# Design and Performance Analysis of Super Highspeed Flywheel Rotor for Electric Vehicle

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design of Flywheel Rotor Energy and Power Parameters

- (1)
- Charge mode. The flywheel control motor works in the state of the motor. After the DC/DC device processes the electric energy, the flywheel control motor is driven, and the coaxial flywheel rotor is accelerated. The electric energy is transformed into the kinetic energy of the flywheel rotation. The flywheel rotor reaches the maximum design speed and can be filled.
- (2)
- Storage mode. The system has neither energy input nor energy output. Due to the use of a vacuum chamber and electromagnetic bearings, the energy loss is very small, and the flywheel is almost maintained at a certain speed.
- (3)
- Discharge mode. The flywheel control motor works in the state of power generation. When the external load has power demand, the high-speed rotating flywheel drives the coaxial flywheel control motor to rotate. The flywheel control motor generates alternating current, and the kinetic energy of the flywheel rotor is converted into electrical energy. The electrical energy is supplied to the load after rectification and transformation. In this process, the flywheel decelerates. The system no longer releases energy when the flywheel speed reaches the minimum design speed.

#### 2.1. Design of Flywheel Rotor Energy Parameters

**P**is the maximum power required by the vehicle, which can be calculated and determined by the vehicle dynamics equation [15].

_{rep_max}**P**is the maximum power of the lithium battery, and

_{bat_max}**P**is the maximum power of the flywheel battery.

_{fb_max}**P**. When the required power of the whole vehicle is less than

_{bat_limit}**P**, the lithium battery assumes all the required power of the whole vehicle. When the required power of the whole vehicle is greater than

_{bat_limit}**P**, the flywheel battery is used for compensation control.

_{bat_limit}**P**is the power of the flywheel battery, and

_{fb}**P**is the required power of the whole vehicle.

_{rep}**P**:

_{bat_limit}**P**of the lithium battery. Further, the PE value in each time period can be calculated according to the PE function. Finally, the maximum PE value in the 0-t time is selected as the CPE value in the whole travel.

_{bat_limit}**(P**is the PE value of the ith time period.

_{bat_limit})#### 2.2. Design of Flywheel Rotor Power Parameters

**P**should satisfy:

_{fb_max}**P**is 59.3 kW, and the lithium battery power threshold

_{rep_max}**P**is 20 kW. Therefore, the maximum power of the flywheel battery

_{bat_limit}**P**≥ 39.3 kW, and take the maximum power of the flywheel battery as 40 kW.

_{fb_max}## 3. Design of Flywheel Rotor Structure and Material

**E**, the moment of inertia $\mathit{j}$ of the flywheel rotor, the maximum working speed of the flywheel ${\mathit{\omega}}_{\mathbf{max}}$, the depth of discharge $\mathit{\lambda}$ and the minimum working speed ${\mathit{\omega}}_{\mathbf{min}}$ satisfy:

_{fb_max}**h**is the height of the flywheel,

**R**is the external diameter of the flywheel, $\mathit{\alpha}$ is the ratio of internal and external diameters, $\mathit{\rho}$ is the material density.

_{0}## 4. Modeling of Flywheel Rotor Stress with Interference Fit

#### 4.1. Modeling Analysis of Single Layer Composite Wheel Flange Stress

#### 4.2. Modeling of Composite Wheel Flange Stress in Multilayer Interference Assembly

**N − 1**times of assembly are required. Figure 5 is a schematic diagram of the assembly of a three layers composite wheel flange. After assembly, the first and second layers of the wheel flange are regarded as a whole without initial stress. The inner radius and outer radius are

**r**,

_{i1}**R**

**, and the inner radius and outer radius ratio is ${\mathit{\beta}}_{\mathbf{2}}^{\mathbf{\prime}}\mathbf{=}{\mathit{r}}_{\mathbf{i}\mathbf{1}}\mathbf{/}{\mathit{R}}_{\mathbf{o}\mathbf{2}}$. Consider the first layer and the second layer as the inner layer and the third layer wheel flange as the outer layer to assemble it.**

_{o2}**P**is the pressure at the contact surface of the first layer wheel flange and the second layer wheel flange.

_{1}**P**, the radial stress and hoop stress of the inner layer are:

_{2}**P**, the radial stress and hoop stress of the outer layer are:

_{2}**N − 1**times of assembly, ${\mathit{\beta}}_{\mathit{N}\mathbf{-}\mathbf{1}}^{\mathbf{\prime}}$ is the ratio of the inner radius and outer radius of the wheel flange after

**N − 1**times of assembly.

**N − 1**assembly, the pressure

**P**of the contact surface is:

_{N}_{−1}**N − 1**th assembly to the total initial stress of the first

**N − 2**assembly, the initial stress of the

**N**-th layer of interference assembly composite wheel flange can be obtained as follows [17].

**(i = 1,2**

**,**

**…, N**

**)**are the initial radial stress and hoop stress of the wheel flange of the

**i**-th layer, ${\mathit{\sigma}}_{\mathit{r}}^{\mathit{i}\mathbf{1}}$,${\mathit{\sigma}}_{\mathit{\theta}}^{\mathit{i}\mathbf{1}}$

**(i = 1,2**

**,**

**…, N**

**)**is the initial radial stress and hoop stress of the

**i**-th layer wheel flange when assembled to the

**i**-th layer rim, ${\mathit{\sigma}}_{\mathit{\theta}}^{{\mathit{i}}^{\mathbf{\prime}}}$, ${\mathit{\sigma}}_{\mathit{r}}^{{\mathit{i}}^{\mathbf{\prime}}}$

**(i = 1,2**

**,**

**…, N − 1**

**)**is the radial and hoop stress of the inner layer

**I − 1**wheel flange when assembled to the wheel flange of the

**i**-th layer.

#### 4.3. Flywheel Rotor Stress Analysis

#### 4.3.1. Analysis of Factors Influencing Stress of Flywheel Rotor

#### 4.3.2. Flywheel Rotor Stress Check

## 5. Conclusions

- (1)
- The selection of the power threshold should try to make the power cover most of the required power of the whole vehicle. If the power threshold is too small, the workload of the flywheel battery will be too heavy. If the threshold value is too high, the flywheel battery will not be able to “cut peaks and make up valleys” for the output power of the lithium battery.
- (2)
- The radial compressive stress can be generated in the flywheel rotor by using the interference assembly method to improve the radial strength of the flywheel rotor. Still, the increase of the radial strength will sacrifice some of the circumferential strength. Multi-layer interference assembly can improve the flywheel rotor’s stress level, improve the flywheel rotor’s strength, and reduce the machining difficulty of the flywheel rotor. However, the wheel flange cannot be infinitely layered. When there are too many layers, material failure occurs due to excessive radial compressive stress. The three layers interference assembly with a layer thickness of 12 mm is adopted, which can meet the assembly stress requirements of a super highspeed flywheel rotor.
- (3)
- The hoop stress will jump at the junction of the two layers, and the jump amplitude is proportional to the interference at the junction. The interference between the outer layer and the middle layer will have a great impact on the peak hoop stress. Therefore, it is necessary to decrease the interference at the junction to avoid fatigue failure caused by the long-term stress of the wheel hub.
- (4)
- From the point of view of improving the stress level of the flywheel rotor, when selecting the interference between wheel flange layers of the flywheel rotor, the smaller interference should be selected in the inner layer of the wheel flange, and the larger interference should be selected in the outer layer. The interference between inner layer and wheel hub, middle layer and inner layer, and outer layer and middle layer are designed to be 0.3, 0.4 and 0.5 mm, respectively, which can meet the design requirements.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Three-dimensional model of flywheel rotor under different schemes. (

**a**) Scheme I; (

**b**) scheme II; (

**c**) scheme III.

**Figure 8.**Stress curve of the flywheel at maximum speed. (

**a**) Radial stress curve; (

**b**) hoop stress curve.

**Figure 10.**Stress curve of the flywheel at maximum speed. (

**a**) Radial stress curve; (

**b**) hoop stress curve.

**Figure 11.**Equivalent stress nephogram of flywheel rotor in a static state. (

**a**) Overall equivalent stress cloud diagram of flywheel rotor; (

**b**) Equivalent stress cloud map of the wheel hub.

**Figure 12.**Wheel flange direction stress cloud in a static state. (

**a**) Radial stress contour of wheel flange; (

**b**) Hoop stress contour of wheel flange.

**Figure 13.**Equivalent stress nephogram of flywheel rotor at maximum speed. (

**a**) Overall equivalent stress cloud diagram of flywheel rotor; (

**b**) Equivalent stress cloud map of the wheel hub.

**Figure 14.**Flywheel rotor stress nephogram at maximum speed. (

**a**) Radial stress cloud diagram of flywheel rotor; (

**b**) Hoop stress cloud diagram of flywheel rotor.

**Figure 15.**Contact cloud diagram of flywheel rotor. (

**a**) Contact state cloud map; (

**b**) Contact pressure cloud map.

Parameter | Value | Parameter | Value |
---|---|---|---|

Circumferential modulus/GPa | 150.7 | Circumferential shear strength/GPa | 5.5 |

Radial modulus/GPa | 7 | Radial shear strength/GPa | 4.9 |

Circumferential Poisson’s ratio | 0.3 | Density/kg m^{−3} | 1590 |

Radial Poisson’s ratio | 0.33 | Circumferential strength/MPa | 3206 |

Ultimate Strength/MPa | Elastic Modulus/MPa | Density/kg·m^{−3} | Yield Strength/MPa |
---|---|---|---|

588 | 2800 | 2760 | 455 |

Component | Moment of Inertia/kg m ^{2} | External Diameter/mm | Internal Diameter/mm | Height/mm | Quality/kg |
---|---|---|---|---|---|

Wheel flange | 0.093 | 300 | 228 | 114 | 5.28 |

Wheel hub | 0.027 | 228 | 212 | 114 | 2.85 |

Scheme | Scheme I | Scheme II | Scheme III |
---|---|---|---|

Interference between the inner layer and the wheel hub/mm | 0.3 | 0.4 | 0.5 |

Interference between the middle layer and the inner layer/mm | 0.4 | 0.4 | 0.4 |

Interference between the outer layer and the middle layer/mm | 0.5 | 0.4 | 0.3 |

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**MDPI and ACS Style**

Wang, P.; Gu, T.; Sun, B.; Liu, R.; Zhang, T.; Yang, J.
Design and Performance Analysis of Super Highspeed Flywheel Rotor for Electric Vehicle. *World Electr. Veh. J.* **2022**, *13*, 147.
https://doi.org/10.3390/wevj13080147

**AMA Style**

Wang P, Gu T, Sun B, Liu R, Zhang T, Yang J.
Design and Performance Analysis of Super Highspeed Flywheel Rotor for Electric Vehicle. *World Electric Vehicle Journal*. 2022; 13(8):147.
https://doi.org/10.3390/wevj13080147

**Chicago/Turabian Style**

Wang, Pengwei, Tianqi Gu, Binbin Sun, Ruiyuan Liu, Tiezhu Zhang, and Jinshan Yang.
2022. "Design and Performance Analysis of Super Highspeed Flywheel Rotor for Electric Vehicle" *World Electric Vehicle Journal* 13, no. 8: 147.
https://doi.org/10.3390/wevj13080147