U.S. patent application number 10/534645 was filed with the patent office on 2006-01-19 for method for controlling a wind-up, including determining running parameters based on models taking un-winding into account.
Invention is credited to Marko Jorkama, Pauli Koutonen, Jari Paanasalo.
Application Number | 20060011766 10/534645 |
Document ID | / |
Family ID | 8564931 |
Filed Date | 2006-01-19 |
United States Patent
Application |
20060011766 |
Kind Code |
A1 |
Koutonen; Pauli ; et
al. |
January 19, 2006 |
Method for controlling a wind-up, including determining running
parameters based on models taking un-winding into account
Abstract
A wind-up is controlled by preparing a winding recipe (13) of a
roll, which winding recipe comprises winding parameters. Based on
calculatory and/or experimental models, running parameters of the
wind-up are determined before the run such that, based on the
models, the roll will withstand unwinding taking place in an
end-use device without being damaged.
Inventors: |
Koutonen; Pauli; (Jokela,
FI) ; Jorkama; Marko; (Jarvenpaa, FI) ;
Paanasalo; Jari; (Jarvenpaa, FI) |
Correspondence
Address: |
STIENNON & STIENNON
612 W. MAIN ST., SUITE 201
P.O. BOX 1667
MADISON
WI
53701-1667
US
|
Family ID: |
8564931 |
Appl. No.: |
10/534645 |
Filed: |
November 10, 2003 |
PCT Filed: |
November 10, 2003 |
PCT NO: |
PCT/FI03/00851 |
371 Date: |
May 12, 2005 |
Current U.S.
Class: |
242/413.2 ;
242/534 |
Current CPC
Class: |
B65H 2557/24 20130101;
B65H 2515/30 20130101; B65H 2220/03 20130101; B65H 2220/01
20130101; B65H 2220/01 20130101; B65H 23/195 20130101; G05B 17/02
20130101; B65H 2601/25 20130101; B65H 2511/142 20130101; B65H
2511/142 20130101; B65H 2515/30 20130101 |
Class at
Publication: |
242/413.2 ;
242/534 |
International
Class: |
B65H 18/08 20060101
B65H018/08 |
Foreign Application Data
Date |
Code |
Application Number |
Nov 13, 2002 |
FI |
20022023 |
Claims
1-16. (canceled)
17. A method of controlling a wind-up in the formation of a roll
from a paper web having a strength, comprising the steps of: a
first step of: selecting a WOT (Wound-On-Tension) curve to be
controlled to, using a selected starting WOT (Wound-On-Tension)
curve, a model of roll stresses, a model of roll relaxation, and a
model of runnability of a selected end use, by using the selected
WOT (Wound-On-Tension) curve as an input to the model of roll
stresses which produces an output which is used in the model of
roll relaxation which produces an output forming the input of the
model of runnability of a selected end use, and determining if the
roll will be damaged in the selected end use, and if it is
determined that the roll will be damaged in the selected end use,
using a method for iteration to modify the selected WOT
(Wound-On-Tension) curve, and then repeating the first step; a
second step of: selecting a winding recipe for forming a roll with
the selected WOT (Wound-On-Tension) curve by using a selected
starting recipe, and a model of the wind-up, using the selected
starting recipe as an input to the model of the wind-up, using the
output of the model of the wind-up in the model of roll stresses to
define a model roll, and determining if the model roll formed by
the selected starting recipe conforms to the WOT (Wound-On-Tension)
curve of the first step within a selected accuracy; if the roll
formed by the winding recipe does not conform to the WOT
(Wound-On-Tension) curve of the first step within the selected
accuracy, using a method for iteration to modify the selected
starting recipe and repeat the second step; winding the roll in the
wind-up and measuring a WOT (Wound-On-Tension) curve; and comparing
the measured WOT (Wound-On-Tension) curve as a function of roll
diameter, or web length, with the selected WOT (Wound-On-Tension)
curve and modifying the winding recipe so that the measured WOT
(Wound-On-Tension) curve is the same as or within a set tolerance
of the selected WOT (Wound-On-Tension) curve.
18. The method of claim 17 wherein the second step includes
constraining the winding recipe to limitations due to the mechanics
of the wind-up and to the strength of the paper web.
19. The method of claim 17 wherein the selected WOT
(Wound-On-Tension) curve and the measured WOT (Wound-On-Tension)
curve are curves of tension vs a function of roll diameter, or a
function web length.
20. The method of claim 19 wherein the function of roll diameter is
a function of roll radius or the thickness of cumulated paper on a
winding core.
21. The method of claim 19 wherein the function of web length is a
function of number of laps of paper on a winding core.
22. The method of claim 17 wherein the method for iteration to
modify the selected WOT (Wound-On-Tension) curve comprises a
variation of the secant method.
23. The method of claim 17 wherein the selected starting recipe is
keeping nip load constant independent of the diameter for as long
as possible, keeping winding force a constant independent of the
diameter, and keeping web tension a constant independent of the
diameter.
24. The method of claim 17 wherein the winding recipe is determined
as a function of the diameter or radius or the degree of thickness
of the cumulated paper on the winding core or as a function of
wound web length or the number of laps of the wound web.
25. The method of claim 17 wherein the model of the wind-up is used
to check that the roll will withstand winding in the wind-up.
26. A method of controlling a wind-up in the formation of a roll
from a paper web having a strength, comprising the steps of: a
first step of: selecting a WOT (Wound-On-Tension) curve to be
controlled to, using a selected starting WOT (Wound-On-Tension)
curve, a model of roll stresses, a model of roll relaxation, and a
model of runnability of a selected end use, by using the selected
WOT (Wound-On-Tension) curve as an input to the model of roll
stresses which produces an output which is used in the model of
roll relaxation which produces an output forming the input of the
model of runnability of a selected end use, and determining if the
roll will be damaged in the selected end use, and if it is
determined that the roll will be damaged in the selected end use,
using a method for iteration to modify the selected WOT
(Wound-On-Tension) curve and then repeating the first step; a
second step of: selecting a winding recipe for forming a roll with
the selected WOT (Wound-On-Tension) curve by using a selected
starting recipe, and a model of the wind-up, using the selected
starting recipe as an input to the model of the wind-up, using the
output of the model of the wind-up in the model of roll stresses to
define a model roll, and determining if the model roll formed by
the selected starting recipe conforms to the WOT (Wound-On-Tension)
curve of the first step within a selected accuracy; if the roll
formed by the winding recipe does not conform to the WOT
(Wound-On-Tension) curve of the first step within the selected
accuracy, using a method for iteration to modify the selected
starting recipe and repeat the second step; winding the roll in the
wind-up; and controlling the wind-up, based on the winding
recipe.
27. The method of claim 26 wherein during winding the roll in the
wind-up, a measured WOT (Wound-On-Tension) curve is monitored to
determine whether the selected WOT curve is realized and, if
necessary, the selected winding recipe is corrected such that a
measured WOT (Wound-On-Tension) curve corresponds to the selected
WOT (Wound-On-Tension) curve.
28. The method of claim 26 wherein the iteration of the winding
recipe is continued in a plurality of rolls formed in the
wind-up.
29. The method of claim 26 further comprising the steps of:
indirectly measuring, in three or two dimensions, the internal
stress distribution of the roll being wound up; calculating with
the model the roll stresses caused by forces directed to the roll
during winding; estimating the relaxation of the internal stresses
of the roll after finishing before the roll is processed in the
selected end use; and calculating with the model of runnability of
a selected end use, stresses and displacements directed to the roll
during unwinding.
30. The method of claim 26 wherein the selected starting WOT
(Wound-On-Tension) curve is based on starting data on the paper
grade obtained through off- and on-line measurements of paper
processing equipment preceding the wind-up and through measurements
made in the wind-up.
31. The method of claim 30 wherein limitations for the winding
recipe are determined on the basis of basic data obtained through
physical properties of the winding device and through the model of
roll stresses.
32. The method of claim 26 further comprising the step of
calculating, in the model of roll stresses, the model of roll
relaxation, and the model of runnability of a selected end use,
slippages or other damage mechanisms generated within the roll.
Description
CROSS REFERENCES TO RELATED APPLICATIONS
[0001] This application is a U.S. national stage application of
International App. No. PCT/FI2003/000851, filed Nov. 10, 2003, and
claims priority on Finnish App. No. 20022023, Filed Nov. 13, 2002,
the disclosure of which is incorporated by reference herein.
STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSORED
RESEARCH AND DEVELOPMENT
[0002] Not applicable.
BACKGROUND OF THE INVENTION
[0003] When, in wind-ups known from prior art, the wind-ups of new
slitter-winders are started up or the winding of new paper grades
is started using slitter-winders already in use, the structure of
the roll is controlled by so-called winding parameters, nip load,
the tension of the web before the wind-up, and winding force,
which, in known applications, are set, based on experience, as a
function of the diameter of the roll to be so-called winding
recipes. The initial guesses for the winding recipes generally
originate from other slitter-winders, with which the same or a
similar paper grade has been run. However, due to the great
variation in the properties of paper grades having the same grade
name when run in different paper machines, case-specific trial runs
are always necessary in order to determine the winding recipe. Each
paper grade and end diameter of a roll is usually provided with a
winding recipe of its own.
[0004] In applications known from prior art the quality of the
finished rolls coming from the wind-ups is primarily determined
based on visual estimation. In most slitter-winders the rolls also
undergo occasional measurements; most often the hardness of the
roll is measured by means of a manually operated roll hardness
sensor.
[0005] It is also known from prior art to provide the
slitter-winders with surface density calculation and display. In
these known applications the surface density value corresponding to
an arbitrary roll diameter has been determined from the surface of
the roll based on the change in the thickness of the paper.
[0006] Applications are known from prior art in which the object is
to estimate the stresses within the roll with the help of
measurements. Patent application WO 9950719 "Verfahren und
Anordnung zur neuronalen Modellierung einer Papierwickel
Vorrichtung" discloses a method in which the tension of the web
when it goes into a roll is determined by means of learning via
neural networks. This enables the calculation, with the help of
winding models, of a two-dimensional stress distribution inside the
roll. Patent application DE 19821318 "Verfahren zum Uberwachen der
Wickerharte einer Wickelrolle" discloses a method for the
measurement of the tension of the web when it goes into a roll,
which method is based on measuring the change in the web length on
the basis of colored marks printed on the web.
[0007] A large number of the winding defects generated during
winding will go unnoticed when visual estimation or measurement
with a hardness sensor is used, David R. Roisum: "How to Measure
Roll Quality", Tappi Journal 71(10) 1988, David R. Roisum: "Reading
a roll", Tappi Journal 81(4) 1998. Even if the two-dimensional
stress distribution of the rolls could be calculated using the
procedure of the patent applications WO 9950719 and DE 19821318, in
most cases it would not be possible to prevent the generation of
potential or actual winding damage, because the above methods do
not take into account the causes of damage due to the loads
directed to the roll in a paper mill slitter-winder (winder) and in
the paper mill customer's finishing device.
[0008] For the paper manufacturer, however, the most important and
critical feedback on the quality of the rolls comes from the
customers, such as printing houses, for example in a case where
running problems have occurred when the rolls have been run, for
example, in a printing machine. In such a case the corrective
measures in the paper manufacturing process or in the winding
recipes of the slitter-winder can only be taken after a delay of
several days or even weeks. If the frequency of the variations in
the properties of paper (mass, surface properties) is greater,
there is no sense in taking corrective measures.
[0009] Due to the above-mentioned quality feedback delay, when
starting up new slitter-winders or when starting the winding of new
paper grades using slitter-winders already in use, the search for
winding recipes is often slow.
[0010] A particular problem in the selection of the winding
parameters of the winding recipes is that most defects cannot be
noticed on the basis of visual examination and are not always
discovered through surface density or equivalent measurements, and,
as explained above, getting actual feedback on quality takes
long.
SUMMARY OF THE INVENTION
[0011] An object of the invention is to provide a method by means
of which the winding parameters can be determined so as to make
sure that the roll withstands handling both in the paper mill and
at the customer end.
[0012] Another object of the invention is to provide a method by
means of which the problems described above are eliminated or at
least minimized.
[0013] A special object of the invention is to provide a control
method for controlling a wind-up, which method also takes into
account the loads directed to the roll in the wind-up and in the
paper mill customer's machinery.
[0014] An essential advantage of the invention is that it is based
on the idea of providing a roll which will go through its entire
life span without being damaged, whereas models and systems known
from prior art aim to provide, on the wind-up, an optimal roll with
respect to winding.
[0015] In the method according to the invention for controlling a
wind-up, in which method a winding recipe is prepared containing
winding parameters, running parameters of the wind-up are
determined on the basis of calculatory and/or experimental models
before the run such that, based on the models, the roll will
withstand the winding up taking place in the end-use device without
being damaged. According to an advantageous additional feature in
the method according to the invention the running parameters of the
winder are determined such that, based on the models, the roll will
withstand the winding up taking place in the wind-up. According to
a further advantageous additional feature in the method according
to the invention the winding recipe of the roll is formed as a
function of the diameter or radius or the degree of thickness of
the cumulated paper on the winding core or as a function of wound
web length or the number of laps of the wound web.
[0016] According to an advantageous application of the invention
the internal stress distribution of the rolls is measured, the
forces directed to the roll during winding are calculated by means
of a load model and the relaxation of the internal stresses of the
roll during transportation is estimated by means of the model and
the forces directed to the roll in the paper mill customer's
finishing devices are calculated by means of the load model.
[0017] According to an advantageous application of the method
according to the invention: [0018] a) the internal stress
distribution of the roll being wound up is measured indirectly in
three or two dimensions [0019] b) the internal stresses caused by
forces directed to the roll during winding are calculated with the
help of a roll load model, Kilwa Arola: "A Simulation Program for
Hyperelastic Rolling Contact Model", Master of Science Thesis,
Helsinki University of Technology 2001. [0020] c) the relaxation of
the internal stresses of the finished roll, before the roll is
processed in the paper mill customer's finishing device (e.g. a
printing machine), is estimated and [0021] d) the stresses and
displacements directed to the roll during unwinding are calculated
by means of a load model (RAMA) of the roll and the unwinding
device.
[0022] The information on the paper material needed in the method
according to the invention is partially obtained through off- and
on-line measurements of the paper processing equipment preceding
the slitter-winder and partially through measurements of the
slitter-winder itself (e.g. radial and tangential modulus of
elasticity).
[0023] In the method according to the invention the winding recipe
is, according to an advantageous application, sought such that the
stress distribution of the roll, calculated with the WOT model
(WOT=Wound-On-Tension i.e. the tension of the uppermost layer on
the web roll, sometimes also referred to as WIT=Wound-In-Tension),
M. Jorkama: "Contact Mechanical Model for Winding Nip".
Dissertation, Helsinki University of Technology, 2001, the roll
structure model and the roll relaxation model provides damage-free
unwinding on the finishing device according to the RAMA model
(=load model of the end-use device). In the search for the winding
recipe, account has to be taken of the physical properties of the
winding device and of ensuring damage-free winding and runnability
on the slitter-winder, which are estimated with the load model of
the wind-up. During running of the slitter-winder the recipe is
being fed back on the basis of WOT measurement so that a stress
distribution according to the previous step is generated in the
roll.
[0024] In the roll structure measuring method it is possible to use
a WOT estimated through the change in the web length measured, for
example, by means of laser speed sensors. The structure of the roll
is in such a case calculated using the Hakiel model, Z. Hakiel:
"Nonlinear Model for Wound Roll Stress". Tappi Journal 70(5) 1987,
or an equivalent model, Zabaras N., Liu S., Koppuzha J. and
Donaldson E. "A Hypoelastic Model for Computing the Stresses in
Center-Wound Rolls of Magnetic Tape" Journal of Applied Mechanics,
Vol 61 No. 2, pp. 290-295, 1994. It is also possible to make use of
a method utilizing the density of the roll, paper thickness and the
winding model, David R. Roisum: "The Measurement of Web Stresses
During Roll Winding". Dissertation WHRC at OSU 1990.
[0025] In the structure models of the slitter-winder wind-up and
the finishing device, slippages generated within the roll and
possibly other damage mechanisms as well are calculated. With the
help of the calculated slippages the damage potential of the roll
is estimated by using empirical data and roll damage models, N.
Vaidyanathan and J. K. Good: "The Importance of Torque Capacity in
Predicting Crepe Wrinkles and Starring within Wound Rolls".
Proceedings of the 3.sup.rd IWEB conference. OSU 1995, Lee,
Ban-Eop: "Buckling Analysis of Starred Roll Defects in Center Wound
Rolls". Dissertation WHRC at OSU 1991.
[0026] When estimating the relaxation of the stresses of the
finished roll, known viscoelastic winding models are used, such as
the reference: W. R. Qualls and J. K. Good: "A Nonlinear
Orthotropic Viscoelastic Winding Model". Proceedings of the
3.sup.rd IWEB conference. OSU 1995.
[0027] The method according to the invention renders winding
"intelligent" i.e. the feedback between the quality of the roll and
the winding parameters, which before had taken several days or
weeks, can now be carried out during the running of the
slitter-winder. Reactions to changes in the paper properties and in
the production conditions in the paper mill take place
automatically and immediately.
[0028] By means of the method according to the invention it is
possible to determine quickly the optimal winding recipes, when
starting up new slitter-winders or when starting the winding of new
paper grades using slitter-winders already in use.
[0029] The method according to the invention enables optimal
individual control of the winding stations, which also reduces
variations in quality between the rolls of the same set.
[0030] By way of summary, in the method according to the invention,
the controlling of the wind-up is based on a prediction drafted
with the help of a model on the runnability of the roll in end-use,
in which prediction, according to an advantageous application, a
WOT vs. diameter reference curve providing optimal runnability
during end-use in the finishing device is determined by iterating
the model before the run. According to advantageous characteristics
of the invention, the running parameters of the wind-up of the
slitter-winder are adjusted such that the measured WOT curve
corresponds to the WOT reference curve obtained by iterating the
model. The WOT reference curve may also be modified based on the
runnability prediction provided by means of the winding model. When
making the runnability prediction, the roll stress relaxation model
is advantageously made use of and the initial estimate for the
running parameters is most appropriately calculated using the
winding nip model.
[0031] The invention will now be described in more detail with
reference to the figures of the accompanying drawing, to the
details of which the invention is, however, by no means intended to
be narrowly confined.
BRIEF DESCRIPTION OF THE DRAWINGS
[0032] FIG. 1 schematically shows the basic principle of the method
according to the invention.
[0033] FIG. 2 schematically shows by means of an example a WOT
curve selection procedure used in the method according to the
invention.
[0034] FIG. 3 schematically shows an example in the method
according to the invention for establishing an initial value of a
winding recipe.
[0035] FIG. 4 schematically shows a subprocess of FIG. 1 during the
running of a slitter-winder, the slitter-winder having WOT
measurement.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0036] FIG. 1 shows the basic principle of an application of the
method according to the invention. The starting data 11 needed
includes basic information on the paper to be wound, such as
thickness, friction coefficient, elastic moduli in thickness and
machine direction, information on the viscoelastic properties of
the paper, air permeability and surface roughness, etc., mechanical
data on the wind-up device as well as mechanical data on the
end-use device of the roll or on the unwinding device on which the
unwinding will take place. In step I an appropriate WOT curve 12 is
selected. This selection process will be explained in more detail
in the description of FIG. 2. To enable the utilization of this WOT
curve WOT.sub.ref(D) (D=roll diameter) the wind-up must incorporate
a method for calculatory or measurement-based estimation of WOT. In
the subsequent step II a winding recipe 13 R.sub.ref(D) is selected
that produces, according to the winding model of the
slitter-winder, step III 14, a WOT curve 12 WOT.sub.ref(D)
according to step I. After this, in step IV, the load model of the
winding device is used to check further that the rolls to be wound
up withstand the loads 15 produced in the winding process. If the
winding model indicates that the rolls withstand the loads, the
process can be continued, i.e. a transition to step V is made,
otherwise a new recipe is generated, i.e. there is a return to step
II R.sub.ref(D), which new recipe provides, based on calculation,
the selected WOT curve 12 WOT.sub.ref(D), and steps III and IV are
gone through again. If, after this, there is still need to continue
iteration, a new recipe can be generated, for example, by means of
a so-called secant method, Erwin Kreyszig: "Advanced Engineering
Mathematics". Sixth Edition, John Wiley & Sons, Inc. 1988, p.
956, meaning that a gradient approximation in the winding parameter
space is formed of the recipes of two successive iterations, the
maximum stresses of the roll, for example, being the object
function to be minimized. A limiting condition for the minimization
task is that the winding recipe produces, in step I, a WOT curve 12
selected on the basis of calculation. Let us assume, for the sake
of simplicity, that a winding recipe is established by iteration as
described above which, based on calculation, a) withstands the
winding process and b) gives the selected WOT curve. Were such a
recipe not found, it would be necessary to return to step I and
establish a new WOT curve WOT.sub.ref(D), etc. As stated, it is
assumed here that an appropriate recipe has been found and the
operation of the slitter-winder 16 can be started, i.e. a
transition to step V can be made. If no WOT measurement has been
performed in the wind-up or slitter-winder, the slitter-winder is
run in step V with the recipe R.sub.ref 13 without changing the
recipe during the running. If the wind-up or slitter-winder has WOT
measurement, the procedure is as follows: During the run this
recipe R.sub.ref selected in the preceding step is corrected so as
to provide the WOT curve 12 WOT.sub.ref(D) according to step I. The
correction of the recipe 13 is made, for example, by adjusting
primarily winding force, secondarily nip load, and finally tension.
Increasing each winding parameter increases WOT. The adjustment can
be carried out, for example, as a simple PID controller, K.
.ANG.strom & T Hagglund: "PID Controllers: Theory, Design, and
Tuning". 2nd edition, 1995, pp. 59-119. If, in the next run, the
paper grade and starting data remain substantially the same, the
realized winding recipe 17 according to step VI can be adopted
directly as the winding recipe 13 of step II of the next run. The
basic principle has been illustrated above by way of a simple
example only. Further adjustments and measurements may be added to
this basic frame. For example, after step IV it is possible to
calculate, by means of the realized winding recipe 17, the winding
model of the slitter-winder to detect possible winding defects. The
end result is checked before the next run. If the calculation
showed that the rolls withstand the load, no further measures are
needed. If, however, the calculation suggested a high probability
of damage, iteration of an appropriate WOT curve 12 has to be
started or additional limitations for the winding parameters have
to be set.
[0037] FIG. 2 describes the selection procedure of the WOT curve 12
in more detail by means of an example. The basic principle for the
selection of the WOT curve 12 is that, based on some argument, said
WOT curve 12 provides damage-free unwinding in the end-use device
of the roll. The argument used can be, for example, the calculation
model RAMA 23, step IIc, as in this example, or a statistical model
or data or a combination of these. The procedure begins with
selecting, in step I, an initial guess as the WOT curve
WOT.sub.0(D), i.e. initialization of iteration is carried out 22
WOT.sub.i=WOT.sub.0 (D), where D=roll diameter. This may be, for
example, a constant independent of the diameter, where the value of
the constant may be 15-20 percent of the tensile strength of the
web. After this, in step II, step IIa, the stress distribution of
the roll directly after winding is calculated with a winding model,
such as the Hakiel or von Hertzen winding model. Next, the
relaxation of stresses, step IIb, is estimated, by using this
result as the initial value, in the time span before the roll is
unwound in the end-use device. In the next step III, the stresses
obtained from the relaxation model in the preceding step II are
used as initial values, and the strength or runnability 24 of the
roll during unwinding in the end-use device is estimated. The
estimation can be based, as is the case in this example, on the
calculation model of step IIc. Statistical and empirical results as
well as combinations thereof may also be used. If, based on the
estimation, the roll will withstand the process, this selection
process of the WOT curve 26 is complete, step IV. If, based on the
estimation, the roll will not withstand it, there must be a return
to step I and a new candidate for a WOT curve WOT.sub.1(D) 22 has
to be selected. Once again, this may be, for example, a constant
independent of the diameter, the value of the constant being, for
instance, 98 percent or 102 percent of WOT.sub.0(D). If this new
WOT curve passes step III, the selection process of the WOT curve
is complete, step IV. If WOT.sub.1(D) 26 does not satisfy step III,
iteration has to be continued 25. A new WOT curve candidate can be
formed of the two previous ones, by using, for example, a variation
of the secant method, Erwin Kreyszig: "Advanced Engineering
Mathematics". Sixth Edition, John Wiley & Sons, Inc. 1988, p.
956. This makes it possible, for instance, to minimize the stress
maximum in the RAMA calculation, step IIc, among other things, in a
normed space formed by continuous functions. Here, in this
description of the procedure, it is assumed that the WOT curve
search process produces a curve WOT.sub.ref(D) 26, which satisfies
step III, after steps IIa, IIb and IIc, even though it could in
principle happen, for example, that the value of WOT would at some
point exceed the tensile strength of the web, meaning that a
suitable solution would not be found.
[0038] FIG. 3 shows an example of the search for the initial value
13 of the winding recipe. In step I, initialization of iteration is
carried out 32 R.sub.j=(N,F,T).sub.j=R.sub.0
(D)=(N.sub.0,F.sub.0,T.sub.0) (D), where (N.sub.0,F.sub.0,T.sub.0)
(D) has to be realizable and R.sub.j=winding recipe, N=nip loads,
F=winding force and T=web tension. The object is to seek the
winding recipe R(D)=(N(D),F(D),T(D)) 32 so that, when calculated
with the WOT model of the wind-up (see Jorkama Dissertation, or
empirical model), the winding recipe gives the WOT curve 12
selected in step I of FIG. 1. Above, N(D) is nip load(s) as a
function of the diameter D, F(D) winding force as a function of the
diameter and T(D) web tension before the wind-up as a function of
the diameter. The winding recipe generated as a result of this
subprocess is marked with R.sub.ref(D) 36. In the function form the
objective is thus to find the winding recipe such that
WOT.sub.ref(D)=WOT.sub.model(R.sub.ref(D),D), where the
WOT.sub.model function represents the WOT model. The procedure is
similar to that of other iterations based on the secant method.
First, an initial guess R.sub.i=R.sub.0 is selected, step I, and a
WOT curve WOT.sub.i=WOT.sub.0 is calculated, step II, with a WOT
model 33 WOT.sub.i=WOT.sub.model (R.sub.i (D), D). For example, the
following values can be used as the initial guess: The nip load a
constant independent of the diameter for as long as possible, the
winding force a constant independent of the diameter, for example,
75 percent of web tension and the web tension also a constant
independent of the diameter, e.g. 15-20 percent of the tensile
strength of the web. If, in the checking of step III 34, WOT.sub.0
is, on the basis of a chosen accuracy requirement, close enough to
WOT.sub.ref, a transition to step IV can be made and R.sub.0 can be
selected as the winder recipe R.sub.ref 36. However, if WOT.sub.0
is not sufficiently accurately WOT.sub.ref, iteration is continued
from step II by selecting a new winding recipe R.sub.1 35. It can,
for example, be selected such that the running tension is selected
to be 98 percent and 102 percent of the running tension of R.sub.0.
If this new recipe 35 passes step III, the winding recipe selection
process is complete. If R.sub.1 does not realize step III either,
iteration has to be continued. A new winding recipe candidate can
be formed out of the two previous ones, e.g. using a variation of
the secant method. This way, for example, the distance between
WOT.sub.i(R.sub.i(D),D) and WOT.sub.ref(D) can be minimized in a
normed space formed by continuous vector-valued functions. A metric
formed, for example, of the L.sup.2 norm can be used as a distance
function. Limitations due to the mechanics of the wind-up and to
the strength of the paper have to be taken into account as a
constraint to minimization.
[0039] FIG. 4 presents step V running of slitter-winder 16 of FIG.
1 in more detail in a case where the slitter-winder comprises WOT
measurement. In short, recipe R.sub.ref 42 is used to run the
slitter-winder in this process. However, during the run 43 the
recipe is corrected so that the measured WOT and WOT.sub.ref are
joined 45. When running the slitter-winder the diameter of the roll
being wound up and WOT 44 are continuously measured. The WOT
measurement can be carried out, for example, according to the
reference Roisum, D., "The Measurement of Web Stresses During Roll
Winding", PhD Thesis, Web Handling Research Center at Oklahoma
State University., May 1990. It is checked, at certain intervals
(e.g. 5 seconds), whether the measured WOT, marked with
WOT.sub.measurement, is the same or at a set tolerance from
WOT.sub.ref. During the run the winding recipe R.sub.ref 46 is
continuously changed so that WOT.sub.measurement is the same or at
a set tolerance from WOT.sub.ref. This adjustment can be carried
out, for example, as a PID controller, K. .ANG.strom & T
Hagglund: "PID Controllers: Theory, Design, and Tuning". 2nd
edition, 1995. Pages 59-119. The correction of the recipe is made,
for example, by adjusting primarily winding force, secondarily nip
load, and finally tension. Increasing each winding parameter
increases the WOT.
[0040] The invention has been described above with reference to one
of its advantageous exemplifying embodiments only, to the details
of which the invention is by no means intended to be narrowly
confined.
[0041] For example, the invention is described above with reference
to an example, in which, in the method, the winding recipe of the
roll is formed as a function of the diameter. It is also possible
to formulate the winding recipe as a function of the radius or the
degree of thickness of the cumulated paper on the winding core or
wound web length or the number of laps of the wound web.
* * * * *