# Optimisation and Management of Energy Generated by a Multifunctional MFC-Integrated Composite Chassis for Rail Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. Finite Element Analysis of the Vehicle

#### 2.1. Finite Element Model

#### 2.2. Vibration Data Analysis

#### 2.3. Stress Responses Used for Power Prediction

## 3. Power Generation and Management

#### 3.1. AC Power Prediction Using MFC Piezoelectric Material

_{x}and E

_{y}aligned to the rod and electrode directions, respectively. The piezoelectric and dielectric properties of the MFC are shown in Table 4. In accordance with the time-varying stress distributions in the chassis structure obtained from FE analysis considering the aim of harvesting the highest power, eight MFC location possibilities (as shown in Figure 8a,b) were evaluated which cover the stress concentration areas and high stress regions. MFC 1 to MFC 4 are designed in rectangular geometry of 100 × 50 × 0.3 mm

^{3}and MFC 5 (same as MFC 6) to MFC 7 (same as MFC 8) are designed in triangular shape with area domains of 13,488.2 mm

^{3}and 17,789.3 mm

^{3}, to fit the geometry of the bogie mount structures. It should be noted that the acoustic impedance mismatch between the piezoelectric MFC and carbon fiber used in the simulation is ignored, as its effect is relatively low compared to the mechanical vibration and also the interested frequency in our application is lower compared to that of acoustic.

_{31}or d

_{33}mode depending on the poling direction and the stress direction. It is typical that the d

_{31}mode is usually seen in piezoelectric films, where the electric field is perpendicular to the direction of mechanical strain; the d

_{33}mode appears as piezoelectric stacks where both electric field and strain are in the poling direction. As charge constant, d, is defined as the short circuit charge density per applied mechanical stress, the generated short circuit charge and current can be summarised by Equations (1) and (2) [29],

_{sc}is the short circuit electrical charge; I

_{st}is the short circuit current; σ

_{av}is the average stress experienced by the piezoelectric domain and A is the active area of the piezoelectric domain; ω is the frequency where the piezoelectric transducer excites, FFT was carried out on the time domain response from the FE simulation in order to assess the frequency characteristics.

_{load}, the current generated across the load, I

_{load}(t) is given by Equation (3). To maximise power output, impedance matching is needed between Z

_{load}and Z

_{i}. For short circuit, Z

_{load}= 0, the factor $\frac{{Z}_{i}}{\sqrt{{Z}_{i}^{2}+{Z}_{load}^{2}}}$ = 1. As Z

_{load}$\to \infty $, $\frac{{Z}_{i}}{\sqrt{{Z}_{i}^{2}+{Z}_{load}^{2}}}$ $\to 0$. Therefore, the generated power across a matched impedance load, P

_{m}can be calculated using the following Equations:

_{p}is the capacitance of the piezoelectric material.

#### 3.2. Rectified Power Prediction

_{S}) used in the simulations were chosen at 1 mF. In the diagrams, the piezoelectric transducer (PT) has been modelled as a current source (I

_{P}) in parallel with its inherent capacitor (C

_{P}). In these three rectifiers, only the FBR is a passive rectifier using four passive diodes. The SO and SSHC rectifiers are active rectifiers requiring additional circuit designs to generate the control signals to drive the switches. The circuit implementations of the SSHC rectifier have been detailed in [35]. The number k represents the number of capacitor stages to perform as a k-stage SSHC rectifier. The SO rectifier is a simplified SSHC rectifier with the ϕ

_{0}switch only by removing all the following capacitor stages. Hence, the SO rectifier can be also regarded as a zero-stage SSHC rectifier.

_{S}, as shown in Figure 11. For the SSHC rectifier, different numbers of employed capacitors are simulated for various output power values with different performance levels. The more capacitors that are employed, the higher the peak output power that is achieved. However, more capacitors in SSHC rectifiers also result in more complicated control circuits, larger system sizes and higher optimal output voltage levels to achieve the peak power. The simulations were performed for V

_{S}values ranging up to 300 V. The peak output power of each rectifier and the corresponding optimal output power are summarised in Table 5. From this table, it can be found that when using a passive FBR, the peak rectified power is around 21.2 mW from all eight MFC elements. When an eight-stage SSHC rectifier is employed, the peak rectified power achieves 181.9 mW, which is more than eight times higher compared to a passive FBR. In order to achieve this high output power, the output voltage, V

_{S}, of the SSHC rectifier needs to be maintained at around 300 V. Since this optimal voltage is usually higher than the supply voltages for most low-power loads, an efficiency DC-DC converter and a voltage regulator are typically required to power the load electronics.

## 4. Discussion on Use of Power Budget

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CFRP | carbon fiber reinforced polymer |

FBR | full-bridge rectifiers |

FEA | finite element analysis |

MFC | micro fiber composites |

SO | switch-only |

SSHC | synchronized switch harvesting capacitors |

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**Figure 2.**(

**a**) Exploded view of the main components in the rail vehicle; (

**b**) multi-material design of a simplified light rail vehicle structure. Units in mm. The vehicle length, width and height are 11.0, 2.7 and 3.1 m, respectively.

**Figure 3.**The schematic of the FE model setup and power prediction from the piezoelectric MFC on composite rail chassis when subjected to vibrational data input discussed in this paper.

**Figure 4.**(

**a**) Boundary conditions of the FE model of the vehicle, (

**b**) mesh convergence study, (

**c**) 1st bending mode (6.018 Hz) and (

**d**) 1st torsional mode (6.763 Hz) of the vehicle.

**Figure 5.**Representative environment vibrations for three axes of train cabin interior, including time domain vibration data and FFT analysis.

**Figure 6.**Left side: displacement and right side: stress distributions of the half chassis model under (

**a**) X-axis (Scale factor = 100), (

**b**) Y-axis (Scale factor = 100) and (

**c**) Z-axis (Scale factor = 50) accelerations at 2.016 s; red and yellow box circles the high stress regions at lower chassis connection and bogie mount, respectively.

**Figure 7.**Von Mises stresses vs. time plots of (

**a**) lower chassis connection, and (

**b**) bogie mount central.

**Figure 8.**(

**a**) The location possibilities of the MFC transducers on carbon fiber chassis structure, (

**b**) the principle of the MFC transducer used to generate electrical power based on an electrical load, Z

_{load}.

**Figure 11.**Simulated rectified output power using FBR, switch-only (SO) rectifier and SSHC rectifier (with different numbers of capacitor stages) for all the eight MFC elements.

**Table 1.**Properties of the materials used in the vehicle structure. (Material breakdown in Figure 2b).

Elastic Modulus (GPa) | Poisson’s Ratio | Density (kg/m^{3}) | |
---|---|---|---|

Steel | 210 | 0.29 | 7850 |

Aluminium | 69 | 0.3 | 2700 |

CFRP (RC200T) [29] | E_{x} = 59.45, E_{y} = 60.30, E_{z} = 3.90G _{xy} = 62.90, G_{yz} = 1.50, G_{x}_{z} = 62.35 | υ_{xy} = 0.3υ _{yz} = 0.4υ _{xz} = 0.3 | 1800 |

Mode | Freq. (Hz) |
---|---|

1st bending (Figure 4b) | 6.018 |

2nd bending | 19.935 |

1st torsional (Figure 4c) | 6.763 |

2nd torsional | 14.407 |

3rd torsional | 21.921 |

1st lateral | 23.839 |

**Table 3.**Mechanical properties of MFC [33], E

_{x}and E

_{y}are the elastic modulus in the rod and electrode directions, respectively.

E_{x} (GPa) | E_{y} (GPa) | G_{xy} (GPa) | ν_{xy} | Density (kg/m^{3}) |
---|---|---|---|---|

30.34 | 15.86 | 5.52 | 0.31 | 5400 |

**Table 4.**Piezoelectric and dielectric properties of MFC [33].

Charge Constant d_{31} (pC/N) | −170 |

Charge constant d_{33} (pC/N) | 400 |

Capacitance per unit area C_{p} (nF/cm2) | 7.8 |

Dielectric permittivity ε_{p} | 0.15 |

**Table 5.**Peak rectifier power for each rectification circuit and the corresponding optimal output voltage.

Rectifiers | Peak Power (mW) | Optimal V_{S} (V) |
---|---|---|

FBR | 21.2 | 48 |

Switch-only | 42.3 | 96 |

SSHC (1-cap) | 63.4 | 144 |

SSHC (2-cap) | 84.6 | 192 |

SSHC (4-cap) | 126.9 | 288 |

SSHC (8-cap) | 181.9 | 300 |

Peak Rectified Power (mW) | Percentage (%) | ||||||
---|---|---|---|---|---|---|---|

MFC No. | FBR | Switch-only | SSHC (1-cap) | SSHC (2-cap) | SSHC (4-cap) | SSHC (8-cap) | |

1 | 0.28 | 0.56 | 0.84 | 1.12 | 1.68 | 2.79 | 1.2 |

2 | 0.31 | 0.61 | 0.92 | 1.23 | 1.84 | 3.06 | 1.3 |

3 | 11.89 | 23.78 | 35.67 | 47.57 | 71.35 | 118.92 | 51.7 |

4 | 9.34 | 18.68 | 28.01 | 37.35 | 56.03 | 93.38 | 40.6 |

5 | 0.24 | 0.47 | 0.71 | 0.94 | 1.41 | 2.36 | 1.0 |

6 | 0.19 | 0.39 | 0.58 | 0.77 | 1.16 | 1.94 | 0.8 |

7 | 0.35 | 0.69 | 1.04 | 1.38 | 2.07 | 3.46 | 1.5 |

8 | 0.41 | 0.82 | 1.22 | 1.63 | 2.45 | 4.08 | 1.8 |

**Table 7.**Estimated power budget of the sensor platform with the application of the route assumption of this vehicle.

Power Budget Item | Power (mW) | Active in Period (%) | Active Time in One Route Cycle (s) | Power in One Route Cycle (mW) |
---|---|---|---|---|

MEMS 9 DOF motion sensor + MPU [42] × 2 units | 0.05 | 100% | 1200 | 1 |

Inclinometers [43] × 2 units | 56.25 | 100% | 1200 | 112.50 |

Distance sensors [44] × 2 units | 13.95 | 100% | 1200 | 27.90 |

Microprocessor unit (MPU) (active mode [45]) × 2 units | 0.36 | 100% | 1200 | 0.72 |

Bluetooth 5 + RF chip (transceiver mode [46]) × 2 units | 27 | 20% | 240 | 10.80 |

Bluetooth 5 + RF chip (sleep mode, clock [46]) × 2 units | 0.045 | 80% | 960 | 0.08 |

Sum | 153.00 |

Type of Rail Harvesting | Energy Harvest | Methodology | Comments |
---|---|---|---|

Train induced track vibration | 2–4 V | Experiments | For 6.35 mm track displacement input, from Wang et al. [36] |

0.02–0.2 mW | Experiments Analytical modelling | For slack-type and patch-type piezoelectric transducers, from Wang et al. [37] | |

100.3–157.1 mW | Analytical modelling | With passing train speed from 190 to 200 km/h, from Cleante et al. [38] | |

Electrification of railway stations | 541.6 kW | Electronics simulation | Jiang et al. [41] |

Unsprung mass vibration | 21.4 mW | Analytical modelling | Ghandchi Tehrani et al. [39] |

1–5 wheel health index | Experiments | Wheelwright et al. [40] | |

Sprung mass vibration | 21.2–181.9 mW | Finite element modelling Electronics simulation | This work |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Du, S.; Micallef, C.; Jia, Y.; Shi, Y.; Hughes, D.J. Optimisation and Management of Energy Generated by a Multifunctional MFC-Integrated Composite Chassis for Rail Vehicles. *Energies* **2020**, *13*, 2720.
https://doi.org/10.3390/en13112720

**AMA Style**

Liu Y, Du S, Micallef C, Jia Y, Shi Y, Hughes DJ. Optimisation and Management of Energy Generated by a Multifunctional MFC-Integrated Composite Chassis for Rail Vehicles. *Energies*. 2020; 13(11):2720.
https://doi.org/10.3390/en13112720

**Chicago/Turabian Style**

Liu, Yiding, Sijun Du, Christopher Micallef, Yu Jia, Yu Shi, and Darren J. Hughes. 2020. "Optimisation and Management of Energy Generated by a Multifunctional MFC-Integrated Composite Chassis for Rail Vehicles" *Energies* 13, no. 11: 2720.
https://doi.org/10.3390/en13112720