The third particle occurred at the interface of contacting surfaces is common situations in relative motion part. This study involved developing an analysis framework to investigate the contact characteristics in the full range of 3-body mixed lubrication. Conventional 2-body mixed lubrication is a special case of 3-body mixed lubrication analysis with particle size of zero. This study revealed that the values of real contact area, film thickness, contact mode, and the solid contact load in 3-body contact were larger than those in ideal 2-body contact in mixed lubrication, and they increased with an increasing particle size or density under the study conditions. The initial stages and transition processes of four types of 3-body contact modes under mixed lubrication were significantly different for different particle sizes and densities. The size of the third particle increased the values of both minimum and maximum values, λ_min and λ_max, of film parameter in the mixed lubrication regime. The particle density did not have a significant effect on the λ_max value in mixed lubrication. Higher particle density led to a larger λ_min value in mixed lubrication. The conventional film parameter, λ, was not a sufficient indicator of the different lubrication regimes in 3-body contact.

Recently, many studies have investigated the friction, wear, and temperature characteristics of the interface between two relative movements. Such analyses often set the coefficient of friction as a fixed value and are analyzed in cases of two-body contact; however, the interface is often a three-body contact and the coefficient of friction varies depending on the operating conditions. This is a significant error in the analysis of contact characteristics, therefore, in this study, the actual interface and the change of the coefficient of friction were analyzed based on three-body micro-contact theory where the contact temperature was also analyzed and the difference between the generally assumed values were compared. The results showed that under three-body contact, the coefficient of total friction increased with an increase in particle size; and at a different particle size and area density of particles, the surface contact temperature increased with the plasticity index and load increases, and the particle contact temperature increased with the increasing particle size. The surface temperature rise was mainly affected by the ratio of the average temperature between surface 1 and surface 2 to the multiplication between the 100th root of the area density of particles and the square root of the equivalent surface roughness (T_{s1s2_ave}^*/η_a^0.01σ^0.5) and the ratio of the 10th root of the mean particle diameter to the 100th root of the equivalent surface roughness (x_a^0.1/σ^0.001). Particle temperature was mainly affected by the ratio of the 10th root of the mean particle diameter to the 100th root of the equivalent surface roughness (x_a^0.1/σ^0.001) and the area density of particles η_a. Our study indicated that when the contact of surface with surface and the contact of the particles with the surface, the resulting heat balance was assigned to the particles and the surface in a three-body contact situation. Under this contact behavior, it could avoid a too high a rise in micro-contact temperature to achieve the material failure temperature.

Nanoparticles as lubricant additives under a certain average diameter and concentration may reduce wear, friction and scuffing damage. However, atmospheric dust particles affect not only human health but also the efficiency of components, and even cause component failures. Therefore, the contact characteristics at interfaces with foreign particles require careful investigation. In this work, a 3-body microcontact mechanics concept is used to analyze the effects of wear debris and foreign particles on real contact area, contact mode, asperity deformation type and separation at interface. The results show that the relationship profile between dimensionless real contact area (A_t^*) and dimensionless normal contact load (F_t^*) is wedge-shaped in a 3-body contact interface. Using surface-to-surface 2-body contact area as upper bound and surface-to-particle 3-body contact as lower bound, the 3-body hybrid contact situation is in between upper and lower bounds. As the dimensionless normal contact load increases, A_t^* increases gradually as well. The order of contact mode is p-s contact, hybrid contact and then s-s contact. If the 3-body contact interface is in hybrid contact mode, the decrease in the hardness and average third body diameter will cause the A_t^* to increase significantly at the same F_t^*. Conversely, the separation and real contact area ratio of plastic deformation decrease gradually. The turning point of contact area (TPCA) occurs when the contact mode is within hybrid contact mode and the ratio of average third body diameter to the composite equivalent surface RMS roughness is about 50–70% for foreign particles and wear debris. When the F_t^* is slightly larger than F_tpca^*, the third body and surface share the total interface load approximately equally which will help reduce the real contact pressure and plastic contact area to improve surface performance.

Purpose: This paper aims to investigate the temperature and wear properties of vertical ball screws and to discuss the surface design of ball screws in industrial applications. Design/methodology/approach: The energy equation of the screw surface considering the frictional heat was established to verify the surface temperature of the ball screw. X-ray diffraction was used to examine the micro-contact temperature between the ball and screw. Debris size and density were examined to investigate wear properties of ball screws and to study the relationship of wear debris and temperature. Findings: First, the main energy source for the surface temperature of high speed vertical ball screws is derived from friction force between ball and screw. Second, the temperature rise between the ball and screw has great relevance with wear debris concentration. Third, the surface temperature of the screw is higher than between the nut and ball for high speed vertical ball screws due to high convection heat transfer. The contact temperature of the nut near the flange is smaller than that of the nut away from the flange end due to the high contact load and thermal conduction. Finally, correlation of particle size and surface roughness value for vertical ball screws was established, and its effects on contact temperature were studied. The theoretical analysis and experiments will help to characterize the design and manufacture of vertical ball screws. Originality/value: The surface temperature and micro-contact temperature analytical model were established to study the ball screw design. Based on the surface-particle micro-contact temperature balance, the optimal range of surface roughness was designed for vertical ball screws, considering the wear debris and micro-contact temperature.

A moving pair with two-body contact is the ideal situation assumed in previous analyses. However, all moving pairs are in a three-body contact state at the start of operation or immediately after the start of operation, such as bearings, ball-screws, gears and engines. This work studies the influence of wear particles (SUJ2), environmental particles (SiO₂ and Al₂O₃) and nano-additives (CuO) on the tribological contact characteristics under different particle concentrations, particle sizes, surface roughnesses and contact modes. The three-body microcontact analysis revealed that the differences in the real contact area, particle contact area and separation of the four-particle materials in the three-body s–s and p–s contact modes are rather small. Under the three-body hybrid contact mode, the difference is relatively large and the sequence of the real contact area value obtained due to the elastic modulus for the four-particle material at this interface is Al₂O₃ > SUJ2 > CuO > SiO₂. The order of the other two contact characteristics is reversed. The difference increases as the particle size or particle concentration increases. The order of the critical load required to transform three kinds of contact modes is SiO₂ > CuO > SUJ2 > Al₂O₃. On the nearly initial three-body hybrid contact mode, the plastic contact area ratio at the interface first increases to a critical value and then decreases as the load increases because the original plastic contact spot area and contact spot number increases with the increase in load. At the same time, the elasto-plastic contact area ratio decreases to a low value and then increases. The elastic contact area ratio at the interface decreases as the load increases. Among the four third-particle materials, the experimental results and theoretical predictions show that the environmental particles, Al₂O₃, cause the maximum friction and wear observed at the interface.