# Calibration of Sliding Friction Coefficient in DEM between Different Particles by Experiment
## 4 Results and Discussion
### Analysis of Sliding Friction Coefficient  
The samples had slight defects on the surface due to insufficient vibration, but these defects had minimal impact on the results. According to the sliding friction coefficient obtained from Tables 2 and 3, the results were fitted. The fitting result of the sliding friction coefficient between sphere particles is shown in Figure 6. Because the variation range of the sliding friction coefficient of the sphere-ellipsoid group was very small, bilinear interpolation was used to calculate the sliding friction coefficient of the sphere-ellipsoid. The sliding friction coefficient of the ellipsoid-ellipsoid group was fitted by plane fitting, and the sliding friction coefficient of the ellipsoid-polyhedron group was fitted by linear fitting. The fitting result of the sliding friction coefficient of the sphere-polyhedron group is shown in Figure 7a. The fitting result of the sliding friction coefficient between the sphere particles and the four different pads is shown in Figure 7b.  
It can be seen from Figure 6 that when two sphere particles are in contact, the sliding friction coefficient changes obviously with the curvature of the particles. The sliding friction coefficient decreases with an increase in the curvature of the two spheres. When the two contact spheres differ in size, the sliding friction coefficient cannot be determined from the curvature of the single sphere. Comparing the fitting results of sphere-sphere, ellipsoid-ellipsoid, and sphere-ellipsoid groups, it is shown that the fitting result shown in Figure 6 is not applicable when ellipsoid particles are involved in contact. The main reason is that the ellipsoid particles have different curvatures at different positions.  
It can be seen from Figure 7a that when the sphere particles and the polyhedron particles are in contact, the sliding friction coefficient of the point-face contact is the largest, the sliding friction coefficient of the point-point contact is the smallest, and the sliding friction coefficient of the point-edge contact lies between the two. The sliding friction coefficient decreases with an increase in the curvature of the sphere. The sliding friction coefficient of the point-face and point-edge contacts change slowly with an increase in curvature, however, the sliding friction coefficient of the point-point contact changes sharply with an increase in curvature. The same conclusion can be obtained by the fitting result of the sliding friction coefficient of the ellipsoid-polyhedron contact.  
Figure 6: Relationship between the sliding friction coefficient and the curvature of sphere particles in the contact of sphere particles with sphere particles.  
It can be clearly seen from Figure 7b that the sliding friction coefficient of the glass in contact with the sphere particles is the smallest, and it is the largest when the flint paper is in contact with the particles; the sliding friction coefficient during contact between the crocus paper and the sphere particles is the second largest, and the sliding friction coefficient during contact between the sphere particles and the wood board is slightly lower than that during contact between the flint paper and the wood board.