where the flux is transfered to and from.
N=50;
i=10; %10A
mmf=N*i;
% RT = R1 + R2 + R3 See Section 5 - figure 9 in the report and the
% individual R values are calculated to be:
% since much of the flux will be in the air gap, the other reluctances will
% be neglected
R2=((lg)/(uo*1*Ac));
flux=mmf/R2; % Wb
Fo=-((0.5)*(flux*flux))/(uo*Ac);
syms dR(x);
dR(x)= -x/(((lg^2)+(x^2))^(3/2));
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x=linspace(-.005,.005,100);
dR(x);
F=Fo*dR(x);
plot(x,F)
grid
ylabel('Force (N)');
xlabel('Displacement x (m)');
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Log book grade (25%): ______________
Report grade (75%):
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Total Grade (100%): _______________
Supervisor’s Comments:
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Supervisor’s name (Print)
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Signature
Date
Notes for the supervisor:
1. Please return the marked hard copy to Prof. Tao Lu by Monday, December 10.
2. Attached additional pages for comments if necessary.
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