How to measure roll quality
W«b Handling Research Cente
Oklahoma State University
How to measure roll quality
David R. Roisum*
The best (est method is the one that can detect a small change in roll structure with
the fewest measurements.
The winding process takes a strip of flexible material and
turns it into a wound roll. We can avoid for a time the
description of the complex details of the winding process by
using a black-box approach, as seen in Fig. 1. The system can
be divided into three categories: input parameters, process
laws, and output results. Input parameters are variables that
we can (sometimes) control to optimize the output results,
which can be loosely described as roll quality. The process
laws are the constant and inviolate behavior of physical
systems that we seek to describe using engineering mechanics
and other methods. Our task as quality control engineers is to
select values for the input parameters so that we maximize
roll quality.
between drum and paper (usually about 0.35) and the normal
force (determined by roll weight, geometry, and nip loading
at the rider roll). Exceeding the friction limit will simply
cause slipping and, possibly, instability and sheet marking.
Nip cannot be negative, nor can it be so high that it kneads
the winding roll, increasing interlayer slippage to the point of
creping or shear burst. If tension is too low, the propensity
for wrinkling is increased, and the sheet run may flutter.
Additionally, web tension cannot be increased too much
because sheet breaks are an exponential function of web
tension.
The point to remember is that although the TNTs are the
most easily controlled inputs, they often have narrow ranges
of useful adjustment. The operator must find a delicate
balance among all of these parameters. Additionally, the task
Winding process—input parameters
is made even more difficult because the material properties
Torque, nip, and tension
change, either intentionally (grade changes) or
The input parameters that are the easiest to control are known unintentionally (manufacturing process instabilities). These
as the TNTs of winding: torque, nip, and tension. Machine property changes cause the optimum winding profiles to vary
operators can usually adjust TNTs via benchboard controls. with time.
As seen in Fig. 2, torque can be applied as a differential
between the front and back drum on a two-drum winder, or Paper properties
through a center-shaft on a duplex winder. Nip is the lineal Some paper properties have a strong influence on roll
pressure between the winding roll and a roller or drum. structure. These include caliper, density, MD (machine
Tension is the lineal load applied on the draw immediately direction) yield and tensile strength, coefficient of friction,
coefficient of hygroscopic expansion, porosity, as well as the
upstream of the winding roll.
As seen in Fig. 3, the TNTs of winding are set point elastic moduli in both the MD and the ZD ( z direction).
functions of wound-roll diameter. The TNTs of winding are Other paper properties that affect web quality—including
often linearly decreasing from start to finish to give the roll a optical properties (brightness and opacity) and hygroscopic
structure that is hard near the core and then decreases properties (freeness and water retention)—have essentially
smoothly to a softer finish at the outside. Rider-roll nip on a no effect on the quality of roll structure. If one were to
two-drum winder is perhaps the most complicated of the choose an optimum web for winding, it would probably have
controls because the total back-drum nip is the sum of rider- (a) high caliper, strength, friction, and porosity and (b) low
anisotropy (MD/ZD modulus) and coefficient of hygroscopic
roll nip, roll weight, and winding-angle geometry (/).
Increasing any one of the TNTs will usually make the roll expansion.
Two points must be made concerning paper properties as
harder at the point of increase. Decreasing them will make
the roll softer. However, we cannot specify the TNTs on an inputs to the winding process. First, though some paper
unlimited range. Torque is limited to the available friction, properties have a profound influence on winding, they
cannot usually be considered an input variable for the
which depends on the coefficient of friction
purpose- of o p t i m i z i n g the w i n d i n g process. Paper
•Roisum is currently a senior research engineer. Web Handling Research
properties are generally specified by the paper mill's
Center. Oklahoma State University. 218 Engineering North, Stillwater, Okla. customers. Therefore, average paper properties are not an
74078.
i n p u t variable at our disposal. In addition, paper properties
are not a modifiable output from the winding system. Paper
Roisum is a winder consultant for Beloit Corp. R&D,
properties are seldom measurably changed by the winding
1165 Prairie Hill Road, Rockton, 111. 61072.
process. As finishing room superintendents would say, "You
cannot make paper on a winder."
October 1988 Tappi Journal 91
1. Knowledge of the winding process can be divided into three
categories: input parameters, process laws, and output results
=3 0
The process
r
Torque ——>i
__ Wound-intension
00 £)
-— Density
___ Stress or
strain
Second, the mechanical properties of paper vary with MD
position (or time) and CD (cross-machine direction) position.
These variations exert a great deal of influence on the
winding process. Web breaks, for example, occur at rare
local weaknesses in the web. It can be shown that the webbreak problem is influenced more by the variations of
strength than by the average strength (2, 3). Another
example is the ropes and corrugations that are almost
entirely related to variations of caliper across the web.
Reducing paper property variations to optimize winding can
be considered a controllable input parameter only if the
finishing room has influence over the paper machine.
Usually, we must wind the paper that is given to us.
3. Typical set points for torque, nip, and tension across the diameter
of a wound roll
£
0
10
20
""*- 30
-----------------------------------.
►10
Q. 0."
Z
0
10
20
30
40
Machine configuration
Winding machines can be classified as centerwinders, center— --------------------------------------------------surfacewinders, surfacewinders. and two-drum winders.
These basic machine classes determine to a large extent the
range over which the TNTs can be controlled. The
centerwinder can vary only tension as a TNT parameter;
0
10
40
center-surfacewinders and two-drum winders can vary any of
20
30 ROLL
the TNTs, and surfacewinders can vary only nip and tension.
DIAMETER, in.
Centerwinders and center-surfacewinders usually give the
highest roll quality, but these machines are often more
expensive and less productive. Additionally, centerwinders
can be speed limited by air entrainment on nonporous webs. 4. Optimum profile for roll-structure parameters (hardness, wound-in
tension, interlayer pressure, density, and stress or strain) across the
However, winding-machine type can only be considered an diameter of a wound roll
input variable when purchasing a new winder.
For any given machine, there are design details that affect
UJ
wound-roll quality. These include the web run, roll diameters
^__
DC
Z>
and grooving, spreaders, as well as the type of TNT controls
HUJ
O-l
and drives. But unless the winder is being rebuilt, these
oc<
design details are not considered to be inputs that can be
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varied to optimize the winding process.
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The winding process can be improved, however, by
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controlling various maintenance parameters. Winder rolls
TENSION, pll
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Nip Tension
Intertayer
pressure
s
"K ° r
Operator __
technique
Torque on a
duplex winder
i— Hardness
g
Machine >___
conliguration ""
Torque on a two-drum winder
>
k.
Nip —
Tension —
Paper _________
properties ~"
< Dutput
oil structure
ORQUE SPLIT,
Input
parameters
2. Torque, nip, and tension are the easiest parameters to control on a
winder Torque can be applied as a differential force between the front
and back drums on rwo-drum winders or through a center shaft on
duplex winders. Nip is the lineal pressure between the paper roll and
a roller or drum Tension is the lineal load applied on the draw
immediately upstream of the paper roll.
92
October 1988 Tappl Journal"
ROLL DIAMETER
5. The Rhometer is an impact-based device tor measuring roll
hardness The instrument measures the peak deceleration of a small
hammer as it strikes the paper roll
must be accurately aligned (0.005 in./lOO in.) to avoid
wrinkling of the web and roll. Drives and brakes must be
tuned so that speed changes result in less than a 5% change
in tension. Rider-roll loading systems and core-chuck slides
must move freely without binding or stick-slip. Finally, the
framework must be rigid, and there must be no looseness or
play in any of the moving parts U).
Operator technique
In addition to setting the TNTs for each run, the operator
also has subtle but important influences on roll-structure
quality while setting up and running a set of rolls. Successful
operators can be identified by objective measurement of
productivity and quality. The techniques of these operators
can be passed to others through training. Thus, operator
technique is another variable that can be used to optimize
roll quality.
Winding process—physical laws
The winding process is the connection between input
variables and output results. The process is not a variable but,
rather, a system of inviolate physical laws that describe the
paper stresses in a roll resulting from the various input
parameters. The importance of these physical laws is that
they quantitatively describe certain aspects of roll quality,
allowing us to predict roll-structure results for any set of
input parameters. These laws, which are usually solid
mechanics formulations, can be coded into a computer. One
can then optimize the winding process by running "what if
scenarios on a computer, much like the business use of
spreadsheets for modeling a product or a company. The
advantage of computer modeling is that numerous
combinations of inputs can be run in a short period of time at
no risk to the product. The user then scans the results and
chooses the best combination of inputs. The disadvantage of
modeling is that stresses are difficult to verify by
measurement. In addition, defect
6. The Schmidt hammer is an impact-based device for measuring roll
hardness The instrument measures the rebound height of a small
plunger after it strikes the paper roll.
models are only now beginning to emerge.
Mechanics equations were used in the first analytical
model of roll winding, which appeared in the late 1950s.
This was an accretion model based on linear, isotropic, hoopstress formulas. The model superimposed the stresses
resulting from the addition of a single wrap upon the existing
stress distribution as each wrap was added from the core to
the finish diameter. Subsequent works removed model
restrictions by allowing for nonlinear anisotropy. Current
winding models provide a close description of
centerwinding. However, the effects of the nip, air
entrainment, interlayer slippage, and CD variations remain to
be incorporated into a single description of winding.
Briefly reviewing the history of winding models, we find
numerous works in the last 25 years, each improving on its
predecessors. In 1962, Catlow and Walls used a linear
isotropic model to derive formulas for the stress distribution
of rolls during winding (5). In the mid '60s, Tramposch
analytically described the isotropic and anisotropic stress
relaxation resulting from creep and thermally induced
stresses in wound rolls of magnetic tape (6, 7). In 1968,
Altmann extended the winding model to include linear
anisotropy (8). In 1974, Blaedel described an optimization
procedure for winding (9). In the early '80s, Yagoda
improved the winding model near the core and accounted for
centrifugal effects during winding (10-18). In 1986, Hakiel
extended the anisotropic winding model to include a
nonlinear radial modulus as a function of interlayer pressure
(H). In 1987, Wu demonstrated that the parameter having the
greatest influence on wound-roll stresses was the radial or
ZD modulus (15).
Measurement of output roll structure
Now that we have covered winding inputs and briefly
reviewed winding process models, we now move to the
winding process outputs, which are the primary topic of
October 1988 Tappl Journal 93
7. The Cameron gap test is a strain-based technique for measunng
the tensile force on the outer layer of a paper roll. The layer is severed,
and strain is calculated based on the width of the gap and the diameter
of the roll.
8. The J-line test is a strain-based technique for measunng the
magnitude of mterlayer slippage as a function of winding or unwinding
cycles c ■ maximum circumferential movement; a = depth to tangent
c a = slope of tip; r * depth; r, - radius when line struck; r2 ■ radius
after winding
this article. Returning to Fig. 1, we see that the output results
are loosely described as roll structure, which is some
measure related to winding stress as a function of roll
diameter. Hardness was the first description of roll structure.
Since then, wound-in-tension, interlayer pressure, density,
and stress have been added as measurable roll-structure
quality variables.
Figure 4 illustrates an ideal roll-structure profile from the
core to the outer layer. The shape of the profile, which shows
a hard (tight) start with a smooth transition to a softer
(looser) finish, is typical for all grades of paper, regardless of
the parameter being measured. Different grades of paper
simply have different values for the starting and finish
hardnesses. This widely used figure is based on the
cumulative experiences of many winding experts, but it is not
easily quantifiable. This means that our roll-structure qualitycontrol efforts are limited to measuring roll-structure profiles
and then comparing them with the ideal profile. Other
techniques, such as judgment or statistics, are used to set
starting and finish magnitudes.
Roll structure is just one measure of roll quality. Paper
properties (tensile strength, burst, caliper, brightness,
printability) must also be tested to meet the customer's
particular needs. Roll quality also can be quantified by
measuring roll geometry (diameter, length, width) against the
target size, as well as the magnitude of dishing or offsets.
Finally, roll quality can be defined qualitatively as the
absence of defects (bursts, corrugations, stars, crushed cores)
(16). In this article, however, we restrict our discussion to
general testing considerations and roll-structure evaluation.
tightness or hardness. Though roll hardness as measured by
the billy club is not a fundamental roll-structure property and
lacks quantitative definition, it is nonetheless a useful device
that can be found at many winder stations. Quantifying roll
hardness became possible with the invention of the
Rhometer and the Schmidt hammer. The Rhometer,
illustrated in Fig. 5. was invented in 1965 and measures the
peak deceleration of a small hammer striking the paper roll
(17). The Schmidt hammer, illustrated in Fig. 6, was
originally developed to measure the hardness of concrete but
later applied to paper rolls. The Schmidt hammer measures
the rebound height of a plunger striking the paper roll and is
related to the impact's coefficient of restitution. The
Rhometer is used extensively for quality control in both the
paper and film industries. The Schmidt hammer is widely
used in European paper mills.
a
o
MD tension, stress, and strain
Another class of roll-structure measurements is based on
web stress or strain. The Cameron gap test, illustrated in Fig.
7, is a TAPPI test method for calculating the tensile strain on
the outer layer of a roll. Tensile strain is calculated by
severing the outer layer and then measuring the resulting gap
and the roll circumference (18).
The J-line test, illustrated in Fig. 8, indicates the
magnitude of interlayer paper slippage as a function of
winding or unwinding cycles (19). This test involves striking
chalk lines on the roll edge. Interlayer slippage can be
measured by the extent of deformation of the J-line tip after
winding. Since both the Cameron gap and J-line tests are
labor intensive and destructive, they are used infrequently in
Hardness impacters
production testing.
The earliest device used to measure roll-structure quality was
Finally, strain gauges can be bonded to the paper web to
the backtender's stick or "billy club," a short wooden stick measure MD stress (20-22). Strain-gauge measurement,
though potentially more accurate, is also a destructive test
that the operator struck against the roll to sound its
and d i f f i c u l t to set up. Consequently, strain gauges are
94 October 1988 Tappi Journal
9. The core-torque test is a fnction-based technique tor measuring
radial stress The pressure al the roll s core is measured by fitting a
core chuck to a torque wrench and measuring the amount of torque
required to cause core slippage
strictly limited to research testing.
V
Interlayer pressure
A third class of roll-structure measurements is interlayer
(radial) pressure or stress. These friction-based measurements
of pressure include the core-torque test, the pull-tab test, and
the Smith needle. Core pressure can be measured indirectly
by fitting a core chuck to a torque wrench and measuring the
amount of torque required to cause the core to slip {23). The
core-torque test is illustrated in Fig. 9. The Smith rolltightness tester (Smith needle), illustrated in Fig. 10, is a
handheld instrument that measures the force required to insert
a needle between adjacent layers on the roll end. The pull-tab
test, illustrated in Fig. 11, measures the force required to
withdraw a tab that is inserted into the roll end during
winding.
Each of these methods measures interlayer pressure
indirectly. Pressure is inferred through the use of simple
mechanics equations based on measurements of force,
friction, and area of contact. The pull-tab technique is not
suitable for production testing, and the core-torque test
measures only the pressure at the core. In addition, the
friction coefficients of paper vary widely, so the resulting
measurements usually have considerable scatter or
uncertainty.
The friction-based techniques are not the only way of
measuring interlayer pressure. Time-of-flight acoustic
measurements can infer interlayer pressure (24) based on the
speed of acoustic waves passing through a stack or roll.
Unfortunately, this method is extremely difficult, and the
resulting measurements of radial pressure have too much
scatter to accurately compute tangential (MD) stresses, which
are the derivative of radial stresses. Another method utilizes
thin pressure gauges, such as capacitance gauges. These are
wound into a roll and directly measure interlayer pressure
(9). Both of these methods are suitable only for research
testing.
Rewinders
The WIT-WOT (wound-in tension-wound-off tension)
winder, illustrated in Fig. 12, is a single-drum duplex
laboratory winder designed and built in late '60s. Pfeiffer
used this instrument to measure the tension wound into a roll
as a function of web tension and nip load (25. 26). The WITWOT winder is able to resolve changes in tension occurring
over less than one wrap while either winding or unwinding.
Many of the tests used to measure roll structure must be
performed on stationary rolls. Such tests may not be suitable
for on-line production testing. However, a rewinder is an
ideal test stand for occasional in-depth testing that would not
be practical on a production winder. A roll is typically
unwound and then stopped. The roll is profiled at this
diameter. The rewinder is restarted and runs until the roll
diameter reaches the next test interval. The roll is profiled
again. This process is repeated through the entire depth of the
roll. Using this technique, hardness profiling can be extended
from a typical one-dimensional function of CD position to a
two-dimensional function of CD position and diameter.
Density
The density analyzer, illustrated in Fig. 13, consists of a
winder or rewinder, two incremental rotary encoders, signal
conditioning, and a microcomputer. One encoder measures
web length and is mounted to a roll or wheel that is in
contact with the free web or paper roll. The other encoder (or
proximity switch or photoelectric eye) counts roll revolutions
and is connected to the paper roll's core through its core
chuck or center shaft. The pulses generated by the roller and
core encoders are counted over some sample interval and
passed to the microcomputer for calculation. The ratio of the
pulses measured by both encoders during a sample interval
provides a measure of the paper roll's diameter.
The density analyzer, the only truly automated rollstructure measurement method, is both sensitive and
repeatable. However, it can only profile as a function of
diameter and not across the width. In addition, the density
analyzer has no absolute reference or calibration, as do many
of the other devices. Thus comparisons between rolls or
grades are not reliable. Despite these limitations, the density
analyzer remains an efficient and sensitive roll-structure test
method.
The importance of density as a roll-structure parameter
was recognized in the late '60s, when various researchers
noted that winding parameters had an effect on roll density
(27-29). In 1980, Eriksson et al. (30) invented a computerized roll-density analyzer. Eriksson showed the
relationship between wound-in and wound-off density as
well as the effect of torque, nip, and tension on wound-in
density. McDonald showed the relationship between Rho
hardness and density, the effect of calendering (caliper) on
density, and the effect of torque on density {HI). Odell's
study was the most complete, providing details al>out how
the density profile at the winder was affected by the source
paper machine, winder torque, nip, speed, acceleration,
splices, and the set location on the parent log (32). Similar
studies were performed by Granlund (33), Holmer (34), and
Komulainen (35). This list of articles indicates that the
density analyzer is the most carefully investigated roll-
Octobcr 1988 Tappi Journal 95
structure test method.
10. The Smith needle is a friction-based technique for measuring radial
stress Roll tightness is measured by determining the amount of force
required to insert a needle between adjacent layers on the roll end.
c/5
-1
s
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o
x
Evaluation of measurement methods
General considerations
There are a number of considerations in selecting a particular
method for testing roll structure. These include the ability to
profile across the width, the ability to profile through the
diameter, accuracy, the ability to automatically record data,
ease of use. whether or not the test is destructive, and cost.
The evaluation chart in Fig. 14 summarizes these criteria.
The relative importance of these criteria varies with
application. Thus the choice of the appropriate test method
depends on the type of problems to be diagnosed, frequency
of testing, production demands, and the level of roll quality
needed to satisfy the customer.
Most of the methods can profile either across the width or
through the diameter, but not both. For example, the impact
testers can easily profile hardness across the width by taking
readings at various points along the width of the roll. On the
other hand, the impact testers cannot profile through the
diameter unless a set of readings is taken as a roll is wound
or unwound. This requires frequent stopping of the winder,
making online testing impractical.
The pull-tab and Smith needle friction testers can only
profile with diameter because readings can only be taken at
the roll ends. The core-torque test cannot be used to develop
a profile of any sort. This test provides only a single reading,
which represents the average core pressure across the width
of the role.
The strain-based tests, such as the Cameron gap and J-line,
can only profile through diameter, and then only with some
difficulty. To profile diameter with the J-line, it is necessary
to strike many J-lines during the winding or unwinding of
the set. This is potentially dangerous because of the amount
of time an operator must spend in proximity to rotating
machinery. To profile diameter with the Cameron gap, the
roll must be completely slabbed down and destroyed.
The density and WIT-WOT analyzers also can only profile
through diameter. However, they are considerably more
convenient than the other diameter-profiling methods
because they are automated and continuous.
The trend toward increased automation of testing
procedures is the result of the escalating demand for higher
quality rolls and the high cost of labor. An ideal system
acquires data through sensors connected to a computer,
which processes the data into statistical reports. Of all the
roll-structure test methods, only the density analyzer and the
WIT-WOT winder can operate unattended from setup
through report generation. The next level of test automation
includes the Rhometer and Schmidt hammer. These devices
must be manually operated, although data recording and
report generation can be automated. The remaining methods
are completely manual and labor intensive.
Another consideration is whether the test can be performed
without damaging the product. Potential test damage to the
product is application dependent. The most destructive is the
Cameron gap, which completely destroys the roll. The Smith
needle can be destructive to lightweight
96 October 1988 Tappi Journal
grades, since the needle can sever a layer on penetration. The
J-line can be destructive if the resultant chalk lines on the
edge of the roll prevent its sale. The impact testers and the
density analyzer can be destructive on carbonizing and other
mark-sensitive grades.
Ease of use is important to reduce both labor costs and the
noisy data that is caused when the results are sensitive to
operator technique. Of all the methods, the density analyzer
is the easiest to use because it can run nearly unattended
after a brief setup. Though the WIT-WOT winder is
similarly capable, it is not easy to use simply because it is
not widely available. At the other end of the spectrum, the
strain-based Cameron gap and J-line tests, the use of strain
gauges, and the pull-tab test are all fairly involved
procedures and thus impractical for use in production
testing.
The cost of testing
The cost of testing is a primary consideration in evaluating a
test procedure. The initial costs for the test equipment and
setup are heavily outweighed by the ongoing cost of test
labor. Thus the analysis of testing costs can be simplified to
a discussion of data gathering and recording capabilities
quality control (QC) or statistical evaluation, and report
generation. Additionally, once the report is generated, it must
be reviewed by QC personnel and/or management for action
if it is to be of use. As we review the elements of testing
costs, it is apparent that the frequency of testing, the ease of
use, and automation of testing and reporting are key
parameters.
In addition to the cost of testing, there are the costs of no
testing. These costs can be in the form of reduced
throughput, high reject and rewind rates, loss of customers
or compensation for dissatisfied customers. To maximize
profits, we must minimize the total costs of testing and no
testing. This approach is illustrated in Fig. 15. Costs are
presented as a function of the amount of testing. As the
amount of testing increases, the cost of testing increases. As
the amount of testing increases, the cost of not testing
decreases as the winding process becomes more efficient and
produces higher quality rolls.
The optimal amount of testing is where the total cost
11. The pull-tab is a friction-based technique for measuring radial
stress The pressure between layers is determined by measuring the
force required to withdraw a tab inserted into the roil end dunng the
winding process
of testing and not testing is at its minimum. Intuition says
that the optimum point occurs at the intersection of the two
curves. However, the true optimum is the point at which the
slopes of the cost-of-testing and cost-of-not-testing curves
are equal in magnitude but opposite in sign. This optimum
test frequency varies considerably with application. Lesscritical heavy grades may require almost no roll-structure
testing to achieve optimum payback, while lighter specialty
grades might require testing of every roll that is shipped.
Figure 15 is widely used in economic analysis and applies
in situations that are much broader in scope than the one
presented here. The figure is useful as a visual aid for the
concept of minimizing total cosLs as a function of some
parameter. However, it is difficult to use this concept to
determine precise magnitudes for optimum testing. Reliable
estimates of the costs of testing and not testing are difficult to
obtain. In addition, these costs depend on both the
application and the chosen test procedure. Different test
methods have different potentials to diagnose different types
of problems. Nonetheless, it is evident that test methods must
be carefully evaluated if we hope to choose the best
procedure for our particular applications and then choose a
test frequency that minimizes the total cost of testing and not
testing.
Accuracy
Testing accuracy is a function of many parameters, including
repeatability, sensitivity to the measured variable, and
sensitivity to noise, drift, or operator technique. The testing
device also must be capable of being calibrated against a
known standard.
If an instrument has no calibration procedure, it cannot be
accurate, since accuracy has no meaning without an
independent standard. The roll-structure test methods based
on the fundamental properties of stress and strain (2, 3) can
be independently checked against each other. Calibratable
test methods include the friction-based radial-stress
measurements (gauge-based tests, core-torque and pull-tab
tests), the strain-based measurements (strain gauges,
Cameron gap, J-line), and the WIT-WOT winder. The Smith
needle and the Rhometer, which have
arbitrary scales, are not truly calibratable. The density
analyzer cannot be calibrated because there is no independent
measure of density with sufficient accuracy against which it
can be checked. Nonquantifiable methods such as the billy
club also cannot be calibrated.
A noncalibratable method is not totally useless. However,
conclusions based on the results of such tests are subject to
restrictions. For example, if a method provides consistent and
repeatable results, it can be used to analyze structural trends
in a single roll. However, it would be risky to compare results
for two rolls, especially if the rolls were of different grades or
measured under different conditions. Without calibration,
accuracy cannot be defined, and magnitudes or values are
suspect.
Repeatability
If a measurement method is to be accurate, it must also be
repeatable. After making two nominally identical
measurements of tension, we expect nearly identical values.
This would be easy to check for the methods that do not alter
the roll in the process of testing. However, if the density
analyzer is used to profile a roll, the roll cannot be rewound
identically to make another run to check for repeatability.
Similarly, the Cameron gap cannot be checked for
repeatability because the tension on each layer is measured
by severing the layer. The process cannot be repeated on the
same layer, and subsequent layers may be under different
tensions. The impact-based hardness tests also cannot be
checked for repeatability because the impact compacts the
paper at that location, making subsequent readings higher.
Adjacent positions may be at different levels of hardness.
The factors that affect repeatability are sensitivity to
operator technique and measurement noise. Handheld
devices are particularly sensitive to operator technique. An
experienced operator can use the Rhometer, the Schmidt
hammer, or the Smith needle and produce consistent,
repeatable results. However, these results can differ from
those obtained by another experienced operator. People with
less experience operating a handheld tester will find
considerable scatter in their results as they alter their grips
and motions from one reading to another. If a short-term
study of roll structure requires high-quality data, a single
experienced operator should perform all of the tests.
Noise
Measurement noise increases data uncertainty and reduces
the quantity and quality of conclusions based on that data.
The total noise comprises the noise from each element in the
test system. Sensitivity to operator technique is one source of
noise. Noise also is generated by worn mechanical
components, which can cause backlash, hysteresis, slip,
friction, or drag. If instrument electronics are in proximity to
motors and other electrical equipment, noise can be picked
up on low-voltage lines or sensors. Electronic equipment can
also experience thermal d r i f t from powerup, grounding
noise, or frequency-response limitations. Digital equipment
always has a minimum one-count uncertainty for pulses and
one-bit uncertainty for analog-to-digital converters.
Test measurements are often sensitive to the orientation of
the testing device and to gravity. If handheld testers
October 1988 Tappl Journal 97
</5
o
are not oriented consistently, noise will be increased. Gravity 12. The WIT-WOT winder is a single-drum duplex laboratory winder for
will always influence measurements because the stresses at measuring the tension wound into a roll as a function of web tension
the top of the roll are different than those at the bottom and and nip load
Nip-loading
sides. Web stresses are the superposition of internal stresses
cylinder
(roll structure) and external stresses (gravity and support
loading). For example, a soft roll supported at the core will
Web carrying
have higher readings at the top than the bottom. Similarly, a
tension
roil that is supported at the core will provide different
readings when it is sitting on the floor. To obtain consistent
results, the most convenient orientation of instrument and
Level rails
roll should be established. All tests should then be conducted
to that standard.
The most apparent type of measurement noise is caused by
simply misreading or misrecording the data provided by a
test device. Parallax errors can occur when reading pointers,
especially those withoutmirrored backs. Noise is also
introduced if averages or conversions are improperly
calculated. For those methods that can be tested for ments with each of the methods to be evaluated. A
repeatability, noise can be quantified by the variance or minimum of five measurements should be made with each
standard deviation of repeated measurements.
of the instruments at diametral increments of 2 in. Some
Noise decreases the ability to reliably distinguish changes planning is required in the sequencing of the measurements.
between one roll and the next, or between positions on the The density analyzer must be run while the roll is being
same roll. The easiest way to increase the accuracy of roll- wound. The friction-based tests (core torque, pull tab, and
structure testing is to decrease noise by taking many readings Smith needle) should be done before unwinding. While
and reporting the average. This increases the cost of testing. most of the other methods will be done on a rewinder's
In principle, it is possible to obtain any specified level of unwind, the Cameron gap must be done last, since it
accuracy simply by increasing the number of measurements. destroys the roll.
Results from each of the measurement methods are then
Resolution
plotted. The plots should show a step decrease in the
How can we rank the various test methods for accuracy measured variable, as seen in Fig. 17. To rank the resolution
under the conditions in our finishing rooms? We begin with of the methods, the Z-test for the significance of means
two premises. First, the best method should be sensitive to applied to our data will calculate the number of
any changes in roll structure. Second, the most efficient measurements needed to resolve roll-structure changes of
method is the one that requires the fewest measurements to any size. (The Z-test is described in the appendix at the end
obtain a specified level of accuracy. In other words, we want of this article.) Data for the Z-test will be the averages and
a method that will detect a small change in roll structure standard deviations of measurements made 1-2 in. on either
with the fewest measurements.
side of the step change. The results of this type of testing are
The test methods can be ranked by subjecting a specially shown as worksheets for two different grades of paper in
wound roll to the different test methods being evaluated. The Tables I and II.
roll is wound with a large known change in a single
It is not surprising that some methods are more sensitive
parameter, such as wound-in stress. Then the various test than others. What is surprising is that some methods require
methods are used to make measurements on both sides of the ten times as many measurements as others to achieve the
change.
same level of accuracy. Even more startling is that one
To input a known change in roll structure, we can make a commonly used method gave the wrong information. This
sudden step change in the TNT winding parameters at some method indicated that the hard interior was softer than the
intermediate diameter, say 20 in., as seen in Fig. 16. The soft exterior. A method that cannot discern gross changes in
larger the step, the more accurate will be our evaluation of roll structure has absolutely no use in QC work.
the test methods under consideration. From the core to 20 in.,
Test names and units have intentionally been removed,
we apply as much torque, nip, and tension as the sheet will since results vary slightly with each particular application,
stand. Then at 20 in., we suddenly drop the torque, nip, and as seen in Tables I and II. Because these methods are grade
tension as much as possible. The objective here is not to and application dependent, they must be tested under the
wind a good roll, but to evaluate the resolution of test production conditions in your mill. However, even though
methods. If a method cannot discriminate these gross the exact numbers vary somewhat, the relative ranking of
changes within the roll, then it will be unable to sense the the methods remains essentially unchanged.
smaller and more typical changes that occur under
The method used in Tables I and II can be extended to an
production conditions. Another way of introducing a step economic analysis of the cost of testing if the costs can be
input would be to splice together two rolls of widely calculated as a function of the number of measurements
different caliper and wind them into a single roll without made. If the number of measurements are multiplied by the
making a step change in the TNT parameters.
cost per measurement, the methods then can be ranked in
Once this unusual roll has been wound, it must be order of the minimum cost per specified
unwound while carefully making numerous measure98 October 1988 Tappi JournaJ
13. The density analyzer is an automated instrument that provides a density
profile as a function of roll diameter
is provided at the end of this article.
Example 1
Premise: Roll A has a hardness of 50 and Roll B has a
hardness of 40, therefore Roll A is harder than Roll B.
Analysis: Our intuition tells us that A is harder than B
because 50 is greater than 40. Even if there is no problem
with the test instrument or procedure, there is not sufficient
information to make this or any other conclusion. We must
at least know the mean (average) hardness of the rolls
coming off the winder and the variance of the readings.
Encoder
pulse trains
from: Rider
roll
Core
Signal
chuck
Back drum condition
Bus
CounterFront drum
timer
Computer
Unwind
level of accuracy. For example, if one roll inspector can
14. Evaluation of the ten test methods in eight performance categories • =
optimal; o = feasible; — = not applicable.
make 0-3 readings in addition to his other duties, it is
obvious that 3 readings per roll will provide greater accuracy
a o
01
E
S
S 2E
?
at a given cost than 0, 1, or 2 readings. If more than three
readings were required, however, the payback would
Prn^cT)
Bil, C,ub
Rhometer
y
I
Schmidt hammer
Friction
Core torque Pull
tab Smith needle
f Strain ] Cameron gap
> ------------ ' J-line
(S STJc
-WOT
decrease, since another roll inspector would need to be
added.
Introduction to statistics
Statistical analysis is an absolutely essential aspect of QC
work. Those who distrust statistical analysis perhaps have
had a bad experience with a statistician who supplanted
judgment and knowledge of the process with mathematical
sophistication. There is no doubt that intuition, experience,
and professional judgment are required in QC work.
However, these tools are not sufficiently reliable for
interpreting QC data. To prove that statistics are also
required, we present four examples illustrating that intuition
and judgment alone can lead to the wrong conclusion. An
appendix of statistical terms and equations
Example 2
Premise: The average hardness of rolls coming off a winder
is known to be 40. Since one roll was tested at 50, it must
have been wound harder.
Analysis: In this case, we have a value for average
hardness. We might assume that a roll with a higher
measured hardness is wound harder. However, by Markov's
inequality, we can show that there is up to an 80% chance
that the harder roll resulted from normal variations in
winding without intentional alteration of the winding
parameters. The formula for Markov's inequality is given in
the appendix at the end of this article.
This example also illustrates the misconception that
measurements can establish cause and effect. If a roll was
known to be wound at ten times the torque, nip, and tension
of previous rolls and had a hardness of 500, we could not
deny that there was a change to the system. However, we
could not establish the cause of the high hardness value
through measurements or statistics. To quote Kendall and
Stuart (36): "A statistical relationship, however strong and
however suggestive, can never establish a causal
connection. Our ideas on causation must come from outside
statistics, ultimately from some theory."
What are the theories that help us establish cause and
effect between the paper properties, the TNTs of winding,
and roll structure? In most cases, these are theories provided
by researchers such as Tramposch (6", 7), Altmann (8),
Hakiel (14), and others.
Example 3
Premise: The hardness of previously produced rolls was 40,
with a standard deviation of 5. Winding parameters are
adjusted to tighten the roll structure, and a set of four rolls
has an average hardness of 44. Therefore, the new rolls
must be harder.
Analysis: Using the Z-test for the difference of means, we
can state that we are 94.5% confident that the new rolls are
harder. (Calculation of this 94.5% confidence level is shown
in the appendix.) Since 90-95% confidence is generally
considered adequate to support a conclusion, we can report
that the newly produced rolls are indeed harder. It is
important to state the level of confidence whenever
reporting the results of a statistical analysis. The confidence
level measures the reliability of your conclusions and
quantifies the risk of being wrong. It also protects you from
stating conclusions with absolute certainty.
Example 4
Premise: The spike in Fig. 18 is a measurement error.
October 1988 Tappi Journal 99
15. The costs of testing and not testing as a function of testing
frequency The cost of testing includes labor, equipment, and
maintenance. The cost of not testing includes such items as reduced
throughput, high reject rates, and loss of customers.
n
16. Sudden step-change in torque, nip, and tension at a roil diameter
of 20 in.
oa
ao
x
2.0
Tension
Rider roll nip
1.5
1.0 8 uj
I
- Torque
10
0
-10
A
were run on recycled newsprint (30 lb/3000 ft2).
Method
measuring roll structure.
Tests
B
C
D
E
F
9
4
3
5
9
8
Mean 1
Mean 2
Std. dev. 1
45.44
39.78
1.13
24.76
24.49
0.05
2.11
1.78
0.04
43.40
40.80
219
37.33
36.11
1.00
240
218
0.59
Std. dev. 2
0.97
0.09
0.16
217
1.27
026
SD
0.70
0.07
0.12
1.95
0.7
0.30
Z
8.09
3.86
275
1.33
1.61
0.73
100
100
91
95
77
5
19
6
23
25
99
Confidence, %
100
40 I
-30
AMOUNT OF TESTING
No. of samples
-
-20
Total cost
I. Results of tests designed to evaluate six methods
of
I
20
30
ROLL DIAMETER, in.
10
Number of measurements needed for 90% confidence
Level of
accuracy, pti
0.33
0.16
1
1
0.083
0.033
c
4
23
1
2
1
3
7
10
74
44
65
464
Analysis: Intuitively, we would expect small spikes to be
random variations resulting from measurement noise. Such
random variation is not statistically significant. With larger
spikes, intuition once again would lead us to suspect that the
deviation might be statistically significant. If the spike is
very large, we would suspect an erroneous reading.
Though intuition in this case is correct, it still does not help
determine whether a given spike is meaningless noise, a
significant event, or an error. To determine the significance
of the spike, we can again use the Z-test. If the significance
exceeds 3a or 99.9%, we can throw away the data because of
suspected error. More conservative criteria include removing
data that has a probability of less than l/2n of occurring,
where n is the number of samples. The most conservative is
Chauvenet's principle, which allows the removal of a single
data point in a set if its deviation ratio exceeds the standard
deviation ratio. Obviously, removal of bad data points
without statistical
100 October 1988 Tappi Journal
92
569
394
2460
justification is dishonest and unprofessional.
All of us are subject to strong unconscious biases when
we are confronted with data that have not been statistically
analyzed. Psychological research shows that when people
are presented with purely random data, they will attempt to
interpret it. The ink-blot test is an instance of the human
tendency to seek order. Where there is no order, we impose
it. In addition, when we try to interpret data, we
unconsciously interpret it so that it confirms our objectives.
If our boss wants harder rolls, we are more likely to see
harder rolls than softer rolls. The danger of misinterpretation
is greatest when we try to interpret data that are largely
composed of random noise. Such data have no rational
trends.
Which problem to tackle?
In any typical finishing room, there are numerous
17. Densrty change in a test roll that was subjected to a sudden step
change in TNT parameters at a roll diameter of 20 in. and spliced with
another roll at 33 in.
18. Change in Cameron gap on a test roll that was subjected to a
sudden step change in TNT parameters at a roll diameter of 20 in.
and spliced with another roll at 33 in. Is the spike at the 38-in. mark
real, or is it a measurement error?
5
Step
Splice
0.0250
40
*
4
a."
<
z 3
o oe
aUJ
t 0.0245
5
z
ill
1
2
v V^-*
\J
<
D
1
10
0.0240
20
Step e=£
Splice c=£
30
ROLL DIAMETER, in.
10
20
30
ROLL DIAMETER, in.
40
II. Results of tests designed to evaluate six methods of measuring roll structure. Tests were run on offset lightweight coated paper
Method
D
No. of samples
A
C
B
f
E
12
9
3
8
9
158.00
966
51.11
35.56
2.82
1.70
43.06
41.60
7.81
5.56
Std. dev. 1
8.12
5.28
0.03
0.46
1.56
1.58
Std. dev. 2
8.91
5.83
0.05
0.89
1.14
2.83
SD
7.62
3.70
Z
8.06
Mean 1
Mean 2
Confidence, %
5
100
34.83
35.25
0.05
0.48
0.90
127
4.2
2.24
3.04
2.50
-0.33
100
99
99
99
0
Number of measurements needed for 90% confidence
Level of
accuracy, pS
1.12
0.56
1
1
1
4
2
14
16
23
38
84
98
142
236
0.28
0.112
,
13
1
4
problems ranging in severity from minor annoyances to lifethreatening situations. Since our resources are limited such
that we cannot usually solve all problems, we would like to
apply effort to the areas that will yield the greatest gain. To
rank problems in order of importance, we can use the Pareto
diagram.
The first step is to carefully define categories or types of
problems. Once this list is made, we need to go through
production records (if they are complete enough) or spend
several weeks counting occurrences of each of the problem
types. Once a good sample has been obtained, a Pareto
diagram can be constructed. Figure 19 illustrates a typical
Pareto diagram, which is simply a bar chart indicating the
number of times a given problem has occurred.
Intuitively, we would begin to tackle those problems with
the highest occurrence rates. However, not all problems
have the same impact on efficiency and quality.
2
4
3
10
For example, usually one or more web breaks can be
tolerated in a set before it must be rejected, while tied up
rolls will send at least two rolls to the beater. Although the
simple Pareto diagram allows better management decisions
than no data at all, it can be improved by multiplying
problem occurrences by the cost per occurrence. The new
Pareto diagram showing the costs for each type of problem
is a better management tool. A final improvement in the
decision-making process involves knowledge of both the
cost of the problem and the cost of the solution. With this
knowledge, we can focus on the solutions that cost the least
and save the most.
What and where to measure?
Many defects are easily detected visually. However, the
trouble with qualitative acceptance criteria is that most
problems are not the black and white issues we would like
October 1988 Tappl Journal
101
mumv^tMi1itmmmmT\i'itmn
^
a
0
maanma&gm
them to be. Starring-, corrugations, offsets, and other defects
are a matter of degree. Without quantitative acceptance
criteria, each inspector will have a different cutoff point that
varies from one roll to the next. Psychological factors play a
large role in qualitative variation. From this point of view,
good quantitative rejection standards are superior to
qualitative judgment.
However, measurements should be sensitive to the
problems one is trying to prevent. Obviously, it would make
no sense to test roll structure as an acceptance criterion for
meeting width tolerances of the cut rolls. Less obvious is
whether roll structure or any other measurement is sensitive
to a particular defect. We can determine the correlation
between the defects we are trying to prevent and the
parameters we are measuring by using either the Z-test or
correlation coefficients. Unless the method has a high
correlation, we risk rejecting good rolls (false negative) or
shipping bad rolls (false positive).
In addition, we need to determine the best location for
testing roll structure. Ideally, the measurement is made as
close to the process as possible so that corrections can be
made quickly. This also reduces the cost of wrapping and
other subsequent operations on rolls that are already beyond
tolerance. An ideal setup automatically senses deviations
from target and uses this information to adjust the process
inputs so that the deviation is eliminated. This process is
known as closed-loop feedback control.
Developing diagnostic capabilities
It is no longer sufficient to merely detect problems after they
occur. Though it may be adequate from the customer's point
of view, a supplier's competitive position can be
handicapped unless it take steps to prevent problems before
they occur. This can be done through the use of such
statistical techniques as the Pareto diagram, the correlation
coefficient, and the Z-test. The Pareto diagram tells us where
to apply our resources. The correlation coefficient tells us
which parameters are relevant and how strongly they effect
our problem. The Z-test tells us the level of confidence in
our results so that we can know whether improvements are
real or not.
A roll-structure testing program
You can set up a quality control program in a finishing room
by applying the concepts discussed in this article.
1. Rank problems in their order of importance using a
Pareto diagram.
2. Select a measurement tool.
3. Select a sample frequency (every roll; randomly
selected rolls; when a problem becomes evident).
4. Select a sample size (e.g., five samples per point, throw
out high and low values).
5. Select a record format (data sheet, database).
6. Develop a statistical analysis procedure.
7. Develop acceptance criteria.
8. Develop diagnostic capabilities.
9. Make changes to improve the process.
10. Make better rolls.
102 October 1988 Tappi Journal
19. Pareto diagrams are used to rank problems in their order of importance
Problems are often ranked based on their frequency of occurrence or their
cost per unit of time.
Web breaks
Corrugations
•v. UJ
(/) UJ Ui
o^
5
Tied-up rolls
Other
UJ </>
C O
tr o
oo
o
o
Offsets
Loose core
Dishing
PROBLEM TYPES
Appendix of statistical techniques
Chauvcnet's principle
A single data point may be eliminated if DR > DRQ. DRQ is
determined by looking up the value in a table. The deviation
ratio (DR) is determined using Eq. 1.
DR = (A, - X)/c
(1)
Correlation coefficient
The correlation coefficient is a measure of the degree of
association between two variables. How much effect does X
have on Yl The effect is large if r is close to +1 or -1.
r^inlXiYi-lXilYO/lnlXMlXifHnXYi'-aYif?
(2)
Markov's inequality
Markov's inequality is used to calculate the probability that
a sample data point X is greater than k
/>(A>k|<Wk)
(3)
Calculation from Example 2:
P\X> 401<
(40/50) P\
A>40|<80%
Mean
The mean is the average value of all the sample points.
A'=ii*l/n£ Xi
(4)
i=l
Standard deviation
Standard deviation is a measure of scatter or variation in the
data.
o=± [{XrXfnn-Dp
(5)
Internal report of the Web Handling Research Center at
Oklahoma State University. July 1987.
For a normal bell-shaped distribution curve:
IK. Gil more. W.t-r «/.. Roll defect terminology, TAPP1 C.A. Rept.
1228. TAPPI PRESS. Atlanta. 1977.
90% of the sample is within A' ± 1.7a
17. Burns. J. W.. Tappi 61(1): 91(1978).
18 Routine control method RL313 (Cameron strain test). Tappi
95% of the sample is within X ± 2.0a
46(12): 12:1(1963).
19. Lucas. R. G., Winder crepe wrinkles—their causes and cures,
99% of the sample is within X± 2.5o
1981 Finishing and Converting Conference Proceedings,
TAPPI PRESS. Atlanta.
Standard error of the estimate
21). Hussain, S. M.. Farrell, W. R..and Gunning, J. R., Most paper
in the roll is in unstable condition. Canadian Pulp and Paper
The standard error of the estimate (SD) is a method of estimating a
Industrv, August 1968.
population mean from a sample mean.
Rand. f. and Eriksson. L. G.. Tappi 56(6): 153(1973).
Example: Given a sample of 20 Rhometer measurements with a
Ryli, N. et ul.. Method to measure the structure of newsprint,
mean of 45 and a standard deviation of 4, what is the 95%
1972 Finishing and Converting Conference Proceedings,
confidence interval for the population?
TAPPI PRESS. Atlanta.
23. Hussain. S. M., and Farrell, W. R., Tappi 60(5): 112(1977).
24. Pfeiffer, J. D.. Tappi 49(8): 342(1966). Pfeiffer, J. D.. Tappi
(6)
SD = a/(n,a)
25. 60(2): 115(1977). Pfeiffer, J. D.. Tappi 60(3): 106(1977).
26. Frede. Pneumatic web tension control and regulation, paper no.
= 4/(20l/2) = 0.89
27 D5 (10 pp.), PRP Automation, Antwerp, October 1966. Frye, K.
G., Tappi 50(7): 81(1967).
Since a 95% confidence interval is equal to ± 2a, we
multiply the standard error of the estimate by 2 and apply it 28. Ul'yanov, V.I., Tensometric apparatus for the control of web
29. winding, USSR patent 249.929, November 30, 1967. Eriksson.
to the sample mean:
L. G. et at., Tappi J. 66(1): 63(1983). McDonald, J. D. and
30 Farrell, W. R., Pulp Paper Can. 86(9): 56(1985).
ti = 45 ± 2(0.89) = 43.22 and 46.78
. Odell, M. H., Symons. R. E., and Brown, G. S., Appita 38(5):
31. 359(1985).
We are 95% confident that the mean hardness of the roll lies
Granlund. B., Computerized on-line fault detection in paper
between 43.22 and 46.78.
32. reels. Proceedings of the First Winding Technology Conference, Swedish Newsprint Research Center (TFC), Stockholm,
33. 1987.
Z-test for differences in means
34. Holmer, H. et at.. Changes in reel-density curves induced by
The Z-test is used to calculate the confidence level for
different winding parameters, Proceedings of the First
results of a statistical analysis.
W i n d i n g Technology Conference, Swedish Newsprint
Research Center (TFC), Stockholm, 1987. Komulainen, P., Roll
x:i
Z = \n-X\/\o/(» )\
(7) 35. quality measurement and control, 1982 Paper Finishing and
Converting Conference Proceedings, TAPPI PRESS. Atlanta,
Calculation from Example 3:
pp. 87-92; ABIPC 54: abstr. 159. Kendall, M. G. and Stuart, A.,
36. The advanced theory of statistics. Vol. I, Charles W. Griffin,
ri
Z = |40 - 441/(5/(4 )l= 1.60
London, 1958.
Significance of standard deviation
We then use a Z-table (standardized normal distribution) and
find that a Z value of 1.6 corresponds to a confidence level
of 94.5%.
Received for review May 18. 1988.
Accepted June 9. 1988.
Presented at the 1988 Finishing and Converting Conference.
Literature cited
1. Hadlock, A., Principles of winding, PIMA Fall Meeting
Proceedings. PIMA, New York. 1978.
2. Roisum, D. R., History of paper stresses during winding, 1986
Finishing and Converting Conference Proceedings, TAPPI
PRESS. Atlanta.
3. Roisum. D. R., Paper stresses during winding, Winding
Technology Conference Proceedings, Swedish Newsprint
Research Center, Stockholm, 1987.
4. Roisum, D. R., Tappi J. 71(1): 87(1988).
5. Catlow, M. G. and Walls, G. W., J. Textile Inst. Part 3,
T410U962).
6. Tramposch, H., J. Appl. Mech. 32(4): 865(1965): Trans. ASME
87:865(1965).
7. Tramposch, H., J. Appl. Mech. 34(4): 888(1967); Trans. ASME
89: 888(1967).
8. Altmann, H. C, Tappi 51(4): 176(1968).
9. Blaedel, K. K., A design approach to winding a roll of paper,
Ph.D. thesis (ME), University of Wisconsin at Madison, 1974.
10. Yagoda, II. P., Mech. Res. Communic. 7(2): 103(1980).
11. Yagoda, H. P.. Mech. Res. Communic. 7(3): 181(1980).
12. Yagoda. H. P., Mech. Res. Communic. 7(4): 233(1980).
13. Yagoda, H. P.. J. Appl. Mech. 47: 847(1980).
14. Hakiel, Z., Nonlinear model for wound roll stress, 1986
Finishing and Converting Conference Proceedings, TAPPI
PRESS, Atlanta, pp. 9-15.
15. Wu, Z., A treatise of wound roll models: the current art,
October 1988 Tappi Journal 103
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