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Research Papers

Lateral Vibration and Read/Write Head Servo Dynamics in Magnetic Tape Transport

[+] Author and Article Information
M. R. Brake1

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213mrbrake@sandia.gov

J. A. Wickert2

Department of Mechanical Engineering, Iowa State University, Ames, IA 50011wickert@iastate.edu

1

Present address: Sandia National Laboratories.

2

Corresponding author.

J. Dyn. Sys., Meas., Control 132(1), 011012 (Dec 22, 2009) (11 pages) doi:10.1115/1.4000665 History: Received March 02, 2007; Revised November 11, 2009; Published December 22, 2009; Online December 22, 2009

Magnetic tape is a flexible mechanical structure having dimensions that are orders of magnitude different in its thickness, width, and length directions. In order to position the tape relative to the read/write head, guides constrain the tape’s lateral motion, but even the modest forces that develop during guiding can cause wear and damage to the tape’s edges. This paper presents a tensioned axially-moving viscoelastic Euler–Bernoulli beam model used to simulate the tape’s lateral dynamics, the guiding forces, and the position error between the data tracks and the read/write head. Lateral vibration can be excited by disturbances in the form of pack runout, flange impacts, precurvature of the tape in its natural unstressed state, and spiral stacking as tape winds onto the take-up pack. The guide model incorporates nonlinear characteristics including preload and deadbands in displacement and restoring force. A tracking servo model represents the ability of the read/write head’s actuator to track disturbances in the tape’s motion, and the actuator’s motion couples through friction with the tape’s vibration. Low frequency excitation arising from pack runout can excite high frequency position error because of the nonlinear characteristics of the guides and impacts against the pack’s flanges. The contact force developed between the tape and the packs’ flanges can be minimized without significantly increasing the position error by judicious selection of the flanges’ taper angle.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Block diagram of the lateral tape vibration and actuator-servo model

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Figure 2

(a) Path layout used in the examples (asterisks denote the tangency points of the tape at the packs, guides, and head), and (b) unwrapped path

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Figure 3

Definition of the misalignment angles for a pack

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Figure 4

(a) A representative guide having ceramic buttons mounted on compliant flexures, (b) schematic of the guide model, and (c) cross section of a pack and its flanges

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Figure 5

Constitutive relations for (a) a deadband guide (K1=K2=K and d1=d2=d/2) and (b) a preloaded guide (K2⪢K1, d2=0, and d1=−f0/K1)

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Figure 6

Characteristics of the read/write head’s tracking servo. (a) Magnitude of the open loop frequency response, (b) phase of the open loop frequency response, and (c) magnitude of the disturbance rejection frequency response.

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Figure 7

(a) Displacement of the tape’s center-line at RW, (b) displacement of the servo track at RW, (c) displacement of the actuator, (d) displacement error between the track and actuator, and (e) the spectrum of the displacement error

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Figure 8

Experimental setup for the natural frequency validation shown from the (a) top and (b) side

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Figure 9

The first two natural frequencies as a function of span length for string theory (⋯), Euler–Bernoulli beam theory (– – –), Rayleigh and Timoshenko beam theory (——), and experimental measurements (×)

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Figure 10

(a) Path layout used in the validation study, (b) time histories of the simulated (– – –) and measured (——) responses, and (c) frequency response of the simulated (– – –) and measured (——) responses

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Figure 11

Displacement at 11 evenly-spaced instants with supply pack runout and (a) pinned guides (d1=d2=−560 μm), (b) preloaded guides (d1=d2=−43 μm), (c) linear guides (d1=d2=0 μm), (d) deadband guides (d1=d2=43 μm), and (e) smooth posts (d1=d2=245 μm). The asterisks on the abscissa denote the locations of G1, G2, and RW; k1=k2=116 N/m, t=100 ms, N=200, and t=10−5 s.

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Figure 12

Guiding forces at G1 with supply pack runout and (a) pinned guides (d1=d2=−560 μm), (b) preloaded guides (d1=d2=−43 μm), (c) linear guides (d1=d2=0 μm), and (d) deadband guides (d1=d2=43 μm)

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Figure 13

Relative displacement between RW and the servo track with supply pack runout and (a) pinned guides (d1=d2=−560 μm), (b) preloaded guides (d1=d2=−43 μm), (c) linear guides (d1=d2=0 μm), (d) deadband guides (d1=d2=43 μm), and (e) smooth posts (d1=d2=245 μm)

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Figure 14

Displacement at 21 evenly-spaced instants with the tape’s sinusoidal natural shape and flanges having clearance (a) dOD=50 μm, (b) dOD=65 μm, and (c) dOD=100 μm. The asterisks on the abscissa denote the locations of G1, G2, and RW, and the flanges of the take-up pack are shown in bold; k1=k2=11.6 N/m, d1=d2=0 μm, hID=50 μm, t=430 ms, N=200, and Δt=10−5 s.

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Figure 15

(a) Displacement of the tape at RW and (b) relative displacement between RW and the servo track with the tape’s sinusoidal natural shape and flanges having clearance dOD=50 μm

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Figure 16

(a) Peak relative displacement between RW and the servo track and (b) peak contact force between the tape and the take-up pack’s flange with the tape’s sinusoidal natural shape

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Figure 17

Resultant contact force between the take-up pack’s upper flange and the tape over one cycle, shown for clearances (a) dOD=50 μm, (b) dOD=65 μm, and (c) dOD=100 μm. The insets depict the tape’s motion and contact with the flange, shown in bold.

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