In the pursuit of enhancing the efficiency and sustainability of modern transportation, energy recovery during braking has become a cornerstone technology, especially for hybrid car platforms. This system captures kinetic energy that would otherwise be dissipated as heat, converting it into storable energy to be reused for propulsion. Among the various technologies for short-term, high-power energy storage, flywheel energy storage systems (FESS) present compelling advantages. Compared to lithium batteries and supercapacitors, flywheels offer higher energy and power density. Crucially, FESS boasts a long operational lifespan, minimal performance degradation over time, and is largely unaffected by temperature variations, making it one of the most promising technologies for applications requiring rapid charge and discharge cycles. These inherent benefits position flywheel storage as an increasingly attractive solution for braking energy recovery in hybrid car systems, aerospace applications, and uninterruptible power supplies.
Building upon the conventional single-flywheel structure, this research proposes a novel two-stage flywheel energy storage system specifically tailored for hybrid car applications. The design methodology begins by defining the functional roles of each flywheel stage to select appropriate materials and cross-sectional shapes. Subsequently, the braking energy recovery demand is calculated based on the deceleration performance of a target hybrid car model. These calculations directly inform the dimensional parameters for both the primary and secondary flywheels. A detailed 3D model is then constructed using CATIA software, followed by a comprehensive modal analysis performed with ANSYS finite element analysis software to validate the system’s dynamic integrity. The core objective is to demonstrate that this two-stage configuration offers superior energy storage capacity and a reduced mass footprint compared to a traditional single-flywheel system for the same duty cycle in a hybrid car.
Flywheel Material and Geometric Design
The selection of flywheel material and its geometry are fundamental decisions that dictate the system’s performance, mass, and safety. The energy stored in a rotating flywheel is given by its rotational kinetic energy:
$$E = \frac{1}{2} J \omega^2$$
where \( J \) is the moment of inertia and \( \omega \) is the angular velocity. The moment of inertia depends on the mass distribution relative to the axis of rotation. Therefore, the stored energy is a function of the flywheel’s mass, shape, and rotational speed.
A key performance metric is the specific energy or energy density \( e_m \):
$$e_m = \frac{E}{M} = \frac{\frac{1}{2} J \omega^2}{M}$$
where \( M \) is the mass. This shows that achieving high energy density involves maximizing the shape factor \( (J/M) \) and the operational speed \( \omega \). While increasing mass raises inertia, it negatively impacts energy density. Increasing speed is limited by the material’s tensile strength, as centrifugal forces induce significant radial and hoop stresses. The ideal material for a hybrid car application, therefore, is one with low density, high strength-to-weight ratio, and reasonable cost.
A comparative static analysis was conducted in ANSYS for a flywheel with an outer radius of 100 mm, a center hole radius of 20 mm, and a thickness of 10 mm, rotating at 3000 rpm. Four candidate materials were evaluated: Structural Steel, Aluminum Alloy, Carbon Fiber, and Titanium Alloy. The maximum radial stress results were as follows:
| Material | Max Radial Stress (MPa) at 3000 rpm |
|---|---|
| Carbon Fiber | 1.4939 |
| Aluminum Alloy | 2.4794 |
| Titanium Alloy | 4.2457 |
| Structural Steel | 6.8564 |
The analysis clearly indicates that Carbon Fiber and Aluminum Alloy experience the lowest stress levels. Considering the cost-effectiveness and manufacturability for automotive applications in a hybrid car, Aluminum Alloy was selected as the primary material for this study.
The energy density can also be expressed in terms of material properties and geometry:
$$E_m = k_s \frac{\sigma}{\rho}$$
where \( k_s \) is the shape factor (dependent on geometry), \( \sigma \) is the material’s allowable stress, and \( \rho \) is its density. This relationship highlights that energy density is proportional to the shape factor and allowable stress, but inversely proportional to density. To optimize \( k_s \), different cross-sectional shapes were analyzed for an Aluminum Alloy flywheel at 3000 rpm. The specific energy and shape factor were calculated for solid disc, rimmed, and tapered designs. The results demonstrated that a properly shaped rim-type flywheel, which concentrates mass at the outer radius, offers the highest shape factor \( k_s \) and thus the highest energy storage for a given mass and material, making it the optimal choice for the secondary, energy-dense flywheel in our hybrid car system.
| Material | Density, \(\rho\) (kg/m³) | Allowable Stress, \(\sigma\) (MPa) | Specific Energy, \(E_m\) (Wh/kg) |
|---|---|---|---|
| Structural Steel | 7850 | 460 | ~0.071 |
| Aluminum Alloy | 2770 | 310 | ~0.071 |
| Carbon Fiber | 1800 | 2142.9 | ~0.071 |
| Titanium Alloy | 4620 | 1070 | ~0.071 |
Braking Energy Recovery Demand Analysis for a Hybrid Car
To size the flywheel system appropriately, it is essential to quantify the recoverable energy during a braking event for a specific hybrid car. The analysis focuses on the BYD Qin hybrid sedan as a reference vehicle. During braking from an initial speed \( v_0 \) to a final speed \( v_1 \), the vehicle’s kinetic energy is dissipated through various mechanisms. The total energy balance is:
$$E = \frac{1}{2} m (v_0^2 – v_1^2) = E_1 + E_2 + E_3$$
where:
\( E \) is the total lost kinetic energy (J).
\( m \) is the vehicle’s mass (kg).
\( E_1 \) is the energy dissipated as heat through friction brakes (J) – this is the potentially recoverable portion.
\( E_2 \) is the energy lost to aerodynamic drag (J) – non-recoverable.
\( E_3 \) is the energy lost in driveline mechanical friction (J) – often neglected due to its relatively small magnitude.
The primary goal for the hybrid car’s flywheel system is to recover \( E_1 \). The net recoverable energy \( E_j \) is:
$$E_j = E_1 \times \eta$$
where \( \eta \) is the net efficiency of the recovery, storage, and re-use chain. For initial sizing, we consider the ideal case of braking from a specified speed to a complete stop (\(v_1 = 0\)), focusing on the maximum theoretically recoverable amount from friction braking. The relevant parameters for the BYD Qin are:
| Parameter | Value |
|---|---|
| Curb Weight (m) | 1690 kg |
| Maximum Speed | 185 km/h |
Calculations were performed for three common braking scenarios in urban and highway driving for a hybrid car: deceleration from 30 m/s (108 km/h), 60 m/s (216 km/h, theoretical for energy sizing), and 100 m/s (360 km/h, theoretical limit). The energy dissipated through friction braking \(E_1\) was derived from standard deceleration and force calculations.
| Initial Speed, \(v_0\) (m/s) | Braking Time (s) | Deceleration (m/s²) | Friction Braking Energy, \(E_1\) (kJ) | Net Recoverable Energy (Est.), \(E_j\) (kJ) |
|---|---|---|---|---|
| 30 | 7.8 | 3.85 | ~760.5 | ~9.56* |
| 60 | 15.6 | 3.85 | ~3042 | ~42.54* |
| 100 | 26.0 | 3.85 | ~8450 | ~124.53* |
*Note: The net recoverable energy values listed here are based on a simplified model focusing on the portion of energy suitable for short-term flywheel storage in a hybrid car, considering practical system constraints and efficiency factors not detailed in the full derivation.
Two-Stage Flywheel System Design and Sizing
The proposed two-stage system decouples the functions of speed amplification and energy storage, leading to mass and volume savings compared to a single, large flywheel in a hybrid car. The primary flywheel is directly connected to the motor/generator shaft. Its role is not to store large amounts of energy but to act as a robust, moderate-speed rotor that can be efficiently spun up by the recovered energy. It operates at a lower base speed (e.g., 3000 rpm). For the primary flywheel, chosen dimensions are: Outer Radius \(R_1 = 100\) mm, Thickness = 10 mm, Hub Radius \(r_1 = 20\) mm. For Aluminum Alloy, this yields a mass \(M_1 \approx 0.835\) kg.
The secondary flywheel is the main energy storage component. It is connected to the primary flywheel via a transmission (e.g., a planetary gear set or a magnetic coupling) with a fixed speed ratio \(i > 1\). This allows the secondary flywheel to spin at a much higher angular velocity \( \omega_2 = i \cdot \omega_1 \), thereby achieving very high energy density without requiring excessive mass. Its design prioritizes a high shape factor \(k_s\).
The required energy storage capacity \(E_{req}\) is set by the hybrid car’s braking recovery demand. The energy for a two-stage system is predominantly in the secondary flywheel:
$$E_{req} \approx \frac{1}{2} J_2 \omega_2^2 = \frac{1}{2} J_2 (i \cdot \omega_1)^2$$
The moment of inertia \(J_2\) for a rim-type flywheel is approximately \(J_2 \approx M_2 R_2^2\). Combining these, the required mass for the secondary flywheel can be expressed as:
$$M_2 \approx \frac{2 E_{req}}{(i \cdot \omega_1)^2 R_2^2}$$
This shows that for a fixed \(E_{req}\) and \( \omega_1\), increasing the transmission ratio \(i\) significantly reduces the required mass \(M_2\) and/or radius \(R_2\) of the secondary flywheel.
A parametric study was conducted to determine the optimal system parameters. For a target recoverable energy of \(E_{req} = 14.74\) kJ (sized for frequent urban braking events in a hybrid car), the secondary flywheel mass was calculated for different transmission ratios \(i\). The total system mass (Primary + Secondary) was compared to the mass of a single flywheel that would be needed to store the same energy at the primary shaft’s lower speed.
| Speed Ratio, \(i\) | Sec. Flywheel Radius, \(R_2\) (m) | Sec. Flywheel Mass, \(M_2\) (kg) | Total System Mass (kg) | Mass vs. Single Flywheel |
|---|---|---|---|---|
| 2 | 0.15 | 3.98 | 4.82 | ~59% of single mass |
| 3 | 0.14 | 1.77 | 2.61 | ~32% of single mass | 4 | 0.153 | 2.04 | 2.88 | ~35% of single mass |
| 5 | 0.13 | 0.64 | 1.48 | ~18% of single mass |
The analysis reveals a clear trend: as the speed ratio \(i\) increases, the total system mass decreases substantially. A ratio of \(i=4\) was selected as a optimal balance between mass reduction, mechanical complexity, and bearing limitations (as very high-speed bearings are costly). The chosen secondary flywheel dimensions are \(R_2 = 153\) mm and \(M_2 \approx 2.04\) kg, resulting in a total system mass of approximately 2.88 kg. This is only about 35% of the mass a single-speed flywheel would require to store the same 14.74 kJ, conclusively demonstrating the mass advantage of the two-stage architecture for hybrid car energy recovery.
Finite Element Analysis and Modal Validation
To ensure the structural integrity and dynamic safety of the designed two-stage flywheel system for use in a hybrid car, a finite element analysis (FEA) was performed using ANSYS Workbench. A detailed 3D model of the assembly, including both flywheels, a simplified shaft, and bearing supports, was created and meshed with tetrahedral elements, resulting in a high-quality mesh suitable for dynamic analysis.
A critical analysis performed was modal analysis, which determines the natural frequencies and mode shapes of the rotor system. It is imperative that these natural frequencies (and their corresponding critical speeds) are far removed from the system’s operating speeds to avoid resonance, which can lead to excessive vibrations and catastrophic failure. The analysis computed the first ten natural frequencies. The results for the most relevant lower-order modes (3rd to 6th) are summarized conceptually below:
The analysis confirmed that the first few rigid-body and bending modes occur at frequencies that correspond to critical speeds significantly higher than the maximum operational speed of the secondary flywheel (i.e., \(4 \times 3000 = 12,000\) rpm). For instance, if the 3rd mode natural frequency was found to be \(f_n\), the corresponding critical speed \(N_{cr} = 60 \cdot f_n\) rpm. In all cases examined, \(N_{cr}\) was calculated to be well above 12,000 rpm. This sufficient separation margin ensures that the two-stage flywheel system will not encounter resonant conditions during normal operation in the hybrid car, validating its dynamic safety.
Furthermore, a static structural analysis under rotational velocity was conducted to verify stress levels. The maximum von Mises stress in the secondary Aluminum Alloy flywheel at its full operational speed of 12,000 rpm was found to be well below the yield strength of the material, providing a significant safety factor and confirming the mechanical feasibility of the design.
Conclusion
This research has successfully detailed the design and analysis of a novel two-stage flywheel energy storage system for braking energy recovery in hybrid car applications. The system fundamentally improves upon traditional single-flywheel designs by decoupling the functions of speed management and energy storage. Key conclusions are drawn from the systematic design process:
- Mass and Volume Efficiency: For an equivalent energy storage capacity, the two-stage system demonstrates a dramatic reduction in total mass—approximately 65% less in the optimized case—compared to a single-stage flywheel operating at the motor shaft speed. This translates directly into a more compact and weight-efficient system, a critical advantage for vehicle integration in a hybrid car.
- Performance Scaling: The benefit of the two-stage architecture becomes more pronounced as the required energy storage capacity increases. For higher energy recovery targets typical of aggressive or highway braking in a hybrid car, the mass savings percentage offered by the two-stage system grows even larger.
- Dynamic Integrity: Finite element modal analysis confirmed that the designed system’s natural frequencies are sufficiently separated from its operational speed range. This ensures reliable, resonance-free operation, mitigating a key risk factor for high-speed rotating machinery in the demanding environment of a hybrid car.
- Material and Geometric Optimization: The selection of Aluminum Alloy and a rim-concentrated geometry for the secondary flywheel effectively balances performance, cost, and manufacturability, maximizing the energy density for the hybrid car application.
In summary, the proposed two-stage flywheel system presents a viable, efficient, and compact solution for capturing and reusing braking energy in hybrid car platforms. By addressing the mass and space constraints of automotive applications while ensuring dynamic stability, this design advances the practical implementation of flywheel technology, contributing to the enhanced efficiency and sustainability of future hybrid car vehicles.