## 3 Comparative Analysis of FEM-Calculated and ART-Measured Eigenfrequencies
### Step-by-Step Analysis of Modeling Errors of Simulated Eigenfrequencies  
Certain deviations of simulated versus measured data are always to be expected, that is, also in the present case with regard to eigenfrequencies. This is due to idealizations, simplifications, and only approximately valid model assumptions used for simulation. Following the analysis in Section 3.1 with the rough model, updated simulation data were analyzed step by step. For data generation, an increasingly complex modeling with regard to geometry or material was assumed. Figure 6 shows again relative deviations of simulation data compared to eigenfrequencies from measurement. Geometric models with different levels of accuracy were used for simulations, namely nominal geometry, standard model with 8 as well as models with 10 or even 17 individually updated geometric values, as explained in Section 2. Amount related error bars of up to almost 2.7% for simulation data compared to experiment can be seen in Figure 6. A stepwise increase in complexity of the geometric modeling results in only slightly different eigenfrequency values up to the model with 10 individually updated geometric values. A further increase in complexity by assuming additional parameters does not lead to any significant improvement, according to our findings. Even the use of the most complex model with 17 updated values does not imply that geometry was already described exactly. It has to be considered that geometry assumed for the simulations has only been measured at local areas of the components. Also, the data are subject to measurement uncertainty effects and the real geometry is reduced from measurement raw data to an idealized parameterizable model with idealized shape. However, there are only small changes associated with an increasingly complicated geometric model. Therefore, it is concluded that the observed differences between simulation and measurement are only to a small extent due to an insufficiently accurate geometric modeling and the potential for improvement is low. The FEM calculations within this study were carried out under numerous simplifications as well as idealizations. Besides the assumption of a completely linear behavior and the neglect of damping or external forces, many aspects were ignored in eigenfrequency simulations that happen in reality, for example, the characteristics of the ART measurement device as well as the chosen experimental set-up or effects from the signal processing strategy. Therefore, some exemplary analyses using different  
Figure 6: Relative deviations between eigenfrequencies of virtual representations simulated by FEM using different geometric models and eigenfrequencies of the machine-made reference parts measured by ART depending on vibration mode (averaged values from all reference part). experimental set-ups and different measurement technology as far as available were performed. This investigations indicate small, insignificant influences to measured eigenfrequencies. In general, the mentioned aspects cannot easily be quantified at this point in most cases, but there is no indication that the differences between simulated and measured eigenfrequencies within the observed magnitude are mainly caused by these neglected or idealistic conditions. Furthermore, material properties have to be taken into account as another modeling parameter. By default, a homogeneous and isotropic material with properties according to literature was assumed for simulation. Beyond that, two further material models were assumed, either a model with averaged isotropic material properties or an orthotropic model. The elastic constants of both models were derived from density and ultrasound time-of-flight measurements. Figure 7 shows results regarding material based on the standard geometric model with 8 individually updated geometric values. It can be seen that the differences between the calculated eigenfrequencies of the virtual representations and ART measured data can be strongly reduced by updating the material model for FEM simulations.