**6. Discussion**

In the first experiment for the artificial damaged rail, Figure 16b obviously shows that the scratch-depth of most rail surface is larger than 1 mm and the specific places of scratch-depth > 1 mm is presented in Figure 20. Table 8 displays the further analysis result in the form of max depth, min depth and Root Mean Square (RMS) acquired by Geomagic Studio 2014 (64 bit). The counterpart results in the second experiment for the practical damaged rail are presented in Figure 21, Figure 22, and Table 9, respectively. Based on the above results, both the artificial rail and the practical rail in the experiment should be replaced with new rails, which is mandatory required by the provisions of the TG/GW102-2019 in China.

**Figure 20.** The specific places on the artificial rail surface with scratch-depth larger than 1 mm.

**Table 8.** The analysis result of the artificial damaged rail.

**Figure 21.** The depth-difference between the reference PCM and the scratch-surface PCM on the practical damaged rail.

**Figure 22.** The specific places on the practical damaged rail surface with scratch-depth larger than 1 mm.

**Table 9.** The analysis result of the practical damaged rail.


In order to verify the accuracy of the complete closed mesh models of the scratch-data acquired in the experiment, the virtual repairs of the rails by cladding the scratch-area with the models are carried out, leading to the results of Figures 23a and 24a, which are corresponding to the artificial rail and the practical rail, respectively. The difference calculated between the repaired artificial rail model and the reference model is shown in Figure 23b and further analyzed in Table 10. The similar results for the practical rail are presented in Figure 24b and Table 11.

**Figure 23.** The accuracy analysis of the scratch-data acquired in the experiment for the artificial damaged rail. (**a**) The result of virtual repair of the artificial rail by using the scratch-data; (**b**) The difference between the repaired artificial rail model and the reference model indicating the scratch-depth on the repaired artificial rail is less than 1 mm.

**Figure 24.** The accuracy analysis of the scratch-data acquired in the experiment for the practical damaged rail. (**a**) The result of virtual repair of the practical rail by using the scratch-data; (**b**) The difference between the repaired practical rail model and the reference model indicating the scratch-depth on the repaired practical rail is less than 1 mm.


**Table 10.** The analysis result of the repaired artificial rail.

The above results show that the scratch-depth on the repaired rails is less than 1 mm, which well meets the requirements in the provisions of the TG/GW102-2019 in China, proving that the complete closed mesh model of the scratch-data established herein is precise enough for the use of online repair. Also, the total time required in the experiments (45.35 s for the artificial rail and 47.51 s for the practical one) is much less than 1 min, fully demonstrating the crucial capability of real-time required by online rail-repair based on the laser cladding technology, so the method proposed in our paper is practical for the online repairing of damaged rails in terms of accuracy and real-time performance.
