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

Transcription

1 Analytcal Approach to Evaluate Maxmum Gravtatonal Sag and ts Varatons of Glass Substrate for LCD Techncal Informaton Paper TIP 37 Issued: November 24 Supercedes: xxxx H. Kurok, A. Kobyakov, and Meda Cornng Incorporated, Cornng, NY Abstract We present analytcal formulas to evaluate the gravtatonal sag of glass substrate for lqud crystal dsplay (LCD). The formulas are derved for the parallel lne supports (knfe-edges). Past studes, and comparson wth fnte element analyss n ths paper, show that a contnuous lne support s a very close approxmaton to collnear pont supports wth the knd of support spacng typcal n today s cassette desgns. Two, three and four supportng lnes are consdered. A new concept of ntal shapes of the glass substrate s ntroduced to enable evaluaton of sag varatons caused by varous process factors analytcally and numercally. We show that both the sag magntude of the glass substrate and ts varatons due to varous process factors may be drastcally decreased wth ncreased number of horzontal supports. The analytcal results are verfed numercally wth the fnte-element method. Introducton There s an ncreasng need to run larger glass substrates by LCD panel manufacturers. The rapd growth of the substrate sze contrbutes greatly to the low cost manufacturng of LCD panels. However, t also poses bg challenges to LCD panel producton processes. One of those challenges s the enlarged gravtatonal sag of the glass substrate. The gravtatonal sag s defned as the devaton from a flat plane that occurs when a sheet of glass s supported horzontally and allowed to naturally bend due to ts own weght. The magntude of the gravtatonal sag s a functon of the locaton wthn a sheet and t has zero value at locatons where a glass substrate s physcally supported. As one moves away from a supportng locaton, saggng of the glass substrate ncreases and eventually reaches ts maxmum value. If the edges of a glass substrate are not supported, saggng of glass substrate also takes place at the edges. Therefore the gravtatonal sag can take ts maxmum ether at these edges of the substrate or somewhere between supportng lnes. For practcal use, the most mportant number of the gravtatonal sag s ts maxmum value. Therefore, we use the

2 term sag to denote the maxmum gravtatonal sag n what follows. As the substrate sze grows, LCD panel makers and equpment vendors need to carefully desgn substrate handlng systems to avod glass breakage or scratches durng processng. Glass breakage may occur at varous process steps f glass handlng systems are not properly desgned and the sag magntude of the glass substrate becomes too large. Scratches or breakage may also occur n glass cassettes due to sag varatons. Major causes for sag varatons nclude varatons of the unsupported spans of the glass sheet between cassette s support pns, thckness varatons of the glass substrate, and varatons and non-unformty of LCD manufacturng processes such as flm deposton. Sag varatons are unavodable to some extent because none of these causes can be elmnated completely. In prevous studes [1-3] the sag magntude has been calculated as a functon of the number of supportng lnes and the optmum support postons (where the sag s mnmum) have been dentfed. In ths paper we extend the approach proposed n [1-3] towards some non-flat ntal shapes of the glass substrate and perform the senstvty study for the large sze (Generaton 7) glass substrates. We ntroduced the non-flat ntal shape to the glass substrate as a proxy for sag varatons caused by prevously descrbed factors. To model sag varatons due to varous factors such as unsupported length of cassette, glass substrate thckness, or flm stress, we ntroduced convex or concave ntal shape to the glass substrate. Ths study s amed to show how gven sag varatons (whatever the causes are) can be reduced by ncreasng number of supportng lnes. The remander of the paper s organzed as follows. In Secton 2 we brefly descrbe the analytcal approach to calculate the LCD glass substrate sag, present formulas for calculaton of the substrate shape, and valdate the approach wth numercal calculatons performed usng the fnte element method (FEM). In Secton 3 we dscuss the sag senstvty to the optmum support poston and the effect of the ntal shape of the glass substrate. Man conclusons are drawn n Secton 4. where x s the transverse coordnate (see Fgure 1), w s the deflecton of the sheet n the vertcal drecton (see Fgure 2), E s the Young modulus, ν s the Posson s rato, I s the moment of nerta of the cross-sectonal area and P s the weght per unt of length. The factor (1-ν 2 ) n equaton (1) apples for plates though not for beams; for detals, see [5]. Substtuton of values of I and P and straghtforward ntegraton of (1) results n the polynomal equaton ( x + Q x + Q x + Q x ) w ( x) = R + Q (2) where ρg(1 ν ) R = (3) 2 2Et and ρ s the glass densty, g = 9.8 m/s 2 s the acceleraton of gravty and t s the substrate thckness. The coeffcents Q ( =,1,2,3) of the polynomal n (2) are to be found from boundary condtons for each secton of the plate (denoted by I and II n Fgure 1). Boundary condtons nclude symmetry consderatons [ w( x) = w( x) ], contnuty at the ponts of support, and fxed support and free end condtons [4]. As a result, four algebrac equatons for four unknown coeffcents Q can be wrtten for the sectons I and II. The straghtforward soluton of the system results n the desred coeffcents of the polynomal (2). Fgure 1 schematcally shows the support confguratons we prmarly study whle the correspondng substrate shapes can be nferred from Table 1 where Q are lsted as a functon of the supportng lnes separaton. Note that for N = 4 the expressons become farly lengthy, so we only lst a partcular case when one of the supports concde wth the substrate edge (d = W). Wth the substrate shape w(x) known, the glass substrate sag s can be found as s = mn w( x). (4) x [, W / 2] 1 2. Analyss To determne the shape of the glass substrate restng on knfe-edge supports we use the same approach as for the analyss of the beam deflecton [4]. Smlarly, the deflecton of the glass substrate on vertcal drecton w(x) wth the homogeneous flexural rgdty can be found from the fourth-order ordnary dfferental equaton [4] EI (1 ν 2 ) 4 d w = P 4 dx (1) TIP 37 2

3 I II 3. Results and dscusson (a) N =2 (b) N =3 - W/2 a b W/2 x 3.1 Senstvty to the optmum support poston Obtaned analytcal results allow for optmzaton of the poston of the supportng lnes that mnmzes the plate sag [2, 3]. For example, for the case of two supportng lnes (N = 2) straghtforward calculatons lead to a cubc equaton 4k k = for the optmum rato k 2 = a opt /W, < k 2 < 1. The only acceptable soluton s k ,.e. for (c) N =4 Fgure 1 Schematc of the glass substrate supports (a) N =2 supports, (b) N = 3 supports, (c) N = 4 supports, W s the wdth of the glass substrate. To valdate ths approach we compared the glass substrate shape due to gravtatonal saggng calculated from equatons (2), (3) and Table 1 wth results of FEM calculatons (Fgure 2). We assume E = x 1 7 kpa, ν =.23, ρ = 2.37 g/cm 3 correspondng to EAGLE2 glass, substrate wdth W = 185 mm and thckness t =.7 mm. Fgure 2 shows very good agreement between numercal and analytcal calculatons. The clear advantage of the analytcal approach s ts computatonal effcency that becomes especally crtcal for large-sze glass substrates. In addton, sag s dependence on the glass thckness can be straghtforwardly obtaned from (3) wthout repetton of the tme-consumng FEM calculatons. c d a opt = W (5) the glass substrate experences the mnmum sag. Smlarly, for N = 3 the correspondng equaton to solve s 6k k k k = (k 3 = b opt /W) from where we obtan b opt = W. (6) The stuaton becomes more nvolved for the case of four supportng lnes where two-dmensonal optmzaton needs to be performed. The support postons mnmzng the sag are [2] copt =.2658 W, d opt =. 799 W. (7) Fgure 3 Sag varaton for the support poston devaton from the optmum value p = a, b, or c dependng on the number of supports and p = p - p opt (see Fgure 1) Fgure 2 Glass substrate shapes w(x) due to gravtatonal saggng for N=2, 3, and 4. For all cases the dstance between the support lnes s kept constant and equal 1 mm. Sold curves: analytcal results, dashed curves: FEM calculatons assumng L =22 mm where L s the length of the glass substrate along supportng lnes (y axs). Instead of knfeedge supports, the FEM calculaton takes 23 dscrete supports wth equal spacng along the y axs. Fgure 3 shows the sag values near the optmum support poston. Both the sag magntude and ts senstvty to support poston (slopes of the lnes n Fgure 3) decrease wth ncreased number of horzontal supports N. TIP 37 3

4 sag, mm p/p opt = - 1% p/p opt = + 1% p/p opt = % number of supportng lnes, N Fgure 4 Sag varatons for the support poston devaton by ±1% from the optmum value of p = a, b, or c and ther dependence on number of supportng lnes N. p = p - p opt. Fgure 4 s another llustraton of the sag senstvty to devaton of the support poston from the optmum value. For N = 2, sag varaton due to ±1% support poston devaton s more than 5mm. On the contrary, for N = 3 and N = 4, the same varaton of the support poston results only n margnal (< 1mm) sag varatons. We also note that the sag value tself s drastcally decreased n those cases. Fgure 4 demonstrates robustness of the glass transportaton system wth larger number of supportng lnes to varaton of the postons of supportng lnes. 3.2 Effect of the ntal shape To take the ntal shape of the glass substrate nto account, we accordngly modfy the boundary condtons when calculatng coeffcents Q. If, for example, for N = 3 the shape devaton at the central support lne (x =) s w ntal; = δ, the modfed coeffcents Q ~ wll be gven by ~ Q = Q + Q (8) where values of Q are lsted n Table 2. The ntal shape s then added to the resultng polynomal gven by Table 2. Results of ths approach are shown n Fgure 5 where we plot the sag value as a functon of N. FEM calculaton results are also shown n Fgure 5 to verfy the accuracy of the analytcal formulas. It should be noted that unsupported lengths are selected (a = 136 mm, b = 185 mm, and c = 98 mm, d = W = 185mm, for N=2, 3, and 4, respectvely) so that the nomnal sag for a flat ntal shape s approxmately 3mm for all cases (N = 2, 3, and 4). As can be clearly seen from Fgure 5, the ncreased number of supportng lnes drastcally decreases the sag varatons even though the nomnal sags are smlar. The range of sag varatons (.e. sag for δ = 1mm devaton from flat plane mnus sag for δ = + 1mm devaton from flat plane) decreases by order of magntude when the number of supportng lnes N changed from 2 to 4. sag, mm -1 mm, analytcal mm, analytcal +1 mm, analytcal -1 mm, FEA mm, FEA 1 mm, FEA number of supportng lnes, N Fgure 5 Impact of the ntal shape of the substrate on the sag varatons. Rectangles: flat ntal shape, damonds: convex parabolc ntal shape towards the ground, trangles: concave parabolc ntal shape towards the ground. EAGLE2 glass s assumed wth the thckness t =.7 mm and the wdth W = 185 mm; a = 136 mm, b = 185 mm, and c = 98 mm, d = W, for N=2, 3, and 4, respectvely. These parameters correspond to approxmately the same sag of about 3 mm for the flat ntal shape. The ntal glass shape s a symmetrc parabola wth the maxmum varaton n the vertcal drecton of +/- 1 mm. 4. Conclusons Analytcal formulas to calculate sag of the glass substrate are obtaned. We ntroduced a concept of ntal shape of glass substrate to smulate sag varatons whch are caused by varous factors. The formulas can deal wth three dfferent types of support confguratons (number of supportng lnes from 2 to 4). It was confrmed that the formulas gve accurate results for parabolc ntal shapes by comparng wth fnte element analyss results. Our study revealed that sag senstvty to the support postons s drastcally reduced as number of support lnes ncreases. By ntroducng ntal shape concept, we showed that sag varatons caused by varous factors are greatly reduced as number of support lnes ncreases. 9% reducton of sag varatons may be possble by ncreasng number of support lnes from 2 to 4 based on the results derved by ths study. These results mply that large glass handlng can be made more relable by ncreasng number of support lnes. Glass substrate transportaton problems wll become more costly as glass substrate generaton advances. It was shown that t s TIP 37 4

5 possble to handle large glass substrate relably by desgnng good supportng system such as ncreasng supportng lnes. These fndngs mply that the technologcal change from sold supports to ar-bearng supports may be very advantageous for the next generaton of glass substrates. References [1] G. Meda, Support desgn for reducng the sag of horzontally supported sheets, Proceedngs of SID, paper 13.2 (2) [2] G. Meda, Optmal support of plates to mnmze sag, Report L-4822 MAN, Techncal Informaton Center, Cornng Inc., Cornng, NY [3] E. G. Callot and G. Meda, Support desgn for reducng the gravtatonal sag of horzontally supported glass substrates, Proceedngs of Tawan FPD Expo Conference (2). [4] E. P. Popov, Mechancs of Materals, 2 nd edton, Chapter 11, Prentce Hall Inc., Englewood Clffs, NJ (1976). [5] Tmoshenko, S. and Wonowsky-Kreger, S., 1959, Theory of plates and shells, 2nd edton, Engneerng Socetes Monographs. Table 1 Coeffcents of the polynomal (2) for sectons I and II as shown n Fgure 1 Q Q 1 Q 2 Q 3 I (N=2) a 2 (a 2-3(2a-W)W/2 12aW+6W 2 )/16 II a 2 (a 2-16aW+6W 2 )/16 3a 2 W/2-3W 2 /2 2W (N=2) I (N=3) 3(b 2-3W-b/4-3W 2 /(2b) 4bW+2W 2 )/8 II -b 2 (b 2-3b(b W 2 /2 2W (N=3) 4bW+6W 2 )/32 4bW+6W 2 )/16 I (N=4, d = W) (c 2 /32)(c 3 -c 2 W- 9cW 2 +3W 3 )/(2c+ (3/8)(c 3 +c 2 W+3c W 2 -W 3 )/(2c+W) II (N=4, d = W) W) (- c 2 W/32)(c+3W)(3 c 2-6cW+W 2 )/((c- W)(2c+W)) (3c 2 /16)(c+W)(c 2-5W 2 )/ ((c- W)(2c+W)) Table 2 Perturbatons of the coeffcents of the polynomal (2) (3W/8)(- c 3 +7c 2 W+cW 2 +W 3 )/ ((c- W)(2c+W)) (c+w)(c 2-5W 2 )/(4(c-W) (2c+W)) Q for the case of N = 3 supports Q Q 1 Q 2 Q 3 I δ/r -6δ/(b 2 R) 4δ/(b 3 R) II 3δ/(2R) -3δ/(bR) TIP 37 5

6 North Amerca and all other Countres Cornng Dsplay Technologes MP-HQ-W1 Cornng, NY Unted States Telephone: Fax: Internet: Japan Cornng Japan K.K. Man Offce No. 35 Kowa Buldng, 1st Floor , Akasaka Mnato-Ku, Tokyo Japan Telephone: Fax: Internet: Nagoya Sales Offce Nagoya Bldg., 7 F , Me-ek, Nakamura-ku Nagoya-sh, Ach 45-2 Japan Telephone: Fax: Chna Cornng (Chna) Ltd., Shangha Representatve Offce 31/F, The Center 989 Chang Le Road Shangha 231 P.R. Chna Telephone: Fax: Tawan Cornng Dsplay Technologes Tawan Co., Ltd. Room #123, 12F, No. 25 Tun Hua North Road, Tape 15, Tawan Telephone: Fax: Internet: Korea Samsung Cornng Precson Glass Co., Ltd. 2th Floor, Glass Tower Buldng Daech-Dong Kangnam-Ku, Seoul Korea Telephone: Fax: Internet: EAGLE 2 s a trademark of Cornng Incorporated, Cornng, N.Y. 24, Cornng Incorporated TIP 37 6