3. Rolling flat rolling Shape Rolling

4. Note appearance of surfaces

5. Hot rolling is used to reduce forces and promote ductility

11. Ring Rolling

16. Thread Rolling

22. Rolled Products Made of Steel

24. Frame, drive, jacks, and rolls comprise a mill or stand which are connected together via conveyors

26. Compressive Stress

27. 2 ‑ high mill Rolling Mill Designs 3 ‑ high reversing mill. 4 ‑ high mill 6 ‑ high or cluster mill

28. where d = draft; t o = starting thickness; and t f = final thickness Reduction = draft expressed as a fraction of starting stock thickness: where r = reduction

29. Tandem Rolling Mill

30. Note how workpiece velocity must increase while roll velocity will be constant Note how workpiece thickness decreases as the material passes through the roll gap - We need to use average flow stress We need to calculate force and power needed to turn the rolls

31. Volume in = Volume Out

32. At point where friction changes direction, this is termed the no-slip point At the no-slip point, the roll pressure distribution is at a maximum We can consider that the average roll pressure is the same as the average flow stress for rolling

33. We can develop an estimate of the force and power for a single stand in cold rolling as follows: For an annealed material: We can also calculate the average flow stress at the i th stand by: In cold rolling, the average flow stress will increase due to work hardening. In hot rolling we often assume that flow stress is constant. Note average yield stress will increase as the next stand in tandem cold rolling.

34. Mill Load Force = Average Yield Stress * area Change in Width of workpiece = 0 (plane strain) Assume rolling is compression between 2 inclined plates L

35. F F Based on the force equilibrium, we can see that a torque is generated on the roll When no front or back pull is applied, F is midway along the contact length, L L Power is more useful for the drive motor

36. We would like to roll a workpiece using the minimum number of stands due to the equipment and operations costs i.e. maximize the reduction taken at each stand Clearly, mill load is one factor Rolling requires that we have sufficient friction to pull the workpiece into the roll gap, this represents a second limiting factor as to the maximum reduction that can be taken Consider an element at the entry to the roll gap -Roll force (normal) -Friction force (parallel)

37.   FNFN FfFf Minimum condition for feasible rolling F n sin  = F f cos   tan  R-d/2 d/2 R Successive Application of Pythagoreans Theorem Yields d max =  2 R Suggests max roughness and roll sizes

39. D = 40” diameter W = 24” What is the rolling load at each stand?.045”.050”.041” Annealed First Stand Second Stand

40. First Stand Second Stand.045”.050”.041” Annealed Note work hardening from first stand

41. Now find contact areas, w is constant in flat rolling First Stand Second Stand Load = 4.6*7.58 = 34.9 kips Load = 6*6.91 = 41.46 kips

42. No-load Loaded Minimum thickness achievable due to roll flattening note aluminum foil is 0.2 mm thick Uneven thickness across workpiece width (crowning)

43. 12 High Sendzimir Mill Stand Used for rolling very thin sheet material Rolling Thin Sheet Work Roll Backer Rolls