With the rapid development of the economy and technology, cars have become common household transportation tools, and their social ownership is increasing year by year. The growing number of internal combustion engine vehicles has led to significant environmental pressure from exhaust emissions. The combustion of gasoline releases large amounts of carbon dioxide, and incomplete combustion produces harmful substances such as sulfur dioxide, carbon monoxide, and nitrogen oxides, which pose serious threats to human health. In contrast, electric cars offer advantages such as zero emissions, low noise, and simple structure, attracting global attention. However, challenges like insufficient charging infrastructure, low battery efficiency, and short driving range severely limit the development of electric cars. Expanding the application of electric cars and enhancing their driving range are current research hotspots in the electric vehicle field.
Research indicates that during urban driving conditions, approximately one-third to one-half of the energy is consumed in the braking process, where kinetic energy is converted into heat through friction and dissipated into the atmosphere. Electric cars can convert the motor into a generator during braking, recovering part of the kinetic energy and transforming it into electrical energy for storage. This energy conversion method not only dissipates kinetic energy to achieve braking but also enables electrical energy regeneration, thereby increasing the driving range of electric cars.
In recent years, universities, research institutions, and major electric car manufacturers worldwide have conducted specialized research on regenerative braking energy recovery for electric cars, achieving some results. For instance, some studies have designed electro-hydraulic composite braking systems and proposed braking force distribution strategies based on braking states, resulting in high braking energy recovery efficiency. Others have analyzed the regenerative braking principles of brushless DC motors and proposed fuzzy neural network control algorithms for regenerative braking in electric cars, achieving energy recovery rates of up to 14.5% through designed controllers. To address the conflict between braking stability and braking energy recovery, some researchers have established braking force distribution models based on the I-curve and proposed dual electro-hydraulic regenerative braking control methods, validated through experiments. Additionally, after analyzing the influencing factors during regenerative braking in electric cars, optimization schemes for braking force distribution have been proposed with braking stability and braking energy recovery efficiency as optimization goals under multiple constraints, with simulation results showing improved regenerative braking energy recovery efficiency. Studies on in-wheel motor characteristics have led to regenerative braking fuzzy control strategies referencing vehicle speed and braking intensity, enhancing braking energy recovery efficiency. Furthermore, fuzzy controllers have been designed with input variables such as battery state of charge, vehicle speed, and braking intensity, and output as braking force distribution, with simulations verifying controller effectiveness. Although extensive research has been conducted on motor braking energy recovery, most studies remain at the theoretical and experimental simulation stages, with few implemented in mass production. Therefore, it is necessary to research more scientific, reliable, and applicable control strategies for braking energy recovery.
From the perspective of improving braking energy recovery in electric cars, this study takes a front-wheel-drive pure electric car as the research object. We design a fuzzy control system with input parameters such as vehicle speed, braking intensity, battery state of charge, and steering wheel angle during braking. Based on the ideal braking force curve, ECE regulation curve, and f-curve, braking force distribution rules are formulated to maximize motor regenerative braking force. To ensure the safety of motor braking, an additional resistor is proposed to dissipate excessive current generated during regenerative braking, ensuring maximum motor participation in braking. Finally, simulation verifies the model’s effectiveness.
In this study, we focus on a pure electric car equipped with a nickel-metal hydride battery and a permanent magnet synchronous motor. The relevant parameters of the electric car are summarized in Table 1.
| Vehicle Parameter | Value |
|---|---|
| Full-load mass (kg) | 1900 |
| Curb mass (kg) | 1500 |
| Wheelbase (mm) | 2675 |
| Wheel rolling radius (mm) | 307 |
| Transmission ratio | 8.28 |
| Battery rated voltage (V) | 326 |
| Battery charging current (A) | ≤ 250 |
| Maximum current charging duration (s) | ≤ 60 |
| Motor base speed (r/min) | 4000 |
| Maximum speed (r/min) | 11500 |
| Rated torque (Nm) | 150 |
| Maximum torque (Nm) | 210 |
The braking system of the front-wheel-drive pure electric car is the research foundation. During braking, the hydraulic braking control unit collects signals such as brake pedal opening, wheel speed, and steering wheel angle, transmitting these signals to the vehicle controller via CAN bus. The vehicle controller then issues braking force distribution information to the motor controller and braking controller based on the current vehicle state. The motor controller controls the motor to transmit braking torque to the drive wheels through the transmission, main reducer, and differential. The braking controller sends hydraulic braking signals to the hydraulic regulation unit, which performs hydraulic braking on all four wheels, adjusting the hydraulic braking force to meet the total braking demand along with the motor braking force.
For the regenerative braking control strategy, we consider vehicle speed, braking intensity, battery state of charge, and steering wheel angle as input variables. After calculation by the controller, output includes motor braking torque, front axle braking torque, and rear axle braking torque. When braking intensity is low, regenerative braking via the motor is utilized. For higher braking intensity, coupling braking with motor regenerative braking and hydraulic braking is employed. During emergency braking, to ensure safe braking distance, only the hydraulic system participates in braking. Considering that the current generated during motor regenerative braking may exceed the maximum allowable charging current of the battery, a shunt resistor is incorporated. When the regenerative braking current exceeds a set value, the shunt resistor activates; otherwise, it remains inactive. Additionally, when the battery state of charge exceeds a threshold, electrical energy from regenerative braking can be dissipated via the additional resistor. During turning braking, to ensure braking performance and directional stability, motor braking is disabled, and only hydraulic braking is applied.
To maximize braking energy recovery while ensuring braking safety, braking force distribution should satisfy the region bounded by the I-curve (ideal braking force distribution curve), ECE regulation curve, and f-curve (braking force distribution curve when the front wheels are locked and rear wheels are not). This region is divided based on braking intensity to prioritize front axle braking for enhanced energy recovery. The distribution rules are as follows:
For region OA with braking intensity Z ≤ 0.2, the required braking force is small. The motor provides braking force to the front wheels, while the rear wheels do not participate. Considering low regenerative braking efficiency at low speeds, a minimum speed limit is set: when speed is below 10 km/h, front axle braking is provided by the hydraulic system, and the regenerative braking system is inactive. The braking force distribution is:
$$F_f = F_{sf} + F_{bf}, \quad F_r = 0$$
where $F_f$ is the braking force provided by the front axle, $F_{sf}$ is the motor regenerative braking force on the front axle, $F_{bf}$ is the hydraulic braking force on the front axle, and $F_r$ is the hydraulic braking force on the rear axle. When speed < 10 km/h, $F_{sf} = 0$; when speed ≥ 10 km/h, $F_{bf} = 0$.
For region AB with 0.2 < Z ≤ 0.55, to ensure braking stability, coordinated braking with hydraulic and motor regenerative braking is required. To obtain maximum motor braking force, front axle braking force is prioritized. The distribution follows the ECE regulation curve in segment AB, given by:
$$F_f = \frac{Z + 0.07}{0.85} \cdot \frac{b + Z h_g}{L} \cdot mg, \quad F_r = \frac{Z + 0.07}{0.85} \cdot \frac{a – Z h_g}{L} \cdot mg$$
where $b$ is the distance from the center of gravity to the rear axle, $h_g$ is the height of the center of gravity, $L$ is the wheelbase, $m$ is the vehicle mass, and $g$ is gravitational acceleration.
For region BC with 0.55 < Z ≤ 0.7, the vehicle undergoes emergency braking with high intensity. To ensure braking effectiveness, distribution follows the f-curve:
$$F_f = \frac{b + Z h_g}{L} \cdot mg, \quad F_r = \frac{a – Z h_g}{L} \cdot mg$$
where $a$ is the distance from the center of gravity to the front axle.
For region C with Z > 0.7, the vehicle is in high-intensity braking. Priority is given to braking safety, so motor regenerative braking is deactivated. Braking force follows the ideal curve for simultaneous locking of front and rear wheels:
$$F_f = \frac{b + \varphi h_g}{L} \cdot mg, \quad F_r = \frac{a – \varphi h_g}{L} \cdot mg$$
where $\varphi$ is the road adhesion coefficient.
Based on experimental data from typical braking scenarios, the relationships between motor braking force, front axle hydraulic braking force, and rear axle hydraulic braking force are illustrated in Table 2.
| Region | Braking Intensity Z | Motor Braking Force | Front Axle Hydraulic Force | Rear Axle Hydraulic Force |
|---|---|---|---|---|
| OA | Z ≤ 0.2 | Maximum | Zero (if speed ≥ 10 km/h) | Zero |
| AB | 0.2 < Z ≤ 0.55 | High | Zero | Moderate |
| BC | 0.55 < Z ≤ 0.7 | Constant power | Low | High |
| CD | Z > 0.7 (initial) | Constant torque | Increasing | High |
| DE | Z > 0.7 (final) | Decreasing to zero | Maximum | Maximum |
For hydraulic control strategy, during turning braking, motor braking is disabled to ensure stability, and hydraulic braking provides all necessary force. During straight-line braking, the hydraulic system assesses vehicle speed, braking intensity, and wheel angular velocity to determine wheel lock-up and slip ratio, providing hydraulic braking for optimal performance.
The coordination control strategy involves conditional checks for motor braking activation. Motor braking is enabled when vehicle speed exceeds a set value, braking intensity is above a threshold, and the vehicle is in straight-line braking. Otherwise, it is disabled. The logic is summarized as: if speed ≥ 10 km/h, Z > 0, and steering wheel angle ≈ 0, then motor braking is active; else, hydraulic braking only.
To maximize motor regenerative braking force, a fuzzy control algorithm is employed for braking force distribution. Given the multiple influencing factors without clear mathematical models, fuzzy mathematics is suitable. Fuzzy subsets are defined for vehicle speed: {Low, Medium, High} with universe [0, 120] km/h; braking intensity: {Low, Medium, High} with universe [0, 1]; battery state of charge: {Low, Medium, High} with universe [0, 1]. Membership functions use triangular and bilateral Gaussian types. The fuzzy rules are designed to output braking force distribution coefficients, optimizing energy recovery while ensuring safety. The fuzzy inference process is based on Mamdani-type rules, such as: if speed is High and braking intensity is Medium and state of charge is Medium, then motor braking force is High. Defuzzification uses the centroid method to obtain crisp values.
Simulations are conducted for a vehicle speed of 100 km/h, road adhesion coefficient of 0.85, initial battery state of charge of 70%, and straight-line braking. Different braking intensities and same braking intensity scenarios are analyzed for braking energy recovery.
For varying braking intensities, as shown in Figure 4 (simulated data), under identical external conditions, increasing braking intensity shortens the time to stop. Air resistance decreases rapidly with speed, and braking energy increases. As braking intensity rises, motor braking gradually phases out for safety, with hydraulic braking taking over. When motor braking is fully active, recoverable braking energy is high; as intensity increases, motor contribution decreases, reducing recoverable energy. The energy metrics are calculated as:
$$E_{total} = \int F_{total} \cdot v \, dt, \quad E_{regen} = \int F_{motor} \cdot v \cdot \eta \, dt$$
where $E_{total}$ is total braking energy, $F_{total}$ is total braking force, $v$ is vehicle speed, $E_{regen}$ is recoverable energy, $F_{motor}$ is motor braking force, and $\eta$ is conversion efficiency.
For a braking intensity of 0.65, the distribution of motor braking force and hydraulic braking forces on front and rear axles is simulated. As speed decreases, motor braking torque increases rapidly. Within a certain speed range, motor braking torque stabilizes slightly as speed drops. Upon further speed reduction, motor braking force diminishes until zero. Both front and rear axle hydraulic systems participate in braking. The distribution adheres to the rules, with actual braking force fluctuating within theoretical limits, meeting requirements. The forces are expressed as:
$$F_{motor} = f(v, Z, SOC), \quad F_{hydraulic,front} = g(Z, v), \quad F_{hydraulic,rear} = h(Z, v)$$
where $SOC$ is battery state of charge.
Regarding battery state of charge, as driving distance increases, battery charge decreases. The electric car with the proposed regenerative braking system maintains a higher state of charge over time compared to without the system, demonstrating improved energy efficiency. The state of charge dynamics are modeled as:
$$SOC(t) = SOC_0 – \frac{1}{Q} \int I_{discharge} \, dt + \frac{1}{Q} \int I_{regen} \, dt$$
where $SOC_0$ is initial state of charge, $Q$ is battery capacity, $I_{discharge}$ is discharge current, and $I_{regen}$ is regenerative charging current.
In conclusion, this study formulates optimal braking curve distribution standards based on the ideal braking curve, ECE regulation curve, and f-curve, maximizing braking energy recovery for electric cars. To ensure motor braking safety, when battery state of charge exceeds a threshold, electrical energy from regenerative braking is dissipated via an additional resistor, enabling maximum motor participation and extending hydraulic braking system lifespan. For turning safety, hydraulic braking is used exclusively. During emergency braking, hydraulic braking provides all force. Simulations validate the model’s effectiveness. Future work could involve real-world testing and integration with advanced driver-assistance systems for broader applications in electric cars.
The proposed strategy enhances the sustainability and performance of electric cars, contributing to reduced energy consumption and extended range. By optimizing regenerative braking, electric cars can better meet consumer needs and environmental goals. Further research may explore adaptive fuzzy controls or machine learning techniques to refine distribution under diverse driving conditions for electric cars.