Geometric Scaling Laws for Axial Flux Permanent Magnet Motors in In-Wheel Powertrain Topologies

TL;DR

This work develops geometric scaling laws for axial flux permanent magnet motors (AFMs) to enable efficient, holistic in-wheel powertrain design. By introducing axial and radial scaling factors $K_ ext{A}$ and $K_ ext{R}$, the authors derive analytical relations for motor torque, power, inductances, flux, resistances, copper losses, and thermal behavior, and they validate these laws with high-fidelity FE simulations. They formulate a drive-cycle energy-minimization optimization that jointly optimizes motor size and transmission ratio across a range of powertrain topologies, using a lumped-parameter thermal network to capture heat transfer. The results indicate that all-wheel-drive configurations with AFMs offer the highest energy efficiency but come with substantially higher material costs, highlighting a trade-off between performance and production expense and motivating further work on component-level validation and cost modeling.

Abstract

In this paper, we present geometric scaling models for axial flux motors (AFMs) to be used for in-wheel powertrain design optimization purposes. We first present a vehicle and powertrain model, with emphasis on the electric motor model. We construct the latter by formulating the analytical scaling laws for AFMs, based on the scaling concept of RFMs from the literature, specifically deriving the model of the main loss component in electric motors: the copper losses. We further present separate scaling models of motor parameters, losses and thermal models, as well as the torque limits and cost, as a function of the design variables. Second, we validate these scaling laws with several experiments leveraging high-fidelity finite-element simulations. Finally, we define an optimization problem that minimizes the energy consumption over a drive cycle, optimizing the motor size and transmission ratio for a wide range of electric vehicle powertrain topologies. In our study, we observe that the all-wheel drive topology equipped with in-wheel AFMs is the most efficient, but also generates the highest material cost.

Figures (6)

• Figure 1: The axial flux motor (AFM) in-wheel powertrain topology for one wheel. This simple powertrain is to be duplicated to two wheels in front and rear-wheel drives, and to four wheels in an all-wheel drive. The AFM design is proportionally scaled in axial and radial direction with scaling factors $K_\mathrm{A}$ and $K_\mathrm{R}$, respectively. AFM picture taken from GCC2021.
• Figure 2: Scaling the phase resistance as a function of $K_\mathrm{R}$ and $K_\mathrm{A}$.
• Figure 3: Scaling the copper losses as a function of $K_\mathrm{R}$ and $K_\mathrm{A}$.
• Figure 4: The assembly of the AFM with the thermal network, given in nodes and thermal connections.
• Figure 5: The LPTN of the referent AFM design.