Multi-Objective Optimization and Performance Comparison of Different Driving Configurations of In-Wheel Motors

Energy consumption and environmental pollution have stimulated the development of electric vehicles (EVs), among which the in-wheel motors (IWMs) are convinced to be the ultimate driving technology for the simplification of the powertrain. In this paper, the advantages and disadvantages of different driving configurations of conventional IWMs are discussed. Subsequently, four dual-motor IWMs including dual-motor torque-coupling driving configuration (DMTDC), dual-motor speed-coupling driving configuration (DMSDC), dual-motor multi-modes driving configuration (DMMDC) and dual-motor power-split driving configuration (DMPDC) are proposed. Thereafter, a two-layer hierarchical multi-objective optimization regarding the parameters of different configurations is proposed. The upper layer contains four multi-objective optimization algorithms while the lower layer runs dynamic programming (DP) to obtain the optimal energy consumption and acceleration time. The results show that the performances of the dual-motor IWM driving configurations have improved significantly compared to single-motor IWM driving configurations.


I. INTRODUCTION
The depletion of petroleum reserves and the exacerbation of environmental degradation are two grave challenges that impede the progression of traditional vehicles equipped with internal combustion engines [1], [2]. Based on the degree of power collaboration between the engine and the motor, new energy vehicles can be classed into hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs), and battery electric vehicles (BEVs) [3], [4]. Due to their advantages of high energy conversion efficiency and zero emissions, The associate editor coordinating the review of this manuscript and approving it for publication was Qinfen Lu .
BEVs are increasingly being viewed as a foremost avenue for the growth of clean energy vehicles [5]. Among the various driving systems for BEVs, the in-wheel motor (IWM) is widely considered to possess the most promising potential for development [6], [7]. The high degree of power source integration and streamlined driveline design of electric vehicles result in significantly increased interior space [8], [9].
Conventional IWM driving configurations typically employ a solitary motor, which can be differentiated into either a direct-driving configuration or a decelerated-driving configuration, depending upon the method by which the rotor is coupled to the wheel hub, either directly or through a gearbox, respectively. There have been numerous studies dedicated to the design and optimization of IWMs. As for the direct IWM driving configurations, Terashima [10] first carried out an outer-rotor IWM named IZA with a rated power of 25kW. Afterward, Gong et al. [11], Ifedi et al. [12], and Chung et al. [13] developed direct driving IWMs based on outer-rotor radial flux permanent magnet synchronous motor (PMSM) separately. Furthermore, outer-rotor PMSMs with different arrangements of permanent magnets such as Halbach type [14], [15] and Spoke type [16], [17] for direct driving IWMs have been researched. Besides, the design and optimization of diverse concepts of IWMs such as reluctance machines [18], [19] and vernier machines [20], [21] have been conducted. Manufacturers have also developed several direct driving IWMs with outer-rotor configurations such as Protean [22], Elaphe [23], and e-Tractions [24], and applied them to various products. With regard to the decelerated IWM driving configurations, Hori [25], Chai et al. [26], Sim et al. [27], and Wang et al. [28] designed and optimized IWMs with planetary gearsets, respectively. Researchers studying decelerated driving IWMs focused more on motor design and optimization, while manufacturers have developed numerous IWMs equipped with gearboxes to meet certain commercial needs. NTN [29] and BYD [30] filed patents for IWM driving configurations with one motor and a two-level gearbox. Likewise, Schaeffler has also proposed several series of IWMs with different reducers [31].
Nevertheless, the single-motor-driven IWM is inferior in terms of dynamics and efficiency. In the research of electric vehicles, a dual-motor powertrain is introduced to tackle the above-mentioned difficulties [32], [33]. Zhang et al. [34], Hu et al. [35], and Wu et al. [36] systematically compared the differences between dual-motor and single-motor driving configurations for conventional EVs with the centralized power source. The simulation results demonstrated that a dual-motor powertrain can perform better both economically and dynamically. As for applications of IWMs, Daisuke [37] first proposed a highly integrated IWM that consisted of two motors and a two-speed gearbox for an auto-guided EV. However, the implementation of the complex design is not practical for challenging road conditions because the two radial flux motors occupy an excessive amount of space, which is a valuable commodity in a wheel hub. This is where the benefits of using an axial flux motor with a small aspect ratio become relevant. Sone et al. [38], and Wang et al. [28] studied the application of IWM with axial flux motors. General Motors first carried out an axial flux IWM with a gearbox and applied it to a Chevrolet pickup truck. Combining the advantages of the existing IWM driving configurations [39], this paper aims to investigate the application of the IWMs with dual axial flux motors.
The optimization of powertrains in EVs has been exploited in plenty of aspects. Kwon et al. [40] studied the multi-objective optimization for EVs with two motors and two-speed powertrains. The gear ratios and motor torque were optimized to obtain the optimal energy consumption and acceleration time based on an adaptive sampling method. Nguyen et al. [41] designed a two-layer optimization scheme to optimize gear ratios and power speed ratios for a dual motor off-road EV. The top layer sets the power envelope and the lower layer minimizes the gap. Silva [42] provided a comprehensive multi-objective optimization regarding the optimum powertrain design, by means of the interactive adaptive-weight genetic algorithm approach. In light of the optimization approaches reviewed, this paper proposes a two-layer hierarchical multi-objective optimization scheme adopting dynamic programming (DP) as the target function to obtain optimal values. The contributions of this paper are as follows: • Four dual-motor IWM driving configurations applying an axial flux motor are proposed, and the dynamic equations of each configuration are deduced.
• A two-layer hierarchical multi-objective optimization scheme is proposed and four multi-objective optimization algorithms are adopted as the upper layer, while DP is implanted as the lower layer to calculate the optimal solution as the target function.
• The economic performances of the proposed IWM driving configurations are compared after the multi-objective optimization of the structural coefficient, and the results are discussed.
The rest of the paper is organized as follows: in Section II, different dual-motor driving configurations that have the potential to be used in IWMs are proposed, and their dynamic equations of them are deduced. In Section III, the multi-object optimization applying dynamic programming (DP) as a target function is conducted to optimize the configuration parameters and solve the performances for each powertrain configuration. In Section IV, the results of the simulation are analyzed. Finally, in Section V, the main conclusions of this article are made.

II. DESIGN OF DUAL-MOTOR IWM DRIVING CONFIGURATIONS
This section introduces six different IWM driving configurations, including two classic single-motor driving configurations as a comparison, which are shown in Fig. 1, and four proposed dual-motor driving configurations, which are shown in Fig. 4. Their lever diagrams are shown in Fig. 2. The single-motor direct driving configuration (SMDDC) and single-motor with planetary gearset driving configuration (SMPDC) are shown in Fig. 1a and Fig. 1b, respectively. For the SMDDC, the speed and torque that the IWM should supply are equal to the wheel, which can be easily derived from the driving condition and vehicle parameters. In accordance with the lever diagram shown in Fig. 2a, the dynamic equations of the SMPDC can be obtained as:   where T out is the torque output, ω out is the rotation speed output, T M is the torque of motor, J M is the rotational inertia of the motor, ω M is the rotation speed and k is the characteristic coefficient of the planetary gearset.
Although the single-motor driving systems have been able to meet most of the dynamics requirements, the limited high-efficiency range does not allow the maximum energy-saving potential of the EVs to be exploited. As a result, dual-motor driving systems were devised to overcome the shortages. According to the coupling method of two motors, the dual-motor driving configurations can be divided into dual-motor torque-coupling driving configuration (DMTDC) and dual-motor speed-coupling driving configuration (DMSDC). A clutch and a brake are designed in DMTDC and DMSDC respectively to further improve the economic performance by extending the driving modes.
The concept of the DMTDC is to combine the advantages of the SMDDC and SMPDC, the structure of which is shown in Fig. 3a. The sun gear of the planetary gearset is connected to the rotor of the disc motor I, while its carrier is connected to the wheel hub, with the output and the ring gear fixed in position. The rotor of the disc motor II is connected to the wheel hub through a clutch so that the torque output to the wheel is the combination of both motors when the clutch is engaged. When the vehicle needs to operate at high torque, such as during rapid acceleration or on steep inclines, the powertrain can operate in torque-coupling mode by engaging the clutch. Based on the lever diagram shown in Fig. 2b, the dynamic equations of the DMTDC can be derived as: where T M 1 , T M 2 are the torque produced by motor I and motor II, respectively, J M 1 , J M 2 are the rotational inertia of the motor I and motor II, respectively, ω M 1 , ω M 2 are the rotation speed of the motor I and motor II, respectively, and p 1 is the torque distribution coefficient of motor I and total power demand. The DMSDC is implemented via a planetary gearset, and the structure is shown in Fig. 3b. The rotor of the disc motor I is connected to the sun gear while the disc motor II is connected to the ring gear. The ring gear is connected to an electronic brake. The carrier is connected to the wheel hub as the output and the speed is the sum of both motors. The system is able to work in the SMPDC mode when the brake is engaged. According to the lever diagram shown in Fig. 2c, the dynamic equations of the DMSDC can be derived as: where p 2 is the speed distribution coefficient of motor I and the total power demand. By integrating the two driving configurations, a dual-motor multi-modes driving configuration (DMMDC), the structure of which is shown in Fig. 3c, can be obtained to further improve economic performance, despite the increased complexity and mass of the IWM with the added components. The implementation is performed by fitting two more clutches on top of the DMSDC as illustrated in the figure. When clutch II is engaged and clutch I and the brake are released, the system operates in speed-coupling mode. Conversely, when clutch II is released and clutch I and the brake are engaged, the system operates in torque-coupling mode. The driving modes of different IWM driving systems are summarized in Table 1. All of the DMTDC, DMSDC, and DMMDC are introduced based on a single-row planetary gearset, and each of their coupling modes can only decouple the target dynamics in one of the aspects of speed or torque. Since the operating point of the vehicle is determined, for DMTDC, the speed of both motors is determined so that only the torque can be distributed using the power distribution rate. As to DMSDC, on the contrary, the speed is allocated under torque determination. In order to distribute the torque and speed of two motors independently to maximize the energy-saving potential, the dual-motor power-split driving configuration (DMPDC) is introduced as a comparison. To achieve this, two rows of the planetary gearset are necessary. As shown in Fig. 3d, the structure of the DMPDC is proposed based on the Ravigneaux planetary gearset, which is the optimal solution to the two-rows planetary gearset because of its high level of integration and small size. Two sun gears are connected to two motors, the ring gear is connected to the wheel hub as the output and the carrier is locked up by an electromagnetic brake. As shown in Fig. 2d, the dynamic equations of the DMPDC can be derived as: where α and β are the parameters of the Ravigneaux planetary gearset.

III. MULTI-OBJECTIVE OPTIMIZATION METHODOLOGY A. DYNAMIC MODEL OF THE EV SYSTEM
To compare the economic performance among the IWM driving systems, the parameters of each driving system need to be optimized to obtain minimal energy consumption and acceleration time [40]. In the optimization process, the dynamic models of the vehicle and battery are first built. Subsequently, the two-layer hierarchical optimization methodology of the multi-objective optimization algorithm using DP as target cost functions is described to determine the best characteristic coefficient of the planetary gearset.

1) VEHICLE DYNAMIC MODEL
The dynamic indicators of the studied vehicles are shown in Table 2. The parameters of the studied vehicle are exhibited in Table 3. The dynamic equation of the EV can be formulated as: where F tra denotes the demand traction force under velocity v and road slope θ, m is the curb weight, g is the gravity acceleration, ε denotes coefficient of rotation mass, ρ denotes the air density, C D denotes the aerodynamic coefficient, and A denotes front area.
where P out denotes power demand of vehicle propelling, T out demand corresponding torque demand, η m is the mechanical efficiency, r is the tire radius, and T b denotes brake torque.

2) MOTORS
The motors can be modeled utilizing maps of torque and speed. The relation between mechanical power at the shaft and electric power is formulated through the electrical efficiency of the map as η e : where P elec is the desired power of the IWM, P mech is the mechanical power of each wheel, ω M and T M are the rotation speed and torque of each motor, where +1 denotes regenerate braking and -1 denotes driving. By substituting different dynamic performance indicators into the above three equations, the output torque and power demand under diverse operating conditions can be calculated. Subsequently, the driving system parameters can be selected as shown in Table 4. In consideration of the design margin, the output-rated power of the IWM systems is set to 20kW. To ensure a fair and reasonable performance comparison, the total powers of the IWM driving systems are set to be the same. Additionally, it is assumed that the distributions VOLUME 11, 2023   of the efficiency map are also the same, as shown in Fig. 4, whereby the values of the maximum speed and torque of the motor from a single-motor IWM driving system are reasonably magnified. After the matching calculation of different modes, the detailed parameters of the IWM powertrains are shown in Table 5.

3) THE BATTERY DYNAMIC MODEL
The open-circuit voltage and the internal resistance of the battery are considered as a function of state-of-charge (SOC) as shown in Fig. 5, and the variation with temperature is not regarded. Furthermore, the equivalent circuit model is employed to formulate the dynamic equation of the battery [43]. Let s denote battery SOC, we have: where I b is the current of battery, U b is the output voltage, P b is the power of battery and Q is the rated capacity of the battery.

B. HIERARCHICAL MULTI-OBJECTIVE OPTIMIZATION
A hierarchical multi-objective optimization method is proposed in this paper motivated by investigating the optimal structural parameter of different IWM driving configurations. The upper layer runs four improved multi-objective optimization methods, and DP is employed at the lower layer to calculate the optimal performance. The result of each DP run is treated as a single target value for the optimization algorithm. Afterward, the average of the four algorithms is taken to ensure the accuracy of the results.

1) DYNAMIC PROGRAMMING
Simulation of an EV under specific operating conditions enables the performance of the proposed IWM system to be evaluated. In EV energy management problems, DP is often utilized to provide the optimal solution as a benchmark.DP is employed to solve multi-step decision problems based on Bellman's optimality principle [44]. The process of solving DP is as follows: Initially, the state and control variables undergo discretization, after which the arc costs of all viable paths are calculated and recorded in a table, commencing from the end of the operating condition. Lastly, the optimal problem is resolved in a reverse equation: [L(x(j), u(j)) + J * (x(j + 1))] (17) 53148 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
where j is the stage index, x(j) denotes the state variable. u(j) is the control variable, J is the optimal cost function, and L is the cost-to-go function, which can be formulated as: (j) = 0 mode unchanged 1 mode changed (19) where x(j) denotes SOC(j), u(j) = [mode,p], δ (j) is a penalty term for mode switching, which is designed to prevent the loss of comfort caused by frequent mode switching. is 0 when the mode remains unchanged and is 1 when the mode changes and δ is the penalty factor. The source code of DP employed in this paper is based on the modification of the literature [45]. The SOC is taken as the state variable, and the mode and power distribution coefficient p are selected as the control variables. The state variable SOC starts from 0.9 and can not exceed 0.1. The common constraints of the state and control variables are reflected in the upper and lower bounds of speed, torque and power. By finding the optimal sequence of control variables u * , the optimal cost of electricity can be computed from a forward equation as: Powertrain parameters exert a significant influence on dynamic performance as well. Since enhancing economic performance often contributes to a reduction in dynamic performance, it is of great necessity to conduct multi-objective optimization to calculate the optimal parameters for the driving configuration. The dynamic performance of the EVs is assessed under 100 km/h acceleration, and the optimal formulation is formulated as: min u(j) where T acc denotes the 10km/h acceleration time, and j denotes the discrete velocity step.

2) MULTI-OBJECT OPTIMIZATION
To determine the most suitable characteristic coefficient of the IWM driving configurations, four typical multi-object optimization algorithms, including non-dominated sorting genetic algorithm II (NSGA II), non-dominated sorting genetic algorithm III (NSGA III), multi-object particle swarm optimization (MOPSO) and multi-object evolution algorithm based on decomposition (MOEA/D), are employed to conduct the optimization in this paper. Two objective functions of the optimization are the electricity consumption from Eq.20 and 100km/h acceleration from Eq.22. The initial population of the evolutionary algorithms and the number of particles of MOPSO are set at 100. The number of iterations is 100. The parameters need to be optimized and their feasible regions are shown in Table 6. Particularly, the maximum characteristic coefficient of the SMPDC and DMTDC needs to be limited in order to satisfy the top speed of the vehicle. The multi-object optimization problem can be written as: NSGA II is used as an example to illustrate the process of the two-layer multi-objective optimization with cost functions being calculated by DP, the flowchart of which is shown in Fig. 6. A population is initiated with variable values selected from feasible regions. The objective functions are then calculated for each individual. The individuals are subsequently sorted based on their non-dominance and subjected to selection, crossover, and mutation. The convergence of the algorithm is then assessed. If it does not converge, the parents and offspring are merged to form the next initial generation in the iteration. The lower layer runs DP to solve the optimal value of energy consumption and acceleration time instead of the target function in NSGA II. Equations Eq.20 to Eq.22 are used as the cost function, and the optimal values can be obtained through a reverse calculation.
In addition, this work focuses more on the comparison of economic performance. Therefore, we accord priority to the influence of the configuration parameters on economic performance while ensuring that the dynamics meet the requirements. Therefore, we select the same acceleration indicator from four optimization algorithms and calculate the average VOLUME 11, 2023 FIGURE 6. Flowchart of the two-layer multi-objective optimization of NSGA-II with DP: an example. In the DP diagram, n is the number of intervals in which the SOC is divided, and N is the total time step. values for the optimized parameters and energy consumption. The optimization of the parameter of the DMSDC under the urban dynamometer driving schedule (UDDS) is used as an example to illustrate the process. Find out the corresponding parameter k and energy consumption at the same acceleration-consuming time for NSGA II. Repeating the process flow for the NSGA III, MOEA/D and MOPSO, as shown in Table 7, the average values are calculated as the final results.

IV. RESULTS AND DISCUSSION
In this work, the UDDS and highway fuel economy cycle (HWFET) are adopted to represent the urban cycle and highway cycle, respectively. Through the method of economic performance calculation and structural parameters optimization, the optimal energy consumption of six driving configurations can be obtained. For the configuration of DMPDC, the energy consumption of the IWM is modified as E = E M 1 + E M 2 /λ due to the driveline of planetary gearset, where λ is the transmission efficiency.
The structural parameters of each configuration before and after the optimization are shown in Table 8. The working points of the motors from each configuration under UDDS after the optimization are shown in Fig. 7, and the comparison of the motors' efficiency before and after the optimization is shown in Fig. 8. Those under HWFET are shown in Fig. 9 53150 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.   and Fig. 10 in the appendix. The distribution of the working points shows that the simulation results are reasonable. Due to the planetary gearset, the working points of the motor of SMPDC are more distributed in the high-efficiency area with high speed and low torque than those of SMDDC. The  involvement of motor II increases from DMTDC to DMPDC under UDDS due to the speed coupling mode. Motor II works more under HWFET than under UDDS because high speed is required. In the figures of efficiency comparison, it can be seen that the motor works more in the high-efficiency region after the optimization for SMPDC under both driving cycles.
As for dual-motor IWMs, all of the motor I work in higher efficiency areas after the optimization under UDDS. Motor II is similar but with the exception of DMTDC. The optimization of DMTDC does not improve the efficiency of Motor II because it is directly connected to the hub, which is tantamount to SMDDC. Hence, DMTDC is suitable for working in low-speed and high-torque applications, such as commercial vehicles. When the driving cycle comes to HWFET where the high rotation speed is required, the efficiency of the motor I of the DMTDC and DMPDC improves and that of DMSDC and DMMDC declines. The changes in the performance of motor II under such conditions are the opposite. Nevertheless, the efficiency improvements of the motor II with DMSDC and DMMDC are tremendous and show that these two configurations can better exploit the advantages of the dual-motor configuration.
The optimal energy consumption of each configuration under each driving cycle before and after the optimization are shown in Table 9. It can be seen that the economic performance of each configuration has improved obviously with the optimization of structural parameters. The average energy consumption of the UDDS and HWFET after the optimization is calculated. Compared to SMDDC, SMPDC has an obvious improvement because low-speed conditions force the motor of SMDDC to work in inefficient areas. Furthermore, the economics of the dual-motor IWMs have significant improvements compared to the single-motor IWMs, all of which are more than 8%. Among dual-motor IWMs, the energy costing performance increases from DMTDC to DMPDC. However, the mass of the actuators such as clutches and brakes are not taken into account in this paper, which means DMMDC has more quality than DMTDC and DMSDC. On the other hand, the space inside the wheel will also limit the arrangement of the actuators. Therefore, the energy-saving potential of the DMSDC is larger than that of the DMMDC. The DMPDC has less energy consumption, but the complexity of the Ravigneaux planetary gearset also makes it difficult to manufacture hub motors. In summary, the DMSDC and the DMPDC are the more preferred configurations. Taking into account the efficiency analysis and energy performance, and considering the complexity of the structure, the DMSDC is the more recommended configuration of the IWM for passenger cars.
This paper is limited to the investigation of the economic and dynamic performance of different drive configurations and does not consider the impact of initial structural cost and unsprung mass on the practical application of IWMs.

V. CONCLUSION AND PERSPECTIVES
In this paper, the driving configurations of IWMs are systematically studied. Four different dual-motor IWM driving configurations utilizing planetary gearset (DMDTC, DMSDC, DMMDC and DMPDC) are proposed and studied, based on the analysis of the advantages and disadvantages of the conventional IWM driving configurations. Firstly, the dynamic equations of each configuration are deduced on the basis of the transmission principle of the planetary gearset. Then, the dynamic models of the battery and the EV are established. Subsequently, a twolayer hierarchical multi-object optimization is conducted. Two objective functions: energy consumption, representing economic performance and 100km/h acceleration, representing dynamic performance, are described using DP. Four multi-object algorithms including NSGS II, NSGA III, MOEA/D, and MOPSO are used to calculate the optimal structural parameters and the minimum energy consumption. Finally, the efficiency of the motors and energy consumption before and after the optimization of each configuration is exhibited and analyzed. The results show that DMSDC and DMMDC maximize the benefits of the dual-motor IWM driving configurations, while DMSDC and DMPDC have the largest energy-saving potential. In conclusion, the DMSDC is the more recommended configuration of the IWM for passenger cars when considering all factors. The energy consumption was reduced by 9.56% as compared to SMDDC.
In the future, we will conduct more in-depth research on the comparison of different IWM driving configurations with consideration of more aspects like upsprung mass and manufacturing cost. Furthermore, prototypes will me developed to validate the comparison results.
MIAO CAO was born in Inner Mongolia. She received the Ph.D. degree from Xi'an Jiaotong University, in 2018. She has been with the School of Navigation, Northwestern Polytechnical University, and the Ningbo Research Institute of Northwestern Polytechnical University, since 2021. She is mainly devoted to the research on the basic theories and key technologies of the whole process of ''material-process-equipment'' manufacturing, and solving the control problems of the integration of macro and micro properties of metal parts, especially in the field of metal plastic forming and semi-solid forming. She is actively promoting the deep integration of process research and development process and intelligent manufacturing technology.
BIZHOU MEI was born in Jiangsu. He was with Zhejiang Yiduan Precision Machinery Company Ltd., in 2018. He received the title of Senior Engineer and a Top Talent of Ningbo City, in 2022. His research interests include intelligent CNC metal-forming machine tools, metal forming, and wheel equipment. He is a member of the Plastic Engineering Branch of the Chinese Mechanical Engineering Society and a member of the National Forging Standard Committee.
SHENGDUN ZHAO was born in Shaanxi, China, in 1962. He received the B.S., M.S., and Ph.D. degrees in mechanical engineering from Xi'an Jiaotong University, China, in 1983China, in , 1986China, in , and 1997 He has been with the Mechanical Engineering Department, Xi'an Jiaotong University, since 1986. He is currently a member of the Degree Committee of the School of Mechanical Engineering, Xi'an Jiaotong University. He is a member of the Semi-Solid Processing Academic Committee and the Technical Committee of the National Forging and Stamping Association. He is an Editorial Board Member of the Journal of Forging Equipment and Manufacturing Technology and a Technical Expert of the China National Laboratory Accreditation Committee (CNACL).