Enhanced modeling, active damping strategies, and design analysis to improve electrodynamic thrust self-bearing machines
(2026)
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Adrien Robert - Thesis Manuscript - Enhanced modeling, active damping strategies, and design analysis to improve electrodynamic thrust self-bearing machines.pdf
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- Abstract
- Magnetic levitation in rotating machinery has emerged as a compelling alternative to conventional mechanical bearings in high-speed electromechanical systems, where contact-induced friction, wear, and thermal stresses significantly limit performance and lifetime. By enabling contactless rotor support, magnetic suspension improves reliability, reduces maintenance, and allows operation in demanding environments such as high-rotation speed, vacuum or high-purity applications. Most levitated systems rely on active magnetic bearings, which require multiple sensors, power electronics, and control loops to stabilize all degrees of freedom, resulting in increased system complexity and volume. Consequently, a key objective in the design of such systems is to reduce the number of actively controlled degrees of freedom by exploiting passive stabilization mechanisms, typically based on permanent magnet interactions. However, Earnshaw’s theorem states that stable levitation cannot be achieved in all degrees of freedom using only static magnetic fields, implying that additional physical mechanisms must be introduced. Among the proposed alternatives, electrodynamic suspension constitutes a promising solution. It relies on the interaction between the magnetic field produced by permanent magnets and currents induced in conductive windings due to relative motion, inherently generating velocity-dependent restoring forces. This principle is exploited in the electrodynamic thrust self-bearing machine (EDTSBM), which integrates passive axial suspension and torque production within a single structure. The system consists of a rotor equipped with permanent magnets and a stator comprising two axially separated windings connected in series. During operation, an axial displacement of the rotor from its centered position creates an imbalance in flux linkage between the windings, inducing a circulating current. This current generates a restoring axial force opposing the displacement, thereby providing passive levitation. Simultaneously, motor currents supplied by an external source produce electromagnetic torque required for rotation. Numerous studies have been conducted on the EDTSBM, addressing both modeling and experimental validation aspects. However, several limitations remain. From a modeling perspective, existing approaches neglect second-order effects, namely the position-dependent variation of inductances and the nonlinear evolution of flux linkage. As a result, these models are primarily restricted to rotor topologies with surface-mounted permanent magnets, for which inductance coefficients can reasonably be assumed constant with respect to rotor position. Moreover, the assumption of a linear dependence of the flux linkage on rotor position implies that the supply currents do not influence the suspension force, leading to an artificial decoupling between the injected currents and levitation. In practice, a nonlinear flux-position relationship may introduce coupling effects, whereby the injected currents contribute to the suspension behavior. To address these limitations, an extended electromechanical model was developed, incorporating both inductance variation with rotor position and nonlinear flux evolution. This formulation reveals additional force components, including reluctance-induced contributions and current-dependent terms enabling active modulation of the suspension behavior. The proposed model was experimentally validated, confirming its accuracy as well as the influence of current injection on suspension performance. A second limitation of the EDTSBM is intrinsically related to electrodynamic levitation. Indeed, this suspension principle exhibits axial instability beyond a critical rotational speed, preventing stable operation over the full speed range without additional damping mechanisms. These limitations motivated the development of control strategies exploiting the additional effects identified in the extended model. In particular, a stabilization method based on current injection proportional to the rotor axial velocity was proposed, enabling stable operation over the full speed range without requiring external damping devices. This approach preserves system compactness while mitigating the intrinsic high-speed instability. Furthermore, sensorless estimation methods were developed to reconstruct the axial position and velocity of the rotor from suspension current measurements, allowing the implementation of closed-loop stabilization without dedicated position sensors. Experimental validation confirmed the effectiveness of both sensor-based and sensorless approaches. Finally, another limitation lies in the limited range of rotor topologies investigated in the literature, largely due to the absence of magnetic circuits in conventional rotor designs. By incorporating inductance variations into the model, magnetic circuits in the rotor can now be explicitly taken into account. This extended modeling framework enables a broader and more systematic exploration of alternative rotor configurations, while also capturing the additional effects previously identified. In this context, the thesis investigates the impact of rotor design on system performance by considering topologies integrating magnetic circuits. A unified design and comparison framework was developed to evaluate multiple configurations under consistent constraints. The analysis highlights fundamental trade-offs between torque production, passive suspension capability, and the ability to modulate forces through current injection. These results provide practical guidelines for rotor topology selection according to application-specific requirements.
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Citations
Robert, A. (2026). Enhanced modeling, active damping strategies, and design analysis to improve electrodynamic thrust self-bearing machines. https://hdl.handle.net/2078.5/279541