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TECHNICAL PAPERS

Modeling Air Entrainment and Temperature Effects in Winding

[+] Author and Article Information
H. Lei, K. A. Cole, S. J. Weinstein

Eastman Kodak Company, Rochester, NY 14652

J. Appl. Mech 70(6), 902-914 (Jan 05, 2004) (13 pages) doi:10.1115/1.1629758 History: Received October 15, 2002; Revised June 04, 2003; Online January 05, 2004
Copyright © 2003 by ASME
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References

Altmann,  H. C., 1968, “Formulas for Computing the Stresses in Center Wound Rolls,” Tappi J., 51, pp. 176–179.
Connolly, D., and Winarski, D. J., 1984, “Stress Analysis of Wound Magnetic Tape,” ASLE Special Publication SP-16, pp. 148–157.
Hakiel,  Z., 1987, “Nonlinear Model for Wound Roll Stresses,” Tappi J., 70, pp. 113–117.
Qualls, W. R., 1995, “Hygrothermomechanical Characterization of Viscoelastic Centerwound Rolls,” Ph.D. thesis, Oklahoma State University.
Good,  J. K., Wu,  Z., and Fikes,  M. W. R., 1994, “The Internal Stresses in Wound Rolls With the Presence of a Nip Roller,” ASME J. Appl. Mech., 61, pp. 182–185.
Good, J. K., and Holmberg, M. W., 1993, “The Effect of Air Entrainment in Centerwound Rolls,” Proceedings of the Second International Conference on Web Handling, James K. Good, ed., Web Handling Research Center, Oklahoma State University, Stillwater, OK.
Good, J. K., and Covell, S. M., 1995, “Air Entrapment and Residual Stresses in Rolls Wound With a Rider Roll,” Proceedings of the Third International Conference on Web Handling, James K. Good, ed., Web Handling Research Center, Oklahoma State University, Stillwater, OK.
Chang,  Y. B., Chambers,  F. W., and Shelton,  J. J., 1996, “Elastohydrodynamic Lubrication of Air-Lubricated Rollers,” ASME J. Tribol., 118, pp. 623–628.
Taylor, R. M., and Good, J. K., 1997, “Entrained Air Films in Center Wound Rolls—With and Without the Nip,” Proceedings of the Fourth International Conference on Web Handling, James K. Good, ed., Web Handling Research Center, Oklahoma State University, Stillwater, OK.
Forrest, A. W., 1995, “Air Entrainment During Film Winding With Layon Rolls,” Proceedings of the Third International Conference on Web Handling, James K. Good, ed., Web Handling Research Center, Oklahoma State University, Stillwater, OK.
Forrest, A. W., 1995, “Wound Roll Stress Analysis Including Air Entrainment and the Formation of Roll Defects,” Proceedings of the Third International Conference on Web Handling, James K. Good, ed., Web Handling Research Center, Oklahoma State University, Stillwater, OK.
Bouquerel, F., and Bourgin, P., 1993, “Irreversible Reduction of Foil Tension Due to Aerodynamical Effects,” Proceedings of the Second International Conference on Web Handling, James K. Good, ed., Web Handling Research Center, Oklahoma State University, Stillwater, OK.
Bourgin, P., 1997, “Air Entrainment in Web Handling: To be Avoided or Mastered?” Proceedings of the Fourth International Conference on Web Handling, James K. Good, ed., Web Handling Research Center, Oklahoma State University, James K. Good, ed., Web Handling Research Center, Oklahoma State University, Stillwater, OK.
Forrest, A. W., 1999, “Optimization of Equipment and Process Conditions for Film Winding,” Proceedings of the Fifth International Conference on Web Handling, James K. Good, ed., Web Handling Research Center, Oklahoma State University, Stillwater, OK.
Pfeiffer,  J. D., 1981, “Measurement of K2 Factor for Paper,” Tappi J., 64, pp. 105–106.
Pfeiffer, J. D., 1999, “Compressive Modulus Measurement Techniques,” Proceedings of the Fifth International Conference on Web Handling, James K. Good, ed., Web Handling Research Center, Oklahoma State University, Stillwater, OK.
Forrest, A. W., 1993, “A Mathematical and Experimental Investigation of the Stack Compression of Films,” Proceedings of the Second International Conference on Web Handling, James K. Good, ed., Web Handling Research Center, Oklahoma State University, Stillwater, OK.
Rice, B. S., Cole, K. A., and Müftü, S., 1999, “An Experimental and Theoretical Study of Web Traction Over a Nonvented Roller,” Proceedings of the Fifth International Conference on Web Handling, James K. Good, ed., Web Handling Research Center, Oklahoma State University, Stillwater, OK.
Timoshenko, S., 1970, Theory of Elasticity, McGraw-Hill, New York, p. 418.

Figures

Grahic Jump Location
Center winding with an idling pressure roll. Center of the winding roll is driven by a motor.
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Continuum differential force element in the wound roll
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In-roll pressure stresses right after winding from both air entrainment model and nonair entrainment model. The gage pressure is the air pressure above the ambient pressure.
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In-roll tension stresses right after winding from both air entrainment model and nonair entrainment model
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Contact clearances under the pressure roller, under the outer lap away from the nip, and after winding
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The effect of roll radial CTE on total interlayer pressure right after winding at 70°F and after heated to 100°F. Results are from the air entrainment model. The radial CTE of the roll is indicated in the figure. Other CTEs are αθ=10−5/°F and αc=10−4/°F.
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The effect of roll radial CTE on contact pressure right after winding at 70°F and after heated to 100°F. Results are from the air entrainment model. The radial CTE of the roll is indicated in the figure. Other CTEs are αθ=10−5/°F and αc=10−4/°F.
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The effect of roll radial CTE on interlayer pressure right after winding at 70°F and after heated to 100°F. Results are from the nonair entrainment model. The radial CTE of the roll is indicated in the figure. Other CTEs are αθ=10−5/°F and αc=10−4/°F.
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The effect of roll core CTE on total interlayer pressure right after winding at 70°F and after heated to 100°F. Results are from the air entrainment model. The core CTE of the roll is indicated in the figure. Other CTEs are αr=10−4/°F and αθ=10−5/°F.
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The effect of roll core CTE on contact pressure right after winding at 70°F and after heated to 100°F. Results are from the air entrainment model. The core CTE of the roll is indicated in the figure. Other CTEs are αr=10−4/°F and αθ=10−5/°F.
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The effect of roll core CTE on interlayer pressure right after winding at 70°F and after heated to 100°F. Results are from the nonair entrainment model. The core CTE of the roll is indicated in the figure. Other CTEs are αr=10−4/°F and αθ=10−5/°F.
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Total mass of air lost from the first lap of a roll after winding 3089 laps at 2.54 m/s (500 ft/min), expressed as a percentage of the original mass in the lap. The half-width of the roller in centimeters, L, is indicated on the figure. Data are presented here for a core having outer diameter of 0.127 m (5 inches), and for a web thickness of 224 μm.
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Total mass of air lost from the first lap of a roll after winding 3089 laps at 7.62 m/s (1500 ft/min), expressed as a percentage of the original mass in the lap. The half-width of the roller in centimeters, L, is indicated on the figure. Data are presented here for a core having outer diameter of 0.127 m (5 inches), and for a web thickness of 224 μm.
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Geometry for lubrication analysis of squeezing flow
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Calculated absolute air pressures under the first lap (circles) from full winding model. These air pressures are used to model the air loss under the first lap.

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