Office of Technology Transfer – University of Michigan

Computationally Efficient 3-D Finite-Element-Based Dynamic Thermal Models of Electric Machines

Technology #7104

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Driving cycle test results with reduced order modeling of stator and rotor modes Locked rotor experiment vs. simulation temperature for contact resistance layer
Heath Hofmann
Managed By
Drew Bennett
Associate Director - Software Licensing 734-615-4004
Computationally-efficient 3D finite-element-based dynamic thermal models of electric machines
Electric Machines & Drives Conference (IEMDC), 2013 IEEE International. 839 - 846, 2013

With the growing popularity of electric and hybrid electric vehicles (HEVs), electric machines are becoming a critical element of the modern powertrain. However, the performance of electric propulsion systems is significantly constrained by the internal temperatures of the electric machine. Hence, in order to determine the torque and power capabilities of an electric machine under real-time operating conditions, dynamic knowledge of internal temperatures is required and needs to be estimated in a computationally efficient manner. Lumped-parameter (LP) based models are sensitive to variations in cooling conditions and introduce large and complex models that require accurate capturing of the distributed nature of the losses, the temperature distribution in the machine, and the complexity of the machine geometry. Model-order-reduction (MOR) techniques are dependent on their original LP models, which have the same limitations mentioned above. As another existing approach, pure finite element (FEA) based analyses are time-consuming (especially 3-D FEA) and not suitable for real-time observers or powertrain-level simulation/optimization. On the other hand, a blend of these latter two methods (FEA-based MOR) can suffer from determination of reduced model size and proper data training issues for accurate estimation of the parameters for the equivalent model. As a result, there is an important need within the numerical analysis software market for improved modeling frameworks that allow computationally efficient, accurate analysis of thermal models of electric machines.

3-D FEA-MOR Based Efficient, Nonlinear Dynamic Thermal Modelling for EV, HEV and Electric Machines

A systems modeling and analysis technique for developing computationally efficient thermal models of electric machines is proposed. It can be used for real-time thermal observers and electrified vehicle powertrain-level simulation and optimization. A large 3-D FEA model can be reduced to a small reduced-order model without the necessity of calculating all the eigenmodes. By using the proposed technique, the computation time of the model can be dramatically reduced compared with the full-order model while maintaining sufficient accuracy.

Based on both simulation and experimental results with locked-rotor, the proposed reduced-order model is shown to be both fast (over four orders of magnitude compared with the full order 3-D FEA model) and accurate enough to be used as a real-time temperature monitor or in powertrain-level simulation and optimization of electric vehicles (EVs) and hybrid EVs (HEVs).


  • powertrain-level simulation and optimization of EVs and HEVs
  • real-time temperature observer
  • temperature-dependent nonlinear electromagnetic FEA
  • electric machine design optimization


  • dramatic reduction in computational time while maintaining sufficient accuracy
  • real-time functionality
  • capable of handling complex electric machine geometries