# Numerical and Experimental Analysis of the Oil Flow in a Planetary Gearbox
## 1 Introduction
#### Literature Review  
The first studies on the no-load power losses arising from the interaction of the moving components with the lubricant in planetary gears date back to [PERSON] et al. [3]. They performed theoretical and experimental studies aimed at studying a two-stage planetary gearbox partially immersed in oil. Further analyses by [PERSON] [4] concentrated on the operating temperature and the heat balance in dip-lubricated planetary gearboxes. The geometrical parameters of the gearbox such as center distance, planet carrier geometry, and the number of planets, as well as the physical properties of the system such as lubricant parameters and immersion depth, were considered to derive analytical equations for the determination of no-load power losses. Subsequent analyses by [PERSON] [5] dealt with the impact of different types of lubricant, namely mineral and synthetic oil, on the no-load power losses for dip lubrication. Studies with injection lubrication were conducted by [PERSON] et al. [6] and [PERSON] [1], who built the FZG internal gear test rig to investigate the flank load carrying capacity of internal gears, and the influence of circumferential speeds, material combinations, surface finishing, and lubricants. Suggestions for lubrication conditions, surface finishing, and drive direction were provided. [PERSON] et al. [7] performed an experimental campaign on a planetary gearbox aimed at studying the impact of injection volume rate, lubricant temperature, and rotational speed on efficiency. Recent experiments by [PERSON] et al. [8; 9] focused on the detailed analysis of the oil distribution in a dip-lubricated planetary gearbox and its efficiency. They used a front housing made from acryl glass that allowed observation of the oil level and its flow during operation. Various observations were made by considering different rotational speeds, lubricant temperatures, and filling levels. As the planet carrier starts to rotate, the oil tends to distribute around the circumference of the covering box creating a dynamic peripheral oil ring. The authors considered the thickness of the oil ring for the estimation of the churning power losses. This phenomenon has not been observed for other gearbox designs, meaning that it is a peculiar characteristic of planetary gearboxes. Due to the difficult visibility of internal gearbox components, it is not trivial to have a deep understanding of the lubrication mechanisms, especially for systems characterized by a compact design as planetary gearboxes. However, recent developments in computer science made it possible to use numerical approaches to study the specific problem of interest. In the case of gearbox lubrication, Computational Fluid Dynamics (CFD) can offer substantial benefits in the prediction of the oil flow inside the gearbox. Indeed, in the post-processing phase, it is possible to analyze the oil distribution inside the considered gearbox and to derive information on the lubrication behavior of the system. However, due to the complex kinematics of planetary gearboxes and the high computational resources needed, the numerical studies available in the literature are limited. Moreover, sometimes significant modeling simplifications have been adopted, making it difficult to assess the models' reliability concerning the oil flow predictions. A recent exhaustive literature review on CFD methods applied to the study of gearbox lubrication and efficiency can be found in [PERSON] et al. [10]. In the following, the sole CFD studies relative to epicyclic gearboxes are reported. [PERSON] et al. [11; 12] exploited the Multiple Reference Frame (MRF) approach to model a planetary gearbox for aeronautic applications. They increased the gear interspacing, i.e., the meshing region between the sun and the planets, and between the planets and the ring gear, was not modelled. In this way, the squeezing effects could not be simulated and the related axial phenomena occurring in the mating zone were neglected. Moreover, only single-phase simulations were performed.