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Journal of Tribology | Volume 139 | Issue 2 | research-article
Research Papers: Friction and Wear

Lateral Friction Behavior of a Thin, Tensioned Tape Wrapped Over a Grooved Roller: Experiments and Theory

[+] Author and Article Information
Hankang Yang

Department of Mechanical Engineering,
Northeastern University,
Boston, MA 02115

Johan B. C. Engelen, Walter Häberle, Mark A. Lantz

IBM Research—Zürich,
Säumerstrasse 4,
Rüschlikon CH-8803, Switzerland

Sinan Müftü

Department of Mechanical Engineering,
Northeastern University,
Boston, MA 02115
e-mail: s.muftu@neu.edu

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received December 11, 2015; final manuscript received April 25, 2016; published online August 11, 2016. Assoc. Editor: Min Zou.

J. Tribol 139(2), 021605 (Aug 11, 2016) (12 pages) Paper No: TRIB-15-1449; doi: 10.1115/1.4033566 History: Received December 11, 2015; Revised April 25, 2016
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Effects of friction forces on the lateral dynamics of a magnetic recording tape, wrapped around a grooved roller are investigated experimentally and theoretically. Tape is modeled as a viscoelastic, tensioned beam subjected to belt-wrap pressure and friction forces. Including the effects of stick and slip and velocity dependence of the friction force render the tape's equation of motion nonlinear. In the experiments, tape was wrapped under tension around a grooved roller in a customized tape path. The tape running speed along the axial direction was set to zero, thus only the lateral effects were studied. The grooved roller was attached to an actuator, which moved the roller across the tape. Tests were performed in slow and fast actuation modes. The slow mode was used to identify an effective static, or breakaway, friction coefficient. In the fast mode, the roller was actuated with a 50 Hz sinusoid. The same effective friction coefficient was deduced from the fast actuation mode tests. This test mode also revealed a periodic stick–slip phenomenon. The stick-to-slip and slip-to-stick transitions occurred when the tape vibration speed matched the roller actuation speed. 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 also shows that an effective friction coefficient can be described that captures the complex interactions in lateral tape motion (LTM) over a grooved roller.
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Figures

Grahic Jump Location
Fig. 2

Dimensions of grooved roller: (a) groove profile and (b) overall dimensions of the roller

+Dimensions of grooved roller: (a) groove profile and (b) overall dimensions of the roller
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Dimensions of grooved roller: (a) groove profile and (b) overall dimensions of the roller
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Fig. 1

Details of the configurable tape path. (a) Photograph of the configurable tape path with the hand-controlled micrometer that moves the TR in the axial direction. (b) The topview schematic of the entire experimental layout. (c) Schematic of the tape as it is laid-out on a flat plane.

+Details of the configurable tape path. (a) Photograph of the configurable tape path with the hand-controlled micrometer that moves the TR in the axial direction. (b) The topview schematic of the entire experimental layout. (c) Schematic of the tape as it is laid-out on a flat plane.
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Details of the configurable tape path. (a) Photograph of the configurable tape path with the hand-controlled micrometer that moves the TR in the axial direction. (b) The topview schematic of the entire experimental layout. (c) Schematic of the tape as it is laid-out on a flat plane.
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Fig. 3

COF–velocity relations modeled by Quinn's model

+COF–velocity relations modeled by Quinn's model
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COF–velocity relations modeled by Quinn's model
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Fig. 4

Results of a typical slow mode friction test (T = 0.25 N, R = 6 mm and θw = 15 deg). (a) Lateral tape displacement near the roller at sensor-2 and the roller displacement. (b) Force acting on the roller representing the friction force.

+Results of a typical slow mode friction test (T = 0.25 N, R = 6 mm and θw = 15 deg). (a) Lateral tape displacement near the roller at sensor-2 and the roller displacement. (b) Force acting on the roller representing the friction force.
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Results of a typical slow mode friction test (T = 0.25 N, R = 6 mm and θw = 15 deg). (a) Lateral tape displacement near the roller at sensor-2 and the roller displacement. (b) Force acting on the roller representing the friction force.
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Fig. 5

Results of slow mode experimental tests for tension values of (a) 0.25 N, (b) 0.50 N, and (c) 0.75 N for 15, and 20 deg wrap angles

+Results of slow mode experimental tests for tension values of (a) 0.25 N, (b) 0.50 N, and (c) 0.75 N for 15, and 20 deg wrap angles
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Results of slow mode experimental tests for tension values of (a) 0.25 N, (b) 0.50 N, and (c) 0.75 N for 15, and 20 deg wrap angles
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Fig. 6

Lateral tape displacement measured by sensors S1 and S4, located near the support rollers 22 and 24 for a tension of 0.5 N and a wrap angle of 20 deg. Note that this displacement is much smaller than the roller actuation amplitude of 200 μm and indicates that the tape can be assumed not moving over these two SRs.

+Lateral tape displacement measured by sensors S1 and S4, located near the support rollers 22 and 24 for a tension of 0.5 N and a wrap angle of 20 deg. Note that this displacement is much smaller than the roller actuation amplitude of 200 μm and indicates that the tape can be assumed not moving over these two SRs.
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Lateral tape displacement measured by sensors S1 and S4, located near the support rollers 22 and 24 for a tension of 0.5 N and a wrap angle of 20 deg. Note that this displacement is much smaller than the roller actuation amplitude of 200 μm and indicates that the tape can be assumed not moving over these two SRs.
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Fig. 7

Lateral tape displacement and roller displacement histories for 0.5 N tension and 20 deg. wrap angle. (a) Tape and the roller move together when no slip is observed. Actuation amplitude is close to 55 μm. (b) Periodic transitions between stick and slip phases occur when the roller actuation amplitude is around 170 μm. (c) Velocity of tape and roller displacements given in Fig. 7(b).

+Lateral tape displacement and roller displacement histories for 0.5 N tension and 20 deg. wrap angle. (a) Tape and the roller move together when no slip is observed. Actuation amplitude is close to 55 μm. (b) Periodic transitions between stick and slip phases occur when the roller actuation amplitude is around 170 μm. (c) Velocity of tape and roller displacements given in Fig. 7(b).
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Lateral tape displacement and roller displacement histories for 0.5 N tension and 20 deg. wrap angle. (a) Tape and the roller move together when no slip is observed. Actuation amplitude is close to 55 μm. (b) Periodic transitions between stick and slip phases occur when the roller actuation amplitude is around 170 μm. (c) Velocity of tape and roller displacements given in Fig. 7(b).
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Fig. 8

(a) The breakaway displacements and (b) friction force for the slow mode tests. (c) Calculated COF. Each case was repeated three times, and each test has duration of 5 s with 50 Hz frequency. Therefore, each data point represents the average of 750 cycles. The error bars represent one standard deviation.

+(a) The breakaway displacements and (b) friction force for the slow mode tests. (c) Calculated COF. Each case was repeated three times, and each test has duration of 5 s with 50 Hz frequency. Therefore, each data point represents the average of 750 cycles. The error bars represent one standard deviation.
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(a) The breakaway displacements and (b) friction force for the slow mode tests. (c) Calculated COF. Each case was repeated three times, and each test has duration of 5 s with 50 Hz frequency. Therefore, each data point represents the average of 750 cycles. The error bars represent one standard deviation.
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Fig. 9

Comparison of simulation results with the fast mode experiments by using the range of COF values found in the slow-mode COF measurements. T = 0.5 N, θw = 15 deg. Simulation results: best match, upper limit, and lower limit and measurements: (a) 0.1 s simulation period and (b) magnification into the simulation span of 46–55 ms.

+Comparison of simulation results with the fast mode experiments by using the range of COF values found in the slow-mode COF measurements. T = 0.5 N, θw = 15 deg. Simulation results: best match, upper limit, and lower limit and measurements: (a) 0.1 s simulation period and (b) magnification into the simulation span of 46–55 ms.
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Comparison of simulation results with the fast mode experiments by using the range of COF values found in the slow-mode COF measurements. T = 0.5 N, θw = 15 deg. Simulation results: best match, upper limit, and lower limit and measurements: (a) 0.1 s simulation period and (b) magnification into the simulation span of 46–55 ms.
Grahic Jump Location
Fig. 10

(a) Simulated and measured displacement, (b) velocity, and (c) phase-plane histories of the lateral tape deflection for the case of 0.25 N tension and 10 deg of wrap. The blue curve indicates the roller motion.

+(a) Simulated and measured displacement, (b) velocity, and (c) phase-plane histories of the lateral tape deflection for the case of 0.25 N tension and 10 deg of wrap. The blue curve indicates the roller motion.
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(a) Simulated and measured displacement, (b) velocity, and (c) phase-plane histories of the lateral tape deflection for the case of 0.25 N tension and 10 deg of wrap. The blue curve indicates the roller motion.
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Fig. 11

Frequency spectra of tape velocity presented in Fig. 10(b) obtained by the FFT algorithm for both simulated and measured signals. Frequency content is shown for (a) several cycles and (b) for the slip phase.

+Frequency spectra of tape velocity presented in Fig. 10(b) obtained by the FFT algorithm for both simulated and measured signals. Frequency content is shown for (a) several cycles and (b) for the slip phase.
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Frequency spectra of tape velocity presented in Fig. 10(b) obtained by the FFT algorithm for both simulated and measured signals. Frequency content is shown for (a) several cycles and (b) for the slip phase.

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