for control of the crown of the rolls dynamically. Pair cross rolling involves using either flat or parabolically crowned rolls, but shifting the ends at an angle so that the gap between the edges of the rolls will increase or decrease, thus allowing for dynamic crown control. Work roll bending involves using hydraulic cylinders at the ends of the rolls to counteract roll deflection. Another way to overcome deflection issues is by decreasing the load on the rolls, which can be done by applying a longitudinal force; this is essentially drawing. Other method of decreasing roll deflection include increasing the elastic modulus of the roll material and adding back-up supports to the rolls. The different classifications for flatness defects are: Symmetrical edge wave - the edges on both sides of the workpiece are "wavy" due to the material at the edges being longer than the material in the center. Asymmetrical edge wave - one edge is "wavy" due to the material at one side being longer than the other side. Center buckle - The center of the strip is "wavy" due to the strip in the center being longer than the strip at the edges. Quarter buckle - This is a rare defect where the fibers are elongated in the quarter regions (the portion of the strip between the center and the edge). This is normally attributed to using excessive roll bending force since the bending force may not compensate for the roll deflection across the entire length of the roll. It is important to note that one could have a flatness defect even with the workpiece having the same thickness across the width. Also, one could have fairly high crown or wedge, but still produce material that is flat. In order to produce flat material, the material must be reduced by the same percentage across the width. This is important because mass flow of the material must be preserved, and the more a material is reduced, the more it is elongated. If a material is elongated in the same manner across the width, then the flatness coming into the mill will be preserved at the exit of the mill. Draught The difference between the thickness of initial and rolled metal piece is called Draught. Thus if is initial thickness and is final thickness, then the draught is given by The maximum draught that can be achieved via rollers of