# Online Deformation Measurement of Laser Repair Substrate Based on Orthogonal Sampling Moire
## 4 Results and Discussion
### Unidirectional Scanning in \(y\) Direction  
In a \(y\)-direction unidirectional scanning period, the laser is excited and moves towards the \(y\)-direction, while the component is heated. After arriving at the end, the laser returns according to the original path without being emitted, while the component is cooled. Additionally, the progress repeats until the cladding is completed.  
Under the unidirectional scanning path in the \(y\) direction, the cladding results corresponding to different scanning speeds are shown in Figure 11a. Set the end of the cantilever beam as the measuring point to obtain the evolution of the displacement in the \(x\) and \(z\) directions during the repair process, as shown in Figure 11b. In the image coordinates, the downward direction of \(z\) is positive and the right direction of \(x\) is positive. It can be seen that the scanning speed has a great influence on the \(z\)-direction displacement of the measuring point and that the absolute value of \(z\)-direction displacement increases along with the scanning speed decreases.  
It can also be seen from the curve in Figure 11b that the absolute value of displacement in the \(z\) direction continues to increase in the periodic fluctuation during the cladding process. It should be noted that, when the absolute value of displacement in the \(z\) direction decreases in a single cycle, it corresponds to the time when the laser acts on the surface of the component (as shown in Figure 11c). This is because when the laser acts on the surface of the component, an area of large positive strain is generated around the molten pool at the upper end of the component due to thermal expansion, making the cantilever beam displaced downward. When the laser is removed and the molten pool is cooled and solidified, the positive strain in the molten pool decreases and the cantilever moves upward.  
The distribution of equivalent strain and the main direction of strain at the beginning and end of repair are calculated, as shown in Figure 12a. It can be found that a concentration of strain exists around the molten pool during repair; after repair, the residual deformation presents the form of upward bending. Select four points A, B, C and D along the length  
Figure 11: (**a**) Cladding results at different scanning speeds, (**b**) displacement evolution at different scanning speeds and (**c**) \(z\)-direction displacement field in a single cycle at 10 mm/s.  
of the cantilever beam, and draw the variation curve of the equivalent strain of these four points with time, as shown in Figure 12b. It can be found that the slower the printing speed is, the greater the deformation becomes; in the initial stage of scanning, when the cladding area gradually moves to the right, the equivalent strain of the four points increases linearly with different slopes; and when the cladding zone passes through points A, B, C and D in turn, the equivalent strain of each point reaches its maximum value in turn and remains unchanged. This is because, when scanning in the \(y\) direction, the beam is thermally expanded and the equivalent strain increases linearly at the beginning. However, once the molten pool passes through a certain point in the \(x\) direction, it will not ever return, and then, the equivalent strain at this point remains constant.