Analytical Approach to Evaluate Maximum Gravitational Sag and its Variations of Glass Substrate for LCD
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Analytical Approach to Evaluate Maximum Gravitational Sag and its Variations of Glass Substrate for LCD Technical Information Paper TIP 307 Issued: November 2004 Supercedes: xxxx H. Kuroki, A. Kobyakov, and Meda Corning Incorporated, Corning, NY 14831 Abstract We present analytical formulas to evaluate the gravitational sag of glass substrate for liquid crystal display (LCD). The formulas are derived for the parallel line supports (knife-edges). Past studies, and comparison with finite element analysis in this paper, show that a continuous line support is a very close approximation to collinear point supports with the kind of support spacing typical in today’s cassette designs. Two, three and four supporting lines are considered. A new concept of initial shapes of the glass substrate is introduced to enable evaluation of sag variations caused by various process factors analytically and numerically. We show that both the sag magnitude of the glass substrate and its variations due to various process factors may be drastically decreased with increased number of horizontal supports. The analytical results are verified numerically with the finite-element method. Introduction There is an increasing need to run larger glass substrates by LCD panel manufacturers. The rapid growth of the substrate size contributes greatly to the low cost manufacturing of LCD panels. However, it also poses big challenges to LCD panel production processes. One of those challenges is the enlarged gravitational sag of the glass substrate. The gravitational sag is defined as the deviation from a flat plane that occurs when a sheet of glass is supported horizontally and allowed to naturally bend due to its own weight. The magnitude of the gravitational sag is a function of the location within a sheet and it has zero value at locations where a glass substrate is physically supported. As one moves away from a supporting location, sagging of the glass substrate increases and eventually reaches its maximum value. If the edges of a glass substrate are not supported, sagging of glass substrate also takes place at the edges. Therefore the gravitational sag can take its maximum either at these edges of the substrate or somewhere between supporting lines. For practical use, the most important number of the gravitational sag is its maximum value. Therefore, we use the

term “sag” to denote the maximum gravitational sag in what follows. As the substrate size grows, LCD panel makers and equipment vendors need to carefully design substrate handling systems to avoid glass breakage or scratches during processing. Glass breakage may occur at various process steps if glass handling systems are not properly designed and the sag magnitude of the glass substrate becomes too large. Scratches or breakage may also occur in glass cassettes due to sag variations. Major causes for sag variations include variations of the unsupported spans of the glass sheet between...

3.1 Sensitivity to the optimum support position Figure 1 Schematic of the glass substrate supports (a) N =2 supports, (b) N = 3 supports, (c) N = 4 supports, W is the width of the glass substrate. To validate this approach we compared the glass substrate shape due to gravitational sagging calculated from equations (2), (3) and Table 1 with results of FEM calculations (Figure 2). We assume E = 7.0967 x 107 kPa, ν = 0.23, ρ = 2.37 g/cm3 corresponding to EAGLE2000™ glass, substrate width W = 1850 mm and thickness t = 0.7 mm. Figure 2 shows very good agreement between numerical and analytical...

lines drastically decreases the sag variations even though the nominal sags are similar. The range of sag variations (i.e. sag for δ = – 10mm deviation from flat plane minus sag for δ = + 10mm deviation from flat plane) decreases by order of magnitude when the number of supporting lines N changed from 2 to 4. 0 2 3 4 number of supporting lines, N Figure 4 Sag variations for the support position deviation by ±1% from the optimum value of p = a, b, or c and their dependence on number of supporting lines N. ∆p = p - popt. Figure 4 is another illustration of the sag sensitivity to deviation of...

possible to handle large glass substrate reliably by designing good supporting system such as increasing supporting lines. These findings imply that the technological change from solid supports to air-bearing supports may be very advantageous for the next generation of glass substrates. References [1] G. Meda, “Support design for reducing the sag of horizontally supported sheets”, Proceedings of SID’00, paper 13.2 (2000) [3] E. G. Caillot and G. Meda, “Support design for reducing the gravitational sag of horizontally supported glass substrates”, Proceedings of Taiwan FPD Expo Conference...

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