Micro-buckling of paper during blade metering

Abstract

Multiphysics models were used to simulate the deformational characteristics experienced by paper under metering blades. Paper is found to slip microscopically at the backing roll interface and subsequently buckle either side of the blade during metering operations. Micro-slippage of the paper at the interface is a linear function of the separation height incurred during buckling. The effects of altering the static coefficient of friction as well as the properties of the backing roll material are studied. Increasing the coefficient of static friction reduces the extent of buckling while a non-linear relationship is found to arise on increasing the elastic modulus of the backing roll material. The mechanisms involved in micro-buckling deformation are explicated herein.

Introduction

The most common high speed paper coating operation is blade metering, which serves to control coat weight, decrease the presence of coating defects and flatten coating films on otherwise rough base paper substrates. This said, metering operations at very high speeds can also be a cause for defects such as sctratches, streaks and other general runnability problems (Gane, NcGenity, & Watters, 1992). By and large, attempts to model the blade metering operation have been something of a conundrum and there is still no generically accepted model that can accurately represent the extent of physical complexities that exist in a metering operation. Nevertheless, analyses in areas of specific interest have yielded fruitful information through both theoretical and experimental methods.

There is some degree of unanimity in agreement concerning several aspects of the blade metering operation. For example, higher blade pressures cause a reduction in the final coating thickness (Kuzmak, 1986), which is quite usually coupled to the rate of dewatering. Coat weight is therefore a function of the force exerted on the metering blade (Fauré, Pluvinage, & Pouyet, 1995). Coat weight non-uniformity, streaking and micro-line formation is contrarily an area where there is little agreement, though thorough investigations have been undertaken. According to Ortman and Donigian (1992) for example, excessive streaking is a function of higher web speeds, softer backing rolls and higher blade tip angles. Operational anomalies such as streaking are thus seen to be related to the deformational characteristics of the fluid–solid media under the metering blade. Manipulations of these as a means of controlling such quality related defects can however, effectively alter other deformational characteristics during the coating operation, which could instigate other operational problems like bleeding and paper web breaks. Several articles have been published on the solid state deformations that arise as a function of the forces at the solid–liquid interfaces with (Bousfield, Wikstrom, & Rigdahl, 1998; Isaksson, Engström, & Rigdahl, 1994; Pajari, Mansikka-ajo, Ketoja, & Bousfield, 2003; Pranckh & Scriven, 1990; Turai, 1971). Turai (1971) for example developed a mathematical model to further understand the deflective motion of steel blades during metering. Coating pressure induced strain profiles in the backing roll materials have been modelled and studied by Bousfield et al. (1998) and Pajari et al. (2003). According to the former, higher forces are necessary to drive a blade into position when the backing roll is softer and deforms more. The governing reason for this is that as deformation of the backing roll material ensues, a larger gap with a different nip geometry is created between the blade and the underlying material. Resultantly, the blade requires extra ‘pushes’ to reach the target coat weight. Bousfield and co-workers further described the pressure profile generated under the blade, which is ultimately the cause of material deformations. Of particular interest is that the peak pressure pulse that develops in the region of the heel decreases smoothly towards the blade toe. The true pressure profile undulates with the contours of surface roughness (Giri, Unertl, & Bousfield, 2001), though the concept of a continual generic decrease in magnitude towards the toe remains. This gives justification to the concept of non-linear deformational characteristics in the solid state media. It is hypothesised herein, that the pressure pulsation, giving rise to lateral deformations in underlying base paper and backing roll materials will exhibit different strains due to the different material properties of each (Ortman & Donigian, 1992). Possible differential straining between the base paper and backing roll materials may give rise to slightly different surface shapes, influencing key runnability characteristics such as the blade stagnation point, calculated as being 5 μm from the heel by Bousfield (2000). Other, more visually appreciable problems may arise as a consequence, such as increased stress intensities around defects/holes in the paper web leading to problems with web breaks. The research reported herein aims to follow up on the previously stipulated hypothesis and elucidate upon whether differential straining results in any solid state shape alterations in the vicinity of the metering blade tip.