In past decades, small spacecraft have raised worldwide interest for their low cost and short development time. In general, three reaction wheels are needed for three-axis attitude control of general satellites. However, for small spacecraft where both volume and power budgets are limited, employing three wheels is a challenge. Therefore, reaction spheres are proposed as a replacement for reaction wheels. In a reaction sphere, the spherical rotor is driven by forces generated between the stator and the rotor. Since the rotor’s spin axis and the output torque could be about any desired axis in the 4¼ space, a single reaction sphere could be sufficient to implement three-axis control. Till today, various reaction spheres have been developed, but their performances are far from satisfactory. A better understanding of reaction spheres is needed and great improvements of these actuators are expected especially for small satellites. This dissertation aims at performance modeling of reaction spheres. Through the modeling process, restricting factors of performances and possible improvements are investigated. This work is focused on induction-based reaction spheres (IBRSs), which are selected as the most promising type of reaction sphere for applications to small spacecraft. @en

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. In this article, 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\ast are identified. T\ast 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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This paper investigates the performance of miniaturized reaction spheres. Currently, a majority of existing reaction spheres are at a technology readiness level of 3 to 4 and prototypes are developed for 50 kg-class spacecraft. Since the motivation of replacing reaction wheels with reaction spheres stems from the limited volume and power budgets of small spacecraft such as nanosatellites, miniaturization of reaction spheres is of relevance. In this paper, reaction spheres with two different types of driving units are miniaturized such that they can be used for CubeSats. Based on the published models and experimental data of prototypes, performances of the miniaturized reaction spheres are estimated. Relations between the estimated performances, such as output torque per power, and scaling factors are investigated. Through comparisons of the scaling characteristics of studied prototypes, reaction spheres with a PM (permanent magnet) based driving unit demonstrate great advantages in the miniaturization. Based on the reference of the Delfi-n3xt CubeSat, performance requirements of a single reaction sphere are derived. By comparing the required and estimated performances of the scaled reaction sphere, it is found that generating required outputs with the limited power budget is the main challenge for electromagnetic induction based small actuators. To improve their efficiency, advances in superconducting and manufacturing technologies are needed. Reaction spheres with a PM based driving unit require advanced sensors and control algorithms to make their applications to small spacecraft feasible.@en

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.

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With respect to spacecraft attitude control, reaction spheres are promising alternatives to conventional momentum exchange devices for the benefits brought by their 4. π rotation. Many design concepts of reaction spheres have been proposed in the past decades, however, developments of the driving unit and the bearing, as well as their combination remain great challenges. To facilitate research and push developments in this field, this paper provides a comprehensive review of reaction spheres. To some extent, an in-depth survey of multi-DOF (degree of freedom) spherical motors and possible bearings is provided, along with their advantages and weaknesses addressed. Some multi-DOF actuators for different applications, such as robotic joints, are investigated since they share many similar challenges and techniques with reaction spheres. The experimental performances of realized reaction spheres are listed and compared. Limits of current designs are identified and their causes are analyzed and discussed. Compared with existing summaries on multi-DOF actuators and some surveys done for specific reaction spheres' design, this paper provides the first thorough review on reaction spheres, considering approaches to excite and support the free 4. π rotation.

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