Width-Wise Variation of Magnetic Tape Pack Stresses

Abstract

A model is developed for predicting the stress and displacement fields within a magnetic tape pack, where those quantities are allowed to vary in both the pack’s radial and transverse (cross-tape) directions. As has been the case in previous analyses based upon one-dimensional wound roll models, the present approach accounts for the anisotropic and nonlinear constitutive properties of the layered tape, and the incremental manner in which the pack is wound. Further, such widthwise variation effects as differential hub compliance and nonuniform winding tension, which can be significant in data cartridge design, are also treated in the model. The pack is analyzed through a two-dimensional axisymmetric finite element model that couples individual representations of the hub/flange and layered tape substructures. The bulk radial elastic modulus of the tape, which depends on the in-pack radial stress, is measured for a variety of media samples, and a reduced-order model is developed to capture the nonlinear modulus-stress correlation. The stiffness matrix of the hub/flange at its interface with the media provides a mixed boundary condition to the tape substructure. In this manner, design-specific hubs can be readily analyzed, and criteria for their optimization explored. Simulations of several cartridge designs are presented, and the roles of hub compliance and wound-in tension gradient in setting the pack’s stress field and cross-tape width change are discussed.