## 2 Experimental Procedure
### Laser Repairing Process  
#### 2.2.1 Parameter Optimization  
The geometry characteristics of the clad track are strongly influenced by the process parameters, as reported in [22; 23]; among them, the dilution ratio \(\beta\) (the ratio of depth (\(h\)) and overall height (\(H+h\))) is directly affected by the quality of longitudinal lap as Equation (1) [24]; the aspect ratio \(\lambda\) (the ratio of width (\(W\)) and height (\(H\))) are directly determined by the quality of transverse lap as Equation (2) [25]. \(S_{m}\) and \(S_{c}\) in Equation (1) represent the melt pool area and the cladding layer area, respectively. Geometry characteristics are shown in Figure 3. The process parameters of LC, including powder feeding rate (\(V_{p}\)), laser power (\(P\)), scanning speed (\(V_{s}\)), and carrier gas rate (\(Q\)), are crucial for the geometry characteristics of LC coating [26; 27; 28]. Therefore, the four parameters were chosen as the key factors to find empirical-statistical correlations between the process parameters and geometrical characteristics. The four-parameter ranges were selected based on the parameters of existing experimental equipment and previous studies of the same equipment [16; 29; 30]. The dilution ratio \(\beta\) and aspect ratio \(\lambda\) was expected to predict the geometric characteristics. To select the ideal process parameters for the LC Ni60 alloy powder on 20 CrMnTi substrate, a single-track orthogonal experiment and an interactive experiment were designed, as shown in Tables 2 and 3.  
\[\beta=\frac{S_{m}}{S_{m}+S_{c}}\approx\frac{h}{h+H} \tag{1}\]  
\[\lambda=\frac{W}{H} \tag{2}\]  
Figure 2: The schematic diagram of the LC experiment device.  
by Equations (3) and (4) [31]. According to orthogonal results, the average value of the cladding layer width of 18 tracks is 1.4 mm. Therefore, the distance (\(D_{1}\)) between two adjacent tracks should be less than 1.4 mm. The laser spot diameter (\(d\)) is 1.0 mm, so the \(D_{1}\) should not be small. The \(D_{1}\) is selected as 0.6, 0.8, 1.0, 1.2, and 1.4 mm, respectively:  
\[W\geq D_{1} \tag{3}\]  
\[\delta=\frac{D_{0}}{W}=\frac{W-D_{1}}{W} \tag{4}\]  
where \(D_{0}\) is the length of overlapping.  
For longitudinal overlapping (z-increment), a part of the liquid metal in the second layer would spread to both sides under the effect of surface tension and gravity, as Figure 4b. When the remelting zone is equal to the filled zone of the peripheral generation, a relatively flat surface can be obtained. Under this premise, the area of quadrilateral ABCD should be equal to the cross-section area of the cladding track. After n-layer LC, the total height is defined as \(H_{T}\), and \(H_{T}=(n-1)\)\(\Delta Z+H\). The \(\Delta Z\) is calculated by Equation (5) [25]. However, considering the errors between the theory and experiment, three groups of experiments are designed, and the \(\Delta Z\) was set as 0.30, 0.28, and 0.26 mm, respectively:  
\[\Delta Z=\frac{\left(4H^{2}+W^{2}\right)^{2}}{64H^{2}W}\text{arcsin}(\frac{4 WH }{4H^{2}+W^{2}})-\frac{W(W^{2}-4H^{2})}{16H} \tag{5}\]  
where \(W\) is approximately 1.4 mm, \(H\) stands for the average value of the cladding height of 18 tracks, and \(H=0.394\) mm.