# Design and FEM Analysis of High-Torque Power Density Permanent Magnet Synchronous Motor (PMSM) for Two-Wheeler E-Vehicle Applications

Authors: Maruthachalam Sundaram; Mouttouvelou Anand; Jaganathan Chelladurai; Paramasivam Varunraj; Sam Joshua Smith; Shubham Sharma; Mamdouh El Haj Assad; Reza Alayi
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

Launch of electric vehicles have seen a substantial rise for the past few years in emerging economies like India. In countries like India, the growth and penetration of the electric vehicles in the Indian automotive industry specifically for the two-wheeler segments are driven by the demand surge where cost and motor metrics have a substantial deciding factor. The in-wheel hub-motor, which is the prime mover for the two wheelers, decides the comfort zone of the customer in various metrics such as efficiency, torque, speed range, charging, and hence the distance covered. This paper addresses the design formulation of achieving a high torque Permanent Magnet Synchronous Motor (PMSM) conventionally known as the hub-motor, explicitly for electric two-wheeler application. The hub-motor is aimed for the definedD and L (280 × 30 mm) of volumetric constraints to deliver the rated torque of 50 Nm at the spinning speed of 400 rpm. The hub-motor design is aimed for distance range of 108 km/charge, at the vehicle speed of 54 km/hr for the designed diametric and volumetric constraints. This will lead to a typical cost-effective e-vehicle system since the required distance range of 108 km is achievable at the defined rim size and geometry with an enhanced efficiency greater than 90%. The design is carried out by Finite Element Analysis (FEA) using the electromagnetic software MotorSolve. The results computed are analyzed and validated for the optimal loading conditions for the ambient temperature of 50°C. The results confirm the effectiveness of the proposed design formulation and methodology for achieving the high power density hub-motors for satisfying the customer’s comfort zone in establishing the performance metrics of the electromagnetic system.


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## Body

## 1. Introduction

There are a lot of acknowledgements for electric vehicles including two wheelers and four wheelers, due to pollution of environment and global changes [1, 2]. The hub-motor or in-wheel motor drive system can be implemented in vehicles like e-bikes and for all two-wheeler segments. The outer rotor PMSM hub-motor should be designed to have improved performance like power density, speed-torque characteristics, rugged nature, efficiency and many necessary parameters that will be required for a good electric vehicle to perform well [3, 4]. Since rare Earth magnetic materials are quite expensive, effective usage of those materials in the machine design and reducing the magnetic material whenever necessary without comprising the motor performance will reduce the cost of the motor and in turn reduce the cost of vehicle as well.PMSM motor is preferred for electric two wheelers due to the reasons of more efficiency, high torque for a wide range of speed, and more reliability [5–7]. The sequential excitation of the winding produces rotating magnetic field. The excited stator attracts the magnets of the rotor. The rotor follows the poles of electromagnet of the stator, and it is the main principle in PMSM. The PMSM rotates based on the position of the rotor, which is sensed by the Hall Effect sensor in the machine. The sinusoidal back EMF in motor will affect the torque developed. The PMSM drive system should be providing constant torque until the base speed of operations [8].Current day electric two wheelers have very low torque, compared to their Internal Combustion (IC) driven counterpart vehicles. Due to low torque of electric vehicle, it might cause some discomfort or certain complications. They will not be able to overtake or accelerate quickly. They are prone to hazardous situations with respect to its length of coverage on road. In this paper, a solution to overcome this problem with the design of PMSM motor with high torque and power density will be discussed.The optimal design for an in-wheel motor for an electric two-wheeler in an economical way is explained [9]. The major development across the segment of the two-wheeler is the introduction of outer rotor hub-motor where the shaft is directly connected to the vehicles’ wheel directly without any use of gear mechanism unlike some mechanical drive systems. The main objective is to arrive at good performance characteristics. Response surface technology is done for obtaining good design results and 2D FEM analysis.A clear comparison with exterior and interior rotor permanent magnet brushless motor is presented [10]. Two 250 W motors are considered for the design configurations, one with exterior rotor and one with interior rotor. Both the motors are designed, and their performances are compared, and it explains, even though interior rotor motor has advantages, why exterior rotor motor is best suited for two-wheeler hub-motor design.The validation for the reason why BLDC motor will be a good choice for being used for an electric vehicle drive source is explained [11]. It compares the characteristics of BLDC motor, PMSM motor, brushed DC motor, and stepper motor, and it will give us an insight to decide why BLDC motor can be used for a two-wheeler application.The no load and full characteristics and cogging torque of BLDC hub-motor in the form of the simulation model of Permanent Magnet Brushless DC (PMBLDC) are studied [12]. If the motor is to be used for a particular application, it must be designed in the right dimensions. This article is intended for simulation of torque and cogging torque with MAGNET Software (FEM ANALYSIS). The analysis of the distribution of flux and of saturation (flux density) in the core is mainly discussed.A 6 kW in wheel out-runner BLDC motor design for electric vehicle in Ansys Ansoft software is discussed [13]. Design specifications such as the number of turns, the winding area, and the stator pole height component of the stator structure are specifically established, and the engine performance characteristics are investigated by the finite element method. In addition, the output of each stator winding is computed and evaluated as regards phase inductance, flux linkage, and static torque at various rotor positions. Analysis is done using electromechanical model of the BLDC motor.The optimization and design of BLDC motor for dimensional constrained E-Max vehicle are discussed [14]. The new proposed design replaces the existing motor present. The author replaces the existing motor of rating 2.5 kW with the new optimized design of motor rated at 13 kW, which can drive up to 125 kmph without compromising the dimension of the machine. The new designed motor can be replaced with the existing motor, which is found in the 13-inch wheel.The two rotor structures for the purpose of finding the appropriate one to conduct an electric bicycle, namely, the internal rotor and the external rotor, is studied [15]. It investigates motor performance effects with certain motor parameters: current, forward angle, length of stack, and outer diameter. MotorSolve software is used to analyze both motors. Both motors have achieved the required rated speed and torque with high efficiency and low cost, based on the simulation and calculation results. However, the inner rotor PMSM obtained the requirements with a lighter weight and smaller size than the external rotor PMSM.Reference [16] gives a complete idea on design of BLDC motor. They explain the design from the number of phases of the machine, stator, and rotor design followed by winding parameters substantiation. They have also explained how to achieve better speed-torque characteristics, good inductance, and air-gap parameters.The design and analysis of BLDC motors suitable for submersible water pumping applications were discussed [17]. The paper gives an insight into the sequential steps to be carried out for a high efficiency BLDC design.The optimal design of BLDC motor for light electric vehicle propulsion application is briefly presented [18]. The study works with the appropriate selection of slot/pole combination to achieve a substantial performance for the application chosen by doing the Finite Element Analysis.Based on the aforementioned literature surveys, it is inferred that the concept of hub-motor exists for a wide category of in-wheel two-wheeler e-vehicle applications. However, there exists a research gap in the design and viability of high power and torque density hub-motors for in-wheel two-wheeler e-vehicle applications, since these is a special category of the PMSM or the BLDC motors, which comes and fits in the rugged environment with very limited volumetric and diametric constraints. There exists a challenging task in the electromagnetic design to achieve a high torque and high power density with limited values ofD and L, which further becomes cumbersome for an extended distance range for the same rim size and geometry.Hence, based on the aforementioned research gaps identified, this paper focuses on the design and FEM analysis of high-torque power density PMSM for two-wheeler E-vehicle applications. The PMSM chosen for the in-wheel hub-motor E-vehicle application is 2 kW, which is translated into the size of 280 × 30 mm, which makes the vehicle attain a speed of 54 km/hr for the designed diametric and volumetric constraints. The hub-motor is designed for the distance range of 108 km/charge, which translates into continuous duty of 5 kwh for a time duration of 2 hours. Hence, for the proposed PMSM design with the specified range, 48 V battery system with approximately 100 Ah is required. This will lead to a typical cost-effective e-vehicle system since the required distance range of 108 km is achievable at the defined rim size and geometry with an enhanced efficiency of PMSM standing greater than 90%.


## 2. Methodology

Permanent Magnet Synchronous Motor can be designed and constructed in different ways based on the application and need. Based on the type of windings used for stator, they can be classified into single-phase, two-phase, and three-phase motors. But generally, 3ϕ motors are commonly used. Based on the construction of stator and rotor, PMSM can be classified into two types, namely, in-runner or out-runner PMSM. In-runner motor has rotor inside and stator outside, while in case of out-runner type, the rotor will be outside, and the stator will be inside making the rotor visible to environment. This out-runner type of motor will be effective in hub-motor for electric two wheelers.Slots of the stator in PMSM will carry windings. The windings can be either star or delta connection. For less complexity and easy installation, most PMSM will be designed with star connection. Every winding is constructed in a way to carry numerous coils. Each slot will be placed with one or more coils. To have even number of poles, the windings will be distributed throughout the periphery of the stator. Proper voltage rating of the stator should be decided for appropriate application. For electric two-wheeler application, the voltage rating will be 36 V, 48 V to maximum of 72 V. For other industrial applications, the voltage rating will be up to 100 V or even higher. The rotor, which is made of magnets in PMSM, has salient pole structure. Based on the application and need, the number of poles may vary from 4 to 36 or even more. Proper magnetic material and thickness of the material will be essential in producing the needed magnetic field density. The permanent magnet material used in rotor of PMSM will be, namely, Neodymium Iron Boron (NdFeB), alloys of Neodymium, and Samarium cobalt (SmCo) [19].


### 2.1. Analytical Design

There is always a way to design anything. In machine design as well, there is some method to proceed with the machine design. If a proper flow of design is followed for the design of PMSM, the product obtained will be proper and will have the desired performance that is required. The flowchart describing the flow of process for design of PMSM is shown in Figure1. The specifications and parameters required for the design of PMSM is given in Table 1. The motor, which is under consideration, will be PMSM with exterior rotor [20]. The magnets will be surface mounted with radial magnets. The whole diameter of the rotor of the motor will be 280 mm, and the active width of machine will be 30 mm.Figure 1
Flow chart of PMSM machine design.Table 1
Specifications of PMSM.
S. noParametersValueUnit1Rated power2kW2Rated speed400rpm3Rated torque50Nm4Efficiency93%5No of poles46—6No of slots51—7Stack length30mm8OD/ID of rotor280/240mm9OD/ID of stator238/156mm10Coil fill factor40%11Magnet thickness3mmThe typical size chosen for the PMSM under consideration is 12-inch hub-motor. The size is selected based on the commercial rim size available in the market, and also, a detailed literature study reveals that the 12-inch in-wheel PMSM dominates the 2-wheeler automotive market in terms of volumetric and quantitative levels, which has made the authors concentrate on this size clearly. Based on the aforementioned fact, the size of the PMSM is chosen as 280 × 30 mm (D × L), which makes the vehicle attain a speed of 54 km/hr, when the rotor spins at 400 rpm. Also, since the designed PMSM is for in-wheel hub-motor application, the authors have chosen the PMSM with exterior rotor type as the configuration in this research work, which explicitly fits in for the application considered. The 2D view of the hub-motor is shown in Figure 2.Figure 2
2D view of the hub-motor.The parameters, which arrived in the design, have some theoretical calculations and derivation to get the answers that are subjected to various iterations. The calculations and the desired outcomes are discussed in the following sections.


#### 2.1.1.L Stack Length

The reason of arriving the stack height of 30 mm comes with the hub design, where theD and L are subjected to volumetric constraints. The total width of the machine is 80 mm. There should be some conditions taken into consideration while freezing the stack height. There will be some other factors like mechanical clearance, bearing, and overhanging of coil. These take some space in the total width. Thus, the L stack will be fixed accordingly.(i)
Mechanical clearance = 20 mm, Bearing = 10 mm, Overhanging of coil = 20 mm(ii)
L stack length = width − (Mech. Clearance +  bearing + overhanging of coil)(iii)
L stack = 30 mm.


#### 2.1.2. Number of Poles/Slots

On freezing the application of the PMSM as hub-motor, and the required power, voltage, and speed ratings, the design starts with freezing the selection of number of stator slots and rotor poles for the PMSM to yield the rated torque under the specified rated speed conditions. The appropriate selection of the slots and pole combination freezes the optimal electromagnetic circuit model of the PMSM [21]. The number of poles and slots can be selected from the chart, which is a part of the literature review of the well-defined principles [16]. This calculation is tentative, and it is done only by empirical way.For a hub-motor, it is not possible to select a smaller number of poles and slots as it is followed for a normal motor design. Based on the aforementioned rules, a cluster of slots/poles configurations are taken into consideration based on the design metrics such as theD and L of the wheel, specific electric and magnetic loadings, winding factor, flux density’s, current density’s, bac-EMF, cogging torque, and torque pulsations. The desirable range of poles is 26, 46, 50, and 74. The desirable number of slots is 27, 51, and 75. The winding factor and the LCM of all the slots/pole combinations are given in Table 2.Table 2
Summary of slots/pole combinations.
Sl. no.Slots/Pole combinationsWinding factorLeast common multiple (LCM)Fundamental frequency (Hz)151 slots 46 poles0.9442346153.33227 slots, 26 poles0.95470286.66351 slots, 50 poles0.9552550166.66475 slots, 74 poles0.9555550246.66The torque developed in an PMSM is proportional to its fundamental winding factor (kw) [16]. The kw is possibly expressed as the product of three major factors, namely, the pitch factor (kp), distribution factor (kd), and the skew factor (ks). These factors are expressed by the following equation:(1)kw=kpkdks.Based on the fact of the winding factor as listed in Table2, it can be inferred that all the slot/pole combinations considered in this research work have the optimal torque contribution by its winding factor in terms of its coil span, slots/pole/phase, and the angular spread since the kw almost remains the same for the PMSM considered. Hence, all the slots/pole combinations considered do not make any significant effect of the kw of the hub-motor.The second critical factor governing the vibration and noise of the hub-motor is its cogging torque. The cogging torque minimization is governed by a set of mathematical formulations, which are governed by the following set of rules by consideration of the cogging torque frequency, which is given by the least common multiple (LCM) of the slots/pole combinations [16].(i)
S⁄p ≮ 0.5 (for a good flux linkage)(ii)
HCF (S,p) ≠ 1 (for avoiding the unbalanced cogging)(iii)
To minimize the effective cogging, it is necessary to choose high value of LCM (S,p).Based on the fact of the LCM of S⁄p configurations as listed in Table 2, it can be inferred that the LCM for the 27-slot, 26-pole configuration is highly lesser when compared to the other configurations, which means that lesser LCM factor will substantially increase the cogging torque of the PMSM, which degrades the performance metrics of the PMSM. Hence, the 27-slot, 26-pole configuration is not viable for the proposed design.The third factor to be considered for the optimalS⁄p configuration of the hub-motor is its core losses, which is the combination of the eddy current and hysteresis loss components. These core losses contribute to the second highest magnitude of loss component in the PMSM. The eddy current loss for the PMSM is governed by equation (2), and the hysteresis loss for the PMSM is governed by equation (3) [22].(2)Eddy current lossPe=KeB2mf2t2V,where Pe—eddy current loss (watt). Bm—maximum flux density (Wb/m2). f—supply frequency (Hz). t—thickness of lamination (m). V—volume of material (M3). Ke—eddy current constant.(3)Ph=khfBn,where Ph—hysteresis loss (watt). kh—hysteresis loss constant. f—supply frequency (Hz). B—amplitude of flux density (T). n—material dependent exponent.It is inferred from Table2 that the 75-slot, 74-pole configuration has a fundamental frequency of 246.66 Hz, and 51-slots, 50-pole configuration has a fundamental frequency of 166.66 Hz. From equations (2) and (3), it is evident that the eddy current loss and the hysteresis losses substantially increase with higher fundamental frequency, which shall result in higher core losses, which eventually reduces the efficiency of the PMSM, and hence, the concept of high power density PMSM for EV application becomes challenging. This is validated from the results of core losses as tabulated in Table 3, where it is inferred that 75-slot, 74-pole and 51-slot, 50-pole configurations result in higher core losses eventually when compared with 51-slot, 46-pole configuration. Based on the aforementioned facts, the proposed design of 51-slot, 46-pole configuration is optimal for the PMSM chosen for the in-wheel hub-motor E-vehicle application.Table 3
Summary of cu and core losses for different slots/pole combinations.
Slots/pole combinations@200 rpm@300 rpm@400 rpmCu loss (kW)Core loss (kW)Cu loss (kW)Core loss (kW)Cu loss (kW)Core loss (kW)27 slots 26 poles0.1915453620.0304708180.1920001930.0382735540.1914967410.04534906575 slots 74 poles0.3648055660.0554560340.3636576120.0609910490.262238450.08767907751 slots 46 poles0.1828353990.0436526690.1828376310.0586851920.1822489610.06990246151 slots 50 poles0.1838718530.2261304530.1836345320.2342022080.1818166580.245574333Computation of the core and copper loss of the PMSM hub-motor is of paramount importance since they have to be lowered for enhancing the overall efficiency of the machine [23, 24]. The iron or the core losses are calculated based on the hysteretic behavior of the PMSM, and also its eddy current losses. However, these loss calculations and the consistent treatment of these losses are more complex since a single model predictive control is not a viable technique as the PMSM is subjected to broad spectrum of different operating variants.Hence, these magnetic losses are computed by the electromagnetic solver, namely, the MotorSolve, based on the typical empirical loss curves as provided by the lamination sheet manufacturers, which gives the total iron losses as function of peak flux density at the specified fundamental frequency. The mathematical formulation for computing the total iron loss of the PMSM using the FEM is given by equation (4), which is commonly referred to as the Steinmetz equation.(4)P=KhfαBβ+KesfB2,where P—iron loss (W/kg). Bm—maximum flux density (Wb/m2). f—supply frequency (Hz). Kh, Ke, α, β—Steinmetz coefficients. s—lamination thickness ratio.The Steinmetz equation consists of two components, namely,KhfαBβ and the Ke (sfB)2. The component KhfαBβ is referred to as the Steinmetz loss, which is a combination of the hysteresis and the anomalous loss, whereas the component Ke (sfB)2 is referred to as the eddy-current loss. Using the Steinmetz equation, the core loss is computed at any peak flux density for the specified fundamental frequency [25]. Similarly, the copper losses in the hub-motor are mathematically formulated by the following equation [26]:(5)Pcu=3Iph2Rph,where Pcu—copper loss (watts). Iph—phase current (A). Rph—DC resistance of each phase (Ω).The computation of copper loss is complex since the resistance of the winding alters with change in temperature, and hence, the copper loss also changes. The copper loss is computed based on the effect of change in temperature, which is represented by the following equation [26]:(6)RphTemp=RphTemp01+αcuTemp−Temp0,where Rph (Temp)—phase resistance at temperature Temp (Ω). Rph (Temp0)—phase resistance at a reference temperature Temp0 (Ω). αcu—temperature coefficient of resistivity.


#### 2.1.3. TRV Value

Torque per unit volume (TRV) is a phenomenon that will be a factor taken while designing a motor. It is a ratio of rated torque with the rotor volume of the motor. There is a reference boundary value of TRV for every class of machine, which is shown in Table4 (Kong et al. [8]). Based on that, we can calculate the D and L values. Based on empirical calculation, for an NdFeB machine to have good desirable characteristics, it is advisable to have a TRV value of 21–30.Table 4
TRV range of machines.
S. noType of machineTRV (kNm/m3)1Small totally enclosed motors (ferrite)7–142Totally enclosed motors (rare Earth magnets)14–423Integral hp industrial motors7–304High performance servo motors15–505Aerospace machines30–756Large liquid cooled machines100–250


#### 2.1.4. Sizing the PMSM Machine Design Metrics

The dimensional metrics of the PMSM are computed using equations (7)–(9) (Kong et al. [8]):(7)P=TRV×Vr×2π⋅N60,(8)D2L=P×4×602×π2⋅TRV×N,(9)P=TRV⋅πD2L4⋅2π⋅N60.The TRV value calculated shall be verified with the proposedD and L of the PMSM using equations (10)–(12) [16]:(10)TRV=π2⋅KW⋅A⋅B,(11)A=2m×Tph×IphπD.(12)Φ1=B×π⋅D⋅Lp.The initial slot geometry is designed as the formulations as listed in Figure1, by fixing the slot area and the yoke thickness. The size of the magnet is critical in the machine design iterations, as any increase in size of the magnet will result in core saturation, whereas reduced magnetic size will result in demagnetization, which degrades the optimal loading of the PMSM. The magnetic metrics are computed taking into effect the core saturation limits, and these are defined by equations (13)–(17):(13)P.C.=BmHm,(14)Bm=Bg⋅AgAm,(15)Hm=Bg⋅LgLm,(16)Ag=π×D⋅L2,(17)Am=π⋅L×120180×D−Lm2.Using equations (14)–(17) in equation (13), we get(18)P.C.=AgAm⋅LmLg.The value ofP. C. determines the load line slope on the demagnetization characteristics of the magnetic grade under consideration at the defined operating temperature. This gives the value of the energy product from which the adequate size of the magnet shall be arrived and designed as per the formulations depicted in Figure 1.


### 2.2. Parameterization of the Geometry of Hub-Motor

The input dimensional parameters of stator and rotor that are given as inputs to the software are shown in Figure3. Slot depth is the total depth of the slot found in stator. The slot opening width is the gap of the width of the slot for which the winding should enter the slot. Tooth tang angle is the angle between the tang and bottom of slot in degrees. The tooth thickness and width are mentioned in Figure 3. The maximum magnet angle that was possible to have in the design is 7.5° since it is desirable to have efficient usage of area and material. The magnet thickness implemented is 3 mm. Since NdFeB material is being used as magnet material for the design, it is not necessary to go beyond 3 mm ,or else, it may lead to saturation of the core. Figure 4 includes the whole sizing parameters of the PMSM design. It includes the dimensional inputs, ratings of machine, permanent magnet material, Torque per rotor volume ratio, desired fill factor, and type of rotor.Figure 3
Stator and rotor dimensions.Figure 4
Sizing parameters for the PMSM design.The input parameters required for the stator windings are given in Table5. Wye (star) connection is being used here. Coil placement method is an over-under method. The number of layers is 2, and the number of turns is 4. The winding type is lap winding. The phase and line resistance are less than 0.1 Ω. Thus, it means that the design of stator windings is optimal and precise. The whole analysis is done in the temperature of 50°C. This temperature is selected considering the maximum worst-case scenario. In ambient temperature, there will be a high chance of better performance and characteristics. The type of materials used in this design of PMSM hub-motor is shown in Tables 4 and 6.Table 5
Stator windings parameters.
S. noStator windingsValueUnit1Turn length163mm2Winding phase resistance0.0304Ω3Winding line-line resistance0.0607Ω4Winding factor94.4%5Angular spread74.1°6Bare slot area134mm27Conductor area7.01mm28Bare slot fill factor42%9Coil fill factor45.8%Table 6
Materials for PMSM hub-motor.
S. noComponentMaterialGrade1Rotor core materialSilicon steelM19-29 Ga2Rotor magnet materialNdFeBN42-SH3Stator core materialSilicon steelM19-29 Ga4Stator coil materialCopperCu 100% IACSFor core material of stator and rotor, M19 silicon steel of gauge 29 is used since it is commonly used for high flux density with less core loss [27]. Neodymium Iron Boron (NdFeB) magnet is used as a permanent magnet material. N42 or N35 grade material can be used. Commonly, an electrical two-wheeler N35SH grade is used due to its performance and economical availability. But to achieve high torque and good performance, N42SH grade can also be preferred.


## 2.1. Analytical Design

There is always a way to design anything. In machine design as well, there is some method to proceed with the machine design. If a proper flow of design is followed for the design of PMSM, the product obtained will be proper and will have the desired performance that is required. The flowchart describing the flow of process for design of PMSM is shown in Figure1. The specifications and parameters required for the design of PMSM is given in Table 1. The motor, which is under consideration, will be PMSM with exterior rotor [20]. The magnets will be surface mounted with radial magnets. The whole diameter of the rotor of the motor will be 280 mm, and the active width of machine will be 30 mm.Figure 1
Flow chart of PMSM machine design.Table 1
Specifications of PMSM.
S. noParametersValueUnit1Rated power2kW2Rated speed400rpm3Rated torque50Nm4Efficiency93%5No of poles46—6No of slots51—7Stack length30mm8OD/ID of rotor280/240mm9OD/ID of stator238/156mm10Coil fill factor40%11Magnet thickness3mmThe typical size chosen for the PMSM under consideration is 12-inch hub-motor. The size is selected based on the commercial rim size available in the market, and also, a detailed literature study reveals that the 12-inch in-wheel PMSM dominates the 2-wheeler automotive market in terms of volumetric and quantitative levels, which has made the authors concentrate on this size clearly. Based on the aforementioned fact, the size of the PMSM is chosen as 280 × 30 mm (D × L), which makes the vehicle attain a speed of 54 km/hr, when the rotor spins at 400 rpm. Also, since the designed PMSM is for in-wheel hub-motor application, the authors have chosen the PMSM with exterior rotor type as the configuration in this research work, which explicitly fits in for the application considered. The 2D view of the hub-motor is shown in Figure 2.Figure 2
2D view of the hub-motor.The parameters, which arrived in the design, have some theoretical calculations and derivation to get the answers that are subjected to various iterations. The calculations and the desired outcomes are discussed in the following sections.


### 2.1.1.L Stack Length

The reason of arriving the stack height of 30 mm comes with the hub design, where theD and L are subjected to volumetric constraints. The total width of the machine is 80 mm. There should be some conditions taken into consideration while freezing the stack height. There will be some other factors like mechanical clearance, bearing, and overhanging of coil. These take some space in the total width. Thus, the L stack will be fixed accordingly.(i)
Mechanical clearance = 20 mm, Bearing = 10 mm, Overhanging of coil = 20 mm(ii)
L stack length = width − (Mech. Clearance +  bearing + overhanging of coil)(iii)
L stack = 30 mm.


### 2.1.2. Number of Poles/Slots

On freezing the application of the PMSM as hub-motor, and the required power, voltage, and speed ratings, the design starts with freezing the selection of number of stator slots and rotor poles for the PMSM to yield the rated torque under the specified rated speed conditions. The appropriate selection of the slots and pole combination freezes the optimal electromagnetic circuit model of the PMSM [21]. The number of poles and slots can be selected from the chart, which is a part of the literature review of the well-defined principles [16]. This calculation is tentative, and it is done only by empirical way.For a hub-motor, it is not possible to select a smaller number of poles and slots as it is followed for a normal motor design. Based on the aforementioned rules, a cluster of slots/poles configurations are taken into consideration based on the design metrics such as theD and L of the wheel, specific electric and magnetic loadings, winding factor, flux density’s, current density’s, bac-EMF, cogging torque, and torque pulsations. The desirable range of poles is 26, 46, 50, and 74. The desirable number of slots is 27, 51, and 75. The winding factor and the LCM of all the slots/pole combinations are given in Table 2.Table 2
Summary of slots/pole combinations.
Sl. no.Slots/Pole combinationsWinding factorLeast common multiple (LCM)Fundamental frequency (Hz)151 slots 46 poles0.9442346153.33227 slots, 26 poles0.95470286.66351 slots, 50 poles0.9552550166.66475 slots, 74 poles0.9555550246.66The torque developed in an PMSM is proportional to its fundamental winding factor (kw) [16]. The kw is possibly expressed as the product of three major factors, namely, the pitch factor (kp), distribution factor (kd), and the skew factor (ks). These factors are expressed by the following equation:(1)kw=kpkdks.Based on the fact of the winding factor as listed in Table2, it can be inferred that all the slot/pole combinations considered in this research work have the optimal torque contribution by its winding factor in terms of its coil span, slots/pole/phase, and the angular spread since the kw almost remains the same for the PMSM considered. Hence, all the slots/pole combinations considered do not make any significant effect of the kw of the hub-motor.The second critical factor governing the vibration and noise of the hub-motor is its cogging torque. The cogging torque minimization is governed by a set of mathematical formulations, which are governed by the following set of rules by consideration of the cogging torque frequency, which is given by the least common multiple (LCM) of the slots/pole combinations [16].(i)
S⁄p ≮ 0.5 (for a good flux linkage)(ii)
HCF (S,p) ≠ 1 (for avoiding the unbalanced cogging)(iii)
To minimize the effective cogging, it is necessary to choose high value of LCM (S,p).Based on the fact of the LCM of S⁄p configurations as listed in Table 2, it can be inferred that the LCM for the 27-slot, 26-pole configuration is highly lesser when compared to the other configurations, which means that lesser LCM factor will substantially increase the cogging torque of the PMSM, which degrades the performance metrics of the PMSM. Hence, the 27-slot, 26-pole configuration is not viable for the proposed design.The third factor to be considered for the optimalS⁄p configuration of the hub-motor is its core losses, which is the combination of the eddy current and hysteresis loss components. These core losses contribute to the second highest magnitude of loss component in the PMSM. The eddy current loss for the PMSM is governed by equation (2), and the hysteresis loss for the PMSM is governed by equation (3) [22].(2)Eddy current lossPe=KeB2mf2t2V,where Pe—eddy current loss (watt). Bm—maximum flux density (Wb/m2). f—supply frequency (Hz). t—thickness of lamination (m). V—volume of material (M3). Ke—eddy current constant.(3)Ph=khfBn,where Ph—hysteresis loss (watt). kh—hysteresis loss constant. f—supply frequency (Hz). B—amplitude of flux density (T). n—material dependent exponent.It is inferred from Table2 that the 75-slot, 74-pole configuration has a fundamental frequency of 246.66 Hz, and 51-slots, 50-pole configuration has a fundamental frequency of 166.66 Hz. From equations (2) and (3), it is evident that the eddy current loss and the hysteresis losses substantially increase with higher fundamental frequency, which shall result in higher core losses, which eventually reduces the efficiency of the PMSM, and hence, the concept of high power density PMSM for EV application becomes challenging. This is validated from the results of core losses as tabulated in Table 3, where it is inferred that 75-slot, 74-pole and 51-slot, 50-pole configurations result in higher core losses eventually when compared with 51-slot, 46-pole configuration. Based on the aforementioned facts, the proposed design of 51-slot, 46-pole configuration is optimal for the PMSM chosen for the in-wheel hub-motor E-vehicle application.Table 3
Summary of cu and core losses for different slots/pole combinations.
Slots/pole combinations@200 rpm@300 rpm@400 rpmCu loss (kW)Core loss (kW)Cu loss (kW)Core loss (kW)Cu loss (kW)Core loss (kW)27 slots 26 poles0.1915453620.0304708180.1920001930.0382735540.1914967410.04534906575 slots 74 poles0.3648055660.0554560340.3636576120.0609910490.262238450.08767907751 slots 46 poles0.1828353990.0436526690.1828376310.0586851920.1822489610.06990246151 slots 50 poles0.1838718530.2261304530.1836345320.2342022080.1818166580.245574333Computation of the core and copper loss of the PMSM hub-motor is of paramount importance since they have to be lowered for enhancing the overall efficiency of the machine [23, 24]. The iron or the core losses are calculated based on the hysteretic behavior of the PMSM, and also its eddy current losses. However, these loss calculations and the consistent treatment of these losses are more complex since a single model predictive control is not a viable technique as the PMSM is subjected to broad spectrum of different operating variants.Hence, these magnetic losses are computed by the electromagnetic solver, namely, the MotorSolve, based on the typical empirical loss curves as provided by the lamination sheet manufacturers, which gives the total iron losses as function of peak flux density at the specified fundamental frequency. The mathematical formulation for computing the total iron loss of the PMSM using the FEM is given by equation (4), which is commonly referred to as the Steinmetz equation.(4)P=KhfαBβ+KesfB2,where P—iron loss (W/kg). Bm—maximum flux density (Wb/m2). f—supply frequency (Hz). Kh, Ke, α, β—Steinmetz coefficients. s—lamination thickness ratio.The Steinmetz equation consists of two components, namely,KhfαBβ and the Ke (sfB)2. The component KhfαBβ is referred to as the Steinmetz loss, which is a combination of the hysteresis and the anomalous loss, whereas the component Ke (sfB)2 is referred to as the eddy-current loss. Using the Steinmetz equation, the core loss is computed at any peak flux density for the specified fundamental frequency [25]. Similarly, the copper losses in the hub-motor are mathematically formulated by the following equation [26]:(5)Pcu=3Iph2Rph,where Pcu—copper loss (watts). Iph—phase current (A). Rph—DC resistance of each phase (Ω).The computation of copper loss is complex since the resistance of the winding alters with change in temperature, and hence, the copper loss also changes. The copper loss is computed based on the effect of change in temperature, which is represented by the following equation [26]:(6)RphTemp=RphTemp01+αcuTemp−Temp0,where Rph (Temp)—phase resistance at temperature Temp (Ω). Rph (Temp0)—phase resistance at a reference temperature Temp0 (Ω). αcu—temperature coefficient of resistivity.


### 2.1.3. TRV Value

Torque per unit volume (TRV) is a phenomenon that will be a factor taken while designing a motor. It is a ratio of rated torque with the rotor volume of the motor. There is a reference boundary value of TRV for every class of machine, which is shown in Table4 (Kong et al. [8]). Based on that, we can calculate the D and L values. Based on empirical calculation, for an NdFeB machine to have good desirable characteristics, it is advisable to have a TRV value of 21–30.Table 4
TRV range of machines.
S. noType of machineTRV (kNm/m3)1Small totally enclosed motors (ferrite)7–142Totally enclosed motors (rare Earth magnets)14–423Integral hp industrial motors7–304High performance servo motors15–505Aerospace machines30–756Large liquid cooled machines100–250


### 2.1.4. Sizing the PMSM Machine Design Metrics

The dimensional metrics of the PMSM are computed using equations (7)–(9) (Kong et al. [8]):(7)P=TRV×Vr×2π⋅N60,(8)D2L=P×4×602×π2⋅TRV×N,(9)P=TRV⋅πD2L4⋅2π⋅N60.The TRV value calculated shall be verified with the proposedD and L of the PMSM using equations (10)–(12) [16]:(10)TRV=π2⋅KW⋅A⋅B,(11)A=2m×Tph×IphπD.(12)Φ1=B×π⋅D⋅Lp.The initial slot geometry is designed as the formulations as listed in Figure1, by fixing the slot area and the yoke thickness. The size of the magnet is critical in the machine design iterations, as any increase in size of the magnet will result in core saturation, whereas reduced magnetic size will result in demagnetization, which degrades the optimal loading of the PMSM. The magnetic metrics are computed taking into effect the core saturation limits, and these are defined by equations (13)–(17):(13)P.C.=BmHm,(14)Bm=Bg⋅AgAm,(15)Hm=Bg⋅LgLm,(16)Ag=π×D⋅L2,(17)Am=π⋅L×120180×D−Lm2.Using equations (14)–(17) in equation (13), we get(18)P.C.=AgAm⋅LmLg.The value ofP. C. determines the load line slope on the demagnetization characteristics of the magnetic grade under consideration at the defined operating temperature. This gives the value of the energy product from which the adequate size of the magnet shall be arrived and designed as per the formulations depicted in Figure 1.


## 2.1.1.L Stack Length

The reason of arriving the stack height of 30 mm comes with the hub design, where theD and L are subjected to volumetric constraints. The total width of the machine is 80 mm. There should be some conditions taken into consideration while freezing the stack height. There will be some other factors like mechanical clearance, bearing, and overhanging of coil. These take some space in the total width. Thus, the L stack will be fixed accordingly.(i)
Mechanical clearance = 20 mm, Bearing = 10 mm, Overhanging of coil = 20 mm(ii)
L stack length = width − (Mech. Clearance +  bearing + overhanging of coil)(iii)
L stack = 30 mm.


## 2.1.2. Number of Poles/Slots

On freezing the application of the PMSM as hub-motor, and the required power, voltage, and speed ratings, the design starts with freezing the selection of number of stator slots and rotor poles for the PMSM to yield the rated torque under the specified rated speed conditions. The appropriate selection of the slots and pole combination freezes the optimal electromagnetic circuit model of the PMSM [21]. The number of poles and slots can be selected from the chart, which is a part of the literature review of the well-defined principles [16]. This calculation is tentative, and it is done only by empirical way.For a hub-motor, it is not possible to select a smaller number of poles and slots as it is followed for a normal motor design. Based on the aforementioned rules, a cluster of slots/poles configurations are taken into consideration based on the design metrics such as theD and L of the wheel, specific electric and magnetic loadings, winding factor, flux density’s, current density’s, bac-EMF, cogging torque, and torque pulsations. The desirable range of poles is 26, 46, 50, and 74. The desirable number of slots is 27, 51, and 75. The winding factor and the LCM of all the slots/pole combinations are given in Table 2.Table 2
Summary of slots/pole combinations.
Sl. no.Slots/Pole combinationsWinding factorLeast common multiple (LCM)Fundamental frequency (Hz)151 slots 46 poles0.9442346153.33227 slots, 26 poles0.95470286.66351 slots, 50 poles0.9552550166.66475 slots, 74 poles0.9555550246.66The torque developed in an PMSM is proportional to its fundamental winding factor (kw) [16]. The kw is possibly expressed as the product of three major factors, namely, the pitch factor (kp), distribution factor (kd), and the skew factor (ks). These factors are expressed by the following equation:(1)kw=kpkdks.Based on the fact of the winding factor as listed in Table2, it can be inferred that all the slot/pole combinations considered in this research work have the optimal torque contribution by its winding factor in terms of its coil span, slots/pole/phase, and the angular spread since the kw almost remains the same for the PMSM considered. Hence, all the slots/pole combinations considered do not make any significant effect of the kw of the hub-motor.The second critical factor governing the vibration and noise of the hub-motor is its cogging torque. The cogging torque minimization is governed by a set of mathematical formulations, which are governed by the following set of rules by consideration of the cogging torque frequency, which is given by the least common multiple (LCM) of the slots/pole combinations [16].(i)
S⁄p ≮ 0.5 (for a good flux linkage)(ii)
HCF (S,p) ≠ 1 (for avoiding the unbalanced cogging)(iii)
To minimize the effective cogging, it is necessary to choose high value of LCM (S,p).Based on the fact of the LCM of S⁄p configurations as listed in Table 2, it can be inferred that the LCM for the 27-slot, 26-pole configuration is highly lesser when compared to the other configurations, which means that lesser LCM factor will substantially increase the cogging torque of the PMSM, which degrades the performance metrics of the PMSM. Hence, the 27-slot, 26-pole configuration is not viable for the proposed design.The third factor to be considered for the optimalS⁄p configuration of the hub-motor is its core losses, which is the combination of the eddy current and hysteresis loss components. These core losses contribute to the second highest magnitude of loss component in the PMSM. The eddy current loss for the PMSM is governed by equation (2), and the hysteresis loss for the PMSM is governed by equation (3) [22].(2)Eddy current lossPe=KeB2mf2t2V,where Pe—eddy current loss (watt). Bm—maximum flux density (Wb/m2). f—supply frequency (Hz). t—thickness of lamination (m). V—volume of material (M3). Ke—eddy current constant.(3)Ph=khfBn,where Ph—hysteresis loss (watt). kh—hysteresis loss constant. f—supply frequency (Hz). B—amplitude of flux density (T). n—material dependent exponent.It is inferred from Table2 that the 75-slot, 74-pole configuration has a fundamental frequency of 246.66 Hz, and 51-slots, 50-pole configuration has a fundamental frequency of 166.66 Hz. From equations (2) and (3), it is evident that the eddy current loss and the hysteresis losses substantially increase with higher fundamental frequency, which shall result in higher core losses, which eventually reduces the efficiency of the PMSM, and hence, the concept of high power density PMSM for EV application becomes challenging. This is validated from the results of core losses as tabulated in Table 3, where it is inferred that 75-slot, 74-pole and 51-slot, 50-pole configurations result in higher core losses eventually when compared with 51-slot, 46-pole configuration. Based on the aforementioned facts, the proposed design of 51-slot, 46-pole configuration is optimal for the PMSM chosen for the in-wheel hub-motor E-vehicle application.Table 3
Summary of cu and core losses for different slots/pole combinations.
Slots/pole combinations@200 rpm@300 rpm@400 rpmCu loss (kW)Core loss (kW)Cu loss (kW)Core loss (kW)Cu loss (kW)Core loss (kW)27 slots 26 poles0.1915453620.0304708180.1920001930.0382735540.1914967410.04534906575 slots 74 poles0.3648055660.0554560340.3636576120.0609910490.262238450.08767907751 slots 46 poles0.1828353990.0436526690.1828376310.0586851920.1822489610.06990246151 slots 50 poles0.1838718530.2261304530.1836345320.2342022080.1818166580.245574333Computation of the core and copper loss of the PMSM hub-motor is of paramount importance since they have to be lowered for enhancing the overall efficiency of the machine [23, 24]. The iron or the core losses are calculated based on the hysteretic behavior of the PMSM, and also its eddy current losses. However, these loss calculations and the consistent treatment of these losses are more complex since a single model predictive control is not a viable technique as the PMSM is subjected to broad spectrum of different operating variants.Hence, these magnetic losses are computed by the electromagnetic solver, namely, the MotorSolve, based on the typical empirical loss curves as provided by the lamination sheet manufacturers, which gives the total iron losses as function of peak flux density at the specified fundamental frequency. The mathematical formulation for computing the total iron loss of the PMSM using the FEM is given by equation (4), which is commonly referred to as the Steinmetz equation.(4)P=KhfαBβ+KesfB2,where P—iron loss (W/kg). Bm—maximum flux density (Wb/m2). f—supply frequency (Hz). Kh, Ke, α, β—Steinmetz coefficients. s—lamination thickness ratio.The Steinmetz equation consists of two components, namely,KhfαBβ and the Ke (sfB)2. The component KhfαBβ is referred to as the Steinmetz loss, which is a combination of the hysteresis and the anomalous loss, whereas the component Ke (sfB)2 is referred to as the eddy-current loss. Using the Steinmetz equation, the core loss is computed at any peak flux density for the specified fundamental frequency [25]. Similarly, the copper losses in the hub-motor are mathematically formulated by the following equation [26]:(5)Pcu=3Iph2Rph,where Pcu—copper loss (watts). Iph—phase current (A). Rph—DC resistance of each phase (Ω).The computation of copper loss is complex since the resistance of the winding alters with change in temperature, and hence, the copper loss also changes. The copper loss is computed based on the effect of change in temperature, which is represented by the following equation [26]:(6)RphTemp=RphTemp01+αcuTemp−Temp0,where Rph (Temp)—phase resistance at temperature Temp (Ω). Rph (Temp0)—phase resistance at a reference temperature Temp0 (Ω). αcu—temperature coefficient of resistivity.


## 2.1.3. TRV Value

Torque per unit volume (TRV) is a phenomenon that will be a factor taken while designing a motor. It is a ratio of rated torque with the rotor volume of the motor. There is a reference boundary value of TRV for every class of machine, which is shown in Table4 (Kong et al. [8]). Based on that, we can calculate the D and L values. Based on empirical calculation, for an NdFeB machine to have good desirable characteristics, it is advisable to have a TRV value of 21–30.Table 4
TRV range of machines.
S. noType of machineTRV (kNm/m3)1Small totally enclosed motors (ferrite)7–142Totally enclosed motors (rare Earth magnets)14–423Integral hp industrial motors7–304High performance servo motors15–505Aerospace machines30–756Large liquid cooled machines100–250


## 2.1.4. Sizing the PMSM Machine Design Metrics

The dimensional metrics of the PMSM are computed using equations (7)–(9) (Kong et al. [8]):(7)P=TRV×Vr×2π⋅N60,(8)D2L=P×4×602×π2⋅TRV×N,(9)P=TRV⋅πD2L4⋅2π⋅N60.The TRV value calculated shall be verified with the proposedD and L of the PMSM using equations (10)–(12) [16]:(10)TRV=π2⋅KW⋅A⋅B,(11)A=2m×Tph×IphπD.(12)Φ1=B×π⋅D⋅Lp.The initial slot geometry is designed as the formulations as listed in Figure1, by fixing the slot area and the yoke thickness. The size of the magnet is critical in the machine design iterations, as any increase in size of the magnet will result in core saturation, whereas reduced magnetic size will result in demagnetization, which degrades the optimal loading of the PMSM. The magnetic metrics are computed taking into effect the core saturation limits, and these are defined by equations (13)–(17):(13)P.C.=BmHm,(14)Bm=Bg⋅AgAm,(15)Hm=Bg⋅LgLm,(16)Ag=π×D⋅L2,(17)Am=π⋅L×120180×D−Lm2.Using equations (14)–(17) in equation (13), we get(18)P.C.=AgAm⋅LmLg.The value ofP. C. determines the load line slope on the demagnetization characteristics of the magnetic grade under consideration at the defined operating temperature. This gives the value of the energy product from which the adequate size of the magnet shall be arrived and designed as per the formulations depicted in Figure 1.


## 2.2. Parameterization of the Geometry of Hub-Motor

The input dimensional parameters of stator and rotor that are given as inputs to the software are shown in Figure3. Slot depth is the total depth of the slot found in stator. The slot opening width is the gap of the width of the slot for which the winding should enter the slot. Tooth tang angle is the angle between the tang and bottom of slot in degrees. The tooth thickness and width are mentioned in Figure 3. The maximum magnet angle that was possible to have in the design is 7.5° since it is desirable to have efficient usage of area and material. The magnet thickness implemented is 3 mm. Since NdFeB material is being used as magnet material for the design, it is not necessary to go beyond 3 mm ,or else, it may lead to saturation of the core. Figure 4 includes the whole sizing parameters of the PMSM design. It includes the dimensional inputs, ratings of machine, permanent magnet material, Torque per rotor volume ratio, desired fill factor, and type of rotor.Figure 3
Stator and rotor dimensions.Figure 4
Sizing parameters for the PMSM design.The input parameters required for the stator windings are given in Table5. Wye (star) connection is being used here. Coil placement method is an over-under method. The number of layers is 2, and the number of turns is 4. The winding type is lap winding. The phase and line resistance are less than 0.1 Ω. Thus, it means that the design of stator windings is optimal and precise. The whole analysis is done in the temperature of 50°C. This temperature is selected considering the maximum worst-case scenario. In ambient temperature, there will be a high chance of better performance and characteristics. The type of materials used in this design of PMSM hub-motor is shown in Tables 4 and 6.Table 5
Stator windings parameters.
S. noStator windingsValueUnit1Turn length163mm2Winding phase resistance0.0304Ω3Winding line-line resistance0.0607Ω4Winding factor94.4%5Angular spread74.1°6Bare slot area134mm27Conductor area7.01mm28Bare slot fill factor42%9Coil fill factor45.8%Table 6
Materials for PMSM hub-motor.
S. noComponentMaterialGrade1Rotor core materialSilicon steelM19-29 Ga2Rotor magnet materialNdFeBN42-SH3Stator core materialSilicon steelM19-29 Ga4Stator coil materialCopperCu 100% IACSFor core material of stator and rotor, M19 silicon steel of gauge 29 is used since it is commonly used for high flux density with less core loss [27]. Neodymium Iron Boron (NdFeB) magnet is used as a permanent magnet material. N42 or N35 grade material can be used. Commonly, an electrical two-wheeler N35SH grade is used due to its performance and economical availability. But to achieve high torque and good performance, N42SH grade can also be preferred.


## 3. Results and Discussion

The final model of PMSM hub-motor as per the requirements is designed based on the parameters mentioned. The software tool used for the simulation is Siemens MotorSolve tool. It is a Finite Element Analysis (FEA) tool for machine designing [28]. The final hub-motor model is designed with 51 slots and 46 poles, which has been chosen for the purpose of torque ripple reduction, and its assembled view is depicted in Figure 5.Figure 5
PMSM motor with 46 poles and 51 slots.The rated parameters of the PMSM as given by the flowchart in Figure1 are computed and validated through the MotorSolve electromagnetic solver under the defined Finite Element Mesh (FEM) Analysis. The PMSM is validated for the ambient temperature of 50°C. The performance metrics such as the efficiency and various loss components that are yielded by the FEM analysis are tested at the full load torque conditions, and the PMSM model is subjected to predictive analysis, and the results yielded are plotted, and iterations are carried out if necessary, subjected to the rated performance metrics of the system. The vital metrics such as the torque ripple, back-EMF, source current, current density, and flux densities are considered for optimizing the losses and hence the efficiency of the PMSM.


### 3.1. Speed-Torque Characteristics and Efficiency Map

The speed-torque characteristics of the hub-motor are depicted in Figure6. The designed PMSM is expected to yield a constant torque characteristic from standstill to the base speed (Region 1) and constant power characteristics greater than the base speed (Region 2). The Region 1 shall be governed by the mathematical formulation, which tunes for the maximum torque per ampere operation, which results in constant torque characteristic until the base speed of 400 rpm of the PMSM, and it is represented by the following equation [29]:(19)φϑMT/A=tan−1ωrτs−1±ωrτϑ1+ωr2τϑ21−ωr2τϑ2ωr4τs2τϑ2−1,where(20)τS=LSSrS,(21)τϑ=λm′2Vs.Figure 6
Torque-speed characteristics.Similarly, Region 2 shall be governed by the mathematical formulation, which tunes for the maximum torque per volt operation, which results in constant power characteristic above the base speed of 400 rpm of the PMSM, and it is represented by the following equation [29]:(22)φϑMT/V=tan−1ωrLSSrS.The electromagnetic torque developed by the PMSM is given by equation (23). The input power drawn by the hub-motor under the balanced conditions is formulated by equation (24), and the output mechanical power is given by equation (25). Equation (26) defines the overall efficiency computation of the PMSM under the rated loaded conditions [29].(23)Te=32P2λm′riqsr,(24)Pe=32ϑqsriqsr+ϑdsridsr,(25)Pm=Teωrm,(26)Efficiency=PmPe.The two main variables required for controlling the PMSM for a smooth torque control and a dynamic response are itsId (d-axis stator current) and Iq (q-axis stator current). The PMSM efficiency map is achieved by examining the Id and Iq for obtaining the maximum efficiency for each speed and torque combination in the speed-torque plane factoring the effect of highest voltage and current limits as set for the PMSM [30].The speed-torque characteristics as inferred from Figure6 have yielded constant torque characteristic as formulated by equation (19) until 450 rpm beyond which the PMSM delivers the constant power region as formulated by equation (22). As it is inferred, the torque is being constant till the rated speed and then attains the field weakening mode. It is also inferred that the toque ripple is minimized. Based on the efficiency map as shown in Figure 7, it is inferred that the PMSM hub-motor design has an efficiency of 90–93% at rated conditions, specifically at the rated speed of 400 rpm delivering the rated torque.Figure 7
Efficiency map of PMSM design model.


### 3.2. Cogging Torque

The cogging torque of the PMSM is depicted in Figure8, which shows 1.7 Nm, which is well within the acceptable limits of 5% of the rated torque of 50 Nm. The cogging torque is reduced due to the optimal selection of the slot/pole configuration, and this can be evident from the back-EMF waveform, which is sinusoidal as shown in Figure 9. The magnetic metrics as defined by equations (13)–(18) are used for optimizing the magnet length and magnet area in obtaining the reduced cogging torque of the PMSM.Figure 8
Torque ripple waveform.Figure 9
Back-emf waveform.


### 3.3. Back-EMF and Current Waveforms

The supply voltage of the PMSM is 48 V. The yielded back-EMF at the base speed of 400 rpm is less than 48 V and sinusoidal in nature, which is depicted in Figure9. The sinusoidal nature of the back-EMF reduces the pulsating spatial harmonics, and hence, the vibrations and noise of the hub-motor are reduced. Also, sinusoidal back-EMF will enhance the overall efficiency of the PMSM since the losses are reduced. The three-phase line current waveforms of the hub-motor are expressed in Figure 10, and it is inferred that the current ripple lies within the acceptable band limits due to the application of the hysteresis band current control for the PMSM drive.Figure 10
Current waveform of PMSM design model.


### 3.4. Analysis of Losses

The PMSM is operated for the ambient temperature of 50°C, and its loss components are predicted using the mathematical formulations as listed in equations (2)–(6), using the FEM analysis. The corresponding losses for the machine are presented in Table 7. The total loss of the PMSM model is 244 W approximately at the rated speed of 400 rpm delivering the full load rated torque. The different losses of the PMSM are shown in Table 7, and Table 8 shows the input and output power of the designed PMSM hub-motor at rated conditions.Table 7
Losses of PMSM motor.
S. noParametersValuesUnit1Total losses0.244(kW)2Winding loss0.186(kW)3Iron loss0.0421(kW)4Stator back iron0.00437(kW)5Stator teeth loss0.0377(kW)6Rotor back iron9.46E−05(kW)7Magnet loss0.00387(kW)Table 8
Input and output power.
S. noPowerValue1Input power (kW)2.3342Output power (kW)2.093Total losses (kW)0.244


### 3.5. Current Density

The Current density of the PMSM is optimized by its electrical winding layout, so that it does not exceed the range of 5–6 A/mm2 based on the volumetric constraints for the hub-motor under consideration since it falls under the category of totally enclosed motors. As it is inferred from the spatial distribution of current density a shown in Figure 11, the maximum peak value of the current density is 7.89 A/mm2, which translates into the rms current density at 5.579 A/mm2. Hence, the optimal current density of the PMSM pays way for an efficient power-to-weight ratio of the hub-motor.Figure 11
Current density in PMSM model.


### 3.6. Flux Density

The flux density should not exceed 1.2 T for high frequency transformers and medium powered electrical machines. But in case of special machines like the hub-motor, it can be enhanced up to 1.6 T. Based on the flux density plot as depicted in Figure12, it can be inferred that the maximum flux density point is 1.57 T. Also, it is inferred from Figure 12 that the motor core has the optimal flux density loading, which prevents the core from saturation. The spatial flux density plot as observed from Figure 12 satisfies the guideline values as tabulated in Table 9.Figure 12
Flux density in PMSM model.Table 9
Flux density guidelines of PMSM.
Flux density spatial areasMaximum value (T)Stator tooth1.80Stator yoke1.1Rotor yoke1.68Airgap0.60


## 3.1. Speed-Torque Characteristics and Efficiency Map

The speed-torque characteristics of the hub-motor are depicted in Figure6. The designed PMSM is expected to yield a constant torque characteristic from standstill to the base speed (Region 1) and constant power characteristics greater than the base speed (Region 2). The Region 1 shall be governed by the mathematical formulation, which tunes for the maximum torque per ampere operation, which results in constant torque characteristic until the base speed of 400 rpm of the PMSM, and it is represented by the following equation [29]:(19)φϑMT/A=tan−1ωrτs−1±ωrτϑ1+ωr2τϑ21−ωr2τϑ2ωr4τs2τϑ2−1,where(20)τS=LSSrS,(21)τϑ=λm′2Vs.Figure 6
Torque-speed characteristics.Similarly, Region 2 shall be governed by the mathematical formulation, which tunes for the maximum torque per volt operation, which results in constant power characteristic above the base speed of 400 rpm of the PMSM, and it is represented by the following equation [29]:(22)φϑMT/V=tan−1ωrLSSrS.The electromagnetic torque developed by the PMSM is given by equation (23). The input power drawn by the hub-motor under the balanced conditions is formulated by equation (24), and the output mechanical power is given by equation (25). Equation (26) defines the overall efficiency computation of the PMSM under the rated loaded conditions [29].(23)Te=32P2λm′riqsr,(24)Pe=32ϑqsriqsr+ϑdsridsr,(25)Pm=Teωrm,(26)Efficiency=PmPe.The two main variables required for controlling the PMSM for a smooth torque control and a dynamic response are itsId (d-axis stator current) and Iq (q-axis stator current). The PMSM efficiency map is achieved by examining the Id and Iq for obtaining the maximum efficiency for each speed and torque combination in the speed-torque plane factoring the effect of highest voltage and current limits as set for the PMSM [30].The speed-torque characteristics as inferred from Figure6 have yielded constant torque characteristic as formulated by equation (19) until 450 rpm beyond which the PMSM delivers the constant power region as formulated by equation (22). As it is inferred, the torque is being constant till the rated speed and then attains the field weakening mode. It is also inferred that the toque ripple is minimized. Based on the efficiency map as shown in Figure 7, it is inferred that the PMSM hub-motor design has an efficiency of 90–93% at rated conditions, specifically at the rated speed of 400 rpm delivering the rated torque.Figure 7
Efficiency map of PMSM design model.


## 3.2. Cogging Torque

The cogging torque of the PMSM is depicted in Figure8, which shows 1.7 Nm, which is well within the acceptable limits of 5% of the rated torque of 50 Nm. The cogging torque is reduced due to the optimal selection of the slot/pole configuration, and this can be evident from the back-EMF waveform, which is sinusoidal as shown in Figure 9. The magnetic metrics as defined by equations (13)–(18) are used for optimizing the magnet length and magnet area in obtaining the reduced cogging torque of the PMSM.Figure 8
Torque ripple waveform.Figure 9
Back-emf waveform.


## 3.3. Back-EMF and Current Waveforms

The supply voltage of the PMSM is 48 V. The yielded back-EMF at the base speed of 400 rpm is less than 48 V and sinusoidal in nature, which is depicted in Figure9. The sinusoidal nature of the back-EMF reduces the pulsating spatial harmonics, and hence, the vibrations and noise of the hub-motor are reduced. Also, sinusoidal back-EMF will enhance the overall efficiency of the PMSM since the losses are reduced. The three-phase line current waveforms of the hub-motor are expressed in Figure 10, and it is inferred that the current ripple lies within the acceptable band limits due to the application of the hysteresis band current control for the PMSM drive.Figure 10
Current waveform of PMSM design model.


## 3.4. Analysis of Losses

The PMSM is operated for the ambient temperature of 50°C, and its loss components are predicted using the mathematical formulations as listed in equations (2)–(6), using the FEM analysis. The corresponding losses for the machine are presented in Table 7. The total loss of the PMSM model is 244 W approximately at the rated speed of 400 rpm delivering the full load rated torque. The different losses of the PMSM are shown in Table 7, and Table 8 shows the input and output power of the designed PMSM hub-motor at rated conditions.Table 7
Losses of PMSM motor.
S. noParametersValuesUnit1Total losses0.244(kW)2Winding loss0.186(kW)3Iron loss0.0421(kW)4Stator back iron0.00437(kW)5Stator teeth loss0.0377(kW)6Rotor back iron9.46E−05(kW)7Magnet loss0.00387(kW)Table 8
Input and output power.
S. noPowerValue1Input power (kW)2.3342Output power (kW)2.093Total losses (kW)0.244


## 3.5. Current Density

The Current density of the PMSM is optimized by its electrical winding layout, so that it does not exceed the range of 5–6 A/mm2 based on the volumetric constraints for the hub-motor under consideration since it falls under the category of totally enclosed motors. As it is inferred from the spatial distribution of current density a shown in Figure 11, the maximum peak value of the current density is 7.89 A/mm2, which translates into the rms current density at 5.579 A/mm2. Hence, the optimal current density of the PMSM pays way for an efficient power-to-weight ratio of the hub-motor.Figure 11
Current density in PMSM model.


## 3.6. Flux Density

The flux density should not exceed 1.2 T for high frequency transformers and medium powered electrical machines. But in case of special machines like the hub-motor, it can be enhanced up to 1.6 T. Based on the flux density plot as depicted in Figure12, it can be inferred that the maximum flux density point is 1.57 T. Also, it is inferred from Figure 12 that the motor core has the optimal flux density loading, which prevents the core from saturation. The spatial flux density plot as observed from Figure 12 satisfies the guideline values as tabulated in Table 9.Figure 12
Flux density in PMSM model.Table 9
Flux density guidelines of PMSM.
Flux density spatial areasMaximum value (T)Stator tooth1.80Stator yoke1.1Rotor yoke1.68Airgap0.60


## 4. Conclusion

An analytical model of PMSM hub-motor for an electric two-wheeler is designed, and FEM analysis is carried out for the optimal loaded conditions. The design methodology for an energy efficient PMSM hub-motor is presented using the MotorSolve electromagnetic package. The desired high torque of 50 Nm based on the design of PMSM hub-motor is obtained within the desired volumetric constraints ofD and L (280 × 30 mm) with high power density, and all other design performance metrics are obtained under the desirable range at the spinning speed of 400 rpm. The hub-motor is designed for a distance range of 108 km, at the vehicle speed of 54 km/hr for the defined D and L values. This will lead to a typical cost-effective e-vehicle system since the required distance range is achievable at the defined rim size and geometry with an enhanced efficiency of PMSM greater than 90%. The results confirm the effectiveness of the proposed design formulation for achieving high power density hub-motors in establishing the performance metrics of the electromagnetic system.



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*Source: 1217250-2022-07-25.xml*