# Model Updating of a Freight Wagon Based on Dynamic Tests under Different Loading Scenarios
## 6 Conclusions  
This paper presents an efficient model calibration methodology for a freight wagon based on experimental modal parameters, particularly natural frequencies and mode shapes. The wagon studied was a _Sgnss_ type vehicle specifically designed for timber logs transport. Figure 20: Comparison between the experimental and numerical modal configurations after updating modal parameters: (a) unloaded configuration, (b) loaded configuration. The identification of the modal parameters was based on dynamic tests performed at the Navigator company facilities for two distinct static loading configurations, rare weight and current operational overload. The experimental natural frequencies and their corresponding modal configurations were later used for calibrating the numeric model. The application of a modal identification technique based on the EFDD method allowed us to identify five operational modes with a very good definition involving structural movements of the vehicle platform, which in some cases, to more or less extent, are coupled with rigid body movements. The natural frequencies for the loaded vehicle are significantly lower in comparison to the unloaded wagon. The range of frequencies values is between 3.65 Hz and 16.63 Hz, for the unloaded configuration, and between 1.54 Hz and 6.66 Hz for the loaded configuration. A detailed 3D numerical model of the freight wagon was developed resorting to the FE method, using a different type of finite elements (beam, shell, mass and spring-dashpot) in ANSYS software. The thickness and cross-sections of the shell and beam elements, respectively, were derived from technical drawings of the vehicle and validated with field observations. The loaded numerical model considered the towel load configuration (load values and layout), similar to the one used during the dynamic test, and for the unloaded numerical model, no overload was considered. The model calibration was based on modal parameters and involved a sensitivity analysis and optimization. The sensitivity analysis allowed the selection of eight numerical parameters that most influence the modal responses, namely, the vertical stiffness of the side bearers, the stanchion masses, the vertical stiffnesses of the primary suspensions, the steel deformability modulus and the masses of the back stop and front stop. The optimization was performed by an iterative methodology using a genetic algorithm. The optimization was performed sequentially, first for the unloaded wagon model and after for the loaded wagon model. The results prove that the vertical stiffness of the coil primary suspensions keeps their behaviour in an elastic or almost elastic regime, independently of the level of the vertical static loads, for unloaded and loaded configurations. On the other hand, the vertical stiffness of the side bearers presents quite distinct calibrated values on the unloaded and loaded wagon models, which is probably associated with the non-linear behaviour of these components. The comparison of experimental and numerical responses before and after calibration revealed significant improvements in the numerical models and a very good correlation between the experimental and numerical responses after calibration. The average error of the natural frequencies decreased from 11.8% before calibration to 3.2% after calibration for the unloaded case, and from 20.4% to 4.8% for the loaded case. The average MAC values improved from 0.85 to 0.87 and from 0.82 to 0.85 for the unloaded and loaded scenarios, respectively. The calibrated loaded freight wagon model constitutes a very good basis for the dynamic analysis of the train-track system under operational conditions, particularly in evaluating the wheel-rail contact stability as well as the cargo stability. In that scenario, a non-linear behaviour of some suspension components is expected, due to the increase of the vibration amplitude under dynamic loading.