# Demand Analysis of Lubricating Oil in Spur Gear Pairs
## 1 Introduction  
Compared with belts, chains and other transmission devices, gear drives are the most widely used in a variety of engines, such as those in automobiles, ships and spacecraft, due to their high efficiency, compact structure and smooth operation [1]. As a major problem in gear drives, lubrication exerts a significant influence on gear drive performance [2]. Good lubrication can improve the life of gears, reduce noise, and increase meshing efficiency [3]. A review of the published literature shows that the field of gear lubrication has two major research focuses. The first focuses on the state of the lubricating oil film on the meshing tooth surfaces, including the model analysis of EHL, in order to establish the nonlinear relationships among oil film thickness, pressure and density [4]; numerical methods for solving the EHL [5]; and measurement of and experimentation on the contact area [6]. The second group focuses on the use of commercial computational fluid dynamics (CFD) software to simulate the flow state of lubricating oil during the gear meshing process and visualise the flow field of lubricating oil [7]. Gears operate under heavy loads and high pair meshing, and contact pressure on tooth surfaces is extremely high. The characteristics of lubricating oil change, and meshing tooth surfaces deform, when under high pressure. The gears are in a state of EHL [4]. The state of the lubricating oil film between the contacting tooth surfaces in EHL is described using the Reynolds equation. This equationreasonably explains the formation mechanism of oil film; this mechanism is the theoretical basis of EHL [8]. The pressure-viscosity effect of lubricating oil and the elastic deformation of contact surfaces are considered in EHL. Thus, the EHL problem is described using a series of nonlinear coupled equations that are extremely difficult to solve. The earliest method used to solve EHL was a direct iteration method that produced considerable errors in the actual results. The inverse, multigrid [9] and finite element [10] methods were subsequently introduced, and their results can accurately describe the shape of the lubricating oil film and the pressure distribution in linear contact EHL. Recent studies have used the Reynolds equation to solve the general lubrication problem in non-Newtonian fluids by regarding lubricating oil flow as the superposition of Poiseuille and Couette flows. The velocity of lubricating oil flow in this equation was solved using the characteristics of Poiseuille and Couette flows, and the other characteristics of lubricating oil film were solved on the basis of Newtonian fluids [11]. The traditional Integral Approach, the Single Domain Full-System Approach and the Double Domain Full-System Approach have been used to solve the EHL problem [12]. The comparisons of velocity and oil film thickness between this method and the conventional approach established the feasibility and validity of the method and illustrated its simplicity of calculation. The influence of the surface roughness of gear teeth on the lubricating oil film was significant [13]. Thus, the modified Reynolds equation in Patir and Cheng [14] and the surface deformation and statistical elasto-plastic asperity micro-contact model in [PERSON] et al. [15] were solved using a systematic approach under steady-state and isothermal operating conditions. The central oil film thickness formula, minimum oil film thickness and asperity-to-total load ratio were obtained via the regression of simulation data [13]. To examine the influence of roughness on EHL, the rough surface was regarded as a rough plane surface with uniformly distributed cylindrical asperities that were evenly truncated on top, and the inlet of the contact area was analysed. Several valuable conclusions, including the reduction of load capacity in the oil film and the increase in friction coefficient due to roughness, particularly at low speeds and under heavy loads, were drawn [16].