# Analysis of the Impact of Magnetic Materials on Cogging Torque in Brushless DC Motor

Authors: K. Karthick; S. Ravivarman; Ravi Samikannu; K. Vinoth; Bashyam Sasikumar
Journal: Advances in Materials Science and Engineering
 (2021)

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## Abstract

The cogging torque is the most significant issue in permanent magnet applications, since it has a negative impact on machine performance. In this article, the impact of magnetic materials on cogging torque is analyzed on brushless DC motors (BLDC). The effect of neodymium magnets (NdFeB), compression molded magnet, and samarium cobalt (SmCo) magnet on the cogging torque is analyzed to the BLDC motor designed for hybrid electric vehicle traction that has the peak power rating of 50 kW motor with 48 stator slots and 8 rotor poles. With the presence of these three magnetic materials, the cogging torque is estimated independently using multiposition simulation. The multiposition is simulated using a transient application that runs at constant speed. The results of cogging torque, rotational speed, angular position of BLDC motor, and magnetic flux density distribution have been presented. Also, the maximal, mean, minimal, rectified mean, and rms values of cogging torque were provided.


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## Body

## 1. Introduction

The BLDC motor is broadly employed in a variety of applications such as home appliances, automotive, aviation, health industry, industrial automation equipment, and instrumentation [1, 2]. When compared to brushed DC or induction motors, BLDC motors have many advantages, including greater efficiency and consistency, reduced acoustic noise, lighter and smaller size, better dynamic response, improved mechanical characteristics, a broader range of angular velocity, and a long lifespan [3]. Electronic commutation is required for BLDC motors, which helps to reduce the frequency of maintenance [4].An important category of these motors is the interior permanent magnet brushless DC (IPMBLDC) electrical motor, which is built with magnets embedded into the steel rotor core instead of glued-like surface mounted permanent magnet motors [5–7]. In permanent magnet brushless DC (PMBLDC) motors, cogging torque is a serious issue. Because of the harmonic magnetic forces produced by cogging torque, redundant vibrations and forbidding noises occur in medium-low power PMBLDC motors [8]. As a result, cogging torque reduction methods are essential in PMBLDC motor design. Cogging torque is generated by motors that use permanent magnets, such as PMBLDC motors and permanent magnet synchronous motors (PMSM) [9]. In PMBLDC motor, the rotor is made of permanent magnetic materials and can have any number of pole pairs from two to eight that alternate between north and south. Magnetic interaction between a permanent magnet and steel in a slotted armature is the main reason of cogging torque creation in BLDC motors [10–12]. In this article, we analyzed the impact of magnetic materials [13] on cogging torque generation in IPMBLDC motor. Temperature influences magnetism by strengthening or weakening the magnetomotive force. Because the molecules in the magnet accelerate faster when it is heated, the magnetic field weakens.


## 2. Related Works

Various investigations on the cogging torque of PMBLDC motors have been performed over the last two decades. Electromagnetic and mechanical methods have been among those employed [13–16]. Conventional electromagnetic techniques have the drawback of diminishing active magnetic flux, which reduces power output and efficiency. Mechanical methods, on the other hand, minimize active magnetic flux much less than electromagnetic techniques, allowing the construction of high-efficiency, high-power motors. A variety of BLDC motor design factors influence cogging torque such as length of air gap, slot opening, and pole pitch of magnet [17]. These methods to minimize the cogging torque magnitude involve adjusting slot and tooth widths, employing permanent magnet skewing, making auxiliary teeth, using slot-less armatures, and including notches in rotor structure [18–21].A slot-less core [19, 22] has a reduced inductance and can thus operate at quite high speeds. The absence of teeth in the lamination stack minimizes the cogging torque that makes it suitable for low-speed operations as well. The major drawback of a slot-less core is that it is more expensive because more winding is required to compensate the larger air gap [23]. The better torque can be achieved with increase in number of poles. The maximum torque also depends on the strength of the flux density of the material used in the fabrication of permanent magnets. The step size and torque ripples in reluctance machine are influenced by rotor magnetic poles. Presence of large number of poles results in smaller step size as well as lower torque ripple [24–26]. Various analytical methods have been proposed to minimize the cogging torque [27, 28]. The skewing in rotor structure is one of the major approaches to minimize the cogging torque [29–32]. Because of the permanent magnet construction, the rotor has a high flux density and there are no losses in rotor because of the absence of winding in rotor core. So, the efficiency of the motor is high.Ferrite magnets have traditionally been used to produce permanent magnets. Rare earth alloy magnets (also known as neodymium magnets) are becoming increasingly popular as technology develops. Ferrite magnets are cost-effective, but they have a less flux density per unit volume. In this article, the slot shape has been fixed as round with slot opening angle of 45  ̊. The impact of magnetic materials on this round stator slot is analyzed for the various magnetic materials.


## 3. Design of BLDC Motor

The configuration or designing of an IPMBLDC motor is more complicated than that of a surface permanent magnet motor. The design process is adopted from [33, 34], as shown in Figure 1. The motor is designed for hybrid electric vehicle traction application with the ratings of peak torque 400 Nm, peak speed 6000 rpm. Maximum power rating is 50 kW at ¼ of maximum speed. The motor has 48 stator slots, 8 rotor poles, outer diameter as 242 Nm, and stack length as 75 mm with an air gap of 0.5 mm. The various BLDC motor parameters are shown in Figure 2. The magnetic pole arc of the rotor is 140 ̊. The slot depth is 30 mm, tooth width is 6.5 mm, and magnetic width per pole is 54 mm. It is observed that the number of excellent quality elements is 97.67% from the simulation. Lap per pole winding is assumed as 6 and number of coils is assumed as 2 while designing BLDC motor.Figure 1
BLDC motor designing process [33].Figure 2
BLDC motor parameters. (a) Rotor poles. (b) Magnetic pole arc. (c) Magnetic width. (d) Stator slots. (e) Slot depth and slot opening angle.
(a)(b)(c)(d)(e)The flux in the core is expressed as(1)∅core≈DPleBg,where le is the effective length of stator, Bg is the flux density in the air gap, D is the stator bore diameter, and P is the number of poles.The maximum value of the net magnetic flux densityBg,pk is defined as(2)Bg,pk=Br,pk∗Cosδ−θ∗π/180PF.The peak winding magnetic flux densityBg,pk is expressed as(3)Ba,pk=Bg,pkSinθ∗π/180+Br,pk∗Sinδ−θ∗π/180,where PF is the power factor, Bg,pk is the peak air-gap magnetic flux density, θ is the power angle, and δ is the torque angle.The pole arc coefficient is expressed as(4)αp≈bτp,where b is the arc length of pole shoe and τp is the pole pitch.The cogging torque (Tcog) is given by(5)Tcog=∑k=1nTksinkZθn+αk,where Tk and αk are the Fourier harmonic development coefficients, Z is the total number of stator teeth, θn is the angular position of the rotor, and n is the harmonics number that defines the actual shape of the cogging torque.


## 4. Cogging Torque Analysis

A multiposition simulation is used to calculate the motor’s cogging torque. The speed is chosen as 1/6 rpm that corresponds to 1 mechanical degree per second. The angle of the rotor is varied over 1 slot pitch, i.e., 7.5 ̊. The analysis is carried out with the range of 0  ̊ to 7.5  ̊ with the step of 0.1875 ̊.To analyze the effect of three magnetic materials such as NdFeB, compression molded magnet, and SmCo, initially the mesh generation has been done, as shown in Figure3, by defining the geometric parameters. The COGENT_M270_35A_50HZ is the silicon steel lamination that has been chosen as the core.Figure 3
Mesh domain.Table1 shows the properties of NdFeB, compression molded magnet, and SmCo. It is observed that compression molded magnet has very low remanent flux density with high relative permeability. The main components of a compression molded magnet are isotropic NdFeB powder and a thermosetting binder. They have improved mechanical properties [35].Table 1
Permanent magnet properties.
Rotor magnet typeChemical compositionRemanent flux density (T)Relative permeabilityCY_N35_20DEGNdFeB1.211.052MQP_B_875_830_150DNdFeB (compression molded magnet)0.5451.3514NewlandMagnet_Sm2Co17_28FSmCo1.081.1018


### 4.1. Results and Discussion

The three magnetic material impacts have been given as Case1, 2, and 3 for NdFeB, compression molded magnet, and SmCo magnetic materials, respectively. Tables 2–4 give the numerical results of cogging torque, angular speed, and angular position for NdFeB, compression molded magnet, and SmCo magnetic materials, respectively. The graphical results of the same are shown in Figures 4–6, respectively. Magnetic flux density distribution of the machine is shown in Figures 7–9 for the presence of rotor permanent magnets NdFeB, compression molded magnet, and SmCo, respectively. The cogging torque maximum magnitudes are 8.015 Nm, 0.784 Nm, and 4.566 Nm for NdFeB, compression molded magnet, and SmCo, respectively. It is observed that the composite molded magnets help to reduce the impact of cogging torque. All these results have been obtained in constant angular speed.Table 2
Magnitude values of BLDC motor parameters.
DescriptionCogging torqueAngular speedAngular positionMinimal value−8.04410Maximal value8.01517.5Mean value−0.02213.75Rectified mean value3.79813.75R.M.S value4.68914.33Table 3
Magnitude values of BLDC motor parameters for Case1.
DescriptionCogging torqueAngular speedAngular positionMinimal value−0.79310Maximal value0.78417.5Mean value−0.00313.75Rectified mean value0.27413.75R.M.S value0.39514.33Table 4
Magnitude values of BLDC motor parameters for Case3.
DescriptionCogging torqueAngular speedAngular positionMinimal value−4.58910Maximal value4.56617.5Mean value−0.01713.75Rectified mean value1.91313.75R.M.S value2.48614.33Figure 4
Cogging torque, rotational speed, and angular position of BLDC motor for Case1.Figure 5
Angular position, rotational speed, and cogging torque of BLDC motor for Case2.Figure 6
Angular position, rotational speed, and cogging torque of BLDC motor for Case3.Figure 7
Magnetic flux density distribution view of BLDC motor of Case1.Figure 8
Magnetic flux density distribution view of BLDC motor of Case2.Figure 9
Magnetic flux density distribution view of BLDC motor of Case3.Case 1.
CY_N35_20DEG magnetic material.Case 2.
compression molded magnet.Case 3.
NewlandMagnet_Sm2Co17_28F.


## 4.1. Results and Discussion

The three magnetic material impacts have been given as Case1, 2, and 3 for NdFeB, compression molded magnet, and SmCo magnetic materials, respectively. Tables 2–4 give the numerical results of cogging torque, angular speed, and angular position for NdFeB, compression molded magnet, and SmCo magnetic materials, respectively. The graphical results of the same are shown in Figures 4–6, respectively. Magnetic flux density distribution of the machine is shown in Figures 7–9 for the presence of rotor permanent magnets NdFeB, compression molded magnet, and SmCo, respectively. The cogging torque maximum magnitudes are 8.015 Nm, 0.784 Nm, and 4.566 Nm for NdFeB, compression molded magnet, and SmCo, respectively. It is observed that the composite molded magnets help to reduce the impact of cogging torque. All these results have been obtained in constant angular speed.Table 2
Magnitude values of BLDC motor parameters.
DescriptionCogging torqueAngular speedAngular positionMinimal value−8.04410Maximal value8.01517.5Mean value−0.02213.75Rectified mean value3.79813.75R.M.S value4.68914.33Table 3
Magnitude values of BLDC motor parameters for Case1.
DescriptionCogging torqueAngular speedAngular positionMinimal value−0.79310Maximal value0.78417.5Mean value−0.00313.75Rectified mean value0.27413.75R.M.S value0.39514.33Table 4
Magnitude values of BLDC motor parameters for Case3.
DescriptionCogging torqueAngular speedAngular positionMinimal value−4.58910Maximal value4.56617.5Mean value−0.01713.75Rectified mean value1.91313.75R.M.S value2.48614.33Figure 4
Cogging torque, rotational speed, and angular position of BLDC motor for Case1.Figure 5
Angular position, rotational speed, and cogging torque of BLDC motor for Case2.Figure 6
Angular position, rotational speed, and cogging torque of BLDC motor for Case3.Figure 7
Magnetic flux density distribution view of BLDC motor of Case1.Figure 8
Magnetic flux density distribution view of BLDC motor of Case2.Figure 9
Magnetic flux density distribution view of BLDC motor of Case3.Case 1.
CY_N35_20DEG magnetic material.Case 2.
compression molded magnet.Case 3.
NewlandMagnet_Sm2Co17_28F.


## 5. Conclusion

In this paper, the impact of NdFeB, compression molded magnet, and SmCo on cogging torque has been analyzed. The results shows that the cogging torque maximum magnitudes are 8.015 Nm, 0.784 Nm, and 4.566 Nm for NdFeB, compression molded magnet, and SmCo, respectively. SmCo reduces the impact to 56.9% as compared to NdFeB. The compressed molded magnet has the large reduction in cogging torque magnitude as 97.8%. The results have been obtained by creating mechanical set parameters, mesh generation, and physic description using flux simulation tool. The initial rotor position has been set to 7.5° to align the phase current with back emf. The selection of magnetic material will primarily depend on the temperature of the application, device size and weight, and cost. According to the existing research, NdFeB outperforms SmCo in terms of flux output between –138 ̊C and 150 ̊C. Above 150 ̊C, NdFeB continues to suffer enough induction loss that SmCo is superior.



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*Source: 5954967-2021-12-17.xml*