Analytical Approach to Evaluate Maximum Gravitational Sag and its Variations of Glass Substrate for LCD0 pages

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