William R. D. Wilson

Real area of contact and boundary friction in metal forming

Abstract Upper-bound models for asperity flattening on a workpiece surface undergoing bulk plastic deformation are developed. It is found that the effective hardness of the surface can be greatly reduced by the presence of underlying plastic flow. Theoretical predictions of the variation of real area of contact with strain show excellent agreement with experiments using model asperities in rolling. Friction models which allow for the reduction in effective hardness are developed for cases in which roughness is concentrated on either the workpiece or tooling.

Surface asperity deformation during sheet forming

Abstract A model for the flattening of asperities on the surface of a sheet undergoing plastic deformation is proposed. A viscoplastic finite element analysis was used to determine the effect of strain rate and straining direction on the rate of flattening of two dimensional asperities resulting from a normal pressure applied with a smooth tool. The strain rate components in the plane of the sheet are treated as independent of the normal pressure. The results can be used to model the evolution of the contact area fraction at the interface as a function of the straining direction in the sheet and the normal pressure.

Mixed Lubrication of Strip Rolling

An analytical model for strip rolling operating in the mixed regime is developed. The model combines analysis for the influence of bulk plastic deformation on the effective hardness of the strip asperities with an approach to allow for the influence of roughness on lubricant flow. An approximate correction for thermal effects is also included. The predictions of the model are compared with experimental measurements of film thickness and slip. Presented as a Society of Tribologists and Lubrication Engineers paper at the STLE/ASME Tribology Conference in New Orleans, Louisiana, October 24–27, 1993

A dynamic concentration model for lubrication with oil-in-water emulsions

Abstract A variety of models for lubrication by emulsions are compared with film thickness measurements made by Dow for elastohydrodynamic lubrication contacts lubricated by oil-in-water emulsions. The results of conventional elastohydrodynamic analysis with effective viscosity models tend to under-estimate the lubricant film thickness. A simplified dynamic concentration model shows much better agreement with the experiments.

Influence of surface topography on the frictional characteristics of 3104 aluminum alloy sheet

A sheet-metal forming simulator which stretches a strip around a cylindrical pin was used to investigate the relationship between friction and process variables including sliding speed, strip strain, and strain rate in the boundary lubrication regime. Measurements were conducted with 3104 aluminum alloy sheet of three different surface conditions on D2 tool steel and cemented carbide tooling. Friction was found to increase with the strain occurring during contact. This supports a friction model which treats the influence of plastic strain on the flattening of strip asperities and real area of contact. The friction measured with stretching and sliding transverse to the rolling direction was 30% to 40% smaller than that measured along the rolling direction. No significant difference in friction coefficient between sand-blasted workpieces stretched and slid along the rolling direction and transverse to the rolling direction was observed and the friction coefficients were found to be close to those obtained with the original workpiece surface transverse to the rolling direction.

A Mixed Flow Model for Lubrication with Emulsions

An oil-in-water emulsion in the inlet zone of a concentrated contact is modeled by treating the oil particles as flattened cylinders surrounded by water. In an independent flow model, the oil and water flows are coupled only through the pressure gradient. However, the model leads to anomalous behavior with regard to the flow of water. To overcome this problem, corrections to the pressure gradients due to interactions between the oil and water were derived. Both models showed that the emulsion became concentrated because the higher viscosity oil was preferentially drawn into the conjunction. The net effect was similar to an inlet starved of oil. The inlet film thickness predicted by the interactive theory was in good agreement with Dows experimental measurements for an EHL contact. Presented at the 48th Annual Meeting in Calgary, Alberta, Canada May 17–20, 1993

A Theoretical Model of Micro-Pool Lubrication in Metal Forming

A model of a secondary hydrodynamic lubrication mechanism, which is called micro-pool or micro-plasto hydrodynamic lubrication, has been developed. It shows that, with sufficiently high viscosity and sliding speed, the lubricant trapped in the micro-pools between the tool and workpiece can be drawn into the interface. The friction force is either increased or decreased, depending on the viscosity and sliding speed. Without bulk stretching, the product of the lubricant viscosity and sliding velocity can be used as an index to indicate whether or not micro-pool lubrication will occur. Stretching the workpiece may make a strong influence not only on the thickness of the permeating film but also on the asperity contact area.

Low speed mixed lubrication of bulk metal forming processes

A simple analysis for the lubrication of saw-tooth surfaces with longitudinal lay under conditions of high fractional contact area is developed. This is then coupled with Wilson and Sheus asperity flattening model to treat the mixed lubrication of a bulk metal forming process (rolling). It is shown that, even under low speed conditions where the inlet zone does not generate significant hydrodynamic pressures, relatively high hydrodynamic pressures can be generated in the work zone. This explains the persistence of hydrodynamic effects noted in low speed experiments.

Lubrication of strip rolling in the low-speed mixed regime

An analytical model for strip rolling in the low-speed mixed lubrication regime is developed. An average Reynolds equation for longitudinal saw-tooth surfaces under conditions of high fractional contact area, is combined with an analysis for asperity flattening under conditions of bulk plastic flow, to treat lubrication in the mixed regime. Analyses for the inlet zone and work zone and the influence of pressure on viscosity are included in the model. The model indicates that hydrodynamic lubrication effects are important at much lower speeds than previously considered possible. The film thickness predicted by the model is somewhat smaller than that measured using the oil drop method in rolling aluminum alloy with a mineral oil. Presented at the 50th Annual Meeting in Chicago, Illinois May 14–19, 1995

A Mixed Lubrication Model for Cold Strip Rolling—-Part I: Theoretical

An analytical model for strip rolling in the mixed lubrication regime is developed. The average Reynolds equation for Christensen surfaces with the arbitrary Peklenik surface pattern parameter is combined with an analysis for asperity flattening under conditions of bulk plastic flow to treat lubrication in the mixed regime. An inlet zone analysis and the influence of pressure on viscosity are included and, by using special numerical techniques, the model can be used over a wide speed range. Presented as a Society of Tribologists and Lubrication Engineers paper at the World Tribology Congress in London, United Kingdom, September 8–12, 1997