3.1 Contact surface analysis of the model
Figure 3 showed the stress cloud diagram of 100 load steps. From the stress cloud diagram, it can be observed that the stress distribution of the contact layer, especially the surface stress close to the contact point, is very complex. The stress started from the contact point and gradually decreased inward. The accelerated splitting near the contact layer itself caused freezing caused by the contact, and also included the extrusion and puffing caused by other contact points.
Figure 4 showed the relationship curve between normal deformation and normal load, in which the abscissa was the normal load value and the ordinate is the displacement in the normal direction of the midpoint of the rigid surface. It can be seen from the figure that the deformation displacement gradually increases with the increase of normal load, and the relationship between the two was generally linear. By comparing with the experiment in Reference 5, the test result curves of the two were consistent, indicating that the model calculation results were reliable.
Figure 5 showed the relationship curve between contact area and normal load, where the abscissa was the size of the normal load and the ordinate was the contact area (contact line length). It can be seen from the figure that when the load was less than 1Mpa, the contact area increased generally linearly with the increase of the normal load. When the load exceeded 1Mpa, the increase in the contact area became smaller and smaller, approaching saturation.
3.2 Effects of different loading conditions on the leakage magnetic field at the contact surface
Figure 6 showed the geometric model and grid model of the two-dimensional magnetic field. The meshing of the ferromagnetic region was the same as the mesh model in the contact analysis. The air mesh in contact with the contact surface was denser, and the air mesh became sparser farther away from the contact surface. The relative magnetic permeability of the ferromagnetic material area was 285, and the relative magnetic permeability of the air area was 1. The model used the PLANE53 unit, which had 8 nodes and each node has 4 degrees of freedom. The boundary conditions of the z component (Az) of the magnetic vector potential were the upper air boundary Az = 39.8 A/m and the lower air boundary Az = 0 A/m.
By writing the APDL program, the stress values of each unit from the contact analysis were brought into the force-magnetic coupling mathematical model, the magnetic permeability of each unit was calculated, the magnetic permeability value of each unit was corrected, the boundary conditions were loaded, and ANSYS magnetostatics was performed Solve, finally. Figure 7 was the result curve of magnetostatic analysis, in which figures (a)-(c) were respectively the tangential and normal leakage magnetic field intensity curves of air 1mm above the rough surface under various loading conditions. In Figure (a), the abscissa was the coordinate value in the actual length direction, and the ordinate was the tangential leakage magnetic field intensity of the air layer above the corresponding position. In Figure (b), the abscissa was the coordinate value in the actual length direction, and the ordinate was the normal leakage magnetic field intensity of the magnetic field in the air layer above the corresponding position. Figure (c) synthesized the leakage magnetic field under normal loads from 0.1MPa to 1MPa. Figure (d) combined the leakage magnetic field under various normal loads from 1MPa to 10MPa, and the differences in the leakage magnetic field under various load conditions can be clearly compared. From Fig. 7, we found that the stress value in the contact area was greater than the stress value in the uncontact area, resulting in the magnetic permeability of the contact area being smaller than the uncontact area, which caused magnetic leakage in the contact area, thereby increasing the normal component of the magnetic field intensity in the leakage magnetic field. All cross zero, and the tangential components all have the maximum value of the curve shape. As the load increases, each curve in the figure had more tangential magnetic field components showing maximum values, and more normal components showing zero crossing points. This is because more contact areas appear as the load increases.
As shown in Fig. 8, the stress cloud diagram of the contact area under 10MPa normal load, it can be observed that there were 4 obvious contact areas, which were related to the number of extreme points of the tangential leakage magnetic field intensity and the normal leakage magnetic field intensity under 10MPa. The number of zero points was the same.
As shown in Fig. 9, under the normal load of 10Mpa, the leakage magnetic field intensity of air layered with different heights from the contact surface. It can be seen from the figure that as the height increases, the values of the tangential and normal leakage magnetic field strengths of the air layer above the contact surface gradually decrease, which indicated that the lifting height has an impact on the leakage magnetic field signal.