ANALYSIS of Surface Roughness of Cold Rolled Aluminium Foil
HR Le and MPF Sutcliffe
Cambridge University Engineering Department, Trumpington Street,
Cambridge, CB2 1PZ, U.K.
ABSTRACT
This paper describes a detailed analysis of the surface finish of aluminium thin strip and foil which have been coldrolled under industrial conditions in the mixed lubrication regime. Initial strip was rolled with freshly ground rolls at constant speed for the first pass and at a wide range of speed for the second pass. Strip samples were collected after the second pass. For comparison, samples were also collected after rolling with worn rolls. Surface replicas of the rolls were taken with surface replicating tape.
The surface roughness of the strip samples and roll surface replicas was measured with a threedimensional noncontact interferometric profilometer. The spectrum of the surface roughness was analysed by the Fast Fourier Transform method to identify the way in which different wavelengths of roughness behave. Theory suggests that longer wavelengths of roughness should be crushed more easily. This was confirmed by results. A new image analysis technique has been developed to identify and quantify the area of the micropits. To differentiate between these pits and grind marks transferred from the rolls, the height information was first filtered in the rolling direction using a digital filter. The low frequency component of the surface roughness, which represents the contribution from the roll marks, was subtracted off to leave the pits. Results showed a significant decrease in deep pits during the pass schedule. There was a significant increase in hydrodynamic pitting on the surface with increasing rolling speed during a pass.
Key words: roughness, surface finish, surface spectrum, hydrodynamic pitting, mixed regime, lubrication and metal rolling
Submitted to Wear, Nov 1999.
Nomenclature
f sampling frequency of surface measurement,
h_{i }(i=1~n) data array of surface heights
h_{w} smooth film thickness using the Wilson and Walowit formula
H () matrix of surface heights (after low pass filtering)
s^{2}(_{1}, _{2}) surface variance of the wavelength between _{1} and _{2 }
mean square of a window vector,
w_{i }(i=1~n) window vector
F_{j }(j=0,n/21) complex coefficients of FFT of a data array
S single sided power spectral density
average entraining velocity,
Y plane strain yield stress of the strip
oil pressure viscosity index
_{0 } inlet angle between the strip and roll (in radians)
_{s} (_{d}) depth of shallow (deep) pits
sampling distance of surface measurement
oil viscosity at ambient pressure
_{r} r.m.s. surface roughness on the rolls
_{s} r.m.s. surface roughness on the strip
_{t} combined r.m.s. surface roughness of the strip and roll
^{2} () variance of all wavelengths greater than
1. INTRODUCTION
Modelling of the metal rolling process is currently an active theme of research as the high tonnage of metal rolled means that better understanding can have a significant economic impact. Particular interest has been arisen in modelling friction and modification of surface roughness, both to improve product quality and mill productivity.
Friction and the surface quality of the rolled strip are closely related to the amount of oil drawn into the bite [1]. The lubrication regime can be characterised by _{s}, the ratio of the lubricant film thickness h_{w }to the combined surface roughness on the strip and roll, . The film thickness h_{w} can be estimated, using the results of Wilson and Walowit for smooth rolls and strip [2] as,
(1)
where is the average entraining velocity, _{}is the inlet angle between the strip and roll and Y is the plain strain yield strength of the strip. is the viscosity of the lubricant at ambient pressure and is the oil's pressure viscosity coefficient. For thick oil films with _{s} greater than about 1, surface roughening occurs due to the unconstrained deformation of different grains [1]. The resulting poor surface quality is unacceptable for most products. To achieve an appropriate surface finish, rolling must operate in the mixed lubrication regime, where the oil film thickness is smaller than the surface roughness. In this regime asperities on the strip are flattened and tend to conform to the bright surface finish of the rolls. Measurements of friction coefficients in mixed regime on an experimental mill by Tabary et al [3] confirm that friction coefficient is correlated with _{s}.
Recent measurements of surface roughness in mixed lubrication regime on an experimental mill [4] interpret the modification of surface roughness by examining the surface spectrum. It is shown that short wavelength components persist more than the long wavelength components. This is confirmed by a new model of surface flattening [5], in which the surface roughness is modelled as two wavelengths with a short wavelength superimposed on a long wavelength component. Ahmed and Sutcliffe [6] describe a method for analysing surface data obtained from cold rolled stainless steel samples to identify hydrodynamic pits and roll marks on the surface. This is particularly suited to the stainless steel case where pits are the dominant features. Although that method has been applied by Le and Sutcliffe [7] to the aluminium foil samples described in this paper, this paper describes a more efficient algorithm which is better suited to aluminium foil where roll marks are the dominant feature.
The purpose of this paper is to look at the details of the surface of aluminium foil rolled under industrial conditions, to confirm the results of the laboratoryscale tests and to provide benchmarks for the theoretical models currently being developed. The spectral analysis of surface roughness described in [8] is applied to the measured surface data. Section 2 of this paper describes the details of the strip samples and measurements of surface roughness. Observations of the surface feature are described in section 3. The methodology of spectral and hydrodynamic pit analysis is described in section 4. Section 5 presents the results and conclusions are given in section 6.
2. EXPERIMENTAL PROCEDURE 
Collection of samples
A coil of 1200 aluminium alloy of initial strip of thickness 0.4 mm was rolled under industrial conditions at a constant speed for the first pass and at a wide range of speeds for the second pass using freshly ground rolls. The reduction in strip thickness during both passes was approximately 50 percent. Lubricant was applied abundantly on both sides of the strip. Samples of the initial strip were collected from the end of the coil. A sample after the first pass was taken from a region where the coil was being rolled at speed. Changes in speed during the second pass were marked on the side of the coil. These were used to identify the rolling speed of samples that were collected from the middle of the coil, which was scrapped after this pass. Samples rolled with worn rolls under similar conditions were collected for comparison. Replicas of the roll surface were taken before the second pass using PressOFilm surfacereplicating tape supplied by Testex.

Measurements of surface roughness
Surface roughness was measured in a Zygo noncontacting 3D interferometric profilometer. The equipment has a lateral resolution of 0.5 m and vertical resolution of 0.1 nm.
Preparation of samples
It is very important to use flat samples, a problem that is especially relevant for thin foil and the replica tape. To ensure this, the samples are carefully cut, trimmed and stuck onto a glass slide. The surfaces of the strip samples were cleaned with acetone to remove residual lubricant before measurements were taken.
Measurements
A 20 objective lens was used to ensure that the field of view and depth of field are sufficient to take in the relevant surface features. For surface roughness measurements, a magnification of 200 is used. Normally ten areas are measured and averaged to give the average r.m.s roughness and standard error. For spectrum and hydrodynamic pit analyses, a magnification of 400 or 800 is used. Details of the measurements are listed in Table I.
Table I Details of the measurements
Magnification

Field of view (mm)

Depth of view (m)

Sampling distance (m)

200

0.710.53

3.5

2.2

400

0.350.26

3.5

1.1

800

0.170.13

3.5

0.55


OBSERVATIONS OF SURFACE FEATURES
To analyse the surfaces, the surface heights on a twodimensional grid are exported from the profilometer to a computer for analysis in Matlab. The columns of the height matrix H correspond to changes in surface height in the rolling direction and the rows correspond to the transverse direction. Surface maps of the initial strip and from samples taken after the first two passes are shown in Figure 1. The surface height is given by the greyscale at the side of the figure. The surface topography is dominated by roll marks running in the rolling direction, but there are also a number of isolated micropits. It is interesting to note that the roll marks seem to be spaced quite uniformly on the initial strip with a wavelength of about 100 m. For the initial strip, micropits are generally on the ridges of the roll marks. It appears that, during subsequent passes, the wavelength of roll marks becomes less uniform and that micropits are found on both the ridges and valleys.

SURFACE ANALYSIS
In this section the change in surface topography during rolling, which can clearly be observed from the surface maps, Figure 1, will be quantified, both to help characterise these surface changes and to provide a more objective definition of the changes in surface topography. In section 4.1 a spectral analysis of the surfaces is described, while section 4.2 outlines a method for identifying micropits.

Spectrum analysis
For a given onedimensional discrete data array of the surface heights, , the single sided power spectral density S (1/) can be found using a Fast Fourier Transformation (FFT) [9, 10] with a Hanning window [11].
, (2)
where is a coefficient of FFT of the data array, is the conjugate of , is the mean square of the window factor, , and is the sampling frequency, . The corresponding frequency is , .
S (1/_{j}) represents the contribution to the variance of heights of the component with wavelength _{j}. Therefore the contribution between wavelengths _{} and _{} is given by
(3)
Taking a fixed upper cutoff at the value of 200 m to eliminate waviness in the strip, ^{2}()=s^{2 }(, 200m) represents a cumulative roughness variance including all wavelength greater than .
For each row of data the onedimensional FFT is used to find the spectrum of the surface roughness across the rolling direction. Spectra for all the rows in the measured area are averaged to give an average spectral density across the rolling direction and the corresponding cumulative variance ^{2}.
4.2 Identification of roll marks and micropits
Although the surface roughness is mainly characterised by longitudinal roll marks, micropits become more prevalent at high rolling speeds. To identify these features, a zerophase forward and reverse digital filter (filtfilt in Matlab [11]) is applied to each column of the height matrix H, using a 4^{th} order lowpass Butterworth filter, with a cutoff wavelength _{r} typically of 25~50 m. The filtered height signal , containing wavelengths longer than _{r}, is taken as corresponding to the roll marks. This is illustrated in Figure 2a which shows the roll marks corresponding to the surface map of Figure 1a. The roll marks are then subtracted from the height array H to leave essentially the micropits. To discriminate between the pits and any 'noise' in the signal, only regions which are deeper than a critical value are identified as pits. These pits are in turn split into shallow and deep pits, with the division at a depth . Typically and are taken as 0.1 and 0.25 m. The shallow and deep pits corresponding to the surface map of Figure 1a are shown in Figures 2b and 2c respectively. The fraction of pitting area is quantified by dividing the total pixel area of the measurement by the pixel area of the pits.
RESULTS 
Roughness amplitude
The r.m.s surface roughness of the initial strip and foil samples taken after the first and second passes is shown in Figure 3a. The roll roughness _{r} is indicated by an arrow on the graph. Each point represents an average of ten measurements. Error bars indicate the standard deviation of measurements within this sample. The results show that the roughness on the bottom surface of the initial strip is significantly greater than on the top surface. Nevertheless, both sides of the surface have nearly conformed to the roll surface after the first pass, so that the difference between the two sides is then negligible. In the second pass, the surface roughness is further reduced slightly. The high degree to which the strip conforms to the roll surface reflects the small value of lubrication parameter _{s}, which is about 0.04 for the first pass and varies between 0.015 and 0.08 for the second pass.
Figure 3b shows the effect of _{s}, which is proportional to rolling speed, on the r.m.s surface roughness after the second pass. Since the surface roughness on both the incoming and outgoing strip is close to that of the rolls, any effect of _{s} on surface roughness is overshadowed by scatter in the measurements. Nevertheless, there appears to be a slight increase in the surface roughness at very small _{s}, which may be associated with a breakdown of lubrication.

Surface spectrum
Figure 4 shows the change in the surface spectrum during the pass schedule. The contribution of long wavelength components to the surface roughness falls through the pass schedule as these components are crushed more rapidly than the short wavelength components. This confirms the results of laboratory experiments [4] and predictions from theory [5]. Although the surface roughness of the strip after the first pass approaches that of the roll surface, there is a slight further change in the relative contributions of long and short wavelength components during the second pass, as the long wavelengths continue to be crushed more readily. Figure 4b shows that, for the second pass, there is no significant effect of rolling speed on the surface spectra. By this pass the actual changes in roughness are slight, and any effect due to differences in hydrodynamic oil entrainment at these small values of _{s} is too small to be detectable.
Figure 5 illustrates the change in surface spectrum from fresh to worn rolls. Figure 5a plots the spectral density and Figure 5b plots the cumulative variance, normalised by the r.m.s. roughness of each roll replica. Figure 5a shows that short wavelength components are most rapidly reduced in amplitude as the roll wears. The way in which the roll surface imprints on the strip surface can be seen from the change in shape of the curves, Figure 5b. The relative contribution from wavelengths shorter than 5µm (1/ > 200 mm^{1}), given by the difference between one and the cumulative variance at this frequency, is significantly greater for the strip rolled with a fresh roll than for the strip with the worn rolls. This reflects the reduction in short wavelength components on the roll surface as the rolls wear.

Variation of hydrodynamic pits
Figures 6 and 7 show the results of the pitting analysis for the first pass at a single speed and for the second pass at two rolling speeds. The dark regions on the maps shown in Figures 6 and 7 identify the shallow and deep pits, respectively. The corresponding maps for the initial strip are given in Figure 2. The fraction of the total area taken up by pits is quantified and plotted against pass number in Figure 8a and against _{s} in Figure 8b. Each point represents an average over an area of 0.350.25 mm^{2}. Figure 8a confirms the visual impression obtained from Figures 6 and 7, that the shallow pit area is almost unchanged but that the area of deep pits is significantly reduced during the schedule. It can also be seen from Figures 2 and 7 that the deep pits are reduced in size and area by each pass. Figure 8b shows that, for the second pass, there is a significant increase in pit area with increasing _{s}. This suggests that hydrodynamic action prevents elimination of the pits.
The earlier analysis of Le and Sutcliffe [7] gave qualitatively similar results for the pitting analysis as those presented here, but showed significant quantitative differences in pit area. For the aluminium foil surface described here the current method is to be preferred, as being both simpler and more accurate.

CONCLUSIONS

Surface roughness measurements on aluminium foil rolled under industrial conditions show that the surface of the strip nearly conforms to the roll surface after the first pass. Subsequent passes slightly reduce the surface roughness on the strip.

Spectral analysis confirms the results of laboratoryscale trials, that long wavelength components on the strip surface are flattened more rapidly than short wavelength components.

A program has been developed which successfully identifies the micropits on the strip surface. Results show that both the area and size of deep pits are reduced during rolling. Deep pits are eliminated more effectively during the second pass at smaller values of speed parameter _{s}.
ACKNOWLEDGEMENTS
The authors wish to thank K. Waterson, D. Miller (Alcan International Ltd.), P. Reeve and C. Fryer (Alstom Drives and Controls Ltd) and all the personnel at Alcan Glasgow for their help with the trials. The authors are obliged to R. Ahmed for his help with the hydrodynamic pitting analysis. Financial support from EPSRC, Alcan Int. Ltd., Alstom Drives and Controls Ltd. and The Newton Trust is greatly acknowledged.
REFERENCES

Schey JA, “Surface Roughness Effects in Metalworking Lubrication”, Lubrication Engineering, 39, (1983) 376382.

Wilson WRD and Walowit JA, “An Isothermal Hydrodynamic Lubrication Theory for Strip Rolling With Front and Back Tension”, Proc. 1971 Tribology Convention, I. Mech. E., London, (1972) 164172.

Tabary PE, Sutcliffe MPF, Porral F and Deneuville P, “Measurements of friction in cold metal rolling”, ASME J. Tribology, 118, (1996) 629636.

Sutcliffe MPF and Le HR, “Measurements of surface roughness in cold metal rolling in mixed lubrication regime”, To be published in STLE Tribology Transactions (2000).
Le HR and Sutcliffe MPF, “A twowavelength model of surface flattening in cold metal rolling with mixed lubrication”, To be published in STLE Tribology Transactions (2000). 
Ahmed R and Sutcliffe MPF, “Identification of surface features on cold rolled stainless steel strip”, Submitted to Wear, 1999.

Le HR and Sutcliffe MPF, “Surface finish of coldrolled aluminium foil”, To be presented at the Institute of Materials Conference on Metal Rolling Processes, London, December 1999.

Sutcliffe MPF, “Flattening of random rough surfaces in metal forming processes”, ASME J. Tribology, 121 (1999) 433440.

Moalie H, Fitzpatrick JA and Torrance AA, “A spectral approach to the analysis of rough surfaces”, ASME J. Tribology, 111, (1989) 359363.

Ju Y and Farris TN, “ Spectral analysis of twodimensional contact problems”, ASME J. Tribology, 118(2), (1996) 320328.

Matlab, The Mathworks Inc., (1994).
