1. Principle of the process Design For Manufacturing (DFM)
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.
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3. Objectives of mechanics analysis
Physical phenomenon
Torque
Power
Productivity
System
parameters
Operating parameters
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4. Spreading: Volume before rolling = the volume after rolling
Physical phenomenon L w t
Spreading: Volume before rolling = the volume after rolling
Volume flow rate conservation
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5. Work velocity = Roll velocity
Vo < Vr < Vf
No-slip point
Slipping
Slipping
Work velocity = Roll velocity
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6. k e Y = + 1 n For the rolling process, the true strain is:
The average flow stress is the same expression, i.e. k e n Y = f + 1 n
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7. The friction force is developed based on
It is the friction between the work and the roll that drives the workflow between two rolls.
Greater
Friction Force
No-slip point
Lesser
Friction Force
The friction force is developed based on
coefficient of the friction and
compression force of rolls
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8. Friction causes Rolling If Friction=0, then draft=0, means NO ROLLING
Condition to roll- Coefficient of the friction
draft, d = |tf-t0|: dmax
Max. Possible Draft
Friction causes Rolling
If Friction=0, then draft=0, means NO ROLLING
Radius of the roll
Friction coefficient
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9. The pressure varies along the contact length
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
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10. N: rotation speed of the roll, rev / min
Contact length
Contact force
Torque
N: rotation speed of the roll, rev / min
Power
Power is a function of D. Increase of D leads to increase of P
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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 = 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.
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13. Given: rolling, t0=1. 0 in. , tf=0. 80 in. , w=10. 0 in. , R=20 in
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.
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14. N = (50 ft/min)/(2π×20/12) = 4.77 rev/min.
Torque T = 0.5(432,149)(2.0) = 432,149 in-lb.
N = (50 ft/min)/(2π×20/12) = 4.77 rev/min.
Power P=2 π (4.77)(432,149)(2) = 25,929,940 in-lb/min
HP = (25,929,940 in-lb/min)/(396,000) = 65.5 hp
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