Contact load and film thickness under three-body contact condition

Jeng-Haur Horng ¹, Yang-Yuan Chen ¹

¹ Department of Power Mechanical Engineering, National Formosa University, Yunlin, Taiwan

INTRODUCTION: The effects of wear particle at the interfaces has been one of the important issues in tribology. This work based on three-body microcontact theory study the characteristics of particle and surface contact load and area with the various operating and particle parameters. The analysis results show that a three-body contact situation occurs in band zone of contact area ratio versus contact load diagram. In the top of the upper bound is the surface-to-surface two-body contact and in the bottom of the lower bound is the particle-to-surface two-body contact. The three-body analysis shows that the MK model of two-body contact is the special case of the result of the present method. At the critical speed value, larger particle size will increase the solid contact load ratio of the interface and enter the mixed and boundary lubrication from the EHD lubrication. It shows that the size and density of particle have a considerable effect on the stribeck curve of contact surfaces.

Theoretical Analysis: When two surfaces slide over each other, roughness of the surfaces and third bodies (particles) cause contact to occur at discrete contact spots, including particle-to-surface and surface-to-surface spots. The three-body contact area can be rewritten as:

where A_n is the nominal contact area, The total real contact area (A_total) is the sum by the real contact area of surface-to-surface (A_aw) and the real contact area of particle-to-surface (A_pw-ap), x is the mean particle diameter, h_a is the area particle density, H_w and H_p are the hardness of surface and particle, E_w and E_p are the Young's modulus of surface and particle, h_a is the particle density, f a(x) and f p(x)  are the Gaussian distribution functions of particle diameter and surface roughness, and x_max is the maximum particle diameter.


Figure 1 - Geometry of three contacting bodies.

Results and Discussion: The material in the analysis was S45C steel. Its properties are listed in Table 1. Fig. 2(A) shows the case of the surface roughness, 50 nm, particle size, 700 nm, and particle density, 10¹¹ /m², the contact area ratio is on the lower bound line before the load is 5.96 x 10^-5. When the load increases, the contact area ratio increases remarkably. This is because high contact load will increase contact spot of surface-to-surface and leads to increase contact area. When the particle size reduce to 300 nm, we can find the load of pull-off the lower bound line reduces to 7.45 x 10^-6 , and the load of pull-off the lower bound line increase to 1.19 x 10^-4 at the particle density increase to 10¹²/m². It indicates that the total real contact area ratio of surface-to-particle decrease when the size and density of spherical particle increases. In the top of the upper bound is the surface-to-surface two-body contact and

in the bottom of the lower bound is the particle-to-surface two-body contact.

Fig. 2(B) shows variation of contact load ratio with speed parameter at various particle density. As shown in the Fig. 2(B), the percentage of solid load decreases with increasing velocity parameters, and increases with increasing particle density at the same velocity parameter. When the particle density is between 7  10^-11 and 10^-12, when the velocity parameter is less than 1 x 10^-11, the solid load percentage is greater than 90 %, the contact condition has entered the boundary lubrication.  It indicates that under this condition wear and friction force will increase rapidly.

In the past studies have shown that the greater the sliding speed, the smaller the film thickness between the contact interfaces in two-body contact condition. However, the lubrication film thickness under three-body contact condition are shown in Fig. 3, When the particle size is smaller, the predictive value have same trend with the film thickness theoretical of Masjedi and Khonsari , the dimensionless film thickness increases as the speed parameter and particle diameter increases; however at the speed parameter smaller, such as U = 10^-11, the dimensionless film thickness H_c = 4.2 x 10^-5 (hc = 0.85 μm) when the particle diameter is as large as 700 nm, and that is about 2.1 times when x_a = 0 nm, and about 1.8 times when x_a =500 nm. It indicates that the wear debris have a considerable deviation on the film thickness at the interface.

Table 1. Material properties of S45C

Figure 2 - A) Total real contact area ratio vs. dimensionless contact load at various particles diameters and particles densities.  B) Variation of contact load ratio with speed parameter at various particle densities.

Figure 3 - Variation of dimensionless film thickness with speed parameter at various particle diameter.