identiﬁcation of surface features on cold-rolled stainless...

Wear 244 (2000) 60–70

Identification of surface features on cold-rolled stainless steel strip

R. Ahmed1, M.P.F. Sutcliffe∗Cambridge University, Department of Engineering, Trumpington Street, Cambridge, CB2 1PZ, UK

Received 9 July 1999; received in revised form 17 May 2000; accepted 15 June 2000

Abstract

A novel method based on three-dimensional profilometry data andMatlab analysis software is described to identify surface featureson cold-rolled stainless steel strip. The aim of the method is to detect automatically pits and roll marks that can be observed in opticalor SEM micrographs. Pits are identified by locating regions which are significantly deeper than the immediately adjacent surface. Deepor steep features which extend a significant distance in the direction of rolling are identified as roll marks. Results for typical cold-rolledstainless steel sheet show that the algorithms are effective in identifying the more obvious pits and roll marks. By suitable adjustment ofthe tolerances used in the analysis, the method can be tailored to detect less severe features. Application of the method, either for researchpurposes or routine industrial inspection, will require tuning of these tolerances to detect pits of the severity relevant to the end use of thestrip. The methodology has been applied to a series of rolled strip samples to track the evolution of pits and roll marks during a schedule.Results show how the initially large area of deep pits is rapidly eliminated and transformed into shallow pits. The pit identification methodis used to estimate the effect of trapped oil on lubrication. Results suggest that this expelled oil will contribute significantly to the lubricationof the surrounding area. Finally, a good correlation is demonstrated between strip surface reflectance measurements and the estimated pitarea. © 2000 Elsevier Science S.A. All rights reserved.

Keywords:Stainless steel; Rolling; Pits; Voids; Surface characterisation

1. Introduction

Control of surface finish is a major concern in the man-ufacture of stainless steel strip. Prior to the cold-rollingoperation, the hot band is annealed, shot-blast and pickled,leaving a comparatively rough and broken surface, as illus-trated in the scanning electron micrograph of Fig. 1a. Thebright finish or gloss required for many products is thengenerated during the cold-rolling operation on a clusterSendzimir mill. The flattening of the strip asperities duringrolling, particularly with a smooth roll surface, is greatlyenhanced by the bulk deformation of the underlying mate-rial [1,2]. As the strip is deformed, the deep features of thepickled surface are eliminated, to leave a large number ofrelatively shallow pits, as illustrated in Fig. 1b and c. Thesepits can significantly affect the visual appearance of thestrip, and may also play an important role in trapping lu-

∗ Corresponding author. Present address: Department of Mechanicaland Chemical Engineering, Heriot–Watt University, Riccarton, Edinburgh,EH14 4AS, UK.E-mail address:[email protected] (M.P.F. Sutcliffe).

1 Present address: Department of Mechanical and Chemical Engineering,Heriot–Watt University, Riccarton, Edinburgh, EH14 4AS, UK.

bricant during subsequent sheet forming operations. Duringrolling, roll grinding marks can also be transferred to thestrip to leave a surface finish on the strip, as illustrated inthe optical micrograph Fig. 4a, which may be undesirable.Hydrodynamic entrainment of oil into the bite tends to keepthe surfaces separated and prevents effective flattening of theasperities on the strip [3–5]. However, it also seems likelythat a significant amount of lubricant is trapped in isolatedpits on the strip surface. Build-up of hydrostatic pressurein this trapped oil will tend to prevent these features beingeliminated. Experimental measurements by Mizuno andOkamoto [6] with an artificial rough work-piece surfaceshow how trapped oil can be drawn out of the pits duringthe rolling process by the sliding action between the stripand the roll. An alternative approach considers the way inwhich oil is not completely trapped in the pits, but can flowout along channels in the rolling direction [7,8]. Variousexperimental [9–11] and analytical [12] studies have con-sidered these mechanisms, but the details of the lubricationmechanisms and the evolution of surface features remainsunclear.

Previous studies to quantify the evolution of surface fea-tures during cold rolling have been limited. Gjønnes [13]used laser-scanning microscopy to identify grooves, roll

0043-1648/00/$ – see front matter © 2000 Elsevier Science S.A. All rights reserved.PII: S0043-1648(00)00442-7

R. Ahmed, M.P.F. Sutcliffe / Wear 244 (2000) 60–70 61

Nomenclature

d Pit depth matrixh Surface height matrixi,j Indices in the rolling and transverse direction,

respectivelyn Number of points averaged to establish a

mean heightr Preliminary identification matrix for a roll markRqr Roll r.m.s. roughness amplitudeL Spanning length for estimating the mean height

either side of a pitM Length scale in the rolling direction for

identifying roll marks

Greek lettersδm Depth tolerance parameter for roll mark

identificationδp Depth tolerance parameter for pit identification∆ Sampling distance of surface measurementsφ Slope tolerance parameterθ Matrix of surface slopes estimated numerically

from height data

ridges and ‘shingles’ on cold-rolled aluminium. Ohkubo etal. [14] investigated the influence on the surface gloss ofaluminium foil of oil pits, ‘slags’, roll marks and small de-pressions. They quantified these defects using two-dimen-sional scanning electron microscope and three-dimensionalatomic force microscope observations, concluding that thedominant factor in determining surface gloss was oil pits.Kuznetsov [15] used a theoretical approach to derive awork-roll imprint factor, assessing the influence of work-rollwear on the formation of roll marks on the strip surface.Most of these studies relate to aluminium rolling. However,rolling of stainless steel strip differs significantly from alu-minium rolling as the pickling and shot blasting processesused in steel rolling may introduce gross surface defectswhich then have to be removed.

Current industrial practice in stainless steel rolling is touse surface reflectance and ‘distinctness of image’ tests tocharacterise the surface quality of rolled sheet. However,these techniques are sensitive to the surface chemistry, sheetroughness and angle of incidence, making accurate quan-titative comparisons difficult. Moreover, such approachesprovide no indication of the potential origin of poor surfacequality. There is, therefore, an urgent need for alternativemethods to be developed in order to better characterise thesheet surface quality. Recent advancements in surface pro-filometry (higher resolution, larger measurement areas andshorter measurement times) have made this possible. Forexample, Schmoeckel and Staeves [16] apply a functionalfilter to three-dimensional profilometry data to assess thetribological performance of steel sheet. Recent work by Leand Sutcliffe [17] describes a Fourier transform filtering

Fig. 1. SEM micrographs of the sheet surface after various passes:(a) the shot-blast and pickled surface; (b) after an intermediate pass; and(c) after the final pass.

technique to estimate the pit area on rolled aluminium sheetwhile Jiang et al. [18] apply wavelet analysis to surfaceroughness characterisation.

The aim of this paper is to use three dimensional profilom-etry to characterise the sheet quality based upon the detectionof surface features. The methodology used to identify perti-nent features is presented in detail, and illustrated by exam-ining the evolution of these surface features during a typical

62 R. Ahmed, M.P.F. Sutcliffe / Wear 244 (2000) 60–70

pass schedule. Results are interpreted in terms of lubricationmechanisms and correlated with surface reflectance tests.

2. Experimental test procedure

Samples of austenitic stainless steel sheet, of width 1.3 mand initial thickness 4.0 mm, were collected at variousintermediate stages of the manufacturing operation. Thehot band was annealed, shot-blasted and pickled prior tobeing cold rolled in a 20-high Sendzimir mill to a finalthickness of 1.5 mm. The work rolls, which were≈50 mmin diameter, were ground after the first pass and then re-placed with polished rolls towards the end of the sched-ule. A low-viscosity rolling oil with a kinematic viscosity<10cSt at 40◦C was used. Strip samples were collectedfrom across the width of the strip at either end of thecoil after selected passes. As the samples were collectedfrom positions on the coil after mill stoppage, potentialeffects due to hydrodynamic lubrication (arising from theentraining action at normal rolling speeds) will not bepresent.

3. Surface profilometry

A Zygo three-dimensional white-light interferometericprofilometer was used to measure the surface roughness ofthe sheet samples. The instrument has maximum lateral andvertical resolutions of≈0.5�m and 0.1 nm, respectively.Typically, the measurement area was 0.34 mm×0.26 mm.The data was recorded over an array of 320×240 pixels andthe pixel spacing for the standard measurements was about1.1�m. For the initial shot-blast surface, a larger measure-ment area of 2.75 mm×2.06 mm was used, with a corre-spondingly larger pixel spacing. The surface roughness ofthe work rolls was measured by replicating the roll surfaceusing a ‘press-on-film’ supplied by Testex, consisting of alayer of crushable plastic microfoam on a polyester sub-strate. The film was placed on the roll surface and rubbedusing a burnishing tool to transfer the roll topography tothe film. The accuracy of the technique was verified bycomparing the roughness measurements of a sheet surfaceand its corresponding replica. Measurements of the stripand roll surface for the various samples were repeated onthree regions of each strip. No filtering of the profile datawas used, except for subtraction of the mean plane. Theinitial roll roughness r.m.s. amplitude varied from 0.15�mfor the earlier passes to 0.05�m towards the end of theschedule. The roughness of the rougher rolls decreasedslightly during the pass schedule while the smoother rollsdid not change significantly. The in-going strip had an r.m.s.roughness amplitude of 6.9�m, which was reduced toabout 0.06�m after the final pass. Identification of surfacefeatures, as described in the following section, was carriedout by importing surface height data from the profilometry

measurements into the mathematical packageMatlab forsubsequent processing.

4. Observation of surface features

Fig. 1a shows a scanning electron microscope (SEM)image of the in-going sheet after annealing, shot blastingand pickling. Various features can be observed, includingshot-blast craters, fissures at the grain boundaries causedby preferential etching and micro-pitting within the grains.Fig. 1b and c show SEM images of the strip surface after anintermediate and the final passes, respectively, while Fig. 3aand Fig. 4a show the corresponding optical micrographs.For all these figures, the rolling direction runs in the verti-cal direction. Pits are typically 5–10�m in size. Althoughthe size and frequency of the larger surface pits decreaseduring the rolling schedule, a significant number of smallfeatures persist after the final pass. The optical micrographsshow clearly the way that the longitudinal roughness of therolls, generated during roll grinding, is transferred to thestrip surface as the strip conforms to the roll roughness inthe bite.

5. Identification of surface features — methodology

The above section shows that the main features observedon these strip surface samples are pits and roll marks. Al-gorithms described in this section aim at identifying thesefeatures automatically, to allow a quick, accurate and ob-jective quantification of the relative proportions of thesefeatures.

5.1. Identification of pits

A large number of dark, rather irregular pits can beobserved on both the optical and SEM micrographs ofFigs. 1, 3 and 4. Observations, both from such micrographsand from profilometry data, show that the size and depth ofthese pits changes during the rolling schedule, but that theyare mainly characterised by having rather steep sides, sothat the surface of a pit lies significantly below the adjacentsurface. This is illustrated by a typical two-dimensionaltrace taken along the rolling direction (Fig. 2). Algorithmsare described below to identify such pits, based on thisobservation.

Consider a matrix containing surface height data obtainedby three-dimensional profilometry. Elements of the matrixare denoted byh(i,j), where changes in theith index repre-sent variations in the rolling direction. To establish the meansurface height on either side of the current data point, wetake the mean ofn points at around a distanceL away fromthe point under consideration. Taking a profile transverse tothe rolling direction, the pit depthdt(i,j) relative to the sur-rounding area is thus given by


Fig. 2. Typical profile of strip after an intermediate pass taken in the rolling direction. Pits identified usingδp=0.66 andL=27�m are shown shaded.

dt(i, j) = 1

2n

k=j−L/∆+n−1∑k=j−L/∆

h(i, k) +k=j+L/∆∑

k=j+L/∆−n+1

h(i, k)

− h(i, j) (1)

Here,∆ is the pixel spacing of the profilometer data (seeSection 3). The spanning lengthL should be chosen to begreater than the width of a typical pit, withL/∆ an integer.A value ofn=4 was found to be appropriate to estimate theheight of the flat regions around the pit. A similar expressionis used to estimate the pit depthdr(i,j) based on a profilein the rolling direction, with the summation of Eq. (1) nowcarried out over theith index. The same values of the pa-rametersL andn are used for this longitudinal direction. Agiven data point is identified as being in a pit when the depthof the pit is greater than a critical value. Because of the rel-atively thin oil films in the rolling operation, we expect theunpitted region to have an r.m.s. roughnessRq close to thatof the rolls. Hence, it is appropriate to scale the pit depthcriterion by the roll roughnessRqr, so that the criterion foridentifying a pit becomes

dr(i, j)

Rqr> δp and

dt(i, j)

Rqr> δp (2)

whereδp is a dimensionless tolerance for the pit depth cri-terion, typically of the order one. In applying this tolerance,although significantly smoother rolls were used for the fi-nal passes, nevertheless the roughness of the rolls used forthe earlier passes (i.e. 0.15�m) was used throughout. Theeffect of this is discussed in Section 6.2. To allow for thepossibility of a neighbouring pit influencing the results ofthe above analysis, the procedure described was refined byrepeating the analysis of equations (1) and (2), replacingLby L/5 and taking a value ofn=2. Any points satisfying thecriterion of Eq. (2) with eitherL andn=4 or L/5 andn=2were included as pitted regions.

Having identified which pixels in an image are pits, thetotal pit area, expressed as a proportion of the total area ofthe sample, can be straightforwardly evaluated, as can the‘deep-pit area’, for a pit depth below 0.5�m.

It is evident that it will be difficult to identify small pitswhose depth is of the order of the roll roughness. The above

method, using rather small values ofn to identify a meanheight, will suffer from inaccuracies in establishing a meanheight. However, the obvious solution of taking more pointsto establish a mean height for the unpitted area does notnecessarily lead to an increase in accuracy, as it becomes in-creasingly likely that the set of points used to find the plateauheight now includes an adjacent pit. The above method waschosen as a compromise. The validity of the approach isjustified and appropriate values for the tolerance parameterssuggested in Section 6.1, where results are compared withvisual observations of the pits.

5.2. Identification of roll marks

Section 4 shows how, as the strip is reduced in thickness,grind marks on the roll may be transferred to the strip. Theseroll marks are characterised by being long, straight valleysor peaks running in the direction of rolling. Although theroll surface has a distribution of asperity shapes, it is onlythose roll marks generated on the strip surface which havea large height, depth or slope which will significantly af-fect its visual appearance. Algorithms are described belowwhich identify and quantify these roll marks, based on theseobservation.

The method described in Section 5.1 is used to assess theamplitude of the roll mark relative to the surrounding areaat a distanceL from the point under consideration, with theasperity depthdt(i,j) given by Eq. (2). For these relativelythin features, the number of pointsn averaged to find theheight of the adjacent region was taken as 2. The slopeθ(i,j),taking a profile in the transverse direction, is given by

θ(i, j) = h(i, j) − h(i, j + 1)

∆(3)

A preliminary identification of roll marks is made by com-paring the magnitude of the strip asperity depth and slopewith an appropriate tolerance value. Hence, a preliminary


identification matrixr(i,j) is given a value of one, represent-ing a putative roll mark, when∣∣∣∣dt(i, j)

Rqr

∣∣∣∣ > δm or

∣∣∣∣θ(i, j)

Rqr/λr

∣∣∣∣ > φ (4)

r(i,j) is put equal to zero when the above criterion is false.The dimensionless tolerances,δm, for the roll mark depthandφ for the slope, are of the order of one. As with the pitanalysis, for all passes the parameters for the roll used in theinitial and intermediate passes are taken. This has the effectrequired in practice of only picking up the severe roll markscoming from these rougher rolls, as discussed in Section6.2. This roll has an roughness amplitudeRqr of 0.15�mand a length scaleλr of 15�m (taking the distance at whichthe autocorrelation function falls to a value of 0.1), givinga typical slopeRqr/λr. of 0.01. Roll marks are characterisedby extending significantly in the rolling direction. To verifythis, the preliminary identification matrixr(i,j) is scanned topick out any features which extend a distance approximatelyequal toM in the rolling direction, giving a final criterionfor identifying roll marks as

i=M/∆∑i=−M/∆

r(i, j) ≥ M

∆(5)

whereM should be chosen so thatM/∆ is an integer. In prac-tice it was found helpful to put equal to zero the heighth(i,j)obtained from the three-dimensional profilometry for thosepixels identified as pits, before using the above algorithm.

6. Identification of surface features — results

The methodology of feature identification describedabove is applied in Section 6.1 to typical strip samples.Emphasis is placed on relating visual observations to thefeatures identified using the new algorithms. Section 6.2 ap-plies the method to a series of passes to show how featuresevolve during the pass schedule. In Section 6.3, a sensitivityanalysis is performed, to give guidance on an appropriatechoice of the various parameters needed in the identificationalgorithm.

6.1. Application of the methodology to typical strip surfaces

In this section, the methodology of Section 5 is appliedto strip samples taken after an intermediate and the finalpass. Fig. 3a shows an optical micrograph of the sheet sur-face after an intermediate pass and Fig. 3b gives the corre-sponding surface map obtained from the profilometer, withthe grey-scale intensity representing height according to thescale on the figure. The same part of the surface is covered inboth Fig. 3a and b, with an area of view of 340�m×260�m.For this pass, the rougher 0.15�m rolls were used. The dark

areas2 shown on Fig. 3c mark the location of pits identifiedusing the methodology of Section 5.1 with a pit depth tol-eranceδp=0.33 (based onRqr=0.15�m) and pit spanninglength L=27�m. Fig. 3d shows the relatively small num-ber of pits deeper than 0.5�m, identified using the sameparameters. Fig. 3e shows the effect on the estimate of thepit area of taking a larger pit depth toleranceδp=0.66. Acomparison of the visual plots, Fig. 3a and b with the anal-ysis plots, shows that the pits observed on the strip surfaceare clearly identified using the larger depth pit toleranceδp=0.66, Fig. 3e, confirming the effectiveness of the algo-rithm. With the smaller pit toleranceδp=0.33, Fig. 3c, manysmaller pits are identified, although it is likely that in thiscase the accuracy in identifying pits is reduced and someof these features are artefacts of the identification method.The location of pits identified usingδp=0.66 andL=27�mare marked by the shaded regions on Fig. 2, which shows atypical profilometer trace taken along the rolling direction.This figure confirms that the deeper pits are clearly identi-fied. The results for the smaller pits are less conclusive. Inthese cases, it is easier to judge the accuracy of the estimatesby comparing the analysis with the optical and profilometrydata (Fig. 3). The value of spanning lengthL is selected asbeing slightly larger than the biggest pits observed.

An appropriate choice of pit tolerance depends on whatpurpose the pit quantification is to be used for. In manycases, only the larger pits identified usingδp=0.66 may berelevant. If even the smaller pits are important, the loss ofaccuracy for a value ofδp=0.33 in identifying the pit areamay be acceptable. The sensitivity to these choices is furtherexplored in the next section.

Similar results are shown in Fig. 4 for the final pass, whichwas rolled with the smoother rolls of roughness 0.05�m.An optical micrograph and corresponding surface map forthis pass are given in Fig. 4a and b, while Fig. 4c shows thetotal pit area identified usingL=27�m andδp=0.33 (basedon Rqr=0.15�m). Pits seen on the visual plots are clearlyobserved using the identification algorithm. The depth tol-erance parameterδp has been based on the roughness of therougher rolls used for the earlier passes, so as to be consis-tent with the results presented in the following section. Acomparison of Fig. 3c and Fig. 4c, with the same nominalvalue ofδp=0.33, shows that the accuracy of the analysis ismuch greater for the final pass. In this case, a better indi-cation of the reliability of the identification method wouldhave been obtained by basingδp on the actual roll roughnessfor this pass to give a value ofδp=1.0.

Turning to the identification of roll marks, Fig. 3f showsresults on the strip sample taken after an intermediate pass,with a roll mark depth toleranceδm=0.66, slope toleranceφ=10, spanning lengthL=16�m and roll mark lengthM=11�m. Dark areas on this figure correspond to rollmarks below the mean surface, while light areas are roll

2 Note that the grid of small black dots on this figure (and similar darkor light dots on other figures) are an artefact of the plotting routine used.


Fig. 3. Surface features on a strip sample taken after an intermediate pass. The measurement area is 340�m×260�m in all cases: (a) optical micrograph;and (b) corresponding surface map obtained from profilometry data. The grey-scale indicates the surface height: (c) pits identified usingδp=0.33 andL=27�m; (d) pits deeper than 0.5�m identified usingδp=0.33 andL=27�m; (e) pits identified usingδp=0.66 andL=27�m; and (f) roll-grind marksidentified usingδm=0.66,φ=10, L=27�m andM=11�m.

marks above the mean surface. A comparison of this figurewith the optical view, Fig. 3a, shows that most work rollmarks have been identified. As with the pit identification,smaller values for the various tolerances can be used to de-tect less obvious roll marks. Fig. 5 shows similar results for

a replica taken from a freshly ground roll used during theintermediate passes, using the same algorithm tolerancesas above. Again dark areas correspond to valleys on thereplica, and hence to peaks on the roll surface. A compar-ison of Fig. 3f for the strip after an intermediate pass and


Fig. 5. Roll-grind marks identified on a replica of a freshly ground rollusing δm=0.66,φ=10, L=27�m andM=11�m. The measurement areais 340�m×260�m.

Fig. 5 for the roll replica show that the pattern of grindmarks on the work roll is very similar to that for the rollmarks seen on the strip, confirming the origin of the rollmarks. The relative area of grinding marks on the roll is≈19%, similar to the roll mark area of 21% on the sheetsurface for the intermediate pass.

6.2. Evolution of surface features during the pass schedule

The methodology described in Section 5 is applied to sam-ples collected during the pass schedule, as described in Sec-tion 2, to track the evolution of surface features. To explorethe effect of pit tolerance parameter on the pit analysis, val-ues ofδp=0.33 or 0.60 are used throughout the pass sched-ule, with L=27�m. For the roll marks, values ofδm=0.66,φ=10, L=27�m andM=11�m are used. Fig. 6 shows theevolution of total pit area, deep pit area (for pits deeper than

Fig. 6. Evolution of the relative area of surface features during the passschedule.

0.5�m) and roll mark area during the pass schedule as afunction of the overall reduction in strip thickness. It is worthremembering that the samples collected were taken fromthe ends of the coil (at reduced speed), so that these resultsmay not be typical of strip rolled under normal conditions.Fig. 6 shows how the initially large area of deep pits, dueto shot-blast damage and grain boundary etching, is rapidlyreduced. After several passes most of these deep pits havebeen eliminated or transformed into shallower pits. In thefinal passes, the area of the shallower pits is further reduced.

Results are qualitatively similar for both values of thedepth parameterδp although the actual pit area is larger forthe smaller value ofδp. Some of this difference in the laterpasses may be due to inaccuracies forδp=0.33. Probablythe value of total pit area withδp=0.60 gives a more ap-propriate measure of the relevant pits (cf. the analyses ofFig. 3). The depth tolerance parameter has been defined forall passes using the Rq of the rougher rolls used for theearlier passes. By using the same value ofδp throughoutthe pass schedule, this means that pits of the same absolutedepth are identified. Since pit identification will be more ac-curate in the later passes where the smooth rolls are used,this would lead to a reduction in the estimated pit area atthe change to the smoother rolls, irrespective of the actualchanges. However, the results of Fig. 3 suggest that this ef-fect is relatively insignificant usingδp=0.60. The alternativestrategy of retaining the same value ofδp, but now basedon the true roll roughness which changes through the passschedule, would introduce its own difficulties, as the abso-lute value of the depth tolerance would now change signifi-cantly between passes.

The roll mark area stays relatively constant up to the fi-nal pass, as the strip conforms to the roll during bulk de-formation. In the final pass, the strip now conforms to themuch smoother roll surface and most of the roll marks lefton the surface from previous passes are eliminated. For thesample taken after the final pass, it is useful to identify anygrinding marks left from the intermediate passes which arenot eliminated in the final pass. This is precisely the effectachieved in Fig. 6, using tolerance parameters based on theroughness of the roll used for the first passes, as describedin Section 5.2. Although we expect that any grinding markson the smooth roll used in the final pass would be trans-ferred to the strip, these small amplitude marks would notsignificantly affect the strip visual appearance.

6.3. Sensitivity analysis

Section 6.1 has demonstrated the applicability of the pitand roll mark identification methods. In this section, thesensitivity of results to the various parameters required isinvestigated. By presenting results for the pit area and rollmark as a proportion of the sample area, results should notbe sensitive to the sample area as long as the measurementarea is sufficiently large to be representative. A comparisonof results for the area used, 340�m×260�m, with measure-


ments at different magnifications confirmed that this sizeof area is adequate. Estimates of percentage pit area usingmeasurements at three locations on the surface of a samplefrom one of the earlier passes typically varied by a maxi-mum of ±3%, for a mean pit area of about 30%. Opticalmicrographs confirm that the pixel spacing of 1.1�m at themagnification used is adequate to resolve most of the rele-vant features on the surface. Although the geometry of thesmaller pits will not be accurately defined, this is not con-sidered to be a significant source of error.

In order to identify a mean height of the surrounding area,values ofn=2 and 4 have been used for the pit-and-roll markidentifications, Eq. (1). These small values were chosen toavoid errors in estimating the plateau height by including ad-jacent pits in the calculation. With these rather small values,the mean height will not be accurate enough to give reliableestimates of pit area for shallow pits associated with smallvalues of the tolerance parametersδm and δp. The results,Figs. 3–5, suggest that, for a value ofd equal to 0.66, thissource of error does not lead to significant errors in locatingthe pits and roll marks. For a value ofδp=0.33, Fig. 3c, itseems likely that some of the smaller pits are erroneouslyidentified or are not detectable in the optical micrograph.

6.3.1. PitsThe pit identification procedure contains two parameters,

the pit depth toleranceδp and pit spanning lengthL. Two ap-proaches are taken to assess an appropriate choice of theseparameters, by comparison with observations and by a sen-sitivity analysis. Section 6.1 illustrates how the choice ofpit-depth tolerance determines the number of pits detected,with a toleranceδp=0.66 appropriate to identify only themore prominent pits, whileδp=0.33 could be used to in-clude very small pits. Fig. 7 plots the effect of pit-depth tol-eranceδp and spanning lengthL on the total pit area, for asample taken after an intermediate pass. For very smallδp, alarge number of very minor dimples on the surface are iden-tified as pits. At the other extreme, with largeδp the analysisis insufficiently sensitive to pick up any of the features ofimportance. As discussed in Section 6.1, at an intermediatevalue of δp=0.66 most of the relevant features are identi-

Fig. 8. Effect of changes in the roll-mark depth toleranceδm and the relative contributions of the depth and slope criteria on the estimate of roll-markarea for an intermediate pass (φ=10, L=27�m andM=11�m).

Fig. 7. Effect of changes in the pit depth toleranceδp and the pit spanninglength L on the estimate of total pit area for an intermediate pass.

fied. At a smaller value ofδp=0.33, some further small pitsare identified, although some of these may be artefacts ofthe method. The value of pit area is sensitive to the exactchoice ofδp, with the correct choice depending on what sizeand depth of pits are considered of relevance. Fig. 7 showsthat, as long asL is greater than typical pit dimensions (e.g.L≥22�m), the analysis is not sensitive to this parameter.

6.3.2. Roll marksA similar sensitivity analysis was performed for identifi-

cation of roll marks. The parameters used in this algorithmare the roll-mark depth and slope tolerancesδm andφ andthe roll-mark spanning lengthL. Similar results to thoseshown in Fig. 7 demonstrated that, as long asL is taken tobe wider than the roll marks, results are insensitive to thechoice of this parameter. For the surfaces studied here,Lshould be >16�m. The relative contributions of the heightand slope criteria (Eq. (4)) to the roll-mark area, and thesensitivity to the choice of the depth toleranceδp are givenin Fig. 8. This figure shows that the roll-mark area is sensi-tive to the choice of depth tolerancesδm. For small values ofδm, the roll-mark area increases significantly as virtually allthe features on the strip surface are sufficiently deep, high orsteep to ‘count’ as roll marks. Fig. 8 shows that, for a valueof slope toleranceφ=10, the contribution from the slope cri-terion is small. As for the pit identification, the choice ofδm


Fig. 9. Oil film thickness due to trapped oil estimated by changes in the pit volume during rolling.

should be made based on the application. It is believed thatonly large or steep roll marks will affect the visual appear-ance, so that relatively large values of the depth and slopetolerances were chosen in the illustrative examples, Fig. 3fand Fig. 5.

Section 5.2 explains how the lengthM is used to verifythe features that extend significantly in the rolling direction.For the surfaces studied, a value ofM=11�m was found toachieve the required effect. Results did not change signifi-cantly whenM was increased to 32�m. The lower value is tobe preferred, as this reduces the accuracy needed in aligningthe samples before making interferometry measurements.

7. Estimate of lubrication conditions

As the samples were collected from positions on the coilwith reduced rolling speeds, hydrodynamic lubrication ef-fects due to the entraining action at normal rolling speedswill not be present. However, the amount of oil trappedin pits may still be representative of that at higher speeds.Hence, it is instructive to make some estimate, from thechange in strip surface during rolling, of the way in which thetrapped oil might be expelled from the pits and so contributeto the lubrication regime. Firstly, the methodology describedin Section 5.1 is used to identify the location and depth ofthe pits for samples from each pass, using the parametersδp=0.33 andL=27�m. It is unclear to what extent the oilcan fill the pits at the entry to the bite, so that two alternativeswere considered, either that the lubricant fills all the valleysor that pits are only filled up to a depth of 0.5�m. This lat-ter assumption is based on the supposition that there may beinsufficient time at the inlet for oil to fill up the deeper pits.The volume of oil trapped in the pits before and after eachpass can then be estimated. The difference is oil which is ex-pelled from the pits into the surrounding area during the pass.By supposing that this expelled oil spreads out over an areaaround the pit equal to the area of the pit itself, we can makean approximate estimate of the film thickness around the pitsat the exit of the bite. Estimates of the film thickness due toexpelled lubricant are shown in Fig. 9, for the assumptions ofeither completely filled pits or pits which are partially filled

Fig. 10. Correlation between the change in total pit area and surface glossduring the pass schedule.

to a depth of 0.5�m. Although this estimate of film thick-ness is very approximate, Fig. 9 indicates that there may be asubstantial film of oil caused by this expelled lubricant, per-haps of the order of 0.1�m. By comparison, hydrodynamicentraining action at normal rolling speeds is only expectedto generate films of the order of 0.01�m in thickness.

8. Effect of remnant features on sheet quality

Current industrial practice is to quantify sheet quality bymeasuring the surface reflectance. The gloss, defined as thepercentage of incident light reflected back, was measuredon the strip samples described in Section 2, at an incidentangle of 20◦, using a standard reflectance measurement de-vice. Typical results are shown in Fig. 10, showing a gradualimprovement in gloss with pass number. Also shown onFig. 10 is the change in total pit area during the pass sched-ule, estimated using a value ofδp=0.33, showing how theincrease in gloss correlates well with the reduction in pitarea. This result demonstrates that a good understanding ofthe evolution of surface features is a key to modelling theindustrially practical changes in surface reflectance.

9. Conclusions

A novel method has been described to identify sur-face features on cold-rolled stainless steel strip from three


dimensional profilometry data. The aim of the approach isto detect and quantify automatically those features that canbe observed in optical or SEM micrographs, to give quicker,more objective and more accurate results than visual meth-ods. Algorithms for identifying pits and roll marks aredeveloped, based on observations of these features on thestrip surface. Results presented in Section 6 show that thesealgorithms are effective in identifying pits and roll marksfor samples taken after an intermediate and the final passesof rolling. By suitable adjustment of the tolerances used inthe analysis, the method can be tailored to detect less severefeatures, although there may be a loss of accuracy. Thechoice of tolerance will depend on the perceived importanceof the size and depth of the features, as discussed in Section6.3. It is expected that application of the method, either forresearch or quality control purposes, would require calibra-tion against existing surface inspection methods, taking intoaccount the surface requirements of the product.

The methodology is applied in Section 6.2 to a series ofsamples taken through a pass schedule. Results show howthe initially large area of deep pits (i.e. >0.5�m in depth) israpidly eliminated and transformed into shallow pits. Theseshallower pits are not eliminated effectively until the finalpasses where a smoother roll is used. Similarly, the roll markarea only falls significantly with use of the smoother roll.The pit identification method is used to estimate the effectof trapped oil on lubrication. By following the change in pitvolume during the pass schedule it is possible to estimatehow much oil is expelled from the pits during each pass.Results suggest that this expelled oil will contribute signifi-cantly to lubrication in the roll bite. A good correlation be-tween strip surface reflectance and pit area is observed, il-lustrating that a good understanding of the evolution of sur-face features is a key to modelling the industrially practicalchanges in surface reflectance.

The method described in this paper gives similar resultsto the Fourier transform filtering method developed recentlyby Le and Sutcliffe [17] to identify pits on rolled aluminiumstrip. The simplicity in implementing that method makes itan attractive alternative to the work presented in this paper.The advantage of the current work is that it is easy to applya variety of criteria tailored to the characteristics of the dif-ferent features observed on the strip. The wavelet analysismethod described by Jiang et al. [18], although more com-plicated to implement, is also an useful alternative, as it candeal efficiently with features occurring at different lengthscales.

Acknowledgements

The authors are most grateful for permission to use thesamples and test results described in Sections 2 and 8, whichwere collected by staff at Avesta Sheffield and Corus plc. Thetechnical assistance of staff at these collaborating compa-

nies, including Dr Didier Farrugia and Mr Peter Freeman, atCorus, Swinden Technology Centre, and Messrs. Ken Kingand Andrew Backhouse at Avesta Sheffield, is gratefully ac-knowledged, as is the financial support of the collaboratingcompanies, the Engineering and Physical Sciences ResearchCouncil and the Isaac Newton Trust. The authors are grate-ful for additional measurements and analysis by Mr FotiosGeorgiades.

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