**2. Simulation Model**

*2.1. The Establishment of Finite Element Model*

The matrix is H13 steel. The sample is a cuboid with the size of 60 mm × 60 mm × 10 mm. The cladding layer is added to the center of the matrix with a length of 60 mm, its height and width are determined by the powder feed amount and laser diameter. In COMSOL, Figure 1 shows the grid division.

The establishment of heat source model will affect the accuracy of laser cladding numerical simulation results. Both plane heat source and body heat source are suitable for laser cladding. The plane heat source model is generally divided into pulse heat source and continuous heat source. Compared with other heat source models, planar continuous heat source is used more. In this study, the planar continuous heat source model shown in Figure 2 is selected. The distribution function is:

$$q(x, y, t) = \frac{Q}{\pi R\_0^2} e^{-\frac{2[(x - x\_0)^2 + (y - v\_0 t)^2]}{R\_0^2}} \tag{1}$$

where *q*(*<sup>x</sup>*, *y*, *t*) is the heat flow at the (*<sup>x</sup>*, *y*) position of time t, *Q* is the laser power, *R*0 is the laser beam radius, *X*0 is the position of the laser center in x direction; *v*0 is the laser cladding velocity.

The matrix used in this experiment is H13 steel, the cladding material is Ni60 alloy powder. The matrix and powder composition are listed in Tables 1 and 2. According to the chemical composition of the matrix and powder, the corresponding materials from COMSOL database were selected, and their physical properties provided by the software were used.

**Figure 2.** Planar continuous heat source model.

**Table 1.** Chemical composition of H13 steel.


**Table 2.** Chemical composition of Ni60 alloy powder.


### *2.2. Simulation Parameters and Sample Points Distribution*

The main parameters of laser cladding include laser power, scanning speed, spot diameter, and powder feeding rate, among which the spot diameter and powder feeding rate mainly affect the height and width of cladding layer, but have little influence on the temperature field distribution. Through simulation calculation, it is found that the temperature field cloud map of different spot diameters and powder feeding rates is basically the same, which is not necessary to be analyzed, but mainly to analyze the influence of laser power and scanning speed on the laser cladding temperature field. The simulation was carried out by changing the laser power and scanning speed. The laser power was 600 W, 800 W, 1000 W, 1200 W, and 1400 W, the scanning speed was 2 mm/s, 3 mm/s, and 4 mm/s.

In order to work out the optimal experimental parameters and analyze the thermal stress cycle of the cladding layer, probes were added to 11 sample points in the cladding layer to record the changes of temperature and thermal stress in real time. Figure 3 shows the locations of the sample points. The cross section is selected in the middle part with stable cladding to ensure the representativeness and accuracy of sample points, avoiding excessive errors as well.
