In our previous interview, the web expansion amount was expressed by the basic theoretical formula in it's simplest form of

Now, please first explain each of the individual elements in the formula. I know that each element relates to the other elements, and therefore the independent explanation of each element is likely to cause misunderstanding. However, if you start, from the beginning, collectively explaining this formula, this would rather put me to great embarrassment. So, an explanation of small pieces one by one would help everyone's understanding.
Tsuchida: All right. First, the elements in the parentheses of this formula are shown in the form of multiplication. However, the web's slippage or flexibility cannot be expressed with a numerical value. So, it would be better to interpret it by saying "the web expansion amount is inseparably connected to its slippage and flexibility". So, let's start this explanation with the web's slip coefficient Ks. Every web more or less slips on the rubber surfaces of an FE roll. The greater the web's slippage, the smaller the web's expansion. Examples of webs that have the most difficulty slipping include a raw nonwoven fabric before thermosetting, while examples of the slipperiest webs include aluminum or copper foils.
Does this mean that when all other conditions are the same, a nonwoven has a greater expansion amount than an aluminum foil with the same FE roll?
Tsuchida: Such tendencies are seen. Furthermore, there is even a difference in expansion amount between two different films. For example, a coating-processed film is more slippery than a raw film, and a thicker film is more slippery than a thinner film. It can therefore be said that when all other conditions are the same, a thinner raw film has a considerably greater expansion amount than a thicker coating-processed film.
So, the issue of web slippage is related not only to web material, but also to its thickness, surface condition, processing or treatment, and the like, right?. On the other hand, is the web's slippage a phenomenon solely resulting from the web itself?
Tsuchida: No. A web may also slip due to external factors. More specifically, not only temperature and humidity, but also line tension and the like have a great influence on web slippage. For example, if the line tension is quite small, the web shows a tendency to slip. Further, there are cases where an FE roll is used as forcibly driven. In such a case, if the driving speed and the line speed are not in synchronism with each other, the web tends to slip easily. Furthermore, the rubber cords on an FE roll, which are articles of consumption, should be regularly replaced every 1 to 2 years. However, if these rubber cords are not replaced and used for a long period of time, the rubber surfaces become worn out. This causes the web to be readily slippery. In short, I would like you to keep it in mind that the web does slip more or less on an FE roll due to a variety of factors including the physical properties inherent in the web and various external conditions, and that the greater the web slippage, the smaller the expansion amount.
That's a little bit surprising. Generally, we are apt to think that the same FE roll gives the same expansion amount for each web, whatever it is. We don't especially care about web slippage on an FE roll surface, much less its influence on the expansion amount.
Tsuchida: It is quite usual with the user, but the issue of web expansion as it is generally understood - "An inclination angle is given to an FE roll. That's all." - is not so simple. As to the web slippage, it's recommended to make provisions to maximize the avoidance of slippage due to external factors such as too small tension, asynchronous drive, the wear and tear of the rubber cords and the like, since the physical properties inherent in the web cannot be changed.
Next, what about the flexibility coefficient Km? In the second part of this interview, about the problems caused by a bow roll, you said that dependent on the flexibility of the web material, there are cases where the structural problems of a bow roll may seriously affect the web, or conversely, affect it very little, and that different problems occur dependent on the varied flexibility of web materials. Web flexibility seems to be an important keyword when discussing expansion by an expander roll. What kind of action does the web flexibility bring to a linear, no-bow FE roll?
Tsuchida: Certainly, the web flexibility is an important factor to be considered in an FE roll, too. The web slippage mentioned earlier has to do with web flexibility. That is, the greater the flexibility, the smaller the slippage and the resulting expansion therefore tends to be greater. When considering flexibility alone, the expansion is generally greater as the flexibility is greater. That is, when you say that a web is flexible, it means the web itself has an allowance to be stretched. Conversely, when a web is less flexible, it has less allowance to be stretched.
Does this mean that the expansion amount is greater for flexible fabrics, films and the like, while the expansion amount is smaller for less flexible glass fibers, metallic foils and the like?
Tsuchida: That's true to a point. However, when discussing flexibility, the incident angle of a web upon an FE roll should also be considered. Now, I'd like to explain the incident angle in reference to the following illustration. When a web fed from the web source is wound and travels over an FE roll, it is gradually transversely spread toward the roll ends because of the presence of an inclination angle given to the FE roll by its adjusting bolts. Accordingly, the web is incident upon the FE roll as it is transversely spread in the vicinity of the FE inlet portion with its width wider than the web width at the web source. That is, the web is wound on the FE roll at a certain angle with respect to a direction at right angles to the longitudinal axis of the FE roll. This angle is called an incident angle.

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The incident angle is greater the more the web is flexible, while the incident angle becomes closer to zero as the flexibility is smaller. For example, a flexible web such as a knitted, woven or nonwoven fabric, is considerably spread in the vicinity of its inlet when wound on an FE roll. This causes its incident angle to be increased. On the other hand, the incident angle becomes smaller with a less flexible web such as paper, glassfiber, aluminum foil or the like.
What relation does this incident angle have with the web expansion?
Tsuchida: This incident angle has a meaning with respect to the roll inclination angle formed by the adjusting bolts of the FE roll. That is, when the incident angle is equal to zero, the web shows a tendency to be spread by an amount corresponding to the roll inclination angle . When the incident angle is equal to the roll inclination angle , the web does not spread further. When the incident angle is smaller than the roll inclination angle , the web tends to be spread by an amount corresponding to ( - ).
So, the greater the web flexibility, the greater the incident angle . When the incident angle is greater, the expansion amount is accordingly reduced. Does this means that a more flexible web is reduced in expansion amount by a greater amount corresponding to its greater incident angle ?
tsuchida: Yes. A more flexible web is expanded more by an FE roll. On the other hand, such a web tends to be greater in incident angle upon the FE roll. This means that the expansion caused by the FE roll is reduced by an amount corresponding to the incident angle . Conversely, a less flexible web such as an aluminum foil is smaller in incident angle upon the FE roll. This means that the amount to be reduced from the expansion caused by the roll inclination angle , is smaller.
I see. This means the difference between the inclination angle of a FE roll itself and the incident angle of a web upon the FE roll, is an expansion angle which actually acts on the web, right? This does not necessarily mean that the greater the flexibility, the greater the expansion, does it?
Tsuchida: Right. I would like you to bear in mind that when considering flexibility and expansion, there is an issue of incident angle . Please also note that, in addition to web flexibility, line tension as an external factor is related to the incident angle . That is, when the line tension is smaller, the incident angle has a tendency to be greater. You should remember this point when setting the line tension value on your production line.
Generally, we are liable to think that the web is expanded solely by the roll inclination angle of the FE roll itself. But, I am now beginning to understand what you say: web expansion is not so simple, but a variety of factors such as the web's slippage, flexibility and its relevant incident angle and the like have to be also taken into consideration. In the next interview, please explain the element Lsin in the theoretical formula of