LionSat, Team 4

Final Report

Magnetic Torquer Project 

 

 

 

 

 

 

 

 

Team Members: Rick Krauland

Adam Salerno

Matt Sams

Asa Wagner

 

EE 403W

Section 1

Dec. 15, 2003

Table of Contents

 

 

 

Abstract ………………………………………………………... 1

 

Introduction …………………………………………………… 2

 

Project Theory ………………………………………………… 3

 

Project Implementation ………………………………………. 7

 

Value Assessment……………………………………………… 11

 

Conclusion …………………………………………………….. 14

 

Appendix A: Circuit Schematic....……………………………. 15

 

Appendix B: Parts List ……………………………………….. 16

 

Appendix C: Gantt Chart……... …………………………….. 17

 

Appendix D: Financial Section... …………………………….. 18

 

References ..……………………………………………………. 19

Abstract

 

The objective of our project is to design, implement, and test the attitude control system of the Pennsylvania State University Local Ionosphere Satellite (LionSat). The control device for this particular nanosatellite is known as a magnetic torque rod, or torquer. A torquer is an electromagnet consisting of an insulated, current-carrying wire wound about a ferromagnetic core rod and enclosed in a protective, non-magnetic housing.

Our specific goal is to design and implement the optimal torquer capable of producing at least 10 Am2. To this end, our task is involves design, construction and testing of torquers made using soft iron and Hiperco 50. We also must observe the output magnetic moments in an attempt to identify the most functional and dimensionally efficient core material.

 

There are three specific processes involved in this project:

 

1. Physical Design (core materials, dimensions, turns, and housing)2. Construction of Prototypes (winding, insulation, and drive circuit)3. Magnetic Moment Testing (magnetometer test)

 

This report includes a summary description of the theory behind the torquer design and testing, an overview of the implementation processes required to carry out the physical construction and testing, and a project value assessment. Data presented indicates that all design constraints are met. Ancillary information includes an organizational Gantt chart, parts list, a control circuit diagram, and references.

Introduction

 

The objective of our project is to design, implement, and test one subsystem of the Pennsylvania State University Local Ionosphere Satellite (LionSat). The LionSat program encompasses five main goals as follows:

 

1. Explore ram/wake structure via plasma probes as the spacecraft “rolls“ along orbit2. Obtain ambient measurements of undisturbed ionospheric plasma environment via two

probes mounted on booms deployed from the endcaps3. Correlate ambient to ram/wake measurements4. Investigate initial spin-up and spin maintenance using a pair of RF ion microthrusters5. Prepare students at undergraduate and graduate levels for productive careers in technical

and non-technical fields relating to space systems

 

Our team's specific focus is on the attitude control subsystem. This subsystem requires the use of a magnetic torque rod to correct for small attitude changes while in orbit. It will also be responsible for satellite spin generation. If attitude changes are left uncorrected, the satellite's course and orientation will make it unusable for the intended scientific measurements.

 

A magnetic torque rod consists of a cylindrical ferromagnetic core wrapped with wire. This solenoid effectively creates an electromagnet whose dipole moment is dependent on the amount of current in the coil. When energized the solenoid creates its own magnetic field which interacts with the earth's magnetic field thereby a creating a controlled torque capable of correcting small deviations in orbital attitude. The control system consists of bi-directional H-drive electronics that allows current flow in both directions across the core.

 

Our design must take into account these factors:

 

1. Identification of an ideal core material. 2. Dimensions of the core material3. Design of an appropriate bi-directional control circuit

 

We have been able to successfully develop a winding procedure and construct two prototypes using both soft iron and Hiperco 50 as core materials. The Hiperco rod has been tested to ensure the accuracy of the derived design equation and to show that a sufficient output magnetic moment (10 Am2) is being achieved.

 

 

Theory

 

Design constraints:

 

1. Rod length < 40 cm2. Rod mass < 0.5 kg3. System voltage = 12 volts4. Power consumption < 1 watt5. Magnetic moment = 10 Am2

 

Power considerations:

 

In order to ensure that the power consumption does not exceed 1 W we solve for the resistance required in a 12 volt system,

 

R = V2/P = (122)/(1) = 144 Ohms

 

Choosing 32 AWG copper wire already available in the lab (at 0.571 ohms/m) results in the required winding length,

 

(144 ohm) / (0.571 ohm/m) = 252.12 meters of 32 AWG copper magnet wire

 

This indicates the required current

 

I = P / V = (1)/(12) = 83.3 mA

 

Physical dimensions:

 

The next step in the design is the determination of the formula relating the length, diameter, and relative permeability of the core material to the number of turns and output moment of the rod.

 

Manipulating the equations where

 

Nd = demagnetization factor

B = magnetic flux density

N = number of turns

I = current in the coil

R = core radius

m = magnetic moment

l = rod length

ur = relative permeability

u0 = free space permeability

 

B = (u0 * N * I) / (l * [(1/ur) + Nd])

m = (B * pi * r^2 * l) / (u0)

Nd = 4*[ln(l/r)-1] / [(l/r)2 – 4*ln(l/r)]

 

 

Gives us

 

m = (pi * r^2 * N * I) / ((1/ur) + Nd)

 

Given that

 

I = 83 mA

 

N = (252.19 m)/(2*pi*r m/turn)

 

m = (10.51*r)/((1/ur) + Nd)

 

m = (10.51*r)/((1/ur) + 4*[ln(l/r)-1] / [(l/r)2 – 4*ln(l/r)]

 

Here moment is given in terms of the core length (l), core radius (r), and relative permeability (ur). This formula indicates that the relative permeability has to be on the order of thousands so as to achieve the desired moment within the mass constraint. This limits the choice of core material to a cheap, high permeability material, with a high magnetic saturation point. Choosing Hiperco 50, we can assume a minimum relative permeability of 2000. Using Matlab we can calculate moments given a range of combinations of core radius and length values, and the corresponding masses associated with each. Analyzing the resultant data it can be seen that the optimal length and diameter occur near l = 27 cm and r = 0.6 cm. The closest available, affordable Hiperco rod comes in diameter of 0.475“ (r = 0.6033 cm). The resultant design of this selection is shown in Figure 1.

 

 

#

Figure 1. Design calculation with 0.475“ diameter Hiperco 50 core

 

Assuming a density of 8200 kg/cu m, the mass of this design is approximately 0.25 kg. This falls within the 0.5 kg per rod mass constraint, with 0.25 kg of mass left for wire and housing materials. All design criteria are met.

 

 

Control driver:

 

Since the torque rod needs a reversible magnetic moment, it is necessary that the drive system be capable of supplying the 83 mA current in either direction. An H-bridge configuration used in conjunction with pulse width modulation (PWM) may allow us to vary the direction and magnitude of the current. To determine if the system response is fast enough for PWM one must calculate the L/R time constant. Inductance L of the solenoid is given by:

 

L = (u0* ur*N2*pi*r2)/(l) = 46.275 Henry

 

The time constant for this design is then calculated:

 

τ = L / R = (46.275 Henry) / (144 Ohm) = 0.32 s

 

This indicates that the drive circuit will have to operate full-on for 4τ = 1.28 seconds in order to achieve maximum current in the coil. The implication is that a solenoid of this size which has large inductance also has a response whose sluggishness may make it difficult to control using PWM.

 

Testing:

 

Magnetic moment testing of the torquer is done with the aid of a magnetometer. Placed axially at a known distance from the center of the rod, the magnetometer indicates magnetic field strength

values dependent on the voltage applied to the solenoid. Plugging the obtained values of Br into the equation shown below, the rod moment can be calculated.

#

Figure 1. Definition of Variables

#

 

Implementation

 

Materials:

 

As discussed above, Hiperco 50, a cobalt/iron composite has been selected as the prototype core material because of its ability to meet cost, mass density, permeability, and saturation requirements. To implement our design we wound the first 27 cm of a 16 inch rod of diameter 0.475 inches. Since our budget only allowed for one sample of Hiperco 50, we also wrapped a 12 inch soft iron rod as practice.

 

The winding apparatus used to construct our prototype is an old coil winder purchased on Ebay that is currently located in the SPIRIT lab in E.E. East. Additionally, our sponsors provided 10 pounds of 32 AWG magnet wire.

 

In order to bi-directionally drive the rod, we utilize a low power H-bridge circuit consisting of two npn and two pnp (TIP 31 and TIP 32) bipolar junction transistors. See appendix A for schematic.

 

Construction:

 

Rod construction consists of wrapping many layers of wire around the core using the coil winder, and then making the necessary connections between the coil leads and the drive circuit.

 

The steps taken to wind our prototype rods are as follows…

 

1. Modify the end caps of the winder so that the core is centered and fits snugly in the apparatus. A piece of foam rubber or cardboard measured and cut to size is sufficient for this.

#

Figure 2. Modified winder end cap

 

1. Place the core in the winder and secure the end cap using a wrench. If the rod is too long for the winder, the right most bolt can be removed from the base of the end cap, allowing an extra two inches of length to work with.

2. Make sure that the rod is clean. Small bits of dirt can cause bumps to form in the winding3. Set up the wire spool 1.5 to 2 feet away from the rod. Make sure that the spool can spin

freely as the wire is wound onto the rod. We used a round metal rod placed horizontally in a table clamp to support the spool.

#

Figure 3. Winding device and spool with rod in place.

 

1. Feed the wire underneath the side of the core and secure the tag end with a piece of tape. Make sure to leave about 12 inches of tag end.

2. Three people are required to wind most efficiently. One person acts as a motor operator, one tensions the wire properly and turns the spool so as to ensure that no snags occur, while a third person acts as a wire guide using their fingers to ensure each turn is wound flush to the last.

 

#

Figure 4. Wire guide (left), spool and wire tensioner (right)

 

1. Begin winding by turning the winding device clockwise by hand using the wheel on the left side of the apparatus. The individual acting as the wire guide must pay close attention

to the turns as they are wound to make sure that no gaps or overlapping occur. One way to avoid gaps is to make sure that the angle between the wire being fed and the unwound rod is just slightly larger than 90 degrees. Too large an angle will cause overlapping. If overlapping or gaps in the coil occur stop winding immediately and remedy the problem. The presence of errors in the windings will make subsequent layers very difficult to wind properly.

2. After 4 or 5 turns of wire are wound, begin running the motor slowly. The individual guiding the wire may find it useful to use a fingernail on their free hand to apply slight pressure to the coil as it is first wound on to the rod.

3. When the coil reaches the end of the rod, stop the winder and secure the end of the coil with a piece of tape.

4. Without breaking the wire, remove the rod and the spool from the apparatus5. Apply a uniform coating of clear-coat spray-on adhesive to all sides of the coil. Have a

paper towel nearby in case of runs.6. When dry, place the rod back into the apparatus and remount the spool.7. Begin the next layer (now going right to left across the rod) again by hand still turning

clockwise. Leave about an eighth of an inch between the end of the previous layer and the start of the new layer.

 

#

Figure 5. Start of a new layer wound right to left

 

1. Turn on the motor slowly and continue winding back to the start of the previous layer, again leaving about an eighth of an inch exposed at the end.

2. Again secure the end of the wire, remove the rod from the apparatus and apply the adhesive.

3. Repeat this process until all six layers have been applied4. Test the resistance using a multimeter to verify design specifications and that the coil

remains continuous.5. When the rod is fully wound solder both ends of the coil onto separate pins of a male nine

pin adapter. The female adapter is soldered to the output leads of the H-bridge circuit.

 

Testing:

 

The final step in the implementation process is the physical testing of prototypes. Utilizing the setup from “On Determining Dipole Moments of a Magnetic Torquer Rod – Experiments and

Discussions,“ we were able to test for the amount of magnetic field produced by the rod at various voltage inputs.

 

The aforementioned paper describes using a magnetometer placed axially at a distance twice the length of the rod to measure the magnetic flux density. The experiment is most effective in an atmosphere with little magnetic field interference, usually created by nearby magnetic materials inside a building. Coupling the magnetometer with a sufficient power source and a voltmeter for displaying data, the acquired magnetic flux data can be converted to magnetic moment values using a dimensionally-dependent formula shown in the testing theory section of this paper.

 

The first step in the testing setup was the use of a compass to determine the direction of magnetic north. The magnetometer was then placed with its x-axis perpendicular to the direction of magnetic north. This allowed us to minimize the effects of the earth's magnetic field in our test setup. The rod under test was placed along the x-axis of the magnetometer at a distance equal to twice the length of the rod. In our case, the rod was 16.1 inches long and the distance from the magnetometer to the center of the rod was 32 inches. Figure 6 is a photograph of our test setup.

 

#

Figure 6. Test setup. Magnetometer is placed at a known distance along rod axis.

 

A 5 volt supply was required for logic switching, while a 12 volt supply was needed to deliver power the rod. The magnetometer was powered with a separate, 28 volt power supply. A digital multimeter was used to display the output voltage of the magnetometer. The calibration curve supplied with the documentation of the magnetometer shows that the output voltage should read 2.5 V when no magnetic field is present. Our zero-point reading of 2.554 V was very close to the reference value, with slight deviation due to residual magnetic effects in the testing environment. Using 1V increments, we progressively increased the voltage supplied through the H-drive to the rod so as to gain a clear representation of the hysteresis curve of the torquer under test. When the full 12 volts was applied, we achieved a maximum reading of 2.886 V from the magnetometer. We then stepped the voltage down from +12 V to -12 V and back to zero. The first zero-point crossing read 2.605 V, at -12 V the output was 2.271 V, and at the final zero-point the magnetometer read out 2.524 V.

 

The hysteresis plot below was created from our recorded test data. It shows that the rod produces linear performance in the intended range of voltages.

 

#

Figure 7. Measured hysteresis curve indicating relatively linear operation

 

The voltage differentials between the zero-points and maximum voltage calculated from the above readings are 0.332V and 0.334V. The supplied calibration curve for the magnetometer was used to relate these voltages to the strength of the magnetic field created. Reading from the calibration curve, we achieved a magnetic field strength of 9500 Gamma.

 

Using the appropriate values from the test setup and the readings documented in our testing, we were able to calculate the magnitude of the magnetic moment produced using the equation shown in the theory section. The maximum resulting magnetic moment was determined to be 22.38 Am2. This value is very close to the magnetic moment calculated using the design equations when the extra length of the core is taken into consideration.

 

 

Assessments:

 

The primary beneficiary of our work this semester has been the LionSat organization. Our Hiperco 50 prototype rod wound with 32 AWG magnet wire successfully generated a magnetic moment large enough to control the nanosatellite while in orbit. Due to the high relative permeability of Hiperco 50, we were able to achieve a low overall weight and length of the rod, allowing more versatility for placement in a space and mass constrictive satellite. Furthermore, we were able to document a procedure for winding a torque rod, allowing easy repetition for future space rated prototypes. We produced a working prototype for less than $250, orders of magnitude cheaper than commercially available rods. As LionSat's budget is very tight, we have added significant value to this project by making it affordable.

 

We have created a torquer that performs as well as others but costs significantly less money to produce. The main advantage to commercially available rods is the included mounting brackets for use on a satellite, though our project objectives did not include designing such a device. Also, since commercial rods are bought ready for use in space while our rod is not, additional work will have to be done to adapt our design to meet space regulations.

 

We have created a valuable working prototype for LionSat that will serve as a solid foundation for its final product. We have tested our prototype for effectiveness, and have provided solid documentation for future winding efforts.

 

Work left to be done:

 

While we were able to make a significant amount of progress this semester, there are a few items that will require more work before the torque rod design can be considered complete.

 

The first item to be examined is the choice of adhesive used to coat each layer of winding. There is a concern that the spray coating we have used for our prototype could possibly outgas in the space environment. As with all components of the rod, it is required that the adhesive be considered space rated by the powers that be. Further investigation must be done to determine what material meets these standards and successfully seal each layer.

 

Another area of concern is the drive circuit. The H-bridge circuit is an acceptable driver for these devices, however, the actual parts we used for our prototype circuit are not military specified. More research needs to be done to determine the space rated equivalent of the parts we used for our prototype display. Additionally, much more research into the logistics of using pulse width modulation in this system must be done. We determined that with a very high inductance, our system has a large time constant. With a large time constant the viability of PWM comes into question. If it is determined that PWM can not be used, a full-on/full-off control scheme will have to be devised.

 

The testing we completed with our prototype indicates that our design achieves a magnetic moment within the acceptable range of values. Because our measurements took place indoors where building steel and other metal items can introduce field distortion, to get a more accurate measurement the test really should be repeated outdoors in an open area.

 

The next major part of this project will have to be the determination of the rod housing system. Factors that must be considered are the makeup of the housing material and thermal expansion issues. All components, in addition to being space rated, must be non-magnetic. A rod will most

likely be placed inside the housing container which will then be filled with an insulating epoxy and sealed. Non-magnetic mounting brackets will also be necessary. It is important to ensure that the changing temperature conditions and the associated material expansions are fully investigated so that no components are damaged while in flight.

Conclusion:

 

In summary, tasks accomplished by this group include:

 

1. Core selection meeting both cost and design constraints 2. Dimensional and turns calculations based on a derived moment formula dependent on

power, rod length, diameter, and permeability3. Identification and construction of a low power driver circuit capable of supplying the

proper bi-directional current to the torque rod4. Creation of a repeatable winding construction process, resulting in the procurement of

two prototype rods5. The successful utilization of a moment-determining test procedure to verify the design

effectiveness.

 

The progress made this fall on the magnetic torque rod prototype is a solid starting point for the for the attitude control system of the LionSat project. The magnetic torquers designed and built over the course of this semester meet all set forth design constraints and successfully create a magnetic moment large enough to control the nanosatellite orientation with respect to the earth's magnetic field.

 

 

Appendix A

 

Schematics / Diagrams

 

 

#

 

Figure 8: H-Bridge Circuit Schematic

Appendix B

 

Parts List

 

H-Bridge Circuit:

 

(2) TIP 31 transistor

(2) TIP 32 transistor

(4) PN2222A NPN transistor

(4) 1N4004 diodes

(2) 1.8k Ohm resistor

(2) 1k Ohm resistor

(1) 9 pin adapter (female)

 

Magnetic Torquer:

 

(1) 5lb spool of 32 AWG magnet wire

(1) 16“ long, 0.475“ diameter Hiperco 50 core

(1) Clear-coat enamel spray can

(1) 9 pin adapter (male)

 

Winding Apparatus:

 

1. Variable speed coil winder2. Table vice3. Metal rod to hold wire spool

 

 

Appendix C

 

Gantt Chart

#

Figure 9: Gantt Chart

Appendix D

 

Financial Section

 

 

Typical Labor Costs

 

1. 4 Engineers @ $35/hr * 20 hrs/week * 12 weeks

$33,600

 

Typical Fringe Costs

 

1. Labor Costs * 15%

$1,260

Parts

 

1. Metal Cores $385

 

1. Small Gauge Wire $25

 

1. Winding Mechanism Provided by sponsor

 

 

Total Parts

$410

Typical Overhead Costs

 

1. (Labor + Fringe + Parts) * 40%

$4,028

 

 

 

Total Projected Cost*

$39,298

 

 

*actual costs incurred this semester do not include labor, fringe, or overhead costs

 

References:

 

Lee, J., and A. Ng, 2002: “On Determining Dipole Moments of a Magnetic Torquer Rod — Experiments and Discussions“ Canadian Aeronautics and Space Journal, Vol 48, No. 1, pg. 61-67.

 

Halliday, D, R. Resnick, and J. Walker: “Fundamentals of Physics“ John Wiley & Sons Inc., Ney York, 1997.

 

Swanson, Tony. 2003: “Monsters of the Midway / Electronics“ Retrieved from: http://pubweb.northwestern.edu/~ams743/Index.htm

 

Radtke, Gregg. 1999: “Technical Note: Magnetic Torquer Overview“. University of Arizona Student Satellite Project. Document No. GNC-014, Revision 2.

PAGE

 

 

3

 

 

PAGE

 

 

14

 

 

 

 

Diameter (m)

0.0121

Length (m)

0.27

Rel. Perm,

2000

Dens.(kg/m^3)

8200

Current (A)

0.083

resistance

143.999919

Radius (m)

0.00603

Nd

0.005663346

 

 

Core Vol. (m^3)

3.10473E-05

N turns

6634.241297

coil length (cm)

134.6750983

moment (Am^2)

10.31465631

Core Mass (Kg)

0.254587966