## 4 Hydraulic-Thermal Coupling Modeling and Analysis for HCS
### Analysis of Oil Temperature Changes under Different Parameters  
The temperature variations of HPP and HOT are calculated for different ORFRs, main circuit flow rates, working loads, and cooling powers, with the corresponding results presented in Figures 5-8. It can be seen from Figure 5 that the effect of ORF on the steady-state temperature of HPP is more significant, while the effect on the steady-state temperature of HOT is smaller. When the ORF increased from 8 L/min to 16 L/min, the steady-state temperature of HPP decreased from 90.38 \({}^{\circ}\)C to 75.11 \({}^{\circ}\)C, while the steady-state temperature of HOT increased from 48.54 \({}^{\circ}\)C to 50.58 \({}^{\circ}\)C. Under the dynamic regulation of the flush valve, ORFR can be considered equivalent to the cooling flow rate. An increase in ORFR corresponds to an increase in the cooling flow rate in the main circuit. More temperature-higher hydraulic oil enters the oil tank. An increase in ORFR indicates a greater involvement of flow rate in the cooling system, leading to a corresponding decrease in the steady-state temperature of the HPP. The steady-state temperatures of the HPP and the HOT are significantly influenced by the main circuit flow rate and the working load. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Hydraulic** & **Parameter Name** & **Value** \\
**Component/System** & displacement & 56 mL/rev \\  & mechanical efficiency & 0.95 \\ hydraulic closed pump & volume efficiency & 0.85 \\  & rotary speed & 1500 rev/min \\ \hline  & displacement & 107 mL/rev \\ hydraulic motor & mechanical efficiency & 0.95 \\  & volume efficiency & 0.85 \\  & load torque & 300 N-m \\ \hline oil refilling system & displacement of refilling pump & 10 mL/rev \\  & pressure of oil refilling system & 1.60 MPa \\ \hline cooling system & power & 5.5 kW \\ \hline environmental temperature & temperature & 20 \({}^{\circ}\)C \\ \hline oil tank & coefficient of heat dissipation & 16 W/(m\({}^{2.}\)\({}^{\circ}\)C) \\  & area of heat dissipation & 1.0 m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The key parameter configurations in the coupling model. Figure 4: Temperature variations of the HPP and HOT. An increase in the main circuit flow rate from 48 L/min to 64 L/min results in a rise in the steady-state temperature of the HPP from 75.37 \({}^{\circ}\)C to 93.29 \({}^{\circ}\)C, while that of the HOT increases from 44.77 \({}^{\circ}\)C to 53.76 \({}^{\circ}\)C. When the working pressure remains constant, an increase in the main circuit flow rate means that the total power of the HCS has increased. If the cooling capacity does not change, the oil temperature will rise. Similarly, when the main circuit flow rate remains constant, an increase in working pressure means that the total power of HCS has increased. If the cooling capacity does not change, the oil temperature will rise. An increase in the working load from 160 N-m to 320 N-m leads to a rise in the steady-state temperature of the HPP from 61.86 \({}^{\circ}\)C to 91.74 \({}^{\circ}\)C, with the HOT's temperature increasing from 39.07 \({}^{\circ}\)C to 52.65 \({}^{\circ}\)C. In reality, the augmentation in primary circuit flow and workload corresponds to an escalation in the system's output power. Given constant cooling power, both the hydraulic oil's steady-state temperature in the HPP and HOT rises. It is evident that the temperature of the hydraulic oil declines as the cooling power increases. The impact of cooling power on the steady-state temperature of hydraulic oil in both systems is substantial. When increasing the cooling power from 4800 W to 6000 W, the steady-state temperature of hydraulic oil in the HPP increases by 9.65 \({}^{\circ}\)C, while that of the HOT increases by 11.2 \({}^{\circ}\)C. This underscores the significance of cooling system power as a pivotal factor influencing hydraulic oil. Figure 5: Temperature variations under different ORFR. Figure 6: Temperature variations under different flow rates of the main circuit.