Intelligent Design Optimization for Traction and Steering Motors of an Autonomous Electric Shuttle under Driving Scenarios

Abstract

Electrified autonomous vehicles have become quite popular and have a wide range of applications. The traction and steering motors to be used on an electrified autonomous vehicle are designed considering the lateral and longitudinal forces in the environment where the vehicle operates, and they are selected with extra safety margins and “over-engineering” features. This causes wastage of rare earth elements, along with both cost and energy inefficiencies. For autonomous shuttle vehicles, traction and steering performances can be analyzed based on driving scenarios. The reference speed and steering signals for the selected driving scenarios were run on a dynamic vehicle model and the minimum performance requirements for the traction and steering motors were determined. Then, the determined design parameters by DoE (Design of Experiments) were trained in two different ANN (Artificial Neural Networks) models created for motor models. The trained ANN models were run according to the minimum performance criteria and predicted motor models with new design parameters for the traction and steering motors. The performance results of the predicted traction and steering motor models showed a significant improvement in terms of the minimum performance requirements.

1. Introduction

In recent years, interest in emission reduction, clean energy and renewable energy sources has been increasing rapidly. This situation has also accelerated the work on electric vehicles. Although electric vehicles have become popular for ground transportation, the market demand is not appropriately increasing due to the limited battery energy. To overcome “range anxiety”, extended-range electric vehicles are increasingly gaining popularity as a solution. To achieve this, an AC system is incorporated into the energy management strategy, allowing for coordinated optimization with the powertrain system. The accurate prediction of the electrical energy consumption along a specific route will significantly reduce drivers’ anxiety and increase their confidence in electric vehicles. A highly accurate energy estimate is based on an accurate velocity estimate. An average model, decision tree, gradient boost decision tree and Neural Network models are being studied in passenger load estimation for the energy management problem of hybrid electric city buses [1,2,3]. Especially in the last 20 years, energy efficiency issues have been focused on to increase the range of electric vehicles [4]. Energy efficiency basically focuses on alternative battery types, battery management, power electronics and drives and electric motor traction units [5]. For electric motor traction units, permanent magnet motors stand out with their high efficiency. While permanent magnet electric motors are generally used in synchronous motor structures, asynchronous and reluctance motors are also preferred because they make it possible to reduce the use of permanent magnets [6]. The geometric structures of electric motors consist of basic elements such as the rotor, stator, winding structures, permanent magnet, rotor–stator groove geometries, core materials and shaft. Basically, electric motors have mechanical and electromagnetic design constraints [7]. In this case, designers are encouraged to perform objective function optimization, that is, efficiency maximization, usually with geometric optimization.

On the other hand, driving assistants, which have become mandatory with the regulations on today’s commercial and passenger vehicle concepts, attract great attention. Driving assistant technologies such as lane tracking, emergency braking and pedestrian detection, as well as speed limit warnings, make it possible to increase the driving safety of passengers and drivers [8]. In the process that started with the development of driving assistant technology, interest in driverless or autonomous vehicle technologies is rapidly increasing. Today, vehicles with internal combustion engines, hybrid engines and electric vehicles have many driving assistant technologies. It is seen that some electric vehicle manufacturers, in particular, focus their efforts on making their vehicles driverless, that is, they invest in developing fully autonomous electric vehicles. Considering autonomous vehicles, especially autonomous electric vehicles, the main focus is on the control of lateral and longitudinal vehicle dynamics [9]. While longitudinal vehicle dynamics basically control the acceleration and braking demands of the vehicle, this issue can already be evaluated in the same concept as normal electric vehicles. On the other hand, lateral vehicle dynamics control tries to meet the demands on vehicle steering. Thus, electric power steering comes to the fore in autonomous vehicles [10].

Therefore, creating electric motor drive units for the traction motor and steering motors in autonomous electric vehicles directly affects driving performance and safety, as well as the use of energy resources.

Design and optimization studies on electric vehicles and electric motors are mostly subjected to component-based verification processes. In recent years, both component-based and system-based optimization studies for electric vehicles have also shown that electric traction motors improve design optimizations [11].

However, studies on autonomous vehicles mostly address issues such as path tracking, path planning, sensor fusion and improved perception. In the literature, it has been seen that some steering motor studies, albeit few, are carried out on a component basis within the scope of driving assist [12].

It is obvious that suitable and optimal electric motors will directly affect the traction and steering dynamics, increase driving performance and driving safety and increase the sensitivity of autonomous driving.

The optimization of the steering and traction motors depends not only on component-based improvement, but also on system-based improvement due to the real-time operations, such as the determined driving cycles and driving scenarios. This situation requires multi-objective optimization. Therefore, the optimization techniques such as the NSGA-II (Non-dominated Sorting Genetic Algorithm) and MOPSO (Multi-Objective Particle Swarm Optimization) are preferred to provide multi-objective functions. In this study, ANN (Artificial Neural Network)-based optimization is dealt with by training the ANN under the different operational conditions.

The reliability of the vehicle in the real-time operation depends on the demand of the torque–speed transmitted by the steering and traction motor. The demand of the torque–speed is based on driving scenarios and driving cycles. Therefore, the driving scenarios and driving cycles are considered to provide the reliability and real-time operations in this study. Furthermore, the initial condition for optimization has already been started by modeling the traction and steering motors used in a real vehicle model.

On the other hand, optimization techniques such as the NSGA-II and MOPSO have some constraint. Once the vehicle model and e-motor model are changed, the optimization dataset must be changed; therefore, they provide optimization for new conditions. However, the proposed methodology based on the ANN provides optimization for previous and new conditions by updating the training dataset for the ANN. Therefore, the proposed methodology in this study provides the generalizability of the optimization process by training the ANN with the different dataset even if the vehicle model and e-motor models are changed.

1.1. Vehicle Model

In this study, a 5 + 1-person golf vehicle was considered. The vehicle data are given in Figure 1. The reason for choosing this vehicle is that, as an autonomous service vehicle, it can meet the service needs in large areas such as schools, hospitals and airports. PC-6 (Pilot Car Golf Cart) is determined as the vehicle model which is shown in Figure 1. PC-6 is modeled and verified by Matlab–Simulink 2022.a, as shown in Figure 2.

Figure 2 shows the dynamic simulation model of this vehicle. Here, the study was carried out on a four-wheel drive (dual track) vehicle model with three degrees of freedom.

For the traction part, the vehicle was driven on the powertrain and wheel model, as seen in Figure 2. In the steering, lateral control was achieved with the rack and pinion system. According to the driving scenario, the control signals (Lateral and Longitudinal) produced by the driver tried to control the steering and traction parts.

To calculate the rigid body kinematics given in Figure 3, Equations (1)–(6) can be used.

$$\dot{r}=\frac{M_z}{I_z}$$

(1)

$${\dot{v}}_x=a_x+v_y.r$$

(2)

$${\dot{v}}_y=a_y+v_x.r$$

(3)

$$a_x=\frac{\left(F_{x1}+F_{x2}\right)cos\delta -\left(F_{y1}+F_{y2}\right)sin\delta +F_{x3}+F_{x4}}{m}$$

(4)

$$a_y=\frac{\left(F_{x1}+F_{x2}\right)sin\delta +\left(F_{y1}+F_{y2}\right)cos\delta +F_{y3}+F_{y4}}{m}$$

(5)

$$M_z=a\left(\left(F_{x1}+F_{x2}\right)sin\delta +\left(F_{y1}+F_{y2}\right)cos\delta \right)-b\left(F_{y3}+F_{y4}\right)-\frac{t_f}{2}\left(\left(F_{x1}-F_{x2}\right)cos\delta -\left(F_{y1}-F_{y2}\right)sin\delta \right)-\frac{t_r}{2}\left(F_{x3}-F_{x4}\right)$$

(6)

In Equations (1) to (6), $r$, $v_x$, $v_y$, $I_z$, $M_z$, $a_x$, $a_y$, $\delta$, $m$, $a$, $b$, $t_f$, $t_r$, $F_{x1}$, $F_{x2}$, $F_{x3}$, $F_{x4}$, $F_{y1}$, $F_{y2}$, $F_{y3}$ and $F_{y4}$ are denoted as the yaw rate, longitudinal speed, lateral speed, inertia of the vehicle, yaw moment, longitudinal acceleration, lateral acceleration, steering angle of the front wheel, mass of the vehicle, distance of the front axle to the center of mass, distance of the rear axle to the center of mass, front axle clearance, rear axle clearance, longitudinal left-front-wheel force, longitudinal right-front-wheel force, longitudinal left-rear-wheel force, longitudinal right-rear-wheel force, lateral left-front-wheel force, lateral right-front-wheel force, lateral left-rear-wheel force and lateral right-rear-wheel force, respectively [14,15,16,17].

Considering the power distribution diagram shown in Figure 4, the requirement to transfer the longitudinal axle force to the wheels can be defined as Equations (7)–(9). The red dash lines as shown in Figure 4 demonstrates to power transfer to the wheels.

$$P_{lon{g}_{axel}}=P_{x1}+P_{x2}+P_{x3}+P_{x4}$$

(7)

$$P_{lon{g}_{axel}}=T_{x1}.{\omega }_{x1}+T_{x2}.{\omega }_{x2}+T_{x3}.{\omega }_{x3}+T_{x4}.{\omega }_{x4}$$

(8)

$$P_{lon{g}_{axel}}=F_{x1}.{cos\delta .R}_{wheel}.{\omega }_{x1}+F_{x2}.{cos\delta .R}_{wheel}.{\omega }_{x2}+F_{x3}.R_{wheel}.{\omega }_{x3}+F_{x4}.R_{wheel}.{\omega }_{x4}$$

(9)

Since this study has a rear-wheel drive system, the power distribution must be rearranged. The regulated equations can be defined by Equations (10)–(12).

$$P_{lon{g}_{axel}}=P_{x3}+P_{x4}$$

(10)

$$P_{lon{g}_{axel}}=T_{x3}.{\omega }_{x3}+T_{x4}.{\omega }_{x4}$$

(11)

$$P_{lon{g}_{axel}}=F_{x3}.R_{wheel}.{\omega }_{x3}+F_{x4}.R_{wheel}.{\omega }_{x4}$$

(12)

Here $P_{lon{g}_{axel}}$,$P_{x1}$, $P_{x2}$, $P_{x3}$, $P_{x4}$, $T_{x1}$, $T_{x2}$, $T_{x3}$, $T_{x4}$, ${\omega }_{x1}$, ${\omega }_{x2}$, ${\omega }_{x3}$, ${\omega }_{x4}$ and $R_{wheel}$ are represented as the total power transmitted to the axles, the power transmitted to the left front wheel, the power transmitted to the right front wheel, respectively, the power transmitted to the left rear wheel, the power transmitted to the right rear wheel, the torque transmitted to the left front wheel, the torque transmitted to the right front wheel, the torque transmitted to the left rear wheel, the torque transmitted to the right rear wheel, the left front wheel’s angular speed, the right front wheel’s angular speed, the left rear wheel’s angular velocity, and the right rear wheel’s angular velocity and wheel radius, respectively.

The transmission model of the vehicle model in this study can be defined as Equations (13)–(19).

$$P_{lon{g}_{axel}}=P_{tractio{n}_{motor}}.\eta$$

(13)

$$P_{lon{g}_{axel}}=T_{lon{g}_{axel}}.{\omega }_{lon{g}_{axel}}$$

(14)

$$T_{lon{g}_{axel}}=F_{x3}.R_{wheel}+F_{x4}.R_{wheel}$$

(15)

$$P_{tractio{n}_{motor}}=T_{tractio{n}_{motor}}.{\omega }_{tractio{n}_{motor}}$$

(16)

$$T_{tractio{n}_{motor}}=F_{tractio{n}_{motor}}.R_{wheel}$$

(17)

$$T_{lon{g}_{axel}}=T_{tractio{n}_{motor}}.N.\eta$$

(18)

$${\omega }_{lon{g}_{axel}}=\frac{{\omega }_{tractio{n}_{motor}}}{N}$$

(19)

$P_{tractio{n}_{motor}}$, $T_{tractio{n}_{motor}}$, ${\omega }_{tractio{n}_{motor}}$,$N$, $\eta$, $T_{lon{g}_{axel}}$ and ${\omega }_{lon{g}_{axel}}$, respectively, represent the power of the traction motor, the torque of the traction motor, the angular speed of the traction motor, the transmission ratio of the transmission [1:8] representing the efficiency of the transmission [95%], the torque transmitted to the rear axle and the angular speed transmitted to the rear axle.

The power transferred by the vehicle traction motor can be defined with Equations (20)–(22) [18].

$$F_{tractio{n}_{motor}}=m.{\dot{v}}_x+F_{rol}+F_{wind}+F_{grad}$$

(20)

$$F_{tractio{n}_{motor}}=\frac{F_{x3}+F_{x4}}{N.\eta }$$

(21)

$$F_{x3}+F_{x4}=\left(m.{\dot{v}}_x+F_{rol}+F_{wind}+F_{grad}\right).N.\eta$$

(22)

Here, $F_{rol}$,$F_{wind}$ and $F_{grad}$ represent the rolling resistance, aerodynamic drag force and slope climbing forces, respectively.

The steering of the vehicle is controlled with the rack and pinion system shown in Figure 5. The kinematic relationship here can be defined by Equations (23)–(26) [14,15,16,17].

$$∆P=R_{rack}.{\delta }_{in}$$

(23)

$$L_1=\frac{t_r-L_{rack}}{2}-∆P$$

(24)

$$L_2=\sqrt{{L_1}^2+D^2}$$

(25)

$$\delta =\frac{\pi }{2}-{\tan }^{-1}\left(\frac{D}{L_1}\right)-{\cos }^{-1}\left(\frac{{L_{arm}}^2+{L_2}^2-{L_{rod}}^2}{2.L_{arm}.L_2}\right)$$

(26)

Here, $∆P$, $R_{rack}$, ${\delta }_{in}$, $L_{rack}$, $L_{arm}$, $L_{rod}$ and $D$ represent the linear change in the rack position, the pinion gear radius, the pinion gear rotation, the rack gear length, the steering arm length, the tie rod length and the distance between the front axle and the rack gear, respectively.

In the electronic steering and assist system shown in Figure 6, the control signal processed in the electronic control unit with both the steering input by the driver and electronic steering commands is transferred to the pinion gear as angular displacement via a geared DC motor [19].

The model of the electronic steering system can be defined by Equations (27)–(35).

$${\theta }_{driver}={\theta }_m$$

(27)

$$P_d=T_d.{\dot{\theta }}_d$$

(28)

$$P_m=T_m.{\dot{\theta }}_m$$

(29)

$$P_d=P_m$$

(30)

$$P_s=T_s.{\dot{\theta }}_s$$

(31)

$$P_s=P_m.\eta$$

(32)

$$T_s=T_m.N$$

(33)

$${\theta }_s=\frac{{\theta }_m}{N}$$

(34)

$$T_s={\delta }_{in}$$

(35)

Here, $P_d$, $P_s$, $P_m$,$T_d$, $T_s$, $T_m$, ${\theta }_d$, ${\theta }_{driver}$, ${\theta }_s$, ${\theta }_m$, $\eta$ and $N$, respectively, represent the requested power, pinion input power, electric motor power, requested torque, pinion input torque, electric motor output torque, the requested angular displacement is represented as the angular displacement applied by the driver, the angular displacement applied to the pinion input, the angular displacement at the electric motor output, the efficiency of the reducer [95%] and the reducer ratio [1:40].

1.2. Driving Cycle and Scenarios

In this study, three different driving cycles and three different driving scenarios were determined to evaluate the traction and steering engine performances and requirements. The determined driving cycles are the NEDC (New European Driving Cycle), US06 and WLTC Class 3 Low (The Worldwide Harmonized Light Vehicles Test Cycles). Reference speed profiles for the determined driving cycles are shown in Figure 7.

Statistical data regarding the determined driving cycles (Figure 7) are given in

Table 1. Statistical Analysis of Driving Cycles.

	NEDC	US06	WLTC Class 3 Low
Total Distance [m]	11,020	12,890	3095
Maximum Speed [m/sn]	33.33	35.9	15.69
Average Speed [m/sn]	9.333	21.44	5.245
Standard Deviation [m/sn]	8.6092	10.99	4.38
Unit Kinetic Energy [KJ/m]	4316	6765	2222
Idle Time [sn]	286	44	149
Maximum Acceleration [m/sn2]	1.042	3.755	1.611

. As can be seen from here, three driving cycles with different characteristics are considered. Since the typical structure of the vehicle model shown in Figure 1 is different, that is, characteristic features such as the maximum speed range cannot be compatible with the determined driving cycles (for example, the maximum speed is 25 km/h (6.94 m/h)), the driving cycles are not simulated in the same way in terms of both duration and time. We have tried to scale the drive cycles appropriately in terms of time and speed in order to have both duration and maximum speed scaling. The driving cycles obtained as a result of the operations performed are given in Figure 8. Additionally, statistical analysis results for the re-arranged driving cycles are given in

Table 2. Statistical Analysis of the Re-arranged Driving Cycles.

	NEDC	US06	WLTC Class 3 Low
Total Distance [m]	1525	2493	1381
Maximum Speed [m/sn]	6.94	6.94	6.94
Average Speed [m/sn]	2.537	4.148	2.299
Standard Deviation [m/sn]	8.6092	10.99	4.38
Unit Kinetic Energy [KJ/m]	1190	1310	992
Idle Time [sn]	204	44	160
Maximum Acceleration [m/sn2]	0.5208	0.7264	0.7192

.

The determined driving scenarios are double lane changing (DLC (Double Lane Change)), turning at a constant radius (CR (Constant Radius)) and slowly increasing the steering angle (SIS (Slowly Increase Steer)). These scenarios are given in Figure 9.

Considering the dynamics of the vehicle in Figure 1, the necessity of rearranging the determined driving scenarios emerges. Therefore, the representation of the rearranged driving scenarios is given in Figure 10. Statistical analysis results of the re-arranged driving scenarios are given in

Table 3. Statistical Analysis of the Re-arranged Driving Scenarios.

	DLC	CR	SIS
Total Distance [m]	273.76	728	170.88
Maximum Speed [m/sn]	4.05	5.78	2.8
Maximum Deviation at Y-axis [m]	2.385	200	28.4
Unit Kinetic Energy [J/m]	29.95	22.94	22.94

.

2. Materials and Methods

2.1. Objective Function

The main aim in this study is to obtain optimal motor designs that can adequately meet vehicle requirements by optimizing the traction and steering motors. In order to achieve this, the objective function will be maximized by optimizing the design variables in line with mechanical, electromagnetic and performance constraints. The mechanical constraints include the diameter, length and shaft geometries of the engine geometry. Electromagnetic constraints represent the maximum flux density requirements coming from the B–H curve of the material in the stator and rotor cores. Performance expectations consist of motor speed–torque–power requirements coming from the driving cycle for the traction motor, while similarly for the steering consistency of motor speed–torque–power demands coming from the driving scenarios.

The design variables are motor general geometry (MG), stator inner diameter (SID), stator outer diameter (SOD), motor length (ML), stator length (SL), rotor length (RL), stator slot geometry (SS), stator winding (SW), number of wires per conductor (NOS), number of conductors per slot (SNOS), conductor wire diameter (WD), rotor outer diameter (ROD), rotor slot geometry (RS), shaft diameter (SD), magnet length (PML), magnet thickness (PMT), commutator diameter (CD), commutator length (CL), gear ratio (GR), number of poles (PN), commutator-winding parameters (WC), rotor winding end width (ERW) and rotor winding tip height (ERH). The objective function is to minimize the weight of the traction motor used initially. Thus, advantages such as weight reduction, efficiency and material usage are expected to be achieved. For the steering engine, it is to maximize efficiency and improve torque–speed correlation. In summary, the aim is to provide a parametric approach for traction and steering motors, as shown in

Table 4. Objective Function, Design Constraints and Design Variables.

Traction	Steering
Objective Function:	Objective Function:
Maximization of Power to Weight Ratio Maximization of Torque–Speed Map Correlation	Maximization of Efficiency Maximization of Torque–Speed Map Correlation
Constraints:	Constraints:
Mechanical:	Mechanical:
SOD ≤ Current, ML ≤ Current, SD ≤ Current	SOD ≤ Current, ML ≤ Current, SD ≤ Current
Electromagnetic:	Electromagnetic:
Flux Density ≤ 1.6 Tesla	Flux Density ≤ 1.6 Tesla
Performance:	Performance:
Torque ≥ Results of Driving Cycles, Speed ≥ Results of Driving Cycles	Torque ≥ Results of Driving Scenarios, Speed ≥ Results of Driving Scenarios
Design Variables:	Design Variables:
MG; SOD, SID, ML, ROD, SD, SS; Hs0, Hs1, Hs2, Bs0, Bs1, Bs2, SW; WD, NOS, SNOS, RS; Hs0, Hs1, Hs2, Bs0, Bs1, Bs2, RW; ERW, ERH	PN; SS; EM, PML, PMT RS; Hs0, Hs1, Hs2, Bs0, Bs1, Bs2, WC; SNOS, NOS, CD, CL, GR;

.

2.2. Optimization Algorithm

Figure 11 shows the flow chart to be followed to determine the performance criteria for traction and steering motors. The driving cycles arranged here will be applied as reference inputs on the vehicle dynamic model and the minimum performance requirements (Torque–Speed–Power) for the traction engine that will be determined. Similarly, driving scenarios will be run on the vehicle dynamic model to determine the minimum performance requirements (Torque–Speed–Power) for the steering motor.

After determining the performance requirements, the traction (DLGF 122200-4) and steering (EPAS01 of DC Electronic) motors currently used on the vehicle must be modeled. The processes followed for modeling are shown in Figure 12.

In Figure 12, the test data shared in the traction and steering motors’ technical specifications list are combined with the design parameters obtained by disassembling the motors. The design parameters obtained here will be analytically modeled using the Ansys RMXprt module and will be verified with test data. Modeling studies will be completed by transferring the performance analysis graphics (Torque–Speed–Power) for the resulting traction and steering motor models to Matlab.

The main purpose of optimizing the currently used traction (DLGF 122200-4) and steering (EPAS01 of DC Electronic) motors is to maximize the power to weight ratio of these motors, reduce the motor geometric dimensions and reduce material usage. To do this, a cost function is needed that must be controlled at each iteration. Essentially, the cost function here represents the difference between the minimum performance criteria obtained in the process in Figure 11 and the performance graphs of the motor models shown in Figure 12. The aim is to reduce this cost by taking other constraints (mechanical, electromagnetic, etc.) into account and by optimal variations of the design parameters. In order to achieve the aims, the traction and steering motors modeled in this study are first transformed to parametric form. Then, the motor models with different design parameters are created using the experimental design method for motor model variations [23,24]. The created motor models are analyzed and performance results are labeled. New motor variations are generated by training an artificial neural network (ANN) model with design parameters as output data and performance results as input data (Figure 13a). The new motor model derived from the ANN is analyzed to check whether the performance results obtained meet the minimum requirements (Figure 13b). If so, the optimization cycle is stopped. If not, this motor variation is added to the previous data set and the ANN is re-trained. Then, the ANN is run again to obtain a new motor variation, and the cycle continues to check whether it meets the minimum performance requirements by analyzing it again [13,18]. The following steps that summarize the process are shown in Figure 13a,b.

3. Results and Discussion

In this section, the findings obtained as a result of the analyses performed by applying the processes specified in the material and method section are presented.

3.1. The Determination of Minimum Performance Requirements for Traction and Steering Motors

By applying the driving cycles (NEDC, US06 and WLTC) and driving scenarios (DLC, CR and SIS) in Figure 11 to the dynamic vehicle model created in Matlab, we attempted to determine the minimum performance requirements with the findings obtained as a result of the analysis. Torque–Speed–Power curves obtained in line with the findings obtained here are given in Figure 14 and Figure 15 for the traction and steering motors.

As can be seen from Figure 14 and Figure 15, WLTC in driving cycles and SIS in driving scenarios need the most demanding performance requirements. Based on this, the minimum performance requirements for the traction and steering motors can be summarized as in

Table 5. Minimum Performance Requirements for Traction and Steering Motors.

Traction Motors	Steering Motor
Constraint:	Constraint:
Performances:	Performances:
Locked Rotor Torque ≥ 22.41 Nm, Maximum Speed ≥ 3543 RPM, Maximum Power ≥ 2801 Watt	Locked Rotor Torque ≥ 94.96 Nm, Maximum Speed ≥ 12.07 RPM, Maximum Power ≥ 107.5 Watt

.

3.2. Modeling of Traction and Steering Motors

The motor design, especially motor sizing, can generally be accomplished through analytical equations. The motor sizing equation developed by Thomas Lipo and Surong Huang is given in Equation (36) [25].

$$P=\frac{\pi }{2}\eta K_p{K}_c{K}_i{B}_{\delta }\frac{f}{p}{D}_{SO}^2{\lambda }^{\prime 2}{L}_{1}A$$

(36)

Here, $P$, $\eta$, $K_p$, $K_c$, $K_i$, $B_{\delta }$, $f$, $p$, $D_{SO}$, ${\lambda }^{\prime }$, $L_1$ and $A$ are, respectively, the motor power, efficiency, back emf coefficient, winding coefficient, ratio of maximum current to RMS current, flux density in the air gap, frequency, pole pair, stator outer diameter, ratio of stator inner diameter to outer diameter (this parameter represents the electric load, current density, slot filling ratio, stator outer diameter, pole pitch and flux density in the air gap), motor length and electric load [18].

As can be understood from Equation (36), the motor efficiency can be improved by changing the motor design parameters to meet the technical requirements and optimization studies at various levels. However, the change of design parameters here also has mechanical and electromagnetic constraints. For example, the split ratio must be considered as an important design parameter as this parameter directly affects the flux density in the air gap. Therefore, it is essential to observe this effect in parameter changes. When iron losses are neglected and an ideal air gap flux density is taken into account, the electromagnetic torque can be expressed as in Equation (37) [26,27,28,29,30].

$$T=2D_{SO}{l}_a{N}_w{I}_a{B}_g$$

(37)

$T$, $l_a$, $N_w$, $I_a$ and $B_g$ represent the electromagnetic torque, active length, number of turns per phase, RMS phase current and air gap flux density, respectively. The split ratio and stator inner diameter can be shown with Equations (38) and (39).

$$\lambda =\frac{D_{RO}}{D_{SO}}$$

(38)

$$D_{SI}=\lambda D_{SO}+2g$$

(39)

$\lambda$, $D_{RO}$, $D_{SI}$ and $g$ represent the split ratio, rotor outer diameter, stator inner diameter and air gap length, respectively. Considering the rotor dimensions, the electromagnetic torque equation can be expressed as in Equation (40).

$$T=2D_{RO}{l}_a{B}_g\sqrt{\frac{p_{cu}{A}_s{K}_s{N}_s}{24\rho l_a}}.$$

(40)

$p_{cu}$, $A_s$, $K_s$, $N_s$ and $\rho$ represent the copper losses, groove area, packing factor, number of grooves and copper resistivity, respectively. The flux density ratio and the flux density ratios in the air gap can be defined by Equations (41)–(43).

$$\gamma =\frac{B_g}{B_{max}}$$

(41)

$$B_g=\frac{3\sqrt{3}}{2\pi }{B}_{gm}$$

(42)

$$B_g=\frac{h_m}{h_m+g}{B}_r$$

(43)

$\gamma$, $B_{gm}$, $B_{max}$, $B_r$ and $h_m$ represent the flux density ratio, maximum flux density in the air gap, maximum flux density in the stator, remanence flux density of the permanent magnet and permanent magnet thickness, respectively.

3.2.1. Modeling Studies for Traction Motor

The traction motor used for the electric golf vehicle discussed in this study is the DLGF 122200-4 induction motor (Appendix A). The DLGF 122200-4 modeled in Ansys RMXprt was compared in terms of the torque–speed and power–speed curves and the results are shown in Figure 16. Considering the results, the Ansys RMXprt model has been verified at an acceptable level.

3.2.2. Modeling Studies for Steering Motor

The steering motor used for the electric golf vehicle discussed in this study is the EPAS01 PMDC (permanent magnet direct current motor) (Appendix B). The EPAS01 modeled in Ansys RMXprt is compared in terms of the torque–speed and power–speed curves and the results are shown in Figure 17. Considering the results, the Ansys RMXprt model has been verified at an acceptable level.

3.3. Comparison of Minimum Performance Requirements for Traction and Steering Motors

In this section, the traction and steering motor models currently used on the golf cart and the minimum performance criteria determined after the driving cycles and driving scenarios have been analyzed. Considering Figure 14 and Figure 16, the potential optimization area for the traction motor is shown in Figure 18. As can be seen here, as a result of the analyses made for NEDC, US06 and WLTC, the minimum performance requirements are well below the DLGF 122200-4 motor model used. Generally, these types of motors are produced by manufacturers with high safety coefficients, the main reason being that they can increase their usage areas. However, considering that the efficiency will decrease in this way, there is an opportunity to optimize the traction motor in a very wide area in Figure 18.

Considering Figure 15 and Figure 17, the potential optimization area for the steering motor is shown in Figure 19. As can be seen here, the minimum performance requirements, as a result of the analysis for DLC, CR and SIS, show that there are optimization regions for the EPAS01 motor model used.

3.4. Creating Training Dataset and Training ANN for Optimization

In this section, the design parameters of the traction and steering motors to be optimized are discussed. The ANN that will be used to estimate the design parameters in the optimization algorithm must be trained with more than one dataset in order to produce the appropriate results. The main purpose of the ANN to be used is to derive the motor design parameters (parameter fitting) that will provide the desired performance requirements for the traction and steering motors. The ANN training datasets are derived from DLGF 112200-4 (traction motor) and EPAS01 (steering motor). The derived datasets for DLGF 112200-4 and EPAS01 are modeled and verified by Ansys RMXprt.

The mathematical function equivalent to the ANN is given in Equation (44). The ANN basically consists of two layers. These are the hidden layer and the output layer. In the hidden layer, the dataset applied as the input is multiplied by the appropriate coefficients according to the priorities and importance levels of the input dataset, collected with the required threshold level and passed through the Activation function to obtain the hidden layer output. The mathematical expression for the activation function in the hidden layer is given in Equation (45). The dataset at the output of the hidden layer is taken as the input dataset of the output layer, and it is subjected to similar processes in the first layer and passed through the activation function to derive the desired motor design parameters. The mathematical expression for the activation function in the output layer is given in Equation (46).

$$y=f\left[{\sum }_{i=1}^m\left(w_i{x}_i+b_i\right)\right].$$

(44)

$$tansin\left(x\right)=\frac{2}{1+e^{-2x}}-1$$

(45)

$$purelin\left(x\right)=x$$

(46)

3.4.1. Experimental Design and Preparation of ANN Training Dataset for Traction Motor

In order to train the DLGF 122200-4 Ansys RMXprt motor model to ANN, the parameters are diversified and the dataset is created using the DoE.

The design of experiments method (DoE) can enable prioritization among design parameters by analyzing the effects of the parameters on the results. Therefore, it enables focusing on the relevant parameters and determining the optimal parameter levels that can meet the desired performance requirements [18]. It also provides advantages such as reducing experiment combinations and, therefore, time and cost. Two studies on the use of DoE in ANN training were found in the literature. These are studies on supporting ANN training with DoE in the estimation of non-linear time series [31,32].

For the experimental design, it is necessary to determine the values of the design parameters that contain differences in levels, such as the minimum, maximum and average values. Experimental combinations for the DLGF 122200-4 Ansys RMXprt Model are given in

Table 6. ANN Output Training Data for DLGF 122200-4.

No	Process	MG (mm)	SS (mm)	SW (mm)	RS (mm)	RW (mm)
Exp.1	-	SOD 170, SID 102, ML 194, ROD 101	Hs0 1.5, Hs1 0, Hs2 16, Bs0 2.8, Bs1 4.8, Bs2 7.6	WD 1.15, SNOS 2, NOS 14	Hs0 0.5, Hs1 0.6, Hs2 14.3, Bs0 1, Bs1 3.3, Bs2 3.3	ERW 8.5, ERH 25
	(N)	0.8	0.8	0.8	0.8	0.8
	(NP)	0.8	0.67188	0.8	0.65629	0.29691
Exp.2	-	SOD 170, SID 102, ML 194, ROD 101	Hs0 1.5, Hs1 0, Hs2 16, Bs0 2.8, Bs1 4.8, Bs2 7.6	WD 1.15, SNOS 2, NOS 14	Hs0 0.3, Hs1 0.4, Hs2 8.4, Bs0 0.6, Bs1 1.9, Bs2 1.9	ERW 5, ERH 10
	(N)	0.8	0.8	0.8	−0.8	−0.8
	(NP)	0.8	0.67188	0.8	−0.65629	−0.29691
Exp.3	-	SOD 170, SID 102, ML 194, ROD 101	Hs0 0.9, Hs1 0, Hs2 9, Bs0 1.6, Bs1 2.1, Bs2 4.5	WD 0.57, SNOS 4, NOS 16	Hs0 0.5, Hs1 0.6, Hs2 14.3, Bs0 1, Bs1 3.3, Bs2 3.3	ERW 8.5, ERH 25
	(N)	0.8	−0.8	−0.8	0.8	0.8
	(NP)	0.8	−0.67188	−0.8	0.65629	0.29691
Exp.4	-	SOD 170, SID 102, ML 194, ROD 101	Hs0 0.9, Hs1 0, Hs2 9, Bs0 1.6, Bs1 2.1, Bs2 4.5	WD 0.57, SNOS 4, NOS 16	Hs0 0.3, Hs1 0.4, Hs2 8.4, Bs0 0.6, Bs1 1.9, Bs2 1.9	ERW 5, ERH 10
	(N)	0.8	−0.8	−0.8	−0.8	−0.8
	(NP)	0.8	−0.67188	−0.8	−0.65629	−0.29691
Exp.5	-	SOD 115, SID 60, ML 97, ROD 59	Hs0 1.5, Hs1 0, Hs2 16, Bs0 2.8, Bs1 4.8, Bs2 7.6	WD 0.57, SNOS 4, NOS 16	Hs0 0.3, Hs1 0.4, Hs2 8.4, Bs0 0.6, Bs1 1.9, Bs2 1.9	ERW 5, ERH 10
	(N)	−0.8	0.8	−0.8	−0.8	−0.8
	(NP)	−0.8	−0.67188	−0.8	−0.65629	−0.29691
Exp.6	-	SOD 115, SID 60, ML 97, ROD 59	Hs0 1.5, Hs1 0, Hs2 16, Bs0 2.8, Bs1 4.8, Bs2 7.6	WD 0.57, SNOS 4, NOS 16	Hs0 0.3, Hs1 0.4, Hs2 8.4, Bs0 0.6, Bs1 1.9, Bs2 1.9	ERW 8.5, ERH 20
	(N)	−0.8	0.8	−0.8	−0.8	0.8
	(NP)	-0.8	0.67188	−0.8	−0.65629	0.29691
Exp.7	-	SOD 115, SID 60, ML 97, ROD 59	Hs0 0.9, Hs1 0, Hs2 9, Bs0 1.6, Bs1 2.1, Bs2 4.5	WD 0.57, SNOS 4, NOS 16	Hs0 0.3, Hs1 0.4, Hs2 8.4, Bs0 0.6, Bs1 1.9, Bs2 1.9	ERW 5, ERH 10
	(N)	−0.8	−0.8	−0.8	−0.8	−0.8
	(NP)	−0.8	−0.67188	−0.8	−0.65629	−0.29691
Exp.8	-	SOD 115, SID 60, ML 97, ROD 59	Hs0 0.9, Hs1 0, Hs2 9, Bs0 1.6, Bs1 2.1, Bs2 4.5	WD 0.57, SNOS 4, NOS 16	Hs0 0.3, Hs1 0.4, Hs2 8.4, Bs0 0.6, Bs1 1.9, Bs2 1.9	ERW 8.5, ERH 20
	(N)	−0.8	−0.8	−0.8	−0.8	0.8
	(NP)	−0.8	−0.67188	−0.8	−0.65629	0.29691

for five groups of parameters and two levels, based on the orthogonal experimental design matrix prepared by Taguchi according to various parameter levels and parameter numbers. Here, eight different experiments for L8 are listed in Table 6. Ansys RMXprt motor models are created and analyzed for eight different motor models. The findings regarding the analysis results are given in

Table 7. ANN Input Training Dataset for DLGF 122200-4.

125 Hz	Process	Exp.1	Exp.2	Exp.3	Exp.4	Exp.5	Exp.6	Exp.7	Exp.8
Motor Weight (kg)	-	25.86	26.50	28.07	28.70	4.965	5.034	6.708	6.778
	(N)	-	-	-	-	-	-	-	-
Rated Torque (Nm)	-	32.45	11.23	6.95	2.22	1.92	2.29	4.76	5.51
	(N)	-	-	-	-	-	-	-	-
Rated Speed (RPM)	-	3600	3600	3600	3600	3600	3600	3600	3600
	(N)	-	-	-	-	-	-	-	-
Rated Power (KWatt)	-	12.23	4.236	2.621	0.837	0.725	0.865	1.796	2.080
	(N)	0.8	−0.312	−0.536	−0.784	−0.8	−0.780	−0.651	−0.611
Efficiency (%)	-	86.15	83.47	77.77	68.05	6.37	7.52	71.23	73.27
	(N)	-	-	-	-	-	-	-	-
Breakdown Torque (Nm)	-	58.14	57.75	10.96	10.86	19.58	19.59	26.70	26.68
	(N)	-	-	-	-	-	-	-	-
Locked Torque (Nm)	-	29.45	47.62	3.97	7.76	19.28	18.77	23.58	22.25
	(N)	0.134	0.8	−0.8	−0.661	−0.238	−0.257	−0.081	−0.129
Maximum Speed (RPM)	-	3747	3741	3739	3716	3711	3716	3732	3734
	(N)	-	-	-	-	-	-	-	-
STFD (Tesla)	-	1.242	1.242	0.376	0.357	4.758	4.759	1.663	1.655
	(N)	-	-	-	-	-	-	-	-
RTFD (Tesla)	-	1.154	0.841	0.523	0.380	1.216	1.216	1.729	1.722
	(N)	-	-	-	-	-	-	-	-
SYFD (Tesla)	-	0.954	0.951	0.294	0.293	1.104	1.104	0.861	0.855
	(N)	-	-	-	-	-	-	-	-
RYFD (Tesla)	-	0.949	0.671	0.471	0.324	0.889	0.889	1.232	1.223
	(N)	-	-	-	-	-	-	-	-
AGFD (Tesla)	-	0.560	0.560	0.254	0.253	0.587	0.588	0.836	0.832
	(N)	-	-	-	-	-	-	-	-

. The motor weight, rated torque, rated speed, efficiency, flux density in stator teeth (STFD), flux density in rotor teeth (RTFD), flux density in stator yoke (SYFD), flux density in rotor yoke (RYFD) and flux density in airgap (AGFD) are included. The results are examined. In the findings obtained, it was observed that some motor models exceeded the BH curve of M19 24G (1.6 Tesla).

As a result of the SNR (signal-to-noise ratio) study, conducted in line with the findings obtained, the factors that the parameters affect and how much they affect them, that is, their degree of importance, are analyzed.

Both input and output data are normalized for ANN training. The prioritization values from DoE are also applied only for the output data after the normalization process. In Table 6 and Table 7, they are named as normalization operations (N) and normalization and prioritization operations (NP). This is also highlighted on the chart.

3.4.2. Experimental Design and Preparation of ANN Training Dataset for Steering Motor

In this section, the parameters are diversified and the dataset is created using the experimental design method in order to train the Ansys RMXprt engine model to ANN.

Here, unlike the traction motor, the design parameters have been changed because, it has been revealed, the power-to-weight ratio of the traction motor can be taken into account and its dimensions can be reduced according to the driving cycle results. However, according to the driving scenario results in the steering motor, the focus should be on reducing the engine speed. Therefore, the number of motor poles (PN), stator poles (SS), rotor slots (RS), winding-commutators (WC) and gear ratio (GR) parameters are discussed.

The L8 matrix is chosen for five groups of parameters and two levels. Considering the L8 matrix, the experimental design for eight different steering motor models is as shown in

Table 8. ANN Output Training Data for EPAS01.

No	Process	PN (-)	SS (mm)	RS (mm)	WC (mm)	GR (-)
Exp.1	-	4	EM 0.726, PML 40, PMT 9	Hs0 1.2, Hs1 1, Hs2 9.8, Bs0 3, Bs1 8.6, Bs2 4	SNOS 25, NOS 6, CD 24, CL 10	1:40
	(N)	0.692	0.692	0.692	0.692	0.690
	(NP)	0.300	0.692	0.021	0.093	0.145
Exp.2	-	2	EM 0.726, PML 32, PMT 7.8	Hs0 1, Hs1 0.8, Hs2 8.6, Bs0 2.6, Bs1 7.4, Bs2 3.4	SNOS 37, NOS 4, CD 20, CL 8	1:40
	(N)	−0.846	−0.846	−0.846	−0.846	0.690
	(NP)	−0367	−0.846	−0.025	−0.113	0.165
Exp.3	-	4	EM 0.726, PML 40, PMT 9	Hs0 1, Hs1 0.8, Hs2 8.6, Bs0 2.6, Bs1 7.4, Bs2 3.4	SNOS 37, NOS 4, CD 20, CL 8	1:80
	(N)	0.692	0.692	−0.846	−0.846	−0.849
	(NP)	0.300	0.692	−0.025	−0.113	−0.202
Exp.4	-	2	EM 0.726, PML 32, PMT 7.8	Hs0 1.2, Hs1 1, Hs2 9.8, Bs0 3, Bs1 8.6, Bs2 4	SNOS 25, NOS 6, CD 24, CL 10	1:80
	(N)	−0.846	−0.846	0.692	0.692	−0.849
	(NP)	−0.367	−0.846	0.021	0.093	−0.202
Exp.5	-	4	EM 0.726, PML 32, PMT 7.8	Hs0 1.2, Hs1 1, Hs2 9.8, Bs0 3, Bs1 8.6, Bs2 4	SNOS 37, NOS 4, CD 20, CL 8	1:80
	(N)	0.692	−0.846	0.692	−0.846	−0.849
	(NP)	0.300	−0.846	0.021	−0.113	−0.202
Exp.6	-	2	EM 0.726, PML 40, PMT 9	Hs0 1, Hs1 0.8, Hs2 8.6, Bs0 2.6, Bs1 7.4, Bs2 3.4	SNOS 25, NOS 6, CD 24, CL 10	1:80
	(N)	−0.846	0.692	−0.846	0.692	−0.849
	(NP)	−0.367	0.692	−0.025	0.093	−0.202
Exp.7	-	4	EM 0.726, PML 32, PMT 7.8	Hs0 1, Hs1 0.8, Hs2 8.6, Bs0 2.6, Bs1 7.4, Bs2 3.4	SNOS 25, NOS 6, CD 24, CL 10	1:40
	(N)	0.692	−0.846	−0.846	0.692	0.690
	(NP)	0.300	−0.846	−0.025	0.093	0.165
Exp.8	-	2	EM 0.726, PML 40, PMT 9	Hs0 1.2, Hs1 1, Hs2 9.8, Bs0 3, Bs1 8.6, Bs2 4	SNOS 37, NOS 4, CD 20, CL 8	1:40
	(N)	−0.846	0.692	0.692	−0.846	0.690
	(NP)	−0.367	0.692	0.021	−0.113	0.165

.

When the experiments are analyzed by modeling Ansys RMXprt in Table 8, the results obtained are given in

Table 9. ANN Input Training Data for EPAS01.

	Process	Exp.1	Exp.2	Exp.3	Exp.4	Exp.5	Exp.6	Exp.7	Exp.8
Motor Weight (kg)	-	1.39	1.53	1.46	1.47	1.47	1.46	1.54	1.39
	(N)	-	-	-	-	-	-	-	-
Rated Torque (Nm)	-	8.406	35.05	15.51	85.84	12.427	74.95	8.905	28.88
	(N)	−0.979	−0.651	−0.892	−0.027	−0.93	−0.161	−0.973	−0.727
Rated Speed (RPM)	-	122.7	29.42	66.61	9.437	83.137	10.77	115.9	35.725
	(N)	0.651	−0.655	−0.134	−0.935	0.096	−0.916	0.555	−0.567
Maximum Efficiency (%)	-	68.52	73.34	68.59	74.29	66.58	74.53	70.2	72.37
	(N)	-	-	-	-	-	-	-	-
Rated Efficiency (%)	-	67.77	42.83	65.95	42.96	64.6	42.99	69.85	42.7
	(N)	-	-	-	-	-	-	-	-
PMFD (Tesla)	-	0.596	0.649	0.675	0.618	0.686	0.42	0.805	0.421
	(N)	-	-	-	-	-	-	-	-
AGFD (Tesla)	-	0.688	0.73	0.778	0.696	0.772	0.491	0.906	0.485
	(N)	-	-	-	-	-	-	-	-
Kt =Ke (Nm/A)	-	0.743	0.407	2.395	5.28	1.9154	4.627	0.789	3.359
	(N)	-	-	-	-	-	-	-	-
Rated Power (Watt)	-	108	38.98	108	84.82	108	84.54	108	39.05
	(N)	-	-	-	-	-	-	-	-
Maximum Power (Watt)	-	382	38.98	181.87	84.82	181.59	84.54	381.9	39.05
	(N)	-	-	-	-	-	-	-	-

. Here, the motor weight, locked rotor torque, no-load motor speed, maximum possible efficiency, rated efficiency, magnet flux density (PMFD), flux density in the air gap (AGFD), torque constant (Kt), back EMF constant (Ke), rated parameters such as power and maximum engine power are examined.

The input data needed for ANN training are taken from Table 9 and the input training set obtained by processing in accordance with the process is given in Table 9. In other words, the process performed here is the normalization process.

It has been handled in a similar manner in accordance with the process for ANN training. First, the data in Table 8 are normalized (N), then prioritized (NP) and converted into an output dataset for the ANN training given in Table 8.

3.4.3. ANN Training of Traction and Steering Motors for Design Parameters’ Estimation

In this section, the parameter estimations are studied with the dataset prepared for the traction and steering motors. As the ANN training algorithm, the Bayesian Regularization algorithm, which is frequently used in the literature, is used because the process to be performed is based on basic parameter fitting to ensure the Regression (R) is determined within the range of 0.85 and 0.95 as the target criterion for successful training. Since the traction motor and steering motor differ in terms of their design parameters, different ANNs are designed and trained for the traction and the steering motors.

For the traction motor, the parameters in Table 7 and Table 8 are trained on the ANN model shown in Figure 20. As can be seen from Figure 20, the ANN designed for the traction motor consists of 2 inputs and 20 outputs. There are 200 neurons in the hidden layer and 20 neurons in the output layer. The performance obtained after training was obtained as regression (R = 0.9362) and mean square error (MSE = 1.4396). Here, the data applied to the input after training are first normalized and then applied to the input of the ANN. The ANN produces parameters at the output after the relevant operations in response to the data applied to its input. The data generated from the ANN output are first denormalized by subjecting them to prioritization correction, and then they are subjected to denormalization (normalization correction) and turned into real design parameters for the traction motor.

For the steering motor, the parameters in Table 8 and Table 9 are trained on the ANN model shown in Figure 20. As can be seen from Figure 20, the ANN designed for the traction motor consists of 2 inputs and 14 outputs. There are 200 neurons in the hidden layer and 14 neurons in the output layer. The performance obtained after training was obtained as regression (R = 0.9124) and mean square error (MSE = 1.6276). Here, similarly, the data applied to the input after training are first subjected to normalization and then applied to the input of the ANN. The ANN produces parameters at the output after the relevant operations in response to the data applied to its input. The data generated from the ANN output are first normalized by prioritization correction, and then subjected to denormalization (normalization correction) and turned into real design parameters for the steering engine.

3.5. Generation of Motor Design Parameters and Motor Variations with ANN

In this section, the trained ANN in Figure 20 will estimate the appropriate parameters for the traction and steering motors.

Table 10. Design Parameters Estimated by ANN for the Traction Motor.

ANN Input Parameters			ANN Output Parameters
Deviation (%)	Power (Watt)	Torque (Nm)	MG (mm)	SS (mm)	SW (mm)	RS (mm)	RW (mm)
Nominal x 0.50	1400	11.2	SOD 150, SID 102, ML 90, ROD 101	Hs0 0.9, Hs1 0, Hs2 2.7, Bs0 1.68, Bs1 2.88, Bs2 4.6	WD 1.024, SNOS 3, NOS 3	Hs0 0.38, Hs1 0.5, Hs2 10.75, Bs0 0.75, Bs1 2.5, Bs2 2.5	ERW 8.5, ERH 25
Nominal x 0.75	2100	16.8	SOD 155, SID 102, ML 90, ROD 101	Hs0 0.9, Hs1 0, Hs2 7.1, Bs0 1.68, Bs1 2.88, Bs2 4.6	WD 1.024, SNOS 3, NOS 5	Hs0 0.38, Hs1 0.5, Hs2 10.75, Bs0 0.75, Bs1 2.5, Bs2 2.5	ERW 8.5, ERH 25
Nominal	2801	22.41	SOD 155, SID 102, ML 90, ROD 101	Hs0 0.9, Hs1 0, Hs2 9.6, Bs0 1.68, Bs1 2.88, Bs2 4.6	WD 1.15, SNOS 3, NOS 7	Hs0 0.38, Hs1 0.5, Hs2 10.75, Bs0 0.75, Bs1 2.5, Bs2 2.5	ERW 8.5, ERH 25
Nominal x 1.25	3500	28.1	SOD 155, SID 102, ML 90, ROD 101	Hs0 0.9, Hs1 0, Hs2 12.29, Bs0 1.68, Bs1 2.88, Bs2 4.6	WD 1.024, SNOS 3, NOS 11	Hs0 0.38, Hs1 0.5, Hs2 10.75, Bs0 0.75, Bs1 2.5, Bs2 2.5	ERW 8.5, ERH 25
Nominal x 1.50	4200	33.6	SOD 155, SID 102, ML 90, ROD 101	Hs0 0.9, Hs1 0, Hs2 13.76, Bs0 1.68, Bs1 2.88, Bs2 4.6	WD 0.922, SNOS 3, NOS 15	Hs0 0.38, Hs1 0.5, Hs2 10.75, Bs0 0.75, Bs1 2.5, Bs2 2.5	ERW 8.5, ERH 25

and

Table 11. Design Parameters Estimated by ANN for the Steering Motor.

ANN Input Parameters			ANN Output Parameters
Deviation (%)	Speed (RPM)	Torque (Nm)	PN (-)	SS (mm)	RS (mm)	WC (mm)	GR (-)
Nominal x 0.50	6	48	2	EM 0.726, PML 32.5, PMT 6.45,	Hs0 0.933, Hs1 0.724, Hs2 8.185, Bs0 2.428, Bs1 7.205, Bs2 3.189,	SNOS 32, NOS 4, CD 20.05, CL 8.98	60
Nominal x 0.75	9	72	2	EM 0.726, PML 35.6, PMT 7.63,	Hs0 0.965, Hs1 0.765, Hs2 8.395, Bs0 2.533, Bs1 7.195, Bs2 3.299,	SNOS 26, NOS 5, CD 22.02, CL 9.01	69
Nominal	12.07	94.96	2	EM 0.726, PML 37.6, PMT 8.64,	Hs0 0.97, Hs1 0.77, Hs2 8.71, Bs0 2.54, Bs1 7.20, Bs2 3.31,	SNOS 21, NOS 7, CD 21.98, CL 8.92	80
Nominal x 1.25	15	120	2	EM 0.726, PML 40.1, PMT 9.59,	Hs0 1.07, Hs1 0.86, Hs2 9.05, Bs0 2.80, Bs1 8.20, Bs2 3.69,	SNOS 17, NOS 9, CD 22.05, CL 9.03	87
Nominal x 1.50	18	144	2	EM 0.726, PML 43.1, PMT 9.87,	Hs0 1.20, Hs1 0.97, Hs2 10.4, Bs0 3.14, Bs1 9.18, Bs2 4.09,	SNOS 13, NOS 10, CD 22.23, CL 9.15	94

show the motor design parameters generated by the ANN for the traction and the steering motor. Here, in addition to the nominal input value, five different input values are applied to the input of the ANN with deviation values of ±25% and ±50%.

3.6. Analysis of Motor Design Parameters Generated by ANN

In this section, the parameters in Table 10 generated by the ANN for the traction motor and the parameters in Table 11 generated by the ANN for the steering motor are modeled and analyzed in Ansys RMXprt. The analysis results obtained for the traction motor are given in

Table 12. Analysis Results of Generated Motor Models Generated from ANN for Traction.

ANN Input Parameters		N × 0.50	N × 0.75	Nominal	N × 1.25	N × 1.50
Input 1	Locked Torque (Nm)	11.2	16.8	22.41	28.1	33.6
Input 2	Rated Power (Watt)	1400	2100	2801	3500	4200
Parameters for Motor Models Generated from ANN	Motor Weight (kg)	10.21	10.63	11.11	11.16	11.34
	Rated Torque (Nm)	15.14	16.11	17.27	17.01	16.28
	Rated Speed (RPM)	3600	3600	3600	3600	3600
	Rated Power (KWatt)	5708	6075	6513	6416	6138
	Efficiency (%)	76.21	80.14	83.9	83.33	81.25
	Breakdown Torque (Nm)	28.31	34.27	41.92	48.34	52.41
	Locked Torque (Nm)	14.46	18.46	24.98	32.11	36.70
	Maximum Speed (RPM)	3744	3744	3744	3744	3744
	STFD (Tesla)	1.334	1.211	1.224	1.161	1.103
	RTFD (Tesla)	1.294	1.307	1.321	1.300	1.259
	SYFD (Tesla)	1.135	1.498	1.516	1.834	1.934
	RYFD (Tesla)	1.121	1.133	1.147	1.128	1.091
	AGFD (Tesla)	0.765	0.773	0.781	0.769	0.745

. The analysis results obtained for the steering motor are given in

Table 13. Analysis Results of Generated Motor Models Generated from ANN for Steering.

ANN Input Parameters		N × 0.50	N × 0.75	Nominal	N × 1.25	N × 1.50
Input 1	Rated Torque (Nm)	48	72	94.96	120	144
Input 2	Rated Speed (RPM)	6	9	12.07	15	18
Parameters for Motor Models Generated from ANN	Motor Weight (kg)	1.688	1.586	1.490	1.355	1.274
	Rated Torque (Nm)	50.79	73.79	96.01	117.7	140.78
	Rated Speed (RPM)	6	9	12.07	15	18
	Rated Power (Watt)	34.24	69.77	108	176.5	250.4
	Rated Efficiency (%)	42.6	42.99	42.87	40.33	31.89
	Locked Torque (Nm)	80.60	139.69	192.51	205.5	255.63
	No-Load Speed (RPM)	16.22	19.07	24.07	35.11	47.32
	Maximum Power (Watt)	34.24	69.77	121.36	188.89	282.73
	Maximum Efficiency (%)	71.67	74.46	76.12	76.43	76.30
	PMFD (Tesla)	0.757	0.616	0.487	0.350	0.303
	AGFD (Tesla)	0.834	0.693	0.557	0.409	0.363
	Kt (Nm/A)	6.126	5.2233	4.144	2.8362	2.0774
	Ke (Vs/rad)	6.126	5.2233	4.144	2.8362	2.0774

.

3.7. Comparison of Traction Motor Torque–Speed Curves Obtained under Driving Cycles and Torque–Speed Curves Generated by ANN

The minimum performance requirements achieved in driving cycles (NEDC, US06 and WLTC) for the traction motor (DLGF 122200-4) are given in Figure 14 and Table 5. The data here and the data given in Table 12 for the traction motor models generated by the ANN are compared in this section. The findings obtained are as shown in Figure 21.

3.8. Comparison of Steering Motor Torque–Speed Curves Obtained under Driving Scenarios and Torque–Speed Curves Generated by ANN

The minimum performance requirements achieved in driving cycles (DLC, CR and SIS) for the steering motor (EPAS01) are given in Figure 15 and Table 5. The data here and the data given in Table 13 for the steering motor models generated by ANN are compared in this section. The findings obtained are as shown in Figure 22.

3.9. Discussion of Analysis Results for Traction and Steering Motors Generated by ANN

According to the minimum performance requirements, five different engine models of traction motors are generated by the DLGF ANN for the nominal input value and its deviation values of ±25% and ±50%. The generated motor models (Table 10) are run by modeling Ansys RMXprt. The obtained results (Table 12) are examined with nominal, maximum and minimum values on parameters such as torque, speed, speed, power, flux density and material consumption. When the parameters of the motor models generated here (Table 10) are analyzed, it is observed that the motor geometric (MG) features are reduced to the smallest geometric dimensions possible by ANN.

Here, it was observed that the motor length (ML) was reduced by 54% and the motor outer diameter (SOD) was reduced by 9%. Similarly, the stator slot geometry (SS) has the smallest possible geometric dimension and the highest slot fill factor when the flux density constraint was taken into account. And it has been observed that the parameter that can be associated with the slot length (Hs2) not only optimizes the flux density in the stator yoke (SYFD), but also correlates the motor efficiency with the slot fill factor. In the stator winding (WC), it has been observed that both the wire diameter (WD), the number of conductors per slot (SNOS) and the number of wires per conductor (NOS) are directly associated with locked rotor torque, breakdown torque, rated torque and motor power by the ANN. The rotor slot (RS) geometry is matched with the smallest possible slot geometry by the ANN. The rotor winding (RW) is matched with the largest geometry. It has been observed here that RS and RW are associated with rotor flux densities (RTFD and RYFD) and are arranged in a way that they can remain below the saturation value depending on the core material.

In addition, it has been observed that the locked rotor torque applied to the DLGF ANN as an input parameter is directly associated with the design parameters and the rated power is indirectly associated with the rated torque and rated speed. This shows that the minimum performance requirements in Table 5 are directly associated with the DLGF ANN. On the other hand, we have attempted to evaluate the maximization of the power-to-weight ratio determined as the objective function in Table 4 and the minimum performance requirements needed in the driving cycles (Table 5) in terms of different aspects in

Table 14. Correlation Results of Motor Models Generated from ANN for Traction Motor.

Evaluation in terms of Material and Geometric Dimensions
Parameter	Unit	DLGF 122200-4		DLGF ANN	Improvement
ML	(mm)	194	>	90	53.61%
SOD	(mm)	170	>	155	8.82%
Motor Weight	(kg)	25.86	>	11.11	57.04%
Usage of Stator Core	(kg)	29.7	>	10.63	64.21%
Usage of Rotor Core	(kg)	11.15	>	5.17	53.63%
Design/Usage	(-)	63%	<	70%	11.08%
Evaluation in terms of Objective Function
Parameter	Unit	DLGF 122200-4		DLGF ANN	Improvement
Power-to-Weight Ratio	(Watt/kg)	110.21	<	256.53	132.76%
Evaluation in terms of Minimum Performance Requirement
Parameter	Birim	DLGF 122200-4		DLGF ANN	Improvement
Rated Torque	(Nm)	32.45	>	17.27	46.78%
Locked Torque	(Nm)	29.45	>	24.98	15.18%
Rated Speed	(RPM)	3600	-	3600	-
Maximum Speed	(RPM)	3744	-	3744	-
Rated Power	(Watt)	2850	-	2850	-
Rated Efficiency	(%)	86.15	>	83.9	−2.61%
Maximum Efficiency	(%)	87.59	>	84.13	−3.95%
Evaluation in terms of Driving Cycles (Correlation)
Driving Cycle	Unit	DLGF 122200 -4		DLGF ANN	Improvement
NEDC (Torque–Speed)	(-)	0.12540	<	0.70880	58.34%
NEDC (Power–Speed)	(-)	0.11450	<	0.64660	53.21%
US06 (Torque–Speed)	(-)	0.12710	<	0.72170	59.46%
US06 (Power–Speed)	(-)	0.11020	<	0.61170	50.15%
WLTC (Torque–Speed)	(-)	0.14360	<	0.84860	70.50%
WLTC (Power–Speed)	(-)	0.12970	<	0.78380	65.41%

.

According to the minimum performance requirements, five different engine models of steering motors are generated by the EPAS ANN for the nominal input value and its deviation values of ±25% and ±50%. The generated motor models (Table 11) are run by modeling Ansys RMXprt. The obtained results (Table 13) are examined with nominal, maximum and minimum values on parameters such as torque, speed, speed, power, flux density and material consumption. When the parameters of the motor models generated here (Table 11) are analyzed, it has been observed that the number of motor poles (PN) is a trend towards the number of poles of motor models with a high gear ratio, since the speed parameter, one of the input parameters of the ANN, is relatively small. The group with motor permanent magnets (SS) showed a downward trend with the need to reduce the power. Both the magnet length (PML) and magnet thickness (PMT) were improved by 6% and 6.67%, respectively. The rotor slot (RS) parameter was also associated with an increase in efficiency with the highest slot fill factor by the ANN due to power reduction. On the rotor and commutator (WC), it was observed that the commutator diameter (CD) and commutator length are close to nominal since they had the lowest relationship with the ANN input parameters. Additionally, depending on the torque–power relationship, the number of conductors per slot (SNOS) and the number of wires per conductor (NOS) tended to decrease. The gear ratio also tended to be selected as the highest possible gear ratio by directly matching it with the ANN input parameter. In addition, the nominal efficiency maximization determined as the objective function in Table 4 and the minimum performance requirements needed in driving scenarios (Table 5) have been evaluated in terms of different aspects in

Table 15. Correlation Results of Motor Models Generated from ANN for Steering Motor.

Evaluation in terms of Material and Geometric Dimensions
Parameter	Unit	EPAS01		EPAS ANN	Improvement
ML	(mm)	100	-	100	0%
SOD	(mm)	79	-	79	0%
Motor Weight	(kg)	1.39	<	1.49	−7%
Usage of Permanent Magnet	(kg)	0.416	>	0.374	10%
Evaluation in terms of Objective Function
Parameter	Unit	EPAS01		EPAS ANN	Improvement
Rated Efficiency	(%)	7.75	<	42.87	453.16%
Maximum Efficiency	(%)	68.52	<	76.12	11.09%
Evaluation in terms of Minimum Performance Requirement
Parameter	Unit	EPAS01		EPAS ANN	Improvement
Rated Torque	(Nm)	99.79	>	96.01	3.79%
Locked Torque	(Nm)	110.72	<	192.51	73.87%
Rated Speed	(RPM)	12.07	-	12.07	-
Maximum Speed	(RPM)	132	>	24.07	81.77%
Rated Power	(Watt)	126	>	108	14.29%
Ke (Back EMF)	(V/rad)	0.743	<	4.144	457.74%
Kt (Torque Constant)	(Nm/A)	0.743	<	4.144	457.74%
Maximum Current	(A)	148.86	>	46.63	68.68%
Evaluation in terms of Driving Scenarios (Correlation)
Driving Scenarios	Unit	EPAS01		EPAS ANN	Improvement
DLC (Torque–Speed)	(-)	0.10790	<	0.12740	1.95%
DLC (Power–Speed)	(-)	0.00930	<	0.08850	7.92%
CR (Torque–Speed)	(-)	0.20820	<	0.37480	16.66%
CR (Power–Speed)	(-)	0.09620	<	0.22620	13.00%
SIS (Torque–Speed)	(-)	0.31130	<	0.56460	25.33%
SIS (Power–Speed)	(-)	0.15430	<	0.45270	29.84%

.

The findings show that the DLGF ANN and EPAS ANN models trained for both the traction and steering motors are able to estimate the design parameters quite successfully.

4. Conclusions

In this study, the optimization of the traction and steering motors, which are the motion units of autonomous and electric vehicles, was studied. The DLGF 122200-4 has been successfully modeled in accordance with the parameters given in the technical specifications, with an error rate of 4.97% in the torque–speed characteristic and 6.77% in the power–speed characteristic. The EPAS01 has been successfully modeled in accordance with the parameters given in the technical specifications, with an error rate of 2.23% in the torque–speed characteristic and 2.34% in the power–speed characteristic. Compared with the minimum performance criteria, it was determined that there was an “over-design” of 87.4% for the DLGF 122200-4 and 85.2% for the EPAS01. After training, the achieved performance for the DLGF ANN was observed to be MSE = 1.4396 and R = 0.9362. The achieved performance for the EPAS ANN was observed to be MSE = 1.6276 and R = 0.9124. In the next step, design parameter derivation studies were carried out with the ANN models with acceptable performance. Here, the locked rotor torque of 22.41 Nm and the rated power of 2801 Watt, determined as the minimum performance requirement, were nominally applied to the input of the DLGF ANN. On the other hand, the locked rotor torque of 94.96 Nm and the rated speed of 12.07 RPM were nominally applied to the input of the EPAS ANN. In addition to the nominal values here, five input vectors with ±25% and ±50% deviations of the input values were applied to the ANN models, and the design parameters obtained from the ANN models were remodeled and analyzed in Ansys RMXprt. For the parameters applied to the input of the ANN models, it has been observed that the nominal motor model derived by the DLGF ANN has a deviation performance of 11.4% on the positive side, and the nominal engine model derived by the EPAS ANN has a deviation performance of 1.1% on the positive side. The analyses here also show that ANN models provide a highly successful performance. In addition, power–speed and torque–speed graphs for the motor models obtained as a result of the analysis were evaluated in terms of correlation with the graphs obtained during driving cycles and driving scenarios. The correlation results show that the DLGF ANN model gives better performances with an average of 59.51% and the EPAS ANN model with an average of 15.78%. In line with the findings obtained from the results here, the following inferences can be made.

• It has been observed that drive cycles and driving scenarios can be used not only to measure the dynamic performance and fuel consumption of existing vehicles, but also to calculate the required engine performance requirements.
• It has been observed that the minimum performance requirements determined by driving cycles and scenarios can determine the optimization criteria for an over-qualified motor selected by “over-designing”.
• It has been observed that the ANN is an effective method for estimating design parameters. Further, engine design parameters can be determined successfully in accordance with the performance requirements.
• It has been observed that using the ANN and DoE together not only shortens the training time, but also provides a better performance by training on meaningful data and qualifying the weight values in the ANN with DoE.