Note: Descriptions are shown in the official language in which they were submitted.
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AN ALTERNATIVE METHOD FOR REDUCING WEB FEED RATE VARIATIONS
INDUCED BY PARENT ROLL GEOMETRY VARIATIONS
FIELD OF THE INVENTION
The present invention relates generally to methods for overcoming the problems
associated with geometrically induced web feed rate variations during the
unwinding of out-of-
round parent rolls. More particularly, the present invention relates to a
method for reducing the
tension variations associated with web feed rate changes that are induced by
parent roll geometry
variations to minimize oscillation while maximizing operating speed throughout
the entire
unwinding cycle.
BACKGROUND OF THE INVENTION
In the papermaking industry, it is generally known that paper to be converted
into a
consumer product such as paper towels, bath tissue, facial tissue, and the
like is initially
manufactured and wound into large rolls. By way of example only, these rolls,
commonly known
as parent rolls, may be on the order of 10 feet in diameter and 100 inches
across and generally
comprise a suitable paper wound on a core. In the usual case, a paper
converting facility will
have on hand a sufficient inventory of parent rolls to be able to meet the
expected demand for the
paper conversion as the paper product(s) are being manufactured.
Because of the soft nature of the paper used to manufacture paper towels, bath
tissue,
facial tissue, and the like, it is common for parent rolls to become out-of-
round. Not only the soft
nature of the paper, but also the physical size of the parent rolls, the
length of time during which
the parent rolls are stored, and the fact that roll grabbers used to transport
parent rolls grab them
about their circumference can contribute to this problem. As a result, by the
time many parent
rolls are placed on an unwind stand they have changed from the desired
cylindrical shape to an
out-of-round shape.
In extreme cases, the parent rolls can become oblong or generally egg-shaped.
But, even
when the parent roll is are only slightly out-of-round, there are considerable
problems. In an ideal
case with a perfectly round parent roll, the feed rate of a web material
coming off of a rotating
parent roll can be equal to the driving speed of a surface driven parent roll.
However, with an
out-of-round parent roll the feed rate can likely vary from the driving speed
of a surface drive
parent roll depending upon the radius at the web takeoff point at any moment
in time.
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=
2
With regard to the foregoing, it will be appreciated that the described
condition assumes
that the rotational speed of the parent roll remains substantially constant
throughout any
particular rotational cycle of the parent roll.
If the rotational speed remains substantially constant, the feed rate of a web
material
coming off of an out-of-round parent roll will necessarily vary during any
particular rotational
cycle depending upon the degree to which the parent roll is out-of-round. In
practice, however,
parent rolls are surface driven which means that if the radius at the drive
point changes, the
rotational speed can also change generally causing variations in the feed
rate. Since the paper
converting equipment downstream of the unwind stand is generally designed to
operate based
upon the assumption that the feed rate of a web material coming off of a
rotating parent roll will
always be equal to the driving speed of the parent roll, there are problems
created by web tension
spikes and slackening.
While a tension control system is typically associated with the equipment used
in a paper
converting facility, the rotational speed and the takeoff point radius can be
constantly changing in
nearly every case. At least to some extent, this change is unaccounted for by
typical tension
control systems. It can be dependent upon the degree to which the parent roll
is out-of-round and
can result in web feed rate variations and corresponding tension spikes and
slackening.
With an out-of-round parent roll, the instantaneous feed rate of the web
material can be
dependent upon the relationship at any point in time of the radius at the
drive point and the radius
at the web takeoff point. Generally and theoretically, where the out-of-round
parent roll is
generally oblong or egg-shaped, there will be two generally diametrically
opposed points where
the radius of the roll is greatest. These two points will be spaced
approximately 900 from the
corresponding generally diametrically opposed points where the radius of a
roll is smallest.
However, it is known that out-of-round parent rolls may not be perfectly
oblong or elliptical but,
rather, they may assume a somewhat flattened condition resembling a flat tire,
or an oblong or
egg-shape, or any other out-of-round shape depending upon many different
factors.
Regardless of the exact shape of the parent roll, at least one point in the
rotation of the
parent roll exists where the relationship between the web take off point
radius and the parent roll
drive point radius that results in the minimum feed rate of paper to the line.
At this point, the web
tension can spike since the feed rate of the web material is at a minimum and
less than what is
expected by the paper converting equipment downstream of the unwind stand.
Similarly, there
can exist at least one point in the rotation of the parent roll where the
relationship between the
web take off point radius and the parent roll drive point radius results in
the maximum feed rate
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of paper to the line. At this point, the web tension can slacken since the
feed rate of the web
material can be at a maximum and more than what is expected by the paper
converting
equipment downstream of the unwind stand. Since neither condition is conducive
to efficiently
operating paper converting equipment for manufacturing paper products such as
paper towels,
bath tissue and the like, and a spike in the web tension can even result in a
break in the web
material requiring a paper converting line to be shut down, there clearly is a
need to overcome
this problem.
In particular, the fact that out-of-round parent rolls create variable web
feed rates and
corresponding web tension spikes and web tension slackening has required that
the unwind stand
and associated paper converting equipment operating downstream thereof be run
at a slower
speed in many instances thereby creating an adverse impact on manufacturing
efficiency.
While various efforts have been made in the past to overcome one or more of
the
foregoing problems with out-of-round parent rolls, there has remained a need
to successfully
address the problems presented by web feed rate variations and corresponding
web tension spikes
and web tension slackening.
SUMMARY OF THE INVENTION
While it is known to manufacture products from a web material such as paper
towels,
bath tissue, facial tissue, and the like, it has remained to provide methods
for reducing feed rate
variations in the web material when unwinding a parent roll. Embodiments of
the present
disclosure described in detail herein provide methods having improved features
which result in
multiple advantages including enhanced reliability and lower manufacturing
costs. Such
methods not only overcome problems with currently utilized conventional
manufacturing
operations, but they also make it possible to minimize wasted materials and
resources associated
with such manufacturing operations.
In certain embodiments, the method can reduce feed rate variations in a web
material
when unwinding a parent roll to transport the web material away from the
parent roll at a web
takeoff point. The method can comprise dividing the parent roll, which has a
core plug mounted
on a shaft defining a longitudinal axis of the parent roll, into a plurality
of angular sectors
disposed about the longitudinal axis. An ideal speed reference signal
corresponding to the web
feed rate of a round parent roll can be used to drive the parent roll at a
driving speed and at a
drive point located on the outer surface either coincident with or spaced from
the web takeoff
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point. The method may further comprise correcting for fluctuations in the
drive point radii
and/or correcting for fluctuations in the web takeoff point radii.
In correcting for the drive point radius variations, the method can include
determining an
instantaneous rotational speed for each of the sectors as the parent roll is
being driven, for
example, by a motor-driven belt on the outer surface thereof. The method
further includes
calculating the radius at the drive point from the driving and rotational
speeds for each of the
sectors. It also includes determining an ideal drive point radius by averaging
the calculated drive
point radii for all of the sectors and calculating a drive point correction
factor for each of the
sectors where the drive point correction factor is a function of the
calculated drive point radius
and the ideal drive point radius.
In correcting for the web takeoff point radius variations, the method includes
measuring
the radius at or near the web takeoff point of the parent roll for each of the
sectors as the parent
roll is being driven at the drive point. In addition, the method includes
calculating an ideal web
takeoff point radius by determining an average for the measured web takeoff
radii for all of the
sectors and calculating a web takeoff point correction factor for the radius
at the web takeoff
point for each of the sectors where the web takeoff point correction factor is
a function of the
ideal and measured web takeoff point radius for each of the sectors.
The method improves the driving speed of the parent roll on a sector-by-sector
basis
using the ideal speed reference signal. The ideal speed reference signal is
initially used to control
the parent roll rotation speed based upon operator input (assuming a perfectly
round parent roll)
as well as other factors, such as tension control system feedback and ramp
generating algorithms.
The ideal speed reference signal is multiplied by the drive point correction
factor or the web
takeoff point correction factor for each sector of the parent roll to generate
an improved speed
reference signal for each sector. The improved speed reference signal is
calculated on the fly
(and not stored) based upon the ideal speed reference signal from moment to
moment, taking into
account factors such as tension control system feedback and ramp generating
algorithms. Finally,
the method in these embodiments includes using the improved speed reference
signal to adjust
the driving speed of the parent roll for each sector to the improved driving
speed.
Adjusting the driving speed of the parent roll in this manner can cause the
web feed rate
of the parent roll to better approximate the web feed rate of an ideal
(perfectly round) parent roll
on a continuous basis during the unwinding of a web material from a parent
roll. As a result,
feed rate variations in the web material at the web takeoff point can be
reduced or even
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eliminated. Thus, any web tension spikes and slackening associated with radial
deviations from a
perfectly round parent roll can be minimized or even eliminated.
BRIEF DESCRIPTION OF THE DRAWINGS
5 Fig. 1 is a diagram illustrating equation concepts involving the web
flow feed rate, Rate,,
the rotational speed, ni, and the web takeoff point radius Rtp, for a parent
roll;
Fig. 2 is a diagram illustrating equation concepts involving the rotational
speed, clõ the
driving speed, Mõ and the drive point radius, Rd, for a parent roll;
Fig. 3 is a diagram illustrating equation concepts involving the web flow feed
rate, Rateõ
the web takeoff point radius, Rtp, and the web drive point radius, Rap, for a
parent roll;
Fig. 4 is a diagram illustrating equation concepts involving the web flow feed
rate, Rateõ
and the driving speed, M,, for the case where the parent roll is perfectly
round;
Fig. 5 is a diagram illustrating an out-of-round parent roll having a major
axis, R1, and a
minor axis, R2, which are approximately 90 degrees out of phase;
Fig. 6 is a diagram illustrating an out-of-round parent roll having a major
axis, R1,
orthogonal to the drive point and a minor axis, R2, orthogonal to the web
takeoff point;
Fig. 7 is a diagram illustrating an out-of-round parent roll having a minor
axis, R2,
orthogonal to the drive point and a major axis, R1, orthogonal to the web
takeoff point;
Fig. 8 is a diagram illustrating an out-of-round parent roll that is generally
egg shaped
having unequal major axes and unequal minor axes;
Fig. 9 is a diagram illustrating the out-of-round parent roll of Fig. 8 which
has been
divided into four sectors, 1-4;
Fig. 10 is a diagram illustrating the out-of-round parent roll of Fig. 8 with
the larger of the
minor axes, R1, at the drive point; and
Fig. 11 is an example of a data table illustrating four actual angular sectors
each divided
into eight virtual sectors for smoothir g transitions.
DETAILED DESCRIPTION OF THE INVENTION
In the manufacture of web material products including paper products such as
paper
towels, bath tissue, facial tissue, and the like, the web material which is to
be converted into such
products is initially manufactured on large parent rolls and placed on unwind
stands. The
embodiments described in detail below provide exemplary, non-limiting examples
of methods for
reducing feed-rate variations in a web material when unwinding a parent roll
to transport the web
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material from the parent roll at a web takeoff point. In particular, the
embodiments described
below provide exemplary, non-limiting methods which take into account any out-
of-round
characteristics of the parent roll and make appropriate adjustments to reduce
web feed rate
variations.
With regard to these non-limiting examples, the described methods make it
possible to
effectively and efficiently operate an unwind stand as part of a paper
converting operation at
maximum operating speed without encountering any significant and/or damaging
deviations in
the tension of the web material as it leaves an out-of-round parent roll at
the web takeoff point.
In order to understand the methods making it possible to reduce feed rate
variations in a
web material as it is being transported away from an out-of-round parent roll,
it is instructive to
consider certain calculations, compare an ideal parent roll case with an out-
of-round parent roll
case, and describe the effects of out-of-round parent rolls on the web feed
rate and web material
tension.
WEB FEED RATE CALCULATION
The instantaneous feed rate of a web material coming off of a rotating parent
roll at any
point in time, Rate!, can be represented as a function of at least two
variables. The two most
significant variables involved are the rotational speed, nb of the parent roll
at any given moment
and the effective radius, R1p, of the parent roll at the web takeoff point at
that given moment. The
instantaneous feed rate of the web material may be represented by the
following equation:
Equation 1 Rate, = 0.,(27rRip)
Where:
Rate, represents the instantaneous feed rate of the web material from the
parent roll
Q, represents the instantaneous rotational speed of a surface
driven parent roll
R1p represents the instantaneous radius of the parent roll at the
web takeoff point
Referring to Fig. 1, the concepts from Equation 1 can be better understood
since each of
the variables in the equation is diagrammatically illustrated.
Furthermore, the instantaneous rotational speed, Qõ of a surface driven parent
roll is a
function of two variables. The two variables involved are the instantaneous
surface or driving
speed, Mõ of the mechanism that is moving the parent roll and the
instantaneous radius of the
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parent roll at the point or location at which the parent roll is being driven,
Rdp. The instantaneous
rotational speed may be represented by the following equation:
Equation 2 SI, = M/(27tRdp)
Where:
represents the instantaneous rotational speed of a surface driven parent roll
represents the instantaneous driving speed of the parent roll driving
mechanism
Rd,,, represents the instantaneous radius of the parent roll at the
drive point
Referring to Fig. 2, the concepts from Equation 2 can be better understood
since each of
the variables in the equation is diagrammatically illustrated.
With regard to the instantaneous drive point radius, Rd, it can be determined
from
Equation 2 by multiplying both sides of the equation by Rd,,,/j to give
Equation 2a below:
Equation 2a Rdp = M/2711-2,
Substituting M/(27tRdp) for SI, in Equation 1 (based on Equation 2) results in
Equation 3
which relates the instantaneous feed rate, Rateõ of the web material from the
parent roll to the
instantaneous driving speed, Mõ of the parent roll driving mechanism, the
instantaneous radius,
Rd,,,, of the parent roll at the drive point, and the instantaneous radius,
Rip, of the parent roll at the
web takeoff point:
Equation 3 Rate, = 1111,/(27tRdp)] x [2n-Ripl
If Equation 3 is simplified by canceling out the br factor in the numerator
and
denominator, the resulting Equation 4 becomes:
Equatirm 4 Rate, = M,x [Rtp/Rdp]
Referring to Fig. 3, the concepts from Equation 4 can be better understood
since each of
the variables in the equation is diagrammatically illustrated.
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IDEAL PARENT ROLL CASE
In the ideal parent roll case (see Fig. 4), the parent roll on the unwind
stand is perfectly
round which results in the radii at all points about the outer surface being
equal and, as a
consequence, the instantaneous radius, Rd, of the parent roll at the drive
point is equal to the
instantaneous radius, R1p, of the parent roll at the web takeoff point. For
the ideal parent roll case,
Rip = Rdp so, in Equation 4, it will be appreciated that the equation will
simplify to Rate, = M,,
i.e., the instantaneous feed rate of the web material from the parent roll
will be equal to the
instantaneous driving speed of the driving mechanism on the outer surface of
the parent roll.
to THE OUT-OF-ROUND PARENT ROLL
In situations where a parent roll is introducing web material into the paper
converting
equipment is not perfectly round, the differences between Rd p and R1p should
be taken into
account. In practice, it is known that one type of out-of-round parent roll
can be an "egg shaped"
parent roll characterized by a major axis and a minor axis typically disposed
about 90 degrees out
of phase. However, the exact shape of the parent roll as well as the angular
relationship of the
major axes and the minor axes will be understood by one of skill in the art to
vary from parent
roll to parent roll.
For purposes of illustration only, Fig. 6 is a diagram of an out-of-round
parent roll having
a major axis, R1, orthogonal to the drive point and a minor axis, R2,
orthogonal to the web
takeoff point, and Fig. 7 is a diagram of an out-of-round parent roll having a
minor axis, R2,
orthogonal to the drive point and a major axis, R1, orthogonal to the web
takeoff point.
EFFECTS OF OUT-OF-ROUND PARENT ROLLS ON WEB FEED RATE AND TENSION
When the driving mechanism on an unwind stand is driving an out-of-round
parent roll,
there can be a continuously varying feed rate of the web material from the
parent roll. The
varying web feed rates at the web takeoff point can typically reach a maximum
and a minimum
in two different cases. To understand the concepts, it is useful to consider
the web takeoff point
while assuming the parent roll drive point and the web takeoff point are 90
degrees apart.
Case 1 is when the major axis of the parent roll, represented by R1 in Figs. 5
and 6, is
orthogonal to the drive point of the parent roll and the minor axis of the
parent roll, represented
by R2 in Figs. 5 and 6, is orthogonal to the web takeoff point of the parent
roll.
For illustrative purposes only, it may be assumed that the parent roll started
out with the
radii at all points about the outer surface of the parent roll equal to 100
units. However, it may
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also be assumed that due to certain imperfections in the web material and/or
roll handling
damage, R1 = Rdp = 105 and R2 = Rtp = 95. Further, for purposes of
illustration it may also be
assumed that the driving speed, A41, of the driving mechanism is 1000 units.
Substituting these values into Equation 4 [Rate, = M, x [Rtp/Rdp]]
produces:
Rate, = 1000 x [95/105] = 904.76 units of web material/unit time
In this case, the paper converting line was expecting web material at a rate
of 1000 units
per unit time but was actually receiving web at a rate of 904.76 units per
unit time.
For the conditions specified above for illustrative purposes only, Case 1 can
represent the
web material feed rate when it is at a minimum value and, consequently, it
also represents the
web tension when it is at a maximum value.
Case 2 is when the parent roll has rotated to a point where the major axis,
represented by
RI in Fig. 7, is orthogonal to the web takeoff point of the parent roll and
the minor axis,
represented by R2 in Fig. 7, is orthogonal to the drive point of the parent
roll.
For illustrative purposes only, it can be assumed that the same parent roll
described in
Case 1 is being used where now R1 = Rd p = 95 and R2 = R1p = 105, and for
illustrative purposes,
it may still be assumed that the driving speed, Mb is 1000 units.
Substituting these values into Equation 4 [Rate, = M, x [R(7/Rd]] produces:
Rate, = 1000 x [105/95] = 1105.26 units of web material/unit time
In this case, the paper converting line was expecting web material at a rate
of 1000 units
per unit time but was actually receiving web at a rate of 1105.26 units per
unit time.
For the conditions specified above for illustration purposes only, Case 2
represents the
web material feed rate when it is at a maximum value and, consequently, it
also represents the
web tension when it is at a minimum value
As Case 1 and 2 illustrate, the variations in radius of an out-of-round parent
roll can
produce significant variations in web feed rate as the parent roll is surface
driven at a constant
speed, M,.
SOLUTION TO THE PROBLEM
The solution to reducing web feed rate variations as the out-of-round parent
roll is being
surface driven can be illustrated by ai example comprising a number of steps,
as follows:
1. Start with an exemplary simple "egg- shaped" parent roll that has the
following
properties:
a. It is asymmetrical.
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b. It has a minor axis of 100 that is shown vertically in Fig. 8 as being
comprised of
a radius RI = 5/ directly opposite a radius R3 = 49.
c. It has a major axis of 110 that is shown horizontally in Fig. 8
as being comprised
of a radius R2 = 56 directly opposite a radius R4 = 54.
5 2. Divide the parent roll into n sectors, e.g., the value of n shown in
Fig. 9 is 4 to simplify
the example, but actual values of n could be 20 or higher depending on the
application,
the speed at which information can be processed, and the responsiveness of the
system.
3. Create a table of n rows (one for each of the n sectors) with columns
for the following
information:
10 a. Sector #
b. Rdp - Drive Point Radius
C. Cdp ¨ Correction Factor for Drive Point
d. Rip - Web Takeoff Point Radius
e. Ctp ¨ Correction Factor for Web Takeoff Point
f. C1 ¨ Total Correction Factor
Sector # Rdp Cdp Rtp C fp
1
2
3
4
Rdp = Rtpi ¨
In addition to creating the table, two new variables need to be defined. These
two new
variables include the Ideal Drive Point Radius, Rdpõ and the Ideal Web Takeoff
Point
Radius, Rim. The manner of determining these variables is described below.
4. Calculate the Drive Point Radius, Rd, for each of the sectors, 1,
2,...n, of the parent roll.
Using a parent roll rotational speed and position determining device, e.g., a
shaft encoder,
it is possible to develop two critical pieces of information for making the
calculation for
each of the sectors, 1, 2,...n, of the parent roll:
a. The present rotational position of the parent roll
b. The present rotational speed of the parent roll
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Thus, as the parent roll rotates, the rotational position information provided
by the parent
roll rotational speed and position determining device is used to determine
which sector of
the parent roll is presently being driven. By using the relationship from
Equation 2a, Rdp
= M/27/11,, it is possible to calculate Rap for that sector by dividing the
driving speed, g,
(which is known by the logic device) by the rotational speed, n,, (reported by
the parent
roll rotational speed and position determining device) times 27c. When this
value has been
calculated, it can be stored in the table above to create a mathematical
representation of
the shape of the parent roll from the drive point perspective.
5. Calculate the Ideal Drive Point Radius, Rdpi, for the parent roll by adding
the Rdp values
from the table for all of the sectors, 1, 2,...n, and dividing the sum by the
total number of
sectors, n, to determine the average.
6. Calculate the Drive Point Correction Factor, Cdp, for each of the
sectors, 1, 2,...n, of the
parent roll using the formula: Cdp (1, 2, ...n) = Rdp(1, 2,...n) /Rd.
7. Measure the Web Takeoff Point Radius, Rtp, for each of the sectors, 1,
2,...n, and store
these values in the table to create a mathematical representation of the shape
of the parent
roll from a web takeoff point perspective. For purposes of illustration only,
it can be
assumed that the measurement of the Web Takeoff Point Radius, Rtp, can occur
at the
exact point where the web is actually coming off of the parent roll so that
the reading of
the Web Takeoff Point Radius, Rip, for a given sector corresponds to the Drive
Point
Radius, Rd, calculated for the sector corresponding to that given sector.
However, in
practice the Web Takeoff Point Radius, Rtp, may be measured any number of
degrees
ahead of the actual web take-off point (to eliminate the effects of web
flutter at the actual
web take off point and also to permit a location conducive to mounting of the
sensor) and
through data manipulation techniques, be written into the appropriate sector
of the data
table.
8. Calculate the Ideal Web Takeoff Point Radius, Rtp1, for the parent roll by
adding the Rtp
values from the table for all of the sectors, 1, 2,...n, and dividing the sum
by the total
number of sectors, n, to determine the average.
9. Calculate the Web Takeoff Point Correction Factor, Ctp, for each of the
sectors, 1, 2,...n,
of the parent roll using the formula: Cfp (1, 2,...n) = Rtp, /R0(1, 2,...n).
10. For each of the sectors, 1, 2,...n, calculate the Total Correction Factor,
C,(1, 2,...n), by
multiplying the Drive Point Correction Factor, Cdp(1, 2,...n), by the Web
Takeoff Point
Correction Factor, C,p(1, 2,...n).
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11. Correct the driving speed, /1//1, of the parent roll on a sector by sector
basis as the parent
roll rotates using an ideal speed reference signal, SRSõ corresponding to an
ideal parent
roll rotation speed. (The ideal speed reference signal, SRSõ is initially used
to control the
parent roll rotation speed based upon operator input (assuming a perfectly
round parent
roll) as well as other factors, such as tension control system feedback and
ramp
generating algorithms.)
12. Multiply the ideal speed reference signal, SRSõ by the Total Correction
Factor, Cd1,
2,...n), for each sector of the parent roll to generate a corrected speed
reference signal,
SRSICorrected, for each sector. (SRSiCorrected for each sector is calculated
on the fly (and not
stored) based upon the ideal speed reference signal, SRSõ from moment to
moment,
noting that SRS, already takes into account factors such as tension control
system
feedback and ramp generating algorithms.)
13. Finally, adjust the driving speed, M,, to a corrected driving speed,
MICorrected, as each
sector approaches or is at the drive point using the corrected speed reference
signal,
SRSICorrectech for each sector. (Adjusting the driving speed of the out-of-
round parent roll
in this manner causes the feed rate of the web to at least approximate the
feed rate off of
an ideal (perfectly round) parent roll. As a result, feed rate variations in
the web material
at the web takeoff point are reduced or eliminated and, thus, web tension
spikes and web
tension slackening associated with radial deviations from a perfectly round
parent roll are
eliminated or at least minimized.)
Following the above procedure, and assuming the measured and calculated values
are as
set forth above for sectors 1-4 where R1= 51, R2 = 56, R3 = 49 and R4 = 54,
the Total
Correction Factor, CT, can be determined using the table above and the steps
set forth above in
the following manner:
Sector Rdp Cdp Ru, CO, Ct
1 51 0.971 54 0.97 0.94
2 56 1.066 51 1.03 1.10
3 49 0.933 56 0.94 0.87
4 54 1.029 49 1.07 1.10
Rdp, = 52.5 Rip, = 52.5
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ALTERNATIVE SOLUTIONS TO THE PROBLEM ¨ DERIVING AN IMPROVED SPEED
REFERENCE SIGNAL
Reduction to web feed rate variations can be achieved through additional
approaches that
may not achieve the same level of correction as the above solution but still
provide an
improvement to the out-of-round case. As detailed below, these solutions
include deriving a
modified total correction factor, correcting for drive point radius variations
alone, and/or
correcting for the web takeoff point radius variations alone. In these
embodiments, an improved
speed reference signal, SRSamproved, is calculated, although the means of
calculating the improved
speed reference signal, SRSdmproved, differs as detailed below. The improved
speed reference
signal, SRSzimproved is then used to adjust the driving speed, M, to an
improved driving speed,
Mdmproved
A. Calculate a Modified Total Correction Factor Using A Percentage of the
Drive Point
Correction Factor and/or A Percentage of the Web Takeoff Point Correction
Factor
In one embodiment, a Modified Total Correction Factor, Grmodified, may be
determined. The
Modified Total Correction Factor, CTmochried, may be calculated by multiplying
(i) a modified
drive point correction factor by a modified web takeoff point correction
factor; (ii)a modified
drive point correction factor by the ,eb takeoff point correction factor; or
(iii) the drive point
correction factor by the modified web takeoff point correction factor.
Essentially, the steps listed
above remain the same, except step 3 (where the table can now include
additional columns as
necessary such as columns for Cdpmodified = Modified Drive Point Correction
Factor, Ctpmoddied=
Modified Web Takeoff Point Correction Factor, Crmodified ¨ Modified Total
Correction Factor
and/or columns for the selected adjustment percentages to be used (x and y))
and steps 10-13. In
this embodiment, steps 1-9 in the above section are repeated followed by:
10. For each of the sectors, 1, 2,...n,
a. select a
drive point adjustment percentage x to be used in association with the
drive point correction factor, Cdp, and/or a web takeoff point adjustment
percentage y to
be used in association with the web takeoff point correction factor, C,,,,.
b.
calculate a modified drive point correction factor and/or a modified web
takeoff
point correction factor using the appropriate formula below:
(i.) use the following
formula to calculate a modified drive point correction
factor: Cdpmodified: Cdpmocfified = 1-(1-Cdp)*X.
(ii)
use the following formula to calculate a modified web takeoff point
correction factor: Cipmochfied : Ctpmodtfied= 1-(1-CtP)*Y=
CA 02889220 2015-04-23
14
c. Calculate a modified total correction factor, CTmodIfied(1,
2,...n), by
(i) multiplying the modified drive point correction factor by the modified
web
takeoff point correction factor;
(ii) multiplying the modified drive point correction factor by the web
takeoff
point correction factor; or
(iii) multiplying the drive point correction factor by the modified web
takeoff
point correction factor.
(The adjustment percentages selected, x and y, may be the same or different.
In one
nonlimiting example, x is 100 and y is less than 100. In another nonlimiting
example, y is
100 and x is less than 100. In yet another nonlimiting example, both x and y
may be less than
100. In one embodiment, either a modified drive point correction factor or a
modified web
takeoff point correction factor is calculated and used. In another embodiment,
both a
modified drive point correction factor and a modified web takeoff point
correction factor are
calculated and used.)
11. Correct the driving speed, Mõ of the parent roll on a sector by sector
basis as the parent
roll rotates using an ideal speed reference signal, SRSõ corresponding to an
ideal parent
roll rotation speed. (The ideal speed reference signal, SRSõ is initially used
to control the
parent roll rotation speed based upon operator input (assuming a perfectly
round parent
roll) as well as other factors, such as tension control system feedback and
ramp
generating algorithms.)
12. Multiply the ideal speed reference signal, SRSõ by the Modified Total
Correction Factor,
CTmodtfied (1, 2...n), for each sector of the parent roll to generate an
improved speed
reference signal, SRSamprowd, for each sector. (SRSthnproved for each sector
is calculated on
the fly (and not stored) based upon the ideal speed reference signal, SRSõ
from moment to
moment, noting that SRS, already takes into account factors such as tension
control
system feedback and ramp generating algorithms.)
13. Finally, adjust the driving speed, Mõ to an improved driving speed,
Milmproved, as each
sector approaches or is at the drive point using the corrected speed reference
signal,
SRS,/,,,proved, for each sector. (Adjusting the driving speed of the out-of-
round parent roll
in this manner causes the feed rate of the web to at least approximate the
feed rate off of
an ideal (perfectly round) parent roll. Fluctuations in the drive point radii
and/or the web
takeoff point radii can be reduced to some degree. As a result, feed rate
variations in the
web material at the web takeoff point are reduced or eliminated and, thus, web
tension
CA 02889220 2015-04-23
spikes and web tension slaening associated with radial deviations from a
perfectly
round parent roll are eliminated or at least minimized.)
Following the above procedure, and assuming the measured and calculated values
are as
5 set forth above for sectors 1-4 where R1= 51, R2 = 56, R3 = 49 and R4 =
54, the Modified Total
Correction Factor, CTmodified, can be determined using the table above and the
steps set forth
above in the following manner:
Sector Rdp Cdp Drive Cdpmothfied Rip Cip Web
Connothfied C7Modified
Point Takeoff
Adjustment Point
Adjustment
(x)
(Y)
1 51 0.971 50 0.985 54 0.97 70 0.979
0.965
2 56 1.066 50 1.033 51 1.03 70 1.021
1.055
3 49 0.933 50 0.967 56 0.94 70
0.958 0.926
4 54 1.029 50 1.015 49 1.07 70 1.049
1.064
Rdp, =52.5 Rtp, =52.5
The calculations in the above table represent one nonlimiting example.
B. Correcting for Fluctuations in Drive Point Radii and Rotational Speed
It may be advantageous to correct for the drive point radii and rotational
speed fluctuations
without addressing fluctuations in web takeoff point radii for various
reasons. For example, by
not measuring the web takeoff point, time and resources can be reduced.
Indeed, the costs of
measuring equipment (e.g., one or more lasers) could be excessive in some
processes. Focusing
on just the drive point radii calculations (and related rotational speed)
avoids such expense.
Reducing web feed rate variations by addressing fluctuations in the drive
point radii (and
consequently rotational speed) as the out-of-round parent roll is being
surface driven can be
illustrated by an example comprising a number of steps, as follows:
1. Start with an exemplary simple "egg- shaped" parent roll that has the
following
properties:
a. It is asymmetrical.
b. It has a minor axis of 100 that is shown vertically in Fig. 8 as being
comprised of
a radius RI = 51 directly opposite a radius R3 = 49.
CA 02889220 2015-04-23
16
c. It has a major axis of 110 that is shown horizontally in Fig. 8
as being comprised
of a radius R2 = 56 directly opposite a radius R4 = 54.
2. Divide the parent roll into n sectors, e.g., the value of n shown in
Fig. 9 is 4 to simplify
the example, but actual values of n could be 20 or higher depending on the
application, the
speed at which information can be processed, and the responsiveness of the
system.
3. Create a table of n rows (one for each of the n sectors) with columns
for the following
information:
a. Sector #
b. Rdp - Drive Point Radius
C. Cdp ¨ Correction Factor for Drive Point
Sector # Rdp Cdp
2
3
4
Rdpi =
In addition to creating the table, one new variable needs to be defined: the
Ideal Drive Point
Radius, Rdp,. The manner of determining this variable is described below.
4. Calculate the Drive Point Radius, Rd, for each of the sectors, 1,
2,...n, of the parent roll.
Using a parent roll rotational speed and position determining device, e.g., a
shaft encoder, it
is possible to develop two critical pieces of information for making the
calculation for each of
the sectors, 1, 2,...n, of the parent roll:
a. The present rotational position of the parent roll
b. The present rotational speed of the parent roll
Thus, as the parent roll rotates, the rotational position information provided
by the parent roll
rotational speed and position determining device is used to determine which
sector of the
parent roll is presently being driven. By using the relationship from Equation
2a, Rdp =
M/27'11,, it is possible to calculate Rdp for that sector by dividing the
instantaneous driving
speed, iv, (which is known by the logic device) by the instantaneous
rotational speed, sz,
(reported by the parent roll rotational speed and position determining device)
times 2n. Once
this value has been calculated, it can be stored in the table above (in the
row associated with
CA 02889220 2015-04-23
17
that sector) to create a mathematical representation of the radius of the
parent roll at that
sector from the drive point perspective. This process can be repeated for each
sector of the
parent roll at which point a mathematical representation of the shape of the
parent roll, from
the drive point perspective, can be stored in memory.
5. Calculate the Ideal Drive Point Radius, Rd,, for the parent roll by adding
the Rdp values
from the table for all of the sectors, 1, 2,...n, and dividing the sum by the
total number of
sectors, n, to determine the average.
6. Calculate the Drive Point Correction Factor, Cdp, for each of the sectors,
1, 2,...n, of the
parent roll using the formula: Cdp (1, 2, ...n) = Rdp(1, 2,...n) / Rdpi.
7. Correct the driving speed, M, of the parent roll on a sector by sector
basis as the parent
roll rotates using an ideal speed reference signal, SRS, corresponding to an
ideal parent roll
rotation speed. (The ideal speed reference signal, SRS, is initially used to
control the parent
roll rotation speed based upon operator input (assuming a perfectly round
parent roll) as well
as other factors, such as tension control system feedback and ramp generating
algorithms.)
8. Multiply the ideal speed reference signal, SRS, by the Drive Point
Correction Factor, Cdp
(1, 2,...n), for each sector of the parent roll to generate an improved speed
reference signal,
SRSihnproved, for each sector. (SRSthnproved for each sector is calculated on
the fly (and not
stored) based upon the ideal speed reference signal, SRS, from moment to
moment, noting
that SRS, already takes into account factors such as tension control system
feedback and ramp
generating algorithms.)
9. Finally, adjust the driving speed, Mõ to an improved driving speed,
Maniproved, as each
sector approaches or is at the drive point using the corrected speed reference
signal,
SRAStImproved, for each sector. (Adjusting the driving speed of the out-of-
round parent roll in
this manner causes the instantaneous rotational speed, Q,, to be substantially
consistent
despite the position of the roll, the sector, the fluctuating radii or other
factors as explained
below. As explained earlier, instantaneous rotational speed, ciõ is a
significant factor in
determining the instantaneous feed rate. Therefore, by holding the rotational
speed constant
throughout the rotation of the entire roll, feed rate variations in the web
material at the web
takeoff point are reduced or eliminated and, thus, web tension spikes and web
tension
slackening associated with radial deviations from a perfectly round parent
roll are eliminated
or at least minimized.)
CA 02889220 2015-04-23
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Following the above procedure, and assuming the measured and calculated values
are as
set forth above for sectors 1-4 where R1= 51, R2 = 56, R3 = 49 and R4 = 54,
the Drive Point
Correction Factor, Cdp, can be determined using the table above and the steps
set forth above
in the following manner:
Sector Rdp Cdp
1 51 0.971
2 56 1.0 6 6
3 49 0.933
4 54 1.0 2 9
Rdp, =52.5
Further to the above, using the relationship in Equation 2, SI, = M,/(27rRdp),
it becomes
apparent how a substantially consistent rotational speed can be obtained. As
explained, the
driving speed, M, is adjusted to become the improved driving speed, M
'Improved, which is
equivalent to drive point correction factor, Cdp, multiplied by the ideal
speed reference signal,
SRS, . Further, Cdp for a given sector is equivalent to Rdp/Rdp,. Substituting
these variables into
Equation 2, results in:
Equation 5 û = M1/(2gRdp) = Cdp x SRS,/(27rRdp) = Rdp/Rdp, x SRSi/(2gRdp)
The drive point radius is canceled out of the equation (as it is in both the
numerator and the
denominator), resulting in:
Equation 6 s-2,= sRs/(27/-Rdp).
In other words, the instantaneous rotational speed is no longer affected by
the actual drive point
in a given sector. Rather, the instantaneous rotational speed becomes a
function of non-changing
variables: the ideal reference signal and the ideal drive point radius. Again,
holding the
rotational speed constant throughout the roll's rotation eliminates or reduces
feed rate variations
normally attributable to fluctuations in the instantaneous rotational speed
that result from
fluctuations in the drive point radii.
C. Correcting for Fluctuations in Web Takeoff Radii
In an alternative embodiment, it may be advantageous to correct for
fluctuations in web
takeoff radii without addressing drive point radii variations. This solution
may be useful, for
example, where the drive point radii cannot be calculated. Reducing web feed
rate variations by
CA 02889220 2015-04-23
19
correcting for fluctuations in the web takeoff point radii as the out-of-round
parent roll is being
surface driven can be illustrated by an example comprising a number of steps,
as follows:
1. Start with an exemplary simple "egg- shaped" parent roll that has the
following
properties:
a. It is asymmetrical.
b. It has a minor axis of 100 that is shown vertically in Fig. 8 as being
comprised of
a radius RI = 51 directly opposite a radius R3 = 49.
c. It has a major axis of 110 that is shown horizontally in Fig. 8 as being
comprised
of a radius R2 = 56 directly opposite a radius R4 = 54.
2. Divide the parent roll into n sectors, e.g., the value of n shown in Fig. 9
is 4 to simplify
the example, but actual values of n could be 20 or higher depending on the
application,
the speed at which information can be processed, and the responsiveness of the
system.
3. Create a table of n rows (one for each of the n sectors) with columns for
the following
information:
a. Sector #
b. Ro, - Web Takeoff Point Radius
c. Co ¨ Correction Factor for Web Takeoff Point
Sector # Rfp cip
1
2
3
4
Rfp, -
In addition to creating the table, a new variable needs to be defined: the
Ideal Web
Takeoff Point Radius, Rtp,. The manner of determining this variable is
described below.
4. Measure the Web Takeoff Point Radius, Rtp, for each of the sectors, 1,
2,...n, and store
these values in the table to create a mathematical representation of the shape
of the parent
roll from a web takeoff point perspective. For purposes of illustration only,
it can be
assumed that the measurement of the Web Takeoff Point Radius, Ro can occur at
the
exact point where the web is actually coming off of the parent roll so that
the reading of
the Web Takeoff Point Radius, Rip, for a given sector corresponds to the Drive
Point
CA 02889220 2015-04-23
Radius, Rd, calculated for the sector corresponding to that given sector.
However, in
practice the Web Takeoff Point Radius, Rip, may be measured any number of
degrees
ahead of the actual web take-off point (to eliminate the effects of web
flutter at the actual
web take off point and also to permit a location conducive to mounting of the
sensor) and
5 through data manipulation techniques, be written into the appropriate
sector of the data
table.
5. Calculate the Ideal Web Takeoff Point Radius, Rtp,, for the parent roll by
adding the Rtp
values from the table for all of the sectors, 1, 2,...n, and dividing the sum
by the total
number of sectors, n, to determine the average.
10 6. Calculate the Web Takeoff Point Correction Factor, Co, for each
of the sectors, 1, 2,...n,
of the parent roll using the formula: Co (1, 2,...n) = R,1 /4(1, 2,...n).
7. Correct the driving speed, M,, of the parent roll on a sector by sector
basis as the parent
roll rotates using an ideal speed reference signal, SRSõ corresponding to an
ideal parent
roll rotation speed. (The ideal speed reference signal, SRSõ is initially used
to control the
15 parent roll rotation speed based upon operator input (assuming a
perfectly round parent
roll) as well as other factors, such as tension control system feedback and
ramp
generating algorithms.)
8. Multiply the ideal speed reference signal, SRSõ by the Web Takeoff Point
Correction
Factor, C1(1, 2,...n), for each sector of the parent roll to generate an
improved speed
20 reference signal, SRSiimproved, for each sector. (SRSIImproved for
each sector is calculated on
the fly (and not stored) based upon the ideal speed reference signal, SRSõ
from moment to
moment, noting that SRS, already takes into account factors such as tension
control
system feedback and ramp generating algorithms.)
9. Finally, adjust the driving speed, Mõ to an improved driving speed,
Mamproved, as each
sector approaches or is at the drive point using the corrected speed reference
signal,
SRSamproved, for each sector. (Adjusting the driving speed of the out-of-round
parent roll in
this manner causes the feed rate of the web to at least approximate the feed
rate off of an
ideal (perfectly round) parent roll by eliminating or reducing variations in
the web takeoff
point radii. As a result, feed rate variations in the web material at the web
takeoff
point are reduced or eliminated and, thus, web tension spikes and web tension
slackening
associated with radial deviations from a perfectly round parent roll are
eliminated or at
least minimized.)
CA 02889220 2015-04-23
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Following the above procedure, and assuming the measured and calculated values
are as
set forth above for sectors 1-4 where R1= 51, R2 = 56, R3 = 49 and R4 = 54,
the Web Takeoff
Point Correction Factor, Ctp, can be determined using the table above and the
steps set forth
above in the following manner:
Sector Ru, Cip
1 54 0.97
2 51 1.03
3 56 0.94
4 49 1.07
R1p1 = 52.5
With each of the above solutions, other factors that may need to be taken into
account can
include the fact that as the parent roll unwinds, the shape of the parent roll
can change making it
necessary to periodically remeasure and recalculate the various parameters
noted above. At some
point during unwinding of the parent roll, the rotational speed of the parent
roll may be too fast
for correction of the driving speed, although typically this will not occur
until the parent roll
becomes smaller and less out-of-round.
From the foregoing, it will be appreciated that the method of the present
invention can
reduce variations in the feed rate, and hence variation in tension in a web
material when
unwinding a parent roll to transport the web material away from the parent
roll at a web takeoff
point. This can be accomplished by initially dividing the parent roll into a
plurality of angular
sectors which are disposed about the longitudinal axis defined by the shaft on
which the core
plug of the parent roll is mounted (see Fig. 9). The angular sectors may
advantageously be equal
in size such that each sector, S, measured in degrees may be determined by the
formula: S =
360 /n where n is the total number of sectors. The method can include using an
ideal speed
reference signal corresponding to an ideal parent roll rotation speed for a
round parent roll to
drive the parent roll at a speed and at a location on the outer surface which
is located in spaced
relationship to the web takeoff point where the web leaves the convolutely
wound roll. It may be
possible in some configurations of the line for the web takeoff point to be
coincident with part of
the surface that is being driven. The method also can include correlating each
of the sectors at
the web takeoff point with a corresponding sector at the drive point to
account for the drive point
and web takeoff point being angularly spaced apart. In addition, the feed rate
variation reduction
CA 02889220 2015-04-23
22
method can include determining an instantaneous rotational speed for each of
the sectors as the
parent roll is driven, e.g., by a motor-driven belt on the outer surface
thereof.
Further, the method can include calculating the radius at the drive point as a
function of
the driving and rotational speeds for each of the sectors. The method also can
include
determining an ideal drive point radiL:s by averaging the calculated drive
point radii for all of the
sectors and calculating a drive point correction factor for the radius at the
drive point for each of
the sectors where the drive point correction factor is a function of the
calculated drive point
radius and the ideal drive point radius. Still further, the feed rate
variation reducing method can
include measuring the radius at the web takeoff point for each of the sectors
as the parent roll is
to driven.
In addition or as an alternative, the method may include calculating an ideal
web takeoff
point radius by averaging the measured web takeoff radii for all of the
sectors and calculating a
web takeoff point correction factor for each of the sectors as a function of
the ideal and measured
web takeoff point radii for each of the sectors.
In some embodiments, the method can also include calculating a total
correction factor
for each of the sectors as a function of the drive point correction factor and
the web takeoff point
correction factor for each of the sectors and multiplying the total correction
factor for each of the
sectors by the ideal speed reference signal to establish a corrected speed
reference signal for each
of the sectors. The method preferably adjusts the driving speed of the parent
roll on a sector by
sector basis to a corrected driving speed as each of the sectors approaches or
is at the drive point
using the corrected speed reference signal to at least approximate the web
feed rate of an ideal
parent roll, thus eliminating or at least reducing geometrically induced feed
rate variations in the
web material at the web takeoff point. In other embodiments, the method can
include calculating
a modified total correction factor for each of the sectors as a function of a
percentage of the drive
point correction factor and/or a percentage of the web takeoff point
correction factor. The
selected percentages may be the same or different. In such embodiments, the
method further
includes multiplying the modified total correction factor by the ideal speed
reference signal to
establish an improved speed reference signal for each of the sectors. The
method adjusts the
driving speed of the parent roll on a sector by sector basis to an improved
driving speed as each
of the sectors approaches or is at the drive point using the improved speed
reference signal to at
least approximate the web feed rate of an ideal parent roll, thus reducing
geometrically induced
feed rate variations in the web material at the web takeoff point.
CA 02889220 2015-04-23
23
In an alternative embodiment, the method includes calculating the drive point
radius for
each sector, the ideal drive point and the drive point correction factor for
each sector but does not
include measuring the web takeoff point radius for each sector, calculating
the ideal web takeoff
point or calculating the web takeoff point correction factor for each sector.
In such embodiment,
an improved speed reference signal is established by multiplying the drive
point correction factor
by the ideal reference signal. The mcthod adjusts the driving speed of the
parent roll on a sector
by sector basis to an improved driving speed as each sector approaches or is
at the drive point
using the improved speed reference signal to at least reduce fluctuations in
the web feed rate
caused by variations in the drive point radii and/or rotational speed.
In yet another alternative embodiment, the method includes measuring the web
takeoff
point radius for each sector, calculating the ideal web takeoff point and
calculating the web
takeoff point correction factor for each sector but does not include
calculating the drive point
radius for each sector, the ideal drive point or the drive point correction
factor for each sector. In
such embodiment, an improved speed reference signal is established by
multiplying the web
takeoff point correction factor by the ideal reference signal. The method
adjusts the driving
speed of the parent roll on a sector by sector basis to an improved driving
speed as each sector
approaches or is at the drive point using the improved speed reference signal
to at least reduce
fluctuations in the web feed rate caused by variations in the web takeoff
point radii.
The ideal speed reference signal can be initially used to control the parent
roll rotation
speed based upon operator input (assuming a perfectly round parent roll) as
well as other factors,
such as tension control system feedback and ramp generating algorithms. As
noted above, the
ideal speed reference signal is multiplied by the total correction factor for
each sector, the
modified total correction factor for each sector, the drive point correction
factor for each sector or
the web takeoff point correction factor for each sector of the parent roll to
generate a corrected or
an improved speed reference signal for each sector. The corrected or improved
speed reference
signal for each sector can be calculated on the fly (and not stored) based
upon the ideal speed
reference signal from moment to moment, noting that the ideal speed reference
signal already
takes into account factors such as tension control system feedback and ramp
generating
algorithms. Finally, and as noted above, the method in these embodiments
includes using the
corrected speed reference signal or the improved speed reference signal for
each sector to adjust
the driving speed of the parent roll for each sector to a corrected or
improved driving speed.
Adjusting the driving speed of the parent roll in the foregoing manner can
cause the web
feed rate of the parent roll to at least approximate the web feed rate of an
ideal parent roll on a
CA 02889220 2015-04-23
24
continuous basis during the entire cycle of unwinding a web material from a
parent roll on an
unwind stand. Accordingly, web feed rate variations in the web material at the
web takeoff point
are reduced or eliminated and, as a result, it follows that web tension spikes
and web tension
slackening associated with radial deviations from a perfectly round parent
roll are eliminated or
at least minimized. It is believed that using the total correction factor to
derive a corrected speed
reference signal reduces the web feed rate variations to a greater degree
and/or on a more
consistent basis than deriving an improved speed reference signal in the ways
explained herein.
This is because the total correction factor addresses both significant
variables that affect the web
feed rate: the rotational speed and the web takeoff point radius. The improved
speed reference
signal only one of the two variables or addresses both variables but to a
lesser degree (i.e.,
through the use of percentages).
As will be appreciated from the foregoing, the parent roll can be divided into
I, 2,...n
equal angular sectors about the longitudinal axis for data analysis,
collection and processing.
Further, the parent roll can be driven by any conventionally known means such
as a motor-driven
belt that is in contact with the outer surface of the parent roll. In such a
case there may not be a
single "drive point" as such but, rather, the belt can wrap around the parent
roll to some degree.
It should be noted that for an out-of-round parent roll, the amount of belt
wrap on the parent roll
can be constantly changing based on the particular geometry of the roll under,
and in contact with
the belt. An advantage of the method described herein is that these effects
can be ignored as the
only data that is recorded is the effective drive point radius, as calculated
elsewhere in this
document. Only for purposes of visualizing the method described herein, a
point such as the
midpoint of belt contact with the parent roll can be selected as the drive
point, although in
practice the actual drive point used by the algorithms described infra can be
based upon
calculated values and may vary from the physical midpoint of the belt.
With regard to other equipment used in practice, they can also be of a
conventionally
known type to provide the necessary data. For instance, a conventional
distance measurement
device can be used to measure the radius at the web takeoff point. Suitable
distance measuring
devices include, but are not limited to, lasers, ultrasonic devices,
conventional measurement
devices, combinations thereof, and the like. One skilled in the art will
appreciate that the
distance reported from the measuring device to the parent roll surface may
need to be subtracted
from the known distance from the measuring device to the center of the parent
roll to derive the
radius of the parent roll from this measurement. Similarly, a conventional
optical encoder, a
resolver, a synchro, a rotary variable differential transformer (RVTD), other
laser devices,
CA 02889220 2015-04-23
ultrasonic devices, other contact measurement device, any similar device, and
combinations
thereof, all of which are known to be capable of determining rotational speed
and position, can be
used to determine the rotational speed and position at the parent roll core
plug.
As will be appreciated, the method can also utilize any conventional logic
device, e.g., a
5 programmable logic control system, for the purpose of receiving and
processing data, populating '
the table, and using the table to determine the total correction factor or
modified total correction
factor for each of the sectors. Further, the programmable logic control system
can then use the
total correction factor or modified total correction factor for each sector to
determine and
implement the appropriate driving speed adjustment by undergoing a suitable
initialization, data
10 collection, data processing and control signal output routine.
In addition to the foregoing, the various measurements and calculations can be
determined from a single set of data, or from multiple sets of data that have
been averaged, or
from multiple sets of data that have been averaged after discarding any
anomalous measurements
and calculations. For example, the web takeoff point radius, 4(1, 2,...n), for
each of the data
15 collection sectors, 1, 2,...n, can be measured a plurality of times and
averaged to determine an
average takeoff point radius, RipAverage(1, 2,...n) , for each of the data
collection sectors, 1, 2,...n,
to be used in calculating the web takeoff point correction factors. Further,
the plurality of
measurements for each of the data collection sectors, 1, 2,...n, of the web
takeoff point radius,
4(1, 2,...n) can be analyzed relative to the average takeoff point radius,
RtpAverage(1, 2,...n) for
20 the corresponding one of the data collection sectors, 1, 2,...n, and
anomalous values deviating
more than a preselected amount above or below the average takeoff point
radius, RtpAverage(l
2,...n), for the corresponding one of the data collection sectors, 1, 2,...n,
can be discarded and
the remaining measurements for the corresponding one of the data collection
sectors, l, 2,...n,
can be re-averaged. Similarly, the drive point radius, Rdp(1, 2,...n), for
each of the data collection
25 sectors, 1, 2,...n, can be calculated a plurality of times and averaged
to determine an average
drive point radius, RdpAverage(1, for each of the data collection sectors,
1, 2,...n, to be used
in calculating the drive point correction factors. Further, the plurality of
calculations for each of
the data collection sectors, 1, 2,...n, of the drive point radius, Rdp(1,
2,...n), can be analyzed
relative to the average drive point radius, RdpAverage(1, 2,...n), for the
corresponding one of the
data collection sectors, 1, 2,...n, and anomalous values deviating more than a
preselected amount
above or below the average drive point radius, RdpAverage(1, 2,...n), for the
corresponding one of
the data collection sectors, 1, 2,...n, can be discarded and the remaining
measurements for the
corresponding one of the data collection sectors, 1, 2,...n, can be re-
averaged.
CA 02889220 2015-04-23
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In addition, the total correction factor Ct(1, 2,...n), modified total
correction factor,
Grmodified (1, 2,...n), the drive point correction factor, Cdp(1, 2,...n), or
the web takeoff point
correction factor, C1p(1, 2,...n), can be determined a preselected time before
each of the data
collection sectors, 1, 2,...n, reaches the drive point to provide time for
adjusting the driving
speed of the motor-driven belt by the time each of the data collection
sectors, 1, 2,...n, reaches
the drive point. It should be noted that it may be desirable to utilize either
ASIC (Application
Specific Integrated Circuit), FPGA (Field Programmable Gate Array) or a
similar device in
conjunction with the logic device which is preferably programmable for the
functions listed
above, such as the taking of multiple taser distance readings, averaging these
readings, discarding
data outside a set range, and recalculating the acceptable readings to prevent
the logic device
from being burdened with these tasks.
As will be appreciated from the foregoing, the terms ideal speed reference
signal, SRSõ
corrected speed reference signal, SRSicorrected, and improved speed reference
signal, SRSIImproved,
as used herein may comprise: i) signals indicative of the ideal driving speed,
the corrected
driving speed, and the improved driving speed, respectively, to at least
approximate the web feed
rate of an ideal parent roll, or ii) the actual values for the ideal driving
speed, the corrected
driving speed and the improved driving speed, respectively and, therefore,
these terms are used
interchangeably herein and should be understood in a non-limiting manner to
cover both
possibilities.
In the several figures and the description herein, the out-of-round parent
roll has been
considered to be generally elliptical in shape and it has been contrasted with
a perfectly round
parent roll. These observations, descriptions, illustrations and calculations
are merely illustrative
in nature and are to be considered non-limiting because parent rolls that are
out-of round can take
virtually any shape depending upon a wide variety of factors. However, the
method disclosed
and claimed herein is fully capable of reducing feed rate variations in a web
material as it is
being unwound from a parent roll regardless of the actual cross-sectional
shape of the
circumference of the parent roll about the longitudinal axis.
While the invention has been described in connection with web substrates such
as paper,
it will be understood and appreciated that it is highly beneficial for use
with any web material or
any convolutely wound material to be unwound from a roll since the problem of
reducing feed
rate variations in a web material induced by geometry variations in a parent
roll are not limited to
paper. In every instance, it would be highly desirable to be able to fine tune
the driving speed on
a sector-by-sector basis as the parent roll is rotating in order to be able to
maintain a constant or
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nearly constant feed rate of a web coming off of a rotating parent roll to
avoid web tensions
spikes or slackening.
In implementing the invention, it may be desirable to provide a phase
correction factor to
present the total correction factor (or other correction factor described
herein) to the drive train
ahead of when it is needed in order to properly address system response time.
To provide a
phase correction factor, it may be desirable to utilize ASIC (Application
Specific Integrated
Circuit), FPGA (Field Programmable Gate Array) or a similar device in
conjunction with a PLC
(Programmable Logic Controller) or other logic device to assist with the high
speed processing of
data. For example, the creation of virtual sectors or the execution of the
smoothing algorithm
(both of which are be discussed below) could be done via one of these
technologies to prevent
the logic device from being burdened with these tasks. However, it should be
noted that the use
of ASICs or FPGAs would be a general data collection and processing strategy
that would not be
limited to implementation of the phase correction factor.
In addition, it is possible that the differences in the total correction
factor (or other
correction factor described herein) from sector to sector are greater than
what can practically be
presented to the control system as an instantaneous change. Therefore, it can
be advantageous to
process the data to "smooth" out the transitions prior to presenting final
correction factors to be
implemented by the control system. Also, due to system response time, it may
be desirable to
present the final correction factors several degrees ahead of when they are
required so the control
system can respond in a timely manner.
In order to facilitate the implementation of these features, it is useful to
further divide the
parent roll into a plurality of virtual sectors that are smaller than the
actual angular sectors which
are used for measuring and calculating the correction factors. The number of
virtual sectors will
be an integer multiple of the number of actual angular sectors, will each be
directly correlated to
an actual angular sector, and will initially take on the same value as the
total correction factor (or
other correction factor) for the actual angular sector to which they are
correlated. For example, if
the parent roll is divided into a total of 20 actual angular sectors, each
actual angular sector
comprises 18 of the parent roll so if:360 virtual sectors are created, each
of the actual angular
sectors can contain 18 virtual sectors. The 18 virtual sectors contained
within each of the actual
angular sectors can each initially be assigned the exact same total correction
factor value, cI, as
that which has been determined as described in detail above for the actual
angular sector in which
they are contained. Next, a new data table can be created with 360 elements,
one for each virtual
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sector, and it can be populated with the information for virtual sectors so a
smoothing algorithm
can be applied to eliminate significant step changes in the actual angular
sectors.
This new table with 360 elements, one per degree of parent roll circumference,
can permit
phasing of data to the control system in one degree increments based upon the
combined
response time of the control system and the drive system. In order to
illustrate the concept, Fig.
11 shows an arrangement in which each of four actual angular sectors has been
divided into eight
virtual sectors. The first, or "Output Data Table", column shows the total
correction factor, C,,
value for each of actual angular sectors 1-4 initially being assigned to all
of the eight virtual
sectors into which the actual angular sector has been divided, e.g., the eight
virtual sectors for
actual angular sector 1 all have a value for the total correction factor, C,,
of 1.02. As shown, the
total correction factor assigned to alreight virtual sectors for actual
angular sector 2 is 0.99, for
actual angular sector 3 is 1.03, and for actual angular sector 4 is 0.98.
Next, the second, or
"After-Data processing to Smooth Transitions," column is completed to smooth
the transitions
between the virtual sectors after the initial data processing has been
completed.
In particular, the step in the total correction factor, C,, between actual
angular sector 1 and
actual angular sector 2 is 0.03 so the last two virtual sectors for actual
angular sector 1 are each
reduced by 0.01, i.e., the second to last virtual sector is reduced to 1.01
and the last virtual sector
is reduced to 1.00 to modulate the step and create a smooth transition between
actual angular
sector 1 and actual angular sector 2. Accordingly, the step from the last
virtual sector for actual
angular sector 1 to the first virtual sector for actual angular sector 2 is
also 0.01 creating a smooth
transition comprised of equal steps of 0.01.
Similarly, the step in the total correction factor, C,, between actual angular
sector 2 and
actual angular sector 3 is 0.04 so the last three virtual sectors for actual
angular sector 2 are each
increased by 0.01, i.e., the third to last virtual sector is increased to
1.00, the second to last virtual
sector is increased to 1.01 and the last virtual sector is increased to 1.02
to modulate the step and
create a smooth transition between actual angular sector 2 and actual angular
sector 3 rather than
a single, large step of 0.04. Accordingly, the step from the last virtual
sector for actual angular
sector 2 to the first virtual sector for actual angular sector 3 is also 0.01
again creating a smooth
transition comprised of equal steps of 0.01.
As will be seen from Fig. 11, the same logic is applied for forming the smooth
transitions
from actual angular sector 3 to actual angular sector 4, although it will be
appreciated that the
number of actual angular sectors, number of virtual sectors, number of steps,
and value for each
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step are merely illustrative, non-limiting examples to demonstrate the process
for smoothing
transitions between actual angular, or data collection, sectors.
After smoothing transitions between the actual angular sectors in the manner
described,
the virtual sectors are each moved ahead by three sectors. In other words, the
first virtual sector
for actual angular sector 1 in column 2 is shifted down three places to the
position for the fourth
virtual sector for actual angular sector 1, the last virtual sector for actual
angular sector 4 is
shifted up three places to the position for the third virtual sector for
actual angular sector 1, the
second to the last virtual sector is shifted up three places to the position
for the second virtual
sector for actual angular sector 1, etc. Fig. 11 illustrates the data for
every one of the virtual
sectors obtained as described above being shifted by three places to a new
virtual sector position
in order to compensate for system response time.
The third column represents a continuous data loop of total correction factors
for all of
the virtual sectors where, in Fig. 11, there are a total of 32 virtual
sectors. While this illustration
is presented to understand the concept, in practice the total number of
virtual sectors comprises X
times n where n is the number of actual angular, or data collection, sectors
and x is the number of
virtual sectors per actual angular sector. The total correction factors for
each of the virtual
sectors in the continuous data loop can be shifted forward or rearward by a
selected number of
virtual sectors.
Fig. 11 illustrates shifting data by three places forward as a non-limiting
example, but it
will be understood that the data can be shifted forward or rearward in the
manner described
herein by more or less places depending upon system and operational
requirements. Further, as
indicated, the same virtual sector approach and logic applies to forming
smooth transitions with
respect to a modified total correction factor, a drive point correction factor
and/or a web takeoff
point correction factor.
The dimensions and values disclosed herein are not to be understood as being
strictly
limited to the exact dimensions and numerical values recited. Instead, unless
otherwise specified,
each such dimension and values is intended to mean both the recited dimension
or value and a
functionally equivalent range surrounding that dimension or value. For
example, a dimension
disclosed as "40 mm" is intended to mean "about 40 mm."
All documents cited in the Detailed Description of the Invention are not to be
construed
as an admission that they are prior art with respect to the present invention.
To the extent that
any meaning or definition of a term in this document conflicts with any
meaning or definition of
CA 02889220 2015-04-23
the same term in a document cited herein, the meaning or definition assigned
to that term in this
document shall govern.
While particular embodiments of the present invention have been illustrated
and
described, it would be obvious to those skilled in the art that various other
changes and
5 modifications can be made without departing from the invention described
herein.
