Analytical model of metalworking fluid penetration into the flank contact zone in orthogonal cutting

Metalworking fluids (MWFs) are used widely in machining process to dissipate heat, lubricate moving surfaces, and clear chips. They have also been linked to a number of environmental and worker health problems. To reduce these impacts, minimum quantity lubrication (MQL) sprays of MWF delivered in air or CO₂ have been proposed. MQL sprays can achieve performance comparable with conventional water-based or straight oil MWFs while only delivering a small fraction of the fluid. This performance advantage could be explained by the enhanced penetration into the cutting zone that results from delivering MWF in high pressure and precise sprays. To explore this hypothesis, an analytical model of MWF penetration into the flank face of the cutting zone is developed and validated using experimental data. The model is based on a derivation of the Navier–Stokes equation and the Reynolds equation for lubrication and applied to an orthogonal cutting geometry under steady-state conditions. A solution to the model is obtained using a numerical strategy of discretizing the analytical scheme with two-dimensional centered finite difference method. Penetration into the cutting zone is estimated for MQL sprays delivered in air, CO₂ and N₂ as well as two conventional MWFs, straight oil and semi-synthetic emulsion. The model suggests that conventional MWFs, do not penetrate the cutting zone fully and fail to provide direct cooling to the flank zone where wear is most likely to occur. MQL sprays do penetrate the cutting zone completely. Using convective heat transfer coefficients from a previous study, a finite element heat balance is carried out on the tool to understand how each fluid impacts temperature near the flank tip of the tool. The results of the modeling effort are consistent with experimental measurements of tool temperature during turning of titanium (6AL4V) using a K313 carbide tool. The prediction of temperature near the flank indicates that MQL sprays do suppress temperatures near the flank effectively. These results help explain the low levels of tool wear observed for some MQL sprays, particularly those based on high pressure CO₂. This modeling framework provides valuable insight into how lubricant delivery characteristics such as speed, viscosity, and cutting zone geometry can impact lubricant penetration.