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Abstract

The braking of the rail transit train consumes a great quantity of energy, and the thermal energy produced in the process of braking can affect the normal operation of the transit train. Thus recycling the braking energy becomes a research hotspot of urban rail train. This paper made an overall analysis of regenerative braking process, the rationale, and the main features and then put forward the optimizing the structure of the composite flywheel concept and design calculation method. This paper also designs a new flywheel structure which can be applied on urban rail operating system. The new flywheel structure should be checked by finite element method and the radius of the rotor should be defined under the condition of meeting the requirements of carbon fiber material strength. Meanwhile, compared with the solid flywheel under the same condition, analysis shows that the maximum rotary inertia of the new flywheel and the quality energy density increased, and the discharge depth also perks up.

1. Introduction

Our country is in a period of high speed development of urban rail transit, and many large and medium-sized cities are planning to construct rail transit. Short station space leads to frequent starts and brakes, along with most of braking energy converted into heat energy to waste. 20 kilometers of subway consumes an average annual energy of 80 million KWH, most of which are used for traction power supplies [1].

The energy which subway brake wastes will be converted to heat energy, leading to the rise of temperature in internal or external environment of the station, having adverse effects on train operation, increasing the cost of operation management [2]. Train regenerative braking energy recovery, therefore, becomes the research hotspot and difficult issue. In this regard, the flywheel energy storage technology is focused on as the main method by academia [2].

There are much more developments and applications of flywheel energy storage in the United States, Germany, Japan, and other developed countries. Japan has created capacity in the world's largest frequency control of motor speed flywheel energy storage power generation systems. The flywheel energy storage technology already mature in the United States, and the University of Maryland has developed 24 KWH electromagnetic suspension flywheel system used for power peak regulation. High temperature superconducting magnetic levitation bearing flywheel energy storage system is being studied by France State Science Research Center, physics institute of technology in Germany and SISE in Italy. Engaged in flywheel research related to the current domestic units are the flywheel energy storage laboratory of engineering physics department of Tsinghua University, North China Electric Power University, Beijing Institute of Flywheel Energy Storage Flexibility, Beijing University of Aeronautics and Astronautics, Nanjing University of Aeronautics and Astronautics, China University, Chinese Academy of Sciences Mechanics, Southeast University, Hefei University of Technology, and so forth, mainly concentrated in small capacity series; among them, BUAA developed for space “energy storage and attitude control/maglev flywheel” has won the first award of national technological invention in 2007. Hebei province in North China Electric Power University and Chinese Academy of Sciences Institute of Electrical and Power Authority had already begun load of power system with flywheel energy storage system to study the subject, which is expected to make gratifying achievements [3].

In this paper, the flywheel battery is used as a way of energy saving, regenerative braking designs in the urban rail train flywheel energy storage control system, and optimizes the structure of flywheel battery. The optimization of the detachable system not only improves the rate of energy storage flywheel rotor structure but also increases the depth of the battery discharge. Finally this paper calculated and analyzed the model to establish a practical new type of urban rail train regenerative braking control system.

2. Based on Analysis of the Flywheel Storage Regenerative Braking System

2.1. The Methods of Urban Rail Train Regenerative Braking Energy Recycling

At present, foreign regenerative braking energy absorption devices mainly include resistor, capacitor energy storage, flywheel energy storage energy consumption, and inverter feedback four types [4].

Resistance energy dissipation type of regenerative braking energy absorption devices mainly adopts the way of absorbing resistor of the multiphase IGBT chopper and cooperates with constant pressure absorption, according to the fact that dc bus voltage of the regenerative braking state changes to adjust the conduction of chopper, so as to change the power absorption, the dc voltage constant in a certain value range, and the braking energy consumption on the absorbing resistor. The absorption device of the electric system is mainly composed of IGBT chopper, absorption resistance, diode, filter unit, dc circuit breaker, electric isolating switch, electromagnetic contactor, sensors, and a microcomputer control unit [5].

Capacitor energy storage type or the flywheel energy storage type regenerative braking energy absorption device mainly adopts IGBT inverter, the regenerative braking energy absorption of the train to the group or the flywheel motor high-capacity capacitor [6]. When the power supply range inside the train starts or speeds up to get flow, the device will store energy release and recycling. The absorption device of the electrical system mainly includes the group or flywheel energy storage capacitor motor, IGBT chopper, dc circuit breaker, electric isolating switch, and microcomputer control unit.

Inverter feedback type of regenerative braking energy absorption devices main power electronics device is adopted to form high power thyristor three-phase inverter; the inverter dc side is combined with the rectifier dc traction substation busbar; it receives an alternating current online communication into line. When regenerative braking making dc voltage is beyond a specified value, inverter startup and absorb from the dc bus current, regeneration can direct current into alternating current (ac) power frequency inverter fed back to the ac grid. The absorption device of the electric system mainly includes thyristor inverter, inverter transformers, balanced reactor, ac breaker, dc circuit breaker, and adjusting control cabinet [7].

The advantage of resistance type energy absorption equipment is easy control and its main drawback is that the regenerative braking energy consumption on the absorption resistance has not been used, and resistance heat dissipation is also contributing to the environmental temperature rise, which needs corresponding ventilation power plant to increase the power consumption. Capacitive energy storage type's main shortcoming is to set up the large capacitor Banks and capacitance caused by frequent in charge and discharge state short service life. The technology of flywheel energy storage type, as the flywheel in high speed rotating condition for a long time, and the quality of the flywheel is bad, the friction energy dissipation is serious and flywheel's life-span is short. Inverter feedback's weakness is to produce more harmonic, so it is needed to take corresponding harmonic control measures [8]. The technology is applied practically in Europe and Japan recently.

2.2. Working Principle of Flywheel Battery

Flywheel battery is the main way of flywheel energy storage. When inputting power, integrated motor works as the motor; the process of battery charging is the process of improving flywheel's speed. We can accelerate the conversion of permanent magnet synchronous motor, making the flywheel speed increase to the rated speed.

When outputting power, integrated motor works as a generator, the output voltage amplitude is similar to sine wave voltage, with the decline in the flywheel speed, and the amplitude of output voltage motor also decreased. Now the technology of DC voltage can be sine wave voltage rectifier with step-down DC chopper circuit for constant amplitude as we generally expect.

When the flywheel is during idle operation, the entire unit runs with minimal loss.

Above three points correspond to the flywheel of the three operating modes: charging mode, the discharging mode, keeping mode. The theory of flywheel battery works as shown in Figure 1.

Figure 1:

Schematic diagram of flywheel battery.

Traditional storage methods such as lead-acid and nickel-cadmium save electricity through a chemical reaction. They are unable to avoid energy density, low power, long charge times, and short life. New superconducting magnetic energy storage, compressed air energy storage, and super capacitor energy storage are still in the research phase, immature [2].

Flywheel batteries, as a new concept, overcome the above shortcomings of chemical batteries; their energy density and specific power are considerably higher than the general chemistry of batteries and internal combustion engines, and flywheel battery energy has high density, light weight, and fast charging, without any exhaust pollution and waste, and is not sensitive to temperature (chemical high or low temperatures; the battery performance drops dramatically, while the flywheel batteries affected are small), easy to measure depth of discharge. Therefore, flywheel batteries were made in the early 90th century, aroused high attention, and became the hotspot of study [8].

3. The Optimization Design of the Flywheel Structure of Split Rotor Which Can Be Split

3.1. Design Idea to Flywheel Structure of Split Rotor Which Can Be Split

The existing flywheel structure characteristics are as follows [9].

The energy storage of flywheel is E_{max ⁡} = (1/2)Jw_{max ⁡}²; accordingly, flywheel energy storage is restricted by the moment of inertia and maximum angular velocity. The traditional approach to improve the moment of inertia is to increase the weight of the flywheel. As a result, the weight of existing flywheel tends to be heavy; the speed is restricted by the flywheel material.

The depth of discharging of the flywheel and the moment of inertia of the flywheel rotor are constant. When speed of the flywheel turned down to a certain value on discharging, the kinetic energy cannot be recycled.

In tackling these questions, this paper puts forward the optimized model as shown in Figure 2(a). The flywheel rotor of the the improved model consists of two parts: external and internal detachable rotor. The mass distribution of the flywheel rotor can change with rotating speed by using the design of the spring and split rotor which can be split in order to change its moment of inertia. Figure 2(c) is for split rotor which can be split.

Figure 2:

Internal structure of the flywheel rotor.

It is important to note that spring stiffness is an important parameter. It involves the most lateral and the most central position that the spring could reach; nevertheless, the two positions are closely related to the minimum and maximum moment of inertia of the flywheel. The stiffness of the spring is related to the diameter, material, wire diameter, and number of turns. Here, we concerned ourselves with the ability against deformation under dynamic loading and that is dynamic stiffness which is the needed dynamic force that caused the unit amplitude. When designing the stiffness of the spring, select the type of increasing stiffness. The stiffness of the spring increases by the increase of the deformation and it also has a good buffer damping performance under the maximum or impact loading. It can ensure that the spring pushes the flywheel to the center at minimum speed; at the same time, it can retain certain space when the flywheel is in the lateral position [10].

Improving the working principle of flywheel is as follows.

Charging mode: when the flywheel started charging, the split rotor is in the center of the flywheel and the flywheel rotor is in the moment of inertia of the minimal state. When the rotor speed increases, the split rotor is by centrifugal force F = mw²r (where w is the moment of inertia of the flywheel rotor and r is a split rotor center of mass to the intermediate distance), and split rotor slips along the connecting rod to the outer wall rotor under the action of centrifugal force. As the spring compression increases, the moment of inertia of the flywheel rotor increases gradually and the power is put into the flywheel. When the moment of inertia increases to the largest, flywheel energy storage and achieve maximum.

Keeping mode: when the flywheel is in keeping mode, flywheel rotor rotates at a constant speed and the device runs with the minimum loss.

Discharging mode: it is the reverse of the charging mode, because of the improved design of flywheel battery using the split rotor structure (as shown in Figure 2). When discharging, the rotor angular velocity reduced, centrifugal force reduced, the amount of compression spring reduced, split rotor sliding to the center, the moment of inertia of the flywheel rotor reduced, and then the battery energy E_{min ⁡} = (1/2)J_{min ⁡}w_{min ⁡}² which is to maintain the same speed reduced to increase the depth of discharging effectively.

3.2. Calculation of Optimizing the Structure of the Flywheel Battery Design Factor

When the flywheel has just started charging, split rotor which can be split is in the center of the flywheel, as shown in Figure 2(a); then the moment of inertia of the flywheel rotor is in a minimum state; its value is

J_{\min} = 4 J_{1} + 4 J_{2} + 8 J_{3} + J_{4} = \frac{π}{2} ρ_{1} h r_{1}^{4} + \frac{π}{2} ρ_{2} h r_{2}^{4} + π ρ_{2} h r_{2}^{2} {(\frac{2 \sqrt{2} r_{2}}{π} + R + r_{2} - δ)}^{2} + \frac{2 π}{3} ρ_{3} d^{2} {(R - δ)}^{3} + \frac{π}{2} ρ h R^{4} - \frac{π}{2} ρ h {(R - δ)}^{4} .

(1)

The energy of flywheel battery is E_{min ⁡} = (1/2)J_{min ⁡}w_{min ⁡}².

After the flywheel fully charged, it rotates with maximum angular velocity high speed, the split rotor is at the most outer edge of the flywheel, as shown in Figure 2(b), and then the moment of inertia of the flywheel rotor is in the maximum state; its value is

J_{\max} = 4 J_{1}^{'} + 4 J_{2} + 8 J_{3} + J_{4} = \frac{π}{2} ρ_{1} h r_{1}^{4} + π ρ_{1} h r_{1}^{2} {(\frac{2 \sqrt{2} r_{1}}{π} R + r_{1} - δ)}^{2} + \frac{π}{2} ρ_{2} h r_{2}^{4} + π ρ_{2} h r_{2}^{2} {(\frac{2 \sqrt{2} r_{2}}{π} + R - r_{2} - δ)}^{2} + \frac{2 π}{3} ρ_{3} d^{2} {(R - δ)}^{3} + \frac{π}{2} ρ h R^{4} - \frac{π}{2} ρ h {(R - δ)}^{4} .

(2)

The energy of flywheel battery is E_{max ⁡} = (1/2)J_{max ⁡}w_{max ⁡}² + (1/2)kx².

Deep calculation of optimization of the flywheel battery discharging:

\begin{matrix} α = \frac{E_{\max} - E_{\min}}{E_{\max}} \\ = \frac{(1 / 2) J_{\max} w_{\max}^{2} + (1 / 2) k x^{2} - (1 / 2) J_{\min} w_{\min}^{2}}{(1 / 2) J_{\max} w_{\max}^{2} + (1 / 2) k x^{2}} \\ = \frac{J_{\max} w_{\max}^{2} + k x^{2} - J_{\min} w_{\min}^{2}}{J_{\max} w_{\max}^{2} + k x^{2}} . \end{matrix}

(3)

The meaning of the letters in the formula is as follows: J₁—a quarter-section of split rotor of moment of inertia, J₂—a quarter-section of the ring wall of the moment of inertia, J₃—moment of inertia of the connecting rod, J₄—moment of inertia of the outer wall, k—the stiffness coefficient of Spring, h—the thickness of flywheel, r₁—the radius of split rotor, ρ₁—the density of a split rotor, ρ₂—the density of the outer wall of a quarter circle, ρ₃—the density of the connecting rod, ρ—the density of the outer wall, m₃—the quality of outer wall of the flywheel rotor, δ—the thickness of the outer wall, R—the radius of outer wall, ω_{min ⁡}, ω_{max ⁡}—the minimum angular velocity and the maximum angular velocity. Take the following simplification: (1) the connecting rod simplified into thin rod; (2) ignore the moment of inertia at the overlap part of the connecting rod with split rotor [11].

4. Finite Element Analysis of Stress Intensity Checking

This paper takes a quarter-section of the rotor. According to the simplified calculation methods, to verify modeling and analysis of the design is reasonable. Use finite element analysis software. When creating the model, take into account the convenience meshing and operation of the rotor. Use basic 3D solid elements SOLID45; it belongs to the linear unit. The rim use SOLID46 unit can ensure the accuracy of the analysis as possible. Meanwhile, the wheel applied full constraint shaft hole, the displacement of constraints section axial and circumferential. To apply load on the model, it can give the angular velocity. To determine the stress-strain laws of different conditions, the flywheel rotor was set different outside diameters.

To verify the rationality of the design, this paper did the simulation calculation of optimization model. According to the characteristics of symmetry, strength calculation is simplified into a quarter model, assuming that it runs with the maximum speed of design; the stress nephogram is shown in Figure 3.

Figure 3:

The maximum principal stress contours with maximum speed flywheel.

As shown in Figure 3 of this paper, it took 60 cm of outer radius. Maximum principal stress of the exterior surface of flywheel is 1.02 GPa, the maximum principal stress of the foot point is 2.32 GPa, and general strength of carbon fiber materials is 4.2 GPa, meeting the strength requirement [12]. Considering that the head space of urban rail train is greater, outer radius can increase appropriately; it makes full use of the characteristics of stable operation and large space of urban rail trains, increasing the battery capacity to control the whole grid system more efficiently. Assuming that other conditions are unchanged, stress intensity and energy storage corresponding to different outer radius are shown in Table 1.

Table 1:

Different outer radius corresponding to stress intensity flywheel energy storage design parameters.

Size of flywheel	Outer radius 60 cm	Outer radius 70 cm	Outer radius 80 cm	Note

Maximum energy that can store (J)	7.60 × 10⁶ > A	1.17 × 10⁷ > 1.5A	$\begin{matrix} 1.17 \times 1 0^{7} > 2 A \end{matrix}$	Carbon fiber material strength σ_y = 4.2 GPa
Maximum stress of outside surface (GPa)	$\begin{matrix} 1.02 < σ_{y} \end{matrix}$	$\begin{matrix} 1.30 < σ_{y} \end{matrix}$	$\begin{matrix} 2.37 < σ_{y} \end{matrix}$
Maximum stress of foot points(GPa)	$\begin{matrix} 2.32 < σ_{y} \end{matrix}$	$\begin{matrix} 3.93 < σ_{y} \end{matrix}$	$\begin{matrix} 5.35 > σ_{y} \end{matrix}$
Maximum energy that can be recycled of every car A = 6.75 × 10⁶ (J)

In Table 1, the results show that when the outer radius of the flywheel is not more than 70 cm, the strength of general carbon fiber 4.20 GPa can meet the value of the maximum principal stress in the outer surface of the flywheel and the foot point; when the outer radius of the flywheel is more than 70 cm, at first the strength of general carbon fibers does not meet maximum principal stress of foot point of flywheel and you can hold that the flywheel rotor cannot work. The above analysis shows that the flywheel rotor outer radius in this paper cannot be more than 70 cm to meet the requirements of the intensity of general carbon fiber material.

4.1. Contrastive Analysis with Solid Flywheel Structure

Flywheel rotor diameter in designed optimization model is D = 60 cm, the thickness of outer wall is δ = 5 cm, internal split rotor diameter is d = 20 cm, height is h = 20 cm, material of flywheel is carbon fiber/epoxy resin (T 300/5208), the density is ρ = 1800 kg/m³, the maximum speed of flywheel rotor is 18000 r/min, and the minimum speed is 1350 r/min.

The diameter of ordinary solid flywheel rotor with the same quality is D = 40 cm, the material is same, the density is ρ = 1800 kg/m, the maximum speed of flywheel rotor is 18000 r/min, the minimum speed is 1350 r/min, under the condition of the same quality, and comparison of various parameters of these two different types of flywheels is shown in Table 2.

Table 2:

Structural specifications comparison of ordinary flywheel and flywheel rotor which can be split.

Parameter variety	Weight (kg)	J_{min ⁡} (kg·m²)	J_{max ⁡} (kg·m²)	Minimum energy (J)	Maximum energy (J)	Mass energy densityJ/kg	Depth of discharging α

Improved flywheel	42.41	4.23	4.86	4.23 × 10⁴	8.71 × 10⁶	2.03 × 10⁵	99.3%
Ordinary flywheel	42.41	0.84	0.84	8.47 × 10³	1.50 × 10⁶	3.55 × 10⁴	98.2%

As shown in the result, comparing the optimization model with the ordinary solid flywheel, the largest moment of inertia increased by 5.79 times, and the quality of the energy density increased by 5.72 times. This shows that the energy storage capacity of improved structure of flywheel was better than solid flywheel [13].

In the experiments, the sliding friction force is proportional to the pressure between the rotor and the outer wall; that is, f = μN; parameter μ is the coefficient of sliding friction [14, 15]. We can adopt vacuum method to reduce the air resistance in order to reduce the energy consumption of the flywheel; the coefficient of friction is between 0.30 and 0.03, increasing with relative sliding velocity; when the actual contact area has a linear relationship with the friction interface load, the sliding friction coefficient has nothing to do with the contact area.

In terms of structural reliability, mechanical structure reliability mainly focused on the response of the probability of random variable parameters under the specific distribution. This paper carries out statistical analysis on the new structure of flywheel using the NESSUS software. Based on the analysis of the cause of failure, the main influence factors are random parameters such as stress and strength. The failure occurring in limit state is discussed in another paper.

5. Conclusion

This paper proposes a detachable rotor structure of flywheel energy storage format and detailed analysis structure design and structural features of this new type. Calculate and analyze flywheel battery structure after it has improved, which derived the formula of depth of the flywheel battery discharge. The formula has important significance on the new math flywheel energy storage can be split rotor structure analysis and it has an important mathematical sense about the analysis of the new structure of energy storage of split rotor.

This paper has analyzed the new structure by the numerical simulation. Meanwhile, based on the premise of the same quality, the new structure compared with the flywheel before it improved; the conclusions are shown as follows.

When the new type of detachable flywheel rotor outer radius is not more than 70 cm, the maximum principal stress can meet the requirements of the intensity of general carbon fiber material; it defines the scope of the outer radius of the new structure of energy storage of split rotor.

The new structure compared with the flywheel before it improved. The maximum moment of inertia is increased by 5.79 times and the quality energy density increased by 5.83 times; that is, the energy storage ability of new flywheel increased, while the battery quality is the same, and also the depth of the battery discharge is increased.

In this paper, although a detailed design theory research has been carried on, to build a practical urban rail trains flywheel energy storage regenerative braking control system remains further model test research and real engineering validation.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

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