## 2 Modeling
### Fluid-Structure-Thermal Interaction  
Due to the eccentricity of the piston, the high peak will appear in the pressure field, as shown in Figure 5. The pressure field Figure 5a is calculated by the fluid model, and the pressure field Figure 5b is calculated by the fluid-structure-thermal interaction model. The maximum pressure is significantly reduced. It indicates that the influence of elastic deformation and temperature on the pressure field of the film is very significant. The high pressure exerted on the piston and the cylinder will lead to elastic deformation \(\Delta h_{p}\), as shown in Figure 5c,d. The elastic deformation cannot be neglected. In the meantime, the change of temperature can also lead to elastic deformation, which is called thermoelastic deformation \(\Delta h_{T}\). In addition, the temperature has a significant influence on the fluid viscosity.  
Figure 4: Film grid.  
The pressure can lead to the elastic deformation of the structure. On the other hand, the elastic deformation of the structure changes the film height and the pressure distribution until the pressure distribution and the elastic deformation do not change. The elastic deformation due to the pressure field is instantaneous, but it is an iterative process to obtain this equilibrium state. When the pressure distribution changes, the elastic deformation changes immediately. However, the change of temperature due to the heat transfer takes time. Therefore, before achieving a thermal equilibrium state, the temperature of the structure is constantly changing. If we couple the process that the structure temperature changes from the initial temperature to steady-state temperature into the dynamic model, the calculation is quite time-consuming. Thus, assume that the temperature distribution  
Figure 5: Pressure field, elastic deformation, and temperature field: (**a**) Predicted by the fluid model; (**b**) predicted by the fluid–structure–thermal interaction model; (**c**) the elastic deformation of the piston’s surface; (**d**) the elastic deformation of the bushing’s surface; (**e**) the temperature distribution of the film; and (**f**) the dynamic viscosity distribution of the film.  
of the piston and the cylinder has been in a steady-state. This paper uses the Roelands equation to determine the viscosity [5]:  
\[\mu=\mu_{0}\exp\left\{(\ln\mu_{0}+9.67)\left[-1+\left(\left(1+5.1\times 10^{-9}p \right)^{Z}\left(\frac{T-138}{T0-138}\right)^{-W}\right)\right]\right\} \tag{17}\]  
The viscosity-pressure relationship and the viscosity-temperature relationship of the fluid are shown in Figure 6. It indicates that the viscosity of the fluid is more sensitive to the temperature than pressure. As shown in Figure 6c, at T = 293.15 K, the viscosity of the fluid is 0.070 Pa-s; at T = 323.15 K, the viscosity of the fluid is 0.019 Pa-s. The viscosity dropped by 73%. On the contrary, as the pressure increases, the viscosity of the fluid increases, as shown in Figure 6b. The proper viscosity can improve the lubrication performance and reduce the leakage [9].  
In this paper, MATLAB is used to solve the pressure field and temperature field, and COMSOL is used to calculate the elastic deformation. As shown in Figure 7, the thermoelastic deformation will be calculated before the fluid-structure interaction simulation.  
Figure 6: (a)Viscosity–pressure and viscosity–temperature relationship; (b) viscosity–pressure relationship at T = 313.15 K; (c) and viscosity–temperature relationship at \(p\) = 0.1 MPa.  
Figure 7: Fluid–structure–thermal interaction.