System and method for measuring untensioned product length of a web during production

1. A method for determining an untensioned product length of a web moving through a printing press under tension, comprising, using a controller:

determining a tensioned repeat length of the web in a span of the printing press while the web is moving through the printing press under tension;

determining an elastic strain of the web in the span of the printing press while the web is moving through the printing press under tension;

calculating an untensioned product length of the web in the span of the printing press while the web is moving through the printing press under tension as a function of the tensioned repeat length and the elastic strain; and

controlling the printing press using the untensioned product length.

2. The method of claim 1 , wherein the step of determining the tensioned repeat length comprises calculating the tensioned repeat length as a function of a reference repeat length and a velocity gain in the span.

3. The method of claim 2 , wherein the velocity gain is calculated as a function of drive setpoints for a motor driving the web in the span, the drive setpoints including a drive for transport gains for tension, and a drive setpoint for transport gains for repeat length.

4. The method of claim 1 , wherein the step of determining the elastic strain comprises

measuring, with a sensor, a tension in the span,

determining a stiffness of the web, and

calculating the elastic strain as a function of the tension and the stiffness.

5. The method of claim 4 , wherein the step of determining the stiffness of the web comprises measuring tension in the web at two different velocity gains.

6. The method of claim 5 , wherein the two different velocity gains comprise a first velocity gain at a first motor, and a second velocity gain at a second motor, the first motor driving the web via a first roller, the second motor driving the web via a second roller.

7. The method of claim 1 , wherein the step of calculating the untensioned product length comprises

calculating, during a production run, an untensioned product length L 0 (t) over time t:

L 0 (t)=L 1 (t)/(1+ε 1 (t)), where, at any given time t, L 0 is the untensioned product length, L 1 is the strained repeat length at the span, and ε 1 is the elastic strain of the web in the span;

and wherein ε 1 =T 1 (t)/E(t), where T 1 is the tension at the span, and E is the web modulus.

8. The method of claim 1 , wherein the tensioned repeat length of the web in the span of the printing press is determined with a camera.

9. The method of claim 1 , wherein the step of determining the tensioned repeat length of the web in the span of the printing press comprises:

measuring a velocity V 1 of the web in the span; and

calculating a tensioned repeat length L 1 , as L 1 =(t repeat )(V 1 ), where t repeat is a time for a plate cylinder of the press to print one non-repeating image.

10. A web fed printing press for printing on a continuous web and cutting the web into printed products having an untensioned product length, the press comprising:

a printing unit including a plate cylinder, a blanket cylinder, and an impression cylinder, the plate cylinder having a reference repeat length;

a plurality of rollers located downstream of the printing unit, the web moving under tension through the printing unit and the plurality of rollers as it moves through the press,

a controller configured and arranged to generate an untensioned product length of the web as it moves through a printing press under tension, the controller determining a tensioned repeat length of the web in a span located between an adjacent pair of the plurality of rollers, while the web is moving through the printing press under tension, determining an elastic strain of the web in the span of the printing press while the web is moving through the printing press under tension, and calculating an untensioned product length of the web in the span of the printing press while the web is moving through the printing press under tension as a function of the tensioned repeat length and the elastic strain.

11. The press of claim 10 , wherein controller calculates the untensioned product length by:

calculating, during a production run, an untensioned product length L 0 (t) over time t:

L 0 (t)=L 1 (t)/(1+ε 1 (t)), where, at any given time t, L 0 is the untensioned product length, L 1 is the tensioned repeat length at the span, and ε 1 is the elastic strain of the web in the span;

and wherein ε 1 =T 1 (t)/E(t), where T 1 is the tension at the span, and E is the web modulus.

12. The press of claim 11 , further comprising a tension sensor for sensing a tension in the span, the controller coupled to the tensor for detecting the tension T 1 .

13. The press of claim 12 , wherein the tension sensor is a first tensioning roller, and wherein the first tensioning roller is one of the plurality of rollers, the first tensioning roller located upstream and adjacent to a first driven roller, wherein the first driven roller is one of the plurality of rollers.

14. The press of claim 13 , comprising a second tensioning roller for detecting a tension T 2 , and wherein the second tensioning roller is one of the plurality of rollers, the second tensioning roller located upstream and adjacent to a second driven roller, wherein the second driven roller is one of the plurality of rollers.

15. A system for determining an untensioned product length of a web moving through a printing press under tension, comprising:

a first tensioning roller, the moving web contacting the first tensioning roller;

a first roller located downstream of the first tensioning roller, the first roller driving the web, a first span of the web extending between the first tensioning roller and the first roller;

a first motor driving the first roller;

a second tensioning roller located downstream of the first roller, the moving web contacting the second tensioning roller;

a second roller located downstream of the second tensioning roller, the second roller driving the web, a second span of the web extending between the second tensioning roller and the second roller;

a second motor driving the second roller; and

a controller, the controller detecting a tension T 1 in the first span with the first tensioning roller, the controller detecting a tension T 2 in the second span with the second tensioning roller, the controller calculating an untensioned product length as a function of T 1 , T 2 , drive setpoints for the first and second motors, a web thickness of the web (h), and a reference repeat length (CO REF ).

16. The system of claim 15 , wherein the drive setpoints include a drive setpoint ∝ 1 of the first motor for transport gains for tension (T 1 ), a drive setpoint (β 1 ) of the first motor for transport gains for repeat length of the first span, a drive setpoint (∝ 2 ) of the second motor for transport gains for tension (T 2 ), a drive setpoint (β 2 ) of the second motor for transport gains for repeat length of the second span.

17. The system of claim 16 , wherein the controller calculates the untensioned product length (L 0 ), according to the formula:

L

0

=

(

CO

REF

⁡

(

1

+

⁢

∝

1

)

⁢

(

1

+

β

1

)

⁢

(

1

+

(

h

/

2

)

R

1

)

)

/

(

1

+

T

1

/

E

)

,

⁢

where

E

=

T

2

-

T

1

(

1

+

⁢

∝

2

)

⁢

(

1

+

β

2

)

⁢

(

1

+

(

h

/

2

)

R

2

)

-

(

1

+

⁢

∝

1

)

⁢

(

1

+

β

1

)

⁢

(

1

+

(

h

/

2

)

R

1

)

and R 1 is a radius of the first roller and R 2 is a radius of the second roller.

18. The system of claim 15 , further comprising a first idler roller forming a first non-slip nip with the first roller.

19. The system of claim 18 , further comprising a second idler roller forming a second non-slip nip with the second roller.

20. The system of claim 15 , wherein the web is arranged in a capstan wrap around at least one of the first roller and the second roller.