A Mathematical Model of a Magnetic Tape and Reel Interaction
Monica Lluis Arroyo
Master of Science, May 1996
ABSTRACT
In this thesis we formulate a mathematical model for calculating pressure
fields, deflections, and descending velocities for a magnetic tape. Understanding
these quantities is essential for solving the problem of tangling of a tape
when it runs at a high speed.
The coupled system of equations consists of two well known equations. For
calculating the pressure field, the Reynolds equation from Lubrication
Theory was used. For the deflection of the tape in the transverse direction,
the beam equation from Elasticity Theory was needed.
This is a generalization of the problem of fluid between two rigid surfaces
moving at a know speed and approaching each other by the action of a load on
the upper surface. In our case the surfaces are flexible.
A computer program was developed in order to understand and solve this problem.
Our analysis could be used to find a better design for a data cartridge.
Research supported by the Minnesota Center for Industrial
Mathematics (MCIM)
