Effect of roughness in cold metal rolling

Transcription

1 International Conference on Tribology in Manufacturing Processes ICTMP 27 International Conference September 27, Yokohama Effect of roughness in cold metal rolling Michael PF Sutcliffe * Cambridge University Engineering Department, Trumpington Street, Cambridge, CB2 1PZ, UK Summary: This paper describes work at Cambridge exploring effects of roughness on cold metal rolling. Earlier work describing the asperity mechanics governing surface conformation in rolling is reviewed. The importance of bulk strain in the surface interaction is emphasised. The role of different wavelengths of roughness on the crushing process and consequent true contact area between the surfaces is explored. The importance of the relatively short wavelengths, which tend to persist, is identified. A model of roughness have been implemented in a cold rolling lubrication model, in which the hydrodynamics in the roll bite is coupled with the asperity mechanics. A multi-scale model of roughness is used to describe the effect of different length scales on friction in rolling. As well as a primary roughness, the effect of secondary roughness on the roll surface (e.g. due to grinding defects, wear or pick-up on the roll) is modelled. This model can predict friction in both strip drawing and industrial rolling experiments. Key words: Lubrication, cold rolling, roughness, asperity, boundary lubrication 1. INTRODUCTION Rolling is a very effective way of generating a very smooth finish so that the surface quality of the rolled produced is often very important. Hence understanding the way in which the roughness is generated is a key aspect of rolling technology. Moreover, in most cold rolling operations lubricant is used to reduce frictional forces, to protect the roll and strip surfaces, and to act as a coolant. In these circumstances the amount of oil drawn into the roll bite and the initial surface roughness are the critical factors determining friction in the contact and surface finish of the product [1]. In the presence of roughness, the ratio Λ s = h s /σ of the smooth film thickness h s to the combined roll and strip roughness σ (σ 2 = σ r 2 + σ s 2 ) is used to characterise the lubrication regime. In order to achieve an acceptable surface finish it is necessary to avoid a complete separation of the surfaces by oil, so that cold rolling tends to operate in the mixed lubrication regime, with Λ s of the order one. In this regime there is some oil lubricating action to reduce friction, but some asperity contact. In order to understand the mixed lubrication regime we need first to understand how roughness conformity can occur in the absence of lubrication. This is discussed in section 2. The inclusion of such a roughness flattening model into a lubrication model for rolling is given in section 3. These models are relevant to rolling of aluminium, where the roll roughness gives a typical longitudinal lay to the roughness of the roll and strip. Section 4 describes an alternative scenario, where roughness is in the form of pits. This is particularly relevant to rolling of stainless steel. Section 5 discusses work on the effect of roughness on boundary lubrication. 2. ROUGHNESS CONFORMITY This section describes how roughness asperities on roll and workpiece conform during rolling. The section first considers unlubricated rolling, then moves on to study the roughness flattening in the presence of lubricant Unlubricated rolling The key to modelling of roughness conformity in deformation processes lies in understanding the role of bulk plasticity. The effect of bulk plasticity was highlighted by the results of Greenwood and Rowe [2], who showed that the presence of sub-surface deformation allows the asperities to be crushed considerably more than in the absence of bulk deformation. The deformation throughout the substrate means that it is at the point of yield and acts as a soft 'swamp' with relatively easy indentation of the asperity tops. Sheu and Wilson [3], Wilson and Sheu [4] and Sutcliffe [5] show how the evolution of the workpiece roughness topography depends on the bulk strain of the material. Depending on the orientation of the roughness relative to the bulk strain direction, either upper-bound or slip line field solutions are used to derive the velocity field at the surface and the corresponding relationship between contact pressure and asperity flattening rate. Sutcliffe [5] describes a series of experiments in which he deformed copper blocks containing machined triangular asperities using flat rigid platens. A comparison of experimental measurements with theoretical predictions of the evolution with bulk strain of the contact area is shown in Figure 1. Good agreement is seen for high normal pressures. Note that the area of contact ratio rapidly rises above the value of about 1/3 associated with zero bulk strain. The excellent conformance achievable between the surfaces explains the remarkable efficiency of rolling as a process to produce good surface finish by imprinting a bright roll finish. The less good agreement at lower normal pressures (corresponding to applied end tension) may be

2 Figure 2.Effect of roughness wavelength on flattening rate [6]. Figure 1. Effect of bulk strain on area of contact ratio [5]. related to work hardening or to changes in the geometry of the asperities during deformation. The above study relates to asperity geometries consisting of a series of identical triangular asperities. Real rough surfaces contain a random profile with a range of roughness wavelengths. To investigate this effect Sutcliffe [6] treated a two-wavelength longitudinal surface profile, applying the asperity flattening model to each wavelength in turn. The long wavelength components are predicted to be eliminated more quickly that the short wavelength, high slope components. Figure 2 shows the excellent agreement obtained between predictions and measurements of the change with bulk strain of the amplitude of the two components of roughness. Measurements were taken from as-received aluminium strips which were cold rolled to various reductions. One important conclusion from this work was that the short wavelength components (typically with wavelengths less than 3 µm) can be expected to have a significant impact on friction, while the longer wavelength components, although making a greater contribution to the initial amplitude of roughness, are nevertheless crushed rather quickly so are less important. It is also important to note that, for these typical roughness slopes, the asperities have almost entirely conformed to the roll roughness after a bulk strain of only 1% Lubricated rolling Neglecting for the moment the surface roughness on the roll and strip, a 'smooth' film thickness h s at the end of the inlet to the bite can be determined by integrating Reynold's equation. Wilson and Walowit [7] derive an expression for h s as h s = θ 6η αu ( 1 exp( αy )) (1) where u is the average entraining velocity, θ is the inlet angle between the strip and roll, Y is the plain strain yield strength of the strip and η is the viscosity of the lubricant at ambient pressure. The pressure viscosity coefficient α in the Barus equation η = η exp(αp) is used to describe the variation of viscosity η with pressure p. As mentioned in the introduction, the ratio Λ s = h s /σ of the smooth film thickness h s to the combined roll and strip roughness can be used to characterize the degree of asperity contact in the roll bite. For large Λ s the surfaces are kept apart by a continuous film of oil which tends to lead to surface roughening. First asperity contact occurs with Λ s below about 3, so that to give substantial asperity contact and a good imprint of the smooth rolls onto the strip, Λ s needs to be below about 1. The ratio of the areas of close contact to the nominal contact area is termed the contact area ratio A. The effect of asperity conformance on lubrication is illustrated by the results of Figure 3, showing the change in roughness during cold rolling of aluminium strip with a reduction of 25%, as a function of speed parameter Λ s [8]. As with dry rolling, there is substantial flattening of the asperities for Λ s < 1. The changes in lubrication parameter Λ s were achieved by varying the rolling speed and by using three mineral oils spanning a wide range of viscosities. The roughness is split into short and long wavelength components σ and Σ respectively, and the measured amplitudes of these components are normalised by the initial values. For Λ s > 1, there is a significant oil film between the surfaces and the strip surfaces roughens during rolling. As with unlubricated rolling, inclusion of a short wavelength component reduces significantly the predicted true contact area between the roll and strip. This confirms the supposition that short wavelengths must be included to develop an accurate friction model for cold rolling. Figure 3 also compares measurements with a theoretical predictions using a lubrication model including a two-wavelength model of roughness [9].

3 The effect of roughness conformance in practical rolling is illustrated by Figure 4, showing the change in the roughness of aluminium foil rolled in an industrial plant. In this case the roughness amplitudes of different frequencies are represented by the power spectral density of the roughness. The initial strip has a peak in spectral density at a frequency of around 1 mm 1, corresponding to a wavelength of 1 µm. In the first pass this low frequency component is significantly reduced, while some higher frequency components are generated, at a frequency corresponding to a peak in the roll roughness spectrum [1]. Figure 4. Change in roughness spectrum during industrial cold rolling of aluminium [1]. Figure 3. Change in short and long wavelength strip roughness amplitudes σ and Σ during lubricated rolling of aluminium with a reduction of 25% [8,9]. 3. LUBRICATION MODELS This section considers with 'mixed lubrication', where the amount of oil drawn into the contact is determined by oil entrainment at the inlet to the bite. A number of groups have developed lubrication models of rolling. These are reviewed in more detail in [11]. The key to these models is to couple an asperity flattening model, taking into account the effect of bulk deformation, with a lubrication model. Section 4 deals with an alternative mechanism, where oil is trapped in pits at the inlet, and then drawn out from the pits due to sliding action in the bite. Two approaches have been widely used to include roughness in the Reynolds' equation for oil pressure build-up. For an assumed deterministic roughness geometry, an 'averaged Reynolds' equation' can be derived [12] to give the variation in oil pressure in the rolling direction. An alternative 'flow factor' approach is based on the numerical simulations of flow by Patir and Cheng [13, 14] Multi-scale model of rolling Le and Sutcliffe have developed a series of models to model lubricated rolling, based on coupling the asperity deformation with a lubricant entrainment model. Various methods were used to deal with the small wavelength asperities. A semi-empirical model used laboratory tests to model this aspect of friction [15] while a two-wavelength model coupled asperity mechanics and lubrication theory across two roughness length scales [9]. Their most recent model [16] provides a relatively simple model that captures the essence of the physics whilst avoiding the complexity of the two-wavelength model. The essence of this model is indicated in Figure 5, showing in the top of the figure the primary length scale of the roughness running in the rolling direction, and in the bottom of the figure secondary-scale transverse roughness situated on the tops of the primary scale roughness. This secondary roughness is on a smaller Combined roll and strip primary-scale roughness Rolling direction λ Secondary-scale roughness on tool Strip δ p Primary scale contact area (A p ) Secondary-scale contact area (A s ) h vp Relative sliding direction Figure 5. A multi-scale model for roughness. Secondary roughness transverse to the direction of rolling lies on top of primary roughness aligned longitudinally [16].

4 scale than the normal roughness considered and is due to grinding defects, wear or pick-up on the roll. The contact area of the primary roughness is found by a coupled hydrodynamics and asperity crushing model. A simple model is used for the secondary contact, assuming that the film thickness under these contacts is given by an asperity-level entrainment analysis, and that the corresponding contact area is found by determining the bearing area at which this amount of oil just fills the gap between roll and strip. The true contact area is given by the contact area of this secondary roughness. The friction coefficient is then given by summing contributions from the valleys, associated with the oil rheology, and from the true contact areas, given by a boundary friction coefficient. Although relatively simple, it is found that this model is able to provide a good model of frictional behaviour across a range of conditions. Strip drawing experiments were used to calibrate the model, in effect extracting a boundary lubrication coefficient, which is found to be.1. The correlation with measured friction coefficients in lab and industrial rolling trials is shown in Figures 6(a) and (b) respectively [16]. Agreement is excellent, choosing a value of boundary friction coefficient between.7 and 1, consistent with the strip drawing tests. For the mill trials of Figure 6(a), the fall in friction as the speed parameter increases reflects the increasing entraining film and hence the significant drop in true contact area. Even for the more limited range of conditions available with the industrial process of Figure 6(b), there is a significant fall in friction with increasing speed which is well modelled by the theory. (a) 4. PIT ROUGHNESS The above models of roughness have been developed for roughness which is longitudinal, as is found in aluminium and some steel rolling. However there are a number of applications where the principle roughness is in the form of pits. Such pits are typically found as the residue of isotropic surfaces, such as generated from the shot-blast finish on stainless steel strip. Build-up of hydrostatic pressure in the pits as they are reduced in volume tends to prevent the pits being eliminated [17]. However, in the presence of sliding between the tool and strip, this oil can be drawn out of the pits due to hydrodynamic action. This has been termed micro-plasto-hydrodynamic lubrication (MPHL). Various experimental studies and models have considered MPHL, frequently using artificial indents to help observe the phenomenon [e.g. 18,19] Pit characterisation Pitting on a cold-rolled strip surface tends to be irregular, with a range of pits of different sizes and shapes. Here 3-D profilometry is invaluable in gathering the data, but it is not obvious how to synthesise it. Sutcliffe and Georgiades [2] show how the raw data can be used to extract statistics of the pit geometry and hence a 'characteristic' pit diameter, spacing, depth and slope. The method is illustrated for samples of industrially-rolled bright annealed stainless steel, which had a rough shot-blast finish prior to cold rolling. The pit identification method is illustrated in Figure 7, for a strip reduction of 43% relative to the initial shot-blast hot band. Figure 7(a) shows the raw data from the profilometer, while Figure 7(b) shows the individual pits which have been identified, along with the 'characteristic' pit diameter and spacing. The method is effective at identifying pits seen visually, while the characteristic values of pit diameter d c and spacing D c seem reasonable. The characterisation method can be used to quantify the change in pit area, size and spacing during a pass schedule. This is illustrated for a roll schedule of stainless steel from a thickness of 4mm in Figure 8. During the schedule the pits are progressively eliminated. (b) Height (µm) µm d c = 12 µm D c =114 µm Figure 6. Effect of speed on inferred friction coefficient during cold rolling of aluminium, (a) laboratory-scale, (b) industrial rolling [16]. Figure 7. Characterisation of pitted stainless steel surface [2].

5 Total fractional pit area A End-coil Mid-coil Fractional pit area A (left scale) R q roughness (right scale) Rq roughness (µm) (a) Centre of tool,.25% aluminium stearate (c) Edge of tool,.25% aluminium stearate (b) Edge of tool,.5% stearic acid (d) Edge of tool, no additive Overall strip reduction r (%) Figure 8. Elimination of pits during cold rolling of stainless steel [2]. 5. BOUNDARY LUBRICATION The original definition of boundary lubrication was for 'lubrication in which friction depends not only on the properties of the lubricant but also on the chemical nature of the solid boundaries' [22]. However, as Ike [23] notes, the distinction between hydrodynamic and boundary lubrication has become increasingly blurred as both measurement and modelling have reached down to molecular dimensions. Interferometry measurements on oil films which are only a few molecules thick show quasi-hydrodynamic behaviour; atomic force microscopy (AFM) measurements show solidification of liquid near a crystalline solid and models of lubricant flow are increasingly concerned with simulation at a molecular level. In this section of work we describe the effect of roughness on boundary lubrication, by which we mean conditions where hydrodynamic effects are very small and lubrication is dominated by the chemistry of the interface. Plane strain compression testing is an effective way to simulate metal rolling conditions in the laboratory. If a series of compression tests are undertaken along a strip (i.e. always indenting a new piece of strip), it is observed that there is often a change in friction conditions associated with evolution of a transfer layer on the tool. Figure 9 illustrates the type of layer observed on a steel tooling after 2 indents on aluminium strip [24]. At the centre of the tool there is very little attachment, Figure 9(a), due to the thicker oil film there, while at the edge of the tool the transfer layer depends on the amount of additive, in this case stearic acid or aluminium stearate, added to the base oil (Figure 9(b)-(d)). The friction results are summarised in Figure 1. This figure shows the friction factor as a function of additive concentration for two tool roughnesses. The shaded horizontal bands represent the friction factor at the first indent. The effect of roughness is apparent, while the friction factor is insensitive to the additive concentration. However, by the 2 th indent the situation is dramatically changed, now the friction factor falls significantly with increasing additive concentration, while the effects of roughness are less apparent. The interpretation of these results is that the transfer layer formed on the tool as a results of the interaction between the aluminium and the additives is the dominant factor in friction, and the quality of this transfer layer determines friction. At least for these conditions the steady state transfer layer does not seem to depend greatly on the roughness of the tool. Friction factor m Figure 9. Micrographs of a steel tool surface after 2 plane strain compression tests on aluminium strip [2]. y First indent Rough tool, 18th-2th indent Smooth tool, 18th-2th indent Rough tool Smooth tool Stearic acid concentration (%) Figure 1. Effect of roughness and additive concentration on friction factor during plane strain compression of aluminium strip [24]. 6. CONCLUSIONS The effect of roughness on the tribology of cold rolling in the industrially-relevant mixed lubrication regime is now reasonably well understood. Section 2 has emphasised the importance of bulk deformation of the strip in facilitating asperity crushing. Details of the roughness topography are seen to be important; in particular the importance of short wavelengths of roughness is highlighted. Lubrication models have also been successfully

6 developed for the mixed lubrication regime where the effects of roughness and lubricant entrainment both play a role. A multi-scale model has been described. This treats a primary wavelength in a rigorous way, modelling the interaction between the asperity deformation and oil pressure. A secondary scale of roughness is treated in a simpler way to allow a relatively robust analysis. This model is able to describe a range of cold rolling processes with a boundary lubrication coefficient for the true contact areas in the range In the alternative scenario pertinent to stainless steel, roughness is dominated by the formation and elimination of isolated pits. Measurements and analysis of the pit geometry using 3D profilometry are described, to show how the pits change during a roll schedule. The paper finishes with a section on boundary lubrication. Plane strain compression tests are used to investigate this regime. It is found that, although the initial friction factor depends on the tool roughness, after a transfer film evolves the role of roughness is relatively slight. Instead friction is controlled by the chemistry, in this case characterised by the concentration of additive, which in turn affects the build up of the transfer layer. ACKNOWLEDGEMENTS The author is grateful for many fruitful collaborations over the course of the work, in particular to Prof KL Johnson, Prof WRD Wilson, Dr HR Le, Dr P Montmitonnet Dr K Waterson and Dr D Farrugia and for support from Alcan/Novelis, Pechiney, Corus, Avesta Sheffield and the EPSRC. REFERENCES [1] J.A. Schey: Tribology in Metalworking Friction Lubrication and Wear. American Society for Metals, Metals Park, Ohio, ISBN: (1984) [2] Greenwood, J.A. and Rowe, G.W. Deformation of surface asperities during bulk plastic flow, Wear, 38, (1965) [3] Sheu, S. and Wilson, W.R.D. Flattening of workpiece surface asperities in metalforming, Proc. NAMRC XI, (1983) [4] Wilson, W.R.D. and Sheu, S. Real area of contact and boundary friction in metal forming, Int. J. Mech. Sciences, 3, (1988) [5] Sutcliffe, M.P.F., 1988, Surface asperity deformation in metal forming processes, Int. J. Mech. Sciences, 3, (1988) [6] Sutcliffe, M.P.F. Flattening of random rough surfaces in metal forming processes, ASME Journal of Tribology, 121, (1999) [7] Wilson, W. R.D. and Walowit, J. A. An Isothermal Hydrodynamic Lubrication Theory for Strip Rolling With Front and Back Tension, Proc Tribology Convention, I. Mech. E., London, pp (1972) [8] Sutcliffe, MPF. Le, HR. Measurements of surface roughness in cold-metal rolling in the mixed lubrication regime, STLE Trib Trans 43, (2) [9] Le, HR and Sutcliffe, M.P.F. A two-wavelength model of surface flattening in cold-metal rolling with mixed lubrication, STLE Tribology Transactions, 43(4), (2) [1] Le, HR and Sutcliffe, M.P.F. Analysis of surface roughness of cold rolled aluminium foil, Wear, 244, (2) [11] Montmitonnet, P. Plasto-hydrodynamic lubrication (PHD) - application of lubrication theory to metal forming processes. C.R. Acad. Sci. Paris, Série IV, t.2, (21) [12] Christensen, H. Stochastic Models for Hydrodynamic Lubrication of Rough Surfaces, Proc. Instn Mech Engrs, 14, Pt 1, (197) [13] Patir, N. and Cheng, H.S. An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication, ASME J. Lub. Tech., 1, pp (1978) [14] Chang, D.F., Wilson, W.R.D. and Marsault, N. Lubrication of Strip Rolling in the Low-Speed Mixed Regime, Tribology Transaction, 39, (1996) [15] Le HR, Sutcliffe MPF. A semi-empirical friction model for cold metal rolling, Tribology Trans. 44 (2), (21) [16] Le HR, Sutcliffe MPF, A multi-scale model for friction in cold rolling of aluminium alloy. Tribology Letters (26) [17] Kudo, H., A Note on the Role of Microscopically Trapped Lubricant at the Tool-Work Interface, Int. J. Mech. Sci., 7, (1965) [18] Kudo, H. and Azushima, A., Interaction of surface microstructure and lubricant in metal forming tribology, Proc. 2 nd. Int. Conf. On Adv. Technol. of Plasticity, Stuttgart, 373 (1987) [19] Wang, Z., Dohda, K., Yokoi, N. and Haruyama, Y., Outflow Behaviour of Lubricant in Micro Pits in Metal Forming, 1st Int. Conf. Tribology in Manufacturing Processes, Gifu, Japan, (1997) [2] Sutcliffe MPF and Georgiades F. Characterisation of pit geometry in cold rolled stainless steel strip. Wear, 253, (22) [21] Le HR, Sutcliffe MPF. Evolution of surface pits on stainless steel strip in cold rolling and strip drawing. ASME J Trib., (23) [22] Hardy, W.B. and Doubleday, I. Boundary lubrication - the paraffin series Proc. Roy. Soc. London, A1, (1922) [23] Ike, H. An AFM analysis of surface textures of metal sheets caused by sliding with bulk plastic deformation, Wear, 224, (1999) [24] Sutcliffe MPF, Combarieu, R, Montmitonnet, P. Effect of additives on friction during plane strain compression of aluminium strip. Wear, 257, (24)