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.
Induction-based reaction spheres have been presented in many references and their performances are normally investigated through experiments or numerical simulations which are time-consuming. Here, an analytical way is presented and it enables researchers to evaluate a new design quickly. The presented performance analysis is conducted through the classical equivalent circuit approach. Involved circuit parameters are determined through the magnetic flux density distribution which is a function of design variables. Based on this, the steady state torque-speed curve and the achievable maximum driving torque T * are identified. T * deviates from the maximum torque obtained from numerical simulations by only 3%. For validation, the presented performance analysis method is applied to an experimental case. Mean absolute percentage errors of predicted torque-speed curves are within 23% and mainly caused by end effects. The presented performance analysis method is generally applicable to induction-based spherical actuators, not only limited to reaction spheres. Additionally, since influences of design variables of the actuator have been formulated analytically through the determined circuit parameters, performance optimizations could be greatly facilitated.
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