Analytical Field and Torque Analysis of a Reaction Sphere

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In recent years, the increasing need in small satellite solutions triggers the miniaturization of attitude control systems. Reaction spheres were proposed as promising replacements of conventional reaction wheels for their 4π rotations. Since the generated control torques could be about any desired axes, a single reaction sphere is sufficient for three-axis stabilizations of spacecraft. This paper presents an innovative design of reaction spheres. Its driving unit is a combination of permanent magnets (PMs) and electromagnetic induction. This enables the generation of torques about three principle axes simultaneously. Meanwhile, a contactless bearing is integrated into the actuator design. Detailed designs and working principles of the reaction sphere are described. To investigate performance characteristics of the actuator, field modeling is of great importance and provides the basis for dynamics modeling. In this paper, an improved analytical model for dynamic fields excited by slotless distributed windings is presented for the first time. To study the cross coupling between PMs and electromagnetic induction, the static field generated by PMs is also modeled analytically. These developed models are validated through comparisons with numerical simulations. Electromagnetic torques generated by the actuator are calculated through the approaches of the Maxwell stress tensor and the Lorentz force law. Torque calculations based on the analytical field models deviate from those based on the numerical model slightly, with the maximum error within 4%;. This means the presented analytical models allow to predict the electromagnetic field distribution and torques precisely.

Original languageEnglish
Number of pages11
JournalIEEE Transactions on Magnetics
Publication statusE-pub ahead of print - 1 Jan 2018


  • Analytical model
  • Analytical models
  • Coils
  • electromagnetic induction
  • magnetic field
  • Magnetic levitation
  • reaction sphere
  • Rotors
  • Stator windings
  • Windings


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