*3.1. FEPG and Test Results*

The finite element study [35–37] was carried out under the loads of 100, 200, 300, 400, 500, and 600 N, respectively, and the rotating speed of the ring was 2000 r/min. The maximum surface temperature and radial diffusion size of the ring under different loads were obtained (Figure 5).

**Figure 5.** Maximum value and radial diffusion size of ring surface temperature.

The maximum temperature and radial diffusion size in Figure 5 are analyzed. When the cylinder loads are 100, 200, 300, 400, 500, and 600 N, the maximum corresponding temperature is 396.8 ◦C and the radial diffusion size is 20.3 mm. With the increase of the load on the cylinder, the maximum temperature and the radial diffusion size of the ring surface are increasing.

When the cylinder loads are 100, 200, 300, 400, 500, and 600 N, the temperature change rule of the cylinder-ring contact surface is studied (Figure 6).

**Figure 6.** Temperature of cylinder-ring contact surface.

The temperature of the contact surface in Figure 6 is analyzed. At the same time, the temperature of the contact surface of the cylinder increases with the increase of the load on the cylinder. However, the change trend of contact surface temperature under different loads is basically the same. After the time reaches about 60 s, the temperature does not rise significantly. When the cylinder loads are 100, 200, 300, 400, 500, and 600 N, the contact surface temperature is stable at 222, 251, 326, 341, 360, and 378 ◦C, respectively.

Through the test, the mean value of the temperature at the acquisition point under the sample loads of 100, 200, 300, 400, 500, and 600 N is obtained. The test result data are processed by high-order function regression through SPSS software (12.0, SPSS Inc., Chicago, IL, USA), and the regression function of temperature relative to time and load is as follows:

$$L = 600.421 - 3.252X\_1 - 8.002X\_2 + 1.763X\_1X\_2 - 0.287X\_1^2 - 0.891X\_2^2 \tag{1}$$

The temperature of the contact surface under different time and load is shown in Figure 7.

**Figure 7.** Temperature obtained at different times.

From Figure 7, when the load of the sample increases from 100 to 600 N, the temperature corresponding to the fixed time increases. When the loads of the sample are 100, 200, 300, 400, 500, and 600 N, the temperature of test and FEPG changes with time (Figure 8).

**Figure 8.** Comparison between test and FEPG.

From Figure 8, when the sample loads are 100, 200, 300, 400, 500, and 600 N, the temperature obtained by FEPG at the same time point is slightly higher than the test result. The reason for the result is that there are many environmental effects, such as heat and air transfer loss, in the actual test. However, when the loads of FEPG are 100, 200, 300, 400, 500, and 600 N, the trend of temperature change is the same, and when the load is 400 N and the time is 80 s, the temperature error is the largest, and the relative error is only 4.3%.
