# Testing the Effectiveness of the Anti-Bending Bar System to Reduce the Vertical Bending Vibrations of the Railway Vehicle Carbody Using an Experimental Scale Demonstrator

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Scale Demonstrator for Carbody with Anti-Bending Bar System

^{®}(PCB Piezotronics, Depew, NY, USA), model 086C03 were utilized (Figure 6). For the acquisition and processing of experimental data, a NI cDAQ-9174 (Emerson, Austin, TX, USA) chassis equipped with a specialized NI 9234 module was used (Figure 6).

## 3. Finite Element Model of Experimental Scale Demonstrator for Carbody without/with Anti-Bending Bar System

## 4. Experimental and Theoretical Results

#### 4.1. Acceleration Measured on the Scale Model of the Carbody

^{2}. The other peaks are much smaller, at 0.791 m/Ns

^{2}, 1.71 m/Ns

^{2}and 1.961 m/Ns

^{2}.

^{2}. The other accelerance peak values also change due to the presence of the anti-bending bar system, but to a much lesser extent.

#### 4.2. Determination of Rubber Support Stiffness

^{2}= −1), $\overline{w}(x)$, $\overline{\mathsf{\theta}}(x)$ are the complex amplitudes of displacement and angle of rotation of the beam in the x-section of the reference system Oxz, $\overline{F}$ the complex amplitude of the harmonic excitation force of angular frequency ω, l

_{1}and l

_{2}determine the position of the rubber supports, x

_{F}= L/2 is the position of the excitation force, where L is the length of the beam and δ(.) is Dirac’s delta function. The last term in Equation (1) represents the sum of the two elastic forces in the rubber supports.

^{w}(x, ξ) is Green’s function associated with the free-free Timoshenko beam.

_{1,2}, it obtains

_{F}= L/2 și l

_{2}= L − l

_{1}, it follows for the reason of symmetry

^{3}, m = 49.4 kg/m, S = 62.93 × 10

^{−4}m

^{2}, I = 1816 × 10

^{−8}m

^{4}, L = 0.82 m, l

_{1}= 0.184 m, l

_{2}= 0.636 m and x

_{F}= 0.41 m; loss factor of rail coupon material (steel) η

_{steel}= 0.17%. With these values, the peak due to the first bending mode of the rail coupon has the frequency 1198 Hz and the value 0.5994 m/Ns

^{2}.

^{2}.

#### 4.3. Accelerance of the Scale Model of the Carbody—Theoretical Results

_{Al}= 2700 kg/m

^{3}, Young’s modulus 70 GPa and Poisson coefficient ν

_{Al}= 0.33. The dimensions of the CAD model are as shown in Section 2.

^{2}, 0.7975 m/Ns

^{2}, 1.713 m/Ns

^{2}and 1.961 m/Ns

^{2}.

^{2}.

## 5. Conclusions

- -
- The first bending frequency of the scale model of the carbody increases from 9.01 Hz to 13.4 Hz and thus goes out of the zone of maximum sensitivity of the human being to vertical vibrations;
- -
- Peak accelerance corresponding to the first bending frequency of the carbody decreases from 14.85 m/Ns
^{2}to 6.562 m/Ns^{2}; - -
- Damping of the first three bending modes of the scale model of the carbody increases especially in the first two modes, by 60% in the first mode and by 71% in the second mode.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The functional principle of the passive system with anti-bending bars: (

**a**) scheme of vehicle with anti-bending bars: 1. carbody; 2. support; 3. anti-bending bar; 4. wheelset; 5. bogie chassis; 6. primary suspension; 7. secondary suspension; (

**b**) carbody when the anti-bending bars are compressed; (

**c**) carbody when the anti-bending bars are stretched.

**Figure 2.**Influence of the anti-bending bar system in terms of PSD of the carbody acceleration at 270 km/h: (

**a**) at the carbody centre; (

**b**) above the front bogie; and (

**c**) above the rear bogie [17].

**Figure 3.**Sketch of experimental demonstrator system for the carbody with anti-bending bar system (after [24]).

**Figure 4.**Experimental scale demonstrator system: (

**a**) carbody scale model without anti-bending bar system; (

**b**) carbody scale model with anti-bending bar system.

**Figure 5.**Details of the experimental scale demonstrator system: (

**a**) support of the anti-bending bar; (

**b**) rubber support.

**Figure 6.**Components of the measurement system: 1. accelerometer; 2. impact hammer; 3. NI cDAQ-9174 type chassis; 4. NI 9234 module.

**Figure 8.**CAD model for experimental scale demonstrator for the carbody with anti-bending bar system.

**Figure 9.**CAD model for experimental scale demonstrator for the carbody without anti-bending bar system.

**Figure 10.**Discretization of element finite model for experimental scale demonstrator for the carbody with anti-bending bar system (1/4 model).

**Figure 11.**Accelerance experimentally determined in the middle of the scale model of the carbody without anti–bending bar system.

**Figure 12.**Accelerance experimentally determined in the middle of the scale model of the carbody with anti–bending bar system.

**Figure 16.**Acceleration in the middle of the scale model of the carbody without anti–bending bar system (FEM model).

**Figure 17.**Accelerance in the middle of the scale model of the carbody with anti–bending bar system (FEM model).

**Figure 18.**Carbody vibration mode 2: (

**a**) no anti-bending bar system; (

**b**) with anti-bending bar system.

**Table 1.**Vibration modes frequency of the scale model of the carbody without anti-bending bar system.

Mode | Frequency [Hz] | Error [%] | |
---|---|---|---|

Experimental | FEM | ||

1 | 9.012 | 9.019 | 0.0777 |

2 | 44.06 | 45.32 | 2.860 |

3 | 78.69 | 78.24 | −0.572 |

4 | 172.3 | 170.7 | −0.929 |

Mode | Frequency [Hz] | Error [%] | |
---|---|---|---|

Experimental | FEM | ||

1 | 13.44 | 13.81 | 2.753 |

2* | 47.44 | 43.63 | −8.031 |

2 | 51.56 | 47.47 | −7.933 |

4 | 92.63 | 91.00 | −1.760 |

5 | 165.8 | 160.2 | −3.378 |

**Table 3.**Damping vibration modes of scale models of the carbody without/with anti-bending bar system.

Mode | Without Anti-Bending Bar System | With Anti-Bending Bar System | ||
---|---|---|---|---|

Frequency [Hz] | Damping Ratio [%] | Frequency [Hz] | Damping Ratio [%] | |

1 | 9.019 | 0.21 | 13.81 | 0.336 |

2* | - | - | 43.63 | 0.02 |

2 | 45.32 | 0.90 | 47.47 | 1.54 |

3 | 78.24 | 1.32 | 91.00 | 1.57 |

4 | 170.7 | 1.005 | 160.2 | 1.005 |

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**MDPI and ACS Style**

Mazilu, T.; Dumitriu, M.; Sorohan, Ș.; Gheți, M.A.; Apostol, I.I.
Testing the Effectiveness of the Anti-Bending Bar System to Reduce the Vertical Bending Vibrations of the Railway Vehicle Carbody Using an Experimental Scale Demonstrator. *Appl. Sci.* **2024**, *14*, 4687.
https://doi.org/10.3390/app14114687

**AMA Style**

Mazilu T, Dumitriu M, Sorohan Ș, Gheți MA, Apostol II.
Testing the Effectiveness of the Anti-Bending Bar System to Reduce the Vertical Bending Vibrations of the Railway Vehicle Carbody Using an Experimental Scale Demonstrator. *Applied Sciences*. 2024; 14(11):4687.
https://doi.org/10.3390/app14114687

**Chicago/Turabian Style**

Mazilu, Traian, Mădălina Dumitriu, Ștefan Sorohan, Marius Alin Gheți, and Ioana Izabela Apostol.
2024. "Testing the Effectiveness of the Anti-Bending Bar System to Reduce the Vertical Bending Vibrations of the Railway Vehicle Carbody Using an Experimental Scale Demonstrator" *Applied Sciences* 14, no. 11: 4687.
https://doi.org/10.3390/app14114687