As a typical representative of clean energy transportation, the pure electric car has become a strategic focus for governments and automobile manufacturers worldwide due to its zero-emission characteristics, efficient energy conversion, and superior NVH performance. However, the limited driving range remains a critical obstacle to wider adoption. In my research, I deeply investigated how the introduction of a two-speed automated manual transmission (AMT) into a pure electric car could improve energy efficiency and dynamic performance. By carrying out a systematic study that couples powertrain parameter matching, multi-objective optimization, and adaptive shifting control, I sought to unlock the full potential of an electric car’s drivetrain. This paper is written from my personal perspective and covers the complete process of modeling, optimizing, and validating a two-speed AMT for a pure electric car.
The work begins with a critical review of the existing literature on electric car transmissions. I noticed that most current pure electric cars adopt fixed-speed reducers, which cannot simultaneously satisfy the demanding torque requirement at launch and the high speed requirement on highways. Many researchers have suggested that adding a second gear can bring substantial benefits. Compared with three-speed or higher transmissions, the two-speed configuration offers the best trade-off between cost, complexity, and efficiency gain. Among various technologies, AMT has advantages in simplicity, efficiency, and low manufacturing cost, especially for city cars. Therefore, I selected a two-speed AMT as the core transmission solution for the studied electric car.
The research follows a structured path. First, the complete drivetrain architecture is defined and the driving dynamics of the electric car are analyzed. Second, key components such as the traction motor, power battery, and transmission ratios are matched according to the design targets. Third, a high-fidelity model of the electric car is built in AVL Cruise software and verified against typical scenarios. Fourth, the final drive ratios are optimized using a multi-objective genetic algorithm through an integration of Isight and Cruise. Finally, an adaptive two-level fuzzy three-parameter shifting strategy is designed in Matlab/Simulink and evaluated in the co-simulation environment. The results prove that the optimized powertrain can significantly improve the comprehensive performance of the electric car.
Architecture and Dynamic Analysis of the Electric Car Drivetrain
When building an electric car with a two-speed transmission, the overall layout must be selected first. In my work, I considered centralized and distributed drive systems. The distributed drive layouts, such as in-wheel motor drives, offer high control flexibility but suffer from high cost, cooling issues, and limited wheel space. For a practical electric car, the centralized drive layout, especially the traditional central motor arrangement, is more mature and cost-effective. I therefore decided to use a central permanent-magnet synchronous motor (PMSM) connected to a two-speed AMT, and the output shaft of the AMT is connected to the drive wheels through a differential.
In the powertrain design, the following components are modeled: the vehicle, the battery pack, the traction motor, the transmission, the final drive, the differential, and the wheels. The main design parameters of the reference electric car are listed in Table 1. These values are used as the baseline for all subsequent calculations.
| Parameter | Symbol | Value |
|---|---|---|
| Curb mass (kg) | m | 1975 |
| Gross mass (kg) | M | 2375 |
| Frontal area (m²) | A | 2.9 |
| Drag coefficient | CD | 0.205 |
| Rolling resistance coefficient | f | 0.015 |
| Gravity acceleration (m/s²) | g | 9.8 |
| Mechanical efficiency | ηT | 0.92 |
| Wheel radius (mm) | r | 354 |
The tractive force required to drive the electric car is the sum of rolling resistance, air resistance, gradient resistance, and acceleration resistance. The fundamental equilibrium equation for a moving electric car is
$$m g f \cos\alpha + \frac{C_D A v^2}{21.15} + m g \sin\alpha + \delta m \frac{dv}{dt} = \frac{T_q i_g i_0 \eta_T}{r},$$
where \(T_q\) is the motor torque, \(i_g\) is the transmission gear ratio, \(i_0\) is the final drive ratio, \(\delta\) is the rotational mass conversion coefficient, and \(\alpha\) is the road gradient. In this study, I used several indicators to assess the performance of the electric car. Dynamic performance indicators include the maximum speed, maximum gradient, and acceleration time from standstill to 100 km/h. Economic performance indicators include the energy consumption per 100 km under specific driving cycles and the corresponding driving range. The design targets for the electric car are listed in Table 2.
| Performance indicator | Design target |
|---|---|
| 0–100 km/h acceleration time (s) | ≤ 7 |
| Maximum gradient (%) | ≥ 30 |
| Maximum speed (km/h) | ≥ 200 |
| Energy consumption under CLTC (kW·h/100 km) | ≤ 16 |
| Driving range (km) | ≥ 605 |
Component Sizing and Parameter Matching for the Electric Car
Proper matching of the traction motor, battery pack, and transmission ratios is the foundation for meeting the design targets. In this section, I address the selection of each component for the electric car.
Determination of Motor Parameters
I compared various motor technologies, including DC motors, asynchronous motors, switched reluctance motors, and permanent-magnet synchronous motors (PMSM). The PMSM offers the highest power density, high efficiency over a wide speed range, low noise, and excellent controllability, making it the dominant choice in modern electric cars. Given abundant rare-earth resources in my country, I chose the PMSM for the electric car.
The peak power of the motor must satisfy three critical driving conditions: maximum speed, maximum gradient, and acceleration. The required power for the maximum speed condition is
$$P_{v,\max} = \frac{1}{3600\eta_T} \left(m g f v_{\max} + \frac{C_D A v_{\max}^3}{21.15}\right),$$
where \(v_{\max}\) is the highest vehicle velocity. For the maximum gradient, I take a climbing speed of 30 km/h and calculate
$$P_{\alpha,\max} = \frac{1}{3600\eta_T}\left(m g f v_\alpha \cos\alpha_{\max} + m g v_\alpha \sin\alpha_{\max} + \frac{C_D A v_\alpha^3}{21.15}\right).$$
The required power for acceleration from 0 to 100 km/h is derived from the instantaneous energy balance. The calculations yield \(P_{v,\max}=86.32\) kW, \(P_{\alpha,\max}=63.14\) kW, and \(P_{t,\max}=146.27\) kW. After reserving some backup power, I selected a peak power \(P_{\max}=150\) kW. With an overload factor of 2.5, the rated power is 60 kW. The rated speed is set to 4340 r/min and the maximum speed to 10,000 r/min, corresponding to a constant-power speed ratio of 2.3. The corresponding rated torque is 145 N·m and the peak torque is 330 N·m. The complete specification of the matched motor is given in Table 3.
| Parameter | Value |
|---|---|
| Motor type | Permanent-magnet synchronous motor |
| Peak power (kW) | 150 |
| Rated power (kW) | 60 |
| Maximum speed (r/min) | 10000 |
| Rated speed (r/min) | 4340 |
| Peak torque (N·m) | 330 |
| Rated torque (N·m) | 145 |
Battery System Sizing
The battery is the energy reservoir of the electric car. I compared five mainstream battery types: lead-acid, nickel-cadmium, nickel-metal hydride, lithium iron phosphate, and ternary lithium. The lithium iron phosphate battery offers good safety, long cycle life, low environmental pollution, and high rate discharge capability. Thus, I chose this type for the electric car.
In sizing the battery, I first set the nominal voltage to 320 V. Using the required driving range of 605 km and a constant-speed condition at 60 km/h, the total needed energy is computed by the energy balance equation:
$$P_{et} = \frac{1}{3600\eta_m \eta_b \eta_T}\left(m g f v_{et} + \frac{C_D A v_{et}^3}{21.15}\right),$$
and the required battery energy \(W_{et} = P_{et} L / v_{et}\). With motor and battery efficiencies \(\eta_m=\eta_b=0.95\), the computation gives \(W_{et}=82.18\) kW·h. The number of cells is found from the nominal cell voltage and capacity. I set the capacity of a single cell to 10 A·h and the cell voltage to 3.2 V. Allowing for a discharge depth of 80%, the total number of cells is calculated as \(N=3300\). They are arranged as 100 cells in series and 33 cells in parallel. Table 4 summarizes the battery parameters.
| Parameter | Value |
|---|---|
| Battery type | Lithium iron phosphate |
| Nominal voltage (V) | 320 |
| Total energy (kW·h) | 82.18 |
| Single-cell voltage (V) | 3.2 |
| Single-cell capacity (A·h) | 10 |
| Series–parallel configuration | 100 serial, 33 parallel |
Transmission Ratio Matching
The gear ratios of the two-speed AMT must be chosen to satisfy both traction and speed requirements. The first gear ratio should provide enough wheel torque for hill climbing and acceleration. The upper limit is determined by the road adhesion condition, while the lower limit is set by the gradient requirement. For the second gear, its upper limit is determined by the maximum speed and motor maximum speed, and its lower limit is determined by the power needed to overcome resistance at the maximum speed. For the selected motor and vehicle parameters, I obtained the following permissible range for the total drive ratio (gear ratio multiplied by final drive ratio):
$$8.098 \le i_1 i_0 \le 11.641, \quad 4.461 \le i_2 i_0 \le 6.673.$$
Additionally, the consecutive ratio gap should lie between 1.2 and 1.8 to ensure smooth shifting. Based on these criteria, I initially chose total ratios of 9.3 for first gear and 5.4 for second gear. This choice gives the electric car adequate hill-climbing ability and a top speed above 200 km/h.
Simulation Model and Multi-Objective Optimization
To verify and further optimize the matched powertrain, I constructed a high-fidelity simulation model in AVL Cruise. The model includes all vehicle components: battery, motor, two-speed AMT, final drive, differential, wheels, brakes, and vehicle body. The mechanical connections are represented by blue lines and the electrical connections by red lines. A dedicated gearbox control program was initially set to shift at 70 km/h (upshift) and 65 km/h (downshift) so that the model could run in a reasonable way. I then created several simulation tasks: a CLTC driving cycle, a constant-speed 100 km/h cycle, a full-load performance task, a maximum-speed task, and a gradient task.
The simulation results of the baseline model are presented in Table 5. The CLTC-consumption is 15.94 kW·h/100 km, giving a range of 647 km, which is above the target of 605 km. The 100 km/h constant-speed consumption is 10.77 kW·h/100 km. The 0–100 km/h acceleration time is exactly 7 s, the maximum gradient is 42%, and the maximum speed is 223 km/h. I verified the model fidelity by confirming that the simulated vehicle speed closely follows the required speed profile within the allowable deviation.
| Performance indicator | Design target | Simulation result |
|---|---|---|
| CLTC energy consumption (kW·h/100 km) | ≤ 16 | 15.94 |
| Driving range (km) | ≥ 605 | 647 |
| 0–100 km/h acceleration time (s) | ≤ 7 | 7.0 |
| Maximum speed (km/h) | ≥ 200 | 223 |
| Maximum gradient (%) | ≥ 30 | 42 |
Co-Simulation Setup with Isight
After confirming that the baseline configuration is feasible, I optimized the two gear ratios using a multi-objective genetic algorithm. I integrated AVL Cruise with Isight optimization software through the Simcode component. In this co-simulation environment, Isight sends the gear ratio values to the Cruise model, runs the simulation, and then extracts the energy consumption and performance metrics. The optimizer module controls the process, and a calculator block handles any algebraic relations.
The NSGA-II (Non-dominated Sorting Genetic Algorithm II) was selected because of its fast non-dominated sorting, elitist strategy, and diversity preservation. It aims to find a Pareto-optimal set in a multi-objective problem. The design variables are the total gear ratios of the two-speed AMT:
$$\mathbf{x} = [i_{g1}, i_{g2}]^T.$$
I define the objective function as the weighted sum of the energy consumption per 100 km under two typical conditions:
$$\min f(\mathbf{x}) = \omega_1 Q_1(\mathbf{x}) + \omega_2 Q_2(\mathbf{x}),$$
where \(Q_1\) and \(Q_2\) are respectively the energy consumptions under the CLTC cycle and the 100 km/h constant-speed cycle, and \(\omega_1,\omega_2\) are weights. In my optimization, these weights are chosen to emphasize the overall economy performance of the electric car. The dynamic requirements are imposed as constraints: the maximum speed must not be lower than 120 km/h, the gradient at 30 km/h must not be less than 30%, and the acceleration time to 100 km/h must be no more than 7 s. The gear ratio boundaries from the matching calculation are also included, along with the constraint that the consecutive ratio gap remains between 1.2 and 1.8.
Optimization Results
After running the iterative algorithm, I obtained the optimized total gear ratios: first gear \(i_{g1}=10.56\) and second gear \(i_{g2}=6.0\). The optimizer converged to this solution after numerous evaluations, and the results are compared with the initial baseline in Table 6. From the comparison, the optimized electric car consumes 15.88 kW·h/100 km in the CLTC cycle and 10.71 kW·h/100 km at a constant speed of 100 km/h, both slightly lower than the initial values. The maximum gradient improves from 42% to 49%, and the acceleration time drops from 7.0 s to 6.65 s. The top speed decreases from 223 km/h to 201 km/h, but it remains above the required 200 km/h. Thus, the overall performance of the electric car is improved: its economic performance is enhanced, and its power performance is strengthened except for the negligible speed reduction that still satisfies the design requirement.
| Parameter | Initial | Optimized |
|---|---|---|
| First gear total ratio | 9.3 | 10.56 |
| Second gear total ratio | 5.4 | 6.0 |
| Maximum gradient (%) | 42 | 49 |
| 0–100 km/h acceleration time (s) | 7.0 | 6.65 |
| Maximum speed (km/h) | 223 | 201 |
| CLTC energy consumption (kW·h/100 km) | 15.94 | 15.88 |
| 100 km/h constant-speed energy consumption (kW·h/100 km) | 10.77 | 10.71 |
Adaptive Shifting Strategy for the Electric Car
The optimized gear ratios are fundamental but not sufficient to ensure the best performance in every scenario. The shifting strategy determines when the electric car will switch between first and second gear. Conventional two-parameter shifting laws use vehicle speed and accelerator pedal opening as inputs, while the driver’s intention is often reflected by the rate of change of the accelerator pedal. My goal was to develop a robust shifting controller that combines driver intention with the current vehicle state and ensures that the gear shifts occur in the proper speed window.
Traditional Two-Parameter Shift Laws
I first formulated the conventional economy-oriented and power-oriented shift schedules. In the economy-oriented schedule, the gear shift points are chosen to maximize the motor’s operating efficiency. Using the motor efficiency map, I calculated the motor efficiency for each gear at different accelerating pedal openings, with the battery state of charge (SOC) fixed at 0.8. The upshift point for a given accelerator opening is the intersection of the efficiency curves of the first and second gears, beyond which the second gear gives higher motor efficiency. By fitting these points, I obtained the economic upshift curve. For the downshift curve, I followed the convergent principle and used a speed difference of 2–8 km/h to avoid cyclic shifting. The resulting economy-oriented shift diagram is shown with two curves.
The power-oriented schedule is based on the acceleration capability of the electric car. I plotted the vehicle acceleration versus speed for both gears at each accelerator opening, also at SOC = 0.8. The best power upshift point occurs when the acceleration of the first gear equals that of the second gear. After fitting the upshift curve, I designed the downshift curve with a speed hysteresis of 5 km/h. The power-oriented shift diagram is then established.
Deriving the Optimal Performance Shift Interval
Both the economy-oriented and power-oriented schedules indicate that, for the given electric car, the admissible shifting speed range is roughly between 70 and 90 km/h. Below this interval, the first gear has higher motor efficiency and higher acceleration than the second gear, so shifting would be unfavorable. Above this interval, the second gear becomes clearly superior. This interval forms the basis of my adaptive controller: whenever the vehicle speed is outside this range, the gear is explicitly set to 1 or 2, whereas within this interval, the actual shift is determined by the driver’s intention and the rate of speed change.
Fuzzy Inference System for the Two-Level Controller
My adaptive shifting controller uses a Takagi–Sugeno (T–S) fuzzy inference engine. The overall structure has two cascaded fuzzy modules. The first module recognizes the driver’s intention from the accelerator pedal opening (APO) and its rate of change. The second module combines the driver’s intention output with the current vehicle speed to determine a fuzzy gear value. Finally, a Stateflow model transforms the fuzzy gear value into a discrete gear command with hysteresis to prevent frequent shifting.
I selected the accelerator pedal opening as a crisp value between 0 and 1, with fuzzy subsets: [small], [medium], [large]. The pedal opening rate of change is in the interval [−1,1] and is classified as [negative], [zero], [positive]. The output of the first fuzzy module is the driver’s intention, a continuous number between 0 and 1, with fuzzy categories: [very slow down], [slow down], [maintain], [speed up], and [very speed up]. The membership functions were chosen as triangular for the pedal opening and π-shaped for the rate of change.
The fuzzy rules for driver intention recognition follow common driving logic. For instance, if the pedal is small and the rate is negative, the driver wants to decelerate; if the pedal is large and the rate is positive, the intention is very strong acceleration. I designed the rule table shown in Table 7.
| Pedal opening | Pedal rate | Driver intention |
|---|---|---|
| small | negative | very slow down |
| small | zero | slow down |
| small | positive | speed up |
| medium | negative | slow down |
| medium | zero | maintain |
| medium | positive | very speed up |
| large | negative | slow down |
| large | zero | speed up |
| large | positive | very speed up |
Since the output of the first fuzzy system is a crisp numerical value representing the driver’s intention, I fed it directly into the second fuzzy module together with the current vehicle speed. The vehicle speed is first limited to the admissible shifting interval between 70 and 90 km/h. Seven fuzzy sets are used for speed: very low, low, slightly low, medium, slightly high, high, and very high. The membership functions are Gaussian. The fuzzy output is a continuous value between 1 and 2, representing the desired gear number in a fuzzy sense. The fuzzy gear rules are collected in Table 8, where the rows denote the driver intention and the columns denote the speed category. The output rule indicates how close the gear should be to 1 or 2.
| Driver intention | very low | low | slightly low | medium | slightly high | high | very high |
|---|---|---|---|---|---|---|---|
| very slow down | 1 | 1 | 1.6 | 2 | 2 | 2 | 2 |
| slow down | 1 | 1 | 1.6 | 1.8 | 2 | 2 | 2 |
| maintain | 1 | 1 | 1.4 | 1.8 | 2 | 2 | 2 |
| speed up | 1 | 1 | 1.4 | 1.8 | 1.8 | 2 | 2 |
| very speed up | 1 | 1 | 1.2 | 1.6 | 1.8 | 2 | 2 |
After the two fuzzy modules produce a fuzzy gear value, the Stateflow logic is used to decide the final gear command. The fuzzy gear value is considered as the desired gear in a continuous sense. If the value is below 1.5, the controller tends to keep first gear; if above 1.5, it tends to use second gear. However, to prevent frequent shifting, the value must remain on one side of the threshold for at least two seconds before the gear command actually changes. This simple hysteresis rule effectively reduces unnecessary shifts while maintaining responsiveness to genuine driver requests. The entire adaptive shifting model is built in Simulink as a compiled DLL file that is integrated into the Cruise simulation through the Matlab DLL interface.
Evaluation of the Adaptive Shift Controller
For verification, I compared the proposed adaptive fuzzy shifting strategy with a conventional three-parameter fuzzy shifting strategy. The conventional strategy also employs accelerator pedal opening and its rate of change as inputs, but it uses the actual vehicle speed without any interval restriction. I ran simulations under both the CLTC and NEDC driving cycles. The key metrics are the shifting frequency and the battery SOC consumption during a single cycle. Figure presents the results of the CLTC cycle. The proposed adaptive controller reduces the number of gear changes from 28 to 6 in the CLTC cycle and from 10 to 2 in the NEDC cycle. The SOC drop slightly decreases from 2.11% to 2.10% in the CLTC cycle and from 1.34% to 1.32% in the NEDC cycle.
| Driving cycle | Strategy | Number of gear shifts | SOC drop (%) |
|---|---|---|---|
| CLTC | Conventional fuzzy | 28 | 2.11 |
| CLTC | Adaptive fuzzy (proposed) | 6 | 2.10 |
| NEDC | Conventional fuzzy | 10 | 1.34 |
| NEDC | Adaptive fuzzy (proposed) | 2 | 1.32 |
The results clearly show that my adaptive controller is effective. The CLTC cycle is characterized by frequent speed variations, and the conventional fuzzy controller often triggers unnecessary shifts that can degrade drivability and increase energy loss. By restricting the shift operation to the optimal speed interval, my controller avoids operating the electric car in conditions where a gear change would be counterproductive. The small reduction in SOC consumption confirms that fewer gear shifts also help to maintain better energy efficiency. In the NEDC cycle, where the speed profile is smoother, the proposed method still reduces shifting counts because it waits for a consistent driver command before executing the shift.
Conclusions and Perspectives
In this research, I have thoroughly investigated the design, optimization, and control of a two-speed AMT for a pure electric car. First, I established a comprehensive simulation model in AVL Cruise and matched the key powertrain components, including the PMSM, lithium iron phosphate battery, and the gear ratios. The baseline simulation confirmed that the electric car satisfies its design targets. Then, using a multi-objective genetic algorithm integrated with Cruise, I optimized the total gear ratios to improve the overall economy while guaranteeing dynamic performance. The optimized ratios, 10.56 and 6.0, result in lower energy consumption under both the CLTC and constant-speed conditions, faster acceleration, and a higher maximum gradient than the initial configuration.
In the second part of the thesis, I designed an adaptive shift control system. I first constructed the traditional economy-oriented and power-oriented shift schedules for the optimized electric car and extracted the admissible shift interval between 70 and 90 km/h. Based on this interval, I built a two-level fuzzy controller with a T–S inference engine. The first level recognizes the driver’s intention from the accelerator pedal opening and its changing rate; the second level combines this intention with the vehicle speed to produce a fuzzy gear value. A subsequent Stateflow model applies hysteresis to avoid frequent shifting. The co-simulation results under the CLTC and NEDC cycles demonstrate that the adaptive controller remarkably reduces unnecessary gear changes while slightly reducing battery SOC consumption. Overall, the proposed method improves the smoothness and economy of the electric car.
Future work can be extended in several directions. The current optimization did not explicitly consider shift quality metrics such as jerk during ratio change. A deeper investigation into the trade-offs between shift comfort, energy consumption, and dynamic response would be valuable. Moreover, the shift interval was derived under a fixed battery SOC of 0.8. In future research, I plan to incorporate a SOC-dependent efficiency model across the entire SOC range so that the optimal shift window adapts to the battery state. With the evolution of intelligent driving, including road gradient, traffic flow, and vehicle-to-everything information into the shift controller will further enhance the performance of electric cars. I believe that this work will provide useful insights for researchers and engineers who are developing advanced transmissions for pure electric cars.