Customers and suppliers both want ever larger rolls. As the diameter increases, so does the run time between roll changes. Fewer roll changes means that the portion of waste at the top and bottom of the roll may be reduced. Fewer roll changes means a reduced chance of a miss during a flying splice or turn-up. It also means reduced labor. The operator can spend more time watching the process instead of prepping rolls. Thus, big rolls are good.

However, as the diameter increases, so does the incidence of defects. As discussed last month, the large roll is much more prone to telescoping during winding or unwinding. Thus, the risk of adding an extra inch on the outside may be losing the entire roll. Since most winders and nearly every unwind is core supported, the core must bear the weight of the roll. If the roll is heavy, the material near the core can be crushed in a variety of ways. Since the web was not 'designed' to be a load-carrying material, it is not surprising to find the core area blocked, squashed or shredded. Thus, big rolls are bad.

How do we find the optimum roll diameter to minimize the losses that can occur due to the roll being either too small or too big? First, we must select a common objective, such as minimizing costs. Second, we plot the costs of being too small as a function of roll diameter. In the cases of top and bottom waste, this is quite simple. Perhaps you lose 1" at the bottom and 1/8" on the top of rolls, regardless of the size. Then the waste can be calculated as shown below. Third, we plot the costs of being too big as a function of roll diameter. Perhaps the incidence of telescoping skyrockets after a certain diameter. Fourth, you sum the curves as shown in the accompanying diagram. Finally, the most effective diameter is at the minima of the sum.

This analysis is adaptable to many different problems of optimizing a setting. It's also quite powerful if the analysis is rigorous and uses accurate costs. However, the analysis can be used even if the costs are not known precisely. As seen in the figure, you are not at the optimum if there are no incidences of telescoping (or whatever the large roll penalty may be). Thus, it may be that striving for Six Sigma or Zero Defects may raise manufacturing costs, or even put you out of business. The purpose of business is to make money. Any analysis that does not consider costs and benefits is incomplete.

David Roisum, Ph.D.

Consulting Technical Editor

920/725-7671

DRroisum@aol.com

www.roisum.com