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Research Papers

Extending the Reach of a Rod Injected Into a Cylinder Through Axial Rotation

[+] Author and Article Information
Connor G. Mulcahy

Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139

Tianxiang Su, Nathan Wicks

Schlumberger-Doll Research Center,
Cambridge, MA 02139

Pedro M. Reis

Department of Civil and
Environmental Engineering,
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 16, 2015; final manuscript received January 12, 2016; published online February 19, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(5), 051003 (Feb 19, 2016) (9 pages) Paper No: JAM-15-1679; doi: 10.1115/1.4032500 History: Received December 16, 2015; Revised January 12, 2016

We investigate continuous axial rotation as a mechanism for extending the reach of an elastic rod injected into a horizontal cylindrical constraint, prior to the onset of helical buckling. Our approach focuses on the development of precision desktop experiments to allow for a systematic investigation of three parameters that affect helical buckling: rod rotation speed, rod injection speed, and cylindrical constraint diameter. Within the parameter region explored, we found that the presence of axial rotation increases horizontal reach by as much as a factor of 5, when compared to the nonrotating case. In addition, we develop an experimentally validated theory that takes into account anisotropic friction and torsional effects. Our theoretical predictions are found to be in good agreement with experiments, and our results demonstrate the benefits of using axial rotation for extending reach of a rod injected into a constraining pipe.

FIGURES IN THIS ARTICLE
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Copyright © 2016 by ASME
Topics: Rotation , Friction , Buckling
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Figures

Grahic Jump Location
Fig. 2

(a) Photograph of the apparatus used to simultaneously rotate and inject a thin elastomeric rod into a borosilicate pipe laid horizontally. (b) Rendering of the rotary injection assembly. A cylindrical PMMA housing (1) is mounted on two rotary bearings. Rotation of this housing is provided by a geared transmission (2) connected to a servomotor (3). (c) Rendering of the injection unit mounted within the rotating housing. The injector head (4) is driven by a stepper motor (5). To prevent twisting, the rod is stored on a spool (6) and the electronics are connected externally by a rotary slip ring (7).

Grahic Jump Location
Fig. 1

Schematic definition of the problem. (a) Diagram of transverse forces exerted on the rod during axial rotation. (b) Representation of the helical buckling configuration that occurs when the injected length of the rod is lh. (c) Definition of the radial clearance, Δr, between the rod and the constraint.

Grahic Jump Location
Fig. 3

Normalized buckling length, lh¯ versus dimensionless rotation speed, α. The experiments were conducted in the following ranges of parameters: 12.1 ≤ D (mm) ≤ 34; 0.25 ≤ v (cm/s) ≤ 1; and 0 ≤ ω (rpm) ≤ 300. The dashed line represents the simplified theory given by Eq. (7), and the solid lines represent the more sophisticated theory given by Eq. (18).

Grahic Jump Location
Fig. 4

Rotation speed of the tip, Ω, as a function of the dimensionless injected length l¯=l/lh (normalized by the helical buckling length lh), for five different values of the drive rotation speed (see legend). Each data point represents an average of Ω for five full revolutions, and the error bars are the associated standard deviation. The diameter of the cylindrical constraint was D = 21.7 mm and the injection speed was v = 1 cm/s.

Grahic Jump Location
Fig. 5

(a) Typical time-series of rise angle θr (t) for ω = 100 rpm and D = 21.7 mm. (b) FFT of the θr (t) signals for different drive rotation speeds. The normalized amplitude of the FFT is provided by the gray scale in the adjacent colorbar. The straight lines correspond to the harmonics of the drive signal (see legend) (c) Average value of the measured rise angle, 〈θr〉 as a function of drive rotation speed. The horizontal lines represent theoretical prediction for the rise angle based on the measured axial coefficient of friction, μa = 0.54 ± 0.05, (solid line) and the measured tangential frictional coefficient, μt = 0.21 ± 0.01, (dashed line). See Sec. 6.3 on details of how these values were measured.

Grahic Jump Location
Fig. 6

Apparatus used to measure the transverse friction coefficient, μt. A polymeric rod (1) is inserted into a 40 cm length of borosilicate tubing (2) and connected via rod clamp (3) to a servomotor (4) which provides axial rotation. The borosilicate tubing is mounted in a rotary air bushing (5) to allow complete transmission of torque through a tubing-mounted reaction arm (6) to a laboratory scale (7) placed below the apparatus.

Grahic Jump Location
Fig. 7

The transverse friction coefficient, μt, is experimentally found to be independent of the rotation speed, ω, and the rod length, l, which is inserted into the constraint. The solid and dashed horizontal lines correspond, respectively, to the average and standard deviation of all the data; μt = 0.21 ± 0.01.

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