Fluid mechanics and design of forming operations for power -law fluids
Abstract
The fluid mechanics of two sheet-forming operations are considered. For the die sheeting operation, a design methodology for linearly tapered coathanger dies (LTCDs) is proposed and explored through 1-D and 3-D analyses. For the calendering operation, a method for on-line rheology measurement is explored and validated for finite- (2-D) and infinite-width (1-D) cases. The design methodology for LTCDs proposes an aspect ratio-dependent critical angle at which the flow distribution is least dependent on changes in the fluid flow index (n). It is generally accepted that the flow distribution in a LTCD is highly dependent on n. The assumptions and conclusions of the 1-D model used to develop the methodology are explored through finite element results of a 3-D model. Upon examination of the distribution of residence times of dies designed at the optimal angle, unique attributes are revealed. The normalized residence time distribution of dies designed at the critical angle is independent of aspect ratio. The developed design methodology may prove useful because of its minimal sensitivity to changes in flow index and its unique scaling properties. Although there exists mention of rheology measurement during calendering in the literature, the current research presents a systematic means of on-line rheology measurement for the case of a finite- (FW) or infinite-width (IW) sheet. For the IW case, power is measured while the ratio of roll radius to gap is held constant; the FW case requires the ratio of sheet width to roll gap also be held constant. The measured power is scaled by system variables, and the power-law parameters are obtained from linear regression statistics. Varying the roll speed and reduction ratio varies the scaled power. The resulting measures of power-law rheology can be fed to an on-line control system or used in a statistical quality control program. The calculated power and normal force on the calendering roll can also be useful in design calculations at the manufacturing stage.
Degree
Ph.D.
Advisors
Okos, Purdue University.
Subject Area
Agricultural engineering|Chemical engineering|Food science
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