Influence of geometry of iron poles on the cogging torque of a field control axial flux permanent magnet machine

Abstract

The paper presents 3D-FEA results of electromagnetic torque characteristics of a Field Control Axial Flux Permanent Magnet Machine (FCAFPMM) obtained for different pole shapes. The influence of the angular span of iron and permanent magnet poles on the cogging torque performance has been analysed at different excitations of an additional stator winding.

Keywords

Axial flux hybrid machine permanent magnet cogging torque torque ripple

1. Introduction

Disc-type machines offer great opportunities to generate high electromagnetic torque. Due to the use of hybrid excitation, the proposed design also allows to regulate back-emf and influence the electromagnetic torque. This extends the range of machine applications, because there is a possibility during flux weakening to increase the rotational speed of the machine, while during flux strengthening, it is possible to increase the electromagnetic torque, necessary for starting electric vehicles.

Machines with surface-mounted permanent magnets that are misplaced or incorrectly shaped have some drawbacks, including electromagnetic torque pulsation, fluctuations in rotational speed, excessive noise and machine vibrations [1]. The machine torque ripple arises mainly as an effect of the cogging torque T_cogg. It is very important to reduce it because it will generate not only noise but also friction on the machines, so it will decrease the efficiency and lifetime of the machine. The cogging torque performance is mainly depended on the stator teeth and rotor poles shapes with, and it is particularly sensitive in hybrid excited machines.

The main aim of the work was to determine the optimal shape of the iron poles in terms of minimizing the cogging torque. Due to the technological possibilities of making the pole pieces, two variants were analyzed:

Iron pole as a segment of a toroid with a specific angular span 𝛼_τIP.

Iron pole in the form of a cuboid with the base of an equilateral trapezoid with a variable 𝛽 angle at one of the bases (the extreme case of this variant is a cuboid with a triangle base - see Fig. 10).

Cogging torque is caused by a change of the system’s total magnetic energy concerning a rotor revolution, shapes of rotor poles and stator teeth, and for hybrid excited machines, stator additional stator winding excitation [2]. The second factor influencing the torque pulsation is the ripple torque T_{el_rip}, which is the result of the non-sinusoidal distribution of the magnetic flux as a function of the instantaneous position of the shaft θ and the stator current component i_q. Advanced research aimed at reducing the ripple of electromagnetic torque of PM machines is going in two directions: by optimizing the machine rotor/stator shapes and by improving stator current control algorithm with stator d-axis current control [3–12]. In [3], the authors decomposed the cogging torque into harmonic components and, using the control algorithm, influenced the four of them with the highest amplitude. The publication [4] proposes an analytical method of testing the cogging torque in order to minimize it at the design stage. It incorporates a new technique of axial pole pairing in radial flux machines. Article [5] also shows the modification of the shape of hexagonal magnets in a disk machine with one rotor and one stator using multi-objective optimization. In [6], the influence of the geometry of the teeth of the modular stator in a machine with 24 slots and 28 poles is analyzed. The publication [7] presents a non-linear control algorithm that observes the phenomenon of meshing and changes in the thickness of the air gap when changing the mutual position of the rotor and stator. The article [8] presents a simulation method called half magnetic pole pair analysis using two computing environments: Maxwell-2D based on FEM and Matlab. This method checks the effect of the skew structures of the rotor on the reduction of the cogging torque. The work [9] also focused on the modification of the stator structure in a disc-type machine with one internal stator and two external rotors with surface mounted PMs. The study investigated, among other things, the slot opening angle. The authors of the article [10] investigate the design of the magnetic cores of disc-type machines and their various electromechanical parameters, including the cogging torque. Similarly, in publication [11], the broadly understood magnetic core shape and its impact on minimizing the cogging torque are investigated. Among others, PM in round, trapezoidal, skewed and dual skewed magnets as well as stator slot opening. Similar studies are shown in [12], where the effects of PM skew in disc machines on minimizing the cogging torque are analyzed. The above review proves that in many research centres scientific works are carried out to reduce the cogging torque of electric machines. The paper investigates the effect of the shape of poles on the cogging torque performance of a hybrid excited axial flux machine with an additional stator winding on machine flux control.

Fig. 1.

Model of the stator.

Fig. 2.

Clasical rotor disk with PMs and FCAFPMM disc design.

2. Research axial flux permanent magnet machines with hybrid excitation

At present, several different designs of axial-flux machines containing permanent magnets and an additional electromagnetic excitation circuit are being designed and researched. Due to their specific features, they can be classified as follows:

Hybrid Excited Synchronous Machine (HESM) [13,14].

Axial Flux Surface Mounted Permanent Magnet Machine (AFSMPMM) [15].

Axial-Flux Hybrid Excitation Synchronous Machine (AFHESM) [16].

Axial Flux Hybrid Excitation Motor [17].

Hybrid-Excited Axial Field Flux Switching Permanent Magnet Machine (HEAFFSPMM) [18].

3. Axial flux machine with additional stator winding

The axial flux machine with additional stator winding [19–21], has a double-disc rotor and a ferromagnetic bushing placed between two rotor discs, and double-sided stator core with three-phase AC winding.

The stator has 36-open slots on both sides. An additional stator DC 500 turns coil copper (Fig. 1). Each steel rotor disc has six N38H-grade permanent magnets with the same polarisation alternating with iron poles (in the classical structure permanent magnets with reverse polarity are used instead of iron poles). The PMs cube shaped are of identical dimensions of 50 × 50 × 12 mm (Length × Weight × Height). The iron poles are made of solid steel with constant height of 15 mm, and its other dimensions are varied (Fig. 2). The main parameters are summarized in Table 1.

Table 1
The main parameters of FCAFPMM

Parameters Value

Number of stator pole pairs 6

Number of turns of stator phase winding 150

Number of stator slots 2 × 36

Number of turns of DC coil winding 500

Stator outer radius (mm) 300

Stator inner radius (mm) 180

PM dimensions (mm) 50 × 50 × 12

Axial length of the active part (mm) 171

Parameters	Value
Number of stator pole pairs	6
Number of turns of stator phase winding	150
Number of stator slots	2 × 36
Number of turns of DC coil winding	500
Stator outer radius (mm)	300
Stator inner radius (mm)	180
PM dimensions (mm)	50 × 50 × 12
Axial length of the active part (mm)	171

Figure 3 shows a model of FCAFPMM (1∕6 part of the machine) and its detailed components.

An additional stator DC coil to control the machine flux, produces a magnetomotive force of MMF_DC = ±2500 AT (for a current of ±5A). Supplying the coil, a constant magnetic field is excited in such a way that air-gap flux can be increased or decreased by changing DC current polarity. Magnetic flux flow in the machine cores is shown in Fig. 4. For considering the cogging torque evaluation, a three-dimensional finite element model of the FCAFPMM (Fig. 5) has been developed by ANSYS. Due to very complicated shape of the 3D model, the computing cost was very high. The model has about 220 thousand nodes and one simple calculation took at least 11 hours (determined on PC: i7 with 64 MB RAM).

Fig. 3.

Model of the FCAFPMM.

Fig. 4.

Distribution of magnetic fluxes in the machine.

Fig. 5.

3D-FEM model with discretisation mesh.

4. Study of iron pole shapes

In this study, the cogging torque analysis was carried on for various shapes of iron poles, for two different parameters describing the shape of the iron pole.

4.1. Variant I

Iron pole geometry was formed by using an iron pole arc angle parameter 𝛼_IP with values: 5°, 10°, 15°, 20°, 25°, 29° and with pole pitch τ_IP = τ_PM = 30° (Fig. 6).

Fig. 6.

Variant I – iron pole pair at 𝛼_IP = 29° (a); 𝛼_IP = 5° (b).

The research shows that the maximum value of the cogging torque occurs for the excitation MMF_DC = −2500 AT and the angle 𝛼_IP = 5°, which results from the location of the pole piece exactly and one slot. The lowest value of the cogging torque is observed for the angle 𝛼_IP = 29°, which is the result of the iron pole filling almost the entire pole pitch and covering the tooth surface (Fig. 7).

Fig. 7.

One pair of poles with 𝛼_IP = 29°.

The maximum value of the cogging torque between 5° and 29° is variable, especially for excitation −2500 AT. Local maxima are detected for 𝛼_IP = 15° and 25°, resulting from the positioning of the pole piece and the edges of the teeth and slots, and local minima for 𝛼_IP = 10° and 20°, when the edges of the pole piece are in the middle of the stator teeth or slots (Fig. 8).

Fig. 8.

Maxium cogging torque versus 𝛼_IP.

Figure 9 shows the 3D-FEA results of cogging torque waveforms obtained at 𝛼_IP = 5° (Fig. 9a) and 𝛼_IP = 29° (Fig. 9b) at two different values of MMF_DC = ±2500 AT and at 0 AT.

Fig. 9.

Cogging torque waveforms at different different values of MMF_DC = ±2500 AT and at 0 AT for 𝛼_IP = 29° (a) and 𝛼_IP = 5° (b).

4.2. Variant II

Iron pole geometry was formed by using an iron pole angle 𝛽 parameter as an angle between the arm and one of the bases of the trapezoid. In this study, the cogging torque analysis was carried out for various values of parameter 𝛽 in the range 56° ÷ 74° (Fig. 10).

Fig. 10.

Extreme angular spans of iron poles at 𝛽 = 56° (a); 𝛽 = 74° (b).

The maximum values of the cogging torque as a function of the angle 𝛽 determined at MMF_DC = ±2500 AT and 0 AT excitations are summarised in Table 2.

Table 2

Results of maximum cogging torque T_cmax [N⋅m]

𝛽 (°)	MMF_DC (AT)
	−2500	0	2500
56	12,84	3,93	4,17
59	18,64	3,97	4,08
62	21,20	4,00	4,09
65	20,62	3,80	3,86
68	15,25	3,45	3,63
71	9,92	2,82	3,26
74	25,66	2,62	3,56

The highest maximum value of the cogging torque was achieved for angle 𝛽 = 74°, which justifies the high filling of the angular compartment, and the lowest for angle 𝛽 = 71°. It should be noted that in the second design variant for excitation MMF_DC = −2500 AT the highest values of the cogging torque were achieved. Figure 11 shows the course of the cogging torque values for one half-period and angle 𝛽 = 74° and 𝛽 = 71°.

Fig. 11.

Cogging torque waveforms at different values of MMF_DC = ±2500 AT and at 0 AT for 𝛽 = 71° (a) and 𝛽 = 74° (b).

For the value of the angle 𝛽 ≥ 71°, a twofold increase in the frequency of occurrence of the cogging torque extremes can be observed in one half-period of the run. This will contribute to an increase in the frequency of machine vibrations.

Fig. 12.

Dependence of the maximum value of the cogging torque on the angle parameter beta.

In Fig. 12 can be observed the quasi-sinusoidal shape of the characteristic curve of the value of the maximum cogging torque for angle values from 56° to about 68°.

It should be emphasized that the rated torque of the machine, depending on the structure of the iron poles for the proposed structure, was around 80 N⋅m, while during the strengthening it was even up to 140 N⋅m, and during weakening it was reduced to approx. 70 N⋅m. Therefore, when analyzing the obtained results, it can be seen that there is a need to reduce the cogging torque, because in the worst case (during strengthening) the cogging torque can reach even 30% of the rated torque (variant I. 𝛼_IP = 5°).

5. Conclusions

The main aim of the study was the analysis of the influence of iron poles shapes on the electromagnetic torque performance of the Field Control Axial Flux Permanent Magnet Machine. For this purpose, two variants of iron pole pieces were analyzed: iron pole as a segment of a toroid with a specific angular span 𝛼_IP (variant I) and iron pole in the form of a cuboid with the base of an equilateral trapezoid with a variable 𝛽 angle at one of the bases (variant II). Thanks to the use of hybrid excitation, the proposed design allows to influence of back-emf and electromagnetic torque. Thanks to this it is possible to extend the use of the machine, because during flux weakening the rotational speed can be increased, while during flux strengthening, the electromagnetic torque can be enlarged.

The biggest growth of the peak value of cogging torque is clearly observed at MMF_DC = −2500 AT, it means at DC field strengthening operation.

The presented results show that, both the angular span of the pole pitch filling 𝛼_IP for variant I, and geometrical parameter 𝛽 for variant II, have significant impact on the shape of cogging torque waveform and its peak value. For the first variant, the lowest maximum value of the cogging torque of 23 Nm was obtained for 𝛼_IP = 29°. For the second variant, a minimum value of about 10 Nm was achieved at 𝛽 = 71°.

The results show that there is an optimal iron pole shape at which a significant ripple torque reduction can be achieved. In the first variant, the value of the cogging torque in the 𝛼_IP angle range from 5° to 29° was, for excitation MMF_DC = −2500 AT from 17.40 AT, from about 22 Nm to 44 Nm. For the second variant of the design, for an angle 𝛽 in the range of 56° to 74°, the value was from about 10 Nm to 25 Nm. This confirms that variant II of the rotor design is more effective than variant I in terms of cogging torque reduction for the presented FCAFPM-machine.

References

Aydin

Zhu

Z.Q.

and Lipo

T.A.

, Minimization of cogging torque in axial-flux permanent-magnet machines: Design concepts, IEEE Trans. Magn.43 (2007), 3614–3622, doi:10.1109/TMAG.2007.902818.

Saygin

and Aksöz

, Design optimization for minimizing cogging torque in axial flux permanent magnet machines, in: 2017 International Conference on Optimization of Electrical and Electronic Equipment (OPTIM) & 2017 Intl Aegean Conference on Electrical Machines and Power Electronics (ACEMP), Brasov, Romania, 2017, pp. 324–329. doi:10.1109/OPTIM.2017.7974991.

Girgin

M.T.

and Aydin

, Elimination of cogging torque for axial flux permanent magnet motors based on current harmonic injection, in: 2020 International Conference on Electrical Machines (ICEM), Gothenburg, Sweden, 2020, pp. 1117–1122. doi:10.1109/ICEM49940.2020.9270642.

Fei

and Luk

P.C.K.

, Torque ripple reduction of a direct-drive permanent-magnet synchronous machine by material-efficient axial pole pairing, IEEE Transactions on Industrial Electronics59 (2012), 2601–2611. doi:10.1109/TIE.2011.2158048.

Usman

Ikram

Alimgeer

K.S.

Yousuf

Bukhari

S.S.H.

and Ro

J.-S.

, Analysis and optimization of axial flux permanent magnet machine for cogging torque reduction, Mathematics2021(9) 1738, doi:10.3390/math9151738.

Carlos

Werner

Danilo

Gerd

Juan

and Javier

A.R.

, Impact of tolerances on the cogging torque of tooth-coil-winding pmsms with modular stator core by means of efficient superposition technique, Electronics9 (2020), 1594, doi:10.3390/electronics9101594.

Pierpaolo

and Saponara

, Design of an observer-based architecture and non-linear control algorithm for cogging torque reduction in synchronous motors, Energies13 (2020), 2077, doi:10.3390/EN13082077.

Hsiao

C.-Y.

Yeh

S.-N.

and Hwang

J.-C.

, A novel cogging torque simulation method for permanent-magnet synchronous machines, Energies4 (2011), 2166–2179, doi:10.3390/en4122166.

Patel

A.N.

and Suthar

B.N.

, Reduction of cogging torque of surface mounted axial flux permanent magnet brushless DC motor with slot shifting technique, International Journal of Engineering and Advanced Technology (IJEAT)8(4) (2019), 1150–1154.

10.

Taran

Heins

Rallabandi

Patterson

and Ionel

D.M.

, Torque production capability of axial flux machines with single and double rotor configurations, in: IEEE Energy Conversion Congress and Exposition (ECCE), 2018, pp. 7336–7341. doi:10.1109/ECCE.2018.8557818.

11.

Aydin

Zhu

Z.Q.

Lipo

T.A.

and Howe

, Minimization of cogging torque in axial-flux permanent-magnet machines: Design concepts, IEEE Trans. Magn.43(9) (2007), 3614–3622, doi:10.1109/TMAG.2007.902818.

12.

Aydin

, Magnet skew in cogging torque minimization of axial gap permanent magnet motors, in: 18th International Conference on Electrical Machines, 2008, pp. 1–6. doi:10.1109/ICELMACH.2008.4799945.

13.

Ostroverkoh

Chumack

and Monakhov

, Robust control of hybrid excited synchronous machine, in: 2020 IEEE 7th International Conference on Energy Smart Systems (ESS), IEEE, 2020. doi:10.1109/ESS50319.2020.9160058.

14.

Ostroverkhov

Chumack

and Monakhov

, Synchronous axial-flux generator with hybrid excitation in stand alone mode, in: 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON), IEEE, 2019. doi:10.1109/UKRCON.2019.8879849.

15.

Aydin

Huang

and Lipo

T.A.

, A new axial flux surface mounted permanent magnet machine capable of field control, in: Conference Record of the 2002 IEEE Industry Applications Conference. 37th IAS Annual Meeting (Cat. No. 02CH37344), Vol. 2, IEEE, 2002. doi:10.1109/IAS.2002.1042719.

16.

Capponni

F.G.

and Borocci

, Axial-flux hybrid-excitation synchronous machine: Analysis, design, and experimental evaluation, IEEE Transactions on Industry Applications50(5) (2014), 3173–3184, doi:10.1109/TIA.2014.2303253.

17.

Gang

Zhang

and Li

, Concept and electromagnetic design of a new axial flux hybrid excitation motor for in-wheel motor driven electric vehicle, in: 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), IEEE, 2019. doi:10.1109/ICEMS.2019.8922430.

18.

Zhang

Liang

Lin

Hao

and Li

, Design and analysis of novel hybrid-excited axial field flux-switching permanent magnet machines, IEEE Transactions on Applied Superconductivity26(4) 1–5, doi:10.1109/TASC.2016.2517662.

19.

Paplicki

and Prajzendanc

, The influence of permanent magnet length and magnet type on flux-control of axial flux hybrid excited electrical machine, in: 14th Selected Issues of Electrical Engineering and Electronics (WZEE), 2018, pp. 1–4. doi:10.1109/WZEE.2018.8749015.

20.

Paplicki

Prajzendanc

and Wardach

, An electrically-controlled axial-flux permanent magnet generator, Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska10(4) 65–68, doi:10.35784/iapgos.2361.

21.

Wardach

Palka

Paplicki

Prajzendanc

and Zarebski

, Modern hybrid excited electric machines, Energies13 (2020), 5910, doi:10.3390/en13225910.