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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.

Thermohydrodynamic lubrication is complicated by the multiplicity of heat transfer paths from the site of dissipation to the surroundings. This has impeded a general understanding of thermohydrodynamic phenomena. The method of lumped variables is applied to a simple slider bearing (as an example) to explore thermohydrodynamic lubrication. This approach leads to a better understanding of the interplay between the different modes of heat transfer and the influence of the associated temperature rises on performance, and how this can be captured by the use of appropriate non-dimensional measures. Such measures also allow the mapping of the problem into a set of regimes characterized by the relative importance of different heat transfer modes.

An alternative average Reynolds equation for use under conditions of large fractional contact area is proposed. The flow factors for this form of the equation are calculated for a variety of longitudinal surfaces and the results are shown to be relatively insensitive to the initial height distribution. Pressure and shear flow factors for the Christensen height distribution and a variety of Peklenik surface pattern parameters are also derived from the work of Patir and Cheng, Lo and Tripp. These are represented by semi-empirical equations over the full range of contact conditions. The implications of the results, with respect to the lubrication of metal forming processes, is discussed.

The tribological aspects of cold metal forming processes is reviewed. Special attention is paid to rolling and stamping operations as these are typical of bulk forming and sheet forming processes, respectively, and are the most important commercial processes. It is shown that a better understanding of tribological fundamentals, as applied to cold metal forming, can result in better lubrication systems and process models.

Emulsions and slurries are commonly encountered in tribology problems. The dispersed phase in the mixture plays an important role in lubrication or wear, but the mechanisms of particle capture by two surfaces have never been well understood. While no similar models have been proposed for slurries, emulsions researchers have attributed lubrication mechanisms to a `plate out' theory through which oil separates from the emulsion and coats the exposed metal surfaces. Observations of particle behavior by Nakahara et al. ( ASME J. Tribol., 110 (1988) 344–353) cast doubt on this theory; particles very close to the tooling were rejected and played no part in the lubrication process. Further, the behavior of a particle depended greatly on its size. This paper offers a potential explanation for this behavior through a computational fluid dynamics model of a rigid particle in an inlet zone. A particle in such a flow field is found to cross streamlines to an equilibrium position a certain distance from the tooling or workpiece. This segregation location is related to the particle size with the same trends of particle penetration as observed by Nakahara et al. The theory applies to emulsion lubrication, slurry lubrication and wear involving solid particles suspended in a liquid.

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 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 Sheu’s 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.

A realistic model for friction in lubricated sheet-metal forming which takes account of the different lubrication regimes which may occur at the sheet/tooling interface is developed. Friction is expressed in terms of internal interface variables (mean lubricant film thickness, sheet roughness and tooling roughness) in addition to the more traditional external variables (interface pressure, sliding speed and strain rate). The new model has been coupled to an existing finite element membrane analysis of axisymmetric stretch forming. Numerical results using the coupled codes showed excellent agreement with measured strain distributions over a range of operating conditions. Computational times with the refined friction model were typically increased by about 10 percent compared to those with a simple Amontons-Coulomb constant friction coefficient model.

The dynamic concentration model for lubrication by oil-in-water emulsions proposed by Wilson el al. (1) is applied to strip rolling to derive a relatively simple equation for inlet film thickness. The predictions of the new model are supported by rolling experiments using emulsions as lubricants, where the film thickness is inferred from the surface roughness that is generated on the workpiece during rolling. The experiments also seem to suggest that the efficiency of oil droplet capture increases with increasing rolling speed. Presented at the 49th Annual Meeting in Pittsburgh, Pennsylvania May 1–5, 1994

A mathematical model for liquid lubricated strip rolling in the full-film regime is developed. The model combines slab plasticity, hydrodynamic lubrication and thermal analyses to relate local and global condition to process variables and material properties. The predictions of the model are compared with experimental measurements of outlet speed ratio, roll separating force and roll torque in rolling 1100-H14 aluminum with a viscous mineral oil and 5P4E polyphenyl ether as lubricants. The excellent agreement which is obtained provides powerful support of the validity of the model.

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 Dow's experimental measurements for an EHL contact. Presented at the 48th Annual Meeting in Calgary, Alberta, Canada May 17–20, 1993

Two mathematical models for axisymmetric stretch forming with a spherical punch are developed. The models combine a finite element representation of the sheet deformation with a hydrodynamic lubrication model. In one model the influence of sheet bending stiffness is taken into account while in the other only the membrane stiffness is considered. Comparison of the predictions of the models with the film thickness measurements of Hector and Wilson indicates that the inclusion of elastic effects is important in predicting lubricant film thickness. The results of the bending model are in particularly good agreement with the experimental data. A useful analytical method for predicting the film thickness at the center of the conjunction at the onset of yield is also developed.

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 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.

The Reynolds equations for viscoplastic lubricants can be quite complex, involving multiple branches which depend on the form of the boundary conditions invoked in their development. Methods of visualizing and understanding the branching problem are explored. This information is used, together with the Reynolds equations developed in the companion paper, in analyses of the lubrication of a wide slider bearing and a metalforming inlet zone. The results of these analyses are used to draw general conclusions regarding the influence of different types of non-Newtonian behavior.

Basic flow relationships are developed for three typical non-Newtonian lubricant models: the pseudo-plastic model, the circular viscoplastic model, and the ideal viscoplastic model. It is found that the conventional no-slip boundary conditions are inadequate to fully treat the latter two models. Conclusions regarding the appropriate boundary conditions for any viscoplastic model and the form of the resulting Reynolds equations are presented.

An improved theoretical model for the hydrodynamic lubrication of axisymmetric, sheet metal stretch forming is presented. The infinite initial film thickness problem, encountered in a previous model, is removed by accounting for the squeeze action occurring during the initial stages of the process. Both isoviscous and thermoviscous theories are developed assuming that the lubricant is a Newtonian fluid. In the thermoviscous model, the lubricant viscosity is assumed to vary exponentially with temperature. The influence of plastic heating of the sheet on the entrainment and transport of the lubricant film is examined. The effects of variable punch speed are also investigated.

In order to test the validity of the theoretical model discussed in Part 1, an experimental technique, employing optical interferometry, has been developed to measure lubricant film thickness during axisymmetric stretch forming. Specially fabricated, transparent punches are used for both double and multiple beam interference studies. The choice of workpiece material, lubricant, and forming speed ensures that the punch/sheet conjunction will be hydrodynamically lubricated during most of the process. Interference patterns, due to the variable film of lubricant separating the punch and sheet surfaces, are formed as the sheet wraps around the punch. These patterns provide a contour map of the lubricant film thickness along the punch/sheet conjunction. The measured film thickness, as taken from an interpretation of the patterns, is compared with the theoretical predictions of Part 1.

Wilson and Shen’s semi-empirical equation for the effective hardness of a plastically deforming workpiece is used to develop models for tool-workpiece friction in metal-forming processes operating in the boundary lubrication regime. The models treat both steady and unsteady conditions and include the influence of tooling and workpiece topography, sliding speed, interface pressure, and workpiece strain rate on friction. Simplified models are suggested for conditions typical of bulk forming and sheet-metal forming processes.

Commercial finite element software, while quite powerful in their treatment of plasticity and constitutive modeling of materials, use quite simple friction and heat transfer models, usually being restricted to constant coefficients. Actual forging operations are known to be much more complex, with evolving friction and heat transfer. The present research presents a model that allows the lubricant film thickness and workpiece surface roughness to evolve with respect to time and location. The model obtains lubricant film thickness from the Reynolds equation, and estimation of a fractional contact area through a contact model approach appropriate for metal forming problems. Heat transfer and friction are then calculated by partitioning between asperity contact and lubricated areas.

Transient effects in the friction and lubrication of metal forming processes are reviewed. These occur in processes that are intrinsically unsteady, during the start-up of nominally steady processes or when self-induced vibration is present. They can have important implications on process economics and product quality. Some suggestions for future research are presented.

Considerations of friction, wear and surface modification are important in many metal forming operations. A better understanding of the fundamentals of lubrication in metal forming can lead to more effective lubrication systems and to better process models. Research on lubrication in different regimes and on the modeling of lubrication and friction is reviewed. Special emphasis is placed on the influence of the plastic deformation of surfaces on lubrication, and on special lubricants, such as emulsions, which are used in metal forming.

Theoretical models for the hydrodynamic lubrication of plane strain and axisymmetric sheet metal stretch forming processes with cylindrical and spherical headed punches, respectively, are developed. The lubricant is treated as an isoviscous Newtonian liquid for both geometries. In addition, the influence of sheet heating due to plastic deformation with an exponential variation of viscosity with temperature is analyzed for the plane strain case.

An upper-bound method is used to model the entrainment of a solid lubricant in a drawing process. The lubricant is treated as a rigid-plastic solid. A semi-empirical equation for the thickness of the lubricant film that will be entrained under ideal fractional conditions is given.

An isothermal model for the transport of lubricant in an upsetting operation with a rough workpiece is developed. It is shown that the workpiece roughness tends to increase the rate of outward lubricant transport. Experiments with rough aluminum workpieces lubricated with a silicone oil show a reduction in lubrication breakdown due to the improved lubricant transport. Transportation rates predicted by the model with a semi-empirical thermal correction show good agreement with experimentally determined transport rates.

The type of lubrication regime which occurs in a metal forming operation has a strong influence on the frictional conditions as well as on other important factors such as product surf ace finish and tooling wear rate. The characteristics of the different types of regimes which can occur are reviewed, together with what is known about their incidence in drawing, extrusion, rolling, and upsetting operations. In the light of this information it is evident that the commonly used methods of characterizing friction can often lead to erroneous results. Suggestions for improved methods of characterizing friction are made.

An analytical model for the hydrodynamic lubrication of high speed strip rolling is developed. The model includes the effect of thermal loading due to back flow and slip on the film formation process. The work zone analysis takes account of thermal effects on film thickness and friction. The influence of geometry, speed and lubricant and work-piece properties on the forward slip, roll load and torque are described in detail and compared with previously published experimental data.

Aluminum alloy workpieces of different roughness, lubricated with graphite, P.T.F.E., lead or polyethylene, were upset between overhanging dies. Measurements of the width of the unlubricated zone formed at the workpiece edge indicated that the rates of outward transport of the lubricants were increased by roughening the workpiece. This was in agreement with a simple analytical model of the lubrication process.

Theoretical analyses for the lubrication of rigid wedge-shaped asperities by a viscoplastic fluid are developed for geometries in which either wedge or squeeze action are dominant. The load support in the wedge action geometry is severly limited by lubricant shear, although the squeeze geometry maintains high load support at small film thicknesses. Results suggest that in cases where macroscopic hydrodynamic lubrication is inadequate, lubricant film breakdown will be promoted by low lubricant shear strength, high sliding speed, low surface roughness, and high surface slope. In addition, results are compared with previous investigations of the factors influencing susceptibility to lubrication failure.

Transient isoviscous hydrodynamic theory is used to investigate the lubrication of plane strain forging processes with flat dies. It is shown that during yielding a film which decreases from a maximum thickness at the center of the contact to zero at the edges is formed. As the deformation continues, the film is transported outwards at half the surface speed of the workpiece. In the case where the dies extend beyond the workpiece, an unlubricated region is formed. The variation in width of this region with reduction predicted by the model is in good agreement with experimental measurements.

Theoretical models for a slider bearing which is lubricated by one of its surfaces melting are developed. Melting is assumed to be caused by frictional heating. Two cases are considered. In the first the slider melts. In the second the track on which the slider rubs melts. The analyses allow prediction of the film thicknesses and friction under conditions in which this mode of lubrication occurs. The results support the idea that the low friction found in contacts with ice near its melting point is due to lubrication by melting.

An analytical model for the hydrodynamic lubrication of hydrostatic extrusion is developed. This includes the effect of viscous heating on the film formation process and the effect of viscous and plastic heating on the friction and film thickness variation in the work zone. Theoretical predictions of film thickness and extrusion pressure show good agreement with experimental measurements for aluminum billets lubricated with castor oil.

The load support generated by sliding asperities, with a lubricant which is newtonian up to some critical shear stress and thereafter behaves plastically, is calculated. Wedge-shaped and cylindrical asperities with their crests normal to the sliding direction are considered. It is found that low load support and potential failure occur with the combination of high roughness and small asperity spacing or with low roughness. This is in agreement with the experimental results of Hirst and Hollander.

A hydrodynamic lubrication theory is developed for a generalized hydrostatic extrusion and drawing process with augmentation and back pressure. The die is assumed to be conical and uniform deformation and isothermal lubrication conditions are assumed to exist. The theory is in good agreement with experimental data previously published by other workers.

A thermal hydrodynamic model of the lubricant transport process in plane strain upsetting between overhanging dies is developed. It is shown that at the start of the process the lubricant is transported at half the workpiece surface speed. As the process proceeds the workpiece heats up and the rate of lubricant transport is reduced. Since the lubricant cannot keep up with the outward motion of the workpiece an unlubricated zone is formed near the workpiece edges. The width of this zone predicted by the model is in good agreement with experimental measurements made on aluminum workpieces lubricated with silicone oils.

Experimental evidence indicates that billet die friction is higher in conventional extrusion than in hydrostatic extrusion. Simple hydrodynamic lubrication theory is used to show that this may be accounted for by the less favorable conditions for hydrodynamic lubrication in the conventional process.

The type of lubrication regime which occurs in a metal forming operation has a strong influence on the frictional conditions as well as on other important factors such as product surface finish and tooling wear rates. The various types of regimes which can occur are reviewed, together with what is known about their incidence in sheet metal forming operations. In the light of this information it can be seen that the commonly used methods of characterizing friction in analytical models of metal forming processes will often lead to erroneous results. Suggestions for improved methods of characterizing friction are made.

As in most metalforaing processes, considerations of friction and lubrication are of vital importance in hydrostatic extrusion. An efficient lubrication system will reduce the pressure required for a given reduction ratio by lowering friction at the billet-die interface. This will reduce the container strength or number of steps required for a particular product with attendant reductions in cost.