# Analysis of Grinding Flow Field under Minimum Quantity Lubrication Condition
## 3 Simulation and Analysis of Three-Dimensional Grinding Wheel Flow Field
### Characterization of Velocity Distribution of Flow Field  
The velocity vector distribution of the flow field can be obtained by fluent simulation, as shown in Figure 3. To facilitate the analysis, three faces of z = 1 mm, z = 4 mm and z = 7 mm are taken, as shown in Figure 4. The velocity vector local enlargement of the wedge introduction area of the three faces is extracted, as shown in Figure 5.  
As can be seen from Figure 5, no significant return flow is found in different cross sections of the wedge introduction zone in the three-dimensional flow field simulation. In the radial direction, the closer to the grinding wheel, the greater the airflow velocity, which is conducive to the grinding fluid entering the grinding zone. When placing the nozzle, it should be placed as close to the grinding wheel as possible. To study the distribution state of the flow field in the wedge region, the x-directional velocity distribution curves were extracted under different conditions, as shown in Figure 6.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Settings** \\ \hline Solvers & 3D Segregated pressure-based \\ Turbulence model & Renormalization Group k-epsilon Model \\ Wall & No slip, standard wall function \\ Moving Wall & \(v_{s}\) = 20, 30, 40 m/s \\ Operating pressure & Atmospheric pressure \\ Pressure outlet boundaries & P = 0 Pa \\ Minimum clearance & \(h\) = 0.05, 0.1, 1 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameter settings.  
Figure 3: Schematic diagram of velocity vector distribution of flow field.  
Figure 2: Schematic diagram of the mesh.  
Figure 4: Interface schematic diagram.  
Figure 5: Partial enlargement of velocity vector distribution in wedge area (**a**) z = 1 mm; (**b**) z = 4 mm; (**c**) z = 7 mm.  
From Figure 6, in the grinding area, the x-directional velocity gradually increases when approaching the minimum gap from both sides. x-directional velocity reaches the maximum value at the minimum gap. This is because the width between the grinding wheel and the workpiece is small. The air driven by the grinding wheel flows to the minimum gap and then flows out from both sides of the grinding wheel. To study the airflow in the wedge introduction zone, the horizontal surface velocity vector distribution was extracted, as displayed in Figure 7.  
As can be seen in Figure 7, there is a clear lateral overflow in the wedge introduction zone, which is marked with in red ellipse and arrows. Due to the presence of the lateral overflow, air flows out from the lateral direction when it flows to the minimum gap. It avoids the formation of a reverse return flow in the wedge introduction zone, which prevents the grinding fluid from going into the grinding zone. However, when the lateral overflow flow rate is too high, the micro-lubrication jet droplets cannot overcome the effect of the lateral overflow. Driven by the lateral overflow, it will flow out of the grinding area from the lateral direction, which is not conducive to the lubrication and cooling of the grinding area by the grinding fluid. This reduces the cooling and lubricating effect of micro-lubrication and greatly lowers the utilization rate of grinding fluid. To investigate the factors affecting the intensity of the lateral overflow, the velocity distribution clouds were extracted in Figures 8 and 9.  
Figure 6: x-directional velocity distribution curve under different linear velocity.  
Figure 7: Velocity vector distribution diagram.  
be seen from the red streamlines. The enhancement of the lateral overflow increases the difficulty of droplets to overcome the air barrier layer. It makes the droplets flow out of the grinding area under the effect of the lateral overflow, which reduces the utilization rate of the grinding fluid and the cooling lubrication effect.