Predicting Traction in

K. S. Ducotey
Web Handling
A simple algorithm has been developed for predicting traction in web handling
J. K. Good applications. Minimal traction exists when the minimum air film height between the
roller and web is greater than three times the rnis roughness of the two surfaces in
Web Handling Research Center, contact. Classical foil bearing theory modified for permeable surfaces is used to
School of Mechanical determine the air film height. A piecewise linear solution using squeeze film theory
& Aerospace Engineering, is also used to account for side leakage. The minimum air film height is a function
Oklahoma State University, of web tension, web and roller velocity, air viscosity, web width, web permeability
Stillwater, OK 74078 and roller radius. The algorithm is applicable for permeable and nonpermeable webs.
Values obtained from the algorithm can be used to predict if sufficient traction is
available between the web and roller for a given set of physical and operating
parameters. Traction values can also be used as input for winding, wrinkling, and
spreading models.

1 Introduction be important variables controlling traction. Knox and Sweeney

(1971) examined the effect of the entrained air film thickness
The importance of accurately predicting traction can be seen on traction in their study of a web and a stationary roller. Jones
in many web handling applications. Traction for web handling (1992) developed a traction model which showed good agree-
purposes is defined as the equivalent frictional force consisting ment with his laboratory scale apparatus, but little agreement
of the tangential tractions between the web and roller, or be- existed between his theoretical and experimental results using
tween adjacent layers in a wound roll. The traction coefficient his plant scale apparatus. Ducotey and Good (1995) conducted
is the ratio of the equivalent frictional force to the normal force. an extensive parameter study on traction. All data was refer-
A web is typically defined as a continuous strip of flexible enced to a single curve because of an additional normal force
media thin in relation to its width that can be in the form of caused by electrostatic effects. Therefore, the study only showed
paper, plastic film, textile fabrics, or metal. the relative effects of the parameters tested. Muftu and Benson
An idler roller driven by a web needs sufficient traction to (1995) included the effects of web permeability and asperity
overcome bearing resistance. If insufficient traction is available contact in their theoretical study of a moving web and a station-
then the roller will move at a slower speed than the web. Low ary roller. However, their study involved one dimensional flow,
traction between a roller and web reduces the tracking ability therefore side leakage was not taken into account. Their numeri-
of the web through the process line and may cause web defects. cal technique involved discretizing the governing equations with
Traction also plays a significant role in determining whether a a finite difference approximation. The resulting system of equa-
wrinkle will form between a web and roller (Good et al., 1997). tions was then solved by a modified Newton-Raphson iteration
A wound roll may telescope (lateral slippage) if insufficient algorithm.
traction exists between adjacent layers. Longitudinal slippage The simple algorithm presented in this paper gives web han-
in a wound roll may also occur if the torque acting on the roll dling engineers a predictive tool for determining traction.
due to the web tension in the unwind process exceeds the torque
capacity (Vaidyanathan, 1996) at any radius within the roll.
A decrease in traction is a direct result of air being entrained 2 Formulation of Predictive Algorithm
between the web and roller. An air film develops between the 2.1 Air Film Thickness. This section summarizes a
roller and web as can be seen in a foil bearing (Gross, 1980). method for calculating the air film thickness between a roller
Some of the operating parameters that affect the air film thick- and a permeable or nonpermeable web. The summary in this
ness are the web velocity, web tension, and roller diameter. section is only intended to present an equation that will be used
When the air film thickness is small, the web is supported almost in the development of the traction algorithm. A more detailed
entirely by the asperities of the roller and web. Increasing the analysis can be found in Ducotey and Good (1998).
air film thickness results in less of the load being supported by A web and roller modeled as a porous journal bearing and a
the asperities and more by the lubrication film. Increasing the foil bearing is shown in Fig. 1. An air film of thickness, h,
air film thickness even further, may result in the web being separates the web from the roller. The web is under uniform
completely supported by the lubrication film. The available trac- tension across its width and its bending stiffness is negligible.
tion is then nothing more than the friction due to the viscous The analysis also assumes that the web and roller are perfectly
resistance of the air (Ducotey and Good, 1995) which is mini- smooth for the air film calculations.
mal.
A constant pressure region {P = TIR) exists between the
References to studies on traction related to webs and rollers web and roller in the fully floating condition. This region exists
in web handling are very limited. The first known study on between 6Q and 9i and has been shown to cover at least 95
traction in the open literature was by Daly (1965). Daly's study percent of the angle of wrap for most operating conditions. It
focused on traction between various grades of paper and steel is in this constant pressure region where the air film thickness
rollers. Web tension, web velocity, wrap angle, roller diameter, is constant for nonpermeable webs and decreases approximately
web permeability, web moisture, and paper grade were found to linearly from 6Q to Oi for permeable webs. This linear decrease
due to permeability can also be seen in IVIuftu and Benson's
(1995) analysis. A decrease in the air film thickness around the
Contributed by the Tribology Division for publication in the JOURNAL OF
TRIBOLOGY. Manuscript received by the Tribology Division February 9, 1998; angle of wrap is also noticed when side leakage occurs. Side
revised manuscript received June 15, 1998, Associate Technical Editor: J. Frene. leakage can become a factor when the web is narrow and the

618 / Vol. 121, JULY 1999 Copyright © 1999 by ASME Transactions of the ASME

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 No Side Leakage , .
Side Leakage r- h = h„-2i — p

h..-!

Fig. 1 Web and roller modeled as a foil bearing. Constant pressure

region shown between 0o and 01.

Fig. 2 Decrease in air film height around the angle of wrap due to web
permeability and side leakage
air film thickness is initially large. Therefore, a narrow perme-
able web such as newsprint running at high speeds can expect
a decrease in the air film thickness due to the combined effects then the change in air film thickness at the exit (see Fig. 2) is
of air flowing through the paper and out of the edges. Pressure expressed as,
preceding the tangent point {6 = 0) of the roller and web is
not great enough to cause any side leakage or permeability A/is.L. = ho - hs,i.. (3)
effects.
For most practical purposes it can be assumed that the con- where the height of the air film thickness due to side leakage
stant pressure region exists over the entire angle of wrap so that is given by.
an expression for calculating the air film thickness can be found 1
without going through a numerical solution. A decrease in the hs.L. = R (4)
air film thickness due to web permeability is indicated as AK i2p_(Ry 1
in Fig. 2 and can be calculated with the following expression.

hn-2[ — \6 xih>Q The air film thickness around the angle of wrap is now found
h{0) = { U (1)
by combining Eqs. (1), (3), and (4),
0 if/i < 0
where the permeability ( a ) is defined as the time required for 2 ( ^ 1 / 3 + A/tsx.
a specified volume (Vol) of air to flow through a given area d if /i > 0
(Ao) under a certain pressure drop ( A P ) , h{e) -= < (5)
_ (Vol/time) if/! < 0
AoAP The air film thickness (Eq. (5)) and the surface roughnesses
and the initial air film height at the entrance is defined as, of the web and roller which will be described in the next section
can now be used to predict traction.
h„ = kRe^" (2)
2.2 Traction Algorithm. A transition region in traction
If the web and roller are thought of as a squeeze film damper was described by Knox and Sweeney (1971) in their study of
consisting of two parallel plates, then a reasonable estimate of a web moving over a stationary roller. They found a distinct
the side leakage can be found. If the web falls uniformly from point at which a reduction in traction begins which will be
the entrance region to the exit region as air leaks out the sides. referred to as transition point " a . " They also found a point

Nomenclature
Ao = permeability tester orifice area w = web width 9= angular coordinate
k = constant = 0.643 P = wrap angle p= web density
m = web mass per unit area a = permeability = (Volume/time)/ lis = static coefficient of friction
Ra = average roughness (AoAP) Hr = traction coefficient
^^^Avg = (Raw + Ran)/! A/js.L. = change in air film height due to X= R/w
Rq = rms roughness side leakage i// = rja/R
Rqc = combined rms roughness = Aha = change in air film height due to e = R'ic/R
Uql + Rql web permeability n = PflAvg/^
R = roller radius /js.L, = height of air film due to side
U=Vw+V^ leakage Subscripts
V = surface velocity E = elastic modulus W = web
T = web tension (force/width) D = E^t = extensional rigidity R = roller
TH = downstream tension (force/ AP = pressure drop across web sample a = beginning of transition region
width) r] = dynamic viscosity of air = 18.3 b = end of transition region
Ti^ = upstream tension (force/width) X 10-'^ N-s/m^
t = web caliper e = 6r]U/iT- mVl)

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 Table 1 Range of operating and physical parameters used In the analy- a to transition point b as the lubrication film increases. Knox
sis
and Sweeney further described transition point b as the point
where the air film thickness is so large that the web and roller
are only touching at the tips of their asperities. Although a clear
Range of Parameters numerical value was not given for the surface roughnesses of
the web and roller in their study, it is commonly known that
Tension (N/cm) 0.17-2.87 minimal asperity contact occurs when the minimum lubrication
thickness (Ami„) is greater than 3 times the combined rms
Web Velocity (m/s) 0.071-25.4 roughness (Rgc) of the two surfaces (Harris, 1991). Hence, the
traction criteria for near zero traction at transition point b is
Wrap Angle (Deg) 90,92, 135, 180
taken as.
Roller Diameter (cm) 7.31, 12.70
hip) = K 3Rgc (6)
Permeability where,
(cmVs/cm^-kPa) 0,0.125,0.273,0.424
Rqc = Uql + Rql
Width (cm) 15.24,30.48
The traction criteria for transition point 'a' is not so easily
Roller Roughness defined. But, extensive experimental results (Section 4) from
(|jm rms) 0.229-11.557
commonly used rollers and webs in web handling suggests that
Web Roughness
the following works well.
0.406,0.737,3.378,
(Hm rms) 4.089, 4.496
h{Q) = RttA.^ (7)
where the average roughness of the web and roller (/JoAvg) is
defined as.
where traction is minimal which will be referred to as transition
point " b . " These transition regions can also be seen in the Ra Avg k{Ra„ + RUR)
work of Ducotey and Good (1995). Knox and Sweeney experi-
mentally measured the apparent coefficient of friction (//) be- Now, if a set of nondimensional parameters are defined as,
tween the web and roller. They found excellent correlation be-
tween the reduction in friction and the increase in air film thicks 6r]U R , rja
ness calculated with the foil bearing equation from Baumeister mVl' w
(1963). Their friction curve resembles a typical Stribeck curve
(Williams, 1994) where fx = fis for a very small lubrication ROA , ^ Rqc
film, then decreases approximately linearly from transition point n= (8)
R R

Table 2 Roller roughness parameters where rollers 7 and 8 were bead blasted and have a ceramic
and Teflon Impregnated coating. The remaining rollers are aluminum with a ground surface.

Roller D Ra Rq Rz Rmax Oa PC HSC

# (cm) (Hm) (Hm) (Hm) (urn) (Deg) (#/cm) (5%)

9 7.62 0.178 0.229 N/A N/A N/A N/A N/A

0.249 0.356 2.718 3.505

10 7.62 (0.086) (0.130) (0.762) (0.965) N/A N/A N/A

11 7.62 0.508 0.635 N/A N/A N/A N/A N/A

0.432 0.686 3.658 5.055 1.3 239 61

! 12.7 (0.127) (0.178) (1.194) (1.473) (0.2) (145) (48)

0.991 1.245
12 7.62 (0.178) (0.229) N/A N/A N/A N/A N/A

1.880 2.438 15.27 18.95

13 7.62 (0.231) (0.305) (1.854) (3.175) N/A N/A N/A

2.642 3.353 14.76 19,02 2.2 76 5

7 12.7 (0.330) (0.406) (1.803) (3.734) (0.1) (10) (3)

3.937 4.953 21.87 26.67 3.7 109 5

8 12.7 (0.533) (0.660) (2.870) (4.293) (0.5) (18) (3)

4.699 6.045 33.43 39.83 • 432 16

5 12.7 (0.533) (0.635) (2.946) (4.521) N/A (33) (10)

5.334 6.731 35 53 41 78 16.1 478 10

4 12.7 (0.203) (0.254) (2.438) (4.470) (0.3) (66) (6)

6 12.7 9.119 11.557 58.72 68.73 N/A 307 9

(0,787) (1.016) (6.477) (7.747) (38) (6)

620 / Vol. 121, JULY 1999 Transactions of the ASME

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 Table 3 Web properties of newsprint and polyester film (PET)

a
Roll (cmVs/cm^- t w P Rii Rq Rz Rmax
Web Type l.D. kPa) (mm) (cm) (kg/m') (11 m) . (urn). (11 m) (lim)

3.175 4.089 22.225 26.975

Newsprint NP-1 0.273 0.0711 15.24 678.2 (0.406) (0.508) (2.667) (3.683)

3,.531 4.496 23.622 28.448

Newsprint NP-2 0.424 0.0762 15.24 661.5 (0,406) (0.533) (3.073) (4.318)

2.667 3.378 17,780 20.853

New.sprint NP-3 0.125 0.0737 15.24 697.5 (0.305) (0.356) (1.727) (2.362)

Polyester 0,432 0.737 2.438 4.420

(PET)' PF-2 0 0.0.508 15.24 27.68 (0.229) (0.305) (1.016) (1,727)

Polyester 0,229 0,406 1.473 2,591

(PET)' PF-3 0 0.0559 30.48 30.45 (0.127) (0.178) (0.559) (0.965)

Polyethylene Terephathalate

These nondimensional parameters are substituted into Eq. (5). had a tip radius of 5 ^m with a measuring force of less than 4
Then using the traction criteria from Eqs. (6) and (7), a pair mN. Measurements were made using 5 evaluation lengths with
of equations for determining e at transition points a and b is the filter cut-off length set to 2.5 mm. The analog signal from
shown to be, the profilometer was also used for further analysis to determine
if the surfaces were Gaussian. A data acquisition system was
(9) used to receive the analog signal and then the surface profile
1 was analyzed with specially written software on a personal
•12^/? + = 3C (10) computer. A Kolmogorov-Smirnov (K-S) goodness-of-fit test
12^ (Bain and Engelhardt, 1992) was used to determine how
X' +
(kefy Gaussian the surfaces were. The K-S test compares the hypothe-
sized cumulative distribution function (CDF) with a CDF as-
A traction algorithm is then determined by solving Eqs. (9)
sembled from the measured results. A modified test statistic (X)
and (10) for e„ and ej, respectively, which are then substituted is calculated and if \ < 1.035 at the 0.01 significance level
into the following equation, then the Gaussian hypothesis is accepted. Most of the test traces
fJ-s 0 < £ < e„ had values of \ in the range of 2 - 3 . Therefore, the surfaces
could not be considered Gaussian at the 0.01 significance level.
fJ'S
(e,, - e) €„ < £ =s £,,
However, in comparing the hypothesized probability density
Me) = < (11)
functions (PDF) with a PDF histogram of the experimental
results, the distributions did take on a Gaussian form. Therefore,
e > £/, the surfaces were considered to be approximately Gaussian.
A total of 11 rollers were used in the experiment. Nine of
3 Experimental Method the rollers (#1, 4, 5, 6, 9, 10, 11, 12, and 13) were made of
3.1 Surface Roughness. Roughnesses of the webs and aluminum and were finished with a lathe mounted belt grinder.
rollers were measured using a stylus profilometer. The stylus Hence, having a circumferentially oriented roughness. The re-
maining two rollers (#7 and 8) were also made of aluminum
but were bead blasted to obtain an isotropic roughness. A ce-
10 ramic and Teflon® impregnated coating was then applied to the
1 1 lllllll 1 \\\m
,1-111111, two bead blasted rollers for wear resistance and low stiction.
R=6,36 cm
w=15,24cr n 0.438 ., Web media consisted of polyester film (PET)' and newsprint.
P=180° 1 1 1
T y 0.8761 ••
Samples of newsprint were retraced five times with the profi-
t=0.0508 m m
o p=27.68 k j 1^ ' lometer to see if ploughing occurred. No significant differences
o 2.189]
occurred in the roughness readings between each successive
trace. Therefore, the stylus force was sufficiently small so that
j ^ the profilometer could be used to measure the roughness of
newsprint.
y ^'
Results of the roughness measurements can be seen in Tables
< • 2 and 3. The following roughness parameters were recorded:
y
{\) Ra = arithmetic average, (2) Rq = rms roughness, (3) Rz
y f
= average peak-to-valley height, (4) Rmax = maximum peak-
/ • Nonpermeable tests
to-valley height, (5) 9a = mean slope, (6) PC = profile peak
"7 1 1 Mini 1 Mill density, and (7) HSC(5 percent) = high spot count at the 5
11 iiiiii 1 1 nil
0.1 1 10 100 percent slice level, Rz and Rmax are defined by DIN standards
(1996), while the remaining parameters are defined by ISO
Web Velocity (m/s) standards (1984). Standard deviations of the results are shown
Fig. 3 Percent decrease in air film heiglit in the exit region due to side
in parentheses ( ).
leakage. Maximum side leal<age that occurred during testing of the poly-
ester film was 2.7 percent at \ / „ = 7.6 m/s and T = 1.751 N/cm which
is negligible. ' Polyethylene Terephathalate.

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 0.35 r- Roller Roughness (jim rms)
Roller Roughness = 6.731 urn rms
Exoerimental Predicted
0.30 • 0.229*' 0.229" Web=PF-2
• 0,356" 0.356" Roller#=4
A 0.635" 0.635"
0.25 V 1.245" 1.245" Predicted
• 2.438" 2.438" — Mean
0.20 • 3.353* 3.353*
MT ® 4.963* 4.953*
Std. Dev.

Tests with PF-2 film Experimental

Tests with PF-3 film • l"Test

0.05

0.00
10 20 30 40
ho (^m)
ho (^^)
Fig. 6 Effects of air film thicliness [ho) and surface roughness on the
Fig. 4 Effects of air film thiclcness {ho) and surface roughness on tfie
traction coefficient (jur)- Roughness parameters used: (1) roller = 6.731
traction coefficient (/itr). Rollers having rms roughnesses ranging from
;<im rms and (2) polyester film - 0.737 /urn rms.
0.229-4.953 iim were tested.

li. 4- Torque//?
Mr In (12)
3.2 Traction Measurements. Most of the traction mea- 71 ,
surements were performed on a closed loop web line capable
of speeds up to 50.8 m/s. Web and roller velocities were mea-
sured with optical encoders. Web tension was controlled with 4 Discussion of Results
a damped pneumatic dancer and was measured using LVDT Experimental testing was done over a wide range of variables
tension load cells. Braking torque was provided by a magnetic as shown in Table 1. Polyester film and newsprint were used
hysteresis brake coupled to the roller. Torque was measured to examine the effects of nonpermeable and permeable webs
with strain gage slip ring torque sensors coupled between the on traction, respectively. Web and roller physical properties can
roller and brake. be found in Tables 2 and 3.
During testing, the web speed and tension are set at a de- The percent decrease in air film thickness due to side leakage
sired level. A back torque is then applied to the roller to can be seen in Fig. 3. This decrease reflects the difference in
intentionally cause slippage between the roller and web. Slip- the air film height (A/?S.L,) between the conditions of no side
page is detected by monitoring the velocity difference be- leakage and side leakage at the exit which can be seen in Fig.
tween the roller and web. Once slippage is detected, the up- 2. Values for the test parameters used in Fig. 3 are the following:
stream tension (TL), the web and roller velocities, and the (1) roller radius = 6.35 cm, (2) web width = 15.24 cm, (3)
amount of torque which caused the slippage is recorded. The wrap angle = 1 8 0 deg, (4) web caliper = 0.0508 mm, and (5)
amount of slip during the test is not critical since U = Vw + web density = 27.68 kg/m^ Rollers 7, 8, 5, 4, and 6 were
VK is included in the traction algorithm. The effective coeffi- tested using these parameters and a maximum side leakage of
cient of friction or the traction coefficient (/ir) is then calcu- 2.7 percent occurred at a web velocity of 7.6 m/s and a tension
lated using the belt equation. of 1.751 N/cm as shown in Fig. 3. Similar test parameters were

0.3 Roller Roughness = 11.557 urn rms

Roller Roughness = 6.045 |im rms
Web=PF-2
Roller#=6
Web = PF-2
Roller* = 5 0.2 Predicted
Predicted — Mean
— Mean • - Std. Dev.
- • - Std. Dev.
^T Experimental
Experimental • l"Test
0.1
• 1 " Test • Repeat
• Repeat w/new film
w/new film

0.0 1111111111 i-i 11 t i I I'ti 11111 ] 1111111

'I I \Jr\' I I I I I I I I
20 30 40 0 "a 10 20 30"b40 50 60 70
ho (lam) ho (^i m)
Fig. 5 Effects of air film thickness {ho) and surface roughness on the Fig. 7 Effects of air film thickness {ha) and surface roughness on the
traction coefficient (/ur). Roughness parameters used; (1) roller == 6.045 traction coefficient {/IT)- Roughness parameters used: (1) roller = 11.557
/um rms and (2) polyester film = 0.737 /im rms. fim rms and (2) polyester film = 0.737 /im rms.

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 0.5 r a = 0.125 (cm^/s)/(cm^-kPa) 0.6 r- a = 0.273 (cm^/s)/(cm^-kPa)
Experimental
0.4 Experimental
• 92°
• 135°
0.3 - A 180°
Predicted
Predicted
i^T 92° 92°
0.2 -
135°
- 180°
- Web = NP-3\ -.^
: Roller = #1 \ •••.
a,
0.0 ~ 1 1 1 1 1 1 1 1 1 K i i' 1 i H ] 1 1 1
Oe+0 1e-5 2e-5 3e-5 4e-5 5e-5

Fig. 8 Effects of web permeability {a = 0.125) and wrap angle {/}) on Fig. 9 Effects of web permeability [a = 0.273) and wrap angle (/3) on
the traction coefficient (jur). Roughness parameters used; (1) roller = the traction coefficient {fir). Roughness parameters used; (1) roller ="
0.686 /Km rms and (2) newsprint ~ 3.378 fim rms. 0.686 fim rms and (2) newsprint = 4.089 fim rms.

also used in testing rollers 9, 10, 11, 12, and 13 except that the a dip in the air film thickness occurs at the exit which is charac-
following were used: (1) web width = 30.48 cm, (2) roller teristic of foil bearings and may result in additional contact.
radius = 3.81 cm, and (3) wrap angle = 90 deg. Less side Licht (1968) indicated that if the foil's extensional rigidity (D
leakage occurred in this set of tests because of the larger web = Ey/t) is small, then the foil has a tendency to close the gap
width, smaller roller radius, and smaller wrap angle. Side leak- at the edges as the air pressure decreases to ambient. Edge
age can be considered negligible since the percent decrease was contact is also demonstrated in Muftu and Benson's (1996)
less than 2.7 percent for all cases. As a result, the air film theoretical analysis of a 2-D foil bearing. Parameters were cho-
thickness can be considered uniform around the angle of wrap. sen in their study so that asperity contact occurs at the edge of
Therefore, the air film thickness is taken as the value calculated the foil. Additional traction from edge and exit contact is not
at the entrance region (Eq. (2)) since no decrease occurs down- critical in the analysis, since its contribution is small compared
stream beyond that point. Data from testing rollers 4 - 1 3 are to what is needed to overcome bearing resistance.
therefore presented as a function of ho as shown in Figs. 4 - 7 . Results of further tests with rougher rollers are shown in
The transition points are still calculated using Eqs. (9) and (10) Figs. 5 - 7 . Polyester film (PF-2) was tested with rollers having
keeping a couple of things in mind. A nonpermeable web means rms roughnesses of 6.045, 6.731, and 11.557 ^m. A set of line
that t/* = 0, and no side leakage means that x = 0 as w -^ » . traces was taken with the profilometer described in Section 3.1.
The transition points can then be expressed as. The mean and standard deviation of the rms parameter (see
Table 2) was then determined from the set of values. The solid
h„ = kRel (13) line in Figs. 5-7 represents the traction curve that was calcu-
and lated by substituting the mean rms value into Eq. (10). Like-
wise, the dashed lines represent the upper and lower limits or the
(14) deviation from the mean found from substituting the standard
deviation of the rms parameter into Eq. (10). The experimental
Equation (11) is still applicable, but it is easier to make compar-
isons between the air film thickness and the surface roughness
when plotting the data as a function of ho which has more of a
physical meaning. In contrast, a uniform air film thickness does a = 0.424 (cm^/s)/(cm^-kPa)
not exist between a roller and a permeable web because of air
Experimental
flowing through the web. Therefore, data acquired from testing
a permeable web (newsprint) and roller #1 will be presented • 92°
as a function of e. Predicted values were calculated using Eq. 0.4 5«H A
• 135°
(11) as can be seen in Figs. 8-10. A 180°
Experimental results are in good agreement with the predicted Predicted
0.3
results shown in Fig. 4. Rollers having roughnesses of 0.229- 92°
4.953 /Lim rms were tested. A wrap angle of 90 deg was used l^T 135°
when testing rollers 9-12. Rollers 7 and 8 were tested with a 0.2 7
wrap angle of 180 deg. Two types of polyester film, PF-2 and ^ ^ . 180°
PF-3, having roughnesses of 0.737 and 0.406 fxm rms, respec-
tively, were used for testing with the various rollers. The traction 0.1 - Web = NP-2 ^
coefficient decreases linearly in most of the region from transi-
P Roller = #1 \ •. \
tion point a to transition point b as ho increases. Data then
appears to deviate from a straight line as transition point b is n n ~ 1 1 1 1 1 1 1 K 1 r, 1 1
approached. Traction beyond transition point 'b' is still measur- Oe+0 2e-5 4e-5 6e-5
able, but too great to be caused by the viscosity of the air alone.
This deviation is probably due to some of the peaks of the
asperities of the web and roller remaining in contact at the web
Fig. 10 Effects of web permeability {a = 0.424) and wrap angle [p) on
edges or at the exit region. Equation (5) assumes the air film the traction coefficient {/IT). Roughness parameters used: (1) roller =
thickness decreases linearly around the angle of wrap. In reality 0.686 fim rms and (2) newsprint = 4.496 iim rms.

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 results in Figs. 5-7 are less than what was predicted, but still Traction can also be increased by increasing web permeabil-
falls within the standard deviation intervals shown in the graphs. ity. Although web permeability is a physical parameter, it can
Experimental traction values less than the predicted value may not be used as a design parameter as easily as roller roughness.
imply that the theoretical air film thickness is larger than pre- For instance, newsprint may have an absorption quality that is
dicted or the surface roughness is smaller than what was mea- controlled by its permeability. If the newsprint is highly absor-
sured. Hamrock (1994) describes a surface roughness correc- bent then excessive ink will be used and a spreading effect may
tion factor where the lubrication film thickness (/!min)smooth calcu- occur. If the newsprint is not absorbent enough then the ink
lated with smooth surface theory is corrected for roughness. His may run off or smear. Therefore, newsprint permeability may
results show that when there is shared loading {h^JRqc < 3) be limited within a certain range. An alternate approach would
between the asperities and lubrication film then a correction be to consider the permeability of the roller which could be
factor is needed. His results also show that if h^\JRqc is greater used as a design parameter. This approach was not experimen-
than 3 then minimal correction is needed therefore, (/Jmin)roiigi. tally verified in this study but the permeability factor ( a ) in the
'^ (Arain)smooth- Experimental results shown in Figs. 5 - 7 suggests traction algorithm can be used for either the web or roller.
that a larger correction is needed as hmiJRqc increases which Further experimental study of this approach would prove inter-
is just the opposite of what is shown by Hamrock. Therefore, esting.
some other reason must exist for the deviation of the experimen-
tal results from predicted. The profilometer filter cut-off length
can significantly affect the values of the surface parameters as Acknowledgments
shown by Thomas (1978). Generally, Rq increases as the cut- This research was made possible through the support of many
off length is increased because longer wave lengths are allowed industrial sponsors at the Web Handling Research Center at
to pass through the filter. Thomas showed one case for a grit Oklahoma State University. The authors would like to express
blasted surface where Rq increased as the square root of the their sincere appreciation to the following companies for their
cut-off. He went further to suggest a need for functional filtering support; Mobil Chemical Company, 3M, AET Packaging Films,
which he defined as a pass-band of wave lengths which take Polaroid Corporation, Rexham Corporation, Xerox Corporation,
part in the actual surface interaction of interest. The profilometer Sonoco Products Company, Eastman Kodak Company, Heidel-
cut-off length, in the present study, was set for 2.5 mm for berg-Harris, Fife Corporation, Hoechst-Diafoil Corporation,
measuring the surface roughness. Good agreement between the Valmet-Appleton, Inc., Proctor & Gamble, E. I. duPont de Nem-
predicted and experimental results exists for rollers having rms ours & Co., Inc., ALCOA, Mead Central Research, American
roughnesses between 0.220-4.953 //m as shown in Fig. 4. How- National Can, Grace Tec Systems, & Rockwell Automation.
ever, when the roller surface roughness was increased to 6.045-
11.557 ixm as shown in Figs. 5 - 7 a deviation exists between
the experimental and predicted results. This may suggest that References
the filter cut-off of 2.5 mm was functionally correct for our Bain, Lee J., and Max Engelhardt, 1992, Introduction to Probability and Mathe-
application in the roughness range of 0.220-4.953 /xm. How- matical Statistics, Duxbury Press, Belmont, CA, pp. 460-462.
Baumeister, H. K., 1963, "Nominal Clearance of the Foil Bearing," IBM Jour-
ever, a smaller cut-off length may have been needed for the nal, p. 153.
roughness range of 6.045-11.557 ^ixn. Further research is Daly, D. A,, 1965, "Factors Controlling Traction Between Webs and Their
needed to explain this phenomenon. Carrying Rolls," Tappi, Vol, 48, No. 9, p. 88.
DIN Standards, 1996,' 'Determination of Values of Surface Roughness Parame-
The effects of web permeability and side leakage on the ters Ra, Rz, R max. Using Electrical Contact (stylus) Instruments," DIN 4768.
traction coefficient can be seen in Figs, 8, 9, and 10. Three rolls Ducotey, Keith S., 1993, "Traction Between Webs and Rollers in Web Han-
dling Applications," Ph.D. dissertation, Oklahoma State University.
of newsprint having permeabilities of 0.125, 0.273, and 0.424 Ducotey, K. S., and Good, J. K., 1995, "The Importance of Traction in Web
cm'/s/cm^-kPa were tested with roller #1. Results in each figure HandUng," ASME JOURNAL OF TRIBOLOOY, Vol. 117, pp. 679-684.
are also shown at wrap angles of 92, 135, and 180 deg. The Ducotey, K. S., and Good, J. K., 1998, "The Effect of Web Permeability and
traction coefficient is fairly insensitive to changes in wrap angle Side Leakage on the Air Film Height Between a Roller and Web," ASME
JOURNAL OF TRIBOLOOY, Vol. 120, pp. 559-565.
as can be seen from the experimental and predicted results.
Good, J. K., Kedl, D. M., and Shelton, J. J., 1997, "Wrinkling of Webs in
Data at low values of e were difficult to obtain because of the Process Machinery due to Shear," Proceedings of the Fourth International Con-
increased stick-slip that occurred between the web and roller. ference on Web Handling, Stillwater, OK.
This is especially apparent in Fig. 9 where the data is quite noisy Gross, W. A., 1980, Fluid Film Lubrication, Wiley, New York, pp. 482-501.
at e = 0.3 X 10"'. Overall, good agreement exists between the Hamrock, Bernard J., 1994, Fundamentals of Fluid Film Lubrication, McGraw-
Hill, New York, pp. 511-514.
experimental and predicted results. Harris, Tedric A., 1991, Rolling Bearing Analysis, Wiley, New York, p. 525.
ISO Standards, 1984, "Surface roughness—Terminology—Part 1; Surface and
5 Concluding Discussion its Parameters," ISO 4287/1.
Jones, D. P., 1992, "Air Entrainment as a Mechanism for Low Traction on
A predictive traction algorithm consisting of a large set of Rollers and Poor Stacking of Polyester Film Reels, and its Reduction," ASME
operating and physical parameters was experimentally verified Applied Mechanics Division, Vol. 149.
with good results. Typical rollers used in web handling having Knox, K. L., and Sweeney, T. L., 1971, "Fluid Effects Associated with Web
ground and bead blasted surfaces were used in the experiment. Handling," Ind. Eng. Chem. Process Des. Develop., Vol. 10, pp. 201-206.
Operating parameters such as web velocity and web tension Licht, L., 1968, "An Experimental Study of Elastohydrodynamic Lubrication
of Foil Bearings," ASME JOURNAL OF LuBRtCATiON TECHNOLOGY, Jan., pp. 199-
greatly affect the amount of air entrained between a roller and 220. Vol. 30.
web. Because of this, air entrainment is difficult to avoid from Mufm, Sinan, and Benson, Richard C , 1995, "Modeling the Transport of Paper
the operator's perspective with the trend towards higher web Webs Including the Paper Permeability Effects," ASME ISPS-1, pp. 247-258.
speeds. In this study an increase in surface roughness was shown Muftu, Sinan, and Benson, Richard C , 1996, "A Study of Cross-Width Varia-
tions in the Two-Dimensional Foil Bearing Problem," ASME JOURNAL OF
to significantly increase traction. Therefore, roller surface TRIBOLOOY, Vol. 118, pp. 407-414.
roughness from the design standpoint can be used to increase Thomas, T. R., and Sayles, R. S., 1978, "Some Problems in the Tribology of
traction where applicable. Although an increase in traction will Rough Surfaces," Tribology International, June, pp. 163-168.
result, scuffing of the web could occur, so a trade off between Vaidyanathan, Nandakumar, 1996, "A Study on Wound Roll Slippage," Ph.D.
dissertation, Oklahoma State University.
traction and the amount of scuffing a customer can live with
Williams, J. A., 1994, Engineering Tribology, Oxford University Press, New
may have to be considered. York, p. 349.

624 / Vol. 121, JULY 1999 Transactions of the ASME

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