Simple indicator of draw resonance instability in melt spinning processes

Lee, Joo Sung; Jung, Hyun Wook; Hyun, Jae Chun; Scriven, L. E.

doi:10.1002/aic.10498

Cited by 21 publications

(20 citation statements)

References 17 publications

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“…Assuming the existence of the minor phase of polystyrene do not influence the viscoelastic behavior of major phase of polypropylene, the modulus can be expressed as [23] (14)…”

Section: Constitutive Equationmentioning

confidence: 99%

Studies on melt spinning of sea-island fibers. II. Dynamics of melt spinning of polypropylene/polystyrene blend fibers

Chen

Zhang

et al. 2015

Fibers Polym

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A two-dimensional (2-D) model for melt spinning of iPP/aPS blend fibers is proposed based on two-phase models on density and crystallinity and log-additive rule on elongational viscosity. A computer program is developed based on a hybrid method of fourth-order Runge-Kutta method and implicit Crank-Nicolson method to solve the model equations to obtain the axial profiles of fiber diameter, velocity, gradient of velocity and crystallinity, and the 2-D profiles of temperature, elongational viscosity and elongational stress. The simulated fiber diameters are compared with the measured diameters to verify the certainness of the simulation. The simulated results show that polymer melt jets solidify at the positions of about 40 cm beneath the spinneret which is verified by on-line measurement of fiber diameter. And the radial gradient of temperature, elongational viscosity and elongational stress reaches to 10 4 to 10 5 o C/m, 10 5 to 10 6 Pa·s/m and 10 5 to 10 6 Pa/m, respectively, at the discussed take-up velocities.

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“…Assuming the existence of the minor phase of polystyrene do not influence the viscoelastic behavior of major phase of polypropylene, the modulus can be expressed as [23] (14)…”

Section: Constitutive Equationmentioning

confidence: 99%

Studies on melt spinning of sea-island fibers. II. Dynamics of melt spinning of polypropylene/polystyrene blend fibers

Chen

Zhang

et al. 2015

Fibers Polym

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“…Melt Spinning Model. Considering the basic conservation laws for mass, momentum and energy of the viscous polymer jet one can obtain by averaging over the cross-section of the slender fiber the following set of equations, see [6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Optimal control of melt-spinning processes

Götz

Perera

2010

J Eng Math

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Abstract. An optimal control problem for a mathematical model of a melt spinning process is considered. Newtonian and non-Newtonian models are used to describe the rheology of the polymeric material, the fiber is made of. The extrusion velocity of the polymer at the spinneret as well as the velocity and temperature of the quench air serve as control variables. A constrained optimization problem is derived and the first-order optimality system is set up to obtain the adjoint equations. Numerical solutions are carried out using a steepest descent algorithm.

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“…As one of industrially and academically important issues, this instability has been theoretically and experimentally exploited by many researchers during four decades. [1][2][3][4][5][6][7][8][9][10][11] Onsets of draw resonance can be typically found by the linear stability method introducing infinitesimal perturbations at state variables from the steady states 3,4,[12][13][14] or frequency response method adopting the transfer function concept in the linearized system. 15,16) And also, periodic solutions or limit cycles of draw resonance which are nonlinear characteristic nature, have been computed by dynamic transient simulation with initial conditions, e.g., a step change of take-up velocity from steady states.…”

Section: Introductionmentioning

confidence: 99%

Direct Calculation of Limit Cycles of Draw Resonance and Their Stability in Spinning Process

Yun

Shin

Lee³

et al. 2008

J. Soc. Rheol., Jpn

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Draw resonance, known to govern the onset of instability occurring in extension-dominant polymer processes, has been investigated using the bifurcation analysis method. Time-periodic trajectories of draw resonance along the drawdown ratio over the onset point or Hopf point, have been directly obtained by Newton's method implemented with pseudo arc-length continuation scheme. Floquet multipliers of the monodromy matrix to determine the stability of limit cycles have been also computed by time-integration during one period of the oscillation. It has been revealed that the limit cycles over the onset are more stable when drawdown ratio rises for both Newtonian and viscoelastic fluids, so draw resonance is a stable supercritical Hopf bifurcation.

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Simple indicator of draw resonance instability in melt spinning processes

Cited by 21 publications

References 17 publications

Studies on melt spinning of sea-island fibers. II. Dynamics of melt spinning of polypropylene/polystyrene blend fibers

Studies on melt spinning of sea-island fibers. II. Dynamics of melt spinning of polypropylene/polystyrene blend fibers

Optimal control of melt-spinning processes

Direct Calculation of Limit Cycles of Draw Resonance and Their Stability in Spinning Process

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