Thermal control of the bead portion of a glass ribbon

A method for fabricating sheets of glass comprising:

• (A) producing a glass ribbon using a drawing process, the ribbon having:
• (i) a center line,
• (ii) a first edge,
• (iii) a second edge,
• (iv) a first bead portion which begins at the first edge and extends inward towards the center line, and
• (v) a second bead portion which begins at the second edge and extends inward towards the center line, and
• (B) cutting sheets from the glass ribbon;
• wherein at a down-the-draw location, step (A) includes cooling at least one of the bead portions at a rate such that the heat flux Q″b in kilowatts/meter2 from the thickest part of the bead portion satisfies within ±10% the relationship:
• Q″b=Q″q+ΔQ;
• where:
• (a) each of Q″b, Q″q, and ΔQ″ are heat fluxes from one side of the ribbon;
• (b) the down-the-draw location is below the point where the center line and bead portions of the ribbon have reached their final thicknesses;
• (C) Q″q is the heat flux in kilowatts/meter2 at the down-the-draw location at a transverse position adjacent to the bead portion at which the ribbon's thickness tq equals 1.05*tcenter, where tcenter is the final thickness of the ribbon at the center line;
• Δ
• ⁢
• ⁢
• Q
• ″
• =
• ρ
• ·
• C
• p
• ·
• v
• ·
• t
• q
• 2
• ·
• T
• q
• ′
• ·
• (
• t
• b
• t
• q
• -
• 1
• )
• (
• d
• )
• where ρ is the glass' density, Cp is the glass' heat capacity, v is the down-the-draw speed of the ribbon, tb is the thickness of the thickest part of the bead portion, and T′q is the rate of change with distance down the draw of the ribbon's temperature evaluated at the down-the-draw location and at the transverse position where the ribbon's thickness equals tq;
• and
• (e) at the down-the-draw location, the temperature of the ribbon at tb is within ±20° C. of the temperature of the ribbon at tq.