## Web Lines: Web Length per Roller Revolution=?

When a roller rotates, how much web does it feed forward per revolution? At first, the answer seems obvious: It feeds forward a length of web equal to the circumference of the roller or Pi (3.14) times the roller diameter. However, this answer is correct only to 99%.

If you want to accurately estimate the feed rate, you need to consider other factors, including the effects of web thickness, web tension, nipping compression, and rubber covering elongations.

Answering this question depends on how sensitive you or your customers (and their lawyers) are to small errors in actual length and how it will be measured. Are you going to measure the web while it is still under tension? Or do you need to consider the length of the web under no tension, such as total length of cut sheets?

Product thickness effects will make you underestimate the web feed per revolution. A web bending around a roller will have different lengths depending on whether you measure the side of the web away from or in contact with the roller.

The effective feeding diameter of a web on a roller is the roller diameter plus the web thickness. For thin webs, this is a small error, but for thicker webs on small rollers, this can become a +0.1-0.3% error.

Web tension will make you overestimate/underestimate the web feed per revolution. If you feed 1,000 in. of web stretched by tension 0.5%, you will have pushed only 995 in. of untensioned web. You are better off sending an overage proportional to the strain of web tension.

When solid nipped rollers rotate, how much web do they feed forward per revolution? This question opens up one of the biggest cans of worms in web handling. Read on if you dare.

If you set the solid nipping rollers of a home pastamaker to a gap less than the dough thickness, the dough will compress as it passes between the nips. If the dough is incompressible, the volume must be constant, and any loss of thickness must be offset by an increase in width or length.

Except for small edge effects, there is no place for dough to move laterally, so the thickness change in a nipped system will mostly become a length change, forcing the web to double its length for a halving of its thickness.

Will the nipped rollers push more or less web per revolution than a wrapped roller? It depends on whether the web recovers from the nipping action. If you are feeding a highly elastic web, like rubber, the web will immediately contract back to its original length once it leaves the nip point. Therefore, your feed length will be less than the roller.

If you are feeding a viscous or deformable web, like soft cookie dough, you will see little or no snap back after leaving the nip point, and web length will be close to the roller circumference.

When a rubber nip system rotates, how much web does it feed forward? This is the real can of worms. The rubber will react like an elastic web pinched between two solid rollers, stretching in the nip zone and snapping back in the unnipped condition.

For the web pinched between the stretching rubber and the rigid metal surface, which will control the web elongation? Since most webs will have a higher coefficient of friction to rubber than hard metals, it is likely the rubber roller will determine how much web is fed forward.

The first estimate of the speed difference between a steel and rubber-covered roller is proportional to the covering indentation divided by four times the covering thickness. For a 20-mil indentation of a 0.5-in. covering, the rubber roller will turn 1% slower than the rigid roller of equal diameter.

Of course there are more worms in our can. Special rubber rollers made of hard skin on a compressible interior may have no or opposite speed differential. If the web slips against any roller, all bets are off on how much web is fed forward per revolution.

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.