# Influence of Contamination of Gear Oils in Relation to Time of Operation on Their Lubricity
## 3 Results and Discussion  
The test results were statistically processed. Table 1 presents descriptive statistics of the test results for the friction coefficient and contains the minimum (min), maximum (max), and average (mean) values and the standard deviation (std. dev.). Figure 3: Parker Laser CM20 automatic particle number meter (**a**) device and (**b**) sample printout of measurements. Figure 2: Diagram of the measuring system, 1—measuring chamber, 2—laser light source, 3—optical scanner, 4—switching valve (hydraulic), 5—dosing pump, 6—flow sensor. The statistical values of the friction coefficient of the fresh oils and the oils with a service history differ. In the case of the used oils, the work of which was expressed as the mileage of a vehicle between 220,000 km and 210,000 km, the friction coefficient demonstrated lower average values than the friction coefficient that was observed for the fresh oils. Oil changes were planned for after these mileages were achieved. T Figures 4-6 present graphs of the friction coefficient based on different paths. The graph presenting linear wear is shown in Figure 7. The graph shows the variability of linear wear depending on the number of friction cycles. It should be noted that the presented curves depend on the sliding wear of the friction pair, but this is not the only thing that should be taken into account. The thermal expansion of the ball and disc that are heated by the conditioned oil was also influenced. Both factors of the experiment have a synergistic influence on the shape of the curves. The variability tests of the friction coefficient can function as a measure for the lubricity of gear and diesel oils [23; 24]. The nonlinear dependence between the friction coefficient and distance (friction path) is defined as follows:  
\[y=\alpha_{0}+\alpha_{1}x^{\alpha_{2}}e^{-\alpha_{3}x}+\varepsilon, \tag{1}\]  
where \(y\) denotes the friction coefficient, \(x\)--distance, and \(\varepsilon\)--disturbances with a normal distribution N(0, \(\sigma\)2) and is connected with measurement. The shapes of the curves for the friction coefficients indicate a gradual friction process. All of the tested oils are characterized by friction coefficient having an increasing curve when friction begins, and then a slight decrease at the first stage of friction. At the next stage, a steady-state friction regime with slight deviations was observed. However, for some oils, the course of the friction coefficient decreased slightly--75W-90 (fresh oil), 75W-140 (after 210,000 km)--at the second stage of friction. The most stable friction curve, which demonstrated the smallest amount of fluctuation, was characterized by oil 80W-140 (after 220,000 km). In this case, the variation seen in the friction function was similar than that of the theoretical  
Figure 5: The curve of the friction coefficient depending on the friction path for oil SAE 80W-140 and fitting Function (1). Figure 6: The curve of the friction coefficient depending on the friction path for oil SAE 75W-90 and fitting Function (1). model, which, as we will see later, was explained by the dependence between the number of particles and the diameters of those particles. For each oil, the parameters \(\alpha_{0},\ldots,\alpha_{3}\) were estimated by applying the least squares method. Parameter \(\alpha_{2}\) corresponds to the shape of the curve, but value \(\alpha_{3}\) corresponds to the scale of descent. The values of these parameters are presented in Table 2. The fitting of model (1) to the data is marked with a black curve in Figures 4-6.