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FLEXO Magazine : November 2010
Technologies & Techniques more absorbent papers. The absorbance, porosity, has also been reported to vary spatially in coated paper (Chinga and Helle 2003). The difference between the low porosity and high porosity areas may lead to non-uniform ink absorption into the coating structure, and this may affect the uniformity of the print density and be a cause of print mottle. The fluid properties, rheological and fluid dynamic force, may be important since the ink film is subjected to pressure, temperature and shear-rate gradients between the substrate and the printing plate, according to Taylor and Zettlemoyer (1958). The temperature and shear-rate affect the ink viscos- ity and the gradients generate regions in the ink film where the viscosity is reduced. These regions control the film split. From a process aspect, it has been shown that the ink viscos- ity affects the penetration and spreading of the ink into the substrate. A higher ink viscosity leads to a lower degree of penetration and less spreading (Hsu 1961a; Karttunen 1973; Lagerstedt and Kolseth 1995). Another property of both the surface and the ink which influences the ink transfer is the surface energy. The effect of surface energy on ink transfer in flexographic printing has been studied by Lagerstedt and Kolseth (1995). They conclud- ed that ink transfer in water-borne flexography is influenced by the surface chemistry of the paper surface and that this influences halftones more than full-tone areas. In the border zone between printed and unprinted regions, the three phase system consisting of air, ink and paper is present. However, it was concluded that other factors, such as printing pressure, printing speed and surface roughness played a greater role for ink transfer. The ratio of the substrate energy to the ink surface energy becomes more important when non-absorptive substrates, such as polyethylene-coated paperboard, are printed (Mesic et al. 2005; Rentzhog 2006). Contact area and contact pressure. Before any further discussion regarding ink transfer, it is useful to consider the concepts of contact mechanics. When the surfaces of two sol- id bodies are brought into contact, stresses and deformations arise. The contact is said to be conforming if the surfaces of the two bodies ‘‘fit’’ exactly or even closely together without deformation. Bodies which have dissimilar profiles are said to be non-conforming (Johnson 1985). When the two bodies are brought into contact, the first contact is at a single asperity, point contact, and as the load increases, an increasing num- ber of asperities, come into contact due to the deformation of the asperities which were first in contact. The real contact area between non-conforming bodies is generally small compared to the nominal contact area, since contact is limited to asperities. This leads to a highly concen- trated stress in the contact regions (Lo 1968; Kagami et al. 1986; Adams and Nosonovsky 2000; Mihailidis et al. 2001). The magnitudes of the real contact area and of the pres- sure at the contact areas are affected by several factors: • Geometry and Topography of the bodies Shape of the bodies. Smoothness of the bodies, size, shape and numbers of asperities. • Material Properties of the bodies E-modulus (E) or Young’s modulus, describing the stiff- ness in compression and tension mode. Poisson’s ratio (ν), describing the strain relations. Shear modulus (G), describing the stiffness in shear mode. Viscoelasticity, describing the combination of viscous and elastic behavior of the material properties, taking into account the time-dependency of the material properties. Friction between the bodies. • Conditions Load applied on the bodies. Time of contact. Temperature of the bodies and the surroundings. Relative humidity of the surrounding air. Compression of paper and printing plate. In mechani- cal printing processes, non-conforming contact is dominant due to the asperities of the paper surface, the heterogeneous topographical structure. In order to obtain satisfactory ink transfer, the non-conforming contact must be minimized. This is naturally done by compression of the printing plate and/or the paper in the printing nip. The compressibility of the printing plate and of the paper has been shown to influence the paper- printing plate contact and the subsequent ink transfer (Miller and Poulter 1961; Bristow 1980; Jensen 1989; Heikkilä 1996; Se- rafano and Pekarovicova 1999; Jansen and Breakspeare 2001; Johnson et al. 2003; Provatas and Uesaka 2003; Endres 2004). Paper is compressible, exhibiting a non-linear strain- hardening behavior in z-direction compression. The strain hardening is due both to an increase in contact area and to the irreversible compaction of the fibre network (Rättö 2005). Several factors influence the compressibility of the paper. Hsu (1963) found that the density of the paper has a great influence on its compressibility. This is closely related to the results presented by Mangin et al. (1993) who found that the compressibility of the paper increased with increasing initial pore volume of the paper surface. It was shown, when comparing TMP (Thermo Mechanical Pulp) and kraft fibres, that the stiffer TMP fibres present more residual compressibility. This can be explained in terms of the fibre flexibility which influences the number of bonds between the fibres and the strength of the bonds on the strength of the formed paper (Torgnysdotter and Wågberg 2004). The TMP fibres are stiffer resulting in fewer and weaker bonds between the fibres than with kraft fibres. The topography of the paper Figure 6. Print density as a function of ink amount on paper according to the equation with D∞ = 1.5 and m = 1. Figure 7. A step function and its Fourier series approximation, using 1 (top left), 7 (top right), 14 (bottom left) and 21 (bottom right) terms in the sum of harmonics. Figure 8. example of an image (left) and its corresponding one-dimensional (middle) and two-dimensional power spectra (right), the magnitude of the harmonic component increases with increasing height in the one-dimensional power spectrum and with the intensity of the darkness in the two-dimensional power spectrum. 84 FLeXO november 2010 www.flexography.org FLX_Nov10_mech.indd 84 11/1/10 2:26 PM
Sustainable Fall 2010