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Research Papers

Contrasting the Predictions for Coulomb and Creep-Rate-Dependent Friction in the Modeling of Fiber-Draw Processes

[+] Author and Article Information
S. E. Bechtel

Department of Mechanical and Aerospace Engineering,  The Ohio State University, Columbus, OH 43210

S. Vohra

School of Polymer, Textile and Fiber Engineering,  Georgia Institute of Technology, Atlanta, GA 30332-0295

K. I. Jacob

School of Polymer, Textile and Fiber Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0295; G. W. Woodruff School of Mechanical Engineering,  Georgia Institute of Technology, Atlanta, GA 30332-0295

J. Appl. Mech 79(6), 061001 (Sep 12, 2012) (14 pages) doi:10.1115/1.4005532 History: Received July 18, 2006; Revised September 15, 2010; Posted January 25, 2012; Published September 12, 2012

One of the most important features in industrial fiber-drawing processes is the friction between filament tow and draw rollers, because it is what creates the tension in the fiber that performs the draw. To understand fiber draw, therefore, it would be valuable to examine the sensitivity of model predictions to the choice of the idealization of the friction incorporated in the model. This paper begins the comparative study by deriving and solving models for fiber draw, which for the first time study the friction between filament tow and draw rollers as something other than Coulomb friction, namely creep-rate-dependent friction. Sensitivity of the draw model to the choice of friction idealization is investigated by contrasting process simulations employing the usual Coulomb model for friction with simulations of the same processes employing the creep-rate-dependent friction model. It is demonstrated that the draw-model predictions of fiber behavior depend both qualitatively and quantitatively on the specific idealization of the friction between filament and rollers. For example, whereas the Coulomb friction model predicts adhesion zones on the rollers, in which the fibers and roller move together with no slip, there are strictly no adhesion zones with the creep-rate-dependent friction model, although with a choice of processing parameters the predicted relative velocity between fiber and roller can be made arbitrarily small. With the creep-rate-dependent friction model the fiber speed at the point of attachment to the draw roller must be greater than the roller surface speed for the equations of momentum to be satisfied. This small, but finite, abrupt change in speed profile can be interpreted as the formation of a neck in the fiber just upstream of the point of attachment to the roller.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) The general two-stage draw process modeled in the simulations; si denote locations of fiber attachment or detachment from the rollers, vi denote accompanying fiber speeds, and yi denote possible slip boundaries. Fiber can be drawn either on take-up to a roller or on feed from a roller, which results in draw zones near the point of entry and point of exit of a roller, respectively. (b) The two-stage draw process for the special case using Coulomb friction; the additional points ya and yb indicate the corresponding velocities vb and vb on the constitutive equation where the transition from the initial stiff region to the soft plateau and from the soft plateau to the final stiff region, respectively, take place. On the first roller there is a no-slip zone followed by a feed draw zone. On the second roller there is no take-up draw zone which was there in the general case. There is only a no-slip zone followed by a feed draw zone. The third roller is entirely bereft of any draw. (c) The two-stage draw process for the special case using creep-rate-dependent friction. In addition to points ya and yb indicating the corresponding velocities vb and vb on the constitutive equation where the transition from the initial stiff region to the soft plateau and from the soft plateau to the final stiff region, respectively, take place. There are the additional points sR 1 and sR 2 on the first roller and second roller, respectively. At these points the corresponding fiber velocities vR 1 and vR 2 mark the speeds at which on the creep-rate-dependent friction model the transition in the relation between relative velocity vrel and friction force f from the linear to constant takes place. Fiber draw takes place on the entire contact wrap on the first and second rollers; there is no draw on the third roller.

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Figure 2

Free-body diagram of a section of fiber on a clockwise-rotating roller showing the sign conventions adopted in this paper

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Figure 3

Constitutive relation between fiber axial force and fiber speed employed in the isothermal simulations with no unloading; va  = 406.4 cm s−1 is the transition speed between the initial stiff regime of fiber behavior to the soft plateau corresponding to strain ɛa , and vb  = 672.8 cm s− 1 is the transition speed between the soft plateau and second stiff regime corresponding to strain ɛb

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Figure 4

Creep-rate-dependent friction model

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Figure 5

Speed profile v(s) for the entire draw line using Coulomb friction and creep-rate-dependent friction coefficient ν, with μ=0.2 and a range of values of ν, for the process of Table 1. The parameter ν has units of dyn s cm−2 .

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Figure 6

Detail of the speed profile v(s) of Fig. 5 on the first roller

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Figure 7

Detail of the speed profile v(s) of Fig. 5 on the second roller

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Figure 8

The fiber tension T(s) plotted against arc length s along the draw line using Coulomb friction and creep-rate-dependent friction coefficient ν, with with µ = 0.2 and a range of values of ν, for the process of Table 1. The parameter ν has units of dyn s cm−2 .

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Figure 9

Detail of the fiber tension T(s) of Fig. 8 on the first roller

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Figure 10

Detail of the fiber tension T(s) of Fig. 8 on the second roller

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Figure 11

Normal force per length n(s) acting on the roller from the fiber for the entire draw line using Coulomb friction and creep-rate-dependent friction coefficient ν, with μ = 0.2 and a range of values of ν, for the process of Table 1

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Figure 12

Detail of the normal force per length n(s) on the first roller

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Figure 13

Detail of the normal force per length n(s) on the second roller

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Figure 14

Friction force per length f(s) versus arc length s along the draw line using Coulomb friction and creep-rate-dependent friction coefficient ν, with μ = 0.2 and a range of values of ν, for the process of Table 1. The parameter ν has units of dyn s cm−2 .

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Figure 15

Detail of the normal force per length n(s) on the first roller

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Figure 16

Detail of the normal force per length n(s) on the second roller

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Figure 17

Creep coefficient versus δ1 on the first roller

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