## 4 Abrasive Belt Wear Measurement Test
### Detection Error Control  
(1) Pre-wear of abrasive belt  
Due to the unevenness and randomness of the abrasive belt sand planting process, it will inevitably lead to the unevenness and randomness of the initial height of the abrasive grains. Therefore, a five-minutes process of pre-wearing is required, which  
\begin{table}
\begin{tabular}{c c c c} \hline
**Trial Number** & **Cutting Speed (m/s)** & **Contact Force (N)** & **Experimental Material** \\ \hline
1 & 8 & 5 & \#20 \\
3 & 2 & 5 & \#20 \\
4 & 2 & 10 & \#20 \\
5 & 5 & 10 & \#20 \\
6 & 8  
helps to maintain the uniformity of the initial abrasive grain height and reduce random experiment errors.  
Figure 5 shows the initial contour morphology of the #80 mesh belt. The uneven distribution of the abrasive grain height can be clearly seen, which further reflects the necessity of initial pre-wear. Figure 6 shows the surface contour of the belt near the end of the severe wear stage. According to the color of height spectrum, it can be seen that the overall height of the abrasive grains is reduced, and the surface height is almost the same. However, as the amount of wear increases, the contact area between the abrasive belt and the workpiece increases during the grinding process, which will generate a lot of heat. On the one hand, it will accelerate the abrasive belt wear, and on the other hand, it may burn the surface of the workpiece. Therefore, it is very critical to accurately predict the degree of abrasive belt wear.  
(2) Calibration of belt position interval  
In order to reduce the influence of random errors, ensure the consistency and integrity of the measurement, and improve the credibility of the data, it is required to calibrate three intervals A, B, and C at equal intervals for the entire belt, as shown in Figures 7 and 8. For each measurement of wear, three points are taken in this area. For example, points taken in area A are recorded as N\({}_{\text{A1}}\), N\({}_{\text{A2}}\), and N\({}_{\text{A3}}\), and the three sets of interval data with better stability are taken as the actual measured value of wear \(\Delta\).  
\[\Delta=\frac{1}{3}\sum_{j=A}^{C}\sum_{i=1}^{3}N_{ji} \tag{14}\]  
Figure 6: End of the severe wear stage.  
Figure 7: Interval labeling.  
(3) Abrasive belt fixture  
For the sanding belt within the interval length, researchers should fix the space position of the microscope lens and the position of the operating platform while framing. Meantime, the belt should be fixed by the self-designed special 3D printing fixture, as shown in Figure 9. The fixture is made of PLA material, which will avoid the damage of the microscope table due to touch and friction. By choosing this material, the repeatability of the measurement field will be maximized and the influence of random errors can be reduced, which will ensure the consistency and integrity of the measurement, as well as improve the data credibility.  
(4) Strategy of taking points under the mirror image  
As shown in Figure 10, there will be huge fluctuations on the height curve at the sampling front end. This is because the VHK-900 Keneyce is a manually adjusted microscrew. It is difficult to achieve a uniform speed when the initial rotation speed is applied, so huge fluctuations will occur. Data removal processing is required to remove invalid information. When taking HorLine and VertLine, points should be taken at the peak and valley stages of smooth changes to calculate the amount of change in wear and thus improve the accuracy of wear measurement.  
Figure 8: Actual interval labeling.  
Figure 10: Sampling positioning diagram.  
Figure 9: 3D printing fixture.