Optimization of Permanent Magnet Parameters in Axial Flux Rotary Converter for HEV Drive

Abstract

This paper focuses on the development and optimization of a special hybrid electric vehicle arrangement known as a four-quadrant rotary converter. The introduction summarizes the main advantages and disadvantages of existing topologies in radial and axial flux arrangements. Based on previous experience, we developed a novel axial flux arrangement that eliminates the problems and disadvantages associated with existing radial flux solutions. In addition, this paper evaluates and subsequently describes the optimization of permanent magnet parameters in an axial flux rotary converter unit. A number of 3D finite element method optimizations were performed to find the optimal mass distribution of permanent magnets on the frontal area of the outer rotor in the axial flux rotary converter unit. The optimization involved the permanent magnets’ material, shape, and thickness in order to achieve maximal efficiency of the entire unit while leaving its nominal output power and speed unaffected. The results show an increase in the overall theoretical efficiency of the outer rotor unit from 90.2% to 94.4% following the optimization.

1. Introduction

The upper efficiency limit of an internal combustion engine (ICE) can be derived from the Carnot cycle. The efficiency of ICEs used in conventional vehicles does not usually exceed 40% [1]. However, this efficiency can only be achieved by an ICE in a relatively narrow area of mechanical conditions. Significant energy savings can be achieved with advanced configurations of hybrid electric vehicles (HEVs), where full speed and torque control is possible [2]. In other words, for an ICE to reach maximal efficiency during active operations and in all possible driving situations, full control of its torque and speed independent of each other is necessary [3,4].

This requirement is met by series hybrid arrangements, however, only at the cost of total mechanical energy being transformed to electricity and back, with power losses during each conversion. Moreover, an electric motor has to be oversized to match the maximal power of an ICE [5,6]. On the other hand, parallel hybrid arrangements utilize low-powered electric motors that are mechanically coupled to the gearbox; however, this only allows full control of the torque produced by an ICE, but not the speed [5,6].

Many of the HEV arrangements used today are based on the series-parallel hybrid topologies, which combine the advantages of both arrangements, such as full torque and speed control in the optimal working area of the ICE, as well as minimization of conversion losses between electrical machines. Among the main disadvantages of the series-parallel HEV topologies are the more complex structural arrangements and the higher demands on the energy flow control [5,6]. Several different topologies in both radial and axial arrangements will be considered in greater detail.

The four-quadrant transducer system in the radial arrangement and the continuously variable electromagnetic transmission in the axial arrangement are among the best-known solutions for series-parallel HEV conceptions [6,7]. The innovative concept presented in [6,7] lies in the synthesis of two electrical machines (the electric motor and generator) into one double-rotor electrical machine with two air gaps. The outer rotor carries the permanent magnets (PMs) on both sides in order to interact with the rotating magnetic field of the stator winding and with the winding of the inner rotor, thereby continuously transmitting speed and torque (i.e., power) to the output shaft. The inner rotor is mechanically coupled with the ICE through the clutch, while the power flow is then completed through the slip rings and the indirect frequency converter, back to the stator [6,7]. Both electric sub-machines consisting of inner rotor and outer rotor (first submachine) and outer rotor and stator (second submachine) can operate here in the motor and generator mode. This concept can replace both the clutch and the gearbox in an HEV [6,7]. The main disadvantages of solutions [6,7] lie in the relatively high mechanical stress placed on the outer rotor structure, the considerable thermal stress placed on the winding and insulation of the inner rotor, problematic cooling, and the need for frequent maintenance of the slip rings. These and similar technical issues, along with the detection of stator turn short-circuits, are discussed in [8,9].

2. Axial Flux Rotary Converter

After carefully analyzing the disadvantages of the aforementioned arrangements, we developed a novel and modified arrangement. This solution is represented in Figure 1 as the axial flux rotary converter (AFRC) unit.

The winding of the axial stator is powered by a three-phase voltage inverter (INV) from the DC power source, which can be built as a combined Li-ion battery (BAT) and ultracapacitor (UC) power source system.

The advantage of this hybrid supply lies in the fast energy intake and outtake of the ultracapacitors combined with the long-term storage ability of the battery. Proper interconnection of these two storage technologies has a crucial impact on the efficiency of the regenerative braking and the dynamic properties of the vehicle drive unit. Other benefits of using ultracapacitors can be found in the wider range of operating temperatures and in the significantly faster charging times in comparison to common Li-ion battery units [11,12].

The control of the system is provided by a digital signal processor (DSP), with an implemented direct torque control (DTC) algorithm providing sufficient computational power and dynamics for the drive system [13,14,15]. The speed of the ICE is measured by an incremental speed sensor (ISS) that sits directly on the input shaft. The ISS provides the speed loop feedback to the DSP.

The main purpose of the AFRC unit is to allow the ICE to work in the maximal efficiency area of the entire torque-speed diagram in the final gear, thereby minimizing fuel consumption and reducing harmful emissions produced. The AFRC unit consists of a double rotor permanent magnet machine, attached to the input shaft end of the induction machine, which is then mounted on the output shaft. The chosen double rotor layout allows changes in both the torque and speed between the two shafts, thereby regulating the amount of power transmitted from the input shaft to the final gear. The power difference between the input and output shaft can be supplied by or drawn through the stator winding, which means that only a part of the total energy necessary for vehicle propulsion passes through the electromagnetic transmission. The surplus mechanical energy from the ICE or from the braking energy of the vehicle can be transformed through electromagnetic couplings between the outer rotor and the stator and then stored in the batteries or ultracapacitors.

The constructional simplicity of the AFRC unit is characterized by a disc arrangement, with two axial air gaps that run alongside the inner rotor. In turn, the inner rotor is equipped with double-sided squirrel cages. Both cages can simultaneously interact with the electromagnetic fields produced by the permanent magnets affixed to the outer rotor disc and/or by the three-phase winding from the stator disc. Thus, there are two different magnetic flux loops in the AFRC unit. The first loop is located on the side of the input shaft, where magnetic flux is produced by permanent magnets which are affixed to the outer rotor. The loop continues through air gap δ₁ (Figure 2), passing to the adjacent squirrel cage of the inner rotor, before looping back along the same path. The second magnetic flux loop occurs on the side of the output shaft and is produced in the stator’s three-phase winding. This loop continues through air gap δ₂ (Figure 2), passing to the adjacent squirrel cage of the inner rotor and then loops back the same way, as seen in Figure 2.

It has been proven that the width of the air gap has a significant influence on the output characteristics and efficiency of axial-flux machines, especially on the ratio between stator copper losses and rotor core losses [16,17,18,19,20,21].

The AFRC unit can be operated in all four quadrants of the torque–speed diagram with respect to the optimal operation point of the internal combustion engine. There are five possible operation modes of the unit, as outlined below.

2.1. Increasing Both Speed and Torque

The required torque and speed at the final gear are greater than the torque and speed produced by the ICE. This mode is used when the HEV accelerates from a higher speed than that of the input shaft. The stator winding is supplied from the battery unit through the voltage inverter and the battery is discharged.

2.2. Decreasing Speed and Increasing Torque

The output shaft rotates at a lower speed than the input shaft and the required torque at the final gear is higher than the ICE’s torque. This mode is used when the HEV is started from a standstill, is traveling loaded at low speeds, or generally when the ICE’s optimal operation point is at a higher speed than that required of the final gear. Depending on the input to output power ratio, the battery unit can be charged or discharged in this mode.

2.3. Decreasing Both Speed and Torque

The ICE operates at a higher speed and torque than is required at the final gear. The induction machine operates in generator mode and charges the battery unit via the voltage inverter. Only part of the ICE’s power is used for vehicle propulsion, with the remaining power being delivered to the battery unit. This mode is used in regenerative braking.

2.4. Increasing Speed and Decreasing Torque

The output shaft rotates at a higher speed than the input shaft and the torque required at the final gear is lower than the ICE’s torque. This mode is generally used when the ICE’s optimal operation point is at a lower speed than the speed required of the final gear. Depending on the input to output power ratio, the battery unit can be charged or discharged in this mode.

2.5. Purely Mechanical or Electrical Mode

The width adjustment of air gap δ₁ enables the AFRC unit to operate in a purely mechanical or electrical mode. In the mechanical mode, only the ICE is used for vehicle propulsion, while the stator of the induction machine is not supplied. In electrical mode, the ICE’s shaft is disconnected and Li-ion batteries and ultracapacitors alone are used for vehicle propulsion.

3. Estimation of Permanent Magnet Parameters

The results from the axial flux permanent magnet machine design were used as input parameters for a subsequent optimization analysis using the 3D finite element method (FEM). The main dimensions of the outer rotor were chosen to equal the dimensions of the inner rotor (rotor thickness (h_r) and inner and outer diameters (D_IN and D_OUT, respectively)). Commonly used NdFeB permanent magnets XG160/120 with parameters B_r = 880 mT, H_c = 640 kA·m⁻¹, (BH)_max = 150–184 kJ·m³, T_c = 700 °C, ρ = 8.0–8.3 g·cm⁻³, and μ_r = 1.05–1.1 were preselected according to [16]. Air gap flux density was calculated using Equation (1), where the coefficient k_δ refers to the attenuation factor of magnetic flux density in the air gap [22].

$$B_{\delta }=\frac{B_r}{k_{\delta }}$$

(1)

The overload factor was estimated using Equation (2), where P_max/P₂ is the ratio between the maximal estimated output power and the nominal output power of the AFRC unit.

$$k_{ocf}=\frac{P_{max}}{P_2}$$

(2)

Equation (3) shows the calculation of the utilization factor, where k_f is the PM’s shape factor. The ratio of induced voltage to nominal voltage is represented by the coefficient k_e, whereas the PM’s utilization coefficient ξ was selected in accordance with [20].

$$c_v=\frac{2k_{ocf}{k}_f\left(1+k_e\right)}{{\pi }^2\xi }$$

(3)

The total volume of the PMs was calculated using Equation (4), where f_n is the supply frequency.

$$V_m=\frac{c_v{P}_2}{f_n{B}_r{H}_c}$$

(4)

The volume of one magnet was then calculated using Equation (5), where 2p is the number of pole pairs.

$$V_{1m}=\frac{V_m}{2p}$$

(5)

The active surface area of the PMs was then calculated using Equation (6), where k_m is the ratio of the active surface area of the PMs to the frontal area of the outer rotor disc and S_R is the frontal area of the outer rotor disc.

$$S_m=k_m{S}_R=k_m·\frac{\pi }{4}\left(D_{OUT}^2-D_{IN}^2\right)$$

(6)

The thickness of the PMs was calculated using Equation (7), and their weight, by using Equation (8).

$$h_m=\frac{V_m}{S_m}$$

(7)

$$m_m={\rho }_m{V}_m$$

(8)

Iron core losses were defined by Equation (9), where Δp_1.0 are specific losses of used steel and β is the exponent dependent on its type. The coefficients k_dj and k_dz are the influence of uneven magnetic flux distribution in particular parts of the magnetic circuit and the influence of production technology, respectively. B_j1 and B_z1 are magnetic flux densities in the stator yoke and stator teeth, respectively; and finally, m_j1 and m_z1 are the weights of the stator yoke and the stator teeth, respectively.

$$\mathsf{\Delta }{P}_{Fe}=\mathsf{\Delta }{p}_{1.0}{\left(\frac{f_n}{50}\right)}^{\beta }\left(k_{dj}{B}_{j1}^2{m}_{j1}+k_{dz}{B}_{z1}^2{m}_{z1}\right)$$

(9)

Mechanical losses were calculated using Equation (10), where n_s is the synchronous speed of the rotor.

$$\mathsf{\Delta }{P}_{mech}=1.3\left(1-D_{OUT}\right)D_{OUT}^4{\left(\frac{n_s}{10}\right)}^2$$

(10)

Additional losses were estimated using Equation (11). These losses arise due to stray fluxes and magnetic flux density pulsations in the air gap. The standard IEC60034-2 defines these losses as 0.5% of the nominal output power.

$$\mathsf{\Delta }{P}_d=0.005·P_2$$

(11)

Stator winding copper losses were calculated using Equation (12), where m indicates the number of phases, R₁ is the resistance of one phase of the stator winding, and I_n is the nominal stator current.

$$\mathsf{\Delta }{P}_{j1}=m{R}_1{I}_n^2$$

(12)

The overall efficiency of the AFRC unit was calculated using Equation (13).

$$\eta =\frac{P_2}{P_2+\mathsf{\Delta }{P}_{Fe}+\mathsf{\Delta }{P}_{mech}+\mathsf{\Delta }{P}_d+\mathsf{\Delta }{P}_{j1}}$$

(13)

4. Optimization of Machine Parameters Using 3D FEM Analysis

We performed 3D FEM optimization analyses in the RMxprt/Maxwell environment. The optimization process focused mainly on material properties, volume, active area, shape, and thickness of the permanent magnets on the outer rotor, the shape and tilt of the inner rotor slots, and the shape of the stator slots, together with the stator winding parameters.

The goal of the PM’s shape optimization analysis was to find the optimal mass distribution of PMs on the frontal area of the outer rotor. The analysis is depicted on the left side in Figure 3 and was solved using a tri-variable solution (width, thickness, and active surface area) through a parametric sweep analysis with a subsequent quasi-Newtonian optimization method, while the key components of total losses, such as stator winding copper losses and iron core losses, were closely monitored in order to find the minimal sum of these functions.

The PM optimization analysis presented in this paper proves the optimal width of permanent magnets located between the outer and inner rotor radius. One of the 3D plots obtained during the optimization process shows the efficiency matrix for constant-width PMs (Figure 4).

The optimal efficiency level achieved was relatively narrow and decreased sharply when the parameters were changed. For example, the air gap flux density dropped rapidly when the magnet thickness (h_m) was reduced. Therefore, the amount of power transferred through the air gap was also reduced [23,24].

Based on the data presented in

Table 1. Characteristics of the AFRC unit using different types of permanent magnets.

Magnet Type	FLN 8	FLN G28	FLN GT31	LN 10	LN G52	LN GT72	XG 112/96	XG 160/120	XG 196/96
Br (T)	0.52	1.05	0.76	0.60	1.30	1.05	0.73	0.88	0.96
Hc (kAm−1)	−40	−46	−107	−40	−56	−112	−520	−640	−690
Bδ (T)	0.25	0.49	0.44	0.28	0.58	0.54	0.60	0.71	0.76
η (%)	87.6	91.6	91.4	88.4	92.7	91.2	90.7	94.1	94.4

, we decided to change the type of PMs to XG196/96 PMs, especially due to the optimal shape of their B/H curve, the resulting value of the magnetic flux density in the air gap, the relatively small volume required, and the highest overall efficiency of the AFRC unit compared to other types of permanent magnets tested during the optimization process.

A summary of the electromechanical parameters of the AFRC unit after conducting the aforementioned optimization is shown in

Table 2. Parameters of the AFRC Unit after permanent magnet optimization.

Optimized Parameter	Value/Unit	Originally	Optimized	Change
Type of PMs	(-)	XG160/120	XG196/96	Yes
Volume of PMs	Vm (cm3)	36	39.5	+9.7%
Width of PMs	wm (mm)	37.5	36	−4%
Active area ratio	km (-)	0.75	0.65	−13.3%
Total area of PMs	Sm (cm2)	91.3	78.5	−14.0%
Thickness of PMs	hm (mm)	4	5	+25%
Weight of PMs	mm (kg)	0.28	0.31	+10.7%
Air gap flux density	Bδ1 (T)	0.87	0.76	−12.6%
Nominal stator current	In (A)	6.02	5.70	−5.3%
Stator winding resistance	R1 (Ω)	0.68	0.43	−36.7%
Iron core losses	ΔPFe (W)	64.10	22.93	−64.2%
Mechanical losses	ΔPmech (W)	17.18	17.18	No
Additional losses	ΔPd (W)	7.50	7.50	No
Stator winding copper losses	ΔPj1 (W)	73.93	41.91	−43.3%
Overall efficiency of AFRC	η (%)	90.21	94.37	+4.2%

; the optimized parameters of the machine are compared with the original parameters obtained in Section 3.

Figure 5 plots the magnetic flux density in air gap δ₁ of the AFRC unit and the cogging torque, both as a function of the outer rotor position.

3D FEM Analysis of the Magnetic Conditions in the Optimized AFRC Unit

For each component of the optimized AFRC machine, the visualization of the magnetic properties was performed by an FEM analysis in Maxwell. Figure 6, Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 show the geometry of the stator and rotor packages with optimized slot shapes, containing winding, squirrel cages, and permanent magnets. Advanced meshing with local refinements in important parts was performed and the magnetic flux density distribution was visualized for each model.

The situation depicted in Figure 11 occurs when the AFRC unit operates in either a purely electrical or mechanical mode when the vehicle is powered only by the battery or the ICE. The left half of the inner rotor faces the active (powered) part of the drive (in this case, the ICE), while the right half of the inner rotor faces the passive part of the drive (in this instance, it is the stator, which is not powered).

5. Conclusions

This paper provides a short overview of the design, optimization, and 3D FEM analysis of an AFRC unit prototype of nominal output power P₂ = 1500 W. It is a novel design, characterized by a high power density. Therefore, the unit may be of use in future hybrid electric vehicles. The unit is highly efficient, combining the advantages of known series and parallel hybrid topologies while eliminating the problems and disadvantages accompanying existing solutions for four-quadrant rotary converters.

Models of AFRC unit components and 3D geometries were designed, analyzed, and optimized in the RMxprt/Maxwell environment, which allowed parallel monitoring of a large number of internal variables in the unit. This assisted our analysis of their dependencies and helped to increase the overall theoretical efficiency of the unit from 90.2% to 94.4%.

Future research will focus on manufacturing a laboratory prototype, through which the results of this study can be verified in real operating conditions. Two series-produced axial flux induction motors are planned to be utilized in the laboratory implementation, where one of the stators will be modified into the outer rotor. The winding will be removed, stator slots milled, and permanent magnets glued in their place.