Winding plastic films: Experimental study of squeeze film flow between one smooth surface and one "rough" surface

The present paper is concerned with experiments which consist in squeezing an air layer between a rigid, smooth surface and a flexible, rough one.The experimental rig is composed of a smooth glass plate, with a circular slit allowing air aspiration to be done around it. A thin (few microns thick) plastic film is laid on the glass plate and air separating the glass and the film surfaces is removed by means of a vacuum pump. A circular front appears on the film surface, and moves towards the centre, as the film is pressed onto the glass plate.A monochromatic lamp is used to insulate the surfaces from above and Newton rings can be observed as the front moves. The duration of this operation is measured by a chronometer.Typically, the measured time depends on the plate diameter, the sub-ambient pressure exerted, the film flexural rigidity (or its thickness) and its surface roughness.A set of experiments have been carried out for several values of the sub-ambient pressure and of the slit diameter.The results are well reproducible: for a given sample, the characteristic time is proportional to the squared value of the diameter. The dependence on the sub-ambient pressure is more complicated. A simple model using a semi-empirical formulation is suggested on the basis of the experimental data

Macroscopic effects of surface roughness in confined air-flow

One challenge when processing flexible media such as plastic films is to obtain rolls without any aspect defect : if one considers that a "defect" (i.e. wrinkling or buckling) is due to the fact that the stress generated within the roll is greater than some "plasticity yield", then it is crucial to predict the internal stress state.Several process parameters must be carefully mastered (winding tension, velocity, etc.) as well as the material pertinent properties. One key issue is to optimize the surface topography of the flexible medium so that to improve the quality of the wound roll.We propose here new parameters which describe the surface roughness of plastic films fairly well. The measurements were carried out by using a 3D roughness measurement device.A mathematical model based on homogenization techniques is proposed, where the heights of the roughness peaks, their diameter and their spatial distribution are the governing parameters.Sampling at different levels is carried out by expressing the percentage of peaks which exceed some given threshold value.For each tested film, the threshold value will be the only adjustable parameter.Introducing these parameters into the mathematical model which predicts the evolution of the squeezed air layer and comparing to the experimental data, the following results are obtained :- It is possible to adjust one single parameter so that to obtain a very good agreement between the experimental data and the theoretical results.- The smoother the film, the more important the highest peaks are in terms of air leakage

New parameter for dynamic characterization of PET film surface topography

It is well-known that handling and winding flexible media involve aerodynamic phenomena which are crucial for the process. Among those parameters which govern the final thickness value of the air layers separating the film layers in a roll of film (for example PET), surface roughness plays an important role. In order to characterize the surface topography of such materials, in a dynamic way, an original experimental set-up was built. It has been described elsewhere, and only its basic features are recalled here. It consists in a polished glass disc with a circular slit connected to a vacuum pump. Having displayed a sample of PET film onto the glass plate, sub-ambient pressure is applied. The air layer which initially separates the film from the plate is partially reduced due to air aspiration: a circular front starts from the slit and propagates towards the center. For prescribed values of the film thickness, the total propagation time depends on sub-ambient pressure and slit diameter (i.e. squeezing surface) through relationships which involve a single parameter characteristic of film roughness.Here the same experimental set up is used to carry out further investigations dealing with the kinetics of both air layer thinning and front propagation. Using a monochromatic light to insulate the film from above, Newton rings are generated allowing the air gap thickness variation to be measured by means of a CCD camera associated with image processing. The main experimental result is that the air layer at the center decreases linearly versus time, the slope being characteristic of the film surface roughness. A simple theoretical model based on the concept of " equivalent smooth surfaces " is developed in order to predict the circular front propagation. Excellent agreement is observed with the experimental data, namely the front propagation kinetics. These results are extrapolated to the configuration of winding, leading to significant improvement of the existing model for lateral evacuation of the air layers confined between the film layers in a roll of film

On-line control of tension in web winding systems based on wound roll internal stress computation

One of the key challenges in the processing of flexible media such as plastic films is to obtain rolls without any aspect defect: if one considers that a "defect" (i.e. wrinkling or buckling) is due to the fact that the stress generated within the roll is greater than some "plasticity threshold", then it is crucial to predict the internal stress. Several process parameters must be carefully mastered, among which the winding tension is very important. Offline optimization of the tension can a priori guarantee the production of perfect rolls, with respect to the internal stress. Nevertheless, the industrial control systems never generate perfect follow-up of the tension reference value, because the tension which is actually imposed (i.e. measured) exhibits oscillations due to the imperfections of the winding system, including geometrical irregularities of the rolls. The fluctuations about the tension nominal value induce variations in the stress within the roll as compared to the value which would result from an ideal control. As a consequence, it is judicious to change the tension reference value during the winding process, according to some criterion defined from the stress computed within the roll, and then to apply this new "up-dated" reference to the forthcoming web layers. This new way of online tension control requires new concepts such as "robust multivariable control", because distributed control may not work as well.The first step consists in computing the internal stress generated within a roll of a wound web (for instance plastic film). For that purpose, a modified non-linear model is developed in the spirit of Hakiel's. The web's winding process can be considered as a continuous accretion process, in the sense that the stress components at a given point are continuously modified by the upper superimposed layers. In addition, the residual air films which separate the web layers are taken into account in an indirect way through the radial Young's modulus of the roll which is a non-linear (polynomial) function of the compressive stress component. Several illustrative examples are presented and commented. Then, having prescribed an optimization criterion for the winding tension, an optimization algorithm based on the simplex principle is described. Finally, a new concept of online tension control, based on prediction-correction is proposed. Dividing the roll radius into several segments, the tension reference is computed and corrected for each range of roll radius values, by using the predictive model for the stress within the roll. The adjusted tension is reactualized step by step, following the optimization principle as described above and it will be considered as the new tension reference value for the coming layers. A comparison between offline and online tension controls clearly shows the improvement given by the new optimization technique (online)

Control and online tension reference optimization in winding systems: Application to an identified three-motors simulator

It is well known that the tension reference value, which a priori guarantees a good quality roll, is based on the stress generated within the roll. However, due to the imperfections of the winding systems and to the limited performances of the disturbances rejection controllers, a control with fixed reference never generates perfect follow-up of the tension. A solution would consist in adjusting the tension reference online, according to real measurements.In a previous paper, the criterion for tension adjustment was the tangential stress. A method for online control based on prediction-correction using the simplex algorithm was presented. This method was tested numerically.In the present paper, we propose to generalize the criterion of tension reference optimization by considering both the tangential and the radial stress within the roll during winding. The same optimization algorithm is used, taking into account the dynamic tension model. Moreover, a dynamic gauge is now introduced, so that it can vary during the winding process. It generally represents the limits of elastic deformations of the web.The new optimization algorithm for the on-line reference tension calculation has been validated on a dynamic non-linear winding model. This complete model used for simulations was validated on a three-motor setup using brushless motors. The setup is with PI controllers, where the web velocity is imposed by master traction motor and the tension is controlled by unwinding and winding motors.In this approach, a new tension-prediction algorithm using a linear parameter varying (LPV) model is used. The influence of the tension prediction algorithm is also analyzed.Several illustrative examples will be presented and the improvement as compared to an offline control will be commented

Gauge optimization of the reference tension in winding systems using wound internal stresses calculation

In winding process, the quality of the roll is directly connected to its stress state. The winding tension is the most significant parameter which plays an important role in the stresses generated within a roll, during winding. If the stresses exceed a critical value, defects can appear in the roll and make the web non usable.This work concerns the estimation and optimization of the maximal dispersion of the reference tension, so that the tangential and radial stresses values remain in a gauge. It aims to find automatically the maximum and minimum limits for the reference tension, so that all curves ranging between these two limits or thresholds, generate radial and tangential stresses, theirs selves included in a gauge fixed in advance. The results lead to a practical gauge optimization of the reference tension for industrial applications

Imaging with therapeutic acoustic wavelets–short pulses enable acoustic localization when time of arrival is combined with delay and sum

—Passive acoustic mapping (PAM) is an algorithm that reconstructs the location of acoustic sources using an array of receivers. This technique can monitor therapeutic ultrasound procedures to confirm the spatial distribution and amount of microbubble activity induced. Current PAM algorithms have an excellentlateral resolution but have a poor axial resolution, making it difficult to distinguish acoustic sources within the ultrasound beams. With recent studies demonstrating that short-length and low-pressure pulses—acoustic wavelets—have the therapeutic function, we hypothesizedthat the axial resolution could be improved with a quasi-pulse-echo approach and that the resolution improvement would depend on the wavelet’s pulse length. This article describes an algorithm that resolves acoustic sources axially using time of flight and laterally using delayand-sum beamforming, which we named axial temporal position PAM (ATP-PAM). The algorithm accommodates a rapid short pulse (RaSP) sequence that can safely deliver drugs across the blood–brain barrier. We developed our algorithm with simulations (k-wave) and in vitro experiments for one-, two-, and five-cycle pulses, comparing our resolution against that of two current PAM algorithms. We then tested ATP-PAM in vivo and evaluated whether the reconstructed acoustic sources mapped to drug deliver

Asymptotic stability of the Cauchy and Jensen functional equations

The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid everywhere with a new error term which is a constant multiple of the original error term. As consequences, we also obtain results of hyperstability character for these two functional equations

What impacts of climate change on surface water in France by 2070? Results of the Explore2070 project in metropolitan France and overseas departments

International audienceLes questions relatives à la disponibilité et à la gestion de l'eau concentreront l'essentiel des mesures d'adaptation qui seront prises dans les décennies à venir pour faire face aux conséquences des changements climatiques. Ces mesures devront également prendre en compte les évolutions socio-économiques, en termes de démographie, d'aménagement du territoire et de politiques publiques (agriculture, énergie, transports, etc.). Il est dès lors primordial pour les décideurs et gestionnaires de quantifier les évolutions socio-économiques possibles, ainsi que le devenir de la ressource en eau et de sa variabilité temporelle et spatiale. C'est dans ce contexte que le projet Explore2070 avait pour objectif d'évaluer les impacts possibles des changements climatiques et socio-économiques futurs sur les grandes masses d'eau (surface, souterrain, littoral) et la biodiversité, en France métropolitaine et sur les départements d'Outre-mer (Guadeloupe, Guyane, Martinique et Réunion). Piloté par le Ministère de l'Ecologie (MEDDTL), ce projet a rassemblé de nombreux bureaux d'études et instituts de recherche pour dresser un panorama général des évolutions à attendre à l'horizon 2070. Par son ampleur et la variété de ses objectifs, ce projet doit permettre de répondre à de nombreuses questions des gestionnaires et de mieux apprécier les enjeux de ces évolutions. Dans la suite, nous présentons les travaux réalisés spécifiquement sur la quantification des évolutions des eaux de surface. Nous détaillerons dans ce qui suit la démarche générale de modélisation proposée, la nature des résultats obtenus, ainsi que la façon dont les incertitudes ont été quantifiées. Ce dernier point est indispensable pour aider à la prise de décision dans un avenir incertain. / Water availability and water management will be the focus of most of the adaptation measures that will be taken in the next decades to face the consequences of climate change. These measures will have to account for the socio-economic evolutions, in terms of population size, town and country planning, as well as public policies (agriculture, energy, transports, etc.). It is therefore essential for decision makers and managers to be able to quantify the possible socio-economic evolutions together with the evolution of water resources and their temporal and spatial variability. In this context, the Explore2070 project aimed at evaluating the possible impacts of future climate and socio-economic changes on water bodies (surface water, groundwater and coastal water) and biodiversity, in metropolitan France and overseas departments (Guadeloupe, Martinique, French Guyana, and Réunion Island). The project was managed by the French Ministry of Ecology (MEDDTL) and gathered several consultancies and research institutes to establish a general overview of the expected evolutions by 2070. Through both the extent and the variety of the project’s objectives, Explore2070 will provide answers to many questions raised by managers and better evaluate the stakes related to these evolutions. In the following, we present the work done specifically to quantify the evolution of surface water. The general modelling approach, the type of results and the way uncertainties were quantified are detailed. Uncertainty quantification is essential to help decision making in an uncertain future