# Influence of Contamination of Gear Oils in Relation to Time of Operation on Their Lubricity
## 3 Results and Discussion
The results indicate that the used oil 75W-140, which performed greater operational work than oils 80W-140 and 75W-90, had worse lubrication properties and was closer to reaching the limit state. It is worth adding that in [32], the limit state of the object is defined as a technical condition in which further operation of the object is not recommended. It should be kept in mind that the quality of a product is determined by its degree of compliance with requirements [30], and the technically justified service life of oil should ensure the maximum use of the potential of oil quality [33]; if this is true, then used oil 75W-140 should not be considered to be suitable for use. Such a performance of this oil is also confirmed by the linear wear results that are presented in Figure 7 (the curve marked in blue). The highest difference in average values of the friction coefficient for the fresh and used oil was found for the oil with the lowest nominal viscosity of 75W-90. The difference was ~37%. The same relationship was also shown in the linear wear measurements. In addition, the average friction coefficient for fresh oil 75W-90 was the highest among all of the tested oils. The linear wear fresh oil 75W-90 was also the highest of all of the fresh oils. It is possible that the condition of the used oil 75W-90 also depended on the type of a gearbox that the oil was worked in. The two other oils worked in axles. Bevel gearboxes are used in the rear axles, and this type of gearbox is characterized as having a much greater degree of slipping compared to hypoid gear boxes, which means that the working conditions of the oil in the axles are more demanding [19]. A different extortion spectrum may be reflected in the dimension of the qualitative changes that were observed in the oils used in axles. The analysis also concerned the impact of the degree of contamination on lubricating properties. An analysis of the relationship between the number of particles and the diameter was conducted. The purpose of this analysis was to identify and compare the trends that were obtained for the fresh and used oils. For each of the oil states (clean and used), the relationship between \(log_{10}n\) (logarithm of the decimal number of particles depending on the diameter of \(x\)) was identified. For this purpose, a linear model with a particular transformation of the dependent variable was considered as follows:  
\[\left(log_{10}n\right)^{b}=\alpha_{0}+\alpha_{1}x+\varepsilon, \tag{2}\]  
where \(\varepsilon\) is a random variable with a normal distribution of N(0, \(\sigma^{2}\)). In the paper, b = 0.2 was assumed (for this parameter, the highest determination indicators of \(R^{2}\) were obtained for both the clean and used oils). From (2), we can see that the dependence between the number of particles and the diameters of these particles is nonlinear. Linear regression plots (2) are presented in Figures 8-10. The parameters of the linear regression model are presented in Tables 3-5. The results of the particle content tests indicated that the number of particles with the largest diameters is clearly higher in the used oils. This means that these oils contain more contaminants. To estimate the unknown parameters in model (2), the least squares method was applied. The linear models of the dependences between the diameters of the particles in the oil samples and the number of these particles are well matched to the empirical data. The values of the coefficients of determination are close to or above 0.9. The best fit of the linear regression model was demonstrated for fresh oil 75W-90. The same oil also had the highest average friction coefficient in the lubricity tests. Figure 10: Regression model of particle content as a function of particle diameter of fresh and used (210,000 km) gear oil SAE 75W-90. Figure 9: Regression model of particle content as a function of particle diameter of fresh and used (220,000 km) gear oil SAE 80W-140.