In the present work we propose a particle approach, which is designed to treat complex mechanics and dynamics of the open-draw sections that are still present in many of today’s paper machines. First, known steady-state continuous solutions are successfully reproduced. However, it is shown that since the boundary conditions depend on the solution itself, the solutions for web strain and web path in the open-draw section are generally time-dependent. With a certain set of system parameters, the nonsteady solutions are common. A temporal fluctuation of Young’s modulus, for example, destabilizes the system irreversibly, resulting in the continuous growth of web strain, i.e., break. Finally we exemplify with some strategic draw countermeasures how to prevent a dangerous evolution in the web strain.

1.
Wahren
,
D.
, 1981, “
Wet Webs in Open Draws—An Engineering Analysis
,”
Tappi J.
0734-1415,
64
, pp.
89
93
.
2.
Seth
,
R. S.
,
Barbe
,
M. C.
,
Williams
,
J. C. R.
, and
Page
,
D. H.
, 1982, “
The Strength of Wet Webs—A New Approach
,”
Tappi J.
0734-1415,
65
, pp.
135
138
.
3.
Kurki
,
M.
,
Pakarinen
,
P.
,
Juppi
,
K.
, and
Martikainen
,
P.
, 2000,
Drying–Papermaking Part 2
,
Finnish Paper Engineers' Association
,
Helsinki
.
4.
Makinen
,
J. T.
, 2004, “
Multi-Variable Controls
,”
Automation
,
2
, pp.
4
7
.
5.
Mardon
,
J.
,
Truman
,
A. B.
,
O’Blenes
,
G.
, and
Meadley
,
K.
, 1958, “
A Consideration of the Factors Involved at the Open Draw at Couch and Presses of Fourdrinier Machines
,” Pulp and Paper Magazine of Canada, Sept., pp.
135
155
.
6.
Österberg
,
L.
, 1962, “
Pappersbanors avtagning från pressvalsar
,”
Sven. Papperstidn.
0283-6831,
65
, pp.
222
233
.
7.
Mardon
,
J.
, 1976, “
Theoretical and Experimental Investigations Into Peeling of Paper Webs From Solid Surfaces
,”
Papper och Trä
,
11
, pp.
797
815
.
8.
Gavelin
,
G.
, 1958, “
The Case of the Open Draw
,”
Sven. Papperstidn.
0283-6831,
61
, pp.
282
286
.
9.
Hristopulos
,
D. T.
, and
Uesaka
,
T.
, 2002, “
A Model of Machine-Direction Tension Variations in Paper Webs With Runnability Applications
,”
J. Pulp Pap. Sci.
0826-6220,
28
, pp.
389
394
.
10.
Kurki
,
M.
,
Vestola
,
J.
,
Martikainen
,
P.
, and
Pakarinen
,
P.
, 1997, “
The Effect of Web Rheology and Peeling on Web Transfer in Open Draw
,”
1997 Proceedings of the Fourth International Conference of Web Handling
, p.
527
.
11.
Ahrens
,
F.
,
Patterson
,
T.
, and
Bloom
,
F.
, 2004, “
Mathematical Modelling of Web Separation and Dynamics on a Web Adhesion and Drying Simulator
,”
Int. J. of Applied Mechanics and Engineering
,
9
, pp.
227
271
.
12.
Frenkel
,
D.
, and
Smit
,
B.
, 2002,
Understanding Molecular Simulation
,
2nd ed.
,
Academic
,
New York
.
13.
Ostoja-Starzewski
,
M.
, 2008,
Microstructural Randomness and Scaling in Mechanics of Materials
,
Chapman and Hall
,
London
/
CRC
,
New York
, p.
157
.
14.
Li
,
S.
, and
Liu
,
W. K.
, 2002, “
Meshfree and Particle Methods and Their Applications
,”
Appl. Mech. Rev.
0003-6900,
55
, pp.
1
34
.
15.
Cundall
,
P. A.
, and
Strack
,
O. D. L.
, 1979, “
Discrete Numerical-Model for Granular Assemblies
,”
Geotechnique
0016-8505,
29
, pp.
47
65
.
16.
Reeves
,
W. R.
, and
Greenspan
,
D.
, 1982, “
An Analysis of Stress Wave-Propagation in Slender Bars Using a Discrete Particle Approach
,”
Appl. Math. Model.
0307-904X,
6
, pp.
185
191
.
17.
Monaghan
,
J. J.
, 1982, “
Why Particle Methods Work
,”
SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.
0196-5204,
3
, pp.
422
433
.
18.
Meguro
,
K.
, and
Tagel-Din
,
H.
, 2001, “
Applied Element Simulation of RC Structures Under Cyclic Loading
,”
J. Struct. Eng.
0733-9445,
127
, pp.
1295
1305
.
19.
Schiehlen
,
W.
, 2007, “
Research Trends in Multibody System Dynamics
,”
Multibody Syst. Dyn.
1384-5640,
18
, pp.
3
13
.
20.
Etzmuss
,
O.
,
Gross
,
J.
, and
Strasser
,
W.
, 2003, “
Deriving a Particle System From Continuum Mechanics for the Animation of Deformable Objects
,”
IEEE Trans. Vis. Comput. Graph.
1077-2626,
9
, pp.
538
550
.
21.
Lloyd
,
B. A.
,
Szekely
,
G.
, and
Harders
,
M.
, 2007, “
Identification of Spring Parameters for Deformable Object Simulation
,”
IEEE Trans. Vis. Comput. Graph.
1077-2626,
13
, pp.
1081
1094
.
22.
Goldstein
,
H.
, 1980,
Classical Mechanics
,
2nd ed.
,
Addison-Wesley
,
Reading, MA
, p.
545
.
23.
Burden
,
R. L.
, and
Faires
,
J. D.
, 1989,
Numerical Analysis
,
4th ed.
,
PWS-Kent
, p.
157
.
24.
Birkhoff
,
G.
, and
Rota
,
G. C.
, 1978,
Ordinary Differential Equations
,
3rd ed.
,
Wiley
,
New York
, p.
126
.
25.
Barzanti
,
L.
,
Corradi
,
C.
, and
Nardon
,
M.
, 2006, “
On the Efficient Application of the Repeated Richardson Extrapolation Technique to Option Pricing
,” Working Paper Series, Department of Applied Mathematics, University of Venice.
26.
Smith
,
M. C.
, 2002, “
Synthesis of Mechanical Networks: The Inerter
,”
IEEE Trans. Autom. Control
0018-9286,
47
, pp.
1648
1662
.
27.
Landau
,
L. D.
, and
Lifshitz
,
E. M.
, 1986,
Theory of Elasticity
,
3rd ed.
,
Reed Educational and Professional Publishing Ltd.
, pp.
64
67
.
28.
Rivlin
,
R. S.
, 1944, “
The Effective Work of Adhesion
,”
Paint Technol.
0094-8691,
9
, pp.
215
216
.
29.
Kaelble
,
D. H.
, 1959, “
Theory and Analysis of Peel Adhesion: Mechanisms and Mechanics
,”
J. Rheol.
0148-6055,
3
, pp.
161
180
.
30.
Nicholson
,
D. W.
, 1977, “
Peel Mechanics With Large Bending
,”
Int. J. Fract.
0376-9429,
13
, pp.
279
287
.
31.
Mardon
,
J.
, 1961, “
The Release of Wet Paper Webs From Various Papermaking Surfaces
,”
Appita J.
1038-6807,
15
, pp.
14
34
.
32.
Wang
,
X.
, 1997, “
Finite Element Analysis of Air-Sheet Interactions and Utter Suppression Devices
,”
Comput. Struct.
0045-7949,
64
, pp.
983
994
.
33.
Pramila
,
A.
, 1986, “
Sheet Utter and the Interaction Between Sheet and Air
,”
Tappi J.
0734-1415,
69
, pp.
70
74
.
34.
Blevins
,
R. D.
, 1990,
Flow-Induced Vibration
,
Van Nostrand Reinhold
,
New York
, p.
1
.
35.
Chang
,
Y. B.
, and
Moretti
,
P. M.
, 1991, “
Interaction of Fluttering Webs With Surrounding Air
,”
Tappi J.
0734-1415,
74
, pp.
231
236
.
36.
Sato
,
J.
,
Hutchings
,
I. M.
, and
Woodhouse
,
J.
, 2007,
Proceedings of the 61st Appita Annual Conference and Exhibition
, Gold Coast, Australia, Apr. 6–9, p.
15
.
37.
Kittel
,
C.
, 1996,
Introduction to Solid State Physics
,
7th ed.
,
Wiley
,
New York
, p.
99
.
38.
Feynman
,
R. P.
, 1989,
The Feynman Lectures on Physics
, Vol.
II
,
Addison-Wesley
,
Reading, MA
, pp.
38
11
.
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