Analysis of Self-Excited Longitudinal Vibration of a Moving Tape

Abstract

Abstract Longitudinal vibration of a moving magnetic tape can be excited by frictional contact with a recording head, or with a guide that defines the path of the tape. The friction force depends on the velocity, relative to a stationary observer, of the tape element that is instantaneously located at the point of contact. The response of a moving tape under such nonlinear dissipation is determined using new methods for the vibration analysis of axially-moving materials. In a particular transport speed range, longitudinal motion of the tape is self-excited through negative (unstable) damping for small amplitude vibration and positive (stable) damping for large amplitudes. Independent of the initial conditions, almost all solutions are attracted to a stable limit cycle, the amplitude of which is sensitive to the transport speed and to the axial location of contact. Parameter combinations that reduce, or eliminate altogether, the self-excited motion are identified. Some of the conclusions differ from those of previous analyses that neglect the effects of convection on the tape’s velocity and acceleration.