C A L C U L A T I O N O F O P T I M U M G L A S S H E A T I N G

R E G I M E S D U R I N G T E M P E R I N G

O. I . P u k h l i k , I . A . B o g u s l a v s k i i , R . Z . F r i d k i n , a n d O. N. K h a l i z e v a

UDC 666.155

The c rea t ion of control lable technological p r o c e s s e s for glass product ion is d i rec t ly re la ted to opti- mizat ion of the p a r a m e t e r s of prequenehing heating of the glass , as well as to development of new effective heating techniques in connection with more rapid cooling reg imes [1].

I t is known f rom p rac t i ce that an inc rease in the cooling r a t e of glasses during temper ing requ i res an inc rease in the t empe ra tu r e to which they a r e f i r s t heated. However , the extent to which the quenching t em- pe r a tu r e can be r a i s ed is l imited by the inc rease in the deformat ion of heated glasses . In o rde r to have a given quenching ra te , it is t he re fo re n e c e s s a r y to find the optimum glass heating reg imes (heating t empe ra - tu re , ra te , and time) to ensure minimum deformat ion of the mate r ia l before quenching and min imum-ampl i - tude t e m p o r a r y tensi le s t r e s s e s in the glass during subsequent cooling.

Until r ecen t ly , the technological p a r a m e t e r s for heating of g lasses with different composit ions, d i - mensions , and shapes were se lec ted exper imenta l ly for each temper ing apparatus.

The improvement of industr ial technology for a i r quenching of glass and the development of new tech- nological p r o c e s s e s involving symmet r i c heating [2], a i r - g a s cushioning [3], in f ra red heating elements [4], and var ious liquids (molten sal ts and metals) [5] made it n e c e s s a r y to find the general pr inciples for calcu- lat ion of the optimum glass heat ing r eg imes .

The p re sen t a r t i c le cons iders a quantitative method for calculat ing optimum glass heating reg imes . The c r i t e r i on of optimum conditions was taken to be minimum deformat ion of the a r t i c l e during heating to

. the minimum quenching t empera tu re ts t below which it fai ls at a given cooling ra te .

The t e mpe ra tu r e t~t for a i r - j e t quenching can be assumed to be 590-610~ for ord inary quenching r e - gime~ and 620-640 ~ for rapid quenching [6, 7]. The instant at which the t empera tu re of the center of the glass sheet r eaches tc*r is designated as T*, while the cumulat ive deformat ion at this instant is designated

as f*.

We will use Solomin's method [8] to calculate the deformat ion, i .e . , we will a s sume that, for sheets with giver, geometr ic dimensions

f N ~P ,

where p is the fo rce under whose act ion deformat ion occurs (the force of gravi ty, forces due to fas teners ,

etc.) and 77 is the v iscos i ty of the glass.

The v iscos i ty of the glass is a function of the t empera tu re t , which in turn var ies both with t ime and with the c r o s s - s e c t i o n of the sheet x. We rep lace the filnction ~(t) = ~(x, T) for a given instant with the quantity ~ (T) averaged over the coordinate .

For the case of s imple extension,

1 ~ (1) n 1

Trans la ted f rom Steldo i Keramika , No. 2, pp. 13-15, F eb ru a ry , 1972.

O 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00.

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f, mhar I I ~o~

,ll b ,1/:,r 3 ~ 5 3 7 8 �9 "r, mill

Fig. 1

lg_ ~ Z]h:O

-8 zlv=107 ~ t~'~~176 /

-8,s / ! / /

-9 /: 'y -g,5 ~

-10 600 700 800 900

',' 600 700 800 900 t,~

Fig. 2

Fig. 1. The dash lines r ep resen t the calculated data and the solid lines the experimental data.

Fig. 2. The solid lines r ep resen t a t r ansparen t sheet and the dash lines a nontransparent sheet.

AT, Ss fo

lg e ,dh=O ~h=0,2

-6'5FT7-~--11~2 [ ~ [.F'[~ 72-!T--I ] /It-t=880; / / ! 2 l

q i i ': ' ; ' " Eli ~ U ]

In the case of bending, total r igidi ty of the sheet,

0 40 80 /20 ifO 200 246AtlP t,oC 7o0 800 900 700 80o 9o0 tf,~

Fig. 3 Fig. 4

Fig. 3. i) * - * tst- 590~ Ah = 0; 2) tst = 590~ &h = 0.2 mm; 3) t* t = 590~C, ~h = 0.4 ram; 4) t* t = 590~ Ah = 0 (nontransparent plate); 5) t~t = 6500c , ~ = 0.

Fig. 4. 1) ~ = 0.003; 2) ~ = 0.02 k c a l / c m 2 �9 sec .deg.

where n is the number of l aye rs into which the sheet is a rb i t r a r i ly divided for the calculation and is the l ayer number (counting f rom the center of the sheet).

taking into account the different contributions of the different l ayers to the

where

I _ _ l

n3 ~q ai, rt ~ ctl 1

!

For a sheet resting horizontally on two supports, T

5 p l 3 ! _d~_

where I is the distance between the supports and I is the equatorial moment of inert ia of the sheet c r o s s - sect ion.

Fo r compara t ive evaluations, it is more convenient to calculate the re la t ive deformation

where k is some constant that depends on the loading conditions and the geometr ic dimensions.

(2)

(3)

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t t

(~) .~ (~) (4)

Solution of Eq. (4) in the general case is possible only by numerica l methods, because Of the c o m - plexity of calculating the t empera tu re field in the glass sheet.

In the p resen t investigation, the calculations were made on a computer ; we calculated the part ia l t r ansparency of the glass in the near infrared and visible regions of the spectrum. The tempera ture of the furnace walls and a i r was assumed to be tf, the heating element was assumed to be an absolutely black body, and the convective heat t r ans fe r constant in all cases was 0.0003 c a l / c m 2 � 9 deg. Equation (2) was used to calculate ~(T), s ince the deformation had a bending cha rac te r in mos t cases , even with the glass posit ioned ver t ica l ly in the furnace. The thermophysica l and spectra l charac te r i s t i c s of the glass and the function 7(7) were taken f rom the data in the l i t e ra tu re [6, 9].

Consider ing the approximate nature of the calculations and the imprecis ion of the physical constants used, we were interested in compar ing the calculated and observed values for the deformation. The ex- per imenta l data were obtained with specimens of type VV glass 120 • 120 • 5 mm in size, which were heated in a muffle furnace in a horizontal posi t ion on two supports . The specimen tempera ture and radius of curva ture were measured continuously during heating. The measuremen t p rocedure adopted made it poss ib le to calculate the absolute deformation f f rom Eq. (3). As can be seen from Fig. 1, the calculated and experimental values were in good agreement .

The subsequent calculations consis ted in determining the t empera tu re field in the glass sheet as it was heated to different t empera tu res and calculat ing the re la t ive sheet deformation with different glass thicknesses and given heating conditions.

As a resu l t of these calculat ions, we determined the influence of the following factors on sheet de- format ion: different sheet thicknesses , the t ime for which the glass was heated above the minimum 7" suf- ficient to heat it to a t empera tu re tst , the furnace tempera ture , and the heating ra te .

The influence of different glass thicknesses on deformat ion is due to the fact that, while the thicker .

por t ions of an a r t i c le a re being heated to a t empera tu re 7st , the thinner port ions a re heated to higher t e m - pe ra tu re s and undergo additional deformation.

The second factor is re lated to instabili ty of the heating reg imes under pract ical conditions, which makes it nece s sa ry to inc rease the t ime for which the glass is held in the furnace 7 h by an amount &~ = 7 h - 7 " . The extra t ime for which the glass is held AT above the minimum heating t ime c rea tes additional

deformat ion Ae = e h - e*.

Most of the calculat ions were made for a sheet of type VV glass 4.8 mm thick with different furnace t empera tu res tf; the values of A7 were assumed to be 2, 5, and 10 sec, while the differences in glass th ick- ness All cor responded to 0, 0.2, and 0.4 mm.

Figure 2 gives the resul ts of calculat ion of the re la t ive deformation e of the glass at t~t = 590 ~ As can be seen f rom Fig. 1, high furnace t empera tu res a r e mos t suitable in the ideal case, where At~ = 0 and AT = 0, but even a small deviation f rom 7" resul t ing f rom differences in glass thickness or extra holding cause the optimum furnace t empera tu re to shift abruptly toward lower t empera tures . The optimum furnace tempera ture AtOP t = t~Pt--t~t for different heating conditions is shown in Fig. 3. For real low-intensi ty

temper ing conditions (tst = 590~ the optimum tempera tu re range is 650-690~ (with A7 _ 5 sec), which is c lose to the heating t empera tu re employed in p rac t i ce for many yea r s . A s imi lar pat tern is observed

. for more intense quenching, i .e. , with l a rge r tst , but the value of AtOP t is somewhat increased.

The deformat ion of glass during heating in ord inary temper ing furnaces can thus be mater ia l ly r e - duced by reducing the difference in glass thickness, stabil izing the heating regime, and increas ing the hea t -

ing-e lement t empera ture .

When the heat-exchange ra te is increased, t~ pt is displaced toward lower tempera tures (Fig. 4). The value of eopt is vir tual ly independent of the heat -exchange ra te at Ah = 0 mm; an increase in the hea t - ex - change coefficient ~ at Ah = 0.2 mm leads to a slight dec rea se in ~opt (but over a na r rower tempera ture range). The hea t - t r ans fe r coefficient can be increased by heating the glass wi tha s t r e a m o f hot gas, as in a i r - g a s cushioning or when liquid media a re used as the hea t - t r ans fe r agent (molten salts and metals) .

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The calculation results given above a re for the comparatively simple case of glass heating without consideration of the convective currents , possible nonuniformity of heating, heating-element spectral char - acter is t ics , and other factors. When numerical calculation methods and a computer are used, a large number of additional factors presents no fundamental difficulties.

The proposed method makes it possible to analyze virtually any heating variants for both existing and planned heating units, taking into account their character is t ics and the propert ies of the art icles (shape, geometric parameters , viscosity, softening temperature, and spectral characterist ics) . Economic indices (electricity consumption, productivity, etc.), can subsequently be included in the calculations.

Use of this method will apparently be most effective in development of new heating methods, such as heating on an a i r - g a s cushion, infrared heating with surface cooling, etc. It permits selection of the opti- mum technological and structural parameters , which will later require comparatively slight correct ion during practical development of the process .

1o 2. 3. 4. 5. 6. 7. 8. 9.

LITERATURE CITED

I. A. Bo~slavskii, High-Strength Tempered Glasses [in Russian], Stroiizdat(1969). A. G. Shabanov, Steklo i Keram., No. 9 (1968). US Patent Nos. 3342573 and 3338697. US Patent No. 3293021. US Patent Nos. 2146224 and 3451797. R. Gardon, The 8th International Congress on Glass, Brussels (1965). A. G. Shabanov et al., Steklo i Keram., No. 5 (1970). N. V. Solomin, Hot Strength of Materials and Components under Load [in Russian], Stroiizdat (1969). Handbook of Glass Production [in Russian], Vol. I, Stroiizdat (1967).

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