Extensive study of stresses induced during and after winding of coils has led to significant improvements to the processing of web-like materials for the packaging industries and consumer goods. The current paper presents an inverse solution for the prediction of the winding tension profile required to satisfy a specified residual stress distribution in the coil, for non-linear material properties (in the radial direction), with allowance for large strain and large deformation in the coil. The inverse solution approach has advantage over the forward solution approach by directly determining the winding tension profile, which can be readily controlled in a processing line, once the desired residual stresses in the coil are known. The current paper, together with several recently published ones, completes the study of stresses in the winding of coils using the inverse solution approach.
YuenW. Y. D.CozijnsenM.Optimum tension profiles to prevent coil collapses. SEAISI Q., 2000, 29(3), 50–59.
2.
AltmannH. C.Formulas for computing the stresses in center-wound rolls. Tappi, 1968, 4, 176–179.
3.
YagodaH. P.Centrifugally induced stresses within centre-wound rolls - part I. Mech. Res. Commun., 1980, 7, 181–193.
4.
YagodaH. P.Centrifugally induced stresses within centre-wound rolls - part II. Mech. Res. Commun., 1980, 7, 233–240.
5.
OlsenJ. E.On the effect of centrifugal force on winding. Tappi, 1995, 78(7), 191–195.
6.
BouquerelF.BourginP.Irreversible reduction of tension due to aerodynamical effects. In Proceedings of the 2nd International Conference on Web Handling, StillWater, Oklahoma, June 1993, pp. 265–285.
7.
JonesD. P.Air entrainment as a mechanism for low traction on rollers and poor stacking of polyester film reels, and its reduction. In Proceedings of Web Handling of the ASME Winter Annual Meeting, Anaheim, CA, USA, 8–13 November 1992, pp. 123–131.
8.
KeshavanM. B.WickertJ. A.Air entrainment during steady-state web winding. ASME, J. Appl. Mech., 1997, 64, 916–922.
9.
BensonR. C.A nonlinear wound roll model allowing for large deformation. Trans. ASME E. J. Appl. Mech., 1995, 62, 853–859.
10.
ZabarasN. A.Theory for small deformation analysis of growing bodies with an application to the winding of magnetic tape. Acta Mech., 1995, 111, 95–110.
11.
QuallsW. R.GoodJ. K.Orthotropic viscoelastic winding model including a nonlinear radial stiffness. ASME J. Appl. Mech., 1997, 64, 201–208.
12.
TramposchH.Relaxation of internal forces in a wound reel of magnetic tape. ASME J. Appl. Mech., 1965, 32, 865–873.
13.
TramposchH.Anisotropic relaxation of internal forces in a wound reel of magnetic tape. ASME, J. Appl. Mech., 1967, 34, 888–894.
HakielZ.Non linear model for wound roll stresses. Tappi, 1987, 70(5), 113–117.
16.
WillettM. S.PoeschW. L.Determining the stress distributions in wound reels of magnetic tape using a nonlinear finite difference approach. Trans. ASME E. J. Appl. Mech., 1988, 55, 365–371.
17.
ZabarasN.LiuS.KoppuzhaJ.DonaldsonE.A hypoelastic model for computing the stresses in center-wound rolls of magnetic tape. Trans. ASME E. J. Appl. Mech., 1994, 61, 290–295.
18.
ColeK. A.HakielZ.A nonlinear wound roll stress model accounting for widthwise web thickness nonuniformities. In Proceedings of Web Handling Symposium, ASME Applied Mech. Div., AMD-Vol 149, 1992, pp. 13–24.
19.
HakielZ.On the effect of width direction thickness variations in wound rolls. In Proceedings of 2nd International Conference on Web Handling, Oklahoma State University, May, 1992, pp. 79–98.
20.
LeeY. M.WickertJ. A.Stress field in finite width axisymmetric wound rolls. ASME J. Appl. Mech., 2002, 69(2), 130–138.
21.
GoodJ. K.The abilities and inabilities of wound roll models to predict winding defects. In Proceedings of 8th International Conference on Web Handling, (Oklahoma State University), 5–8 June 2005, pp. 1–71.
22.
de HoogF. R.CozijnsenM.YuenW. Y. D.HuynhH.-N.Predicting winding stresses for wound coils of linear orthotropic material. Proc. Instn Mech. Engrs Part C: J. Mechanical Engineering Science, 2004, 218(C1), 13–25.
23.
de HoogF. R.CozijnsenM.YuenW. Y. D.HuynhH.-N.Predicting winding stresses for wound coils of non-linear orthotropic material. Proc. Instn. Mech. Engrs Part C: J. Mechanical Engineering Science, 2004, 218(C1), 27–38.
24.
de HoogF. R.YuenW. Y. D.CozijnsenM.An inverse solution for winding stresses for wound coils of linear orthotropic material with large deformations. Proc. IMechE Part C: J. Mechanical Engineering Science, 2007, 221(C6), 639–652.
25.
CozijnsenM.YuenW. Y. D.Stress distributions in wound coils. In Proceedings of 2nd Biennial Australian Engineering Mathematics Conference, Sydney, 15–17 July 1996, pp. 117–124.
26.
ChenK.WangZ.Investigation of buckling of coiled strip under high winding tension (in Chinese). Iron Steel (China), 1989, 24(11), 34–38.
27.
AuzingerW.KochO.WeinmüllerE. B.Theory and solution techniques for singular boundary value problems. In Ordinary differential equations, parallel processing and applied mathematics, vol. 2328 of Springer Lecture Notes in Computer Science, 2002, pp. 851–861.
28.
AscherU.MattheijR. M. M.RussellR. D.Numerical solution of boundary value problems for ordinary differential equations, 1988 (Prentice-Hall, Englewood Cliffs, New Jersey).
29.
OliveG. A.A study of wound rolls during winding and unwinding. MS Thesis, Department of Mechanical Engineering, University of Rochester, Rochester, NY, 1994.
30.
LinP. N.WickertJ. A.Corrugation and buckling defects in wound rolls. Trans. ASME E. J. Appl. Mech., 2006, 128, 56–64.
