# Wheel-Rail Contact-Induced Impact Vibration Analysis for Switch Rails Based on the VMD-SS Method

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Extracting and Analyzing Methods for Impact Vibration Signals

#### 2.1. Impact Vibration Signal Extraction Method

#### 2.2. Feature Analysis of Impact Vibration

#### 2.3. Optimizing Sensor Arrangements

## 3. Experimental Study and Results

#### 3.1. Experiment Scheme and System

#### 3.2. Determining Passing Time and Correcting Velocity

_{1}–W

_{8}, respectively, could be observed from raw vibration signals. To determine the distances between each of the two adjacent pulses, the appearance time parameters of W

_{1}–W

_{8}were firstly extracted. Then, based on the preseted 16 km/h velocity, the distances between each two adjacent pulses can be calculated:

_{1}and W

_{2}: $v=2.6\text{}\mathrm{m}\xf70.5478\text{}\mathrm{s}\approx 4.75\text{}\mathrm{m}/\mathrm{s}=17.1\text{}\mathrm{km}/\mathrm{h}$. Then, the distances of ${d}_{{W}_{23}}$-${d}_{{W}_{78}}$ were recalculated and are illustrated in Table 2. Then, they were compared with the distances in Figure 3b. It can be observed from this table that the calculated distances were basically consistent with the actual distances with small errors, which verifies that the eight pulses were caused by the wheel–rail impacts when the vehicle passed the joint.

#### 3.3. Impact Vibration Extraction

^{−6}and 2–5, respectively. The central frequencies of the different IMF component numbers were calculated and are shown in Table 3. As seen in this table, when the number was two and three, the central frequency difference between the two IMFs was large, which was due to the under decomposition; when the number was five, the center frequencies of IMF3 and IMF4 were close, which was due to the over decomposition. Therefore, the IMF component number was selected as four in this section.

_{3}, W

_{5}and W

_{7}in IMF4, which are marked with red dotted lines. The possible physical meaning is that the impact vibrations were generated at a certain distance from the left side of the joint before the third, fifth and seventh wheelsets passed the switch rail area. This is consistent with the fact that the target damage in Figure 4b was located on the left side of the joint. However, the amplitudes of the three candidate impulses were almost equivalent to those of the background noise. To further extract the candidate impact vibrations, the SS method was applied to denoise the IMF4 component in this section.

_{3}, I

_{5}and I

_{7}, respectively. Then, the distances between I

_{3}-W

_{3}, I

_{5}-W

_{5}and I

_{7}-W

_{7}were calculated with the corrected velocity of 17.1 km/h. The calculated results are shown in the fifth row of Table 4. It can be observed that the distance between the small impulses and the joint was basically consistent with the 2.5 m in Figure 4b. Therefore, we assume that the small impulses were caused by the damage-induced impact vibrations.

_{4}, W

_{6}and W

_{8}. One possible reason for these phenomena is that the distance between each two adjacent wheelsets in a bogie is close to 2.5 m. This leads to the damage-induced impact vibrations with small amplitudes being masked by the joint induced impact vibration with large amplitudes from W

_{3}, W

_{5}and W

_{7}. The other possible reason for these phenomena is the wheel–rail contact states. Under different velocities of the track inspection vehicle, it is impossible to ensure that all wheels have good contact states at the damage and to generate corresponding impact vibrations.

## 4. Influences of Damage Dimensions and Velocities

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**The track inspection car and wheelset distances: (

**a**) track inspection car; (

**b**) wheelset distance parameters of track inspection.

**Figure 8.**Sensor results of different velocity impact vibrations. Sensor 1: (

**a**) 16 km/h, (

**b**) 12 km/h, (

**c**) 14 km/h, (

**d**) 18 km/h, (

**e**) 20 km/h; Sensor 2: (

**f**) 16 km/h, (

**g**) 12 km/h, (

**h**) 14 km/h, (

**i**) 18 km/h, (

**j**) 20 km/h.

**Figure 9.**The other damage and location parameters: (

**a**) damage 1 and location; (

**b**) damage 2 and location.

**Figure 10.**Extracted impact vibrations: (

**a**) results of sensor 1 from damage 1; (

**b**) results of sensor 2 from damage 1; (

**c**) results of sensor 1 from damage 2; (

**d**) results of sensor 2 from damage 2.

**Figure 12.**Frequency and amplitude features from different damage: (

**a**,

**d**) damage 2.5 cm × 2 cm; (

**b**,

**e**), damage 3 cm × 1.5 cm; (

**c**,

**f**) damage 1 cm × 1 cm.

Young’s Modulus/GPA | Poisson’s Ratio | Density/kg/m^{3} |
---|---|---|

206 | 0.3 | 7850 |

${\mathit{d}}_{{\mathit{W}}_{23}}/\mathbf{m}$ | ${\mathit{d}}_{{\mathit{W}}_{34}}/\mathbf{m}$ | ${\mathit{d}}_{{\mathit{W}}_{45}}/\mathbf{m}$ | ${\mathit{d}}_{{\mathit{W}}_{56}}/\mathbf{m}$ | ${\mathit{d}}_{{\mathit{W}}_{67}}/\mathbf{m}$ | ${\mathit{d}}_{{\mathit{W}}_{78}}/\mathbf{m}$ | |
---|---|---|---|---|---|---|

Calculated value | 9.44 | 2.58 | 4.44 | 2.62 | 9.39 | 2.57 |

Actual value | 9.4 | 2.6 | 4.46 | 2.6 | 9.4 | 2.6 |

Error | 0.43% | 0.77% | 0.45% | 0.77% | 0.1% | 1.1% |

IMF Component Number | Central Frequency of Modal Component/Hz | ||||
---|---|---|---|---|---|

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | |

2 | 33 | 1229 | |||

3 | 33 | 1229 | 2900 | ||

4 | 33 | 1229 | 2900 | 3655 | |

5 | 33 | 1229 | 2611 | 2900 | 3655 |

Preseted Velocity /km/h | Wave Crest | Measuring Point 1 | Measuring Point 2 | ||||
---|---|---|---|---|---|---|---|

I3 | I5 | I7 | I3 | I5 | I7 | ||

12 | Calculated value | 2.49 m | 2.62 m | 2.47 m | 2.55 m | 2.65 m | 2.48 m |

Error | 0.4% | 4.8% | 1.1% | 2% | 6% | 0.8% | |

14 | Calculated value | 2.53 m | 2.68 m | 2.5 m | 2.56 | 2.68 | 2.5 |

Error | 1.2% | 7.2% | 0% | 2.4% | 7.2% | 0% | |

16 | Calculated value | 2.55 | 2.69 | 2.52 | 2.49 | 2.64 | 2.49 |

Error | 2% | 7.6% | 0.8% | 0.4% | 5.6% | 0.4% | |

18 | Calculated value | 2.56 | 2.71 | 2.57 | 2.55 | 2.7 | 2.56 |

Error | 2.4% | 8.4% | 2.8% | 2% | 8% | 2.4% | |

20 | Calculated value | 2.58 | 2.7 | 2.56 | 2.55 | 2.65 | 2.53 |

Error | 3.2% | 8% | 2.4% | 2% | 6% | 1.2% |

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**MDPI and ACS Style**

Hu, P.; Wang, H.; Zhang, C.; Hua, L.; Tian, G.
Wheel-Rail Contact-Induced Impact Vibration Analysis for Switch Rails Based on the VMD-SS Method. *Sensors* **2022**, *22*, 6872.
https://doi.org/10.3390/s22186872

**AMA Style**

Hu P, Wang H, Zhang C, Hua L, Tian G.
Wheel-Rail Contact-Induced Impact Vibration Analysis for Switch Rails Based on the VMD-SS Method. *Sensors*. 2022; 22(18):6872.
https://doi.org/10.3390/s22186872

**Chicago/Turabian Style**

Hu, Pan, Haitao Wang, Chunlin Zhang, Liang Hua, and Guiyun Tian.
2022. "Wheel-Rail Contact-Induced Impact Vibration Analysis for Switch Rails Based on the VMD-SS Method" *Sensors* 22, no. 18: 6872.
https://doi.org/10.3390/s22186872