Wear 244 (2000) 71–78
Analysis of surface roughness of cold-rolled aluminium foil
H.R. Le∗ , M.P.F. Sutcliffe
Cambridge University Engineering Department, Trumpington Street, Cambridge, CB2 1PZ, UK
Received 24 December 1999; received in revised form 17 May 2000; accepted 15 June 2000
Abstract
This paper describes a detailed analysis of the surface finish of aluminium foil which has been cold-rolled under industrial conditions
in the mixed lubrication regime. The foil was rolled with freshly ground rolls at a constant speed for the first pass and at a wide range
of speeds for the second pass. 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 three-dimensional non-contact 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 micro-pits. 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 pit area during the pass schedule, while there was a significant increase in pit area with increasing rolling speed during a single pass.
© 2000 Elsevier Science S.A. All rights reserved.
Keywords: Roughness; Surface finish; Surface spectrum; Hydrodynamic pitting; Mixed regime; Lubrication; Metal rolling
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 arisen in
modelling friction and modifications of surface roughness
during rolling, 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 and
the surface roughness on the rolls and the in-going strip [1].
The lubrication regime can be characterised by Λs , the ratio
of the lubricant film thickness hw to the
p combined surface
roughness on the strip and roll, σt = σs 2 + σr 2 . The film
thickness hw can be estimated, using the results of Wilson
and Walowit for smooth rolls and strip [2] as,
hw =
6ηα Ū
θ0 (1 − exp (−αY ))
(1)
∗ Corresponding author. Tel.: +44-1223-332609; fax: +44-1223-332662.
E-mail address: hl220@eng.cam.ac.uk (H.R. Le).
where U is the average entraining velocity, θ 0 the inlet angle
between the strip and roll, Y the plain strain yield strength
of the strip, η the viscosity of the lubricant at ambient pressure and α the oil’s pressure viscosity coefficient. For thick
oil films with Λs greater than about 1, surface roughening
occurs due to the unconstrained deformation of different
grains [3]. 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 [4–7].
Measurements of friction coefficients in mixed regime on an
experimental mill by Tabary et al [8] show that the friction
coefficient is also correlated with Λs .
Details of the surface roughness topography may influence the behaviour of the strip both during rolling and in
subsequent use. Moreover, they often give clues as to the tribological behaviour in the bite. The effect of wavelength of
roughness has been explored using measurements of the surface spectrum on strip rolled in the mixed lubrication regime
on an experimental mill [9]. It is shown that short wavelength components persist more than the long wavelength
components. This is confirmed by a new model of surface
0043-1648/00/$ – see front matter © 2000 Elsevier Science S.A. All rights reserved.
PII: S 0 0 4 3 - 1 6 4 8 ( 0 0 ) 0 0 4 4 1 - 5
72
H.R. Le, M.P.F. Sutcliffe / Wear 244 (2000) 71–78
Nomenclature
f
sampling frequency of surface
measurement, f=1/1
Fj
(j=0,. . . ,n/2−1) complex FFT coefficients of a
data array
data array of surface heights
hi (i=1,. . . ,n)
smooth film thickness using the
hw
Wilson and Walowit formula
H (H̃ )
matrix of surface heights (after
low-pass filtering)
surface variance of the wavelength
s2 (λ1 ,λ2 )
between λ1 and λ2
S
single-sided power spectral density
U
average entraining velocity,
U =(Ur +Us )/2
w̄
meanP
square of a window vector,
w̄ = wi 2 /n
wi (i=1,. . . ,n) window vector
Y
plane strain yield stress of the strip
Greek
α
θ0
δ
∆
η
λ
σr
σs
σt
symbols
oil pressure viscosity index
inlet angle between the strip and roll (radians)
depth of pits
sampling distance of surface measurement
oil viscosity at ambient pressure
wavelength of the surface spectrum
r.m.s. surface roughness on the rolls
r.m.s. surface roughness on the strip
combined r.m.s. surface roughness of
the strip and roll
σ 2 (λ) variance of all wavelengths >λ
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 laboratory-scale tests and to
provide benchmarks for the theoretical models currently being developed. The spectral analysis of surface roughness
described in Ref. [16] 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
2.1. 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 ≈50%. Lubricant
was applied abundantly on both sides of the strip. Samples
of the initial strip were collected from the end of the coil.
After the first pass, a sample 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
Press-O-Film surface-replicating tape supplied by Testex.
2.2. Measurements of surface roughness
flattening [10], in which the surface roughness is modelled as
two wavelengths. Several authors have identified various features on the strip surfaces. For example, Gjønnes [11] used
laser-scanning microscopy to identify grooves, roll ridges
and ‘shingles’ on cold-rolled aluminium while Ohkubo et al.
[12] investigated the influence on the surface gloss of aluminium foil of oil pits, ‘slags’, roll marks and small depressions. Staeves and Schmoeckel [13] relate the tribological
behaviour to the surface topography. Ahmed and Sutcliffe
[14] describe a method for analysing three-dimensional surface topography obtained from cold-rolled stainless steel
samples to identify hydrodynamic pits and roll marks on the
surface, by considering the local differences in height between the pits and the un-pitted regions. 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 [15] 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.
Surface roughness was measured in a Zygo non-contacting
three-dimensional interferometric profilometer. The equipment has a lateral resolution of 0.5 ␮m and vertical resolution of 0.1 nm.
2.2.1. 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.
2.2.2. 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, 10 areas are
measured and averaged to give the average r.m.s roughness
H.R. Le, M.P.F. Sutcliffe / Wear 244 (2000) 71–78
Table 1
Details of the measurements
Magnification
Field of
view (mm)
Depth of
view (␮m)
Sampling
distance (␮m)
200
400
800
0.71×0.53
0.35×0.26
0.17×0.13
3.5
3.5
3.5
2.2
1.1
0.55
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 1.
3. Observations of surface features
In order to analyse the surfaces, the surface heights on
a two-dimensional 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 are shown in
Fig. 1. The surface height is shown on the grey scale at the
side of the figure. On both the top and bottom surfaces, the
surface topography is dominated by roll marks running in
the rolling direction, but there are also a number of isolated
Fig. 1. Surface maps for the initial strip of: (a) top surface (400×); and
(b) bottom surface (400×).
73
micro-pits. Clearly the roll marks are transferred directly
from the roll topography. However, the origin of these pits is
unclear. Suggestions that they may arise from unconstrained
deformation, in the regions where there is an oil film between
the surfaces [3], seem to be confirmed by the way that the
pits in Fig. 1a are strung along in rows running in the rolling
direction. Once created, these pits may persist for several
passes before they can be eliminated (c.f. Ref. [14]). It is
interesting to note that the bottom surface is much rougher
than the top surface, with more closely spaced and much
higher ridges but fewer pits. These differences presumably
arise from differences in roll roughness and lubrication conditions between the top and bottom surfaces in the previous
passes. The roll marks seem to be widely spaced on the
initial strip with a wavelength of about 100 ␮m. The surface
maps of the first and second passes are shown in Fig. 2. It
appears that, during these subsequent passes, the wavelength
of roll marks becomes less uniform and that micro-pits on
the surface are smaller than those on the initial strip.
4. Surface analysis
In this section, the change in surface topography during rolling, which can clearly be observed from the surface
Fig. 2. Surface height maps for the top surface of strip: (a) after first pass
(800×); and (b) after second pass (800×).
74
H.R. Le, M.P.F. Sutcliffe / Wear 244 (2000) 71–78
maps, Figs. 1 and 2, 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 micro-pits.
4.1. Spectrum analysis
For a given one-dimensional discrete data array of the surface heights, hi , (i=1,. . . ,n), the single-sided power spectral
density S (1/λ) can be found using a fast Fourier transformation (FFT) [17,18] with a Hanning window [19].
2Fj F j
n
1
, j = 0, . . . , − 1
(2)
=
S
λj
nwf
2
where Fj is a FFT coefficient of the data array, F̄j the conjugate
P of Fj , w̄ the mean square of the window factor, w̄ =
( wi2 )/n, and f the sampling frequency, f=1/∆. The corresponding frequency is 1/λj =jf/n, (j=0,. . . , n/2−1).
Now, S (1/λj ) represents the contribution to the variance
of heights of the component with wavelength λj . Therefore,
the contribution between wavelengths λ1 and λ2 is given by
Z 1/λ1 1
1
2
d
(3)
S
s (λ1 , λ2 ) =
λ
λ
1/λ2
Taking a fixed upper cut-off at the value of 200 ␮m to eliminate waviness in the strip, σ 2 (λ)=s2 (λ, 200 ␮m) represents
a cumulative roughness variance including all wavelengths
>λ, but less than the upper cut-off.
For each row of data, the one-dimensional 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 σ 2 .
Fig. 3. Surface height maps for initial strip: (a) roll marks; (b) pits
identified by λr =50 ␮m, δ=0.10 ␮m; and (c) pits identified by λr =50 ␮m,
δ=0.25 ␮m.
4.2. Identification of roll marks and micro-pits
Although the surface roughness is mainly characterised
by longitudinal roll marks, micro-pits become more prevalent at high rolling speeds. To identify these features, a
zero-phase forward and reverse digital filter (filtfilt in Matlab [19]) is applied to each column of the height matrix H,
using a 4th -order low-pass Butterworth filter, with a cut-off
wavelength of λr , typically of 25–50 ␮m. The filtered height
signal H̃ , containing wavelengths longer than λr , is taken as
corresponding to the roll marks. This is illustrated in Fig. 3a
which shows the roll marks corresponding to the surface map
of Fig. 1a. The roll marks are then subtracted from the height
array H to essentially leave the micro-pits. To discriminate
between the pits and any ‘noise’ in the signal, only regions
which are deeper than a critical value δ are identified as pits.
Typically, 0.1<δ<0.25 ␮m. The pits corresponding to the
surface map of Fig. 1a are identified using different δ and
shown in Fig. 3b and c, respectively. It is noted that some
small areas in Fig. 3b are probably due to noise in the height
signal rather than being hydrodynamic pits. Therefore, it is
more appropriate to identify the pits with δ=0.25 ␮m. The
fraction of pitting area is quantified by dividing the total
pixel area of the measurement by the pixel area of the pits.
5. Results
5.1. 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
Fig. 4a. The roll roughness σ r is indicated by an arrow on the
graph. Each point represents an average of 10 measurements.
Error bars indicate the standard deviation of measurements
within this sample. Results show that the roughness on the
H.R. Le, M.P.F. Sutcliffe / Wear 244 (2000) 71–78
Fig. 4. Roughness amplitude (r.m.s.) of strip samples. (a) Change during
the pass schedule; and (b) the effect of Λs during the second pass.
bottom surface of the initial strip is significantly greater
than on the top surface, as observed in Fig. 1. 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 Λs , which is about 0.04 for
the first pass and varies between 0.015 and 0.08 for the
second pass.
Fig. 4b shows the effect of Λs , 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
Λs 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 Λs , which
may be associated with a breakdown of lubrication.
5.2. Surface spectrum
Fig. 5 shows the change in the surface spectrum during the pass schedule. The contribution of long wavelength
75
Fig. 5. The change in the strip surface spectrum during rolling: (a) spectral
density; and (b) cumulative surface variance, normalised by the strip
roughness variance.
components to the surface roughness falls through the pass
schedule as these components are crushed. The increase in
the high-frequency components (30–100 mm−1 ) in the first
pass arises as the strip conforms to the fresh rolls used for
this pass, which contain large high-frequency components.
Presumably worn rolls were used to produce the initial strip
surface, giving only a small high-frequency component to
the ingoing strip. Although the surface roughness amplitude
of the strip after the first pass approaches that of the roll
surface, there is an increase in the relative composition of
short wavelength components during the second pass, as the
long wavelengths are crushed more readily. This is in line
with the results of laboratory experiments [9] and predictions from theory [10]. Fig. 5b 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 Λs is too small to
be detectable.
Fig. 6 illustrates the change in surface spectrum from
fresh to worn rolls. Fig. 6a plots the spectral density and
76
H.R. Le, M.P.F. Sutcliffe / Wear 244 (2000) 71–78
Fig. 6. The effect of roll roughness on strip surface spectrum: (a) spectral
density; and (b) cumulative surface variance, normalised by the strip
roughness variance.
Fig. 6b plots the cumulative variance, normalised by the
r.m.s. roughness of each roll replica. Fig. 6a 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, Fig. 6b. The relative contribution
from wavelengths <5 ␮m (1/λ>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.
5.3. Variation of hydrodynamic pits
Fig. 7 shows 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 Fig. 7 identify the pits. The corresponding map of pits for the initial
strip is given in Fig. 3c. The fraction of the total area taken
Fig. 7. Identification of pits for: (a) first pass; (b) second pass (Λs =0.015);
and (c) second pass (Λs =0.08); λr =25 ␮m, δ=0.25 ␮m.
up by pits is quantified and plotted against pass number in
Fig. 8a and against Λs in Fig. 8b, for two values of pit depth
tolerance δ. Each point represents an average over an area of
0.35×0.25 mm2 . The estimated area of pitting is larger for
the smaller value of δ. Also including shallower pits using
the smaller δ, some points are spuriously identified as pits.
The curve for δ=0.25 ␮m is, probably, to be preferred, unless the smaller pits are expected to play a significant role
in subsequent operations. A value of δ equal to 0.25 ␮m
corresponds to about 60% of the Rq roughness of the rolls.
Ahmed and Sutcliffe [14] come to similar conclusions about
the appropriate choice of pit tolerance parameter using their
H.R. Le, M.P.F. Sutcliffe / Wear 244 (2000) 71–78
77
6. Conclusions
1. 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.
2. Spectral analysis confirms the results of laboratory-scale
trials, that long wavelength components on the strip surface are flattened more rapidly than short wavelength
components.
3. A program has been developed which successfully identifies the micro-pits 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 Λs .
Acknowledgements
The authors wish to thank K. Waterson, D. Miller (Alcan
International Ltd), P. Reeve and C. Fryer (ALSTOM Power
Conversion 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
Power Conversion Ltd and The Isaac Newton Trust is gratefully acknowledged.
Fig. 8. Pitting area of strip samples: (a) change during the pass schedule;
and (b) the effect of Λs during the second pass.
References
alternative identification algorithm. Fig. 8a confirms the visual impression obtained from Fig. 7, that the area of pits
is significantly reduced during the schedule. It can also be
seen from Fig. 3c and Fig. 7 that the deep pits are reduced
in size and area by each pass. Fig. 8b shows that, for the
second pass, there is a significant increase in pit area with
increasing Λs . This suggests that hydrodynamic action may
prevent the elimination of the pits.
The earlier analysis of Le and Sutcliffe [15] gave quantitatively similar results for the pitting analysis as those
presented here for δ=0.25 ␮m. Their method, which uses
a linear least-squares fit to data in the rolling direction to
eliminate the roll marks, falls half-way between the approach described in this paper and the ad-hoc and more
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