## 3 Finite Element Analysis Results
### Validation of the Analysis Process  
To validate the proposed methodology, the front-end analysis results of induction hardening were compared with the actual product. The induction hardening system used for this validation consisted of a TruHeat MF Series 7000 generator (Trumpf SE + Co., KG, Ditzingen, Germany) and a cooling system [21], as shown in Figure 11. The generator  
Figure 8: Result of martensite after induction hardening: (**a**) actual and (**b**) ideal conditions.  
Figure 10: (**a**) Result of z displacement and (**b**) difference in geometry comparing CAD data (left: CAD, right: analysis).  
Figure 9: Hardness distribution after induction hardening (**a**) actual and (**b**) ideal conditions.  
provided an output power of 40 kW with an operating frequency range of 20-100 kHz. The cooling system maintained stable heat transfer during the process by regulating the water temperature within the range of 5-35 \({}^{\circ}\)C.  
The deformation of the actual product was measured using a GOM ATOS 3D scanner (GOM mbH, Braunschweig, Germany) [22], a high-precision device equipped with dual cameras for accurately capturing reflective and curved surfaces. The scanning process and the appearance of the scanner are presented in Figure 12. To ensure an accurate comparison with finite element analysis (FEA) results, the scanned surface data were processed using Zeiss Quality Suite software (Ver. 4.5) [23]. The software aligned the experimental scan data with the original computer-aided design (CAD) model using a best-fit algorithm, correcting for positioning deviations. It then quantified shape deviations and visualized discrepancies between the scanned data and the FEA results. Additionally, the software identified localized defects and generated comprehensive analysis reports.  
The validation results are presented in Figure 13a, illustrating the direct comparison between the scanned product data and numerical analysis outcomes. Figure 13b provides a visual representation of this comparison: the left section displays the actual product alongside the CAD model, while the right section highlights the deviation analysis between the CAD model and the simulation results. In addition to this overall analysis, the experimental and simulation results were compared by evaluating displacement values at specific points. Identical reference points were marked on both the experimental and simulated data, and the displacement occurring between these points was analyzed. Furthermore, the trend in temperature distribution legends was compared between the experimental and simulated results to confirm consistency in thermal behavior.  
Figure 11: Induction hardening system setup showing the heating coil, workpiece, generator, and cooling system configuration.  
Figure 12: Three-dimensional scanning-based deformation measurement and CAD model comparison.  
The maximum z-direction deformation at Point P was found to be highly consistent between the actual product and the simulation results. The measured deformation values were 0.97 mm and 0.93 mm, respectively, indicating an accuracy of approximately 96%. Additionally, the z-direction deformation along the product cross-section, spanning from welding Point A to center Point B, was analyzed, as depicted in Figure 13b. However, some discrepancies were observed between the experimental results and the FEA predictions, which are likely attributed to the simplifications in the FEA modeling. In particular, the omission of convection heat transfer in the simulation may have led to an underestimation of the cooling rate. In real-world cooling conditions, heat exchange occurs between the surrounding fluid and the workpiece, whereas the FEA model did not account for such external convection effects, potentially leading to variations in temperature distribution and deformation. Based on these results, the proposed analysis methodology is expected to demonstrate validity and reliability in predicting deformation behavior under real operating conditions.