# Demand Analysis of Lubricating Oil in Spur Gear Pairs
## 1 Introduction
The load transmitted by a gear tooth during the meshing process may fluctuate significantly due to time-varying meshing stiffness and torque fluctuation. The influence of dynamic load on the minimum oil film thickness, pressure distribution and temperature distribution were analysed on the basis of the quasi-static tooth force solved via finite element contact analysis [17]. The results showed that a dynamic load will reduce the thickness of the oil film, increase its pressure and temperature and destroy the EHL of the contact surface. A tribo-dynamic model for spur gear pairs combining dynamic loading with EHL theory was proposed in 2016 [18], this model can predict the contact force and velocity of dynamic teeth. A method that combined the Runge Kutta and multigrid methods was used to solve the aforementioned tribo-dynamic model, and the results were compared with those of the model under quasi-static conditions. Starved lubrication conditions will occur when an incomplete oil film is formed between contact surfaces. To investigate the influences of starved lubrication on minimum film thickness, maximum temperature and friction coefficient, a thermally starved EHL model was proposed [19]. This previous research found that the minimum oil film thickness was thinner, and the friction coefficient and maximum temperature were higher, in starved lubrication than those in EHL. CFD is a new branch of fluid mechanics that has been widely used in gear lubrication. [PERSON] et al. [20] built a CFD model based on the finite volume method to investigate the lubricating oil distribution and the churning power losses of a gearbox. The results were obtained by considering the 3D finite volume simulation model as a two-phase flow, and the results were compared with the measurements of churning losses and high-speed camera recordings. The comparisons exhibited good agreement in predicting lubricating oil distribution and churning power losses. [PERSON] et al. [21] presented a CFD model combined with turbulence to investigate the lubricating oil distribution and churning power losses of a moving gearbox. The influences of gear rotation, immersion depth, gearbox motion frequency and amplitude on the results were determined. On the basis of the preceding statement, current studies have explored effective methods for establishing a lubrication analysis model that can realistically and accurately describe the contact state among tooth, the characteristics of oil film and the distribution of lubricating oil. However, these studies on gear lubrication are based on the condition that the lubricating oil supply and the lubrication state of the gear are known. A method that can analyse the lubricating oil demand of gears under specific operating conditions could help significantly in the design of gear lubrication systems. In the current work, new calculation and analysis models of the lubricating oil demand of spur gears are proposed by considering lubricating oil demand as the superposition of oil for lubrication and cooling. This study aims to understand variations in oil for lubrication and cooling during a mesh cycle under different parameters and working conditions. The calculation models of lubricating oil demand are established in accordance with the meshing of spur gears and EHL theories. The influences of modulus, number of teeth, input speed and input torque on oil for lubrication and cooling are simulated. This study provides guidance for the appropriate design of gear lubrication systems.