Inner-Rotor Thermal Coupling as a Design Constraint in Multistage Axial-Flux Permanent-Magnet Machines with Directly Cooled Stators: A Research Framework
Electric propulsion systems for vertical take-off aircraft and podded marine drives must deliver high torque within a tightly constrained outer diameter. Axial-flux permanent-magnet machines meet this requirement well, and stacking several stages on a common shaft is the established way to raise torque without increasing diameter. Direct liquid cooling of the stator windings has matured in parallel and now permits current densities well beyond those of jacket-cooled designs. However, studies that optimise the number of stages have so far treated the problem electromagnetically, and the thermal consequences of stacking have been explicitly left outside their scope. This working paper identifies a component that exists only in stacked machines: the inner rotor. It has no coolant path of its own and is bounded on both sides by stators that, although cooled, operate at elevated temperature. The paper describes the resulting heat-transfer problem, outlines an analytical framework that yields a size-independent screening criterion relating permissible magnet loss to gap heat transfer and stator temperature, and states a hypothesis on how inner-rotor thermal coupling alters the optimum stage count. A validation programme based on three-dimensional finite-element analysis and a two-stage prototype is proposed.
The gap
Studies that optimise how many stages to stack have treated the problem electromagnetically and left the thermal side explicitly out of scope. Studies of directly cooled stators examine one stator on its own. Nobody has treated the stacked machine as one coupled thermal system.
The problem
In a stack of N stators and N + 1 rotors, each inner rotor faces a stator on both sides. Its only ways to shed heat are across two narrow air gaps to warm stator surfaces, or inward through its carrier to the shaft and bearings. A single stage machine has no such rotor.
The approach
A lumped steady state thermal model of the rotor stack, coupled to an analytical model of the directly cooled stators. From it comes a closed form screening criterion for the magnet loss an inner rotor can tolerate. It does not depend on machine size, so it can be used before the geometry is fixed.
Inner-rotor thermal coupling introduces a permanent-magnet temperature limit that is absent from single-stage machines. This limit reduces the allowable current density and torque density of stacked designs by an amount governed by the inner-rotor magnet loss density, the air-gap heat transfer and the thermal conductance of the rotor carrier. Rotor thermal management can partly recover this penalty and so changes the optimum design.
It is testable: it predicts that the binding constraint moves from the winding to the inner rotor magnets as stages are added.
This is a research framework and a hypothesis. It does not yet report verified results, and it contains no finite element or test data. The central unknown is the eddy loss in the inner rotor magnets, which only three dimensional analysis and measurement can establish, so the framework carries it as an explicit parameter instead of assuming a value. Detailed results will follow in a peer reviewed paper once the model has been verified against published data.
Check the analytical model against published experimental and numerical data from other groups and report the errors.
Three dimensional electromagnetic FEA of eddy loss in the inner rotor magnets, including magnet segmentation.
Coupled electromagnetic and thermal analysis with a detailed model of heat transfer in the rotating air gap.
A two stage prototype with rotor temperature telemetry, so model, simulation and measurement can be compared directly.
Mohammad, I. (2026). Inner-Rotor Thermal Coupling as a Design Constraint in Multistage Axial-Flux Permanent-Magnet Machines with Directly Cooled Stators: A Research Framework. Preprint, Orbitronix Technologies. https://doi.org/10.13140/RG.2.2.16963.98086
Licence: CC BY-NC-ND 4.0. The paper includes a declaration of the AI assistance used in its preparation.
The next steps need simulation capability, measured data and a test bench. If your lab works on electric machines or thermal engineering, we would like to hear from you.