## Web Lines | The Case of the Missing Pacer

I recently visited a converter that had a rewinder with no apparent direct-driven pacer roller. The unwind had brake torque control, and the rewind had a slipping differential shaft. No rollers were driven. Yet the equipment did have speed control somehow.

How can a system with only two slipping torque elements control speed?

Traditionally, both the braked unwind and the clutched winder would control tension in their own zones. Most rewinders would have an intermediate driven roller or section to control speed. The unwind brake torque would control tension up to a pacer roller or section, and the differential shaft torque would control tension from the pacer to winding.

Two opposing torque systems without a pacing section normally would not be a stable system. Newton’s second law of motion is F = ma (Force equals mass times acceleration). Rearranging this equation yields a = F/m. When a force is applied to a mass, the mass will accelerate. This is true for a rotation system, too. Torque applied to rotating mass will create rotational acceleration.

The unwind and winder torque control will create applied tension equal to torque divided by radius. Two opposing torque systems can have three cases:

• If the unwind brake tensioning force is higher than the winder tensioning force, the brake should not slip and the line will remain stopped.
• If the unwind brake tensioning force equals the winder tensioning force, the brake will maintain whatever speed it is at (including remaining stopped, if it is not in motion).
• If the unwind brake tensioning force is less than the winder tensioning force, the brake will slip and the rolls and web will accelerate.

So to get this two-torque rewinder up to speed, first the winder-created tension must be greater than the unwind-created tension. Then, when it reaches the desired speed, the two tensions from torqueing the unwind and winder need to be equal. This is a challenging balance, especially considering that the diameters of the unwind and winding rolls are constantly changing.

This system can be stable, it just needs some feedback to control speed. In this particular case, the unwind was pacer. The unwinder was turned into the pacer by adding an encoder to a non-slipping roller to measure web speed. Speed was controlled by adjusting unwind brake torque to create tension just above or just below the rewind tension to control acceleration, deceleration, and speed set point. The air pressure supplied to the differential shaft controlled tension. The differential shaft over-speed was fixed to ensure slippage at full speed of a small winding roll.

How does a torque-controlled unwind control speed?

This is similar to using your car’s brakes to control speed as you go downhill. Gravity wants to make the car accelerate, but by applying just the right amount of break force, you can control speed. When you let off the brake, the car accelerates. To stop, you apply more brake than the gravitational pull. To maintain a constant speed, you have to continually adjust the brake above and below the force balance point, making subtle adjustments as the road slope changes or the wind changes direction.

An unwind brake can control speed similar to how you can use your brakes to control your car's speed when you are going downhill. In brake-controlled coasting downhill, gravity pulls you forward as you adjust the brake to balance the driving and braking force to stop accelerating and maintain desired speed. Using a brake to regulate rewinding speed, in this case, the differential winding shaft is the forward-driving force, and the unwind brake applies the right amount of force to avoid aggressive acceleration and maintain target speed.

If the unwind brake is on, the slitter will not move until the differential over-speed is turned on and the air pressure supplied to the differential shaft creates a force greater than the unwind braking tension. If the differential tensioning is greater than the unwinding force, the system will accelerate. This is where the “cruise control” kicks in.

The system will accelerate until the forces between unwind and rewind are balanced. The web speed monitor is waiting for the web to reach target speed. When target speed is reached, the “cruise control” increases the unwind brake pressure to keep the slitter at the target speed. If the slitter “cruise control” did not continue its function, the slitter would stop.

Unwinding rolls with constant torque will create increasing tension force as roll radius decreases. Therefore, to keep the balance of winding and unwinding tension and maintain the desired speed, the slitter cruise control will continue to decrease the air pressure to the brake.

This system works, and lacking an intermediate driven roller, it costs less. But I don’t advocate this design. I am a strong believer in separating unwind and winding tensions. These two processes often are not compatible.

Unwind tension may need to be low and constant to avoid cinching and telescoping and to provide a constant tension baseline into slitting or other intermediate processes. Winding needs to be high or low and tapering to build the right roll structure for the material, thickness, and roll geometry of winding. The intermediate driven roller enables this two tension zone plan. And as long as you have an intermediate driven roller, you might as well make it the pacer.

Web handling expert Tim Walker, president of TJWalker+Assoc., has 25 years of experience in web processes, education, development, and production problem solving. Contact him at 651-686-5400; This email address is being protected from spambots. You need JavaScript enabled to view it.; www.webhandling.com.

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