Mechanism of abrasion reduction in polydisperse system with carbon nanoparticles

. The research is focused on the problem of abrasive wear. The authors proposed a model based on the adsorption theory, where abrasive particles are used as transport of nanoscale additive for lubricant. Laboratory tests have been performed to determine tribotechnical, physico-chemical and rheological properties of polydisperse suspensions. It was determined that the suspensions consisting of lubricant and carbon nanotubes have high stability when pretreated by ultrasound. Rheological tests performed by rotational viscometry indicated that the insertion of carbon nanotubes slightly increases the kinematic viscosity of the lubricants. Modification of liquid lubricants with multi-walled carbon nanotubes results in wear reduction of friction surfaces by up to 10%. The combined use of an abrasive contaminant increases the efficiency of the additive by up to 35%. Carbon nanotubes provide a shielding effect and reduce the cutting effect of abrasive particles. The analysis of temperature dependences obtained in the tribological experiments allowed us to conclude that modification of lubricants with carbon nanotubes can increase thermal conductivity of compositions, which contributes to effective heat transfer from the friction zone.


Introduction
The problem of wear reduction is a relevant aspect for machines operating in various industries. Wear is one of the main factors affecting the operational and economic efficiency of transport, agricultural, textile and other machines.
One of the factors affecting the wear of machine parts is the anti-wear properties of lubricants. It is known to increase service life of friction units of machines by using nanoscale additives, for instance, on the carbon basis. At the same time the usage of nanoscale additives in specific conditions of abrasive wear is not investigated enough.
Actual scientific problem is the increasing of lubricants efficiency due to application of additives of allotropic modifications of carbon in conditions of abrasive wear.
Analysis of researches has allowed to reveal the basic factors influencing wear of mechanisms working in conditions of abrasive wear. Such factors include: hardness and modulus of elasticity of surfaces of friction parts, hardness and modulus of elasticity of abrasive particles, cutting ability (form, size) of abrasive particles, size of a gap between friction surfaces.
The service life of friction units can be improved in various ways: by improving sealing devices designed to isolate the contact area from abrasion particles, by reinforcing the surfaces of friction units, by applying additives-modifiers of various nature for lubricants [1][2].
Analysis of the current lubricant additive segment has highlighted nanoscale structures with a high specific surface area. We identified the main categories of additives based on carbon nanoparticles in the form of allotropic modifications of carbon: single-and multiwalled carbon nanotubes, graphene and graphene oxide, shungite nanoparticles [10][11].
The purpose of this study is to increase the efficiency of lubricants by using additives of allotropic carbon modifications under abrasive wear conditions.
Objectives set in the work: 1. To construct a physical model of the lubricating effect of nanosize additives for the lubricants contaminated with abrasive particles.
2. To reveal the influence of nanoscale additives inclusion into lubricating materials on tribotechnical, physical-chemical and rheological parameters of the systems.

Mathematical model of the nanoparticle transport process
We suggest a model for the interaction of nanoscale additive particles (in the form of carbon nanotubes) with abrasive particles. Our model proposes to consider abrasive particles in the role of additive transport to surfaces of friction. Both abrasive particles of external nature (dust, contamination) and particles that are formed during the wear process (wear particles) can act as such transport. The hardness of wear particles is higher than that of the main volume of friction surfaces. The transport of nanoscale additive will be accelerated when the concentration of abrasive particles increases.
We can define the kinetics of additive adsorption on a solid in the tribosystem by the equation: Where is β the "structuring" (or aggregation) coefficient of the triboactive additive, which is responsible for the changing behavior of the triboactive component in the volume, which is a function of the concentration.
In Eq. 2, ap is the equilibrium concentration of the adsorbate described by the Freundlich power model; k is a constant in Freundlich's law, and C is the concentration of the additive. By integrating over time Eq. 1, we obtain Using the model of linear dependence of wear and additive adsorption value, we assume that: Where K(C) is wear factor as a function of concentration, K(0) is the wear factor in the additive adsorption absence, n is the proportionality factor. Substituting Eq. 3 into Eq. 4 we obtain It follows from equation (1) that β(C) has dimension [sec-1]. Then: Where τ(C) is the characteristic adsorption time. Substituting Eq. 6 into Eq. 5, we obtain: Where t is time parameter, A = nk is a constant. The characteristic adsorption time depends linearly on additive concentration Where γ is proportional coefficient characterizing additive aggregation.
The application of analytical expression Eq.9 for analysis of results of laboratory tests of model lubricant (Vaseline oil -VO) on testing machine MTU-01 allows to estimate wear characteristic and marked out a number of characteristic areas ( Fig. 1): I -up to 0.5 wt. % additive; II -from 0,5 wt. % to 2,0-2,5 wt.% additive (depending on abrasive concentration); III above 2.0 to 2.5 wt. % additive (depending on abrasive concentration). We consider the parameter of additive activity at low concentrations as a characteristic of additive effectiveness at these wear modes.
Adhesive wear will prevail if there are no abrasive particles in the lubricant (Fig. 1, a). We assume that in region I the additive activity is close to zero, resulting in no reduction in wear intensity.
Wear particles which play the role of abrasive particles and are generated in the friction process will be limited in number. In this case it is not possible to use such abrasive particles as transport, so the carbon nanotubes cannot effectively enter the friction zone.
The maximum wear rate reduction (up to 40%) is observed when the additive concentration is increased and moves to region II. Further increasing the additive concentration and transition to area III reduces efficiency. This effect may be associated with aggregation of nanoparticles, increasing their size and decreasing the probability of their entrance into the friction zone. In the case of abrasive wear (Fig. 2, b and c), the concentration of the abrasive contaminant, which is added externally to the tribosystem, plays a major role.
In the area I, with the abrasive concentration of 0.5 wt. %, high additive activity and a significant concentration dependence of the efficiency is observed. The nature of this process is associated with an active increasing number of wear particles due to the abrasive cutting effect on the friction surfaces. In this case more significant transport action of the dispersed phase in the suspension is observed. Optimum efficiency of additive action is observed at transition to area II (similar to adhesive wear). In this case two opposing processes are observed: The shielding effect of the additive introduced into the friction zone with abrasive particles and wear particles; Transient processes in the volume of the additive, leading to aggregation of nanoparticles, an increase in their size and a decrease in activity.
Stabilization of the wear process occurs in zone III in all cases (adhesive and abrasive wear). The nano-additive activity decreases when the mass concentration is high enough. This effect can be confirmed by the sedimentation acceleration of such systems.
We can analyse Eq. 9 by variation of basic coefficients. The variation of the aggregation parameter γ results in a significant change of the characteristic dependence of the wear coefficient on concentration (Fig. 2). Thus, when the parameter increases from γa =300 sec/(wt. %) to γe=1500 sec/(wt. %) in steps of 300 sec/(wt. %) a shifting of optimum concentration towards decrease is well traced with significant decrease of additive effectiveness.
Variation of adsorption time τ0 does not modify general pattern of wear coefficient dependence on concentration (Fig. 3). When the parameter τ0 is increased from τa=100 sec to τe=500 sec in steps of 100 sec, the shift of optimum concentration is observed to decrease with significant reduction of additive efficiency.

Laboratory tests of modified lubricants
We selected two main lubricant groups (liquid and grease) for modification. Parameter groups such as tribotechnical, physico-chemical, rheological and environmental were investigated to assess the effect of modification with nanoscale additives. Electrocorundum 25A 0.063-0.125 (F180) was selected as the abrasive contaminant. The abrasive agent and carbon nanotube additive were added to the lubricant by mechanical mixing and then by ultrasonic dispersion.

Sedimentation stability and rheological properties of suspensions
As a result of laboratory tests on the stability of compositions consisting of liquid lubricants and Taunit carbon nanotubes, it was found that the suspensions after ultrasound dispersion for 15 minutes showed high stability.
The optical density measured by spectrophotometric method changes not more than 20% after 168 hours of sedimentation. It allows to draw conclusions about the possibility of using such nanostructures as additives for lubricating materials LM, satisfying the conditions of storage and transportation of the final product. The high stability of suspensions with carbon nano-additives makes it possible to preserve the efficiency of the modified LM during equipment downtime.
Laboratory experiment to measure the surface tension of the suspensions showed a slight increase in the value of surface tension, indicating the inertness of the additive.
Rheological tests by rotational viscometry with Brookfield DV-II+Pro and RPE-1M viscometers made it possible to conclude that the insertion of carbon nanotubes in the lubricant insignificantly increases the kinematic viscosity of suspensions, while the viscosity dependence on the concentration is exponential.
It should be noted, that the additive does not change the character of the lubricant flow thus not affecting the operation modes of the friction units designed for strictly definite characteristics of the lubricant.

Tribological testing of modified lubricants
The modification of liquid lubricants (Vaseline oil, industrial oils I20-A, I40-A, high-alloy oil VNII NP 406) with multiwalled carbon nanotubes results in insignificant increase of friction coefficient of compositions (Fig. 4). Such an effect could be associated with the high tensile strength and elastic properties of the nanotubes [17]. Investigation of tribotechnical properties of lubricating systems based on plastic lubricant (petrolatum) with additives of carbon nanostructures with different concentrations and spatial structure revealed two groups of allotropic modifications of carbon: one group decreases friction coefficient (by 67 % at most), the other group increases it (by 33 % at most) in comparison with the basic lubricant.
The first group includes multi-layer oxidised graphene, single-wall and multi-wall nanotubes. The second group includes multi-wall nanotubes Taunit-M and fullerene C60.
The effect of the additive in the form of shungite carbon nanoparticles is insignificant (friction coefficient reduction not exceeding 12%).
The reduction of wear of friction pairs as a result of laboratory tests of liquid lubricants contaminated by abrasive particles and modified by carbon nanotubes was established (Fig.  5). Decrease in value of wear of friction surfaces up to 10 % is observed in case of not contaminated by abrasive particles modified lubricants. The insertion of an abrasive contaminant increases the effectiveness of the additive. Carbon nanotubes have a shielding effect and reduce the cutting effect of abrasive particles by electrostatically interacting with them. Carbon nanotubes "Taunit", having enough big hardness and small sizes, being fixed on abrasive particles, dampens an abrasive particle impact on friction surface, being transferred directly to the surface itself. Laboratory tests of abrasive particle-contaminated lubricants with carbon nanotube additives confirm the proposed physical model. The wear reduction efficiency varies from 15% with manufacturer-modified liquid lubricants to 23% with industrial oils and petroleum jelly.
Investigation of temperature dependences obtained from laboratory tests (Fig. 6) allows to conclude that modification of lubricants with carbon nanotubes increases thermal conductivity of suspensions. The effect of the additive, in addition to reducing the wear value, is to increase the heat transfer from the friction zone. Testing of suspensions consisting of liquid lubricant, carbon nanotubes and copper micropowder proved that the insertion of "Taunit" carbon nanotubes as an additive reduces wear in both base oil and oil with addition of copper micropowder. The characteristic minimum of wear value in the system "Base oil -CNT" is observed at concentration 1.0 wt. %, at insertion of copper micropowder there is a further wear reduction, at the same time the optimum concentration of CNT is 1.5 wt. % that may indicate the synergistic effect of additives.
Practically no carbon and carbon nanotube marks are observed on friction surfaces when modified lubricants with carbon nanotubes are used. This effect could be suggested as indirect evidence of the interaction of carbon nanotubes directly with abrasive particles. The optical microscopy images of the friction surfaces are shown in Fig. 7 (a) and the electron microscopy images in Fig. 7 (b).

Conclusions
A physical model of nanoscale additive mass transfer in lubricants contaminated with abrasive particles has been developed and verified.
Experimental investigations determined that the modified lubricant's use resulted in wear rate reduction by up to 35% in the case of compositions consisting of industrial oil and 2.0 wt.% carbon nanotubes.
These researches may form a base for development of new speciality lubricating compositions, which use the effects of additive transfer in abrasive wear conditions into the fracture zone. One of the important perspectives of development is further research of polydisperse mixtures, consisting of lubricants, nanoscale additives, abrasive particles and surfactants.