Electromagnetic Accelerator Progress Report

Christopher Alix

Justin Nash

William Wilkinson

Advisor: Professor Kent Chamberlin

Date: 12 December 2012

Courses Involved: ECE 541, 603, 651, 704, 775, PHYS 407, 408

Completion Date: May 2012

Design Objectives

Our team's goal is to produce a fully functional multi stage coilgun by May of 2013. The

system should consist of 2 to 5 stages and will be designed to use a projectile that is between 1

and 2 inches in diameter. To provide more efficient projectile acceleration, the use of Bitter

plate coils in the design is currently being pursued. With the increased power density of Bitter

plate coils and the improved mechanical ruggedness of this design, our team hopes to break

the sound barrier.

Progress

The progress we made in our first semester can be subdivided into two categories. First,

several different drive coils were built as test stages. These test stages used rare earth magnets

as projectiles instead of a powered coil in order to simplify the design. The second area of

progress made this semester was the design and construction of a firing control circuit. This

circuit is essential for any further testing of our design, since the firing process requires precise

timing.

Test Coil Progression:

Two different size test coils were built and tested during this semester. A large diameter

barrel (Figure 1) using a 2 inch diameter PVC pipe wrapped with 4 gauge wire was built first,

and then a smaller 1 inch diameter model (Figure 2) was built later. The thicker gauge wire has

a large current capacity and a low input resistance, allowing the capacitor bank to work

efficiently. Serving as the projectile is a 2 inch diameter rare earth magnet boasting a magnetic

field density of 1.5 T at its surface. This design has several downsides, however. The large 4

gauge wire has very thick insulation, limiting the packing efficiency of the wound coil. The large

gauge wire is also expensive compared to the smaller and thinner insulated 10 gauge wire. Also,

the thickness of our 2 inch PVC barrel prevents optimum inductive coupling between the rare

earth magnet and the drive coil. This lack of coupling makes the passive switching of our design

much more difficult to attain. For these reasons a smaller coil with a 1 inch diameter barrel was

constructed.

The 1 inch diameter coil has 10 gauge stranded core wire wound around a PVC drain

pipe. The projectile is a 1 inch diameter rare earth magnet of the same type used before. The

thinner walled drain pipe allows greater magnetic coupling between the projectile and coil. The

change in voltage of the coil resulting from the moving projectile is more easily observed using

an oscilloscope. This voltage transient demonstrates the inductive coupling that pushes the

drive coil current through zero. The thinner insulated and more inexpensive wire allows more

turns to be wound in the drive coil. Our most recent coil uses nearly 100 feet of wire.

One of the problems encountered during drive coil testing was the small time constant

of our coils. This resulted in the magnetic field completely collapsing before the projectile

reached the coil. The high number of turns present in the smaller test coil design increased the

overall inductance of the circuit, allowing us to observe the magnet interacting with the

collapsing magnetic field of the coil.

The 1 inch diameter drive coil design allowed us to test our control circuitry and verify

the feasibility of passive switching. It serves as a valuable test platform , although it is not the

long term answer. The smaller gauge wire combined with the increased length of wire present

in the coil results in a higher resistance (around 0.12 Ohms) than desired. This high resistance

limits the maximum current to a little more than 100 amps at peak capacitor bank voltage.

Looking forward, the finished project will ideally feature an energized projectile. Building a

useful projectile on the scale necessary to fit within the 1 inch barrel would be fairly difficult.

Also, despite the improved inductance of the smaller coil, the time constant is still too short,

allowing most energy present within the drive coil to decay away instead of being transferred

to the projectile. To correct these deficiencies, a two inch inner diameter Bitter plate coil is

being designed as a replacement.

Firing Circuitry:

Figure 3 shows the block diagram of the launch system. The system consists of a drive

coil, a rare earth magnet, a capacitor bank, beam break sensors, a monostable 555 timer

producing an adjustable pulse, a 555 timer configured as a latch, a launch switch, a solid state

relay, a high current solenoid switch, a MOSFET, and a bank of SCRs. The firing process begins

when the launch switch is used to trigger the latch. This provides a signal to the solid state

relay, which switches on power to the high current solenoid switch. The solenoid switch closes

and allows current to flow through the drive coil. This current stores energy in the magnetic

field of the coil, which pulls a rare earth magnet towards it. Just before the rare earth magnet

reaches the coil, it passes through a set of beam break sensors. When the beam is broken, a

reset signal is sent to the latch. This shuts the solid state relay off and opens the high current

switch. The beam break signal is also sent into the monostable 555 timer. This creates a signal

pulse that switches on a MOSFET and provides power to the SCR bank gates. The pulse width is

adjusted based upon the necessary duration of SCR triggering. This system allows the rare earth

magnet to be drawn in to the drive coil, making use of the energy stored in the magnetic field

of the coil after the capacitor bank is disconnected, and it also allows the rare earth magnet to

move through the coil without having any braking force applied. Each sub-component of the

system will now be described in greater detail.

The first sub-component of the system is the rare earth magnet projectile (Figure 4).

The magnet is a Neodymium magnet (NdFeB) with a length of 2 inches and a diameter of 1 inch.

The magnet has polls on either end of the long axis, and the estimated pull force is 180 pounds.

Although the magnet has a metallic coating, the bulk of the magnet is a brittle, ceramic

substance. The magnet was chipped several times over the course of testing the system.

The capacitor bank for this system consists of 5 threaded terminal Maxwell

ultracapacitors that are connected in series by steel bus bars (Figure 5). The bank has a

capacitance of 600 F, a voltage of 13.5 V, an effective series resistance of 1.45 mΩ, and the

ability to store 54,675 joules of energy. The bank is series connected in order to get as close to

an impedance match to the drive coil as possible for maximum power transfer. Although 1.45

mΩ is far from matching the 120 mΩ resistance of the coil, it is the best that we could do with 5

ultracapacitors.

The high current switch for the system is built around a 12 V solenoid (Figure 6). The

solenoid is threaded in to a circuit breaker box. Two copper blocks are used to conduct high

currents. One block is connected to a non-conducting material in the circuit breaker box, and

the other block is attached to the solenoid plunger. Wires from the drive coil and capacitor

bank are bolted to the blocks. When the solenoid power is switched on by a solid state relay,

the plunger is pulled into the solenoid. This causes the copper block attached to the plunger to

make contact with the stationary copper block, producing a secure electrical connection. Once

power is removed from the solenoid, a return spring attached to the rear of the plunger draws

the plunger out of the solenoid and breaks the high current connection. Power for the solenoid

is supplied by a modified computer power supply.

The beam break sensor for this system is built with an infrared photo transistor and a

spectrally matched photo emitter, both produced by Optek (Figure 7). The photo emitter is

connected between 8 V and ground by a 165 Ω resistor, providing the maximum current level of

50 mA to the emitter. The photo transistor is tied to ground by a 2.7 kΩ resistor and tied to 8 V

by 660 Ω. The output of the photo transistor is taken between the transistor and the 2.7 kΩ

resistor. When the photo emitter illuminates the photo transistor, the conduction path through

the transistor is opened and 80% of the voltage drops across the 2.7 kΩ resistor. When the

beam is broken, the conduction path is closed and the 2.7 kΩ resistor transitions to 0 V. Taking

the output of the photo transistor on the ground side is necessary because both 555 timer

circuits rely upon low voltage trigger signals. The emitter and transistor are positioned on holes

drilled through opposite sides of the PVC pipe near the drive coil, and are held in place with

electrical tape.

A relay is used to turn the high current switch on and off (board placement is shown in

Figure 8). The relay chosen is a solid state relay produced by International Rectifier. This IC is

capable of handling 6 A of continuous current. As Figure 9 shows, the switching is accomplished

through an optical channel in the chip. In order to turn the relay on or off indefinitely with only

short signal pulses, a latch is used to provide the control signal. A 555 timer is configured for

this purpose (Figure 8 shows board placement, and Figure 10 shows latch configuration). A

momentary on push-button switch provides the trigger input, and the beam break sensor

provides the reset input.

The final sub-component of the system consists of the SCR bank and triggering circuitry.

The bank is made up of 5 SCRs produced by Littlefuse (Figure 11). Each SCR is capable of

handling 40 A of continuous current and 520 A of surge current. The gate requires between 5

and 40 mA of current in order to trigger properly. A 555 timer in monostable configuration is

used to produce the trigger pulse for the SCR bank (Figure 12 shows the circuit configuration,

and Figure 8 shows board placement). When the sensor beam is broken, the 555 timer receives

a trigger pulse at the input terminal. The timer then produces a single output pulse. The

duration of this pulse is set by an external RC network. The potentiometer seen in Figure 8 is

used to set the width of this output pulse. The output pulse of the timer is sent into a power

MOSFET. This is necessary because the 555 timer alone is not able to provide the current

necessary to trigger all 5 SCRs in the bank. The MOSFET is connected to 8 V at the drain and

connected to the SCR bank gate through the source. Two 10 Ω, 10 W resistors are placed in

series between the MOSFET and the SCR gates in order to limit current.

Testing Results

Our design worked well and allowed us to collect useful data. The first parameter we

measured was projectile velocity. Initially, we intended to use a chronograph to measure the

velocity of our projectile. However, the chronograph has a minimum velocity of 30 feet per

second, and the projectile was not able to reach it. Instead, the distance traveled by the

projectile both horizontally and vertically was measured. The projectile traveled 59 inches and

dropped 26.25 inches. The equations of motion were used to calculate velocity:

Xf = Xi +ViΔt +1/2aΔt2

The velocity was found to be 13.3 feet per second. Once velocity was determined, the

kinetic energy of the projectile was calculated:

Kinetic Energy = 1/2 mv2

The mass of the rare earth magnet was estimated using its volume and density. At a

mass of 193 grams, the projectile had a kinetic energy of 1.57 joules. Next, we compared the

kinetic energy of the projectile to the energy removed from the capacitor bank. Voltage

measurements were taken both before and after projectile launch, and the energy removed

was calculated:

Energy Removed = 1/2CVi2 - 1/2CVf

2

The voltage level in the capacitor bank dropped from 13.36 V to 13.35 V, meaning that

80 joules of energy were removed. This gave the system an overall efficiency of 2%. The energy

stored in the magnetic field of the drive coil was also calculated:

Energy = 1/2 LI2

The peak current value through the coil was 110 A, and the inductance was found to be

250 µH, meaning that 1.51 joules of energy were stored in the magnetic field. Although much of

the energy transfer to the projectile took place while the capacitor bank was still connected to

the coil, a portion of the energy stored in the drive coil after disconnect contributed to

projectile kinetic energy as well.

An oscilloscope was used to take several measurements. Figure 13 shows a waveform

screenshot of the voltage across the drive coil. The negative square pulse corresponds to the

portion of the launch process where the capacitor bank and drive coil are connected. The sharp

spikes at the beginning of the pulse are due to bouncing of the high current switch. Once the

negative pulse ends, the voltage reaches a positive value and quickly decays. This positive peak

shows the current in the drive coil decaying through the SCR bank. The current in the coil is

driven to zero as the projectile approaches the coil and induces an opposing voltage. As the

projectile passes through the center of the drive coil and moves on, the polarity of the induced

voltage flips. The data collected proves the passive switching theory by showing that the drive

coil decay current is driven to zero and does not reestablish as the projectile moves on.

Plan for the Next Semester

Our next step will be to develop and test a design featuring a Bitter plate drive coil.

Using metal plates instead of wire will allow us to match the coil to our capacitor bank and

achieve the current levels and inductance needed for higher efficiency operation. Since we are

fabricating the Bitter plate coil ourselves, we can build it to our exact specifications, allowing for

a higher level of inductive coupling to be achieved. The drive coil will be designed to fire 2 inch

diameter projectiles. This will allow us to use the 2 inch diameter rare earth magnet during

initial testing. Ultimately, we plan to replace the rare earth magnet with a powered projectile

coil, which will most likely be made with Bitter plates as well.

Our team has developed FreeMat code that will help us to build a Bitter plate coil

efficiently (see Appendix B). Data inputs for the code are plate inner and outer diameter, plate

thickness, insulator thickness, intended coil resistance, capacitor bank specifications, and metal

type used to construct the coil. The code first calculates the number of turns necessary to

achieve the design resistance. This is accomplished by partitioning each plate into a number of

wire loops and finding the equivalent resistance of the loops in parallel. Next, the dimensions

and number of turns are used to estimate the inductance of the coil. This data is used to plot

the transient current response of the circuit. This is accomplished by a loop that solves the RLC

differential equation in small time steps and plots the result (example result shown in Figure

14). Finally, the peak current value of the circuit is used to calculate the energy stored in the

magnetic field of the coil and the strength of the field. This model is simple and does not take

resistance change due to heat into account. However, it should provide enough information to

allow us to build a drive coil that performs significantly better than our wire wound designs.

Conclusion

Our team has made considerable progress so far. Our fire control system allowed us to

prove the passive switching theory that is central to our design. Now, we are free to focus our

efforts on making the system more efficient. Our test coil produced satisfying results, so it will

be exciting to see how much more power we can get out of an improved design. Building Bitter

plate coils will be the key to maximizing the power output of our system.

Appendix A: Figures and Diagrams

Figure 1: Two Inch Diameter Drive Coil

Figure 2: One Inch Diameter Drive Coil

Figure 3: Block Diagram of Launch Control Circuitry

Figure 4: Rare-Earth Magnet

Figure 5: Capacitor Bank

Figure 6: High Current Switch

Figure 7: Beam Break Sensor Components

Figure 8: Integrated Circuit Board Layout

Figure 9: Solid State Relay Diagram

Figure 10: 555 Timer in a Latch Configuration

Figure 11: SCRs

Figure 12: 555 Timer in Monostable Configuration

Figure 13: Screen shot of Voltage across the Drive Coil

Figure 14: FreeMat Plot of Transient Current Response

Appendix B: FreeMat Code

clear all; clc;

Cu = 1.68*10^-8; %Resistivity of Copper

Al = 2.82*10^-8; %Resistivity of Aluminum

%%%%Capacitor Bank Parameters%%%%

Cap = 3000; %Capacitance in Farads

VCap = 5.4; %Voltage

ESR = 0.00029; %Effective Series Resistance (Ohms)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%Coil Dimensions (Inches)%%%%%

OuterDia = 12;

InnerDia = 1.5;

PlateThickness = 0.1;

InsulatorThickness = 0.001;

%%%%Coil Design Parameters%%%%%%%

Material = Al;

designRes = 0.00029;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Innerrad =0.0254*InnerDia/2; %Converts inner radius to meters

Outerrad =0.0254*OuterDia/2; %Converts outer radius to meters

n = 10000; %Number of partitions for resistance estimation

Thickness = 0.0254*PlateThickness; %Converts plate thickness to meters

Ressum = 0; %Initializes resistance sum

Seglen = (Outerrad - Innerrad)/n; %Sets length of calculated segment

R = 0; %Initializes resistance value

for j = 1:n

R = Material*2*pi*(Innerrad + 0.5*Seglen + (j-1)*Seglen)/(Seglen*Thickness); %Calculates resistance of a single band on a metal disk

Ressum = Ressum + 1/R; %Sums up inverse of resistance values

end

FinalR = 1/Ressum; %Finds the equivalent resistance of all bands in parallel

turns = designRes/FinalR %Determines the number of coil turns

length = turns*PlateThickness + turns*InsulatorThickness %Determines overall coil length

Inductance = 4*pi*10^-7*turns^2*pi*Outerrad^2/(0.0254*length) %Estimates coil inductance based upon number of turns and geometry

TotalR = designRes + ESR; %Finds total system resistance

%This section plots the transient current response of the RLC circuit

alpha = TotalR/(2*Inductance); %Calculates alpha parameter for current analysis

omega = 1/sqrt(Inductance * Cap); %Calculates omega parameter for current analysis

omegaD = sqrt(omega^2 - alpha^2); %Calculates damping factor

S1 = -alpha + sqrt(alpha^2-omega^2); %Calculates parameter for differential equation

S2 = -alpha - sqrt(alpha^2-omega^2); %Calculates parameter for differential equation

A1 = VCap/(Inductance * (S1-S2)); %Calculates constant for differential equation

A2 = -A1; %Calculates constant for differential equation

B = (VCap/Inductance)/omegaD; %Calculates constant for differential equation

CalcTime = 5; %Length of calculation time in seconds

Points = 2000; %Number of data points per second

for j = 1:(CalcTime*Points)

if omega > alpha %Handles underdamped circuits

I(j) = B*exp(-alpha*j/Points)*sin(omegaD*j/Points); %Calculates current for each time step

x(j) = j/Points; %Sets x values for horizontal plot scale

end

if omega < alpha %Handles overdamped circuits

I(j) = A1*exp(S1*j/Points) + A2*exp(S2*j/Points); %Calculates current for each time step

x(j) = j/Points; %Sets x values for horizontal plot scale

end end

%Plots current plot(x,I); title('RLC Transient Current Response'); xlabel('Time (Seconds)'); ylabel('Current (Amps)');

PeakAmps = max(I) %Determines peak current level

Energy = max(I)^2*Inductance*.5 %Calculates energy stored in magnetic field

Strength = PeakAmps*turns*1/(0.0254*length)*4*pi*10^-7 %Determines field strength based upon ampere-turns per meter %And free space permeability