# Influence of Contamination of Gear Oils in Relation to Time of Operation on Their Lubricity
## 3 Results and Discussion
Additionally, the basic indices of fitting function (1) were determined using the sum of squares (\(SSE\))  
\[SSE=\sum_{i=1}^{n}\left(y_{i}-\hat{\alpha_{0}}-\hat{\alpha_{1}}x_{i}^{\hat{ \alpha_{2}}}e^{-\hat{\alpha_{3}}x_{i}}\right)^{2},\]  
where \(\hat{\alpha_{0}},\ldots,\hat{\alpha_{3}}\) denote the estimator of unknown parameters, and the sum of squares total (\(SST\)) is a sum of the squared differences between the observed dependent variable and its mean  
\[SST=\sum_{i=1}^{n}\left(y_{i}-\overline{y}\right)^{2}.\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & **75W90** & **75W90** & **80W140** & **80W140** & **75W140** & **75W140** \\ \hline Category & Used oil & Fresh oil & Used oil & Fresh oil & Used oil & Fresh oil \\ \(\alpha_{0}\) & 0.04784 & 0.09997 & 0.00000 & 0.00025 & 0.01341 & 0.08129 \\ \(\alpha_{1}\) & 0.00276 & 0.02276 & 0.00798 & 0.05168 & 0.07399 & 0.03602 \\ \(\alpha_{2}\) & 0.76353 & 0.00000 & 0.42336 & 0.07891 & 0.05117 & 0.03766 \\ \(\alpha_{3}\) & 0.01342 & 0.00801 & 0.00141 & 0.00055 & 0.00034 & 0.00386 \\ SSE & 0.31497 & 0.32592 & 0.06434 & 0.13916 & 0.21841 & 0.33773 \\ SST & 2.07269 & 1.22027 & 1.38345 & 0.38203 & 0.35047 & 2.93344 \\ \(R_{pseudo}^{2}\) & 0.84804 & 0.73291 & 0.95349 & 0.63573 & 0.37680 & 0.88487 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter values of Function (1) for different types of oils and values for fitting this function to real measures. Figure 7: Linear wear of friction pairs in oil bath. _SST_ represents the deviance of the intercept-only model, but \(SSE\) represents the deviance of the fitted nonlinear model. According to [25], we can calculate the pseudo \(R^{2}\), which presents the goodness of fit model to the data as follows:  
\[R^{2}_{pseudo}=1-\frac{SSE}{SST}.\]  
The figures that are presented below present the fitting of Function (1) to the measured data for the different oils. In the literature, the stage at which the curve of the friction coefficient is constant is called stationary or normal [26]. The stability of the friction process is important when assessing oils. However, the lubricity of the oils that were tested is of practical significance. The SAE (Society of Automotive Engineers) defines lubricity as a measure of the difference in friction when comparing the properties of different oils with the same viscosities under the same conditions [27]. In the results from the tests that were conducted in the current research, the nominal viscosities of the fresh oil and used oils were the same, as the assumed mileages (km) were not exceeded. Three different oils were tested in these tests. When comparing the gear oils with different SAE viscosity classes, the following definition of lubricity proposed in [28] may be relevant: lubricity is the liquid's ability to cause low static resistance when moving solid surfaces and high resistance when bringing them together under a normal load. According to [29], lubricity is the ability of a substance to provide better lubricating properties in conditions where the lubricant film is so thin that its action is not only determined by viscosity. This is probably related to the occurrence of mixed friction in many steel friction nodes. The approach presented in these works is utilitarian, and the value of the friction coefficient is of practical importance when assessing oils. According to the criterion for assessing the condition of oil, i.e., lubricity, the condition of these oils can be considered suitable for use with high probability. A similar relationship was demonstrated for engine oils composed of mineral oils that were used in heavy trucks [30; 31]. After 350,000 km, the used oil demonstrated a friction coefficient that was slightly higher than that of the average value of the friction coefficient that was obtained for fresh oil, and the standard deviation of the used oil's friction coefficient was clearly lower.