# Model Updating of a Freight Wagon Based on Dynamic Tests under Different Loading Scenarios

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^{2}

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## Abstract

**:**

## 1. Introduction

- -
- The calibration of a freight wagon numerical model considering both the loaded and unloaded configurations. This aspect is of the utmost importance when it comes to freight vehicles in which the towed load can be significantly higher than the vehicle tare weight, and consequently, can considerably change its dynamic behaviour.
- -
- The development of a FE numerical model of an existing freight vehicle. This detailed model is rarely found for freight vehicles, due to difficulties in obtaining technical details from the manufacturers; however, it can constitute a basis for a much more accurate evaluation of the wheel–rail contact forces and cargo stability in the scope of the dynamic analysis of the train–track–bridge system.

## 2. Freight Train

#### 2.1. Description

#### 2.2. The Sgnss Wagon

## 3. Dynamic Tests

#### 3.1. Overview

#### 3.2. Loading Configurations

#### 3.3. Measurement Setup

#### 3.4. Modal Identification

## 4. Numerical Modelling

#### 4.1. Description

_{1}to K

_{4}, was considered independent since there was no guarantee that all the sets of coil springs had the same conservation state.

#### 4.2. Modal Parameters

## 5. Calibration

#### 5.1. Sensitivity Analysis

_{i}) and R(y

_{i}), by the expression:

_{i}) and R(y

_{i}), respectively, and n is the number of samples of each vector.

_{t}). Curiously, there are other numerical parameters, namely the vertical stiffness of the primary suspensions (K

_{1}to K

_{4}), that reveal a high sensitivity with the responses in the loaded model, particularly with the MAC values. The additional mass of the braking system (M

_{c}) and the steel equivalent density (D) proved to have no influence, or negligible influence, on the modal responses, and, consequently, were not included in the optimization phase. Thus, from the 10 numerical parameters evaluated, 8 of them proved to have an influence on the modal responses, particularly on the side bearers’ vertical stiffness (K

_{s}), the stanchion masses (M

_{t}), the vertical stiffness of the suspensions (K

_{1}to K

_{4}), the steel deformability modulus (E

_{S}) and the masses of the back stop and front stop (M

_{e}).

_{c}, M

_{e}, M

_{t}) present a negligible sensitivity to the modal configurations, probably due to the symmetry/near symmetry of the vibration modes, which means that a variation in the values of these symmetrically positioned masses will not change its symmetrical configuration.

#### 5.2. Optimization

#### 5.2.1. Unloaded Vehicle

#### 5.2.2. Loaded Vehicle

_{1}to K

_{4}) and the vertical stiffness of the side bearers (K

_{s}), as well as 10 modal responses.

_{e}and M

_{t}) and steel deformability modulus (E

_{s}) were assumed as deterministic and derived from the optimization of the unloaded vehicle numerical model.

_{1}as a function of the number of individuals and for the unloaded and loaded vehicle models, respectively.

#### 5.3. Correlation Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Freight train locomotive EURO 4000 with Sgnss type wagon: (

**a**) general overview; (

**b**) loading scheme (distances in metres and loads in kN).

**Figure 4.**Y21 bogie: (

**a**) overview and main elements, (

**b**) primary suspension detail, (

**c**) cross-section in the transverse direction (adapted from [22]).

**Figure 5.**Dynamic tests of Sgnss wagon: (

**a**) loaded configuration, (

**b**) detail of the central stowage, (

**c**) unloaded configuration.

**Figure 6.**Dynamic tests of Sgnss wagon: measurement setup (reference points in red and mobile points in blue).

**Figure 8.**EFDD method—average normalized singular values of the spectral matrices: (

**a**) unloaded configuration, (

**b**) loaded configuration.

**Figure 11.**Numerical modal parameters before calibration (undeformed mesh in grey and deformed mesh in red).

**Figure 14.**Values of the optimal parameters for the optimization runs GA1–GA4 for the unloaded vehicle numerical model: (

**a**) stiffness parameters, (

**b**) additional mass parameters and steel deformability modulus.

**Figure 15.**Residue of the objective function throughout the optimization process for the unloaded vehicle numerical model.

**Figure 16.**Values of the optimal parameters for the optimization runs GA1–GA4 for the loaded vehicle numerical model.

**Figure 17.**Residue of the objective function throughout the optimization process for the loaded vehicle numerical model.

**Figure 18.**Variation of the optimal values of numerical parameter K1: (

**a**) unloaded vehicle; (

**b**) loaded vehicle.

**Figure 19.**Errors between experimental and numerical modal responses, before and after calibration: (

**a**) natural frequencies, (

**b**) MAC.

**Figure 20.**Comparison between the experimental and numerical modal configurations after updating modal parameters: (

**a**) unloaded configuration, (

**b**) loaded configuration.

Number | Element | Cross Section | Dimensions (mm) | Properties | Short Description |
---|---|---|---|---|---|

1 | Central girders | 785 × 240 × 12 | A: 1.52 × 10^{−2} m^{2} | Twin I-girders on the central frame of the wagon | |

I_{x}: 1.34 × 10^{−3} m^{4} | |||||

I_{y}: 2.78 × 10^{−5} m^{4} | |||||

2 | Lateral side girders | UPN 200 200 × 75 × 8.5 | A: 3.61 × 10^{−3} m^{2} | Longitudinal side girders of the wagon frame | |

I_{x}: 1.89 × 10-5 m^{4} | |||||

I_{y}: 1.43 × 10^{−6} m^{4} | |||||

3 | Transversal connectors | T profile 100 × 180 × 12 | A: 3.63×10^{−3} m^{2} | Transversal secondary girders connecting the central girders and the lateral side girders | |

I_{x}: 2.49 × 10^{−6} m^{4} | |||||

I_{y}: 5.86 × 10^{−6} m^{4} | |||||

4 | Transversal girder | 265 × 550 × 8 | A: 1.32 × 10^{−2} m^{2} | Main transversal girder over the supports | |

I_{x}: 1.73 × 10^{−4} m^{4} | |||||

I_{y}: 5.81 × 10^{−4} m^{4} | |||||

5 | Rear girders | UPN 300 300 × 100 × 10 | A: 4.94 × 10^{−3} m^{2} | Longitudinal girders of the rear wagon frame | |

I_{x}: 6.29 × 10^{−5} m^{4} | |||||

I_{y}: 4.07 × 10^{−6} m^{4} | |||||

6 | Rear-edge girder | 76 × 125 × 6 | A: 1.17 × 10^{−3} m^{2} | Rear-edge closing girder | |

I_{x}: 2.12 × 10^{−6} m^{4} | |||||

I_{y}: 3.25 × 10^{−7} m^{4} |

Parameter | Description | Starting Value | Limit Lower/Upper | Unit | References |
---|---|---|---|---|---|

D | Steel equivalent density | 80 | 70/85 | kN/m^{3} | - |

E_{s} | Steel deformability modulus | 210 | 180/230 | GPa | - |

K_{1} | Spring set 1 vertical stiffness | 1000 | 500/8000 | kN/m | [14,20,22,23,53] |

K_{2} | Spring set 2 vertical stiffness | ||||

K_{3} | Spring set 3 vertical stiffness | ||||

K_{4} | Spring set 4 vertical stiffness | ||||

K_{pivot} | Central pivot vertical stiffness | 1 × 10^{9} | -/- | kN/m | [23] |

K_{s} | Side bearers vertical stiffness | 750 | 200/2000 | kN/m | [22,23,53] |

M_{e} | Mass of back stop and front stop (per node) | 100 | 50/500 | kg | - |

M_{t} | Mass of stanchion (per node) | 150 | 20/200 | kg | - |

M_{c} | Mass of braking system and piping | 150 | 50/500 | kg | |

M_{w} | Mass of wheelset | 1112 | -/- | kg | - |

M_{s} | Mass of suspensions components | 220 | -/- | kg | - |

C_{s} | Suspensions vertical damping | 19 × 10^{3} | -/- | N·s/m | [53,54] |

K_{Hertz} | Hertz spring vertical stiffness | 1.53 × 10^{9} | -/- | N/m | - |

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**MDPI and ACS Style**

Silva, R.; Ribeiro, D.; Bragança, C.; Costa, C.; Arêde, A.; Calçada, R.
Model Updating of a Freight Wagon Based on Dynamic Tests under Different Loading Scenarios. *Appl. Sci.* **2021**, *11*, 10691.
https://doi.org/10.3390/app112210691

**AMA Style**

Silva R, Ribeiro D, Bragança C, Costa C, Arêde A, Calçada R.
Model Updating of a Freight Wagon Based on Dynamic Tests under Different Loading Scenarios. *Applied Sciences*. 2021; 11(22):10691.
https://doi.org/10.3390/app112210691

**Chicago/Turabian Style**

Silva, Rúben, Diogo Ribeiro, Cássio Bragança, Cristina Costa, António Arêde, and Rui Calçada.
2021. "Model Updating of a Freight Wagon Based on Dynamic Tests under Different Loading Scenarios" *Applied Sciences* 11, no. 22: 10691.
https://doi.org/10.3390/app112210691