Anisotropic Relaxation of Internal Forces in a Wound Reel of Magnetic Tape

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Abstract
Equations were developed to describe the relaxation of the internal stresses of a wound reel of magnetic tape, with allowances for the effects of surface roughness between tape layers and unequal thermal expansion of hub and tape-layer body. Numerical examples obtained with the aid of a high-speed digital computer indicated that the surface roughness as well as the unequal thermal expansion of hub and tape-layer body greatly affect the internal stress distribution. Essentially independent of the surface roughness, a typical reel, when stored at 120 F after being wound at 70 F and when the coefficient of thermal expansion of the hub is three times the value of the tape material, will approach stress-free conditions about 80 percent earlier than when it is stored at the winding temperature.

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