Measurement of Random Rough Surface Modification in Mixed Lubrication

Measurements of surface roughness in cold metal rolling
in the mixed lubrication regime

MPF Sutcliffe and HR Le

Cambridge University Engineering Department, Trumpington Street,
Cambridge, CB2 1PZ, U.K.

Abstract

This paper describes measurements of the change in surface roughness of aluminium strip due to cold rolling. Rolling is in the mixed lubrication regime, where there is both asperity contact and hydrodynamic action. The strip is in the as-received condition before rolling, with a continuous spectrum of roughness wavelengths. The spectra of roughness for both the initial and rolled surfaces are used to extract amplitudes for long and short wavelength components, with an arbitrary division between these components at a wavelength of 14 mm. It is found that the short wavelength components persist more than the long wavelength components, and that flattening of the strip increases with increasing reduction in strip thickness. The qualitative effect of wavelength on flattening is similar to that observed with unlubricated rolling, and is in line with theoretical models of mixed lubrication. The effect of reduction is not predicted by existing theories, but is in agreement with measured variations of friction with reduction.

Keywords: Asperity, Friction, Lubrication, Metal Rolling, Tribology, Roughness.

To be submitted to ASME Journal of Tribology, Sept. 1988

Nomenclature

A Fraction of nominal area in contact between roll and strip

h Film thickness separating strip and roll

hs Theoretical film thickness in the bite for smooth rolls and strip

h* Film thickness corresponding to zero pressure gradient

 Characteristic hydrodynamic inlet length

L Length of the bite

Reduced hydrodynamic pressure;

r Reduction in strip thickness

R Roll radius

t0 Initial strip thickness

Mean entraining velocity

Co-ordinate in rolling direction

Plane strain yield strength of the strip

a Pressure viscosity coefficient of lubricant

b Temperature viscosity coefficient of lubricant

h (h0) Viscosity of lubricant (at ambient pressure)

Ratio of the theoretical smooth film thickness to the initial combined strip and roll roughness

m Average friction coefficient

µp Friction coefficient on the plateaux

Friction coefficient in the valleys

q0 Angle between roll and strip at the inlet to the bite

s, (s0) (Initial) r.m.s. amplitude of the short wavelength components of strip roughness

st0 Initial combined r.m.s amplitude of the strip and roll including both short and long wavelengths

sr , Sr r.m.s amplitudes of the short and long wavelength components of the roll roughness

S, () (Initial) r.m.s. amplitude of the long wavelength components of strip roughness

1. Introduction

Accurate models of metal rolling are needed 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 '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 determined by the lubricant rheological properties, the rolling speed and the roll geometry. Wilson and Walowit derive an expression for the 'smooth' film thickness hs as

(1)

where is the average entraining velocity, is the inlet angle between the strip and roll, Y is the plain strain yield strength of the strip and is the viscosity of the lubricant at ambient pressure. a is the pressure viscosity coefficient in the Barus equation used to describe the variation of viscosity with pressure p.
The ratio of the smooth film thickness hs to the combined roll and initial strip roughness st0 is used to characterise the lubrication regime. For large L, the surfaces are kept apart by a continuous film of oil. The mixed lubrication regime, with some asperity contact, occurs when Ls falls below about 3. A simple picture of the interface between the roll and strip divides the contact into areas of contact and areas separated by an oil film, as illustrated schematically in Fig. 1a. The area of contact ratio A can then be used to estimate a mean friction coefficient µ by

(2)

where the friction coefficient µp of the plateaux is frequently modelled using a boundary friction coefficient, and the coefficient of the valleys µv can be estimated knowing the oil viscosity and film thickness. In industrial practice the valley contribution is generally small.

Several recent models of mixed lubrication have been published (Sheu 1985, Sutcliffe and Johnson 1990, Sheu and Wilson 1994, Lin et. al. 1998, Marsault et. al. 1998). These consider both the pressure build-up in the lubricant and the contact between the two surfaces. The more recent models include the way in which asperities deform when on a substrate which 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 value. 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 Ls, to complete conformance of the surfaces and friction typical of boundary additives for very small Ls. 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 Ls, which does not seem physically likely.

It is the authors' hypothesis that these differences arise due to an oversimplification in the modelling 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. Fig. 1a and b, for triangular and pseudo-Gaussian 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. 1c, 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 (1977) 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 (1998), 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 idealised 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 behaviour 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 summarised in the following section. Section 3 presents the results and discussion and conclusions are drawn in section 4.

2. Experimental details

2.1 Rolling details

Most of the experimental details are as for the unlubricated rolling experiments of Sutcliffe (Sutcliffe, 1998). 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 in a two-high mill with roll diameters of 51 mm at roll speeds between 0.003 and 1.0m/s. Before rolling, the strips had a micro-Vickers hardness Hv of 550 MPa, giving an estimated yield strength Y (= Hv/2.57) of 214 MPa ??. The reduction is 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%, were used; actual reductions were within 1% of these values. Three naphthenic base oils were liberally applied to both sides of the strip (except were 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 , where t and tr are actual and reference temperatures, to extract values for the temperature viscosity coefficient b and the viscosity h at a typical rolling temperature of 25°C. These are detailed in Table 1. Room temperature was recorded to estimate values for h in each set of tests.

Table 1 Properties of lubricants

The pressure viscosity coefficient 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 oil in the bite). A value of a equal to 3.0×10–8 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 value hs, equation 1, for film thicknesses much greater than the combined surface roughness st0 of the roll and strip (here st0 = 0.38 µm). The measured film thickness equals the theoretical film thickness along the dashed line in Fig. 2. For the 500 SUS oil, a value of a equal to 2.0×10–8 m2/N 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%. With the larger reduction of 50%, however, the strip roughness was flattened significantly more in the oil drop tests than 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.

2.2 Surface roughness details

The roughness of the strips was measured with a standard diamond-stylus profilometer at a traverse speed of 0.3 mm/s. Roll roughness was measured from an acetate impression of the roll. A profile of length 3mm was sampled at an interval of 0.3 mm and the digitised 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 behaviour of different wavelengths, some way is needed of representing the continuous spectrum of wavelengths in a digestible form. Here we follow the method described in detail by Sutcliffe (1998) 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 a short wavelength components s, while wavelengths between this arbitrary breakpoint wavelength and an upper cut-off are summed to estimate a long wavelength amplitude S. In this case we choose to divide the spectrum between short and long wavelengths at 14 mm, with an upper cut-off wavelength of 250mm. The initial r.m.s. contributions from the short and long wavelength components s0 and S0 for the initial strip surface were 0.12 and 0.36 mm and the corresponding values sr and Sr for the roll were 0.024 and 0.048 µm. The total combined roughness for the initial strip and roll surfaces equalled 0.38 mm.

3 Experimental results

Measurements of surface roughness of the strip were made and split into long and short wavelength components s and S at an arbitrary wavelength of 14 mm, as described in the previous section. Results for the effect of film thickness ratio , roughness wavelength and strip reduction ratio on the flattening behaviour are presented in this section.