Application of the FiniteElement Analysis to the Pass Rolling Process

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Applicationof the Finite-Element Analysisto the
Pass Rolling Process

• Professor, D.Sc. Chumachenko E.N.

Moscow State Instituteof Electronics and
Mathematics (Technical University),Dep.
Mathematical Simulation www.miem.edu.ru mmkaf_at_miem
.edu.ru
General Director KOMMEK Ltd. www.kommek.ru kommek_at_
miem.edu.ru
IKI Seminar Mechanics, Control and Informatics
Moscow 2005
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• Introduction
• The basic ratios and results of pass rolling
  process simulation using the SPLEN computing
  system developed based on the finite-element
  method (FEM) are discussed.
• The computing system allows setting any
  configuration of a roll profile, and presently it
  is used for studying isothermal and
  non-isothermal rolling processes with two
  symmetric rolls. In this model a rigid-ductile
  statement of the problem and special system of
  friction implementation are used.
• The computer system simulating the process of
  metal deformation in passes allows avoiding
  labor-consuming and expensive industrial
  experiments and reduces the time of developing
  technological solutions. Besides, at the design
  stage already, one can reveal defects of the
  rolled product form and working degree of the
  metal and thereby maximally approach a
  technological draft to the working one.
• To increase a solution algorithm speed, the
  half-analytical finite-elements method was used.

IKI Seminar Mechanics, Control and Informatics
Moscow 2005
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Mathematical model of form changing hot
materials
Boundary conditions on the on the
(1) on the
- velocity of particles of continuum
- mill roller speed - normal
pressure - normal to mill roller
- tangent stress
- directional cosines - orthonormal
frames - constant of friction.


(2)


(3)



Then
and condition
entry (4)
IKI Seminar Mechanics, Control and Informatics
Moscow 2005
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Heat exchange

• The heat exchange of the strip with rolls and
  with environment is described by the following
  variational equation
• (5)
  
  
  
• where - is heat conductance coefficient
• - is thermal capacity and density of the strip
  material
• - is a generalized parameter dependent on the
  temperature difference of the strip and
  environment, Stephen-Boltsman constant, blackness
  coefficient of the body and on relative position
  of the surfaces when radiating
• - is linear expansion coefficient for
  environment and rolls
• - is relative speed module of the
  movement with friction
• - is a coefficient taking into account
  the part of released heat energy.

IKI Seminar Mechanics, Control and Informatics
Moscow 2005
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• For an arbitrary element of the strain focal
  point of a little enough thickness, the
  value characterizing relative elongation
  speed of the fibers in an element of the
  thickness dz, is constant .
  In this case constant C in each section
  has its own value. Speed components of
  particles movement in any fixed element
  relative to the rolls surfaces look like
• (6)
• a)
• b)
• A diagram of a focal point of strain at a
  longitudinal rolling (a) and stresses
  (b) applying to a layer of an infinitesimal
  thickness.

IKI Seminar Mechanics, Control and Informatics
Moscow 2005
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• Half-analytical of finite-elements method
• Thus, the three-dimensional speed field of an
  element is divided into two components.
  The speed field of in the section
  perpendicular to the rolling direction is
  determined from a finite-element approximation.
  The speed component along the rolling
  direction is calculated using an iterative
  procedure with a search of the constant C. So
  an initial volume problem for an element
  was reformed into a "generalized"
  two-dimensional problem which can be solved using
  the finite-element method.
• For a spatial stress-deformed state to be
  constructed, the length focal point of strain is
  divided into m parts by means of cross sections,
  and the value in each
  section at is
  determined.

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• A spatial problem solution algorithm for each
  individual element is based on a
  minimization of the functional
• (7)
• Finally the longitudinal movement speed of the
  particles in an arbitrary section
  can be determined by the ratio
  , (8)
• where
• is the movement speed of
  an element at the focal point of
  strain input .

IKI Seminar Mechanics, Control and Informatics
Moscow 2005
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Experimental verification
For model verification the experimental data
obtained in expertises on study of a tension at
rolling in smooth rolls, obtained earlier by
professor Tarnovskiy I.J. utilized.
?0 , W0 - initial height and width of a
strip WF - averaged finite width of a
strip.
IKI Seminar Mechanics, Control and Informatics
Moscow 2005
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Experimental verification
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Moscow 2005
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Compare 3D and 2.5D simulators
A comparison of the considered model with a
three-dimensional pass rolling version of
J.J.Park and S.I.Oh accomplished in the SHPROL
program based on the finite-elements method was
carried out.
SHPROL

? Distribution of strain intensities on the
surface of a rolled square section strip into
oval at a stable mode. ? Diagrams of
normal stresses at a focal point of strain when
rolling a square section strip into oval..
SPLEN

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Moscow 2005
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• An experimental test of the calculation results
  showed a high enough accuracy of forecasts for
  passes fillability at a profile rolling. The
  maximum error of the values characterizing
  geometrical parameters of a strip at a focal
  point of strain output in laboratory and
  industrial conditions did not exceed 6.4 per
  cent.
• Axial section of rolls when rolling a
  strip
• of square section in oval pass
• - initial section of the strip
• - section of the deformed strip.
• System SPLEN allows
• - to model the rolling in groove
• - to analyze the groove for optimal the
  ultimate article
• with respect to of process productivity
  filling the groove,
• the friction, the drawing, influence of
  roller temperature.

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Moscow 2005
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• When developing a new industrial calibration of
  rolls at the profiled rolling mill 320/250
  ("SerpMolot Works) for rolling strip steel of
  the 18x36 mm size of Steel 35, they decided to
  carry out a preliminary analysis based on
  imitating simulation using the SPLEN computing
  system.
• In conformity with the algorithm of numerical
  calibration test, of search and correction of the
  intermediate passes form, we accomplished a
  sequential change of initial calibration and
  solved problems of imitating simulation.
• Technological diagram of check and change of
  calibration

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Moscow 2005
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Change of a leader pass to product the most
qualitative profile
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Moscow 2005
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Change of a leader pass to product the most
qualitative profile
IKI Seminar Mechanics, Control and Informatics
Moscow 2005
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• Physical simulation as result the mathematical
  simulation
• According to the changed calibration, a rolling
  was carried out, as a result of which a strip
  satisfying all preset requirements was
  manufactured. The deviation of the calculated
  results from the contour of a real template at
  the same mill adjustment did not exceed 1.5 per
  cent.
• The templates of a finish strip
  manufactured when rolling according
  to an initial (a) and changed (b)
  calibrations, and also according to
  a new calibration when rolling
  strips with cross sections of 18 x
  36 (c), 20 x 32 (d) and 16 x 36 mm (e)
• a) b)
• c) d) e)

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Moscow 2005
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• A trial test of the SPLENsystem during real
  calibrationsof the profile mills 500,300-2,
  250-1 and the wiremill 250-2 is accomplishedin
  the Calibration Bureauof the MagnitogorskyMetall
  urgical Works.Specialists of the Worksmade the
  conclusion thatthe received results hada high
  degree of reliability,and graphic possibilities
  of the calculation results presentation are
  convenient to operate with.

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Moscow 2005
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Resume
The mathematical model and algorithms define a
simulation of steadied calibrating process is
designed.
The response rate of designed systems on the
degrees exceeds response rate of existing
algorithms of spatial simulation calibrating
process that is the important advantage at
problem solving of optimization.
On the basis of the above-stated method of
application the operations on creation of a
service system of simulation and optimization of
manufacturing processes of rolling calibrating
process are carried on.
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Moscow 2005
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We employ the positive scientific results which
came aboutdue to our extensive cooperation with

• National Institute of Aviation Technology (NIAT),
  Moscow, Russia
• Research Institute of Metallurgical Machinery
  (VNIIMetmash), Moscow, Russia
• Moscow Institute of Heat Technic (MIT), Russia
• Harkov's Plant of Malushev, Ukraine
• Joint Stock Corporation "Technomash", Moscow,
  Russia
• Miass's Design Department of Machinery, Russia
• Zlatoust's Machinery plant of V.I.Lenin, Russia
• AIRBUS INDUSTRY
• Aerospatiale Societe Nationale Industrielle,
  FranceDaimler-Benz Aerospace Airbus GmbH,
  GermanyConstrucciones Aeronauticas S.A.,
  SpainBritish Aerospace (Operations) Ltd.,
  England
• Research and Industrial Company "Igsteel",
  Igevsk, Russia
• Research and Industrial Aviation Company, Kazan,
  Russia
• Bearing plants (Vologda, Kursk, Volgskiy), Russia
• REINZ Dichtungs GmbH, Germany
• Rolling plant SerpMolot, Moscow, Russia
• Magnitogorsky Metallurgical Works, Russia

IKI Seminar Mechanics, Control and Informatics
Moscow 2005