# Demand Analysis of Lubricating Oil in Spur Gear Pairs
## 3 Lubricating Oil Demand during Meshing Process  
The curvature radius and load of a tooth surface are continuously changing during the gear meshing process. Thus, the change in lubricating oil demand during the meshing process should be analysed. The parameters of gears, lubricating oil and working conditions are provided in Table 1.  
The solution for lubricating oil demand can be attributed to solving complicated nonlinear equations. A compound iterative method is used to obtain the demand of lubricating oil. The central film thickness and entrainment velocity of each meshing tooth are compared during the meshing process, as shown in Figure 2. The two vertical coordinates shown in Figure 2 represent the central film thickness (\(\mu\)m) and entrainment velocity (m/s), respectively. The abscissa denotes the coordinates on the meshing line. Figure 3 shows the oil volume for the lubrication of each meshing tooth during the meshing process and the total oil volume for the lubrication of a gear. Meshing teeth 1 and 2 mesh simultaneously in the first two tooth meshing area. The entrainment velocity of meshing teeth 1 and 2 in the first two tooth meshing area increases continuously with gear meshing. An oil film easily forms at high entrainment velocities. Thus, the oil film thickness of the two meshing teeth in the meshing area of the first two teeth increases with gear meshing. A positive correlation exists between oil film thickness and oil volume for lubrication. The oil volume for the lubrication of meshing teeth increases along the meshing line, reaching the maximum value at the end of the meshing area of the first two teeth. The total oil volume for the lubrication of a gear is the sum of the oil volume for the lubrication of meshing teeth 1 and 2. As the gear rotates, meshing tooth 2 moves gradually away from the meshing. Thus, the gear is in the single tooth meshing area. The sudden increase in load of meshing tooth 1 reduces the oil film thickness. Therefore, the oil volume for the lubrication of meshing tooth 1 plummets at the intersection of the meshing areas of the first two teeth and the single tooth. The total oil volume for the lubrication of the gear is the same as the oil volume for the lubrication of meshing tooth 1. Oil film thickness and oil volume for the lubrication of meshing tooth 1 increase linearly in the single tooth meshing area. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Modulus, \(m\) & 5 mm \\ Number of teeth, \(z_{1}/z_{2}\) & 23/68 \\ Pressure angle on pitch circle, \(\alpha\) & 20\({}^{\circ}\) \\ Tooth width, \(b\) & 30 mm \\ Poisson’s ratio of gear material, \(\mu_{1}\mu_{2}\) & 0.3 \\ Elastic modulus of gear material, \(E_{1}E_{2}\) & 206 Gpa \\ Density of lubricating oil, \(\rho_{0}\) & 890 kg/m\({}^{3}\) \\ Viscosity of lubricating oil, \(\eta_{0}\) & 0.01 m-s \\ Viscosity-pressure index of lubricating oil, \(a\) & \(2.2\times 10^{-8}\) m\({}^{2}\)/N \\ Specific heat capacity of lubricating oil, \(c\) & 2000 J\(\cdot\)kg\({}^{-1}\cdot^{\circ}\)C \\ Maximum temperature rises of lubricating oil, \(\Delta T\) & 20 \({}^{\circ}\)C \\ Input speed, \(n_{1}\) & 8000 rpm \\ Input torque, \(T_{1}\) & 80 N\(\cdot\)m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for simulation. Figure 2: Central film thickness and entrainment velocity during the meshing process. Meshing tooth 3 begins to mesh at the end of the single tooth meshing area, and the gear is located in the second two tooth meshing area. Entrainment velocity, oil film thickness and oil volume for the lubrication of meshing tooth 1 are larger than those for meshing tooth 3, and they increase continuously with gear meshing. The oil volume for the lubrication of two meshing teeth reaches the maximum value at the end of the second two tooth meshing area. The total oil volume for the lubrication of the gear is the sum of the oil volume for the lubrication of meshing tooth 1 and 3.