# Demand Analysis of Lubricating Oil in Spur Gear Pairs
## 3 Lubricating Oil Demand during Meshing Process
The meshing process involves the continuous and repeated movement of a meshing point on a meshing line. In a meshing circle, two equal maxima for the oil volume for lubrication exist at the ends of the first two tooth meshing and the second two tooth meshing areas. The analysis of the second section shows that the relative slide velocity and friction coefficient play key roles in the calculation of the oil volume for cooling. Therefore, the relative slide velocity and friction coefficient are compared during the meshing process, as shown in Figure 4. The two vertical coordinates that represent the relative slide velocity and friction coefficient are established in this figure. The abscissa denotes the coordinates along the meshing line. The area selected by the wireframe is magnified 10 times for clear visualization. Figure 5 illustrates the oil volume for the cooling of each teeth and the total oil volume for the cooling of a gear. The image is partially enlarged. Figure 4 shows that the friction coefficient at the pitch point is equal to zero and that of the tooth surface increases as the distance between the meshing and pitch points increases, because the friction force between meshing tooth surfaces is the same as the shear force of the oil film in the EHL of a smooth surface. The friction coefficient increases as the relative slide velocity increases and oil film thickness decreases. The friction coefficient in the beginning of the meshing process is greater than that at the end of meshing process because the oil film thickness and relative slide speed at the end of the meshing process help reduce friction. The friction coefficient of meshing tooth 1 is at its maximum value at the beginning of the first two tooth meshing area, resulting in the maximum value of oil volume for cooling, as shown in Figure 5. This finding is attributed to the relative slide velocity being at its maximum value and the oil film thickness being at its minimum value. In the first two tooth meshing area, the total oil volume for the cooling of the gear is the sum of the oil volume for cooling of meshing tooth 1 and 2. The relative slide velocity, oil film thickness and oil volume for the cooling of meshing tooth 1 decrease with gear rotation, and those of meshing tooth 2 increase with gear rotation, albeit with a small increment, and the total oil for cooling continuously decreases. Figure 3: Oil volume for lubrication during the meshing process. Figure 4: Relative slide velocity and friction coefficient during the meshing process. Figure 5: Oil volume for cooling during the meshing process. When the gear is in the single tooth meshing area, meshing tooth 1 meshes separately. The friction coefficient and oil volume for the cooling of meshing tooth 1 increase suddenly at the beginning of the single tooth meshing area due to the decrease in oil film thickness. The oil volume for the cooling of the gear is equal to that of meshing tooth 1, but less than that of two tooth meshing area. Meshing tooth 3 starts to mesh at beginning of the second two tooth meshing area. The maximum friction coefficient and oil volume for the cooling of meshing tooth 3 occur at this point. The total oil volume for the cooling of the gear is the sum of the oil volume for the cooling of meshing teeth 1 and 3. As the gear meshes, the relative slide velocity, oil film thickness and oil volume for the cooling of meshing tooth 3 decrease, but those of meshing tooth 1 increase. The total oil for the cooling of the gear still decreases because of the small increment of oil for the cooling of meshing tooth 1. Oil volume for the cooling of the gear has two maxima, which are located at the beginning of the first two tooth meshing and the second two tooth meshing areas.