1. 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

2. References

3. 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).

4. The Problem = So how can I make my rolling operations more profitable?

5. Solutions? = 1.Modernize/enhance rolling mill setup 2.Explore/implement innovative rolling designs/processes 3.Specialize in market niche 4.Other? ENHANCE REDUCTION SCHEDULE!

6. 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.

7. Reduction Schedule Homework Problem 19.6–constant % reduction A constant reduction schedule is also known as geometric

8. Reduction Schedule What about Harmonic, Linear, & Quadratic Schedules?

9. 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.

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

11. Math Model POWERPOWER 1. Axial Equilibrium Equation 2. Rearrange and solve for σ using the Runge Kutta Method 3. Use σ to find normal pressure

12. 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 (Δh max = μ 2 R) 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.

13. Results Test results run for various schedules were matched against a previously suggested reduction schedule (Roberts); the harmonic arrangement yielded the least power consumption

14. Results

15. Conclusion Distributing the strip thicknesses in harmonic series will minimize power consumed and create savings in tandem mill operations!