Introduction The strain transport formula has been around for many years. It is often glossed over in training, and taken for granted. But, it can do so many things for the informed user.

the velocity of any other roller divided by one plus its web strain. Background The velocity of a roller divided by one plus the web strain at the roller is equal to the velocity of any other roller divided by one plus its web strain. Vref V1 V2 V3 Vn eref e1 e2 e3 en Where:

Tension Calculation If you know the reference strain and velocity, you can: Vn en V3 e3 V2 e2 V1 e1 Vref eref Load Cell calculate any other strain, if you know the velocity calculate the required velocity, if you know the desired strain

Length of relaxed web past Rollern : Length Calculation Length of relaxed web past Rollern : where

Length Calculation Relaxed length of a cut sheet: Where CPT = Cuts Per Time

Strain Sensitive Process If your process is strain sensitive: Tref should be as low as possible! Vn en V3 e3 V2 e2 V1 e1 Vref Tref Load Cell Use Vn to control en

Strain Sensitive Process If your process is strain sensitive, but you need high tension at the parent roll! Load Cell Vn en V3 e3 V2 e2 Vref Tref V-1 T-1 Use Vn to control en

If your process is tension sensitive, Vn should equal Vref ! Tension Sensitive Process If your process is tension sensitive, Vn should equal Vref ! Vn Tn V3 T3 V2 T2 V1 T1 Vref Tref Load Cell

Some times tension goes up, sometimes down, sometimes both? Tension Troubleshooting Some times tension goes up, sometimes down, sometimes both? Vn Tn V3 T3 V2 T2 V1 T1 Vref Tref Load Cell If Vn>Vref , when EA increases, Tn increases. If Vn<Vref , when EA increases, Tn decreases. If Vn=Vref , when EA increases, Tn is unchanged.

Parent Roll WOT at Winding What is the wound on tension, WOT, in the outer layer on the parent roll? V2 T2 V1 T1 Load Cell

What tension was the parent roll wound at? Parent Roll WOT at Unwind What tension was the parent roll wound at? V2 T2 V1 T1 Load Cell

Modulus Measurement If you know two tensions and two velocities, you can calculate modulus. V2 T2 V1 T1 Load Cell

If you know the strain that damages your web, and its thickness: Smallest Bending Radius If you know the strain that damages your web, and its thickness: ro ri h

The Small Strain Assumption The small strain assumption is sometimes used to make it easier to solve difficult formulas.

Conclusion The strain transport formula has been around for many years. It is often glossed over in training, and taken for granted. But, it can do so many things for the informed user. Now, You Are Informed!

RJLynch & Associates, LLC Questions? Ron Lynch RJLynch & Associates, LLC ronjlynch@hotmail.com 513-503-5160