Lateral dynamics of an axially translating medium: A theoretical and experimental study on the effects of guiding components

By 2020, the average of data stored for each person will reach 5,200 GB. This will put increased demands on cost and reliability of data storage. Compared to its competitors, tape storage technology is more energy efficient and operates at lower cost, with longer media life, hence improved reliability. Nevertheless, there are market and technology pressures to improve all aspects of tape recording. One of the key factors that influence tape storage density is the drive's ability to follow written data tracks. Lateral tape motion (LTM) which can be described as a deviation of the tape from its prescribed, linear path could cause the read/write heads to lose track of the data and lead to lower reliability. LTM is caused by periodic and non-periodic effects. All of the guiding elements, including rollers, stationary guides, read/write head assemblies, and packing reels present rich sources of dynamic effects due to friction, sliding contacts, impulses, and damping effects due to air bearing/entrainment.;The research presented in this thesis is motived by the need to understand the causes of LTM, in order to help increase the volumetric storage density of magnetic tape storage systems. To this end tape is modeled as tensioned, axially moving beam with viscoelasticity. Two major studies were undertaken to investigate the effects of imperfections in roller geometry, and dynamic friction between the tape and a grooved roller. In addition, the effects of periodic impulses, such as those that could develop due to flange contacts, on tape dynamics were investigated. A new model for the coupling between lateral and longitudinal tape vibrations was also presented.;Accuracy of Numerical Solution: All of the models presented in this work were solved numerically, by using the finite element method in spatial and the Newmark's method in temporal dimension. A comprehensive study of the convergence characteristics of the numerical methods was carried out. The numerical and analytical dispersion relations (DR) were compared, in order to measure the accuracy of the fully discretized direct solution method. The waveguide-finite element (WFE) method was used to find the DR for the finite element solution. Good agreement was found between the numerical and analytical solution. Effects of using finite difference discretization in space were also investigated. For the system under study, it was found that high frequency behavior can be simulated with high accuracy by using the finite element discretization, at a relatively modest computational cost.;Eigenvalue Analysis: In this work we also introduce a way to carryout eigenvalue analysis of gyroscopic systems by using the finite element discretization. It was shown that the results match the classical work. This method was used to find the natural frequencies of the system with internal damping.;Roller Mechanics: A mechanics based model to describe the lateral positioning of a tape over a tilted roller is introduced. It is shown that this condition requires the slope of the neutral axis of the tape and the slope of the centerline of the tilted roller to be the same over the wrapped segment. An experimental setup was used to verify the model. The effects of the roller tilt angle, tape wrap angle, and the lengths of the free-tape spans upstream and downstream of the tilted roller on the steady state lateral tape position were investigated experimentally and by simulations. The experiments show that the circumferential position of the wrap on the upstream side of a tilted roller has the strongest effect on pushing the tape in the lateral direction. The total wrap angle around the roller has a smaller effect. It was also shown that the tape segments upstream and downstream of the tilted roller interact, and the combined effect results in a different overall lateral tape response in steady state.;Lateral Friction over Rollers: Effects of friction forces on the lateral dynamics of a magnetic recording tape, wrapped around a grooved roller were investigated experimentally and theoretically. It was shown that including the effects of 'stick-slip' and velocity dependence of the friction force render the tape's equation of motion non-linear. In the experiments, tape was wrapped around a grooved roller in a customized tape path, and tensioned. The tape running speed along the axial direction was set to zero, thus only the lateral friction effects were studied. The grooved roller was attached to an actuator, which moved across the tape. The test was performed in slow and fast actuation modes. Slow mode was used to identify the static, or breakaway friction coefficient. In the fast mode, the roller was actuated and a periodic stick and slip phenomenon was observed. The stick-to-slip and slip-to-stick transitions occurred when the tape vibration speed matched the roller actuation speed. The breakaway forces in the slow and fast actuation modes were similar one another. Both experiments and theory show that upon slip, tape vibrates primarily at its natural frequency, and vibrations are attenuated relatively fast due to frictional and internal damping. This work showed that by making a single experimental measurement of friction for a given roller design and tape type, our model can be used to predict the behavior over a wide range of wrap angles and tape tensions.;Flange Impacts: In this work the tape response due to flange hits was investigated by a mathematical model of the tape path. It was shown that flange hits can cause a wide-band frequency response in the tape, and the tape can have a very non-periodic motion. While the head induces vibration during servo tracking, most of the non-rotating guides reduce LTM due to frictional damping. Friction in the system helps reduce some of the complexity of the response.;Coupling between In Plane and Lateral Vibrations: The coupling between lateral and longitudinal deflection component that is due to non-linear longitudinal strain is considered. The equations of motion of the longitudinal and lateral tape motion were derived from first principles. The entire tape path is modeled directly, where the interaction of the tape with the recording head and the guides are represented as concentrated forces, and moments. It was shown that the tension impulse can cause a high frequency high amplitude wave in the longitudinal direction, and also excites lateral motion. The effect of the longitudinal wave can potentially cause local stretching of the bits. The amplitude of the longitudinal and lateral deflections due to tension impulse varies linearly with the impulse strength. It was also shown that the tension fluctuation, which primarily affects the longitudinal tape deflection, can excite resonances in the lateral tape motion. Tape velocity and tension have relatively small effects on the resonant frequencies in the range considered, but deflection amplitudes increase with increasing values of applied tension and transport velocity as expected. The position of the frictional guides was found to have a significant effect on the damping and natural frequencies.