John H. Chumley

Advanced Projects Group

The paper describes a technique for modeling the forming of a TV glass panel from the formation of the droplet of molten glass (gob) delivered to the forming machine (ELP) through the pressing and cooling operations including the annealing oven (lehr). To assure the continuity of the solution the model also tracks the return of the empty mold parts to their initial position on the ELP. Because of the complexity of the problem and variety of solution domains involved multiple solution techniques are required, however, the basic strategy is the sequential solution of individual finite element models first to determine the temperature history. That thermal history is then used as an input for the structural solution of the glass including residual stress calculations, after the Narayanaswamy model. The intent of the model is to be of sufficient detail and robust enough to accurately predict the condition of the actual product during and after this complex operation from first principles using only readily observable forming parameters as input. One way coupling is achieved by taking the ending temperature of each component from the previous time-step it participated in as the starting temperature for the current time-step. Since the process is cyclic the process is allowed to loop back upon itself until a quasi-steady state temperature is achieved. The only new heat energy input for each new cycle is from a fresh gob. Film coefficients, which are only weakly coupled to the temperature of the mold equipment, have been calculated off line using the FLOTRAN CFD code. Since the actual, filling of the mould takes only a small percentage of the process time – and occurs above the glass temperature – it was also modeled offline using the DeForm finite element code. The pressing model results are only used to map the temperature drop during the pressing operation from the gob to the fully formed panel. The gob’s initial temperature distribution is taken as a given for the analysis.

Figure 1 Panel Forming Machine (ELP)

Figure 2a Process Steps (Prc0 through Prc9).

Figure 2b Annealing Lehr air Temperature Curves

As state above, the film coefficients for air-cooling are calculated in a supplemental CFD code. The pattern of the film coefficients is determined by the geometry and flow rate of the air but is not strongly influenced by the actual panel temperature. Therefore, for a given experimental setup the film coefficients at each location can be represented as a polynomial in T and v₀ and calculated in real time for each node as required. There are three separate CFD models used to calculate film coefficients for the forming operation, The film coefficient for the plunger has been estimated from process data. Shown below are the some figures, which illustrate the CFD calculations.

Figure 3a -CFD mesh, 2-Vsum Plot, 3-Film coefficients map, 4-Flow Vectors

Figure 3b (Table Air) 3-CFD mesh Figure 3c (Fixed Wind-Header) 1-CFD mesh

  Figure 3b (Table Air) 1-Vsum Plot, 2-Flow Vectors

Likewise the mould filling during pressing was calculate using a supplemental Program DeForm. Since the pressing operation is only a small part of the total cycle and occurs above the glass transition temperature, it was only necessary to extract the temperature difference from the gob to the finished panel to link the process to the overall model. This task was accomplished by doing a particle trace (backwards in time) in the DeForm code from the panel node positions and calculating the delta temperatures for later use in the ANSYS process model. See Figure 4

Figure 4. Deform Model of Panel Filling.

The results of the model are shown in the following figures which display the ending temperatures for each of the nine temperature calculation processes and the one residual stress calculation plot.

Figure 5. Prc 0 Figure 6. Prc 1

Figure 7. Prc 2 Figure 8. Prc 3

Figure 9. Prc 4 Figure 10. Prc 5

Figure 11. Prc 6 Figure 12. Prc 7

Figure 13. Prc 8 Figure 14. Residual Stress Plot

Figure 15. Temperature Plot for first 200 seconds of Panel Pressing

Figure 16. Temperature Variation of Panel Center Face

Future work will include the use of Discrete Ordinate Method (DOM) radiation analysis capability for calculating heat transfer by radiation within the glass at elevated temperatures. Also, a model of the gob formation process including initial shape and temperature distribution will be added. In the current model radiant heat transfer within the glass is approximated using the Rosseland formulation which is known to over estimate the effect near the surface of a semi-transparent medium, such as glass. For this model an idealized gob shape with a uniform (center to edge) temperature was assumed. The improved gob model will improve the initial temperature distribution for the overall model as well. Work has begun and will continue using the results of the model to refine the forming process to produce desirable changes in the product especially as they relate to residual stress in the finished panel.

A procedure has been demonstrated which combines a variety of distinct sub-modeling techniques into a single coherent model of a complex glass forming process. The model is useful not only to predict the final state of the product, but also to predict the contributions of the various components of the process and assess their effect on the final outcome. A significant fact is that input to the model is only readily measurable physical properties and process parameters that are routinely monitored for process control.

ANSYS users Guide 5.6 (on-line Help System)

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