- May 09, 2013, Timothy J. Walker
In Part 3 of this four-part series, web handling expert Tim Walker discusses internal stresses and strain.
Most wound rolls are held together with the friction. The tensioned (elongated) layers create pressure pushing toward the core, much like the stretched rubber of an inflated balloon pushes against the balloon’s internal air pressure. Tension is proportional to the web strain (defined as the percent change in length from the web’s untensioned length). The pressure of one layer equals web tension divided by roll radius (P=T/R, with tension in units of force per width).
As a roll builds, each layer can add to the tightness of the roll. One layer wound on a core may create a low pressure (less than 1 psi or 7 kPa), but a wound roll may have thousands of layers and potential interlayer pressure greater than 1,000 times the pressure from one layer. Where 1 psi (7kPa) may not be enough pressure to hold a roll together against forces of winding, handling, and unwinding, 1,000 psi (7 MPa) is certainly excessive and can cause unneeded defects, such as impressions, core crushing, or blocking of layers within the roll.
In most winding, the adding of 1,000 layers does not increase the roll tightness by 1,000 times. In winding a soft film, like polyethylene, you might get close. In winding papers, you won’t come close. The difference in winding these two materials is due to strain and strain losses (Remember ‘strain is the secret to web handling?’).
Low modulus films will have more strain for a given tension and require more compression or radial shifting to lose their in-roll tension. Since the stack of polyethylene is relative stiff compared to the machine direction modulus, it won’t compress enough to have big strain losses. This combination makes polyethylene very easy to wind too tight.
Papers are stiff and will have low strains for a given tension. Papers also will be relatively soft in the stack direction and can have large strain losses from compression. This combination makes it difficult to wind an extremely tight roll of paper.
The winding torque and nip load determine the initial tension for a layer as it enters the winding roll, but the stress and strain within the roll of any given layer may be much lower than its initial wound-on tension, often approaching zero tension (circumferential stress in the roll) or even going below zero into circumferential compression).
The loss of circumferential tension is due to radial shifting or compression within the winding roll. Layers typically shift to a lower radial position due to core compression; compression of inner roll layers from the added pressure of outer roll layers; compression of surface roughness features of the product; density increases in the product; air escaping the roll; and lateral flow of any layers (such as adhesive layers in sticky tape products). The compressibility of the winding roll is characterized in stack compression testing and is a critical product mechanic property required for advanced understanding of winding any product.
The stack modulus (considered the radial modulus of a winding roll) is different from tensile or Young’s modulus of elasticity (which is the circumferential modulus in the winding roll) in two ways. First, stack modulus is not a constant, increasing under higher pressures. Second, stack modulus is often much lower than tensile modulus (except in highly compressible soft film stacks).
Wound-on tension, roll geometry, and stack modulus are all needed to model internal roll stresses and strains as a function of radial position. In most cases, interlayer pressure will be highest at or near the core and decreasing to zero at the outside of the roll. Internal roll tensions will vary greatly by product and winding condition, but will be low through most of the roll with the greatest variations at or near the core, depending on the magnitude of compression vs. the initial strain of wound-on tension.
One of my constant problem-solving tips of web handling and winding is that "secret to web handling is strain." The loss of in-roll tension and pressure from compression occurs with what seem like minor radial changes. However, a 0.2% strain is the same magnitude as a 7 mils (0.1 mm) shift in a layer at a radius of 4 in. (200 mm). For materials that are stiff in the machine direction, but relatively soft in the thickness direction, radial compression of web, surface roughness, and entrained air will greatly reduce the tensions and pressures within a wound roll. Many layers of a wound roll have lost more than 90% of their wound-on tension, with near core layers commonly with zero tension or even pushed in to circumferential compression.
Even when winding is finished, the roll likely will continue to have changes in internal roll stresses and strains. If rolls were purely elastic, they would remain in the same stress and strain condition until unwinding; however, several factors can make a wound roll structure change over time.
Entrained air and its escape is one of the most common causes for roll structure changes over time. Excess air wound into a roll will slowly escape over times of hours, days, or weeks. As the air escapes, layers will fall toward the core and lose their machine direction tension. As the web loses MD tension, it will attempt to regain Poisson’s effect width losses. In some materials, this width recovery will appear as MD buckles in the wound roll (a.k.a. tin-canning defects).
Other potential dynamic effects on winding include: visco-elastic recovery of pre-winding tension; creep of visco-elastic materials (especially adhesive coated products); and any change than will change the length, thickness, or width of layers within the roll, including hygro and thermal expansion.
Click here to read Part 1 of this series.
Click here to read Part 2 of this series.
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; email@example.com; www.webhandling.com.