2. 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.

3. 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:

4. 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

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

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

7. 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

8. 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

9. 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

10. 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.

11. 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

12. 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

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

14. 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

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

16. 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!

17. RJLynch & Associates, LLC
Questions?
Ron Lynch
RJLynch & Associates, LLC