## Friction Circles on a Winter's Day

Doing doughnuts — this was the term my high school friends called the art of driving around in snow-covered parking lots, spinning your back tires during a hard turn to get your car to fishtail in a circle. We thought we were James Garner on the Rockford Files. The onset of front wheel drive ruined one of life's simple pleasures.

Little did we know “doing doughnuts” was an educational endeavor that helped us better understand a curious, yet practical, mechanism in web handling — the friction circle.

The friction circle is a common term among racing enthusiasts. In racing, it describes the combination of conditions that will lead to a spinout in the third turn.

As your car races down the straightaway, the only way your tires will slip is if you try to accelerate or brake too much. If the inertial load is greater than the tire-to-road traction, you will slip relative to the road. With experience, you learn quickly to control how much gas or brake to apply without slipping.

“Brake before the turn” is good advice given to new drivers. Why? Why should it matter whether you brake while driving straight or while turning? The answer lies in the friction circle. When you are turning, there is another demand on the friction between your tires and the road — centrifugal force.

A moving object will travel in a straight line unless acted upon by an outside force. To redirect your car, you will use the traction or friction forces between the tires and road to overcome centrifugal force. If you try to turn too fast or on too sharp a radius, you will spin out.

If you coast through a turn, you can make a tighter radius without slipping than if you accelerate or brake while in the turn. The friction circle is the combined limit of friction available to be used in any direction. If your 4,000-lb car creates 1,000 lb of friction, you can use that to accelerate or brake and offset centrifugal forces in a turn, but if the combination of these exceeds 1,000 lb, you will slip.

The limit is actually the vector sum of the applied forces, so you will be able to support 700 lb of load in perpendicular directions but not much more.

How does the friction circle apply to web handling? The friction circle applies any time you are trying to use web-to-roller (or web-to-web) traction in the machine and transverse directions at the same time.

Following are three cases in which the friction circle explains what may otherwise seem inexplicable web behavior.

Case 1: A steering style web guide uses web-to-roller traction in the transverse direction to create the bending force that redirects the web, but it also uses traction in the machine direction to overcome roller bearing and inertial drag. I've had clients tell me “the steering roller slips before the other idler rollers.” Since a steering roller has more lateral traction demand, it will have less traction available to overcome the machine-direction loads and therefore slip before similar non-steering rollers.

Case 2: To hold a wrinkle, the roller must exert forces laterally on the buckled web. Rollers with wrinkles also need traction to oppose machine-direction drag. If the roller machine-direction load increases, the wrinkles will disappear just before the roller slips. A roller on the fine edge of slipping will have difficulty holding in a wrinkle. This phenomenon is a powerful anti-wrinkle tool when properly applied.

Case 3: Early last year (February and March), I wrote columns on cinching, where the winding roll's torque capacity is exceeded. The friction circle concept explains why cinching typically is accompanied by telescoping. When the machine-direction applied torque consumes all roll's internal traction, there is nothing left to hold the roll laterally.

I expect you wondered how I was going to get from doing doughnuts in my high school parking lot to a useful principle of web handling, but there it is. Think about the friction circle this winter next time your traction-control braking system kicks in on that snow-covered road.

Timothy J. Walker has 20+ years of experience in web handling processes. He specializes in web handling education, process development, and production problem solving. Contact him at 404/373-3771; This email address is being protected from spambots. You need JavaScript enabled to view it.; tjwa.com.