# Thermal Modelling and Experimental Validation in the Perspective of Tool Steel Laser Polishing
## 4 Conclusions  
A thermal model based on the Chernoff formula was developed and compared to experimental data for the laser polishing of rough tool steel. The main properties missing from the model were the light absorption coefficient evolution with the temperature especially in the liquid state of the steel. The best results are obtained with two constant coefficients; one for the solid based on the measurement at room temperature (\(a_{s}=35\%\)) and one for the liquid fixed so that the model fits the experiment data (\(a_{l}=25\%\)). A lower value can be explained by the smoother surface of the steel in the liquid state as compared to the rough solid.  
The model was first tested with some static experiments with the laser spot not moving and a long illumination time of close to 1 s. In these conditions, the model shows some limitations due to the lack of coupling between the convection and thermal model. The experimental melt pool is wider and shallower than the simulated melt pool. The volume of the liquid is well simulated with a liquid coefficient of absorption of 0.25. Due to the shallower melt pool and increased surface of the experimental melt pool the solidification time of the experiment is also shorter.  
The limitation of the model not taking account of the convection in the thermal model is less important in the real process with a moving laser beam as the interaction time is decreased. The model can estimate the elongation of the melt pool with increasing speed and the trailing of the melt pool with regard to the laser spot. The volume is also relatively  
Figure 19: (**a**) Example of the temperature field simulated for LP of tool steel (complete domain), (**b**) zoom on the fine mesh region, (**c**) 3D representation of the melt pool only with temperature.  
well simulated with an absorption of 0.25 in the liquid state. As for the static experiment, the experimental melt pools have a slightly larger surface but a shallower depth than the simulated melt pools. Again, this can be explained by the lack of coupling between convection and thermal models in the simulation.  
Finally, the results show that the model is able to represent the thermal behavior of the tool steel during laser polishing. The melt pool is relatively well estimated and we are confident that the thermal fields simulated are close to the reality. In the next study, a flow model will be applied in the simulated melt pool to observe the effect of laser polishing on the surface roughness.  
Conceptualization, B.M., A.M., E.B., I.C. and K.W.; methodology, B.M., A.M., E.B., I.C. and K.W.; experiments, B.M. and I.C.; software, A.M. and E.B.; validation, K.W.; formal analysis, B.M., A.M., E.B. and I.C.; writing--original draft preparation, B.M. and A.M.; writing--review and editing, B.M., A.M., E.B., I.C. and K.W.; supervision, K.W.; project administration, K.W.; funding acquisition, I.C. and K.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Swiss Commission for Technology and Innovation (CTI), grant number 25363.1 PFNM-NM.  
[[https://www.empa.ch/web/s204/modellinglaserpolishing1](https://www.empa.ch/web/s204/modellinglaserpolishing1)]([https://www.empa.ch/web/s204/modellinglaserpolishing1](https://www.empa.ch/web/s204/modellinglaserpolishing1)) (accessed on 8 July 2022).  
The authors would like to thank the Swiss Commission for Technology and Innovation (CTI-project No. 25363.1 PFNM-NM) and the industrial partner Untichnologies SA for the financial support of this work.  
The authors declare no conflict of interest.