Further Investigations on Unconventional Slot Numbers in Concentrated Winding Electric Motors: Rotor Eccentricity and Conventional Methods for Torque Ripple Reduction

Previously, we discussed an unconventional winding system for concentrated windings with an arbitrary number of slots in terms of cogging torque reduction (Koenigs et al., 2025). Linear combinations of the m phases are chosen so that the complex magnetic scalar potential of the tooth is identical to the optimum based on sinusoidal magnetisation. The result is a quadruple layer that is winded with fractionally filled slots (Barbini and Tessarolo, 2019; Tessarolo et al., 2019; Totoki et al., 2022). When considered as a means of using a prime number of stator slots, this concept drastically reduces torque ripple under load and cogging torque. Cogging torque is the torque experienced when the motor is rotated without load in the stator windings due to the rotational change in reluctance. Torque ripple in general adds a current- and winding-dependent torque ripple component to the cogging torque and is therefore experienced under load. In the previous publication, the unconventional concentrated winding was compared to an 8-pole 12-slot concentrated winding motor. Although this 8p12s variant is used in the industry, it is not the industry standard for low-torque, ripple-concentrated winding motors (Azar et al., 2012; Jussila et al., 2007; Parsons, 2019). Additionally, state-of-the-art concentrated winding motors use breadloaf magnets, which was not the subject of the investigation in the previous study. This study compares an industry-standard 10p12s concentrated winding motor to a 10p13s concentrated winding motor with unconventional winding. In addition to rotor skewing, breadloaf magnets are investigated. Skewing magnets (Dai and Lee, 2024; Liang et al., 2019; Petrov et al., 2020), breadloaf magnets (Hsieh and Hsu, 2005; Suriano-Sánchez et al., 2022), and other conventional measures (Brescia et al., 2020; Hu et al., 2018) reduce the cogging torque locally, while unconventional windings eliminate torque ripples based on a global concept. An investigation of eccentric rotors is conducted to confirm that the novel unconventional motor winding is prone to torque ripple due to static eccentricity.

This section is a short recapitulation of the design of unconventional slow-number electric motors with concentrated windings. Assuming a strictly theoretical sinusoidal magnetisation, the air gap field is sinusoidal, the teeth of the stator act as a window function, collecting the magnetic flux. The flux in a stator tooth is therefore sinusoidal as well. Ideally, the current in a concentrated coil in this stator would be in phase with the induced voltage. However, this is not always possible. With conventional symmetric three-phase systems, only three currents represented as complex vectors, spaced equally by 120°, are available. In two dimensions, two linearly independent vectors are sufficient to obtain any given vector by linear combination. Therefore, it is possible to find a linear combination of the three-phase currents so that the total current around the tooth matches the phase of the induced voltage. Only two phases are optimally used. The result is a concentrated quadruple-layer winding (Figure 1), although the concept applies to distributed windings as well. The unconventional quadruple-layer winding can be manufactured with industry-standard flyer coil winders on prefabricated insulation forms. The connection of multiple coils can be done with a standard contact ring. Winding two coils on each tooth and connecting them to the contact ring slightly increases the cost of those components. The other parts of the electric motor are unaffected by the winding design.

Figure 1.

Two concentrated coils on a single tooth.

Four configurations were simulated using ANSYS Maxwell 2D software. The first three variants use an identical stator. One variant has a skewed rotor with four stages. To simulate the skewed model, multiple slices are simulated and then combined in the software package. The other variant has breadloaf magnets. All configurations are simulated using ideal sinusoidal currents in a balanced three-phase system. The cross section of the conventional concentrated winding 10p12s machine is shown in Figure 2. Each tooth has a single concentrated winding. The winding layout is given in Table 1. Usually, a winding distribution in each slot is given as a winding layout. In this case, the strand contribution to the coil around each tooth is used, as it is more intuitive to understand the unconventional winding.

Figure 2.

2D cross section of a 10p12s machine with concentrated windings.

Figure 3 shows the same stator as in the previous figure; however, the permanent magnets are replaced with breadloaf magnets.

Figure 3.

2D cross section of a 10p12s machine with breadloaf magnets.

Lastly, the geometry of the 13-slot 10-pole slot machine is given in Figure 4. Around each tooth, two coils are wound; the distribution of partial coils is not equal as depicted in the geometry. The distribution is fractional and optimized based on the ideal magnetic flux. In a real machine, rounding errors occur based on the integer number of turns in the winding. The rounding error is different for every machine size and rated voltage. This is neglected in this work as an ideal current distribution is assumed. In this case, the induced voltages are almost balanced. The winding layout is given in Table 2. As can be seen in the sum column, the filling factor in each slot varies. In the lowest filled space, 87% of the conventional copper fill factor is used.

Figure 4.

2D cross section of a 10p13s machine.

Compared to the 8p12s motor design investigated in our previous publication (Koenigs et al., 2025), the 10p12s design performs better in terms of torque ripple, both under load and under no load conditions. Breadloaf magnets significantly reduce torque ripple in the 10p12s variants. Four skew steps show the largest reduction in both cogging torque and torque ripple under load. When subjected to an axis misalignment of 0.2 mm, the 10p12s variants show a similar behaviour regarding the cogging torque and torque ripple reduction, as the measures of torque ripple reduction are based on a local reduction. The unconventional 10p13s variant, on the other hand, reduces torque ripple on a global scale. Therefore, it can be observed that the unconventional design is prone to torque ripple increase due to axis eccentricity. The increase in torque ripple in the unconventional winding design is similar to the torque ripple in the conventional breadloaf configuration.

Conventional concentrated windings synchronise machines with 10 poles and 12 slots without skewing, and 4 skewed stages and breadloaf magnets have been compared with an unconventional concentrated winding with 10 poles and 13 slots. The unconventional design significantly reduces the cogging torque and torque ripple. Similar results can be achieved with skewing and breadloaf magnets. The unconventional design has significant high-frequency radial force components. When subjected to rotor axis eccentricity, the cogging torque and torque ripple in the unconventional design increase significantly to levels of the unskewed breadloaf magnet in the 10p12s topology. Furthermore, under load, all three 10p12s variants experience a fluctuation in radial force greater than the high-frequency component of the unconventional design.