This website stores cookies on your computer. These cookies are used to collect information about how you interact with our website and allow us to remember you. We use this information in order to improve and customize your browsing experience and for analytics and metrics about our visitors both on this website and other media. To find out more about the cookies we use, see our Privacy Policy.
If you decline, your information won’t be tracked when you visit this website. A single cookie will be used in your browser to remember your preference not to be tracked.
Electric motors often have a form of symmetry or repetition that can be exploited in simulations. When this is the case, a fraction, or sector, of the motor can be simulated to save time and computational resources. The number of sectors is determined by the greatest common denominator between the number of poles and the number of slots. You can then divide your geometry by the result to find the sector size. The sector can then be configured so that the physics, continuity, antiperiodicity, mesh, and results align with expectations.
Watch the video below to learn the details about modeling motors with sectors.
Tutorial: Sector Modeling for Motors
18:38
Introduction to Sector Modeling
Understanding Sector Symmetry
Creating the Geometry for Sector Modeling
Implementing Physics in Sector Models
Determining Continuity and Antiperiodicity
Mesh Generation Techniques
Analyzing Simulation Results
Challenges with Permanent Magnets
Key Takeaways on Sector Modeling
Sector modeling is a technique in COMSOL Multiphysics that reduces computation time by simulating only a repeating fraction of an electric motor's geometry rather than the full model. Because coils and magnets typically repeat in a circular, alternating pattern, only one representative sector needs to be modeled, with the remaining geometry treated as periodic. In a simple generator example featuring eight poles and eight slots, the geometry can be divided into one-eighth sectors. The number of sectors is determined by the greatest common divisor between the number of poles and the number of slots.
Building a sector begins by drawing a circle with a sector angle of 360 degrees divided by the number of sectors, then using Boolean intersections and partitions to isolate the stator and rotor portions. A form assembly step creates an identity boundary pair at the rotor-stator interface, which should always be verified along with material assignments after modifying geometry. The rotating domain in the moving mesh setup remains unchanged, with only the rotor rotating. In the Rotating Machinery, Magnetic interface, a Sector Symmetry feature is added under Pairs and assigned to the identity boundary pair, and the number of sectors is entered as a parameter. The symmetry type is either continuity or anti-periodicity: as a rule of thumb, an odd number of poles in the sector requires anti-periodicity, while an even number allows continuity. Alternating coil and pole directions in the example make anti-periodicity the correct choice.
The outer boundaries of the sector must be defined as periodic using a Periodic Condition on the interface, applied separately for rotor and stator parts with automatically assigned source and destination boundaries. Circular magnet patterns are removed since only one magnet remains in the sector. For meshing, generating a physics-controlled mesh first and then converting to a user-controlled mesh produces an identical mesh feature that matches source and destination boundaries at the periodic conditions. This identical mesh significantly improves convergence when values are mirrored or anti-periodically transferred between sides. Cutting permanent magnets in half is numerically challenging because a magnet interface acts as a flux singularity; while acceptable in 2D, it is advisable in 3D to rotate the cutting circle slightly so the magnet is left intact rather than divided.
When interpreting results, quantities calculated over a single sector must be scaled appropriately. Induced voltages and cycle-averaged losses, such as those integrated over an iron domain using rmm.Qh, represent only one sector and must be multiplied by the number of sectors to obtain full-model values. In contrast, the Arkkio torque calculation in the air gap automatically incorporates the number of sectors from the continuity or sector symmetry feature, so the computed torque (rmm.T) already reflects the full model and requires no additional scaling. This content is part three of the online course Modeling Electric Motors with COMSOL Multiphysics, covering the fundamentals of sector modeling including periodicity selection, magnet cutting considerations, and correct result scaling.