LionSat, Team 4

Critical Design Review

Magnetic Torquer Project

Team Members: Rick Krauland

Adam Salerno

Matt Sams

Asa Wagner

EE 403W

Section 1

Nov. 20, 2003

Table of Contents

Abstract ………………………………………………………... 1

Introduction …………………………………………………… 2

Project Theory ………………………………………………… 3

Project Implementation ………………………………………. 5

Conclusion …………………………………………………….. 7

Appendix A: Financial Summary ……………………………. 8

Appendix B: Gantt Chart …………………………………….. 9

Appendix C: Statement of Work …………………………….. 10

References ..……………………………………………………. 11

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 magnetic core rod and enclosed in a protective, non-magnetic housing.

Our specific goal is to design and implement the optimal torquer capable of producing 10 Am². To this end, we will be constructing and testing torquers made using soft iron and Hiperco 50. We will then contrast 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 design implementation)
3. Magnetic Moment Testing (magnetometer test)

This proposal includes a description of the theory behind the torquer design and testing, as well as an overview of the implementation processes required to carry out the physical construction and testing. Ancillary information includes an organizational Gantt chart, 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 orbit
2. Obtain ambient measurements of undisturbed ionospheric plasma environment via two probes mounted on booms deployed from the endcaps
3. Correlate ambient to ram/wake measurements
4. Investigate initial spin-up and spin maintenance using a pair of RF ion microthrusters
5. Prepare students at undergraduate and graduate levels for productive careers in technical and non-technical fields relating to space systems

Our team will focus on the attitude control subsystem. This subsystem requires the use of a magnetic torquer to correct for small attitude changes of the satellite while in orbit as well as generation of spin. If the attitude changes are left uncorrected, the satellite's orientation would make it unusable for the intended scientific measurements, as well as stray from its orbital path. The magnetic torquer consists of a cylindrical metallic core wrapped with wire. This solenoid is an electromagnet that can be controlled by the varying of current through the surrounding wire. The purpose of the solenoid is to create a magnetic field that will interact with the earth's magnetic field in order to correct for small deviations in orbital attitude. Our finalized design for the magnetic torquer will be linked to a control system that will regulate the current flow scheme of the wire. The control system will consist of bi-directional control electronics that will allow current flow in both directions across the core.

Our design must take into account several factors:

1. Identification of an ideal core material.
2. Wire winding pattern
3. Dimensions of the core material
4. Design of an appropriate bi-directional control circuit

We plan to construct two prototypes consisting of soft iron and Hiperco 50. Each prototype will be tested to determine which design will produce a moment closer to our desired magnetic moment of 10 Am².

Theory

Design constraints:

1. Rod length < 40 cm
2. Rod mass < 0.5 kg
3. System voltage = 12 volts
4. Power consumption < 1 watt
5. 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 (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 results in the required current:

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

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:

N_d = demagnetization factor

B = magnetic flux density

N = number of turns

I = current in the coil

R = core radius

m = magnetic moment

l = rod length

u_r = relative permeability

u₀ = free space permeability

B = (u₀ * N * I) / (l * [(1/u_r) + N_d])

m = (B * pi * r^2 * l) / (u₀)

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

Gives us…

m = (pi * r^2 * N * I) / ((1/u_r) + N_d)

given that:

I = 83 mA

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

m = (10.51*r)/((1/u_r) + N_d)

m = (10.51*r)/((1/u_r) + 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 (u_r). This formula indicates that the relative permeability will have to be on the order of thousands 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 a core material called Hiperco 50, we can assume a 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.

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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 will need 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 allows us to use pulse width modulation to vary the direction and magnitude of the current. To ensure that the switching frequency on the pulse width modulator is high enough, one must calculate the L/R time constant. Inductance L of a solenoid is given by:

L = (u₀* u_r*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 to achieve maximum current in the coil.

Implementation

Materials:

The focus of this project will be fabricating a solenoid using Hiperco 50, a cobalt/iron composite core that will act as our final prototype. We have a 16 inch sample with a diameter of 0.475 inches. Since our budget only allowed for one sample of Hiperco 50, we also have a soft iron sample to be used for winding practice.

We have 10 pounds of 32 AWG magnet wire for winding, and recently were given access to a coil winder. The Hiperco and iron solenoids will require 6600 and 6200 turns, respectively, so we will use the coil winder to expedite the process.

We will also need control electronics for generating power. We will implement an H-bridge device, consisting of two npn and two pnp transistors, a capacitor, and a series of resistors. This device will allow bi-directional control of our torquer, meaning quicker and more powerful reactions to an applied current. See appendix A for schematic.

Construction:

Construction will consist of winding the wire about the core using the coil winder, then making the necessary terminations.

We will mount the core on the winder using the vice, and then feed the wire along the length of the core as the coil winder turns. We will either manually feed the wire to the core as it progresses across the rod, or construct another wheel with a lead screw for moving the wire across the rod. We can easily achieve a single coil solenoid with this procedure, though multiple layers are possible.

Once wound, we will terminate the ends for attaching to the drive electronics. This will likely be done by soldering the ends of the wire, then attaching the ends to the H-bridge outputs.

Testing:

The final step in the fabrication process is the physical testing of the prototypes. Utilizing the setup from “On Determining Dipole Moments of a Magnetic Torquer Rod – Experiments and Discussions,“ we will test for the amount of magnetic field produced via pulse-width modulation.

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 will need to take place in an atmosphere with little to no magnetic field interference, usually created by nearby magnetic materials inside any building. Coupling the magnetometer with a sufficient power source and a computer for storing data, the acquired magnetic flux data can be converted to magnetic moment values using a formula presented in the paper.Conclusion

Our magnetic torquer prototype will be the basis for the attitude control system for Penn State's LionSat project. The magnetic torquers will create a magnetic moment, which will allow the nanosatellite to be oriented with respect to the earth's magnetic field.

Our first task was to determine a core material best suited for our given design constraints. We believe that Hiperco 50 is the best choice due to its high permeability and low mass, and have purchased a 16 inch piece to build a prototype. We also purchased 12 feet of soft iron to compare moments and to practice the winding procedure.

We have calculated that the number of turns required to create a moment of 10 Am^2 using Hiperco 50 is approximately 6635. We have determined the length of our core material, as well as the overall length and diameter of magnet wire required.

We have begun testing an H-bridge circuit that will allow bi-directional current flow. Not only will we have to troubleshoot the logic in the circuit, but we also have to test our torquer with a magnetometer to prove that a moment of 10 Am² is physically attainable.

The results of our project will be the following:

1. A prototype torquer
2. A recommendation regarding core material and design specifics
3. A detailed testing procedure to determine the magnetic moment
4. A procedure for accurately winding the torquer

Appendix A

Schematics / Diagrams

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Figure 1: H-Bridge Circuit Schematic

Appendix B

Parts List

H-Bridge Circuit:

(1) 470 uF capacitor

(2) TIP125 Darlington PNP transistor

(2) TIP120 Darlington NPN transistor

(4) PN2222A NPN transistor

(2) 47 ohm resistor

(2) 3.3k resistor

(2) 10k resistor

(2) 470 ohm resistor

Magnetic Torquer:

(1) 5lb spool of 32 AWG magnet wire

(2) 6ft of ½ inch diameter soft iron core

(1) 16in of .475 inch diameter Hyperco core

Winding Mechanism:

(1) Variable speed winding machine

Appendix C

Gantt Chart

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Figure 2: Gantt Chart

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.

Blick, Robert. 2002: “H-Bridge / Projects for Students and Hobbyists.“ Retrieved from: http://www.bobblick.com/techref/projects/projects.html

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

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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