How to simulate synchronous reluctance machines

By Nigel Atkinson

This blog will discuss how to design synchronous reluctance machines in Opera. Here is some sample geometry of a typical Synchronous Reluctance, or SyncRel, machine, showing a cross-section of the laminations.

You can clearly see the outer stator lamination and the inner rotor lamination. The stator is very similar to a brushless permanent magnet motor. It is typically a multi-phase stator, usually 3-phase, and it could be a single-or double-layer winding. We then have, essentially, a salient pole rotor. The way that the saliency is provided is by the introduction of non-magnetic barriers. They could be left as simply air-gaps, but more usually they will be pockets of epoxy, for structural integrity reasons. These barriers make it easy for the flux to flow parallel to the barrier, through the steel, but it is difficult for the flux to cross the barrier. You can see that there are no windings on the rotor, and there are no permanent magnets used at all in its construction – it isn’t a permanent magnet-assisted SynchRel. It is purely due to the reluctance torque that the machine turns, and as the name implies, the rotor is synchronised with the travelling field provided by the stator windings. This type of machine is not new, thus far having been used primarily for industrial processes running at mains frequency and synchronous speed.
Above we take a look at why the design of a SyncRel machine is a multi-physics challenge. Magnetic Flux flows freely parallel to the barriers in the rotor, and hence there is a low reluctance Ld. Flux on the quadrature axis is impeded by the barriers, and hence there is a high reluctance Lq.  Torque is increased by improving the Ld/Lq ratio. Hence, we want to increase the width of the magnetic barriers, but this affects the mechanical integrity of the rotor. To improve structural strength, bridges can be introduced into the barriers. This has the effect of locally strengthening the component, without overly affecting the magnetic circuit. An example of this is shown at the bottom of the slide where two designs, each consisting of a single bridge of varying width, have been investigated. The wider supporting bridge reduces the peak stress from 300 to 220 kPa, as you might expect, but this does also reduce the torque from 27.6Nm to 25.7Nm. So you can see that there is a trade-off in the geometrical design between mechanical integrity and operating torque.

Obviously, this happens because you are affecting the Ld:Lq ratio. As you increase the thickness of the bridges to improve mechanical stiffness, we reduce the reluctance on the quadrature axis.  So we have a trade-off between electromagnetic and mechanical design, which means that if we design for one set of physics exclusively, we will end up with, overall, a poor design. And we cannot analyse the different physics in isolation because of the inter-dependence of loadings. For example, we need to add electromagnetic forces to the mechanical forces when performing the structural analysis, or we will possibly exceed allowable stresses. And we need to feedback the deformed shape into the electromagnetic analysis because this will tend to close the airgap and affect the torque curve in an unpredictable fashion.

It is very quick and easy in Opera to carry out an electromagnetic analysis, pass forces to a structural analysis, then re-perform the electromagnetics analysis using the deformed shape. There is, in essence, no limit to the complexity of the sequence and we have implemented this for all of our physics solutions.
In some designs this will be more important than others, but with this toolset at least investigating the level of influence is relatively simple.  Above we can see an exaggerated deformed shape superimposed on the SynchRel. The actual deformations are of the order of 20 microns, so not so large, even against the small actual airgap of a couple of millimetres. But you can see that it is not a uniform reduction of the airgap, so a simple sensitivity analysis sweep scaling the rotor diameter would not give the same insight as this true deformed shape. This deformation leads to a change in electromagnetic performance, which again is relatively easy to perform.
If we look at the radial component of the air gap flux density around the machine, and superimpose the results for the deformed shape on top of the undeformed shape there is barely any noticeable difference at first sight. But if we zoom in on part of the graph we can see the change in performance due to this deformation under load.  This is a successful prototype design, so the difference is not significant versus the desired performance, but this was not the case for all of the possible designs considered in the design space. If this is not considered early in the design process then a lot of time can be wasted on a machine that is too flimsy to achieve the rated performance in practice. It is not that the machine is mechanically unsound, just that the electromagnetic performance is too sensitive to the induced deformations under load.

Opera has, for some time, contained a module called the Machines Environment, which uses a wizard-style data-entry for ease-of-use. The Environments are written in the Opera programming language that is fully documented and available to users, so they are not merely a closed executable. Common types of machines are offered, but in the Developer version the command files are, mainly, open-source so the user is free to make adjustments to the standard command file. This could be a small tweak to a slot shape right through to a completely new topology of rotor or winding. Relevant data, in terms of standard machine parameters, is gathered for the machine being analysed then the environment builds a full-fidelity finite element model. Analyses are submitted automatically to the Batch processor, then standard post-processing commands automatically generate plots and reports such as torque-speed curves. This Environment has been extended under this program for SynchRels.

Here we see two typical dialogs presented to the user to start the machine definition. Some basic dimensions start the process, with the stator properties being entered first. Then, moving onto the rotor, multiple-choice menus allow the user to select from circular or trapezoidal voids, and the number of barriers. The shape of the void then governs the subsequent geometrical data input – more data is requested of the user for a trapezoidal void than a circular one, for example.

Following this, the geometric model and the mesh are created automatically. The mesh size is calculated automatically, but the user has the chance to override the default setting to either perform a quick, coarse analysis, or to define a fine, high-resolution mesh for final detailed checking.

Further dialogs prompt for the required material properties, and also the properties of the drive. For example, the user can specify the windings, operating voltage and current, and the frequency and speed. Users have the chance to override default drive circuits with circuits or their own. If loss calculations are required the user enters properties required for copper and iron losses.

There are a list of analyses to choose from in the Machines Environment for a SynchRel, or any other type of machine for that matter. The simplest is an electromagnetic analysis looking at static torque vs angle at multiple current levels. This is performed automatically in the static electromagnetic solver for a given number of rotor positions.  The next is one of two possible dynamic analyses. The user can choose to run a fixed speed of rotation in an electromechanical analysis, and generate iron loss calculations. Or you can run a transient analysis against a given mechanical load. The user is also given a choice of two pure mechanical analyses – an eigenvalue analysis of the unloaded structure, or a static stress analysis of the rotor under centrifugal loading.

Next on the menu is the option to run investigations of mechanical effects on electromagnetic performance. This consists of, again two choices. Firstly, an iterative coupling of electromagnetics and stress to look at the effect of the rotor deformation on the electromagnetic behaviour. Or, secondly, a perturbation analysis, looking at the effects of manufacturing tolerances on the electromagnetic performance, including unbalanced magnetic pull. The final choice on the menu is an option to calculate D, Q and cross­coupling inductances using a series of static analyses at different rotor positions. This will produce a look-up table against current for use in a system-level analysis.

Here we see the static torque analysis results. Shown are graphs of radial flux density versus angle, and also the torque versus angle for different operating currents. Moving on to the multi-physics analyses, here we have the results of the coupled run.
This has converged after a series of electromagnetics and stress analyses, and we’re showing the converged deflections due to electromagnetic forces and static displacements. Anyone currently performing three-dimensional machines analysis is probably wondering at this point how they can fit such wide-ranging, but computationally expensive analyses within their development timescales. Two-dimensional analysis is normally used up-front to perform some conceptual design, before embarking on the more accurate and rigorous three-dimensional work. There is in the Machines Environment, basically, a switch for the user to say whether they want a two-dimensional run, or a three-dimensional run. And no data is lost, no extra is required.  We have also worked on implementing parallelisation of the solution process, to make the most of the multi-core processors being installed in standard laptop or desktop computers as well as high-end servers.
Here we see the effect of switching between two-dimensional analyses and three-dimensional. The 3D model, as shown previously, took 41 minutes to solve over a million elements. Cut that to a 2D slice, and you are left with 7000 elements. The conductor lengths are adjusted automatically by the software, so as not to introduce spurious end-effects, and appropriate boundary conditions are automatically added to the model. The solution then takes a mere 2 minutes, even though we are solving a full 360 degrees. So, a 20 fold increase in throughput. But we haven’t lost any of the data from the 3D model, so reflation of the model back to 3D is a simple task.
If we look at the results for air gap flux density at the centre of the machine, we can superimpose the results for the 2D slice on the results for the full 3D model. You’ll see that there is very little difference, because the lossy flux at the ends is relatively small for this particular device. So if you were designing for air gap flux density, the 2D slice results would most likely be adequate for a first-pass design.
But of course, what we are not doing with 2D slice is capturing the end effects. The fact that we can simply switch between the 2D and 3D analysis at the model build stage means that we can accurately, but easily, investigate the end effects when we are ready to do so. Thank you for reading and I hope that you have found this useful. More information about machine design can be found at the link below.