Hi guys,
my last post was about prototyping of axial flux electric motor with two rotors and a single stator. You can see the short video of the acceleration of the motor: https://youtube.com/shorts/GOyh1Yr8v1A?feature=share
After completing our first prototype, my team and I are now working intensively on building and testing the second prototype. As part of this process, we plan to develop an analytical model to estimate the eddy current losses in the magnets and the rotor. This model will be validated first through numerical simulations, and subsequently through experimental testing.
However, after reviewing several key papers—such as "General Analytical Model of Magnet Average Eddy-Current Volume Losses for Comparison of Multiphase PM Machines With Concentrated Winding" and "Why state-of-the-art analytical models for eddy current losses in PM of PMSM are insufficient for variable-speed motors"—as well as literature on numerical simulation techniques, I've encountered challenges.
In particular, the accuracy of numerical results appears to be highly sensitive to the mesh resolution in the magnets and rotor, as well as the number of time steps. This has made it difficult to achieve consistent results across different modeling approaches.
Does anyone have suggestions on how to numerically simulate eddy current losses in magnets and rotors, specifically, how many time steps to use and why? Also, how should the mesh size be defined in the magnets or rotor? If you have a validated analytical model and are willing to share it, that would be greatly appreciated!
Thank you all and have a wonderful day,
Marko
Eddy losses in magnets and rotor of axial flux electric motor using concentrated winding
Re: Eddy losses in magnets and rotor of axial flux electric motor using concentrated winding
Hi,
and congrats on the progress! I'm first and foremost an FEA person myself, so my two cents are coming from that perspective:
Regarding the number of time-steps, 2 steps per period of the fastest interesting harmonic is the absolute minimum, as per Nyquist's criterion. Never tested this, but I have a strong hunch that the accuracy improves dramatically if you move to 10, with incremental gains after that. That's for cases when you have a highest harmonic - in reality you of course have an infinite series of weaker and weaker harmonics. But still, stuff like that switching frequency and its sidebands should definitely be covered.
Tangentially, the time-stepping scheme can SOMETIMEs influence the results quite a bit. I normally jump between pure implicit Euler, and a hybrid between that and trapezoidal method (you can express both them with a single scalar factor in [0,1] or [1,2] depending on your syntax), and move freely between the two. Pure trapezoidal rule is prone to spurious oscillations that never decay, so I normally only go up to 80% trapezoidal 20% implicit Euler. Then again, implicit Euler introduces some artificial non-physical damping, so you have to balance things out.
Regarding mesh density, something like 1-2 edge lengths per skin depth is often touted as a rule. It works, but sometimes you can get away with a little less, depending on the geometry. Again, you'll have to do some educated guesses as to which frequency to define the skin depth for (and which level of saturation in case of nonlinear materials).
One more important detail: please be aware of the so-called anomaly of segmentation. It refers to a phenomenon where (inductance-limited) eddy losses first grow when magnets are segmented, and only start to decrease when the segment size drops on the level of the skindepth or similar. The phenomenon is not always present (mostly an issue in high-speed machines), but it's definitely something to watch out for. Tangentially, when developing analytical / post-processing methods, it's better if the methods can catch the phenomenon.
and congrats on the progress! I'm first and foremost an FEA person myself, so my two cents are coming from that perspective:
Regarding the number of time-steps, 2 steps per period of the fastest interesting harmonic is the absolute minimum, as per Nyquist's criterion. Never tested this, but I have a strong hunch that the accuracy improves dramatically if you move to 10, with incremental gains after that. That's for cases when you have a highest harmonic - in reality you of course have an infinite series of weaker and weaker harmonics. But still, stuff like that switching frequency and its sidebands should definitely be covered.
Tangentially, the time-stepping scheme can SOMETIMEs influence the results quite a bit. I normally jump between pure implicit Euler, and a hybrid between that and trapezoidal method (you can express both them with a single scalar factor in [0,1] or [1,2] depending on your syntax), and move freely between the two. Pure trapezoidal rule is prone to spurious oscillations that never decay, so I normally only go up to 80% trapezoidal 20% implicit Euler. Then again, implicit Euler introduces some artificial non-physical damping, so you have to balance things out.
Regarding mesh density, something like 1-2 edge lengths per skin depth is often touted as a rule. It works, but sometimes you can get away with a little less, depending on the geometry. Again, you'll have to do some educated guesses as to which frequency to define the skin depth for (and which level of saturation in case of nonlinear materials).
One more important detail: please be aware of the so-called anomaly of segmentation. It refers to a phenomenon where (inductance-limited) eddy losses first grow when magnets are segmented, and only start to decrease when the segment size drops on the level of the skindepth or similar. The phenomenon is not always present (mostly an issue in high-speed machines), but it's definitely something to watch out for. Tangentially, when developing analytical / post-processing methods, it's better if the methods can catch the phenomenon.