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Rolling

Principle of the process Structure Process modeling Defects Design For Manufacturing (DFM) Process variation. Metal forming. Rolling. Rolling Process: Mechanics Analysis.

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Rolling

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  1. Principle of the process Structure Process modeling Defects Design For Manufacturing (DFM) Process variation Metal forming Rolling Module 8

  2. Rolling Process: Mechanics Analysis • Two opposite rolls and a piece of material flows between them. The shape of rolls can be designed in a different form to construct a product with different cross sections. handout 8 b

  3. System parameters Operating parameters Objectives of mechanics analysis • Physical phenomenon • Torque • Power • Productivity Product parameter handout 8 b

  4. w t L Physical phenomenon Spreading: mass conservation (volume before rolling = volume after rolling) Volume flow rate conservation • Product parameter (t0, tf) cannot be changed, and they need to be achieved through the process. • In the process, w, L, and vf are derived parameters. • Vf represents the productivity, while w and L are product parameters. handout 8 b

  5. Vo < Vr < Vf No-slip point Slipping Slipping Work velocity = Roll velocity Production rate handout 8 b

  6. For the rolling process, the true strain is: The average flow stress is the same expression, i.e. e n k = Y f + 1 n handout 8 b

  7. It is the friction between the work and the roll that drives the workflow between two rolls. Greater Friction Force Lesser Friction Force No-slip point The friction force is developed based on • coefficient of the friction and • compression force of rolls handout 8 b

  8. Max. Possible Draft Radius of the roll Friction coefficient Friction causes Rolling If Friction=0, then draft=0, means NO ROLLING Condition to roll- Coefficient of the friction draft, d = |tf-t0|: dmax handout 8 b

  9. Condition to roll- Power to drive the roll and work piece Roll Force (F) Integrating “unit roll pressure” over roll work “contact area” • The pressure varies along the contact length. • F is assumed to be at the middle of the L. • W is the width of the roll. handout 8 b

  10. Torque Contact length d Contact force N: rotation speed of the roll, rev / min Power Power is a function of d. Increase of d leads to increase of P handout 8 b

  11. Condition to roll- Power to drive the roll and work piece When the required power (d) is greater than the supplied power, the rolling of a work piece with d is not possible. Therefore, the required power = supplied power will lead to a critical draft d or maximum d. Criterion 1: Criterion 2: required power = supplied power  The actual maximum draft for a rolling system is the smaller one computed from the two criterions above.

  12. Example: A 10-in. –wide, 1.0-in – thick plate is to be reduced in a single pass in a two-high rolling mill to a thickness of 0.8 in. The roll has a radius = 20 in., and its speed = 50 ft/min. The work material has a strength coefficient = 35.000 lb/in.2 and a strain hardening exponent = 0.2. Determine (a) roll force, (b) roll torque, and (c) power required to accomplish this operation. handout 8 b

  13. Given: rolling, t0=1.0 in., tf=0.80 in., w=10.0 in., R=20 in., vr=50 ft/min, flow curve n=0.20 and K=35,000 lb/in2. Find: (a) F, (b) T, (c) HP. Draft d=1.0-0.8=0.2 in. Contact length L = (20×0.20)0.5 = 2.0 in. True strain ε = ln (1.0/0.8) = ln 1.25= 0.223 Average flow stress f = 35,000(0.223)0.20/1.20 = 21,607 lb/in2 Rolling force F = 21,607(10)(2) = 423,149 lb handout 8 b

  14. Torque T = 0.5(432,149)(2.0) = 432,149 in-lb. L: contact length Unit of R is converted from in to ft N = (50 ft/min)/(2π×20/12) = 4.77 rev/min. Perimeter 12,951,849 Power P=2 π (4.77)(432,149)(2) = 25,929,940 in-lb/min HP = (12951849 in-lb/min)/(396,00) = 134.9 hp handout 8 b

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