# Thermal-Hydraulic Modeling of Oil-Inmersed Motor Pump
## 1 Introduction  
The oil-immersed motor pump is a novel electro-hydraulic integrated power unit comprising an axial piston pump and a motor, exhibiting remarkable advantages of high efficiency, compact size, high energy utilization rate, high power density, and extended lifespan. It constitutes the essential component of the rudder control system for future large airliners and advanced warplanes, and represents a critical technology for the realization of intelligent actuation of high-end equipment [1; 2; 3]. However, due to its high-speed operation, it generates considerable heat within a limited time [3]. A considerable percentage of aviation safety accidents, approximately 40%, are caused by hydraulic system malfunction. Abnormal temperature elevation in the aircraft's hydraulic system contributes to 15% to 20% of these incidents [4]. Therefore, it is crucial to establish a thermodynamic model of the oil-immersed motor pump to accurately analyze its temperature distribution, enhanceits heat transfer and dissipation capacity, and effectively lower the system temperature. The establishment of a thermodynamic model is deemed crucial for the accurate analysis of the temperature distribution, enhancement of the heat transfer and dissipation capacity, and effective reduction of the system temperature in the oil-immersed motor pump. The 3D model diagram of the motor pump is presented in Figure 1, where the motor and pump are interconnected via a rotating axis. The cylinder block is driven by the motor to rotate, thereby enabling the piston cavity to perform the oil-draining and oil-absorbing action. The pump comprises several components, including the cylinder block, valve plate, piston, and slipper [5]. The motor is primarily composed of the stator, rotor, permanent magnet, and winding. The practical application of high-speed motor pumps has long been impeded by their thermal management. The heat generation in the piston pump is specifically attributed to the frictional forces between its sliding surfaces and the mixing losses arising from the interaction of the cylinder and piston assembly, which are the underlying causes of heat generation. Additionally, core loss is induced by the high-speed motor's alternating magnetic field during operation, and a significant amount of heat is generated by energizing the stator winding [6; 7; 8; 9]. Failure to effectively manage the aforementioned heat sources can result in the hydraulic system's abnormal temperature rise; ultimately a failure of the hydraulic system is caused. The heat generated by oil-immersed motor pumps is primarily derived from fluid energy loss and electromagnetic heat generation resulting from the winding current. Researchers from various countries have investigated the thermodynamics of oil-immersed motor pumps. [PERSON] et al. [10] examined high-speed pumps, analyzing their power loss mechanisms, and establishing churning loss and thermodynamic models that account for churning loss. [PERSON] et al. [11] employed the control volume method to establish a thermodynamic simulation model of an axial piston pump, predicting the temperature rise in each node and optimizing the piston design. [PERSON] [12] proposed models of hysteresis and eddy current losses based on the mechanism of core loss generation, while [PERSON] [13; 14] built on this work by introducing additional loss. [PERSON] et al. [15] constructed a mathematical model of the fluid and temperature field coupling solution for high-speed hydraulic pump motors using the finite volume method, deriving the temperature field distribution of motor pumps. [PERSON] et al. [16] analyzed the losses of motor pumps and introduced them into the flow field as heat sources, accurately predicting the motor temperature. [PERSON] et al. [17] directly fed electromagnetic losses into a collective parametric thermal model to obtain temperature distribution. [PERSON] et al.