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 m. 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
1
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
q
Reduced hydrodynamic pressure; q  1  exp( pv ) 
r
Reduction in strip thickness
R
Roll radius
t0
Initial strip thickness
U
Mean entraining velocity
x
Y
Co-ordinate in rolling direction

Pressure viscosity coefficient of lubricant

Temperature viscosity coefficient of lubricant
 (0)
Viscosity of lubricant (at ambient pressure)
 s  hs  t 0
Ratio of the theoretical smooth film thickness to the initial combined
strip and roll roughness

Average friction coefficient
µp
Friction coefficient on the plateaux
v
Friction coefficient in the valleys
0
Angle between roll and strip at the inlet to the bite
, (0)
(Initial) r.m.s. amplitude of the short wavelength components of strip
roughness
t0
Initial combined r.m.s amplitude of the strip and roll including both
short and long wavelengths
rr
r.m.s amplitudes of the short and long wavelength components of the
roll roughness
, (  0 )
(Initial) r.m.s. amplitude of the long wavelength components of strip
roughness
Plane strain yield strength of the strip
2
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
hs 
6 0U
 0 1  exp  Y 
(1)
where U is the average entraining velocity,  0 is the inlet angle between the strip and
roll, Y is the plain strain yield strength of the strip and  0 is the viscosity of the
lubricant at ambient pressure.  is the pressure viscosity coefficient in the Barus
equation   0 exp(p) used to describe the variation of viscosity with pressure p.
The ratio  s  hs  t 0 of the smooth film thickness hs to the combined roll and
initial strip roughness t0 is used to characterise the lubrication regime. For large 
the surfaces are kept apart by a continuous film of oil. The mixed lubrication regime,
with some asperity contact, occurs when s falls below about 3. A simple picture of
the interface between the roll and strip divides the contact into areas of contact and
3
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
  A p  1  A v
(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 s, to complete conformance of the surfaces and friction typical of boundary
additives for very small s. 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 s, 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
4
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 1.0 m/s. Before rolling,
the strips had a micro-Vickers hardness Hv of 550 MPa, giving an estimated yield
5
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   0 exp   t  t r  , where t and tr are actual and reference
temperatures, to extract values for the temperature viscosity coefficient  and the
viscosity  at a typical rolling temperature of 25°C. These are detailed in Table 1.
Room temperature was recorded to estimate values for  in each set of tests.
Oil type
 (Pas, 25C)
 (C–1)
 (m2/N)
100 SUS
0.041
0.0419
(2.010–8)
500 SUS
0.271
0.0647
2.010–8
2000 SUS
1.44
0.0896
3.010–8
Table 1 Properties of lubricants
The pressure viscosity coefficient  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 
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 t0
of the roll and strip (here t0 = 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  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  are in good agreement
with published figures (Evans and Johnson, 1986). For the thinnest 100 SUS oil,
6
where it was not possible to make accurate film thickness measurements due to the
thinness of the films, a value of  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 m 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 , while wavelengths between this
arbitrary breakpoint wavelength and an upper cut-off are summed to estimate a long
wavelength amplitude . In this case we choose to divide the spectrum between short
and long wavelengths at 14 m, with an upper cut-off wavelength of 250m. The
initial r.m.s. contributions from the short and long wavelength components 0 and 0
for the initial strip surface were 0.12 and 0.36 m and the corresponding values r and
r for the roll were 0.024 and 0.048 µm. The total combined roughness
 t 0   02   02   r2   2r for the initial strip and roll surfaces equalled 0.38 m.
3 Experimental results
7
Measurements of surface roughness of the strip were made and split into long and
short wavelength components  and  at an arbitrary wavelength of 14 m, as
described in the previous section. Results for the effect of film thickness ratio  s ,
roughness wavelength and strip reduction ratio on the flattening behaviour are
presented in this section.
3.1 Effect of film thickness parameter and wavelength
Figures 3 and 4 show changes in strip roughness amplitude with film thickness
parameter  s , for reductions in strip thickness of 25% and 50 %, respectively. The
roughness is split into short and long wavelength components  and , which are
normalised by the original strip roughness amplitudes  0 and  0 . Note that  s is
based on the initial combined roughness t0, which includes short and long
wavelengths. The wide range of  s was achieved in the experiments by varying the
speed and by using the three different oils. The range of  s covered by each oil is
indicated at the bottom of the figures. The corresponding roll roughness amplitudes
 r  0 and  r  0 are indicated by arrows at the left hand side of the figures. For
 s greater than about 2, 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 micrometres. For  s less than 2, 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  s 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  of the amplitudes of the short and long wavelength components. When the
speed parameter is greater than about 2, the ratio  falls below the corresponding
value of 0.33 for the initial strip roughness due to the roughening of the long
wavelength component. For  s between about 0.5 and 2,  increases with
decreasing  s as the long wavelength components flattens faster than the short
wavelength components. For  s below 0.5,  falls off again with decreasing  s as
8
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  s  approaches the value of 0.5 corresponding to the roll roughness.
3.3 Effect of reduction
To compare the effect of reduction on flattening behaviour, Fig. 6 shows the change
in the short wavelength component of roughness  for the two reductions of 25% and
50%, as a function of  s . The amount of asperity flattening and the conformity of the
strip surface to the roll surface is significantly greater, at the same values of  s , for
the higher reduction. Existing theoretical models suggest two reasons why reduction
might affect the flattening behaviour. 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.
In the Appendix, however, it is shown that the transition region is short compared
with the bite length in these experiments, so that the theoretical models cannot explain
the difference between results at the two reductions satisfactorily. However, the
experimental results of Tabary et. al. (1996) showed that, at the same value of  s
friction was significantly greater at a higher reduction. This is in accordance with the
greater conformance between roll and strip observed here.
3.4 Height probability density functions
Height probability density functions for typical tests with 500 SUS oil at a 25%
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
250µm. A smooth curve has been drawn through the average of histograms from 3
roughness profiles. The speed parameter  s and smooth film thickness hs
corresponding to each curve are included in the figure. As  s 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.
4. Conclusions
9
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 behaviour is similar to that observed for
unlubricated strip rolling (Sutcliffe, 1998). Other surface roughness changes confirm
previous observations. For example a good conformance between roll and strip is
observed at small values of s, (the ratio of the smooth film thickness to the combined
surface roughness), and hydrodynamic roughening occurs for s greater than about 1.
Flattening of both short and long wavelengths was significantly greater, for the same
value of s, 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 behaviour 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.
Acknowledgements
The authors wish to thank Prof. Bill Wilson and Mr. Heng-Sheng Lin at Northwestern
University, USA for their assistance and Mr Chris Pargeter at Alcan Int. Ltd. for his
measurements of oil viscosity. The financial support of the Centre for Surface
Engineering and Tribology at Northwestern University, the Fulbright Commission,
the Engineering and Physical Sciences Research Council, Alcan Int. Ltd. and Cegelec
Projects Ltd. is gratefully acknowledged.
10
References
Azushima, A. 1978, “Characteristics of lubrication in cold sheet rolling”, Proc. 1st Int Conf. On
Lubrication Challenges in Metalworking and Processing, (IITRI, Chicago).
Cheng, H. S., 1966, “Plasto-hydrodynamic Lubrication”, ASME, Friction and Lubrication in Metals
Processing, New York, pp 69-89.
Evans, C.R. and Johnson, K.L. 1986, The rheological properties of elastohydrodynamic lubricants.
Proc. Instn. Mech. Engrs., Part C 200(C5), 313-324
Greenwood, J.A. and Rowe, G.W., 1965, Deformation of surface asperities during bulk plastic flow,
Wear, 38, 201-209
Hooke, C.J. 1977, The elastohydrodynamic lubrication of heavily loaded contacts. J. Mech. Engrg. Sci.
19, 149-156.
Lin, H. S., Marsault, N. and Wilson, W. R. D., 1998, “ A Mixed Lubrication Model for Cold Strip
Rolling Part I: Theoretical”, Submitted to Tribology Transaction.
Marsault, N., Montmitonnet, P., Deneuville, P. and Gratacos, P., 1998, “ A Model of Mixed
Lubrication for Cold Rolling of Strip”. Submitted to Tribology Transaction.
Marsault, N. 1998, Modélisation du régime de lubrification mixte en laminage à froid. PhD Thesis,
L'Ecole National Superieur des Mines de Paris, France.
Schey, J. A., 1983, “Surface Roughness Effects in Metalworking Lubrication”, Lubrication
Engineering, Vol. 39, pp 376-382.
Sheu, S. 1985. Mixed lubrication in bulk metal forming. PhD Thesis, Northwestern Univ., Illinois,
USA.
Sheu, S. and Wilson, W. R. D., 1983, “Flattening of workpiece surface asperities in metalforming”,
Proc. NAMRC XI, 172-178.
Sheu, S. and Wilson, W. R. D., 1994, “Mixed Lubrication of Strip Rolling”, STLE Trib. Trans., Vol.
37, pp 483-493.
Steffensen, H., and Wanheim, T., 1977, “Asperities on Asperities”, Wear, Vol.48, pp 89-98.
Sutcliffe, M. P. F., 1988, “Surface asperity deformation in metal forming processes”, Int. J. of Mech.
Sciences, 30, 847-868
Sutcliffe, M. P. F., 1998, “Flattening of Random Rough Surfaces in Metal Forming”, To appear in
A.S.M.E. J. Tribology.
Sutcliffe, M. P. F. and Johnson, K. L., 1990, “Lubrication in Cold Strip Rolling in the ‘Mixed’
Regime”, Proc. Instn. Mech. Engrs., Vol. 204, pp 249-261.
Sutcliffe, M. P. F.., 1990, “Experimental measurements of lubricant film thickness in cold strip
rollling”, Proc. Instn. Mech. Engrs., Vol. 204, pp 263-273.
Tabary, P. T., Sutcliffe, M. P. F., Porral, F. and Deneuville, P., 1996, “Measurements of friction in
Cold Metal Rolling”, ASME J. Tribology, Vol. 118, pp 629-636.
Tsao, P. and Wilson, W.R.D., 1981, Entrainment of lubricant in the cold rolling of steel and
aluminium, Proc. Int. Conf. On Steel Rolling, The Iron and Steel Institute of Japan, 49-64
Wilson, W.R.D. and Chang D.F. 1994, Low speed mixed lubrication of bulk metal forming processes,
ASME J Tribology ??
Wilson, W. R. D. and Walowit, J. A., 1972, “An Isothermal Hydrodynamic Lubrication Theory for
Strip Rolling With Front and Back Tension”, Proc. 1971 Tribology Convention, I. Mech. E., London,
pp 164-172.
Wilson, W.R.D. and Murch, L.E., 1976, A refined model for the hydrodynamic lubrication of strip
rolling, J. Lubrication Tech., 98, 426-432
Wilson, W.R.D. and Sheu, S., 1988, Real area of contact and boundary friction in metal forming, Int. J.
Mech. Sciences., 30, 475-489
11
Appendix
To evaluate the relative lengths of the inlet region and the bite, we adapt Hooke's
(1977) analysis for elastohydrodynamic contacts. Consider Reynolds' equation for the
variation in reduced oil pressure q  1  exp  p  for smooth surfaces

dq 120U h  h*

dx
h3

(3)
where x is a co-ordinate in the rolling direction, h is the separation between the roll
and strip and h* is the value of h at zero pressure gradient. The reduced pressure
gradient is zero far from the roll, and returns to zero at h = h*, which we can assume
occurs as the end of the inlet when the strip starts to deform plastically. The variation
in q with position x has a point of inflection some distance  ahead of the inlet; this
distance can be taken as a typical hydrodynamic inlet length. The position of this
inflection is given by the condition
d 2q
dx
2
 0  h  32 h *
(4)
Putting h* equal to the smooth film thickness hs (equation 1), and taking the bite
length L and the inlet angle 0 from the rigid roll geometry as
L  rRt 0 ;  0  rt0 R
(5)
where r is the strip reduction, R is the roll radius and t0 is the inlet strip thickness, we
deduce that the ratio of a typical hydrodynamic inlet length to the length of the bite is
equal to
h
 
3 0U

 s  s t0 
L 2 0 L
2rt 0
rt 0 1  exp  Y 
(6)
For a typical value of s equal to 0.1, and a reduction of 25%, the corresponding value
of /L is 10–3 in the present experiments. This suggests that changes in hydrodynamic
pressure are confined to a short inlet region. Similar conclusions can be drawn using
the non-dimensional speed groups defined by Wilson and co-workers (e.g. Wilson and
Chang, 1994).
12
Figures
Fig. 1. Schematic of surface roughness idealisations (a) triangular asperities,
(b) pseudo-Gaussian roughness (c) two superimposed wavelengths of roughness.
Fig. 2. Variation of experimental oil film thickness with smooth film thickness
parameter hs.
Fig. 3. Variation of short and long wavelength roughness amplitudes with s. Strip
reduction r = 25%.
Fig. 4. Variation of short and long wavelength roughness amplitudes with s. Strip
reduction r = 50%.
Fig. 5 Variation in the ratio / of the amplitudes of short and long wavelengths with s.
Fig. 6. The effect of reduction on the crushing of short wavelength asperities.
Fig. 7 The effect of s on the probability density function for the strip roughness
(r = 25%).
13
Area of contact
(a)
Valley
(b)
(c)
Fig. 1. Schematic of surface roughness idealisations (a) triangular asperities,
(b) pseudo-Gaussian roughness (c) two superimposed wavelengths of roughness.
14
Huirong
1. Could you please fill in the question marks in the paper.
2. Figure Changes
Fig 1 Correct this fig, the text and associated values of  and the other figures if
necessary to allow for thinning in the bite. Change the axes - x axis change hw for hs,
y axis delete ht
New fig 2 and new fig 3. Add bars to give the range of each of the oils. Add arrow
heads to the roll roughness points
X axis - delete speed parameter, leaving just Ls
Y axis - add amplitudes (i.e. surface roughness amplitudes S/S etc)
Figs 4 and 5 x axis - delete speed parameter, y axis add amplitude. Add arrow heads
to the roll roughness points
New Fig 6 needed.
Fig 7. Add arrows from labels to histogram plots.
3. Could you send a draft (with token figures but not necessarily all the changes) to
Keith Waterson and Peter Reeve(s) (could you check his name! and title) with a letter
with a Cambridge return address and the following text, putting my name at the
bottom and signing it yourself (adding after the signature (Huirong Le for Michael
Sutcliffe)
Dear Keith/Peter (as appropriate)
Friction in cold rolling project
Please could you look over the enclosed draft paper and confirm that it is OK for
publication, as per our agreement re publications in the friction modelling project. In
fact, in this case I believe that there should be no problem, as the work was essentially
done by myself in Northwestern, with writing-up help from Huirong. Please could
you write to the above address in confirmation. Thanks, and looking forward to seeing
you presently for further discussion of the project.
Michael Sutcliffe
(Signed by Huirong Le for M Sutcliffe)
Once we have heard back from Alcan and Cegelec, plus any further comments from
yourself, then this is ready to go.
michael
15
16