• Vol 9, No 3 (2018)
  • Electrical, Electronics, and Computer Engineering

Edge-rounded Magnet Poles for Reducing the Torque Ripple on a Radial Flux Inset Permanent Magnet Generator

Wike Handini, Rudy Setiabudy, Ridwan Gunawan, Chairul Hudaya

Cite this article as:
Handini, W., Setiabudy, R., Gunawan, R., Hudaya, C., 2018. Edge-rounded Magnet Poles for Reducing the Torque Ripple on a Radial Flux Inset Permanent Magnet Generator . International Journal of Technology. Volume 9(3), pp.613-621
Wike Handini Department of Electrical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok 16424, Indonesia
Rudy Setiabudy Department of Electrical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok 16424, Indonesia
Ridwan Gunawan Department of Electrical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok 16424, Indonesia
Chairul Hudaya Department of Electrical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok 16424, Indonesia
Email to Corresponding Author


This study reports a novel strategy for minimizing torque ripple in a radial flux inset permanent magnet (RFIPM) generator by using a geometric modification of the magnet poles. We simulate the design of three different types of edge-rounded magnet (ERM) poles using finite element method magnetics (FEMM) software for a 16 poles and 24 slots RFIPM generator. We found that the edge-rounding of magnet poles significantly lowered the torque ripple of the generator with a reduction of about 74% (torque ripple of 7.76%). In addition, the modified RFIPM generator exhibited enhanced flux density uniformity in the air-gap of the generator (up to ~ 48.8%), leading to a smoother line of flux density.

Edge-rounded magnet poles; Finite element method magnetic; Flux density uniformity; Radial flux inset permanent magnet generator; Torque ripple reduction


Permanent magnets have been widely used in electrical machines, such as motors and generators, since they improve the efficiency and reliability of the machines due to the absence of excitation losses (Yicheng et al., 2005; Gieras, 2010). Moreover, electrical machines using permanent magnets such as direct-drive permanent magnet machines have other advantages compared to gear box-based machines, including higher reliability and efficiency, less maintenance, less noise and as low weight (Meier, 2008). One of the main challenges in designing a permanent magnet-based generator is the torque quality. Torque distortion such as cogging torque and torque ripple may cause a magnetic vibration and noise. This distortion may be transmitted directly to the load and drive shaft, degrading the lifetime of the electric machines (Islam et al., 2009). Torque ripple is mostly caused by the non-homogeneous distribution of flux density in the air-gap of the generator due to the interaction of the current fundamental harmonic and the EMF harmonics (Gasc et al., 2003).

Several studies have been devoted to overcome the aforementioned problems. In general, there are two approaches for reducing torque ripple. The first strategy is to improve the magnetic design of the electric machines by changing the geometry of the stator and rotor poles. The other one is to use the electronic control technique, which is based on control parameters such as supply voltage, turn-on and turn-off angles, and current level (Husain, 2002, Sunan et al., 2010). Compared to the latter technique, the former method is more desirable because it may effectively reduce torque ripple, whereas the electronic control technique requires a precise real-time excitation current, according to the real-time computations. In addition, real-time computation is very sensitive in terms of the reliability and accuracy of the sensors used in the control system (Weizhong et al., 2011).

Ahsanullah et al. proposed a method for optimization for the reduction torque ripple and cogging torque by changing the magnet arcs and choosing an optimum flux barrier in the interior permanent magnet machine using two-dimensional finite element analysis (Ahsanullah et al., 2013). Using this method, they successfully decreased the cogging torque to be less than 1%. Another approach involved using  a multilayer structure for stator windings and changing the rotor geometry (Alberti et al., 2014). The authors reported a torque ripple lower than 1.5% at full load. An asymmetric flux barrier and asymmetric lamination method was proposed by Ki-Chan Kim to reduce torque ripple and cogging torque (Ki-Chan, 2014). Their effort resulted in an asymmetric barrier in a permanent magnet rotor without permanent magnet skew. A similar approach by Dajaku and Gerling reduced torque ripple through a new stator design with right- and left-shifted slot openings to minimize the cogging torque (Dajaku & Gerling, 2014). Upadhayay and Rajagopal used the magnet pole shaping technique for torque ripple reduction on a 12 poles and 18 slots surface mounted permanent magnet brushless DC motor (Upadhayay & Rajagopal, 2013). The performance parameters were computed and analyzed by two-dimensional finite element analysis. Gyeong-Chan et al. proposed a design of pole arc and permanent magnet structure to reduce cogging torque and torque ripple for an outer rotor radial flux surface mounted permanent magnet generator (Gyeong-Chan et al., 2014). Nur and Haroen investigated the influence of a magnet pole slot of 6 poles and 18 slots of an inset permanent magnet synchronous machine on cogging torque. They found that slotting the edge of the magnet reduced the cogging torque effectively (Nur & Haroen, 2014). Recently, our group successfully simulated the combination of ERM and stator teeth notch techniques with optimum parameters and found that the torque ripple was significantly reduced up to 80% (Handini et al. 2016).

In this paper, we investigate the effect of edge-rounding of permanent magnet poles on torque ripple reduction of a 16 poles and 24 slots radial flux inset permanent magnet (RFIPM) generator. We simulated the system using FEMM software and found the proposed method effectively decreases the torque ripple and improves the uniformity of electromagnetic flux density.

Experimental Methods



The electromagnetic torque of electric machines has two main torque components, and is expressed as (Gieras, 2010):2. 


where T0 is a constant or average component and Tr(?) is a periodic component, which is a function of time or angle ?. The periodic component causes the torque pulsation called torque ripple. Torque ripple is given by (Gieras, 2010):



and Tp is the period of the torque waveform.


We are interested in a RFIPM generator with 16 poles and 24 slots because this typical generator is mainly used for a low-speed wind power system. In this study, we designed three different models of edge-rounded magnet (ERM) poles. Figure 1 shows the cross-section view of the basic model and the respective developed ERM model of the RFIPM generator. The main parameters are presented in Table 1. 

Figure 1 Cross-sectional view of RFIPM generator for (a) basic model; (b) ERM 1; (c) ERM 2; (d) ERM 3

Table 1 Parameters of RFIPM generator









Number of slots




Number of poles




Stator outer radii




Stator inner radii




Rotor outer radii




Rotor inner radii




Magnet pole thickness




Air gap length




Pole arc/pitch ratio




Since the geometric modification of magnet poles does not change their thickness and width, the cross-section area of the ERM models are slightly smaller than that of the basic model owing to the removal of the magnet material. This phenomenon causes a higher air gap volume in the ERM models compared to their basic counterpart. The cutting residue in the ERM poles D (mm2) is identified by blue color in Figure 2.


This study investigated the effects of edge-rounded magnet poles on the torque ripple reduction and flux density uniformity in an RFIPM generator. Using FEMM 4.2, we simulated the electromagnetic torque of three different magnet shapes with edge-rounding techniques. We found that ERM 2 showed the lowest torque ripple (7.76%), the smoothest flux line, and the best flux density uniformity (48.8%). These phenomena were closely correlated with the optimized volume of the air-gap and the magnet volume, leading to better performance of the RFIPM generator.


The authors are grateful for the financial support provided by Universitas Indonesia through the 2017 PITTA (No. 831/UN2.R3.1/HKP.05.00/2017) funding scheme managed by the directorate for Research and Community Engagement (DRPM). C. Hudaya is grateful for the support of World-Class Professor Program, Faculty of Engineering - Universitas Indonesia funded by Ministry of Research, Technology and Higher Education of Republic of Indonesia.


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