# Effect of Third-Particle Material and Contact Mode on Tribology Contact Characteristics at Interface

^{*}

## Abstract

**:**

_{2}and Al

_{2}O

_{3}) 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 Al

_{2}O

_{3}> SUJ2 > CuO > SiO

_{2}. 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 SiO

_{2}> CuO > SUJ2 > Al

_{2}O

_{3}. 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, Al

_{2}O

_{3}, cause the maximum friction and wear observed at the interface.

## 1. Introduction

_{a}/σ) is below 0.75. The results of three-body contact analysis [9] obtained in 2022 showed better contact characteristics near the turning point of contact area (TCPA) at the interface. These two articles show that replacing the sliding motion of two surfaces by the rolling motion of particles is not the sole reason for nanoparticles’ effectiveness in lubricants [10,11,12]. In the same year, the three-body mixed lubrication analysis framework was established [13]. Theoretical analysis shows that the specific film thickness criterion for two-body mixed lubrication is not suitable for three-body mixed lubrication.

_{2}nanoparticles to desert date oil had on tribological characteristics. Their findings revealed that the introduction of SiO

_{2}nanoparticles led to an improvement in the interaction between the surfaces, resulting in reduced friction and surface wear upon contact. In 2023, Wang et al. [29] focused on the development and testing of environmentally friendly lubricants and additives to enhance manufacturing processes and tribological performance. They investigated the effects of nano-lubricants, cellulose nanocrystal, and MoDTC on friction and wear reductions, and suggest their potential for sustainable machining and manufacturing. A tribology experiment [30,31,32,33,34,35] found that the use of certain sizes and concentrations of CuO in lubricant leads to the best tribology properties. In relation to these specific environmental controls, the air in factories is full of dust. The main components of dust are silicon dioxide (SiO

_{2}) and aluminum oxide (Al

_{2}O

_{3}). Nabhan et al., in 2021, [36] conducted a study that found that Al

_{2}O

_{3}nanoparticles can effectively improve the wear resistance and load-carrying capacity of lithium grease. H. Chen et al. [37] reported that Al

_{2}O

_{3}nanoparticles can effectively improve the wear resistance and load-carrying capacity of lithium grease. Furthermore, WC and Al

_{2}O

_{3}were found to enhance the wear resistance and friction performance of ZrB2-20% vol SiC composite material at high temperatures. If the transmission element is made of bearing steel (SUJ2), the interface during operation will produce wear debris formed by the bearing steel material. The transmission components generally operate under medium- and high-load conditions. In order to study the influence of different material particles on the interface contact properties, this work will analyze the microcontact characteristics of bearing steel components when there are four kinds of material particles (SiO

_{2}, SUJ2, Al

_{2}O

_{3}and CuO) at the interface.

## 2. Theoretical Analysis

- All surface asperities and third particles are far apart and there is no interaction between them.
- The surface asperities and third particles deform during contact with no bulk deformation of the two surfaces.
- The slopes of the surface asperities are considered to be negligible in the contact model.

_{n}represents the total number of peaks in the contact area between two surfaces, Z

_{max}represents the maximum distance from the reference plane of the lower surface to the summit of asperity and d represents the separation between surface 1 and mean height of asperities. The height variation in surface 2 peak is represented by a distribution function ϕ(z), where η represents the peak density per unit area (asperity density) and A

_{n}represents the nominal contact area. The actual contact area between two surfaces is the sum of elastic deformation, elastoplastic deformation, and plastic deformation. According to the Zhao, Maietta and Chang proposed two-body contact formula (ZMC model) [20], where A

_{ss}is the real contact area of two surfaces, this can be written as follows:

_{ss,e}represents the area of elastic deformation in the real contact area between two surfaces, A

_{ss,ep}represents the area of elastoplastic deformation in the contact area between surface 2 peak and surface 1, A

_{ss,p}represents the area of plastic contact between surface 2 peak and surface 1, R represents the radius curvature of surface peak, δ

_{ss}represents the interference amount between two surfaces, δ

_{ss,}

_{1}represents the initial yield interference amount of elastic deformation between two surfaces, and δ

_{ss,}

_{2}represents the critical yield interference amount required for the complete plastic deformation between two surfaces. Where E

_{ss}represents the composite Young’s modulus between two surfaces, this can be expressed as follows:

_{s}

_{1}is the Young’s modulus of surface 1, ν

_{s}

_{1}is the Poisson’s ratio of surface 1, E

_{s}

_{2}is the Young’s modulus of surface 2, and ν

_{s}

_{2}is the Poisson’s ratio of surface 2. Where F

_{ss}contact load of two surfaces, the contact load can be expressed as follows:

_{sa}, and contact load F

_{sa}can be written as follows [33]:

_{a}(x) and ϕ (z) are assumed to follow the Gaussian distributions, where, x

_{max}, E

_{sa}, H

_{s}

_{1}, H

_{s}

_{2}, η

_{a}and x

_{a}represent the maximum particle diameter, the equivalent elastic modulus of the third particle and surface, surface 1 hardness, surface 2 hardness, the number of third particles per unit area, and the mean size of the third particle, respectively. To obtain the real contact area between the two surfaces, the contact area of particles deposited on the surface peaks must be subtracted, as shown in Figure 2. The contact area of two surface, A

_{ss-sa}, can be expressed as follows:

_{ss}. The total contact area A

_{t}and the total contact load F

_{t}can be obtained from Equations (6) and (7) for the three-body system. Therefore, the three-body microcontact model is formulated.

_{a}= 0), then Equations (9) and (10) reduce to the results of another surface-to-surface contact model for two bodies.

_{n}E

_{ss}and A

_{n}, respectively. To obtain the dimensionless contact area ratios (A

_{p,t}

^{*}, A

_{ep,t}

^{*}, A

_{e,t}

^{*}, A

_{ss,t}

^{*}, and A

_{sa,t}

^{*}), the individual components of A

_{t}, which include A

_{p}, A

_{ep}, A

_{e}, A

_{ss}, and A

_{sa}, were divided by A

_{t}.

## 3. Experiment

## 4. Results and Discussion

_{2}, Al

_{2}O

_{3}(foreign particles) and SUJ2 (wear debris). SiO

_{2}and Al

_{2}O

_{3}particles were used as third particles because dust in the environment contains about 80.78% of SiO

_{2}and 10.52% of Al

_{2}O

_{3}[44]. The reason for selecting a particle material with the same material properties as the surface material (SUJ2) in this study is to consider the wear debris generated during operation as another scenario for the influence of third particles. The effects of work hardening are not taken into account in the selection of the particle material [45,46]. Table 3 provides the material characteristics of surface 1, surface 2, and the third particle, while Table 4 outlines the input parameters in the three-body contact model, where σ represents the equivalent surface RMS roughness.

_{t}

^{*}) for various third particles, with σ = 50 nm, η

_{a}= 10

^{12}/m

^{2}and x

_{a}= 100 nm, as shown in Figure 5a. The yellow dashed line represents the A

_{t}

^{*}at the different F

_{t}

^{*}for traditional two-body contact (x

_{a}= 0 nm). This curve is calculated using the ZMC two-body contact model. The orange dashed line represents the A

_{t}

^{*}when the particle size is relatively large and the surface is completely supported by particles (p–s mode). This shows that the real contact areal calculated by the traditional two-body s–s contact assumption is overestimated. Both curves linearly increase with the increasing F

_{t}

^{*}and form an upper and lower limit for all three-body contact situations. In this paper, we defined that when A

_{sa,t}

^{*}> 95%, the contact interface is in p–s mode; when A

_{sa,t}

^{*}< 5%, the contact interface is in s–s mode; and when 5% < A

_{sa,t}

^{*}< 95%, the contact interface is in hy. mode, as shown in Figure 5b. Under the same σ, the A

_{t}

^{*}varies with the load and the four third-particle materials, as shown in Figure 5a. For example, with third-particle material SUJ2, as the F

_{t}

^{*}becomes lower than 3.96 × 10

^{−6}, the curve overlaps with the curve of p–s mode in the first stage. This indicates that the contact pressure between the support surfaces is mainly borne by the third particles at this load. In the second stage, 5.08 × 10

^{−5}> F

_{t}

^{*}> 3.96 × 10

^{−6}, the A

_{t}

^{*}increases rapidly and the 5% < A

_{sa,t}

^{*}< 95%. This indicates that the contact interface has entered the hy. mode. In this contact mode, the size order of A

_{sa,t}

^{*}under fixed load is SiO

_{2}> CuO > SUJ2 > Al

_{2}O

_{3}. In the third stage, F

_{t}

^{*}> 5.07×10

^{−5}, the A

_{t}

^{*}almost overlaps with the s–s mode situation. The particle area ratio A

_{sa,t}

^{*}is less than the 5% presented, as shown in Figure 5b.

_{2}particles needs a larger contact load to enter hy. mode compared to other third-particle materials. The sequence of critical contact load is SiO

_{2}> CuO > SUJ2 > Al

_{2}O

_{3}. Figure 5c shows the variation in dimensionless separation (d

^{*}= d/σ) and F

_{t}

^{*}for all kinds of particles. The yellow dashed line represents the linear relationship between d

^{*}and F

_{t}

^{*}for the traditional two-body contact mode. For four materials, the relationship between d

^{*}and F

_{t}

^{*}is almost the same under s–s mode. The deviation of the effect of particle material on d

^{*}is obvious from near p–s to hy. mode. At the same F

_{t}

^{*}, the sequence of d

^{*}is SiO

_{2}> CuO > SUJ2 > Al

_{2}O

_{3}. The separation was obtained from Equation (6). The separation value, d, is influenced by the hardness, Young’s modulus, and Poisson ratio of three body. Among the four-particle materials, SiO

_{2}show the largest (H

_{s}

_{1}

^{2}/E

_{sa}

^{2}+ H

_{s}

_{1}

^{2}/E

_{ss}

^{2}) and the smallest values of h

_{e}. Therefore, d is the largest compared to other particles.

_{2}O

_{3,}CuO and SiO

_{2}. However, the interface with SUJ2 particles has a lower friction coefficient than that of the interface with CuO particles. A possible reason for this is that the other three material particles are different from the workpiece material, so their friction order is consistent with the real contact area ratio. The SUJ2 particle is the same as the workpiece material, so that different bonding patterns are produced at the interface. The interface with Al

_{2}O

_{3}particles has a much larger average friction coefficient than the other third-particle interfaces. The reason for this is the relatively high hardness, which means that the plowing friction is relatively large. Figure 6c shows that the main wear pattern of the four wear scars is a three-body abrasive wear. From Figure 6b, the size order of A

_{sa,t}

^{*}under fixed load is SiO

_{2}> CuO > SUJ2 > Al

_{2}O

_{3}. Therefore, the size order of real contact pressure between surface and particles under fixed load is Al

_{2}O

_{3}> SUJ2 > CuO > SiO

_{2}. According to the wear theory, the greater the contact pressure, the greater the wear volume. We find that the wear diameter in Figure 6d and real contact pressure between surface and particles in Figure 6b have a positive relationship for four-particle materials. These experimental results are in good agreement with the theoretical analysis.

_{t}

^{*}. Comparing Figure 7a and Figure 7b show that these situations are in the s–s mode. This means that third particles sink into valleys in the surface roughness. The third particles have almost no effect on the change in real contact area. The A

_{t}

^{*}for σ = 300 nm was 11.35% higher than for σ = 500 nm under all load conditions. When σ = 100 nm (red line), the F

_{t}

^{*}range for entering the hy. mode is much larger than that of when σ = 50 nm (black line) and is true for all third-particle materials. The A

_{t}

^{*}is close to overlapping the four-particle materials, which are in s–s mode for which A

_{sa,t}

^{*}< 5%, as seen in Figure 7b. In addition, the A

_{t}

^{*}for three different surface roughnesses (σ = 100 nm, σ = 300 nm and σ = 500 nm) decreases with the increase in σ. When the interface with σ = 50 nm is under a high load, the interface enters the s–s mode. This kind of s–s mode situation for all materials shows that the larger the surface roughness, the smaller the real contact area. This conclusion is the same for an ideal two-body contact situation. However, the interface with σ = 50 nm under a low load is in the p–s contact mode for which A

_{sa,t}

^{*}> 95%, as seen in Figure 7b. The A

_{t}

^{*}is lower than that of the other roughness surfaces. The real contact area of an interface with σ = 50 nm in the hy. mode does not show a uniform trend with surfaces with different roughness values. The findings emphasize that decreasing the value of equivalent surface roughness σ or increasing the x

_{a}can have a significant impact on the A

_{t}

^{*}, which may lead to unstable operation of the components and surface damage.

_{2}O

_{3}> SUJ2 > CuO > SiO

_{2}. Interfaces with σ value of 500 nm are mostly found in the s–s mode, as seen in Figure 7a. This indicates that the third particles sink into the valley of surface roughness. When the load is high, it enters the hy. mode. However, the interface between the surface roughnesses of 50 nm and 100 nm enters from the p–s mode to the hy. mode. As a result, the real contact area of the two contact modes differs greatly at low loads. However, the gap narrows at a high load and the order of the real contact area caused by different materials is different, as shown in the enlarged picture of SUJ2 material.

^{*}value decreases as the σ and F

_{t}

^{*}increase under the same F

_{t}

^{*}. The interface between 50 nm and 100 nm at the initial p–s mode of the low load overlaps for four materials, and then the difference becomes larger as the load increases. The larger the x

_{a}/σ value of the interface, the larger the initial separation. However, at the s–s mode interface with a σ of 500 nm, the separations of the four materials are almost the same. When the surface roughness and particle size are almost equal, x

_{a}≅ σ, A

_{sa,t}

^{*}and d

^{*}first increase and then decrease with the increase in load, as shown in Figure 7 and Figure 8. This phenomenon will be further explained in Figure 9 and Figure 10.

_{e,t}

^{*}), elastoplastic deformation(A

_{ep,t}

^{*}), and plastic deformation(A

_{p,t}

^{*}). The plastic deformation spots in the real contact area are the main areas of surface damage, such as plowing groove, pitting and delamination wear. Figure 9 shows the deformation components’ variation in the total real contact area ratio versus the F

_{t}

^{*}for A

_{e,t}

^{*}, A

_{ep,t}

^{*}, and A

_{p,t}

^{*}, with η

_{a}= 10

^{12}/m

^{2}. Three different values of σ and, x

_{a}are considered: (a) σ = 100 nm, x

_{a}= 100 nm; (b) σ = 300 nm, x

_{a}= 300 nm; and (c) σ = 500 nm, x

_{a}= 500 nm. As shown in Figure 9a, the A

_{e,t}

^{*}decreases with increasing F

_{t}

^{*}. In contrast, the A

_{ep,t}

^{*}increases with increasing F

_{t}

^{*}, and the A

_{ep,t}

^{*}increases at the initial stage and then decreases. This behavior is different from that of the A

_{p,t}

^{*}and A

_{ep,t}

^{*}. The reason for this is that original plastic contact area increases, and new contact spots occur, as the load increases. The real contact pressure at parts of the original plastic contact spots decreases and results in the plastic area transferring to the elastoplastic area. At the same time, part of the real elastic area changes to the elastoplastic area due to the decreasing separation of the two surfaces. It is interesting to note that the ratio of plastic contact area for the four-particle materials starts to make a difference near the hy. contact. Their order of magnitude is SiO

_{2}> CuO > SUJ

_{2}> Al

_{2}O

_{3}. The order of their magnitude is opposite to the value of Young’s modulus. The results of a previous two-body contact analysis show that, even at extremely low loads, the elastoplastic area accounts for more than 80% and only a small part is the plastic and elastic deformation area [18]. The results of the three-body contact analysis are obviously more reasonable.

_{p,t}

^{*}first increases and then decreases with increasing F

_{t}

^{*}, as described in Figure 11a. The order of magnitude for four-particle materials is the same for different surface roughness and contact loads. However, in Figure 9b, showing the results for σ = 300 nm and x

_{a}= 300 nm, the A

_{p,t}

^{*}and deviation of four-particle materials are greater than that of the surface, with σ = 100. The A

_{p,t}

^{*}of SiO

_{2}reached 50%, and the A

_{e,t}

^{*}was smaller than 0.15 for all materials. Because the increase rate of the plastic area with the increase in load is larger than that of the surface with small roughness, the elastoplastic deformation area will drop to the lowest value and then rise. The interface with a higher roughness and larger particle size is shown in Figure 9c. The A

_{p,t}

^{*}of SiO

_{2}reached 80% at a high load. The larger the surface roughness, the smaller the elastic deformation area for all materials. This concludes that higher roughness and a larger particle size have a greater chance of causing wear and damage.

_{ep,t}

^{*}and A

_{p,t}

^{*}versus the F

_{t}

^{*}for various third-particle materials and the η

_{a}. Regardless of the material, the greater the particle concentration, the smaller the A

_{ep,t}

^{*}. However, the order of the A

_{ep,t}

^{*}produced by different material types does not change. As analyzed in Figure 10, the A

_{e,t}

^{*}linearly decreases with the increase in load. Therefore, the A

_{p,t}

^{*}shows an opposite trend to the A

_{ep,t}

^{*}. The real plastic deformation area is the main area in which wear occurs. This also shows that the concentration of wear particles will gradually increase with the prolongation of the mechanical parts’ operation part, and the parts will be damaged by failure due to excessive wear or fatigue.

_{a}(particle concentration) on the contact characteristics at the interface. The three-body contact situation interface with a low concentration of 10

^{10}/m

^{2}, x

_{a}= 100 nm and σ = 50 nm, has almost the same linear relationship between A

_{t}

^{*}and F

_{t}

^{*}as in the two-body contact situation. Comparing Figure 11a with Figure 11b, the interfaces for all particle materials are shown to be in the s–s mode. However, when the concentration of third particle rises to 10

^{12}/m

^{2}, the interface enters the p–s, hy. and s–s modes as the load increases. The three-body contact situation interface with a concentration of 10

^{11}/m

^{2}occurs between the above two conditions. Therefore, under the same load, the greater the concentration, the smaller the value of the real contact area ratio.

_{t}

^{*}range of SiO

_{2}in the hy. mode is the largest (F

_{t}

^{*}= 8.60 × 10

^{−6}~1.53 × 10

^{−4}) when η

_{a}= 10

^{12}/m

^{2}, followed by CuO, and Al

_{2}O

_{3}is the smallest. However, the interface with Al

_{2}O

_{3}can easily enter the hy. mode compared to interfaces with other third-particle materials under smaller loads. In summary, the smaller the equivalent elastic modulus of the third particle, the larger the load range it can withstand. On the other hand, the larger the equivalent elastic modulus, the earlier it can enter the hy. contact under smaller loads. This also indicates that the four different third-particle materials are suitable for different mechanical surface motion conditions.

^{*}increases with the increase in particle concentration. When the particle concentration is η

_{a}= 10

^{10}/m

^{2}, the d

^{*}values of the four different third-particle materials are almost the same. However, as the particle concentration increases to η

_{a}= 10

^{12}/m

^{2}, the differences in d

^{*}values among the four different third-particle materials become larger. After F

_{t}

^{*}> 3.96 × 10

^{−6}, the d

^{*}value of Al

_{2}O

_{3}is smaller than that of other third-particle materials. This result is consistent with the results shown in Figure 11b. This indicates that the interface with Al

_{2}O

_{3}enters the hy. mode earlier than interfaces with the other third-particle materials. The findings of this study suggest that the concentration of third-particle materials significantly affects the real contact area and interface separation. This is also the reason why, as the operating time of the machine increases, the concentration of the third particle also increases, resulting in the end of life.

_{t}

^{*}and the F

_{t}

^{*}at various third-particle sizes and materials, with σ = 50 nm, and η

_{a}= 10

^{12}/m

^{2}. Figure 12a shows that A

_{t}

^{*}increases as the A

_{t}

^{*}increases. As explained above, within the load and particle concentration range of general components, when x

_{a}/σ is less than 1, the interface is almost the s–s mode. When x

_{a}/σ is far greater than 1, the interface is almost the p–s mode. When there is a third particle present between the two surfaces under the same F

_{t}

^{*}, the A

_{t}

^{*}decreases. This phenomenon is consistent with the inference made by Ghaednia et al. [52]. Figure 12c shows that as the average third-particle diameter (x

_{a}) increases, the d

^{*}also increases at all load ranges. Figure 8c illustrates the relationship between x

_{a}/σ and d

^{*}. The larger the x

_{a}/σ value of the interface, the larger the initial separation. At the s–s mode interface, the separations of the four materials are almost the same. The interface at the initial p–s contact mode overlaps for four materials, and then the difference becomes larger as the load increases. Figure 12c shows that the analysis results have the same trend as the results from Figure 8c.

## 5. Conclusions

- The difference in the dimensionless separation and real contact area ratio of the four-particle materials in the three-body s–s and p–s contact modes is rather small. The biggest difference occurs near the transition area from the p–s contact mode to three-body hy. contact mode. Regardless of the contact mode, the order of the dimensionless separation of the four-particle materials is SiO
_{2}> CuO > SUJ2 > Al_{2}O_{3}. The separation value, d, is influenced by the hardness, Young’s modulus, and Poisson ratio of three body. The order of the real contact area ratio is reversed. The experimental results regarding friction and wear for the four third-particle materials show that the theoretical predictions are reasonable. - Under the same particle size, particle concentration and surface roughness, the critical load level sequence from three-body p–s contact mode to three-body hy. contact mode is SiO
_{2}> CuO > SUJ2 > Al_{2}O_{3}. The critical load sequence from three-body hy. contact mode to three-body s–s contact mode is the same. The smaller the particle size, the lower the concentration, and the three-body interface only needs a relatively low load to enter the three-body s–s contact mode. - The difference in the contact deformation type of the four-particle materials in the three-body s–s and p–s contact modes is rather small. In the three-body hy. contact mode, the plastic contact areas of the four materials first increase to a critical value and then decrease as the load increases. This is because the area of the original plastic contact spot gradually increases with the increase in load. At the same time, the number of contact spot also increases. The contact pressure at the plastic contact spot is reduced. As a result, some plastic contact spots enter the elastic–plastic region.
- The order of plastic contact area value in the hy. mode is SiO
_{2}> CuO > SUJ2 > Al_{2}O_{3}. The load required to achieve the maximum plastic contact area ratio is also in the same order. The larger the particle size, the greater the plastic contact area for all particle materials. The lower the particle concentration, the greater the elasto-plastic contact area for all particle materials.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Godet, M. The third particle approach: A mechanical view of wear. Wear
**1984**, 100, 437–452. [Google Scholar] [CrossRef] - Godet, M. Third particles in tribology. Wear
**1990**, 136, 29–45. [Google Scholar] [CrossRef] - Heshmat, H.; Godet, M.; Berthier, Y. On the Role and Mechanism of Dry Triboparticulate Lubrication. In Proceedings of the 49th STLE Annual Meeting, Pittsburgh, PN, USA, 1–5 May 1994. [Google Scholar]
- Stachowiak, G.B.; Stachowiak, G.W. The effects of particle characteristics on three-body abrasive wear. Wear
**2001**, 249, 201–207. [Google Scholar] [CrossRef] - Ruling, C.; Shaoxian, L. Novel three-body nano-abrasive wear mechanism. Friction
**2022**, 10, 677–687. [Google Scholar] [CrossRef] - Popov, V.L. Is tribology approaching its golden age? grand challenges in engineering education and tribological research. Front. Mech. Eng.
**2018**, 4, 16. [Google Scholar] [CrossRef] - Greenwood, J.A. Metal transfer and wear. Front. Mech. Eng.
**2020**, 6, 62. [Google Scholar] [CrossRef] - Peña-Parás, L.; Gao, H.; Maldonado-Cortés, D.; Vellore, A.; García-Pineda, P.; Montemayor, O.E.; Nava, K.L.; Martini, M. Effects of substrate surface roughness and nano/micro particle additive size on friction and wear in lubricated sliding. Tribol. Int.
**2018**, 119, 88–98. [Google Scholar] [CrossRef] - Chern, S.Y.; Chen, Y.Y.; Liu, W.L.; Horng, J.H. Contact Characteristics at Interface in Three-Body Contact Conditions with Rough Surfaces and Foreign Particles. Lubricants
**2022**, 10, 164. [Google Scholar] [CrossRef] - Singh, Y.; Rahim, E.A.; Singh, N.K.; Sharma, A.; Singla, A.; Palamanit, A. Friction and wear characteristics of chemically modified mahua (madhuca indica) oil based lubricant with SiO
_{2}nanoparticles as additives. Wear**2022**, 508–509, 204463. [Google Scholar] [CrossRef] - Miftakhova, A.; Chen, Y.Y.; Horng, J.H. Effect of rolling on the friction coefficient in three-body contact. Adv. Mech. Eng.
**2019**, 11, 1687814019872303. [Google Scholar] [CrossRef] - Boungomba, H.; Moreau, P.; Sadat, T.; Dubois, R.; Dubar, M.; Dubar, L. Influence of oxide polluted lubricants on friction: Trapping mechanisms. Tribol. Int.
**2023**, 179, 108164. [Google Scholar] [CrossRef] - Horng, J.H.; Yu, C.C.; Chen, Y.Y. Tribological Characteristics and Load-Sharing of Point-Contact Interface in Three-Body Mixed Lubrication. ASME J. Tribol.
**2021**, 144, 052201. [Google Scholar] [CrossRef] - Horng, J.H.; Lin, J.F.; Li, K.Y. Scuffing as Evaluated from the Viewpoint of Surface Roughness and Friction Energy. ASME J. Tribol.
**1996**, 118, 669–675. [Google Scholar] [CrossRef] - Horng, J.H. Contact Analysis of Rough Surfaces at Transition Conditions in Sliding Line Lubrication. Wear
**1999**, 219, 205–212. [Google Scholar] [CrossRef] - Pawlus, P.; Zelasko, W. The importance of sampling interval for rough contact mechanics. Wear
**2012**, 276–277, 121–129. [Google Scholar] [CrossRef] - Beheshti, A.; Khonsari, M.M. Asperity micro-contact models as applied to the deformation of rough line contact. Tribol. Int.
**2012**, 52, 61–74. [Google Scholar] [CrossRef] - Li, L.; Etsion, I.; Talke, F.E. Contact Area and Static Friction of Rough Surfaces with High Plasticity Index. ASME J. Tribol.
**2010**, 132, 669–675. [Google Scholar] [CrossRef] - Kogut, L.; Etsion, I. Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat. ASME J. Appl. Mech.
**2002**, 69, 657–662. [Google Scholar] [CrossRef] - Zhao, Y.; Maietta, D.M.; Chang, L. An Asperity Microcontact Model Incorporating the Transition from Elastic Deformation to Fully Plastic Flow. ASME J. Tribol.
**2000**, 122, 86–93. [Google Scholar] [CrossRef] - Jamari, J.; Schipper, D.J. Plastic deformation and contact area of an elastic–plastic contact of ellipsoid bodies after unloading. Tribol. Int.
**2007**, 40, 1311–1318. [Google Scholar] [CrossRef] - Lin, L.P.; Lin, J.F. A New Method for Elastic-Plastic Contact Analysis of a Deformable Sphere and a Rigid Flat. ASME J. Tribol.
**2006**, 128, 221–229. [Google Scholar] [CrossRef] - Qiu, S.; Dong, J.; Cheng, G. A review of ultrafine particles as antiwear additives and friction modifiers in lubricating oils. Lubr. Sci.
**1999**, 11, 217–226. [Google Scholar] [CrossRef] - Rapoport, L.; Leshchinsky, V.; Lvovsky, M.; Lapsker, I.; Volovik, Y.; Feldman, Y.; Popovitz-Biro, R.; Tenne, R. Superior tribological properties of powder materials with solid lubricant nanoparticles. Wear
**2003**, 255, 794–800. [Google Scholar] [CrossRef] - Wornyoh, E.Y.A.; Jasti, V.K.; Higgs, C.F. A review of dry particulate lubrication: Powder and granular materials. J. Tribol.
**2007**, 129, 438–449. [Google Scholar] [CrossRef] - Asnida, M.; Hisham, S.; Awang, N.W.; Amirruddin, A.K.; Noor, M.M.; Kadirgama, K.; Ramasamy, D.; Najafi, G.; Tarlochan, F. Copper (II) oxide nanoparticles as additve in engine oil to increase the durability of piston-liner contact. Fuel
**2018**, 212, 656–667. [Google Scholar] [CrossRef] - Bhaumik, S.; Maggirwar, R.; Datta, S.; Pathak, S.D. Analyses of anti-wear and extreme pressure properties of castor oil with zinc oxide nano friction modifiers. Appl. Surf. Sci.
**2018**, 449, 277–286. [Google Scholar] [CrossRef] - Aghbashlo, M.; Tabatabaei, M.; Khalife, E.; Najafi, B.; Mirsalim, S.M.; Gharehghani, A.; Mohammadi, P.; Dadak, A.; Shojaei, T.R.; Khounani, Z. A novel emulsion fuel containing aqueous nano cerium oxide additive in diesel–biodiesel blends to improve diesel engines performance and reduce exhaust emissions: Part II—exergetic analysis. Fuel
**2017**, 205, 262–271. [Google Scholar] [CrossRef] - Singh, Y.; Singh, N.K.; Sharma, A. Effect of SiO
_{2}Nanoparticles on the Tribological Behavior of Balanites Aegytiaca (Desert date) Oil-Based Biolubricant. J. Bio Tribo Corros.**2021**, 7, 1–6. [Google Scholar] [CrossRef] - Wang, W.; Yu, M.; Ma, J.; Jia, Y. Tribological Properties of Nanoparticles in the Presence of MoDTC. Lubricants
**2023**, 11, 132. [Google Scholar] [CrossRef] - Kumar, S.; Kumar, R. Tribological characteristics of synthesized hybrid nanofluid composed of CuO and TiO
_{2}nanoparticle additives. Wear**2023**, 518–519, 204623. [Google Scholar] [CrossRef] - Wu, C.; Xiong, R.; Ni, J.; Yao, L.; Li, X. Effects of CuO nanoparticles on friction and vibration behaviors of grease on rolling bearing. Tribol. Int.
**2020**, 152, 106552. [Google Scholar] [CrossRef] - Alves, S.M.; Barros, B.S.; Trajano, M.F.; Ribeiro, K.S.B.; Moura, E. Tribological behavior of vegetable oil-based lubricants with nanoparticles of oxides in boundary lubrication conditions. Tribol. Int.
**2013**, 65, 28–36. [Google Scholar] [CrossRef] - Choi, Y.; Lee, C.; Hwang, Y.; Park, M.; Lee, J.; Choi, C.; Jung, M. Tribological behavior of copper nanoparticles as additives in oil. Curr. Appl. Phys.
**2009**, 9, e124–e127. [Google Scholar] [CrossRef] - Wei, C.C.; Horng, J.H.; Lee, A.C.; Lin, J.F. Analyses and experimental confirmation of removal performance of silicon oxide film in the chemical–mechanical polishing (CMP) process with pattern geometry of concentric groove pads. Wear
**2011**, 270, 172–180. [Google Scholar] [CrossRef] - Nabhan, A.; Rashed, A.; Ghazay, N.M.; Abdo, J.; Haneef, M.D. Tribological Properties of Al
_{2}O_{3}Nanoparticles as Lithium Grease Additives. Lubricants**2021**, 9, 9. [Google Scholar] [CrossRef] - Chen, H.; Wu, Z.; Hai, W.; Liu, L.; Sun, W. Tribo-oxidation and tribological behaviour of ZrB
_{2}-20%volSiC composites coupled with WC and Al_{2}O_{3}at high temperatures. Wear**2021**, 464–465, 203534. [Google Scholar] [CrossRef] - Greenwood, J.A.; Tripp, J.H. The contact of two nominally flat rough surfaces. Proc. Inst. Mech. Eng.
**1970**, 185, 625–633. [Google Scholar] [CrossRef] - Shi, W.; Zhang, Z. Contact characteristic parameters modeling for the assembled structure with bolted joints. Tribol. Int.
**2022**, 165, 107272. [Google Scholar] [CrossRef] - Wu, H.W.; Chen, Y.Y.; Horng, J.H. The analysis of three-body contact temperature under the different third particle size, density, and value of friction. Micromachines
**2017**, 8, 302. [Google Scholar] [CrossRef] - Xie, H.; Jiang, B.; He, J.; Xia, X.; Pan, F. Lubrication performance of MoS
_{2}and SiO_{2}nanoparticles as lubricant additives in magnesium alloy-steel contacts. Tribol. Int.**2016**, 93, 63–70. [Google Scholar] [CrossRef] - Rigney, D.A. The role of characterization in understanding debris generation. In Wear Particles, 1st ed.; Dowson, D., Taylor, C.M., Childs, T.H.C., Godet, M., Dalmaz, G., Eds.; Elsevier Science: Amsterdam, The Netherlands, 1992; pp. 405–412. [Google Scholar]
- CPC Corporation, Taiwan. Available online: https://cpclube.cpc.com.tw/en/C_ProductDetail.aspx?n=7547&s=840 (accessed on 23 March 2023).
- Mir, A.H. Improved Concrete Properties Using Quarry Dust as Replacement for Natural Sand. Int. J. Eng. Res. Dev.
**2015**, 11, 46–52. Available online: http://www.ijerd.com/paper/vol11-issue3/Version_1/E1134652.pdf (accessed on 23 March 2023). - Shi, X.; Zou, Y. A Comparative Study on Equivalent Modeling of Rough Surfaces Contact. J. Tribol.
**2018**, 140, 041402. [Google Scholar] [CrossRef] - Croné, P.; Gudmundson, P.; Faleskog, J. Analytical prediction of yield stress and strain hardening in a strain gradient plasticity material reinforced by small elastic particles. Int. J. Plast.
**2022**, 151, 103200. [Google Scholar] [CrossRef] - Umbrello, D.; Hua, J.; Shivpuri, R. Hardness-based flow stress and fracture models for numerical simulation of hard machining AISI 52100 bearing steel. Mater. Sci. Eng. A
**2004**, 374, 90–100. [Google Scholar] [CrossRef] - Jang, J.S.; Bouveret, B.; Suhr, J.; Gibson, R.F. Combined numerical/experimental investigation of particle diameter and interphase effects on coefficient of thermal expansion and young’s modulus of SiO
_{2}/epoxy nanocomposites. Polym. Compos.**2012**, 33, 1415–1423. [Google Scholar] [CrossRef] - Yao, B.; Zhou, X.; Liu, M.; Yu, J.; Cao, J.; Wang, L. First-principles calculations on phase transformation and elastic properties of CuO under pressure. J. Comput. Electron.
**2018**, 17, 1450–1456. [Google Scholar] [CrossRef] - Abyzov, A.M. Aluminum Oxide and Alumina Ceramics (review). Part 1. Properties of Al
_{2}O_{3}and Commercial Production of Dispersed Al_{2}O_{3}. Refract. Ind. Ceram.**2019**, 60, 24–32. [Google Scholar] [CrossRef] - Liang, X.M.; Xing, Y.Z.; Li, L.T.; Yuan, W.K.; Wang, G.F. An experimental study on the relation between friction force and real contact area. Sci. Rep.
**2021**, 11, 20366. [Google Scholar] [CrossRef] - Ghaednia, H.; Jackson, R.L.; Khodadadi, J.M. Experimental analysis of stable CuO nanoparticle enhanced lubricants. J. Exp. Nanosci.
**2015**, 10, 1–18. [Google Scholar] [CrossRef]

**Figure 1.**The contact mode at the contact interfaces: (

**a**) two-body s–s mode, (

**b**) surface-to-particle mode, (

**c**) surface-to-surface mode, and (

**d**) three-body s–s mode. (The light purple circles is contact spots between the two surfaces and the light blue circles is contact spots between the third particle and the surface.)

**Figure 5.**Contact characteristics as a function of dimensionless contact load for various third-particles, with σ = 50 nm, η

_{a}= 10

^{12}/m

^{2}and x

_{a}= 100 nm, (

**a**) dimensionless real contact area (

**b**) real contact area ratio of two surfaces, and real contact area ratio of third particle and surface (

**c**) dimensionless separation.

**Figure 6.**Experimental results of lubricating oil with different third-particle materials: (

**a**) variation in friction coefficient, (

**b**) average coefficient of friction, (

**c**) wear scar, (

**d**) wear diameter.

**Figure 7.**Contact characteristics as a function of dimensionless contact load for various third-particles and equivalent surface RMS roughnesses, with η

_{a}= 10

^{12}/m

^{2}, and x

_{a}= 100 nm, (

**a**) dimensionless real contact area (

**b**) real contact area ratio of third particle and surface (

**c**) dimensionless separation.

**Figure 8.**Contact characteristics as a function of dimensionless contact load for various third-particle materials and equivalent surface RMS roughnesses, with η

_{a}= 10

^{12}/m

^{2}, and x

_{a}= 300 nm, (

**a**) dimensionless real contact area (

**b**) real contact area ratio of third particle and surface (

**c**) dimensionless separation.

**Figure 9.**Deformation components of total real contact area ratio as a function of dimensionless contact load for A

_{e,t}

^{*}, A

_{ep,t}

^{*}, and A

_{p,t}

^{*}, with η

_{a}= 10

^{12}/m

^{2}(

**a**) σ = 100 nm, x

_{a}= 100 nm (

**b**) σ = 300 nm, x

_{a}= 300 nm (

**c**) σ = 500 nm, x

_{a}= 500 nm.

**Figure 10.**Real contact area ratio of elastoplastic and plastic deformations as a function of dimensionless contact load for various third-particle materials and concentrations.

**Figure 11.**Contact characteristics as a function of dimensionless contact load for various particle concentrations, with σ = 50 nm, and x

_{a}= 100 nm, (

**a**) dimensionless real contact area (

**b**) real contact area ratio of third particle and surface (

**c**) dimensionless separation.

**Figure 12.**Contact characteristics as a function of dimensionless contact load for various third-particle and average third-particle diameters, with σ = 50 nm, and η

_{a}= 10

^{12}/m

^{2}(

**a**) dimensionless real contact area (

**b**) real contact area ratio of third particle and surface (

**c**) dimensionless separation.

Component Properties | C | Cr | Cu | Fe | Mn | Ni | P | Si | S |
---|---|---|---|---|---|---|---|---|---|

Value (%) | 0.42~0.48 | ≤0.20 | ≤0.30 | 97.6~98.8 | 0.60~0.90 | ≤0.20 | ≤0.030 | 0.15~0.35 | ≤0.035 |

Sp. Gr. | Viscosity, Kin. (cSt) | Viscosity Index | Pour Point (°C) | Flash Point (°C) | ||
---|---|---|---|---|---|---|

40 °C | 100 °C | |||||

Lubricant | 0.878 | 67.18 | 8.70 | 101 | −12 | 264 |

Surface 1 | Surface 2 | Third Particle | ||||
---|---|---|---|---|---|---|

Materials | SUJ2 | SUJ2 | SUJ2 | CuO | SiO_{2} | Al_{2}O_{3} |

H (GPa) | 6.3 | 6.3 | 6.3 | 1.143 | 7 | 14.12 |

E (GPa) | 210 | 210 | 210 | 87.9 | 70.55 | 375 |

ν | 0.27 | 0.27 | 0.27 | 0.39 | 0.17 | 0.22 |

Property | Value |
---|---|

F_{t} (N) | 0.31–160 |

σ (nm) | 50, 100, 300, 500 |

η_{a} (m^{−}^{2}) | 10^{10}, 10^{11}, 10^{12} |

x_{a} (nm) | 25, 100, 300, 500 |

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## Share and Cite

**MDPI and ACS Style**

Horng, J.-H.; Yu, C.-C.; Chen, Y.-Y.
Effect of Third-Particle Material and Contact Mode on Tribology Contact Characteristics at Interface. *Lubricants* **2023**, *11*, 184.
https://doi.org/10.3390/lubricants11040184

**AMA Style**

Horng J-H, Yu C-C, Chen Y-Y.
Effect of Third-Particle Material and Contact Mode on Tribology Contact Characteristics at Interface. *Lubricants*. 2023; 11(4):184.
https://doi.org/10.3390/lubricants11040184

**Chicago/Turabian Style**

Horng, Jeng-Haur, Chia-Chun Yu, and Yang-Yuan Chen.
2023. "Effect of Third-Particle Material and Contact Mode on Tribology Contact Characteristics at Interface" *Lubricants* 11, no. 4: 184.
https://doi.org/10.3390/lubricants11040184