How accurate is EMDtool?

EMDtool is on par with any other commercial or open-source software, in terms of accuracy. It may lose a bit in some very specific aspects to competitors, and will certainly win in others. For a deeper discussion, please read on.

How accurate is finite-element analysis?

EMDtool is based on finite-element analysis, so it makes sense to start with the accuracy of finite element analysis in general. For instance, we can look at three factors:

  • How well does the mathematical model represent the actual physics.

  • How well does our model represent the reality.

  • How precisely is our FE model solved.

Mathematics versus reality

The first factor boils down in the ability of Maxwell’s equations to represent reality. We can probably safely say that they are good enough for our purposes - we are not dealing with quantum gravity nor relativistic effects here.

Admittedly, we are typically ignoring the displacement current term of the equations, for its contribution is typically rather negligible. However, the topic is of some increasing importance due to the ever-increasing switching frequencies. But, pretty much every other software does the same, for now.

Model versus reality

While the mathematics are more or less exact, our models don’t reflect reality nearly as well. The associated differences can be divided (for instance) into two categories:

  • Aspects that are neglected on purpose. Examples include doing 2D analysis instead of 3D, and simplifications to the geometry modelled. Many statistical phenomena also fall within this category, like circulating currents in random-wound stranded windings, or inter-bar currents in induction machines.

  • Aspects that should be modelled accurately but doing so is difficult. Prime examples include iron losses (especially due to material-degrading phenomena like laser-cutting and punching, shrink-fitting stresses, and so on), the exact end-winding length, or the exact dimensions due to manufacturing tolerances etc.

Solution versus mathematics

Even though the mathematics underlying finite elements are pretty much exact, our solution isn’t. Finite elements always deal with an approximate solution, the accuracy of which depends the most on the mesh density. Spend more time computing on a denser mesh, and you’ll get a solution that is closer to the exact solution of the equations.

Now, it is possible to perform adaptive mesh refinement, to refine the mesh only where it probably counts. EMDtool does not support this, while some competitors may do so. There, I said it. Nevertheless, for a given overall mesh density, with models being otherwise equal, you can trust that EMDtool will return a solution on par with any other properly-implemented competitor out there.

Factors influencing EMDtool accuracy

In practice, one is probably interested in getting the most accuracy out of EMDtool. Again, this can be divided into two categories:

  1. Solving the existing model as accurately as possible, i.e. getting as close to the exact solution to the quasi-static Maxwell’s equations.

  2. Getting the model to represent reality as well as possible.

Solving the model accurately

Solving the existing model as accurately as reasonably possible is relatively simple, boiling down to two steps:

  • Using a sufficiently dense mesh

    • This can be modified using the GeoBase.scale_mesh_density function, or via input arguments to some geometry templates.

  • Using a sufficiently short time-step

  • You could also include some more-numerical stuff here, like solving the nonlinear problem to a tighter tolerance, i.e. spending more Newton iterations on it, or even shifting from double to quadruple precision floating point numbers, if you hate all things.

Please note the pairing of the words ‘reasonably’ and ‘sufficiently’. While EMDtool will converge towards the exact solution of the Maxwell’s equations with a dense-enough mesh and a short-enough time-step, this will also result in an exponential increase in CPU time. This is universal to any software.

Getting the model to represent reality as well as possible

Now, this is where the ways to improve get numerous. A non-exhaustive list includes:

  • Making the geometry represent the final manufactured product as closely as possible.
    • This includes aspects like including manufacturing tolerances, and coordinating with the manufacturer(s) to get an as-good-as-possible estimate of dimensions such as the realized stack height and total conductor length (including the end-winding length and coil connections).
  • Using a realistic voltage supply, instead of an ideal one or fixed-current supply.
  • Performing transient analysis with eddy-currents rather than non-transient stepping.
  • Matching the operating point as closely as realistic
    • Remember: torque or power are outputs - what goes into the simulation is some specification of the supply (typically either in the dq-frame, or a combination of amplitude and an angle of some kind)
  • Computing a larger number of operating points when generating efficiency maps
  • Getting a better estimate of the winding and magnet temperatures
  • Moving to more high-fidelity eddy-current loss models: for instance moving from no eddies in magnets to conductive magnets (2D only) to the EMDtool-exclusive hybrid 3D-2D method accounting for axial segmentation.
  • Using better iron loss models.
    • This is rather obviously an everlasting problem on the field. Users are invited to implement their own models by subclassing the Material or MaterialBase classes. The current version (2023-09) version of EMDtool ships with support for hysteretic materials, with the HystereticMaterial base class. Currently, only a stop-hysteron model has been implemented so far.