Since the beginning of the space race in 1957, the number of objects sent into orbit is continuously growing, as does the amount of space debris orbiting the Earth. This is becoming a real threat for operational space missions around the Earth. Space debris can be the result of:
- A collision between two satellites, two debris or a satellite and a debris/meteoroid
- A battery which became unstable and exploded
- Fuel leftovers in a satellite or a launcher stage which became unstable and exploded
- A planned destruction
- An out of control satellite or a launcher stage
Today, the population of space debris is estimated to be more than 500 000 trackable objects where 20 000 of them are bigger than a tennis ball. In addition, there are millions of pieces too small to be detected.
The vast majority of space debris is located in Low Earth Orbit (LEO) where most space missions are located or planned. Figure 1 illustrates the distribution of debris around the Earth in 2013.
The ECE3SAT project is a student project developed at the french engineer school, ECE Paris. The goal of the project is to send a CubeSat in space to verify a physical theory permitting a fast deorbiting.
A CubeSat (1U-class spacecraft) is a nanosatelite satellite for space research that is made up of multiples of 10x10x11.35 cubic units, with a weight less than 1.33 kilograms. CubeSat are most commonly put in low Earth orbit by deployers on the International Space Station (ISS).
The Attitude Determination and Control System (ADCS) is focused on the control of the rotating motion of the satellite. Through sensors it will determine the attitude and act using it’s environment to reach the required orientation.
To test and validate the ADCS of the CubeSat, the team decided to build a device that can generate a steady and controlled magnetic field: a Helmholtz coils magnetic simulation environment.
What are Helmholtz coils?
The CubeSat uses the geomagnetic field (the Earth's magnetic field) for two important tasks: detecting its orientation, using magnetometers, and rotate, with magnetorquers. Magnetorquers are coils, in the nanosatelite, that can generate a torque, according to this formula:
The Helmholtz coils are two separate coils facing each other like described in the scheme below.
By Ansgar Hellwig, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=193184
This combination can generate a magnetic field between the two coils that is uniform on one axis. Here is a spatial representation of this magnetic field on a plane orthogonal to the coils.
The norm of this field depend of the radius of the coils, the number of windings and, more importantly, the intensity of the electric current. This means that, by controlling the amperage, we can chose the magnitude of the magnetic field. In order to achieve a three dimensionnal magnetic field, we use three pairs of Helmholtz coils, orthogonal to each other.
By building a device like this, it is possible to generate a magnetic field with a control on the norm and direction using the current. Thus we can:
- Test and calibrate magnetometers in a controlled environment.
- Test and validate the sizing of the magnetorquers
- Integrate those two in a CubeSat model to test our filtering and positioning algorithms
- Build a visual representation of the CubeSat progress.
Video of the Helmhotlz Magnetic Simulation System
These were our design specifications:
|Volume of the constant filed zone||64L (40x40x40cm)|
|Output magnetic field range||-5 to 5 Gauss|
|Input voltage range (per coil)||20V to 60V|
|Max. input current (per coil)||3A|
|Coils equivalent series resistance (ESR)||22.5Ω|
|Time of assembly and disassembly||Less than 5 min.|
|Maximum variation of the field||< 10µT|
To achieve this, we used the Wolfram Square Helmholtz Coils demonstration by Peter Euripides. This is a simulation with 80 windings, with 80 cm square Helmholtz coils at 1.5 A.
With this configuration, we get an amplitude of 5 Gauss (five times the geomagnetic field in each direction). By putting a current of 3A per coil instead, this rises to 10 Gauss.
Design & Construction
As discussed earlier, we chose the following dimensions for our simulator: 80cm square coils with 80 turns. This adds up to about 256m of copper per coil. The wire used for the windings is 0.5mm (AWG 24) diameter copper enameled magnet wire.
To wind these coils, the frame is made out of aluminum profile, U-shaped. The outside width of the profile is 7.5mm, which is enough to store about 140 turns of our wire. It is also fairly rigid and inexpensive.
In order to ensure that the assembly and disassembly time meet our constraints, we designed a 3D-printed clip that attaches the 6 coils of our Helmholtz simulator together and makes a rigid cage.
A circuit is required to control the current that goes through the 6 coils and therefore the magnitude and direction of the magnetic field.
The subsystems are the following:
- Logic computational unit: this board drives the power modules according to the software that is loaded on the micro-controller
- Power H-Bridge: these modules control the amount and the direction of the current that goes through each coil
This is the circuit we designed for each these modules:
Using the open-source CAD software Kicad, we designed a compact, single-sided PCB to build 6 identical modules.
The purpose of this board is to run the software and drive the H-bridges. It is based around an Arduino Nano with an Atmel ATMEGA328P mainly because of the cost and the simplicity of the programming tool-chain compared to other more powerful micro-controllers.
We also used Kicad to design a PCB to layout the connectors to the LEDs and the power modules.
To program the Helmholtz coils, the user can simply provide a three dimensional waveform of the desired magnitude of the magnetic field. The software reads the arrays and handles all of the low level tasks: calculation of the PWM duty cycle, changing the pins’ states, etc. There are also built-in safety procedures to avoid the sudden collapse of the magnetic field, which might be dangerous for the user and the electronics.
To validate our simulator, it is necessary to check two aspects of the magnetic field it generates:
- The constancy of it with a fixed input current on each of the three axes
- The full control of the magnitude of the field on each of the three axes
Constancy of the field
To make sure that the field in the working volume is constant, we ran several series of tests. For each of the axes, a constant current is fed into the pair of coils, and a sensor is moved within the cage.
For instance, this capture was taken during a back and forth movement of the sensor along the X axis, while the X axis pair of coils was powered to reach 2.15 Gauss (215 µT).
The field is very constant: within 0.06 Gauss of variation in the X axis. This matches our specifications.
With the same test performed on the three axes, we validated the constant nature of the magnetic field in our Helmholtz simulation environment. This is a very important result as it proves that the coils are well wound, that the electronics manages to power them with a constant current, and that any testing we will later do in the simulator is meaningful no matter where it is placed in the working volume.
Control of the field
After it is proved that the field is constant within the working zone, we ran another set of test to check the control that we have on the generated field.
The experimental protocol is the following: a description of several magnetic field waveforms is done in the software, and a sensor is placed in the Helmholtz coils. If the measured waveform corresponds to the one described in software, it proves that we have control over the magnetic field.
For instance, we described in the software triangle waveform for the magnitude of the X axis magnetic field. This waveform has an amplitude of 2.15 gauss (215 µT) and a period of 7.5s.
As shown by this capture, the waveform corresponds to the one we described in software. With the testing of the magnetic field with different waveforms in each of the three axes, we validated our control of the Helmholtz simulation environment.
By popular demand, I added an archive containing Helmholtz coil ressources (more design details, code, electronic schematics, etc.). Click on this button to download it:
Notice: the content of this archive is provided "as-is", under the terms of the CC0 1.0 Universal (CC0 1.0) Public Domain Dedication license.
Author: Charles Grassin
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