## Differential Winding Limits: Part I

Web Lines

The purpose of differential winding is to apply a desired torque to two or more rolls winding on a single shaft. Differential winding allows multiple rolls to turn at differing speeds, with each roll free to slip at the speed required to compensate for roll-to-roll diameter variations and strand-to-strand length variations.

For more on why differential winding is needed, how it compares to locked-shaft winding, and some of their limitations, check out my three columns starting in November 2002 at pffc-online.com/web_lines.

Differential shafts in all their varied designs are a great invention. They are the “sliced bread” of slitter/rewinding operations. However, what I’d like to cover in this and next month’s columns is the idea that even a great invention has its correct application and limitations. Let’s start with what is at the heart of differential shafts—torque. How do they create torque and are you getting what you need?

Most webs run at 0.3-3.0 lbf/in. of width (a.k.a. PLI). On a typical 3-in. inner diameter core, this is nominally a starting torque of 0.6-6.0 in.-lbs of torque. Many small rolls will wind great at constant torque, allowing the web tension to drop off inversely with the roll diameter. With large roll buildups (final diameter/core diameter > 4), the tension of constant torque winding may drop too much, making the roll’s outer layers too loose to hold the roll together.

The primary differential winding torque is created by the shaft’s frictional slip clutching mechanism. A clutch is any device that engages or disengages a rotating shaft and a driving mechanism. A slip clutch is a clutch in that when you engage it, instead of locking gears together like a car’s clutch, loads two non-locking surfaces together. By controlling the load between the two slipping surfaces, you control the friction-limited force that develops when the clutch slips. Most differential shafts have their torque regulated by air pressure, either the air pressure that pushes laterally on a stack of slipping cores and locked spacers or that pushes radially from an internal bladder out against slipping elements or the core’s inner diameter.

As you apply more pressure, the clutching mechanism will slip at a higher frictional force and a winding roll will receive more torque. The torque applied at the core then is transmitted out through the radius of the winding roll to create tension at the roll’s outer diameter.

Unfortunately, this is not the only torque-creating mechanism of a differential shaft. Gravity creates a force on the differential shaft from the roll’s weight, creating an increased torque component as the roll grows. For larger rolls, this may be all the torque you need, and the applied load from air pressure should be turned off.

An advanced differential slitter has a roll weight compensation control, but if you don’t tell your machine the roll diameter, material density, and roll width, you probably don’t have this important capability.

Two last factors that add to torque are nips and inertias. If you use a winding nip roller to prevent air lubrication at high-speed winding, the nip load also loads the core against the differential shaft, creating an additional torque. Inertia isn’t much at roll starts, but as a large winding roll decelerates, it doesn’t want to slow down (it’s a flywheel) and creates an additional torque proportional to your deceleration rate.

Differential torque is the sum of torques created by:

• applied load and slip clutch friction
• roll weight