A Set-up Model for Tandem Cold Rolling Mills (October 24, 2001)

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A Set-up Model for Tandem Cold Rolling Mills
(October 24, 2001)

• by
• N. Venkata
• G. Suryanarayana

Paper Presented By Nathan Zollinger September
13, 2004
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References
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Background
The demand for rolled products has increased
tremendously in automobile, aircraft, food and
other industries.
With the increase in the demand for rolled
products, the focus has shifted towards the
tandem rolling mills which can operate at very
high speeds and in which large reductions can be
achieved with relatively close tolerance on
flatness and thickness (269).
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The Problem

So how can I make my rolling
operations more profitable?
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Solutions?

1. Modernize/enhance rolling mill setup
2. Explore/implement innovative rolling
   designs/processes
3. Specialize in market niche
4. Other?

ENHANCE REDUCTION SCHEDULE!
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Reduction Schedule

• A reduction schedule assigns thickness
  reductions for a given amount of roll passes.
  For a series of rollers, a tandem setup, each
  roller will be assigned a reduction percentage.
• In rolling, a strip is rolled continuously
  through 4-7 individual mills (tandem setup) at
  high speed with no stopping between mills. This
  requires much investment into efficient
  calculations and controls to minimize rolling
  costs.
• Perhaps there exists an optimum reduction
  schedule that will lower energy consumption,
  i.e., minimize rolling costs.

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Reduction Schedule

• Homework Problem 19.6constant reduction

A constant reduction schedule is also known as
geometric
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Reduction Schedule

• What about Harmonic, Linear, Quadratic
  Schedules?

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The paper
N. Venkata and G. Suryanarayana seek to establish
an optimum tandem roller reduction schedule that
will result in better energy efficiency during
rolling processes. How? Utilize understanding of
deformation mechanics to model power requirements
for a few reduction schedules.

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Math Model

• Utilize one-dimensional mathematical models
• Less computational time than other methods
• Predicts Roll Force, Roll Torque, and Pressure
  distributions with reasonable accuracy
• Axial Equilibrium Equation

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Math Model
P O W E R
2. Rearrange and solve for s using the Runge
Kutta Method
3. Use s to find normal pressure
1. Axial Equilibrium Equation
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Math Model

• ASSUMPTIONS
• Material is isotropic, incompressible, and
  yields according to the Von Mises Criterion
• Rolls are rigid and the coefficient of friction
  is constant over the roll-work interface
• Deformation is homogenous and takes place under
  isothermal conditions
• CONSTRAINTS
• Minimum µ required at the maximum possible
  reduction (?hmax µ2R) is

The von Mises Criterion (1913) is often used to
estimate the yield of ductile materials. The von
Mises criterion states that failure occurs when
the energy of distortion reaches the same energy
for yield/failure in uniaxial tension.
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Results
Test results run for various schedules were
matched against a previously suggested reduction
schedule (Roberts) the harmonic arrangement
yielded the least power consumption
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Results
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Conclusion
Distributing the strip thicknesses in harmonic
series will minimize power consumed and create
savings in tandem mill operations!