A Novel Magnetic Suspension Flywheel Battery with a Multi-Function Air Gap

Abstract

In this study, a novel magnetic suspension flywheel battery with a multi-function air gap is proposed. Based on the unique multi-function air gap, the degrees of freedom between the control magnetic circuits can be independent of each other, reducing the coupling effect between degrees of freedom. The proposed flywheel battery system topology inherits the unique advantages of the magnetic suspension flywheel battery. However, due to the breakthrough of the overall topology in the air gap, flywheel, and protection measures, the system has more advantages in the precise design of the magnetic circuit, decoupling, high-stability control, and energy storage. First, the advantages, geometric characteristics, and magnetic circuit of the flywheel battery system are introduced and analyzed. Then, the position and length of the multi-function air gap and conventional air gap in the magnetic circuit are optimized to ensure the best magnetic performance of the entire magnetic circuit. Then, the flywheel, motor, and protection settings are introduced in detail. Finally, performance tests are conducted, and the good experimental results show that the proposed flywheel battery has good anti-interference ability and decoupling ability.

1. Introduction

A flywheel battery is a type of physical energy storage mechanical battery with high energy conversion efficiency, no chemical pollution to the environment, safety, and a long life [1,2]. The application of flywheel batteries in vehicles can significantly improve energy efficiency, so they have received a lot of attention in the past few years [3,4]. Due to the unique mobile-based background of the vehicular flywheel battery, it is easily affected by road conditions and vehicle driving conditions. The magnetic suspension support system supporting the flywheel has extremely high requirements [5]. The design result of the magnetic circuit in the magnetic support system is very important, which will directly lead to the accuracy of the control precision of the whole magnetic suspension system. How to reduce the interference between magnetic circuits and try to avoid the coupling between various degrees of freedom to improve control accuracy and efficiency is very important [6]. Air gap, as the most critical link in magnetic circuit design, directly affects the control effect of magnetic circuits [7,8].

The most classic and common magnetic circuit design of the vehicle-mounted flywheel battery magnetic suspension support system is based on a class of air gaps. Take the most classic and common hybrid magnetic bearings as an example. This kind of magnetic circuit design based on a class of air gap topology can only realize the superposition of magnetic flux in the air gap, so the overall magnetic circuit has a single function. A high-integration flywheel battery topology structure in which part of the magnetic bearing was embedded with the flywheel is proposed in [9]. The decoupling between the magnetic circuits of various degrees of freedom was realized by completely independent arrangement and placement of magnetic isolation aluminum rings at appropriate positions. However, the overall magnetic circuit integration was not high and eddy current loss was large. Magnetic suspension support systems proposed in [10,11] are all classical cylindrical, hybrid magnetic-bearing topologies and their magnetic circuits are all designed based on a classical class of air gap. This kind of magnetic circuit design generally adopts magnetic separation aluminum rings to avoid the phenomenon of self-loop around permanent magnets. Although the biased loss of the system is reduced to a certain extent and the magnetic properties of ferromagnetic materials are improved, it also increases the risk of eddy current loss of the system. A flat-type solid disk flywheel battery device was proposed in [12,13]. Five-degrees-of-freedom magnetic bearing was arranged above the flywheel in a radially tiled way, but the tilt control flux and axial control flux were coupled. In conclusion, the current magnetic circuit design based on a class of air gap flywheel battery maglev support systems makes it difficult to solve the coupling, integration, and loss of the magnetic circuit. Therefore, in order to solve the problem of a class of air gap, some magnetic circuit design schemes based on secondary air gap are put forward. The introduction of the concept of a double air gap in a magnetic circuit was proposed in [14], through which the magnetic field loss in the whole magnetic bearing can be reduced, and the magnetic properties of materials can be greatly improved. A second type of air gap to the main magnetic circuit was proposed in [15,16]. By changing the direction of the control magnetic circuit, the air gap can effectively realize the decoupling of the control magnetic circuit between the two degrees of freedom in the radial direction and greatly reduce the control loss. However, in the added second air gap, there will still be biased magnetic flux generated by permanent magnets flowing through, and a self-coupled circuit will also be formed. Therefore, the optimal magnetic properties of permanent magnet materials cannot be used efficiently. Moreover, the design of a magnetic circuit is more challenging for the five-degree-of-freedom maglev bearing system; that is, the magnetic circuit coupling between radial translation, radial deflection, and axial freedom is also easy to occur. Therefore, how to design air gap in a magnetic circuit cleverly can solve the coupling characteristics of magnetic circuit and reduce eddy current loss. At the same time, it is the trend of magnetic circuit design to realize the effective utilization of magnetic properties of materials with high integration and maximum, and then complete the preset magnetic circuit.

In addition, the magnetic circuit and air gap are closely related to the flywheel because the shape of the flywheel not only affects the magnetic circuit but also directly affects the flywheel energy storage properties. Compared with the flywheel made of composite material, the metal flywheel has a higher shape variable degree, is easier to fit with various air gaps, and has higher cost performance, which makes it more suitable for the promotion of the flywheel battery system. However, the vehicle-mounted flywheel battery has stricter requirements on the volume and weight of the flywheel, so it is very important to optimize the material and shape design of the metal flywheel [17,18]. A system optimization design method of traditional flywheel topology with center hole was proposed in [19]. The optimization scheme can be obtained faster by systematic method, but the energy storage characteristics of center hole flywheel are not as good as that of a solid disc flywheel. Therefore, a novel magnetic suspension flywheel battery with a virtual axs spindle was presented in [12]. Compared with the flywheel with center hole, the energy storage density of cylindrical solid disk flywheel has higher energy storage density and improved the cost performance of the flywheel. However, the shape of the flywheel has not been optimized further, and the energy storage characteristics still have room for improvement. So, there is still a lot of room for improvement in the structure and shape of the flywheel.

Therefore, in view of the problems existing in the current flywheel battery system, a novel vehicle-mounted flywheel battery with a multi-functional air gap is designed in this paper. The concept of a “multi-functional air gap” is introduced in this flywheel battery, which can solve the coupling characteristics of the magnetic circuit without affecting the integration of the magnetic suspension support system and, at the same time, can maximize the utilization rate of magnetic properties of materials. In addition, in order to cooperate with the proposed multi-function air gap, realize the preset magnetic circuit better, and further improve the energy storage characteristics of the system, an improved bowl flywheel is proposed. This paper first introduces the overall structure of the flywheel, then analyzes the magnetic circuit and air gap of the magnetic bearing, optimizes the design of the multi-function air gap and other air gaps, and determines the optimal air gap length matching relationship. Then, the external shape of the flywheel is analyzed and optimized to improve the energy storage characteristics of the flywheel. Finally, the whole flywheel battery is tested in basic working condition using the anti-interference test and complex road performance test, which verify the advantages and feasibility of the new flywheel battery.

2. Geometry Design and Optimization of Flywheel Battery System

2.1. Topology

The geometric characteristics of the proposed magnetic suspension flywheel battery with a multi-function air gap are shown in Figure 1. The battery includes a decoupled and highly integrated five-degree-of-freedom hybrid magnetic bearing (5-DOF HMB), a bowl-shaped solid flywheel, an outer rotor brushless DC motor, three sets of sensors, and a protective casing.

The specific advantages are as follows: (1) High stability: Due to the addition of a multi-function air gap, the control flux of magnetic bearings is independent of each other, and the control coupling effect is greatly reduced, which reduces the control difficulty, improves the control accuracy, and then improves the stability of the flywheel. (2) High integration: Through clever magnetic circuit design, the axial magnetic circuit and the torsional magnetic circuit can share the biased magnetic circuit using only one main permanent magnet, so the whole magnetic bearing volume is greatly reduced. Additionally, the magnetic bearing as a whole is wrapped by the flywheel, so the integration of the entire flywheel battery system is greatly improved. (3) High material utilization rate: This multi-functional air gap and the appropriate auxiliary permanent magnet in the magnetic circuit cooperate with each other so that the magnetic circuit can run according to the planned magnetic route so that the material utilization rate of the magnetic bearing can be greatly improved. (4) Energy storage: The proposed flywheel system topology inherits the unique advantages of the original maglev flywheel battery. However, the optimized flywheel has a higher shape factor, and the system has a greater advantage in energy storage.

2.2. Geometric Characteristics Analysis of Flywheel Battery with Multi-Function Air Gap

The structure of the 5-DOF HMB is shown in Figure 2. The magnetic bearings in the traditional 5-DOF flywheel battery are controlled by three independent stators, which have low integration, a scattered structure, and a large volume. If the stator can share the permanent magnet and control the radial and axial magnetic circuits without coupling, it will greatly reduce the volume of the magnetic bearing and improve the overall integration. The following will introduce the design optimization process of magnetic bearing in detail.

As we all know, when two stators with different degrees of freedom share a permanent magnet, if no effective measures are taken, a serious coupling phenomenon will occur in the magnetic circuit. Therefore, an innovative magnetic bearing structure design is proposed in this paper, in which the design of the axial part is the key to the overall magnetic bearing design. The main permanent magnet, auxiliary permanent magnet, and multi-function air gap cooperate with each other to realize the highly integrated magnetic bearing, while all magnetic circuits have almost no coupling. The magnetic circuit diagram of axial and torsional hybrid magnetic bearings can be seen in Figure 2.

As shown in Figure 2, the red arrow marks the static biased flux magnetic circuit of the hybrid magnetic bearing. Since the auxiliary permanent magnet guides the magnetic circuit, most of the magnetic circuit generated by the N pole of the main permanent magnet will flow to the S pole of the auxiliary permanent magnet. The overall direction will flow through the axial stator, flywheel, and torsional stator poles according to the design requirements and finally reach the S pole of the main permanent magnet to form an axial closed-loop. Axial control flux and torsional control flux have no contact and are two independent closed loops. The blue arrow indicates the control flux of the hybrid magnetic bearing. The axial control flux can adjust the axial position of the flywheel, and the torsional control flux can control the torsional deviation of the flywheel. This new type of hybrid magnetic bearing has high integration and control magnetic circuit coupling. It mainly benefits from the multi-functional air gap in the axial part. The following will focus on the function of the multi-functional air gap and the optimization process.

As the name implies, the multi-function air gap has multiple functions for the overall prototype. Its functions are mainly manifested in three aspects. First, auxiliary permanent magnets are used to guide the magnetic circuit towards the axial air gap while the control air gap is minimized. Second, the multi-function air gap provides a complete circuit for the control magnetic circuit, making it completely separate from other control magnetic circuits to avoid coupling. Finally, by adding a multi-function air gap, axial and torsional stators can share permanent magnets for integration. In order to achieve the above functions, the three air gaps need to be optimized to identify a group that not only meets the bearing capacity requirements but also meets the stability control. At the same time, it can realize the combination of decoupling control of different degrees of freedom and reduce the coupling of five degrees of freedom as far as possible. Therefore, the next step is to focus on the optimization process.

2.3. Magnetic Circuit Optimization Analysis with All Air Gaps

The three air gaps in the axial part all play their respective important functions, so they need different lengths of air gap distance to better complete their functions. The comprehensive optimization of three air gaps is complicated; the traditional parametric analysis method will take a lot of time, and the analysis results are not accurate enough. Using genetic algorithm non-dominated sorted genetic algorithm-II (NSGA-II), the priority of the three air gaps can be judged and calculated according to the priority distribution, which shortens the time and improves the accuracy of the result. These air gaps are labeled l₁, l₂, and l₃, respectively, as shown in Figure 2. The axial air gap l₁ must provide a sufficient carrying capacity for the flywheel. If the air gap distance is set too large, permanent magnets with greater magnetic force will be needed to satisfy the stable suspension of the flywheel, which increases cost. Therefore, the preset range of axial air gap is in the range of 0.3–0.7 mm. The main purpose of control air gap l₃ is to enable the axial control magnetic circuit to go through completely and, at the same time, avoid coupling with the torsional magnetic circuit as much as possible. Therefore, the air gap distance should be selected as the atmospheric gap, so the preset range of the control air gap is in the range of 0.6–1 mm. Due to the need to prevent the auxiliary permanent magnet from self-coupling, the multi-function air gap distance l₂ also selects a large gap distance.

$$\left\{\begin{array}{l}0.3\mathrm{mm}\le l_1\le 0.7\mathrm{mm};0.6\mathrm{mm}\le l_2\le 1.0\mathrm{mm}\\ 0.6\mathrm{mm}\le l_3\le 1.0\mathrm{mm}\end{array}\right..$$

(1)

At the same time, the optimization results require the magnetic bearing to provide a suspension force F_Z1 greater than the mass of the flywheel, and the maximum displacement stiffness of the flywheel F_Z2 should not exceed the current control stiffness provided by the axial control coil. The influence on radial displacement stiffness F_Y of the flywheel should be minimized when axial displacement occurs.

$$F_Z{}_1\ge 350\mathrm{N};F_Z{}_2\le 950\mathrm{N};-1\mathrm{N}\le F_Y\le 1\mathrm{N}.$$

(2)

In order to control the variables more precisely and maximize the optimization effect, the priority order of the optimized air gap can be determined according to the influence of each air gap provided by the NSGA-II algorithm on the optimization target, as shown in Figure 3.

According to the results of sensitivity, multi-function air gap and axial air gap have a relatively great influence on the axial suspension force, axial displacement stiffness, and axial radial coupling degree. Therefore, their dimensions are determined first. The comprehensive simulation results of the three groups of optimization objectives are shown in Figure 4.

In Figure 4a–c, three sets of data showing the optimal sizes of l₁ and l₂ corresponding to the three groups can be obtained. By combining the optimization results of the three groups, the size of l₁ is finally determined to be 0.5 mm, while the size of the multi-function air gap is determined to be in the range of 0.7–0.8 mm. Based on the above results, when the axial air gap l₁ is determined, the multi-function air gap l₂ and control air gap l₃ are optimized.

In Figure 5a–c, using three sets of data, the length of the multi-functional air gap l₂ is determined to be 0.8 mm, the length of control air gap l₃ is 0.8 mm, and the specific length of the three air gaps is finally determined. Detailed data on axial air gap and suspension force are shown in

Table 1. Air gaps and suspension force data.

Parameter	Quantity	Parameter	Quantity
Multi-function air gap	0.8 mm	Torsional air gap	0.5 mm
Axial air gap	0.5 mm	Axial suspension force	357 N
Control air gap	0.8 mm	Axial maximum displacement stiffness	810 N

.

In order to make the flywheel operation easy to control and more stable, the air gap between the flywheel and magnetic bearing requires stable biased air gap flux, small displacement stiffness, and linear current stiffness. Therefore, the displacement stiffness generated by flywheel bias is also an important index to measure structural performance. According to the above requirements, a radial structure with an inward stator pole is proposed, as shown in Figure 6.

As shown in Figure 6, the radial control magnetic circuit is represented by red lines in the top view and the biased magnetic circuit is represented by dark blue lines in the section view. The control flux c changes by changing the current of the energized coil. The biased magnetic circuit starts from the N pole of a permanent magnet, passes through the upper stator through the radial upper air gap, passes through the flywheel, passes through the radial lower air gap, and the radial lower stator finally reaches the S pole to complete the biased magnetic circuit.

This design can reduce the displacement stiffness of the flywheel, the control force required to balance the displacement stiffness is reduced, and the energy consumption of the flywheel battery is reduced. At the same time, the air gap flux between the stator pole and the flywheel is more stable and easier to control stably. To prove the superiority of this structure, the structure was compared with the structure of the stator pole facing outward, as shown in Figure 7. When the stator pole thickness, pole width, and air gap distance are the same, the two different structures can be compared and simulated. Their magnetic density distribution cloud map is shown in Figure 8, and their stiffness pair is shown in Figure 9.

When the flywheel is in a stable suspension, the air gap flux between the radial stator pole and the flywheel should be kept as uniform as possible and close to the preset biased flux size. If the air gap flux is not uniform in normal suspension, the flywheel will be affected by the radial offset force, which will not only affect the stable suspension but also increase the overall control difficulty of the system. The details are as follows:

The arrows in Figure 8 represent the distribution of magnetic field lines in the two magnetic bearings. Compared with the two simulation results in Figure 8, when the magnetic flux at the air gap between the stator pole and the flywheel reaches 0.3 T, the magnetic density map of the internal structure of the stator pole in Figure 8a is obviously uniform, while in Figure 8b, although the air gap magnetic flux of the stator pole outward is mostly 0.3 T, there is obvious magnetic saturation on both sides of the stator pole. When the flywheel is unstable due to external interference, the magnetic saturation in the air gap will interfere with the control system to stabilize the flywheel, which will seriously interfere with the stable operation of the flywheel. The external influence of the flywheel due to unbalanced displacement can be called displacement stiffness. Figure 9 shows the displacement stiffness generated when the flywheel displaces 0.3 mm in the x direction under simulated unbalance. By comparing the displacement stiffness of the two structures, it can be seen that the displacement stiffness of the default substructure shown in Figure 9a is significantly smaller than that of the external stator structure shown in Figure 9b, and the displacement stiffness curve is more linear, which can reduce the difficulty of flywheel control. Because the external stator structure exerts control to achieve the same effect when the flywheel produces deviation, it requires a larger current, a larger volume of stator poles, and permanent magnets, which causes material waste and increases the instability of the system. As shown in Figure 9b, due to the above reasons, the displacement stiffness linearization of rotor migration is significantly reduced. In summary, the inner radial stator improves the stability of the flywheel during normal operation and reduces the control difficulty of flywheel offset. At the same time, the stator pole’s inward magnetic bearing occupies a small space, which improves the integration of the whole system and reduces the processing cost.

2.4. Design and Optimization Analysis of Flywheel

The key factor of flywheel optimization design is energy storage performance. A solid disc flywheel can provide a higher energy density. Therefore, the system chooses a solid flywheel with grooves in the middle, but the flywheel itself is a separate steel structure from the magnetic bearing assembly, and there is only an air gap connection between the flywheel and the magnetic bearing. As shown above, the flywheel, magnetic bearings, and motor are highly integrated, reducing the size of the overall system.

Since the same material is selected, the two flywheels have the same maximum allowable stress. According to the calculation formula of the maximum mass–energy density E_m and the shape coefficient K of the flywheel, increasing the shape coefficient of the flywheel can obtain greater mass–energy density under the same condition. Because the same material is selected, the two flywheels have the same maximum allowable stress.

$$E=\frac{1}{2}I{\omega }^2.$$

(3)

where E is rotational energy storage. I is the rotational inertia of the flywheel. ω is the rotational speed of the flywheel.

According to the calculation formula of the maximum mass–energy density E_m and the shape coefficient K of the flywheel, increasing the shape coefficient of the flywheel can obtain greater mass–energy density under the same condition.

$$E_m=\frac{K{\sigma }_{max}}{\rho }$$

(4)

$$K=\frac{1}{2V{\sigma }_{\max }}{\displaystyle \int \begin{array}{c}r\\ 0\end{array}{\displaystyle \int \begin{array}{c}2\pi \\ 0\end{array}[h_{\theta }{\sigma }_{\theta }+h_r{\sigma }_r]}}r\mathrm{d}r\mathrm{d}\theta ,$$

(5)

where ρ is the mass density. V is volume. σ_max is the maximum value allowable stress. r is the radius of the flywheel. h_θ and h_r are the inner diameter and radial thickness. σ_θ and σ_r are the inner diameter and radial stresses.

According to the formula, the shape coefficient K of the cylindrical flywheel is approximately 0.588, while that of the bowl flywheel is roughly 0.596, which is slightly larger than that of the cylindrical flywheel. Figure 10 shows the equivalent stress of two flywheels under the same environment and speed.

The geometry and rotation speed of the flywheel are the key factors of energy storage. Therefore, the flywheel with a higher shape coefficient is used to compare with the traditional cylindrical flywheel. Both flywheels have the same internal slot size and the same overall mass. Only the external geometry of the flywheel is changed, as shown in Figure 10. By comparing Figure 10a,b, it is obvious that the stress distribution of the bowl-shaped flywheel with optimized shape factor is more uniform than that of the traditional cylindrical flywheel. The maximum stress appears at the top of the flywheel, while the maximum stress of the bowl-shaped flywheel is smaller than that of the traditional cylindrical flywheel. The specific parameters of the new flywheel are shown in

Table 2. Flywheel geometry parameters and energy storage characteristics.

Parameter	Quantity	Parameter	Quantity
Overall weight	35 kg	Inside diameter	200 mm
Maximum outside diameter	262 mm	Motor space inside diameter	116 mm
Minimum outside diameter	240 mm	Maximum energy density	2.441
Virtual spindle diameter	70 mm	shape coefficient	0.596

.

2.5. Design Analysis of Motor and Other Protective Settings

Since the flywheel is suspended in normal working conditions without considering the influence of gravity and has a high requirement on the overall weight of it when it is applied to vehicle-mounted working conditions, the external rotor permanent magnet brushless motor with light weight, high efficiency, and large driving force is selected. The overall motor and torque and efficiency of the motor are shown in Figure 11.

In addition, the flywheel needs to run inside the vehicle and work at a very high speed, so it is very important for the safety and protection of flywheel energy storage. The flywheel can work for a long time at high speed; however, it can suddenly become out of control. If no protection measures are added, the flywheel may hit the stator, affect the magnetic circuit, or even paralyze the whole device. Therefore, a cylindrical ball bearing and a plane bearing are added to the protection shell and the top of the flywheel to protect the flywheel in real-time, as shown in Figure 12.

Furthermore, the five-degrees-of-freedom sensors are also shown in Figure 12. The five degrees of freedom require a total of nine eddy current sensors to carry out the flywheel in the five-degrees-of-freedom real-time position. The radial (x₁, y₁) and torsional (x₂, y₂) degrees of freedom are, respectively, detected by differential detection to improve the detection accuracy. In order to facilitate installation, only one sensor is required for the axis, and the function of differential detection is realized in the algorithm.

3. Experiments

3.1. Experimental Platform

In order to verify the above optimization results and flywheel stability and anti-interference, a series of performance verification experiments are conducted. The overall structure and its key components of a flywheel battery with a multi-function air gap are shown in Figure 13.

Two different experimental operating platforms are used in this paper. The performance test of the new flywheel battery is carried out on the fixed slide operating platform. On the complex road experimental platform, more realistic conditions are simulated.

Figure 14a shows the fixed slide operating platform designed to simulate the basic working conditions of the car, similar to starting, braking, and horizontal movement. As shown in Figure 14a, the experimental platform is equipped with two long and short slide rails. In addition to the horizontal movement of the x and y axes, a slope can also be created by adjusting the horizontal angle of the long slide rails. It can simulate the flywheel battery to accelerate, decelerate, start and stop, turn, travel uphill, and perform other movements. In addition, the operating platform is also equipped with horizontal and vertical shakers, which can be controlled by a separate controller to simulate the starting, braking, and other operating conditions of the flywheel battery under large acceleration and also simulate the vehicle-mounted operating conditions of the flywheel battery under different road excitation signals. This bench can collect test data of flywheel battery systems under precise signal excitation, so it is ideal for quantitative experimental testing.

In addition, road excitation experiments were carried out on the complex road experimental platform, as shown in Figure 14b. The mobile vehicle simulation platform mainly consists of an experimental car, a new flywheel energy storage system, a magnetic bearing control device, an experimental oscilloscope apparatus, and a distribution system. The flywheel battery system is placed on the experimental car. The experimental car has two control modes: pre-programming and remote control. The control system used in the experiment, the oscilloscope, and the mobile power supply for the control platform were fixed in a trailer, which was attached to the back of the experiment car. During the experiment, the experimental data of the car were received by the control system in real-time. The complex road test platform uses electric vehicles to carry the new flywheel battery, which more truly and intuitively simulates whether the flywheel battery has anti-interference ability and stable operation ability under complex road conditions.

3.2. Performance Tests

To verify the stable suspension performance of the flywheel battery system and ensure the real-time response is good, the basic magnetic suspension verification experiment was carried out first. The experimental conditions are as follows: the flywheel battery first moves uniformly forward along the long slide rail in the x direction. The magnetic suspension control system is suddenly applied at a certain moment. At this time, it is observed whether the flywheel battery can respond quickly and suspend stably. Figure 15 shows the displacements of the five-degrees-of-freedom flywheel. In order to more clearly represent the movement of the flywheel, the data measured by the two groups of radial sensors along the positive direction of the slide rail are set as x₁ and x₂, and the data measured by the two groups of radial sensors horizontally and vertically along the slide rail are set as y₁ and y₂, respectively. The data measured by the axial sensor are set to z. The offsets of the five degrees of freedom all decrease significantly and remain stable after the control current is applied. Since the flywheel battery is of vertical structure, the z displacement shown in Figure 15c has almost no displacement when there is no interference. At the same time, the flywheel rotates through the motor at the bottom. Because the sensor is placed in different positions, the peak-to-peak value of x₁ displacement and y₁ displacement at the top is slightly larger than x₂ displacement and y₂ displacement. Before the control is applied, the maximum offset of the displacement of flywheel x₁ is 0.05 mm. The flywheel tends to be stable soon after 50 ms adjustment, and the peak value of the displacement of flywheel x₁ decreases significantly to 0.021 mm. Similarly, the other four degrees of freedom also achieved stable suspension. It was proved that the design of the magnetic bearing system of the flywheel battery is reasonable and has a fast response speed, which can effectively and stably suspend the flywheel in the equilibrium position. Compared with the classic flywheel battery with a virtual inertia spindle in [9], the novel magnetic suspension flywheel battery with a multi-function air gap proposed in this paper significantly improved its stability and control response performance. Moreover, it was found that compared with the classical prototype in [9], the prototype proposed in this paper is still more stable and has faster control response speed under the condition of larger flywheel mass and more freedom of control, which shows the superiority of the new topological prototype proposed in this paper.

Further, in order to verify whether the magnetic circuit of the designed flywheel battery magnetic bearing system is truly decoupled, that is, to verify the decoupling performance of the flywheel battery, a decoupling verification experiment was carried out. This experiment was based on the fixed operation platform shown in Figure 14a. The experimental conditions were as follows: by adjusting the vibrator, the deceleration motion of the vehicle with an acceleration of 5 m/s² in x direction was simulated. The displacement of each degree of freedom of the flywheel is shown in Figure 16. As shown in Figure 16a,c, it can be seen that the on-board flywheel battery was impacted in the x direction, so the flywheel was offset due to interference in the x direction. Figure 16f shows the simulation curve of the x-direction offset made in the same environment as the flywheel simulated in the dynamics model. By comparing Figure 16a,c,f, the correctness of the optimized model can be obtained. After the transient disturbance disappears, the flywheel can quickly return to the equilibrium position after a period of adjustment of the magnetic suspension. At the same time, it was found that the displacements in the y and z directions were almost unaffected by interference in the x direction. It was proved that the design of the flywheel battery has good decoupling between multiple degrees of freedom. Therefore, the flywheel battery was designed with higher control efficiency. Compared with the original prototype, the new flywheel battery system can still have higher decoupling capability under the premise of improved integration [9].

Furthermore, anti-disturbance experiments were also conducted using the mobile car simulation platform, and their purpose was to verify the stability of flywheel batteries under complex road conditions. To better verify the performance of the vehicle in the face of real bumps, speed bumps commonly used on the road were selected. The experimental conditions were: the vehicle is moving in the x direction and passing the speed bump. Since the force on the flywheel when it passes over the speed bump under this working condition is mainly concentrated in the x and z directions, the displacement change in the x and z directions should be focused on. Figure 17a,b shows the x₁ displacement and z displacement of the flywheel after the car completely passes over the speed bump. The maximum deviation in the x direction was 0.074 mm, and the maximum deviation in the z direction was 0.072 mm. From the experimental results, the flywheel battery responded very quickly when deflected by continuous road excitation and had good anti-interference performance. Compared with the original prototype, although there was little change in the offset when encountering interference, it reacted in a shorter time and had a stronger anti-interference ability [20,21].

4. Conclusions

Because the traditional flywheel battery is difficult to balance in terms of energy storage density, volume, anti-interference ability, security protection, etc., it is difficult to promote and apply in the automotive field on a large scale. In order to solve the above problems, a new multi-functional air gap magnetic bearing flywheel battery was proposed. It is difficult to balance the volume and control accuracy of traditional magnetic bearings. The new magnetic bearing with a multi-function air gap can share a permanent magnet with different degrees of freedom, the structure is more compact, the control magnetic circuit is independent, and the coupling effect is reduced in the control process. The integrated design of the new bowl-shaped virtual axis flywheel has a higher energy storage density than the traditional flywheel and is matched with the new magnetic bearing only through several air gaps, which does not produce mechanical friction when rotating at high speed and can run higher speeds. In the performance test, the flywheel rotates smoothly under the control of the magnetic bearing, the magnetic bearing system design is reasonable, the control speed is sensitive, and the flywheel can be quickly and stably suspended. In the experiment, when one degree of freedom is disturbed, the other degrees of freedom are almost unaffected, which proves that the new flywheel battery has good control decoupling ability and the magnetic bearing can control the flywheel more quickly and efficiently. In the road excitation experiment, when many degrees of freedom are violently disturbed, they can all recover to the equilibrium position in a very short time, which proves that the new flywheel battery system has good anti-interference ability.