# The Effect of Clamping Force on the Wear Behavior of a Steam Generator Tube
## 4 Results and Discussion
### Experimental Validation  
The contact type between the tube and the AVB in the experiment is line contact. The wear depth of the tube at the middle line in the contact area is the deepest so that it is selected as an analysis object. There is a corresponding relationship between wear depth and wear volume, which means that wear volume can be estimated as long as wear depth is obtained. [PERSON] [5] divided the wear scar into two categories according to the vibration amplitude and gave the calculation method of the wear volume. [PERSON] et al. [23] refined the types of wear scars based on the work of [PERSON]. Four types of wear scars, such as round, crescent, flat and oblique, were analyzed in their study, and the calculation method for each kind of wear scar was proposed. Figure 8: Static finite element analysis: (**a**) schematic diagram of static loading; (**b**) clamping force-displacement curve. Wear scars in our experiments are not the regular flat-shaped type. To calculate the total volume of the scar, we divide it into n regular flat-shaped scars, as shown in Figure 10. The wear volume of each flat-shaped scar is calculated according to the method mentioned by the above scholars. Finally, the total wear volume in the irregular shape of the scar is obtained by summing the volume of n flat scars. Wear scar in A-A view is shown in Figure 10b, where \(h\) represents the maximum wear depth of the tube, \(D\) represents the outer diameter of the tube, and \(\theta\) represents the central angle of wear scar. The central angle and wear volume of the \(i\)th flat-shaped scar of the tube are calculated according to Equations (3) and (4). \[\theta_{i}=\arccos(1-\frac{2h_{i}}{D}), \tag{3}\]  
\[V_{i}=\frac{D^{2}}{8}\cdot(2\theta_{i}-\sin 2\theta_{i})\cdot l_{i}, \tag{4}\]  
The central angle \(\theta\) expressed in radians can be calculated according to the wear depth measured by LSCM. Because of limited value on \(\theta\), Equations (3) and (4) are simplified to:  
\[h_{i}\approx\frac{D\theta_{i}^{2}}{4}, \tag{5}\]  
Figure 10: Irregular flat-shaped wear scar: (**a**) n regular flat-shaped scars; (**b**) wear scar in A-A view. Figure 9: (**a**) Friction energy in each cycle; (**b**) Maximum sliding distance and average friction energy under different clamping forces. \[V_{i}\approx\frac{D^{2}l_{i}\theta_{i}^{3}}{6}, \tag{6}\]  
Then we can obtain the relationship between the wear depth and the wear volume of the flat-shaped scar. On the basis of measured wear depth, corresponding wear volume can be estimated, as shown in Equations (7) and (8). \[V_{i}=\frac{4}{3}D^{\frac{1}{2}}h_{i}^{\frac{3}{2}}l_{i}, \tag{7}\]  
\[V_{total}=\sum_{i=1}^{n}\frac{4}{3}D^{\frac{1}{2}}h_{i}^{\frac{3}{2}}l_{i}, \tag{8}\]  
Figure 11 shows the 3D morphology of wear scars under different clamping forces. The corresponding wear depth along the axial direction of the tube is shown in Figure 12, and the wear data are shown in Figure 10.0  
Mark 1 in Figure 12 illustrates that obvious boundaries were generated between the unworn surface and the worn surface, caused by the accumulation of wear debris during the wear process. Under the impact of greater clamping force, the wear debris of the AVB transfers to the worn surface of the tube, or plastic deformation occurs in the wear area, as shown in Mark 2 of Figure 12c. Figure 10.1 3D morphology of wear scar and worn surface under operating conditions: (**a**) clamping force of 53 N; (**b**) clamping force of 80 N; (**c**) clamping force of 126 N.  
The maximum wear depth with a clamping force of 53 N is largest among the three groups of wear experiments under different clamping forces, accounting for 2.35% of the thickness of the tube, and wear volume in this experiment is also the largest. Both maximum wear depth and wear volume in another experiment with a clamping force of 126 N are the smallest, with wear depth accounting for 1.62% of the thickness of the tube.