A simple tape wrap around a guide: Some complexities

Magnetic tape, pulled around a cylinder, will exert pressure against the cylindrical surface, and will experience flexural stresses due to its curvature. The nature of these effects may be important where concern exists regarding the life or performance of the tape. The magnitude of these pressures and tensions are usually calculated by simple equations, based on the assumption that the tape follows a path which is concentric with the cylindrical surface. These simple calculations are usually acceptable, but, for certain more demanding applications, a more rigorous analysis should be employed. There are also two ambiguities associated with the simple theory. A more realistic mathematical model is used here which recognizes a compressibility of the tape surface. The consequent analysis eliminates the two ambiguities. Some simple tests were conducted to measure the compressibility of two tape surfaces, yielding useful numerical values. A formal mathematical analysis, leading to flexure stresses and pressure was made. Numerical values for sample configurations are presented. These show the peak tape contact pressure to be significantly higher than that predicted by simple theory. They also confirm the "anomaly" of flexure stresses decreasing with small wrap angles.