Heating Effects in the Drawing of Wire and Strip Under Hydrodynamic Lubrication Conditions

The use of high metal processing speeds to meet the demands for increased productivity has focused attention on the pronounced heating of tooling and workpiece which occurs under these conditions. In the present study, heating under hydrodynamic conditions in wire and strip drawing is addressed by considering a two-dimensional representation of the tool-lubricant-workpiece interface. An analytical formulation is presented for prediction of the resultant temperatures. The model considers deformation heating in the strip, lubricant viscosity to be a function of temperature and pressure, and matches the heat flux at the strip-lubricant boundary. Convection of heat in the lubricant film is considered. The model is constructed in terms of the governing non-dimensional parameters and solved by a Crank-Nicolson finite difference technique. By comparison with solutions which do not consider convection, it is found that convection only begins to play a role in the resulting temperatures when the Graetz number U₀h₀²/α_Ll is greater than 0.4. For the high speed drawing of aluminum with mineral oil used as a lubricant, the model predicts a monotonic increase in mean lubricant temperatures from 366 K to 404 K over a range of initial strip velocities of 20.3 m/s to 50.8 m/s. The maximum strip surface temperature is predicted to monotonically decrease from 345 K to 335 K over this range of strip velocities. The ratio (k_Lρ_Lc_pL/k_sρ_sc_pS)^1/2 is shown to be important in determining the relative temperatures of lubricant and strip. Results are compared to those metalworking analyses which do not consider the role of the lubricant film.