Efficiency-optimized design of PCB-integrated magnetorquers for CubeSats

TL;DR

This article extends such analysis to larger CubeSat configurations, and finds that these larger implementations increase magnetorquer efficiency, and provides a sufficient alternative to commercial coil magnetorquers, particularly in volume-restricted configurations.

Abstract

CubeSats are miniature satellites used to carry experimental payloads into orbit, where it is often critical to precisely control their attitude. One way to do this is through the use of magnetorquers, which can be integrated into PCBs. This technique saves considerable space and capital when compared with more common torque-rod magnetorquer systems. Here we derive a method of analyzing different PCB-integrated magnetorquer geometries, parametrizing them such that the magnetic moment and efficiency are optimized. Furthermore, by modulating the trace width, the trace number, and other electrical characteristics of the magnetorquer coil, this paper optimizes the generated magnetic moment. Both constant voltage and constant current sources are analyzed as inputs. These optimizations are then simulated in COMSOL for multiple geometries, and it is found that there exists an optimal geometry, given a specified power dissipation. Simulations verify the general trend and maxima of these derivations, barring small, consistent re-scaling in the magnitude of the coil resistance. It is also found that these PCB-integrated magnetorquers provide a sufficient alternative to commercial coil magnetorquers - particularly in volume-restricted configurations. This study extends such analysis to larger CubeSat configurations, and finds that these larger implementations increase magnetorquer efficiency. Optimizations for common PCB-implementable geometries on small satellites are tabulated in the Appendix.

Figures (8)

• Figure 1: Geometrical and dimensional definitions of a trace magnetorquer. Note that $t$ is expanded in scale from its actual size $(t \approx 0.07mm \leftrightarrow 2$ oz/ft). $x$ and $y$ are the width and height restraints, respectively, and $w$ and $s$ are the individual trace width and trace separation. $N$, unlabeled, is the number of traces; here $N=3$. a) Full, simplified geometry. b) Zoomed corner of geometry. c) Projected view of trace.
• Figure 2: Given a fixed $x$, $y$, $\rho$, and (small) s, the efficiency, $\eta$, decreases as trace width increases for CV. For CC, however, the efficiency increases as trace width increases. Note that these efficiencies assume a spin rate of $\omega = 1$ Hz, $B = 1$ T, with $\bm{B}$ oriented in a direction orthogonal to $\bm{m}$. These are not realistic in a space environment, and efficiency would be many orders of magnitude lessened (though the same trends remain; see Equations \ref{['eq:eff3']} and \ref{['eq:eff7']}).
• Figure 5: Comparison plots of power consumed, and power efficiency (fixed parameters given in Table \ref{['ta:parameters']}) for (a) CV and (b) CC PCB magnetorquers. The surface plots denote the efficiencies of the systems given the number of coils and their trace width. There are isometric power contours with labeled powers in W. Above the greyed boundary, the data becomes non-physical. Also, note that the color scaling is inconsistent between plots. Reference Equations \ref{['eq:eff3']}, \ref{['eq:eff7']}, \ref{['eq:power4']} and \ref{['eq:power5']}.
• Figure 8: Optimization of magnetorquer power efficiency given both (a) CV and (b) CC systems, introduced in Figure \ref{['E_power']}. Power is maximized at the scatter point on each isometric line. Note that only points below the grey boundary are physical. Further, note that the imaginary line that could connect the maxima is not smooth. As the number of traces is discrete, there is erratic stepping of the line of maxima. Reference Equations \ref{['eq:eff3']}, \ref{['eq:eff7']}, \ref{['eq:power4']} and \ref{['eq:power5']}.
• Figure 11: Comparison plots of power consumed, and magnetic moment (fixed parameters given in Table \ref{['ta:parameters']}) for (a) CV and (b) CC PCB magnetorquers. The surface plots denote the magnetic moments of the systems given the number of coils and their trace width. There are isometric power contours with labeled powers in W. Above the greyed boundary, the data becomes non-physical. Also, note that the color scaling is inconsistent between plots. Reference Equations \ref{['eq:mag3']}, \ref{['eq:mag5']}, \ref{['eq:power4']} and \ref{['eq:power5']}.