Measurements of Surface Roughness in Cold Metal Rolling in the ...

Measurements of Surface Roughness in Cold Metal Rollinq - in the Mixed Lubrication ~ e ~ i r n e @ M. P. F. SUTCLIFFE and H. R. LE

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Cambridge University Engineering Department Cambridge CB2 IPZ, United Kingdom

This paper describes measurements of the change in surface roughness of aluminiur~istrip due to cold rolling. Rolling is in the mixed lubrication regime, where there is both asperity contact and

KEY WORDS Asperity; Friction; Lubrication; Metal Rolling; Tribology; Roughness

hydrodynamic action. The strip is in the as-received condition before rolling, with a continuous spectrum of roughness wave-

INTRODUCTION

lengths. The spectra of roug/~rless for both the initial and rolled

Accurate models of metal rolling are required by industry to increase productivity and improve quality. For cold strip rolling, the key areas where industry needs more reliable and accurate models are in friction and surface finish. Lubrication is applied to reduce frictional forces, to protect the roll and strip surfaces, and to act as a coolant. To meet surface finish requirements on the strip, it is essential that the asperities on the roll come into contact with the strip, so that the smooth ground finish of the rolls is imprinted onto the strip. To meet the needs both of low friction and good surface finish, most cold rolling operates in the I 'mixed' regime, where there is some hydrodynamic action drawing lubricant into the bite, but also some contact between the asperities on the roll and strip. During the last three decades, many tribological models of cold rolling have been proposed. In the early models (Cheng, 1966, Wilson and Walowit, 1972), surface roughness was ignored and the one-dimensional Reynolds' equation was integrated in the inlet zone. The lubricant film thickness at the end of the inlet is

sugaces are used to extract amplitudes for long and short wavelength componerrts, with an arbitrary division at a wavelength of

14 ptn between these components. It is found that the short wavelength components persist more than the long wavelength components, and that flattening of the strip increases with reduction in strip thickness. The qualitative effect of wavelength on flattening is similar to that observed with unlubricated rolling (Sutcliffe,

1999),and is in line with theoretical models of mixed lubrication. The effect of reduction is not predicted by existing theories, but is ill agreement with measured variations of friction with reduction.

Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLWASME Tribology Conferonce in Orlando, Florida, October 11-13, 1999 Final Manuscript approved April 6,1999

= fraction of nominal area in contact between roll and strip = theoretical film thickness in the bite for smooth rolls and strip = length of the bite = dimensionless speed parameter S = 2qo DRIYLo,, = roll radius = mean entraining velocity = plane strain yield strength of the strip = pressure viscosity coefficient of lubricant = temperature viscosity coefficient of lubricant = viscosity of lubricant (at ambient pressure) = ratio of the theoretical smooth film thickness to the initial combined roughness

P

= average friction coefficient

PP

= friction coefficient on the plateaux

P" 6 ' 0

a (0,) or0

0,.,L x

3

(xoJ

nents

= friction coefficient in the valleys =angle between roll and strip at the inlet to the bite = (initial) r.m.s. amplitude of the short wavelength components of strip roughness = initial combined r.m.s amplitude of the strip and roll including both short and long wavelengths = r.m.s amplitudes of the short and long wavelength components of the roll roughness = (initial) r.rn.s. amplitude of the long wavelength compoof strip roughness

M. SUTCLIFFE AND H. LE


Area

of contact \

Flg. l-Schernatlc of surface roughness idealizations. (a) trlanguiar asperlties (b)pseudo-Gaussian roughness (c) two superlrnposed wavelengths of roughness

clctcrtiiinctl by tlic lubricant rhcological properties, the rolling speed and tlic roll geometry. Wilson and Walowit derive an cxprcssioli for the 'smooth' fill11 thickness h, as

wlicrc othe inlet angle is the average entraining veloc~ty,€lis bctwccn thc strip arid roll, Y is the plain strain yield strength of the strip ant1 q,, is rhc viscosity ol' the lubricant at ambient pressure, a is tlic ~~rcssurc viscosity coell'icient In the Barus equation q = il,,cai' used to tlcscribc the variation of viscosity with pressure p. 'I'lic txrio A, = 11, lo,,, of the sniooth film thickness hs to the combiticd roll and initial strip roughness o,ois used to characterize the lubrication rcginic. For large A,, the surfaces are kept apart by a contini~ousfilm of oil. The tiiixcd lubrication regime, with some aspcrity contact, occurs when A, kills below about three. A simple pict~rcof the interface betwccn the roll and strip divides the contact into arcas ol' cotitact and areas separated by an oil film, as illustrntctl schcliintically in Fig. I(a). The area of contact ratio A ciiti tlicti bc used to cstininte a mcan friction coefficient p by

wlicrc tlic friction coefficient p, of the plateaux is frequently modclccl usitig n boundary friction coell'icient and the friction coefficictit for tlic valleys pv call be estimated knowing the oil viscosity and film thickness. In industrial practice the valley contribution is gc~icrullysmall. Several rcccnt tiiodels of mixed lubrication have been publisliccl (Slicu 1985, Sutcliffe and Johnson 1990, Sheu and Wilson 1994, Lin ct. al. 1998, Marsault ct. al. 1998). These consider both tlic prcssurc build-up in the lubricant and the contact between the two surf;~ccs.Thc more recent models include the way in which

asperities deform when on a substrate that is deforming plastically (Greenwood and Rowe 1965, Sheu and Wilson 1983, Wilson and Sheu 1988, Sutcliffe 1988). This feature of the contact is peculiar to metal working tribology, and renders studies of lubrication without a deforming workpiece of very limited applicability to metal forming processes. Experimental measurements of oil film thickness and surface roughness in the mixed regime have confirmed the main points of these models (Sheu 1985, Sutcliffe, 1990, Sheu and Wilson, 1994). As predicted by these models, Tabary et. al. (1996) showed a transition from hydrodynamic friction for large A,, to complete conformance of the surfaces and friction typical of boundary additives for very small As. However, in the transition regime, the measured frictional traction was significantly smaller than would be predicted by the existing models. For example, Marsault (1998) showed that these results could only explained by assuming a large drop in apparent boundary friction coefficient with increasing As, which does not seem physically likely. It is the authors' hypothesis that these differences arise due to an oversimplification in the modeling of surface roughness. A weakness in all the above models is that roughness is represented by an array of asperities with a uniform height and wavelength of roughness (c.f. Figs. ](a) and I(b), for triangular and pseudoGaussian roughness), while in practice the roughness is made up a spectrum of different wavelengths of roughness. Although results are sensitive to the roughness wavelength, with asperity crushing being much greater for longer wavelengths of roughness, theoretical models give no guidance as to an 'appropriate' wavelength to choose for practical rough surfaces. If small wavelength asperities persist on top of larger scale asperities, as illustrated in Fig. I(c), then models which only include the longer wavelength component could predict the film thickness with reasonable accuracy, but would still be considerably in error in estimating the area of contact ratio A and hence friction. This effect is suggested by the work of Steffensen and Wanheim (1 977) for unlubricated contact. They considered roughness consisting of a series of triangular arrays of asperities of successively shorter wavelengths, superimposed on each other. Using this model they showed that the real contact area is significantly reduced by including more than one wavelength of roughness. This effect was further considered by Sutcliffe (1 999), again for dry contacts. Aluminium sheet with an as-received random surface finish was rolled using smooth rolls. Experimental measurements of the spectrum of roughness were used to show that the short wavelength components were crushed much more slowly than the long wavelength components. Sutcliffe's model, using an idealized roughness composed of just two wavelengths, showed good agreement with measured changes in roughness amplitude. The purpose of this paper is to establish experimentally the flattening behavior of different wavelengths of roughness for lubricated cold rolling in the mixed regime. The measurements are made using strip with a random rough surface typical of industrial practice. This work aims to confirm the above hypothesis and to provide useful data to validate theoretical models. Experimental details of the work are summarized in the next section, followed by results, discussion and conclusions.

Measurements of Surface Roughness in Cold Metal Rolling in The Mixed Lubrication Regime

TABLE I-PROPERTIES OF LUBRICANTS


2000 SUS

"'I

940

,,'

+."

5

.sC f

0

0

0

2000 SUS, 25% reduction 0

.

5 W SUS. 25% reduction

+ 500 SUS. 50% reduction

,#'-

+,

Od

0.5

1

1,s

2

Smooth film th~cknessh s ( ~ m )

2.5

3

Fig. 2-Variation of experimental oil film thickness with smooth film thickness h,.

EXPERIMENTAL DETAILS

41

Pepeane v k a d y dEet a was estimated from measurements of the film thickness, using the oil drop method described by Azushima (1978). Results of these film thickness measurements are given in Fig. 2. A correction has been applied to the measured film thickness to allow for thinning of the oil in the bite. The measured film thickness equals the theoretical film thickness along the dashed line in Fig. 2. A value of a equal to 3.3 x m2/N was chosen for the most viscous 2000 SUS oil so as to match the measured film thickness with the theoretical smooth film thickness h,, for film thickness much greater than the combined surface roughness o,o of the roll and strip (here o,,= 0.38 m21~ pm). For the 500 SUS oil, a value of ci equal to 2.2 x was chosen to produce a smooth transition between results for this oil and the 2000 SUS oil. These values for a are in good agreement with published figures (Evans and Johnson, 1986). For the thinnest 100 SUS oil, where it was not possible to make accurate film thickness measurements due to the thinness of the films, a value of a equal to that for the 500 SUS oil was assumed. Thermal effects and the effects of roll curvature on the calculation of smooth film thickness were found to be negligible (Wilson and Murch 1976, Tsao and Wilson 1981). A comparison between roughness measurements made with the oil drop and fully lubricated rolling experiments showed insignificant differences for the smaller reduction of 25 percent. With the larger reduction of 50 percent, however, the strip roughness was flattened significantly more in the oil drop tests than that when oil was applied to both sides of the strip. This was attributed to deflection of the strip in the inlet due to the unsymmetrical rolling conditions (c.f. Sutcliffe 1990). Results presented in this paper apart from those of Fig. 2 are for symmetrical lubrication conditions.

Rolling Details

Surface Roughness Details

Most of the experimental details are as for the unlubricated rolling experiments of Sutcliffe (Sutcliffe, 1999). The only significant change in methodology is in the inclusion of a lubricant. Cold-rolled 5052 work-hardened aluminium strips of thickness. 0.82 mm, length 200 mm and width 50 mm were rolled at roll speeds between 0.003 and 1.0 m/s in a two-high mill with roll diameters of 5 1 mm. Before being rolled, the strips had a microVickers hardness H, of 550 MPa, giving an estimated yield strength Y (= HJ2.57) of 214 MPa. The reduction in strip thickness was measured with a micrometer, taking the average of a number of readings for each specimen before and after rolling. Nominal reductions of 25 and 50 percent were used; actual reductions were within one percent of these values. Three naphthenic base oils were liberally applied to both sides of the strip (except where film thickness measurements were made as described below). These oils had nominal viscosities of 100, 500 and 2000 SUS at 39'C and the actual viscosities were determined at temperatures of 30 and 50°C using a capillary viscometer. These measurements were fitted by the exponential equation q=%,-a(t-l,) where t and t, are actual and reference temperatures, to extract values for the temperature viscosity coefficient p and the viscosity q at a typical rolling temperature of 25°C. These are detailed in Table I. Room temperature was recorded to estimate values for q in each set of tests.

The roughness of the strips was measured with a standard diamond-stylus profilometer at a traverse speed of 0.3 mmls. Roll roughness was measured from an acetate impression of the roll. A profile of length 3 mm was sampled at an interval of 0.3 pm and the digitized profile transferred to a computer to estimate the roughness parameters. An average of three measurements was used for each specimen. Since the experiments are designed to investigate the behavior of different wavelengths, some way is needed of representing the continuous spectrum of wavelengths in a digestible form. Here the authors follow the method described in detail by Sutcliffe (1999), to divide the spectrum into long and short wavelength components. Contributions for wavelengths below an arbitrary wavelength are summed up to give the amplitude of short wavelength components o, while wavelengths between this arbitrary breakpoint wavelength and an upper cut-off are summed to estimate the long wavelength amplitude 1.In this case the authors choose to divide the spectrum between short and long wavelengths at 14 pm, with an upper cut-off wavelength of 250 pm. The initial r.m.s. contributions from the short and long wavelength components a, and X, for the initial strip surface were 0.12 and 0.36 pm and the corresponding values orand Xr for the roll were 0.024 and 0.048 pm. The total combined roughness for the initial strip and roll surfaces equalled 0.38 pm.

=Jw

M.SUTCLIFFE AND H.LE

25% reduction

0.6 50% reduction

.

O . O


Q

Flg. 3-Varlatlon of short and long wavelength roughness amplitudes wlth A,. Strlp reductlon = 25%.

0

Fig. 5--Variation In the ratio a / I of the amplitudes of short and long wavelengths wlth As.

xo.

500 SUS

a

* 0

. 0 0

.

. 0

0

0

Flg. 4--Varlatlon of short and long wavelength roughness amplitudes with A,. Strlp reductlon = 50%.

EXPERIMENTAL RESULTS Measurements of surface roughness of the strip were made and split into long and short wavelength components o and 1 at an arbitrary wavelength of 14 pm, as described in the previous section. Results for the effect of film thickness ratio As, roughness wavelength and strip reduction ratio on the flattening behavior are presented in this section.

Effect of Film Thickness Parameter and Wavelength Figures 3 and 4 show changes in strip roughness amplitude with film thickness parameter A,, for reductions in strip thickness of 25 percent and 50 percent, respectively. The roughness is split into short and long wavelength components o and 1,which are

normalized by the original strip roughness amplitudes o, and Note that A, is based on the initial combined roughness G , ~which , includes short and long wavelengths. The wide range of A, was achieved in the experiments by varying the speed and by using the three different oils. The range of A, covered by each oil is indicated at the bottom of the figures. The corresponding roll roughness amplitudes orloo and x j Z o are indicated by arrows at the left hand side of the figures. For A, greater than about two, the long wavelength component increases in amplitude due to hydrodynamic roughening (Schey, 1983). There is little change in short wavelength component. It seems that this roughening occurs on the scale of the grain size of the order of a few tens of microns. For A, less than two, both long and short wavelengths are flattened, although the relative amplitude of the long wavelength component is always significantly smaller than for the short wavelength component, as expected from theoretical models of asperity crushing. For very small A, both components of roughness approach the corresponding roughness amplitudes for the roll. To help compare the way in which the two wavelengths behave, Fig. 5 shows the ratio d C of the amplitudes of the short and long wavelength components. When the speed parameter is greater than about two, the ratio o/Z falls below the corresponding value for the initial strip roughness due to the roughening of the long wavelength component. For A, between about 0.5 and 2, o/C increases with decreasing As as the long wavelength components flattens faster than the short wavelength components. For A, below 0.5, 012 falls off again with decreasing A, as the long wavelength component is by now effectively equal to the roll roughness, while there is further flattening of the short wavelength component. At the smallest values of A,, 012 approaches the value of 0.5 corresponding to the roll roughness.

Effect of Reduction To compare the effect of reduction on flattening behavior, Fig. 6 shows the change in the short wavelength component of rough-


Measurements of Surface Roughness in Cold Metal Rolling in The Mixed Lubrication Regime

a

25% reduction

0

50% reduction

.

Asperity height (vm) Fig. &The effect of reduction on the crushing of short wavelength asperities. ness o for the two reductions of 25 percent and 50 percent, as a function of A,. The amount of asperity flattening and the conformity of the strip surface to the roll surface is significantly greater, at the same values of As, for the higher reduction. Existing theoretical models suggest two reasons why reduction might affect the flattening behavior. Firstly there is a relative minor effect due to thinning of the oil film as the strip surface elongates. Secondly, where asperity flattening extends through the bite, then the reduction ratio could become important. Wilson and Chang (1996) characterize this effect using the dimensionless parameter S, defined by

where R is the roll radius and L is the length of contact in the bite. When S is greater than about 0.01, the majority of the asperity flattening is confined to a short inlet region. For a typical value of A, equal to 0.2, the corresponding value of S is about 0.01 6. This suggests that, although this effect may play a small role, it cannot explain the significant difference between results at the two reductions. Detailed calculations using the model of Marsault (1998) confirm this conclusion. Although theoretical models do not explain this effect, the experimental results of Tabary et. al. (1996) showed that, at the same value of A,, friction was significantly greater at a higher reduction. This is in accordance with the greater conformance between roll and strip observed here. Height Probability Density Functions Height probability density functions for typical tests with 500 SUS oil at a 25 percent reduction are shown in Fig. 7. These are constructed from the original profiles, eliminating long wavelengths using an eighth order digital filter with a cut-off of 250 pm. A smooth curve has been drawn through the average of histograms from three roughness profiles. The speed parameter A, and smooth film thickness h, corresponding to each curve are

Fig. 7-The effect of h, on the probability density function for the etrlp roughness (reduction = 25%).

irrhdBSin ttE figne. fs A, decreases, the strip surfaces are flattened. This is reflected in a narrowing of the probability density function. These results are similar to those found by Tabary et. al. (1996). 'Theoretical predictions using a single wavelength and amplitude and assuming an unchanged valley shape would fail to predict the shape observed. In particular the right hand side of the peak is significantly shallower than would be expected. CONCLUSIONS The object of this paper was to test the hypothesis that short and' long wavelengths would flatten at different rates in strip rolling in the mixed lubrication regime. Results clearly confirm this hypothesis, with short wavelength asperities persisting more than those with long wavelengths. This behavior is similar to that observed for unlubricated strip rolling (Sutcliffe, 1999). Other surface roughness changes confirm previous observations. For example a good conformance between roll and strip is observed at small values of A,, (the ratio of the smooth film thickness to the combined surface roughness), and hydrodynamic roughening occurs for As greater than about one. Flattening of both short and long wavelengths was significantly greater, for the same value of A,, at higher strip reductions. Although this effect is not be predicted by existing theories, this observation is in line with experimental observations of friction (Tabary et. al., 1996). As well as providing a quantitative measure of the difference in behavior between different wavelengths, these experiments also provide useful data of roughness amplitude and height distribution for validating any theoretical model. It is expected, as suggested by Fig. 1 and existing experimental measurements, that it will be important to include more than one wavelength of roughness in order to determine the area of contact ratio accurately. Errors in predicting the contact ratio and hence friction will become increasingly significant as thinner strip is considered. It is unlikely that a foil model for the mixed lubrication regime that does not take this effect into account will be accurate.

ACKNOWLEDGMENTS l'hc authors wish to thank Prof. Bill Wilson and Mr. HengSlicng Liri at Northwestern University, USA for their assistance :MI Mr Chris Pargeter at Alcan Int'l. Ltd. for his measurements of oil viscosity. 'The financial support of the Center for Surface Enginccririg and Tribology at Northwestern University, the 1:ulbright Com~nission,the Engineering and Physical Sciences Kcscarch Council, Alcan Int'l. Ltd. and Alston Drives and Controls Ltcl. is gratefully acknowledged.


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(8) Schey, J. A,, "Surface Roughness Effects in Metalworking Lubrication." Lubr Eng.. 39. pp 376-382, (1983). (9) Sheu. S., "Mixed Lubrication in Bulk Metal Forming." Ph.D. Thesis. Northwestern Univ., Illinois, USA. (1985). (10) Sheu, S. and Wilson, W. R. D.. "Flattening o f Workpiece Surface Asperities i n Metalforming," i n Proc. NAMRC XI, pp 172- 178, (1983). (11) Sheu. S. and Wilson, W. R. D.. "Mixed Lubrication o f Strip Rolling." Trib. Trans., 37. pp 483-493, (1994). (12) Steffensen, H. and Wanheim, T., "Asperities on Asperities." Wear, 48, pp 89-98, (1977). (13) Sutcliffe, M. P. F.. "Surface Asperity Deformation in Metal Forming Processes." Inr 'I. Jour: of Mech. Sciences, 30, pp 847-868, ( 1988). (14) Sutcliffe, M. P. F., "Flattening o f Random Rough Surfaces in Metal Forming Processes," ASME Jouc Trib. 121. pp 433-440 (1999). (IS) Sutcliffe, M. P. F. and Johnson. K. L.. "Lubrication in Cold Strip Rolling in the 'Mixed' Regime." in Proc. Insr. Mech. Engrs., 204, pp 249-261, (1990). (16) Sutcliffe. M . P. F., "Experimental Measurements o f Lubricant FilmThickness in Cold Strip Rollling," in Proc. Insr. Mech. Engrs., 204, pp 263-273, (1990). (17) Tabary, P. T., Sutcliffe, M. P. F., Porral, F. and Deneuville. P. "Measurements of Friction in Cold Metal Rolling," ASME Jouc Trib.. 118, pp 629-636, (1996). (18)Tsao. P. and Wilson. W. R. D., "Entrainment of Lubricant in the Cold Rolling o f Steel and Aluminium." in Proc. Inr'l. Conf. On Sreel Rolling. The Iron and Steel lnsrirute of Japan, pp 49-64, (1981). (19) Wilson. W. R. D. and Chang D. F., "Low Speed Mixed Lubrication o f Bulk Metal Forming Processes. ASME Jour Trib.. 118, pp 83-89. (1996). (20) Wilson. W.R. D. and Walowit, J. A,. "An Isothermal Hydrodynamic Lubrica~ion Theory for Strip Rolling With Front and Back Tension," in Proc. 1971 Trib. Cotlv.. IMechE, London, pp 164- 172, (1 972). (21) Wilson, W. R. D. and Murch. L. E.."A Refined Model for the Hydrodynamic Lubrication o f Strip Rolling," Jouc Lube Tech., 98, pp 426-432, (1976). (22) Wilson, W. R. D. and Sheu, S., "Real Area o f Contact and Boundary Friction in Metal Forming," Int'l. Jour Mech. Sciences. 30, pp 475-489, (1988).