Development of an “In-Wheel” Architecture for a Formula SAE Hybrid Car: Electric Motor Design and Transmission Sizing ^†

Abstract

In-wheel motor (IWM) systems enable compact architectures and advanced control strategies, making them increasingly relevant in hybrid and electric vehicle applications. This work presents the design and the integration of a front-axle IWM system for a Formula SAE combustion vehicle, within a parallel hybrid configuration. The study includes vehicle dynamics analysis, battery pack sizing under strict regulatory constraints, and an initial evaluation of motor and transmission requirements. A MATLAB R2023a-based algorithm was developed to design and optimize a compact two-stage planetary gearbox. This structured and scalable approach supports future development phases and offers a valuable methodology for early-stage hybrid powertrain design.

1. Introduction

In recent years, the automotive industry has undergone a profound transformation, commonly referred to as the energy transition. This shift has been driven by growing awareness of environmental concerns and the urgent need to reduce greenhouse gas emissions while improving energy efficiency [1].

Within this framework, electrification has emerged as a particularly promising solution, alongside alternative technologies such as biofuels, synthetic fuels, and hydrogen, as extensively documented in the literature [2,3,4]. Electric and hybrid vehicles, in particular, have taken on a central role in global strategies aimed at decarbonizing the transportation sector [5,6].

The inherent flexibility of electric motors enables the development of a wide range of vehicle architectures. Among them, the in-wheel motor (IWM) configuration [7] has attracted increasing attention due to its advantages in terms of compactness, modularity, improved energy efficiency, and its ability to implement advanced dynamic control strategies—such as torque vectoring—in a more responsive and refined manner compared to conventional layouts [8,9].

In the IWM architecture, the electric motor, and optionally the transmission, is integrated directly within the wheel assembly. This eliminates traditional mechanical components such as the driveshaft and differential, enabling a comprehensive reorganization of the vehicle’s spatial and mechanical layout. However, this configuration also introduces significant challenges, including an increase in unsprung mass and the need for careful integration of components to ensure overall system compatibility and performance.

Although the concept of in-wheel motors is not new to the automotive landscape, with an early example being the Lohner–Porsche at the beginning of the 20th century [10], recent advances in electric motor technologies have renewed interest in this solution. Several manufacturers have recently explored IWM implementations [11]. In the broader automotive industry, interest in in-wheel motor systems is growing. Hyundai Mobis presented the “e-Corner” module at CES 2023, integrating motor, steering, braking, and suspension systems into a single wheel assembly. This concept shows the potential of in-wheel architecture for both motorsport and production vehicles [12]. Companies such as Elaphe have also contributed to the development of in-wheel motor systems through technical studies and real-world applications in road and off-road contexts [13,14,15]. The IWM systems can be implemented either with or without a transmission system. In direct-drive configurations, the absence of a reduction gear simplifies the drivetrain, reduces the number of mechanical components, and lowers internal losses. However, it requires motors capable of delivering high torque at low speeds. This typically necessitates larger electric motors, which in turn require a greater quantity of rare-earth materials for permanent magnets. In contrast, integrating a reduction gear allows the use of a smaller, higher-speed motor, reducing both the mass of the motor and the demand for rare-earth materials, while maintaining the required torque at the wheel. The selection between these approaches is therefore dictated by packaging constraints, performance targets, and resource considerations, making it a critical factor in the overall vehicle architecture design.

The energy transition has also had a significant impact on motorsport, fostering the development of innovative architectures and offering valuable opportunities for experimental validation. In this context, the Formula SAE (Society of Automotive Engineers) competition represents a unique testing ground for emerging technologies. This international academic event involves universities from around the world in the design and development of a single-seater race car, under strict technical regulations [16]. Within these constraints, IWM solutions offer an ideal opportunity to demonstrate their potential.

This work is set within that context and presents a methodological approach for the design and optimization of an IWM system applied to the front axle of a Formula SAE combustion vehicle with rear-wheel drive, thereby realizing a parallel hybrid configuration. The project involved the sizing of the battery pack, the electric motor, and the transmission system, with the aim of delivering high performance while limiting the increase in unsprung mass and ensuring full compliance with both regulatory requirements and design constraints imposed by the existing vehicle layout and components, thus paving the way for future development and validation phases.

2. In-Wheel Motor Technology in Formula SAE

The main goal of the Formula SAE competition is to promote innovation and research in vehicle engineering. The competition is currently divided into two main categories, each defined by specific technical rules based on the powertrain type: the EV class for fully electric vehicles and the CV class for vehicles with internal combustion engines.

In the EV class, the use of in-wheel motors has quickly become widespread. To reduce unsprung mass, most teams adopt radial flux permanent magnet synchronous motors, which provide high power density. A popular configuration includes four independent motors, one per wheel, allowing precise control of traction and vehicle dynamics. Some teams develop their own powertrain systems, while others rely on commercial kits. Among the most commonly used are solutions from AMK-Motion, which offer compact inverters and permanent magnet motors compliant with Formula SAE regulations [17].

The CV class, originally limited to internal combustion vehicles, has recently been updated with new rules allowing electric auxiliary systems [18]. Hybrid setups are now permitted under specific limits, such as a maximum voltage of 60 V and a maximum energy storage active material mass of 3 kg. These changes have encouraged the integration of electric motors into traditional powertrains.

Despite the advantages, in-wheel systems still present key technical challenges. The added unsprung mass may negatively affect vertical dynamics. Effective thermal management is required due to the compact packaging of the motors, and the limited space inside the wheel imposes strict constraints on the mechanical and electrical integration of components.

This study builds upon this context and focuses on the M23-L single-seater developed by the More Modena Racing team (Università degli Studi di Modena e Reggio Emilia, Modena, Italy). The objective is to design a high-performance in-wheel motor system that integrates with the vehicle’s existing geometry and complies fully with Formula SAE regulations.

3. Reference Vehicle and Mechanical Integration Constraints: The M23-L Case

The MoRe Modena Racing team made its debut in the Formula SAE competition during the 2003/2004 season with the M04T, a single-seater powered by an internal combustion engine. Since then, the team has continuously developed and refined each subsystem of the vehicle, keeping pace with evolving technical regulations. Within this framework, reusing existing components whenever possible represents a strategic approach that reduces both costs and development time.

The reference vehicle, M23-L, features a rear-wheel drive layout based on a Suzuki GSXR engine mounted longitudinally. The engine has been modified to reach the maximum allowed displacement of 708 cc and to support bioethanol operation.

The composite chassis is equipped with a double wishbone suspension: a pull-rod at the front and a push-rod at the rear. The wheel assembly includes a 10-inch rim with a tire, brake disc and caliper, wheel hub, upright and bearing. This assembly will serve as the integration platform for the electric motors and reduction gear, forming an in-wheel motor (IWM) system on the front axle and converting the vehicle into a parallel hybrid with all-wheel drive.

To evaluate the mechanical feasibility of this layout, a detailed analysis of the available space within the wheel assembly was carried out. The most critical suspension configuration, in terms of available space, was considered, corresponding to maximum suspension compression and maximum camber angle. The IWM unit is designed to replace the existing upright and the wheel hub and can integrate with the surrounding components, as shown in Figure 1a.

Given the current configuration of the M23-L, characterized by a total mass of approximately 200 kg and a combustion engine output of 90 hp, the in-wheel motor system must be designed in compliance with regulatory, performance, and dimensional constraints. These requirements also include compatibility with the existing components of the reference vehicle, ensuring integration without the need for extensive modifications.

4. System Design and Integration Strategy

The integration of an in-wheel electric drive system on the front axle of the M23-L vehicle was approached through a structured engineering methodology, aimed at achieving a parallel hybrid configuration, as shown in Figure 1b, compatible with the existing vehicle geometry and in accordance with Formula SAE regulations.

The design process (see Figure 2), given the competitive context, begins with the regulatory constraints that define the boundaries for system implementation. It then proceeds with the sizing of the battery pack and with the analysis of the longitudinal dynamics of the reference vehicle. Based on these steps, the sizing of the main components of the in-wheel motor system is carried out. Each design decision was guided by dimensional, regulatory, and functional constraints, with the objective of developing a high-performance and compact system, which is fully integrable within the front wheel assembly of the reference vehicle.

4.1. Preliminary Battery Sizing

The battery is responsible for supplying energy to the in-wheel electric motors and recovering it during braking phases. As previously mentioned, the Formula SAE regulations impose specific constraints on the energy storage system. In particular, the maximum operating voltage is limited to 60 V and the total mass of the active material must not exceed 3 kg [18]. An additional constraint concerns the maximum allowable cell temperature, which is not considered in the current analysis but will be addressed in future studies focusing on battery thermal management.

For this preliminary sizing phase, two commercially available lithium-ion cells were considered: Sony-Murata US18650VTC6 and Molicel INR-21700-P45B. For each cell type, the optimal battery configuration was derived while ensuring full compliance with the regulatory constraints. The results are summarized in

Table 1. Comparison of candidate lithium-ion cells for the energy storage system.

Parameter	Sony-Murata VTC6 18650	Molicel INR 21700-P45B	Unit
Cell mass	46.6	70	g
Nominal cell voltage	3.6	3.6	V
Max cell voltage	4.2	4.2	V
n° cells max	64	42	-
n° cells series	14	14	-
n° cells parallel	4	3	-
n° cells total	56	42	-
Total voltage	58.8	58.8	V
Total mass	2609.6	2940	g
Continuous discharge current	30	45	A
Power	7056	7938	W
Capacity	12	13.5	Ah

, which presents a comparative overview of the two configurations based on the selected cells.

Among the options, the configuration based on Molicel INR-21700-P45B cells emerged as the most suitable for the intended application. The resulting pack consists of a 14s3p arrangement (14 cells in series and three in parallel), comprising a total of 42 cells. This configuration provides a total output power of approximately 8 kW, which corresponds to about 4 kW per motor, neglecting inverter efficiency.

4.2. Longitudinal Dynamics Analysis

This section presents a key phase in the definition of the electric traction system requirements. In order to properly size the electric components of the hybrid powertrain, a set of preliminary considerations on the longitudinal dynamics of the reference vehicle is required, including the maximum attainable speed, the maximum transmittable torque at the ground due to tire grip limits, and the total resistance to motion.

The top speed of the vehicle is constrained by the engine speed limiter and the total gear ratio between the crankshaft and the wheels. These parameters also define the maximum rotational speed that the front electric motor must withstand. Based on the maxi- mum engine speed (12,000 rpm) and the transmission ratio in top-gear (7.45), the wheel speed, and thus the vehicle’s top speed, can be calculated.

The maximum torque that can be transmitted to the ground can be estimated analytically using the equations of longitudinal vehicle dynamics (see Figure 3a,b), which allow for the evaluation of the forces and moments acting along the vehicle’s motion direction. The required torque at the front wheels was estimated under maximum load transfer conditions during acceleration. In this scenario, the IWM system must provide effective traction support without exceeding the available grip, thus avoiding tire slip. This condition defines the upper torque limit for the electric drive system. This condition can be expressed by the following equation:

$${\mathrm{M}}_{\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{n}\mathrm{t} \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{l}}={\displaystyle \frac{1}{2}}·\mathsf{\mu }·\mathrm{r}·\left({\mathrm{F}}_{+\mathrm{x}}-{\mathrm{F}}_{-\mathrm{x}}\right)$$

(1)

where μ is the static friction coefficient between tire and road, r is the radius of the wheel, F_+x represents the total driving forces acting on the vehicle (e.g., traction force), F_−x represents the total resisting forces acting on the vehicle (e.g., aerodynamic drag, rolling resistance) and the factor ½ accounts for the torque distribution between the two front wheels.

To complete the analysis, the vehicle’s resistance-to-motion curve was also considered. This force represents the minimum threshold that must be overcome to maintain motion at a given speed, and it depends on aerodynamic drag, internal friction, and tire–road interaction. Due to the complexity of a full analytical model, this resistance curve was derived experimentally, as shown in Figure 4.

4.3. Preliminary Sizing of the Electric Motor

Once the nominal power available from the battery was defined and the longitudinal vehicle dynamics were analyzed, the electric motor sizing could be addressed. These two analyses provide the torque and speed requirements at the wheel, which represent the foundation for the motor specifications after accounting for the selected transmission ratio. From this process, high power density emerged as the primary requirement, since minimizing both mass and volume is essential for integration within the wheel assembly. Consequently, a Permanent Magnet Synchronous Machine (PMSM) was identified as the most suitable topology.

The mechanical power output of an electric motor is generally expressed as follows:

$$\mathrm{P}=\mathrm{T}·\mathsf{\omega }$$

(2)

where P is power, T is torque, and ω is angular speed. Although power is commonly used to characterize electric machines, torque is the parameter that most directly influences the motor’s size. At constant torque, and thus constant volume, increasing the rotational speed yields higher power output.

For PMSMs, a simplified analytical expression for estimating torque can be given as:

$$\mathrm{T}={\displaystyle \frac{\mathsf{\pi }}{2}}·{\mathrm{D}}^2·\mathrm{L}·\mathrm{A}·\mathrm{B}$$

(3)

where D and L are the diameter and length of the active part of the motor, while A and B are constants that are dependent on electromagnetic material properties and design factors.

Among PMSM topologies, the interior PMSM (IPMSM) was selected because of its intrinsic feature of having a base speed that is approximately one-third of the maximum speed. This characteristic aligns well with the torque requirements at the wheel. The base speed is defined as the nominal speed at which the motor delivers constant torque.

Since the gearbox is developed in parallel with the motor selection, a single, definitive gear ratio cannot be fixed at this stage. To address this, a preliminary assumption can be made by directly relating the base speed of the wheel to one-third of the vehicle’s maximum rotational speed:

$${\mathrm{T}}_{\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{l}}={\displaystyle \frac{{\mathrm{P}}_{\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{y}}}{2·\frac{{\mathsf{\omega }}_{\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{e}\mathrm{l} \mathrm{m}\mathrm{a}\mathrm{x}}}{3}}}$$

(4)

where ω_{wheel max} represents the maximum angular velocity of the wheel at the vehicle’s top speed and P_battery is the total output power of the battery. This simplification enables a first approximation of the torque requirements at the wheel, which can subsequently be converted to motor torque by means of the gear ratio. Consequently, three motor sizes were analyzed, corresponding to transmission ratios of 5, 7.5, and 10. The ratio of 5 represents the lower limit, since further reduction would require an oversized motor incompatible with the wheel assembly. The ratio of 10 represents the upper limit, as higher values would lead to excessive motor speed and mechanical stress. The key results are summarized in

Table 2. Electric motors key parameters.

Parameters	τ = 5	τ = 7.5	τ = 10	Unit
Diameter	95	85	80	mm
Length	46	40	43	mm
Torque	13.76	9.17	6.88	Nm
Max speed	7950	12,150	16,050	rpm
Mass	2.166	1.466	1.371	kg

and Figure 5a.

Once the final motor–gearbox configuration has been selected, a more detailed design and optimization process, potentially including Finite Element Analysis (FEA) of the magnetic and thermal behavior, will be carried out. This advanced design phase is outside the scope of the present work but will be explored in future developments.

4.4. Transmission System Sizing and Design

The gearbox is a key element in the IWM system architecture, as it allows the adaptation of the electric motor’s speed and torque to the values required at the wheel. The need to achieve a high transmission ratio, combined with the constraint of full integration within the wheel assembly, led to the selection of a two-stage compound planetary gearbox, a configuration that is particularly advantageous due to its compactness.

A planetary gear box consists of a sun gear, one or more planet gears, a ring gear, and a rotating carrier. The three main components, sun gear, ring gear, and planet carrier, serve as the kinematic nodes through which mechanical power is transmitted, while the planets connect and transfer motion between them. However, a single stage is insufficient to meet the required reduction. A two-stage compound configuration with rigidly coupled planet gears (as shown in Figure 5b) is therefore adopted: on a single planet carrier, two coaxial planet gears are mounted; one meshes with the sun gear (first stage), and the other with the ring gear (second stage).

To analyze the behavior of the system, Willis’ formula is used, allowing the planetary gear train to be modeled as an equivalent simple gear train.

$${\mathrm{\tau }}_0=-{\displaystyle \frac{{\mathrm{Z}}_{\mathrm{p}1}{\mathrm{Z}}_{\mathrm{r}}}{{\mathrm{Z}}_{\mathrm{s}}{\mathrm{Z}}_{\mathrm{p}2}}}$$

(5)

The total transmission ratio depends on which components are selected as the input, output, and fixed elements. In the specific case of the current wheel group configuration, particularly due to the type of rim and hub employed, the most suitable arrangement is obtained by using the sun gear as the input, the carrier as the output, and the ring gear fixed. In this configuration, the carrier directly constitutes part of the wheel hub, the ring gear is fastened to the upright, and the sun gear acts as the power input from the electric motor. This configuration also corresponds to the one that achieves the highest reduction ratio in a planetary gear train:

$$\mathrm{\tau }=1-{\mathrm{\tau }}_0$$

(6)

To identify the optimal configuration of the two-stage compound planetary gearbox, a MATLAB-based algorithm was developed to systematically explore feasible solutions within the transmission ratio range defined in the previous sections. The algorithm generates all valid gear combinations by varying the number of teeth on the sun, ring, and planets gears. For every configuration, the script verifies compliance with geometric and kinematic constraints, including proper meshing conditions and equally spaced, interference-free planet arrangement. These constraints are defined in accordance with the ANSI/AGMA 6123-C16 standard [19], which governs design practices for planetary gear systems. The script considers only configurations in which the satellites of all pairs are phase-aligned in the same manner. By imposing this constraint, the design ensures uniform angular positioning across the planetary gear set, which significantly simplifies both manufacturing and assembly processes. Additionally, the gear module is varied within a range from 0.6 mm to 1.0 mm, in 0.2 mm steps.

For each gear, the minimum volume required to ensure mechanical strength against pitting and bending fatigue is calculated based on the ISO 6336 standard [20]. These values are then used to estimate the mass of each component in both the first and second stages. Stage combinations that do not satisfy geometric compatibility or assembly constraints are discarded. The Hertzian contact stress, σ_H, and the tooth-bending stress, σ_F, are calculated using the following equations:

$${\mathsf{\sigma }}_{\mathrm{H}}={\mathrm{Z}}_{\mathrm{E}}·{\mathrm{Z}}_{\mathrm{H}}·{\mathrm{Z}}_{\mathsf{\epsilon }}·{\mathrm{Z}}_{\mathsf{\beta }}·\sqrt{{\displaystyle \frac{{\mathrm{F}}_{\mathrm{t}}}{\mathrm{b}·{\mathrm{d}}_{\mathrm{p}}}}·{\displaystyle \frac{\mathrm{u}\pm 1}{\mathrm{u}}}}·\sqrt{{\mathrm{K}}_{\mathrm{A}}·{\mathrm{K}}_{\mathrm{v}}·{\mathrm{K}}_{{\mathrm{H}}_{\mathsf{\alpha }}}·{\mathrm{K}}_{{\mathrm{H}}_{\mathsf{\beta }}}}$$

(7)

$${\mathsf{\sigma }}_{\mathrm{F}}={\mathrm{Y}}_{{\mathrm{F}}_{\mathrm{a}}}·{\mathrm{Y}}_{{\mathrm{S}}_{\mathrm{a}}}·{\mathrm{Y}}_{\mathsf{\epsilon }}·{\mathrm{Y}}_{\mathsf{\beta }}·{\displaystyle \frac{{\mathrm{F}}_{\mathrm{t}}}{\mathrm{b}·\mathrm{m}}}·\left({\mathrm{K}}_{\mathrm{A}}·{\mathrm{K}}_{\mathrm{V}}·{\mathrm{K}}_{{\mathrm{F}}_{\mathsf{\alpha }}}·{\mathrm{K}}_{{\mathrm{F}}_{\mathsf{\beta }}}\right)$$

(8)

In both expressions, F_t is the tangential force acting on the tooth, b is the face width, d_p is the reference diameter of the pinion and m is the module. The coefficient Z and Y represent geometry and load distribution factors, while the K coefficients account for application conditions and dynamic effects, as defined by ISO 6336. This approach enables a reliable preliminary assessment of the mechanical strength of each gear stage, ensuring resistance to both contact fatigue and tooth root-bending stress under expected loading conditions.

For all valid first- and second-stage combinations, the total transmission ratio is computed, considering the sun gear as the input and the carrier as the output. The total gearbox mass is estimated by summing the contributions of the gear wheels and a simplified model of the carrier. The results are filtered based on the allowable transmission ratio range, and the admissible configurations are presented in tabular and graphical form. This automated approach enables rapid identification of feasible designs that align with the packaging constraints of the in-wheel system and are suitable for further detailed design and optimization.

A representative plot of the MATLAB output is presented in Figure 6, illustrating the feasible gear configurations. The plot highlights the distribution of total transmission ratios across the solution space.

5. Optimization of Motor and Gearbox Integration

The optimal transmission ratio is the one that minimizes the total mass of the electric motor–gearbox assembly while also limiting its overall volume. Compactness directly influences the vehicle’s handling and leaves room for future developments. An assembly that reaches the maximum allowable dimensions would not allow for the replacement of the current motor with a more powerful one, which would likely have larger dimensions.

Once the mass trends of the electric motor and the gearbox as functions of the transmission ratio have been determined, the total mass of the assembly can be straightforwardly estimated by summing the two contributions. A graphical representation of the mass trend of both the electric motor and the gearbox as a function of the transmission ratio is shown in Figure 7.

The resulting trend reveals a decrease in the total mass as the transmission ratio increases. This behavior can be attributed to the fact that, for a given power requirement, a higher transmission ratio allows the use of a more compact and lightweight electric motor, while the corresponding mass increase in the gearbox remains relatively moderate. As a result, higher transmission ratios are generally preferable, as long as the design constraints are met. However, the maximum allowable transmission ratio is constrained by the rotational speed limit of the electric motor.

Based on the outcomes of the MATLAB-based gear design algorithm described in the previous section, the gear combination that best approximates the target transmission ratio was selected. The selected configuration satisfies all geometric, kinematic, and assembly requirements. Among the feasible combinations, the most advantageous in terms of weight and compactness includes the following components, detailed in

Table 3. Gearbox specifications.

Gearbox
	Zsun	18
	Zring	99
	Zplanet1	62
	Zplanet2	39
	Modulestage1	0.6
	Modulestage2	0.8
	bstage1 [mm]	8
	bstage2 [mm]	4
	α	25°
	τ	9.74
	Mass [kg]	0.447

and

Table 4. Electric motor specifications.

Electric Motor
	Diameter [mm]	80
	Length [mm]	43
	Torque [Nm]	6.88
	Max speed [rpm]	16050
	Mass [kg]	1.371

:

6. Conclusions

This work has presented the design and integration of an IWM system for the front axle of the M23-L combustion vehicle developed by the MoRe Modena Racing team, in the context of a parallel hybrid architecture compliant with Formula SAE regulations. The study addressed the challenges and opportunities associated with the implementation of IWM systems, highlighting their potential benefits in terms of packaging flexibility, dynamic control, and energy efficiency.

A structured design methodology was adopted, beginning with the sizing of the battery under strict regulatory constraints. Different commercially available lithium-ion cells were compared, and the optimal configuration was identified based on power density and system compliance. The analysis of the vehicle’s longitudinal dynamics was then conducted to derive the torque and speed requirements of the electric motor. An IPMSM was selected as the most suitable motor type, with preliminary sizing performed across a range of gear ratios.

To support the integration of the motor within the wheel assembly, a two-stage compound planetary gearbox was designed using a custom MATLAB-based optimization algorithm. The approach enabled the identification of geometrically feasible gear configurations with minimal mass, ensuring compatibility with both packaging and performance constraints. The final motor–gearbox configuration achieved a high transmission ratio while maintaining compact dimensions and reduced unsprung mass.

The results of this preliminary phase demonstrated the technical feasibility and design potential of implementing a high-performance IWM system in a Formula SAE hybrid vehicle. A first prototype of the proposed in-wheel architecture has been designed and assembled on the Formula SAE vehicle, as shown in Figure 8a,b, marking a significant step toward system validation.

Future work will include both bench and on-road testing to evaluate the dynamic behavior of the in-wheel architecture and to verify its performance and reliability under real operating conditions.

Beyond the competition context, the proposed methodology can be extended to road-going vehicles, from compact city cars to high-performance sports cars, thereby offering a versatile framework for future developments in electric and hybrid powertrain design.