## 3 Results and Discussion
### Oil-Film Temperature
#### 3.2.2 Prediction of Operating Temperature  
In order to study the influence of load cases on oil-film temperature and further analyze the operating performances of both oils with the same viscosity, the temperatures of S220 and M220 are compared under the same load and at different speeds, as shown in Figure 7, and the temperatures of S220 and M220 at the same speed and under different loads are shown in Figure 8.  
Figure 7 shows the comparison of temperature under the same load and at different speeds. The operating temperature increases with time, but the gradients of temperature rise at 200 rpm-6 MPa is larger than that at 100 rpm-6 MPa. The equilibrium temperature of both oils at 100 rpm-6 MPa and at 200 rpm-6 MPa are respectively about 50 \({}^{\circ}\)C and 60 \({}^{\circ}\)C which indicates that the increase of rotational speed leads to the increase of the gradient of temperature rise. This is because the increase of rotational speed results in the generation of more friction heat. Figure 8 shows the comparison of temperature at the same speed and under different loads. The operating temperature increases with time, but the gradients of temperature rise at 150 rpm-12 MPa is larger than that at 150 rpm-6 MPa. The ultimate temperature of both oils at 150 rpm-6 MPa and 150 rpm-12 MPa is respectively about 55 \({}^{\circ}\)C and 60 \({}^{\circ}\)C, which indicates that the increase of load leads to the increase of the gradient of temperature increase. This is because the increase of load also results in the generation of more friction heat. Figure 8: Comparison of temperature at the same rotational speed and different loads. (**a**) S220; (**b**) M220. Figure 7: Comparison of temperature under the same load and at different speeds. (**a**) S220; (**b**) M220. In order to predict oil-film temperature at a given time, the temperature of both oils was compared and analyzed. A large amount of test data indicates that the relationship between temperature and time conforms to Formula (1) as below through the data fitting method [25; 26]. \[T=A_{2}+\frac{(A_{1}-A_{2})}{1+(\frac{t}{t_{a}})^{p}} \tag{1}\]  
where \(T\) is Oil-film temperature, \({}^{\circ}\)C; \(t\) is operating time, min; \(A_{1}\), \(A_{2}\), \(t_{a}\), and \(p\) are constants of which the value can be fitted based on the test data, \({}^{\circ}\)C, \({}^{\circ}\)C, min, 1. Oil-film temperature under some load cases and at given times can be predicted through Formula (1). Similarly, if the permitted temperature is given, the operation time of the system can be predicted. For instance, the temperature of S220 and M220 at 100 rpm-6 MPa is fitted respectively as shown in Formulas (2) and (3), in which each related parameter is shown in Table 6. If the operation time \(t\) tends to be infinite, the extreme temperature \(T\) of oil-film will be \(A_{2}\). The extreme temperature of S220 and M220 is 52.64 \({}^{\circ}\)C and 51.29 \({}^{\circ}\)C respectively through Formulas (2) and (3). From the calculated results, it can be concluded that there exists a difference in operating temperature of both oils, but the difference is not very large. For S220:  
\[T_{\text{S220}}=52.64-\frac{20.8}{1+(\frac{t}{78.46})^{1.08}} \tag{2}\]  
For M220:  
\[T_{\text{M220}}=51.29-\frac{21.47}{1+(\frac{t}{9\text{T}.93})^{1.12}} \tag{3}\]  
Figure 9 shows the relative error [27] of temperature of both oils between test data and fitted data, and the calculation equation is as Formula (4). As shown in Figure 9, the relative error is less than 0.5% at almost all times except at a few moments such as at the beginning of operation. Therefore, it is relatively accurate to describe the operating performance of oil with Formula (1). \[\delta=\frac{|T_{\text{test}}-T_{\text{fitted}}|}{T_{\text{test}}}\times 100\% \tag{4}\]