Hydrodynamic Lubrication in Wire Drawing

Abstract

Part I. It was shown by Christopherson and Naylor that hydrodynamic lubrication in wire drawing could be provided by supplying lubricant at the entry of the die at a pressure comparable with the yield stress of the wire. The necessary pressure could be conveniently generated by causing the wire to approach the die through a tube of a diameter slightly larger than the wire diameter, sealed on to the inlet side of the die. They carried out experiments with oil as the lubricant, on wires of copper and mild steel, and developed a theory which accounted for their experimental results but suffered from the defect that all their equations contained two dependent variables, P the pressure developed and q the quantity of lubricant flowing.

In the present paper a theory is developed by considering all regions up to that in which the wire deforms, and equations are obtained by means of which P and q are expressed in terms of independent variables. The calculated values of pressure for Christopherson and Naylor's conditions show good agreement with their experimental results but the theoretical values of lubricant flow are too high by a factor of two to three. The probable reason for this discrepancy is that the breakdown of the oil under shear has been ignored.

Part II. In Part I of this paper a theory is developed for hydrodynamic lubrication in wire drawing with oil as the lubricant, and the calculated values of P the lubricant pressure and q the lubricant flow are compared with values taken from previously published experimental work. Part II is concerned with the case when the lubricant is a soap.

Experiments were carried out, in which P and q were measured as a function of wire speed u for a series of accurately made tubes (or nozzles) of a range of dimensions, and for about a dozen soaps of widely varying rheological properties. It is shown that there is a maximum value of both P and q and that this result can be explained in terms of the theory with the additional condition that the apparent viscosity of the soap is an exponential function of wire speed of the type μ = μ₀ exp (–Bu).

The wire speed at which the maxima occur is the same for P and q and appears to be independent of nozzle dimensions but dependent on soap properties. It is equal to I/B.

For a given soap with different nozzles the value of the maximum pressure P_max is proportional to l/h² where l is the length of the parallel portion of the nozzle and h is the clearance over the wire diameter, provided the thickness of the lubricant film is small compared with 1/2h. For a given soap with different nozzles P_max is proportional to μ₀/B.