TWI392846B - Method for predicting conformability of a sheet of material to a reference surface - Google Patents

Description

Method for predicting sheet material compliance on a reference surface

The present invention is directed to a method of predicting the conformation of a sheet of any shape material to a reference surface. In particular, the present invention is directed to a method of predicting the ability of a glass sheet (e.g., suitable for use in a flat panel glass sheet) to conform to a support surface that can be used during sheet processing.

Many environmentally sensitive electronic or photonic devices can benefit from the use of hermetic sealed glass packages. Such devices include photovoltaic devices, organic light emitting diode (OLED) displays, OLED light panels, plasma displays, surface conduction electron emitter displays (SED), and electric field emission displays (FED). For example, a liquid crystal display (LCD) is a passive flat panel display that relies on an external illumination source. It is generally a display that produces segments, or one of two basic designs. The substrate requires two different array types (in addition to being transparent, it can withstand the exposed chemical conditions during display processing). The first type is an internally addressed array based on the low limit characteristics of the liquid crystal material. The second is an externally addressed array or an actively addressed array where a diode array, metal-insulator-metal (MIM) device or thin film transistor (TFTs) is provided for each pixel electronic switch. In both cases, two sheets of glass form the structure of the display. The spacing between the two sheets of glass is a critical gap size of about 5-10 μm. Each substrate glass piece is typically less than about 0.7 mm thick.

Glass processing for large electronic devices for displays or light panels The glass piece is required to conform to the planar shape. Generally, the glass piece can be lightly pressed into a planar shape. Although the glass sheet has strict manufacturing process and specifications, it can be as large as 10 square meters or more, but it is not perfect flat. Therefore, when the forced compliance conforms to the support surface, a tap error may occur and the glass piece may not be completely placed in the plane. This does happen when the glass piece is not a purely developable shape, especially if the support surface itself is not planar.

In view of the broader nature, the present invention illustrates a method for determining the surface compliance of a glass sheet comprising determining the shape of the glass sheet, using a shape at a plurality of points on the glass sheet to calculate a Gaussian curvature value, and a Gaussian curvature from the corresponding support surface. The value is subtracted from the plurality of Gaussian curvature values of the glass piece to determine the Gaussian curvature value difference of each point of the plurality of points on the glass piece, and the maximum Gaussian curvature value difference of the glass piece is selected from the plurality of Gaussian curvature value differences, and the maximum Gaussian curvature value is compared. The difference and the set maximum low limit value. If the maximum Gaussian curvature value is equal to or less than the maximum low limit value, the glass piece is classified as acceptable. If the maximum Gaussian curvature value is greater than the maximum low limit value, the glass piece is classified. To be unacceptable.

In some embodiments, the feature classification of the glass sheet shape can be via a gravity-free method, such as placing the glass sheet in a medium density fluid, or supporting a glass sheet on an adjustable support bed, such as an adjustable pin.

The invention will be more readily understood and other objects, features, details and advantages of the invention will be It is clear that in any case it is not intended to limit the use. All such other systems, method features, and advantages are intended to be included within the scope of the invention and the scope of the invention.

In the following detailed description, numerous specific details are set forth However, it will be apparent to those skilled in the art that <RTIgt;the</RTI> <RTIgt; </ RTI> <RTIgt; </ RTI> <RTIgt; In addition, detailed descriptions of well-known devices, methods, and materials are omitted so as not to obscure the description of the invention. Finally, as far as possible, the same reference numerals are used to refer to the same or similar elements.

One method of making flat glass sheets is the so-called melt down draw method. In a molten overflow down draw process forming a glass ribbon, such as shown in Figure 1, the overflow trough member forming the wedge 20 includes an upwardly open passage bounded by the wall portion 24 on the longitudinal side of the wedge 20. 22, suspended above the opposite longitudinally extending overflow lip or weir 26. The outer band of the opposite of the weir 26 and the wedge member 20 forms a surface connection. As shown, the wedge member 20 provides a pair of substantially perpendicular forming surface portions 28, the surface portion 28 and the weir 26 are joined, and a pair of downwardly sloping gathered surface portions 30, substantially in the form of a straight glass draw line. The vertices or roots 32 below the level are aborted. It should be understood that the surface portions 28, 30 are provided at each longitudinal edge of the wedge 20.

The molten glass 34 is fed to the transfer conduit 36 connected to the passage 22 to Channel 22. Feed to channel 22 can be single ended or, if desired, double ended. A pair of dams 38 for restriction are provided over the weirs 26 adjacent the respective ends of the channels 22 to direct the overflow of the free surface 40 of the molten glass 34 above the weir 26 as a separate flow, down to the opposite formation The surface portions 28, 30 reach the root portion 32 where they are gathered to form a ribbon of the initial surface glass 42 as shown by the chain lines. The draw roller 44 is placed downstream of the root 32 of the wedge member 20 and serves to adjust the speed at which the glass forming ribbon exits the collection forming surface, thereby determining the nominal thickness of the ribbon.

Preferably, the trailing roller is designed to contact the glass ribbon at its outer edge, specifically, a beaded inner region that is thickened at the edge of the ribbon. The edge portion of the glass that contacts the drag roller will be removed from the glass sheet. At each edge of the ribbon, a pair of opposing counter-rotating pull rollers are provided.

The glass ribbon 42 is pulled down through the pull-out portion of the device, and the ribbon undergoes intricate structural changes, not only in physical dimensions but also at the molecular level. For example, in forming a wedge-shaped root that changes from a thick liquid form to a hard band about half-millimeter thick, by carefully selecting the temperature field or temperature distribution, carefully balancing the mechanical and chemical requirements to complete the liquid or The transition from a viscous state to a solid or elastic state. At a point within the elastic temperature region, the ribbon is cut at the cutting line 48 to form a glass sheet or panel 50.

While glass manufacturers use strict manufacturing controls like the one described above to form glass, these glasses may not be perfect planar shapes. For example, in the above melt drawing process, by only contacting the strip side The roller of the edge portion may warp the central portion of the ribbon from the glass ribbon that is drawn by the wedge. This warpage may be caused by the movement of the ribbon or by the interaction of various thermal stresses within the ribbon. For example, the vibration generated by the downward cutting process on the ribbon may propagate upward to the viscoelastic region of the ribbon, freezing into a sheet shape, confirming the deviation of the planarity of the elastic strip. Variations in the overall ribbon width and/or length temperature may also result in variations in planarity. Indeed, when each piece of glass is cut from the strip, it may partially relieve the stress of the ribbon freezing, perhaps resulting in an uneven surface. In short, the shape of the glass sheet derived from the ribbon is determined by the thermal history of the ribbon during the transition of the ribbon through the viscoelastic region, and this thermal history may also vary. Such changes in stress and/or shape may be detrimental to processes that rely on dimensional stability, such as the deposition of circuitry onto a substrate as seen in the fabrication of liquid crystal displays. For example, in the manufacture of liquid crystal displays, large glass sheets that are cut from a drawn glass ribbon can themselves be cut into a plurality of smaller sections. Each block can therefore cause a re-distribution of the stress redistribution and thus a change in shape. Thus, when the resulting glass sheet is generally considered to be planar, the surface of the glass sheet will actually exhibit amplitudes and troughs that may interfere with the planarization of the glass during subsequent processing. Therefore, this method is preferably designed to accurately determine the shape of the glass sheet that is cut from the strip. The information obtained can thus be used to modify the thermal history of the drawn glass ribbon.

The display manufacturer receives the glass flakes from the glass manufacturer and further processes the glass flakes to form a display device, or other device that includes a glass sheet. For example, the system of the organic light emitting diode display shown in FIG. One or more layers of organic material 54 are deposited on the first glass sheet 56 (e.g., substrate 56). The first piece of glass is often referred to as the backing plate. Backsheet 56 may also include thin film transistors (TFTs) and electrodes (not shown) to supply organic layer current and cause it to illuminate. However, since the organic material layer 54 is sensitive to various environmental factors such as moisture and oxygen, the organic layer must be closely isolated from the surrounding environment. Thus, the organic layer is tightly sealed within the glass envelope formed by the backsheet 56 and the second glass sheet 58, sometimes also referred to as a cover, and the sealing material 60 is placed between the backsheet and the cover glass.

A number of sealing methods can be used to join the backsheet and cover glass sheets, including the use of an adhesive. Adhesives are easy to apply and use, but must be tolerant of the tightness required to ensure that the device can exhibit an industrially viable service life before failure. That is, moisture and/or oxygen may eventually penetrate the adhesive seal, causing degradation of the organic layer and display device.

A more practicable way is to form a frit seal between the backsheet and the cover glass. In this way, the strands of the frit seal material are distributed in the form of a loop or frame to the cover, after which the frit cover is heated to adhere the frit to the cover. The cover 58 is then placed on the backing plate 56 with the frit 60 (and the organic layer 54) placed therebetween. The frit 60 is then heated, such as by launching a laser beam 66 with a laser 64, softening the frit and forming a tight seal between the backing plate 56 and the cover plate 58.

It is conceivable from the above description that during the various deposition processes of the organic layer and the TFT and the joining and sealing of the glass sheets, it is necessary to precisely align the back sheets and/or the cover sheets. In general, the substrate needs to be planar during this forming process. For example, the back substrate usually has a vacuum to a flat support table. Face, used to deal with.

One way to measure the flatness of flat glass is to measure the maximum "warpage" of the glass. That is, measuring the distance (or deviation) of a plurality of points on the surface of the glass sheet, which is determined according to the reference surface, and the deviation of the distance represents the deviation of the shape of the glass sheet from the true plane, that is, the warpage of the glass sheet. It is then possible to use the maximum warpage to measure the shape of the glass sheet (such as the flatness of the glass sheet), although it may not be accurate.

Figure 3 illustrates a method of determining the shape of a glass article such as a glass sheet in accordance with an embodiment of the present invention. In accordance with the embodiment of the invention of FIG. 3, generally designated reference numeral 68, a glass sheet 70 is placed in a container 72 containing a fluid 74. The glass sheet 70 can be placed on the surface of the fluid or immersed in the fluid, as described in more detail below. The glass sheet has a predetermined average density and a predetermined average refractive index. The fluid also has a predetermined average density and a predetermined average refractive index. Preferably, the fluid has an average density of at least about 85% of the average density of the glass sheets; more preferably at least about 90%; still more preferably at least about 95%. When the average density of the fluid is at least about 85% of the average density of the glass sheets, it can be said that the fluid 74 is of medium density relative to the glass sheet 70. The glass sheet is considered to be moderately floating, so the glass sheet should be maintained in the fluid 74. A fixed position inside, without the need for mechanical support, has enough time to complete the desired measurement. For example, a suitable fluid is available from Cargille Inc., which is a refractive index matching liquid, immersion liquid, light coupling liquid, refractometer liquid, and other special liquids. These liquids are very beneficial because they are generally non-toxic and it is easy to adjust the fluid density, such as increasing or decreasing the concentration of evaporation. Fluid tight The degree of adjustment can also be achieved by mixing two or more fluids of different densities to achieve a desired average density of the mixture. For example, Eagle 2000 glass manufactured by Corning Incorporated has an average density of about 2.37 g/cc. A plurality of fluids such as a first fluid having an average density of 2.35 g/cc and a second fluid having an average density of 2.45 g/cc can be mixed in an effective amount to obtain a third fluid having an average density of 2.37 g/cc. Those skilled in the art will appreciate that any fluid of the desired density properties can be used.

Continuing with Figure 3, sensor 76 can be used to measure the distance of the sensor from the surface of the glass sheet. The glass sheet 70 includes a first face 78 (sensor face) facing the sensor 76 and a second face 80 that does not face the sensor. In the current embodiment, the sensor face 78 may be referred to as a top face 78 and the non-sensor face 80 may be referred to as a bottom face 80. To ensure that the glass surface is detectable by the sensor 76, the average refractive index of the fluid 74 preferably detects an average refractive index different from that of the glass sheet 70. The allowable difference between the average refractive index of the fluid and the average refractive index of the glass sheet is determined by factors such as the sensitivity of the sensor 76. Alternatively, if a sensor cannot distinguish the difference between the average refractive index of the glass sheet and the average refractive index of the fluid, a film or coating (not shown) may be applied to the surface of the glass sheet 70, preferably coated on the glass. The bottom side of the sheet is used to obtain the distance measured between the sensor and the glass coating interface. If the coating is tightly adhered to the top surface 78 (sensor surface), measurement of the coating itself may also result in erroneous measurements, as that would measure the surface of the film rather than the surface of the glass. Although not required, the coating is preferably opaque and may comprise a coating of ink or colorant. We found a white opaque coating for optimum results. However, any measurable Coatings having a refractive index different from the refractive index of the fluid are acceptable. For example, the coating can comprise a polymeric film where the average refractive index of the polymer can be measured differently than the average refractive index of the fluid. Any stress applied to the glass sheet 70 is preferably insufficient to additionally cause malformation of the glass sheet. For this reason, the coating can be applied to the glass sheet in a discontinuous manner, such as in a series of dots, lines or other shapes. Alternatively, the thickness of the glass sheet can be measured as a function of the position on the glass sheet, combined with the distance data of the film-glass interface to create the contoured surface of the glass sheet sensor surface.

Depending on the embodiment, once the glass sheet 70 is placed in the fluid 74, the sensor 76 can be utilized to measure the distance from the sensor to the surface of the glass sheet. The sensor 76 can be utilized to measure the distance d ₁ between the sensor and the top surface 78 of the glass sheet, or the sensor 76 can be used to measure the distance d ₂ between the sensor and the bottom surface 80 of the glass sheet. . The sensor 76 can be used to measure d ₁ and d ₂ , from which it can be determined that the thickness of the glass sheet at any point is t = d _{2 -} d ₁ . For example, sensor 76 can include a laser shift sensor. However, sensor 76 may also include other devices known in the art, such as a sensor for sound as a measurement. The laser device can include a simple laser ranging device, or a more sophisticated device such as a Michelson interferometer. The sensor can be time-based, here like sound, and the sensing energy with a known velocity in the fluid is temporal. One suitable sensor is the LT8110, a laser-shifted sensor that is manufactured by Keyence Corporation of the United States. While the sensor 76 can be placed over the surface of the fluid, the sensor preferably contacts the fluid, thereby advantageously eliminating the air-fluid interface of the fluid surface 82. The sensor 76 can also be completely submerged in the fluid.

Another way to determine the shape without gravity is to use a so-called nail bed (BoN) measurement system, as depicted in Figure 4. In the BoN measurement system, the glass piece is supported by the following set of pins. This pin can move vertically and measure the support of the glass piece. It is also possible to measure the movement of each pin.

The height of the pins can be adjusted until each pin supports a specific target weight. For example, a planar substrate placed on an equally distributed pin has a target weight equal to the equivalent fraction of the entire weight of the substrate. However, each target weight may not equal the next one, and the target weight is determined based on the stress analysis of the finite element analysis. When all the pins are of a specific weight, the supported substrate is its gravity-free shape. The pin array with its gravity-free position can measure the gravity-free shape by optically scanning the surface of the substrate and measuring the height of the entire surface of the pin and the pinch therebetween.

The problem with BoN measuring instruments is that changing the height of a single pin may change the weight on all other pins. An extreme example, for example, is that a pin is lifted high enough to lift the substrate onto the top of the mating pin. The mating pins do not bear any weight and therefore do not touch the substrate. Therefore, when the height of the pin is adjusted, the target weight of the support changes immediately, and when the height of the other pin changes, the supported weight changes. If the system is manually adjusted, it will take a lot of time to adjust the pin. If the system is automated, an algorithm is needed to adjust the pin.

In the earlier system, the manual adjustment was made to adjust each pin separately. Adjust the height of each pin until the target weight is reached. This adjustment Make one adjustment of the pin at a time, from the first pin to the last pin. However, since adjusting one pin will change the load of all other pins, this program must be repeated over and over again, each cycle correcting small deviations caused by the previous cycle.

In accordance with one or more embodiments, the present invention includes adjusting the height of the pin to simultaneously support the target weight of all of the pins. In particular, the calculation and execution of a system of pin pin arrays with appropriate pin height adjustment is provided. When all the pins are at a certain height, the height is the gravity-free height of that substrate. The gravity-free pin array provides a gravity-free shape measurement, if any, with potential shape distortion. The height adjuster of the pin can also record the height of the pin and eliminate additional height measurement methods such as optical scanners.

However, all pins can be adjusted at the same time. There is no need to evaluate the power of the pin until all pins are adjusted at the same time. If the pin does not move, the force of the pin is the upward force of the pin equal to the downward force supported by the pin. By adjusting a full set of pins, this process illustrates the fact that adjusting one pin affects all other pins. Thus, the benefits of achieving the target pin force on all pins can be achieved in almost every example.

Referring to Figure 4, illustrated is a nail bed shape meter 100 in accordance with one or more embodiments of the present invention. The BoN meter can include a plurality of pins 110, at least three pins 110, a meter base 120, and a processor 130. An elastic plate-like object is taken as the measuring body 140, which is described herein as a glass substrate 140. The substrate 140 is placed at the top end of the plurality of pins 110, and when the measuring body 140 is flexed under gravity, each pin 110 Will bear a specific weight. Each pin 110 includes a load element 112 to measure the weight supported by the pin 110. The load element 112 can be placed above the height adjuster 114. This device is preferably automated with a motor to adjust the height of the pin 110 in a known manner. Other arrangements, such as having the load element 112 underneath to burden the height adjuster 114, may also be used.

The load element 112 can transmit and measure the pin force related measurement signal 132 to the processor 130 via the circuit 116, and the processor 130 then performs an algorithm to calculate the height adjustment required for each pin 110. The processor 130 can transmit the adjustment signal 134 to the height adjuster 114 via the circuit 116 to perform the calculated height adjustment. It is often the case that the better the algorithm, the faster the load component 112 can read the target load.

The present invention takes advantage of the fact that changing the height of one of the pins 110 generally changes the load of all of the pins 110. N pins 110 are used in the gauge 100. The purpose is to find the pin height so that the force of each pin 110 is at a certain value. For example, in a substantially planar substrate 140 of relatively uniform thickness and density, it can be assumed that the masses are approximately equally distributed, assuming that there are N pins 110 that are equally distributed such that a particular weight value is equal to 1/N of the weight of the substrate.

According to one embodiment, three of the pins 110 are not adjusted, so these are not moving in each cycle. The three stationary pins 110 are fixed to the reference plane, so the three pins 110 should not be in a straight line. These three pins remain fixed in each cycle. Can be adjusted in the continuous cycle. Therefore, all remaining N-3s can be adjusted as described below. A pin 110 is also used to support a particular weight.

Calculating the pin height adjustment of the remaining N-3 pins 110 can be considered as a set of simultaneous equations, with N-3 equations and N-3 unknowns, used to indicate the association between pin height change and pin weight change. . The three fixed pins define the reference plane for the association of the equations. From a physical point of view, the sum of the forces, the sum of one of the axle moments, and the sum of the other axle moments represent the three equations that must be met. By fixing the three pins, the target weight of the three pins can be systematically satisfied by adjusting other pins, and thus the target weight of the pins is satisfied. From a geometric point of view, these three points are not fixed, although less than ideal, rigid motion is possible. Rigid motion can translate the substrate and rotate along two different axes, producing more than one set of solutions for the pin height adjustment equations. Therefore, these three points are fixed so that there is only one set of solutions for the pin height adjustment equations.

The warpage measurement just described can only simply indicate the surface topography of the glass sheet, so the ability to flatten the glass sheet itself is a weak indicator, such as vacuuming the glass sheet into a flat pedestal. For example, a sheet of material 200, such as a thin glass sheet, includes a longitudinal ridge 202 that extends along the length of the "sheet" such that the maximum deviation of the ridge from the reference plane 204 is parallel to one side of the sheet. L + δ, as shown in Figure 5. It is assumed that the shape of the ridge is like a part containing a cylindrical shape. The second sheet of material 206 comprises a concave surface 208 (such as a hillock or bubble) on the surface of the sheet of material, as shown in Figure 6, where the maximum deviation from the concave surface to the same reference plane 204 is also L + δ. Two sheets of glass show the same maximum warpage (δ). However, due to The inclusion of a cylindrical shaped ridge (Fig. 5) for the sheet of material 200 is expandable and is easier to planarize than a sheet of material 206 having a concave surface.

The expandable surface is a surface that does not need to be stretched, compressed or torn to flatten the surface. For example, as shown in Figure 7A and the cylindrical shape discussed above, the expandable surface is included because the cylindrical surface can be flattened without the need to stretch or tear the surface (Figure 7B). In other words, the spherical surface (Fig. 8A) is not expandable. Try to flatten a portion of the sphere, such as a hemisphere, which must extend or tear along multiple edges to conform (Figure 8B). Thus, in the previous embodiment, a glass sheet having a cylindrical ridge may be flattened into a planar pedestal without deforming the sheet of material, but conforming to the second exemplary sheet of material to the pedestal requires deforming or tearing the sheet of material.

The expandable surface is convertible into a planar surface by retaining angles and distances. When the deployable surface is converted into a planar surface, no strain is introduced into the surface. Alternatively, the deployable surface is a surface that can be formed from a planar surface without the need to stretch, compress or tear. It is clear that the glass sheet characterized by maximum warpage may be sufficient to show that the glass sheet is not flat, but it is quite unsuitable for measuring how the glass sheet is forced to become a flat design.

The Gaussian curvature K of the surface is the geometric property inside the surface and is defined as the product of the major curvatures k ₁ and k ₂ at a point on the surface. That is, K = k ₁ k ₂ . In fact, the Gaussian curvature is a description of how the surface is offset from the planar surface. The mathematical derivation of Gaussian curvature is well known and will not be widely covered here. It is more instructive to consider the practical significance of Gaussian curvature. First, just measure the distance and angle on the surface. For example, if the Gaussian curvature of the surface is positive, the surface at that point will contain bumps or sharp peaks; if the Gaussian curvature is negative, the surface will contain a saddle point. However, if the Gaussian curvature is zero, the surface at that point is equal to the flat surface. A simple experiment can be used to illustrate this difference. The sum of the angles of the triangles drawn on the spherical surface (positive Gaussian curvature) is greater than 180 degrees, and the sum of the angles of the triangles drawn in the cylindrical (Gaussian curvature = 0) must be equal to 180 degrees. The expandable surface Gaussian curvature is zero and can be converted to a planar surface without the need to stretch, compress or tear. If the surface can be flattened without causing strain, the Gaussian curvature remains fixed. It is therefore instructive to know the size of the Gaussian curvature of the surface to understand the extent to which one surface conforms to the other.

In accordance with an embodiment of the present invention, Gaussian curvature can be utilized to describe the compliance of a glass sheet to a reference surface, such as a surface of a supporting glass sheet. The glass sheet preferably conforms to the support surface, meaning that the Gaussian curvature at each point of the glass sheet conforms to, or nearly conforms to, the Gaussian curvature at each point of the support surface. If the reference surface is planar, the glass sheet should also have a zero Gaussian curvature at each point on the surface to accurately conform to the reference (eg, support) surface. The greater the magnitude of the difference between the Gaussian curvatures, the greater the resistance of the glass sheet to compliance. In another way, the difference between the Gaussian curvature value at each point on the glass sheet and the corresponding point on the support surface should be equal to or less than the predetermined maximum difference (ΔK=∥K _sheet |-|K _support ∥≦G, where G It is the predetermined maximum value. G is usually determined from experiments or models depending on the application of the glass sheet. Corresponding points refer to the point at which a point on the glass sheet overlaps the support surface a little when the glass sheet is pressed against the support surface. If ΔK is greater than G, the glass sheet may not be sufficient to conform to the support surface. When flattening the glass, the strain energy generated in the glass may cause buckling or stress-induced birefringence in the glass.

From the above point, as shown in Figure 5, the glass sheet is placed on a support surface such as a flat surface. If the glass sheet is only subjected to heavy forces and the reaction force of the pedestal, we can expect that the Gaussian curvature value of a single peak or trough will not Change too much. This is more realistic as the Gaussian curvature increases. As the Gaussian curvature increases, the resistance of the glass sheet to flattening increases, and more force must be used to flatten the glass. As described above, this can lead to increased damage effects (buckling, stress, etc.) that can affect a particular manufacturing process. Conversely, a larger Gaussian curvature value requires more force to flatten the glass sheet. First, the curvature of the glass sheet appears in the area with the expandable shape because it requires less energy than the area of the non-expandable shape. Figure 9 shows the relationship between the flatness of the glass sheet and the force that must be applied to achieve the corresponding flatness. The surface to the left of the vertical dashed line represents the expandable shape, while the surface to the right of the line represents the shape that is not expandable. As shown, the area 210 of the expandable surface of the plot curve can be easily flattened with only a small amount of force, and the only resistance to flattening is the stiffness from the surface. In other words, an unexpandable surface requires more power. The buckling of the surface may occur in the region 210 of the plotting curve, and as the force of the flattening increases, a large film force and force moment are produced in the region 214. For large singular points of Gaussian curvature values, when applying relatively weak forces (such as only heavy forces), we hope that the singular points of Gaussian curvature values will not be affected.

In order to make good use of Gaussian curvature, we better understand the gravity-free shape of the glass piece. That is, the shape of the glass piece is to be obtained without gravity. When the true gravity-free state is to be achieved on Earth, the condition of the gravity-free state can be approximated. For example, we can use a medium density system.

Once the shape of the glass sheet is determined, such as by a gravity-free glass sheet shape measurement method to determine the deviation of a plurality of points in the reference plane, the Gaussian curvature of the glass sheet can be determined at each point. For example, a close paraboloid approach can be used to determine the Gaussian curvature of a localized area of the glass sheet. Gaussian curvature K, mean curvature H, paraboloid 2z = ax ² + bxy + cy ² at its vertex K = ac - b ² , and H is (a + c) / 2. The intersection of the paraboloid and the normal at its apex P is a parabola, and the curvature at P is k _n =k ₁ cox ² θ+k ₂ sin ² θ, where k ₁ and k ₂ are equations k ² -2Hk+K=0 root, and this plane is θ and an angle between k _n reaches its maximum (or minimum). The extreme values of K _n , k ₁ and k ₂ are the principal curvatures previously described. The use of close paraboloids to determine Gaussian curvature is a known method and will not be further covered here.

Alternatively, a portion of the glass sheet, or the entire sheet of glass, can be calibrated by a continuity function such as z = f(x, y). The Gaussian curvature at any point on the glass sheet becomes K = ( f _xx f _yy - f ² _xy ) / (1 + f ² _x + f ² _y ) ² 1

among them , , , ,and .

In addition to the example where the glass sheet contains singular points (very small areas where the Gaussian curvature difference between the glass sheet areas and the corresponding support areas may be large), the glass sheets may include relatively large areas with small but limited ΔK. In this example, flattening a large area of low magnitude will add up to a large area resulting in the same damaging effect. In order to illustrate a large area associated with a small amount ΔK, the absolute value of ΔK must be integrated over the window of surface movement and the result normalized to the integrated area. The resulting fine value K(K _int ) can then be used as a measure of the shape of the glass sheet. which is This situation is shown in Figure 10, in which the integration region S is performed on the surface of the glass sheet.

It should be apparent that if the support is known to be flat (K is 0 everywhere), then ΔK at each point of the glass piece is only the Gaussian curvature value that determines each point of the Gaussian curvature of the glass piece. It is then easy to determine ΔK without worrying about the point-to-point correspondence between the glass sheet and the support. This may occur, for example, during TFT deposition of a display panel. This deposition treatment may weigh several tons and can be cut to extreme high tolerances.

If the support surface is not planar, a similar analysis of the support surface must be performed to determine the Gaussian curvature of the support surface at the point corresponding to the Gaussian curvature glass sheet.

Figure 11 shows a three-dimensional simulation of a non-flat glass sheet containing bubbles (spikes) defined by the following formula Where c is the height of the bubble and a and b are half the width of the bubble along the x and y axes, respectively. For the purposes of this example, a is chosen to be 150 mm, b is 50 mm, and c = 30 mm. Figure 12 shows the Gaussian curvature of the bubble of Figure 11. The maximum Gaussian curvature value is expressed by the following formula:

Equation 4 above demonstrates that the elongated bubble, such as b>>a, is easier to planarize than the equally highly symmetrical bubble (b=a) because the largest Gaussian bubble The curvature becomes lower. Figure 13 shows a graph of diameter versus height for a symmetrical bubble having a Gaussian curvature of 1 x 10 ^-8 /mm ² . The height-diameter bubble on the right side of the curve tends to show excellent light strike behavior (it is easy to flatten on a flat support via a vacuum tap), while the height-diameter relationship is easy to display on the bubble to the left of the curve. Poor tapping performance (such as vacuum cracks, incomplete flatness, etc.). Figure 13 shows that a certain diameter bubble should be effectively planarized below a certain height. Experimental work confirmed that the maximum Gaussian curvature value of 1x10 ^-8 /mm ² is the upper limit low limit of the maximum Gaussian curvature value of the sheet glass of the display (its thickness is less than 1 mm).

Gaussian curvature is used as a feature of material sheet compliance, especially in sheets of elastic material such as sheet glass, which can be used to describe the possibility of sheet glass being deformed into any given shape. This method is not limited to flat and horizontally supported designs; it can be used to help Understand the behavior of glass flicks to optimize the tapping method, because according to the knowledge of Gaussian curvature, it is known that the thin glass sheets placed on the flat table mostly rest on the area of the expandable surface; Development, preferably linked to the glass flick behavior, rather than warping a single maximum; Can help estimate changes in strain and total height at the time of tapping.

It is to be understood that the above-described embodiments of the invention, particularly, "preferred" The above-described embodiments of the present invention are capable of many changes and modifications without departing from the spirit and scope of the invention. For example, although the exemplary embodiment shown herein is a vertical configuration, the present invention is equally effective in horizontal pointing. All such changes and modifications are intended to be included within the scope of the disclosure and the invention is protected by the following claims.

20‧‧‧Wedge/Wedge Element

22‧‧‧ channel

24‧‧‧ siding section

26‧‧‧Overflow

28, 30‧‧‧ forming the surface part

32‧‧‧ Root

34‧‧‧Solid glass

36‧‧‧Transportation pipeline

38‧‧‧ dam

40‧‧‧Free surface

42‧‧‧Initial surface glass/glass ribbon

44‧‧‧Drag roller

48‧‧‧ cutting line

50‧‧‧ panel

54‧‧‧Organic material layer/organic layer

56‧‧‧First glass/substrate/backplane

58‧‧‧Second glass piece/cover

60‧‧‧Sealing material/glass frit

64‧‧‧Laser

66‧‧‧Ray beam

68‧‧‧Measurement device

70‧‧‧Stainless glass

72‧‧‧ Container

74‧‧‧ fluid

76‧‧‧Sensor

78‧‧‧Sensor/top/first side

80‧‧‧Non-sensing surface/bottom surface/second surface

82‧‧‧ fluid surface

100‧‧‧BoN measuring instrument

110‧‧‧ Pin

112‧‧‧Load components

114‧‧‧ Height adjuster

116‧‧‧ Circuitry

120‧‧‧Measurer base

130‧‧‧Processor

132‧‧‧Measurement signal

134‧‧‧Adjust the signal

140‧‧‧Measuring body/glass substrate

200,206‧‧‧Materials

202‧‧‧ ridge

204‧‧‧ reference plane

206‧‧‧Second piece of material

208‧‧‧ concave

210,212,214‧‧‧Area

Figure 1 is a perspective view showing a partial section of a thin glass sheet fused downward drawing device.

2 is a broken side elevational view of a glass assembly including a frit seal using a laser seal.

3 is a side elevational view of a device for measuring the shape of a sheet or material, such as a glass sheet, in a medium density, non-gravity environment.

4 is a side elevational view of a device for measuring the shape of a gravity-free sheet or material, such as a glass sheet, using a "nail bed."

Figure 5 is a perspective view of a sheet of material comprising a longitudinal ridge on a flat reference surface and a sheet of material having a ridge representing a deployable surface.

Figure 6 is a perspective view of a sheet of material comprising a central peak or bubble on a flat reference surface, the sheet of material having a peak representing an unexpandable surface.

Figures 7A and 7B are perspective views of an expandable cylindrical surface (Figure 7A) that can be unrolled into a flat (planar) surface as shown in a perspective view of Figure 7B.

Figure 8A is a perspective view of an unexpanded sphere.

Figure 8B is a perspective view of a tear that would necessarily occur in the planar half (hemispherical) of Figure 8A, forming an undeployed hemisphere.

Figure 9 is a graph of the flattening force of a sheet of expandable and non-expandable material, such as a glass sheet.

Figure 10 is a perspective view showing a Gaussian curvature moving window of a sheet of material having a wide twist but a low degree of distortion.

Figure 11 is a three-dimensional graph of a sheet comprising a Z-axis of non-planar material.

Figure 12 is a three-dimensional graph of the Gaussian curvature of the surface of Figure 9.

Figure 13 is a graph showing the relationship between the height of the symmetrical bubble and the lateral dimension, the bubble having a maximum Gaussian curvature value of 1 x 10 ^-8 /mm ² .

68‧‧‧Measurement device

70‧‧‧Stainless glass

72‧‧‧ Container

74‧‧‧ fluid

76‧‧‧Sensor

78‧‧‧Sensor surface (top surface)

80‧‧‧ Non-sensing surface (bottom side)

82‧‧‧ fluid surface

Claims (8)

A method of determining the compliance of a glass sheet to a surface, the method comprising the steps of: determining a shape of the glass sheet; using the shape to calculate a Gaussian curvature magnitude of a plurality of points on the glass sheet; a corresponding Gaussian curvature magnitude of the surface minus the plurality of Gaussian curvature magnitudes of the glass sheet to determine a Gaussian curvature magnitude difference for each of the plurality of points on the glass sheet; from the plurality of Gaussian The curvature magnitude difference selects a maximum Gaussian curvature magnitude difference of the glass piece; compares the maximum Gaussian curvature magnitude difference with a predetermined maximum low limit value; and if the maximum Gaussian curvature magnitude is equal to or less than the maximum lower limit value, The piece of glass is then classified as acceptable, and if the maximum Gaussian curvature value is greater than the maximum lower limit, the piece of glass is classified as unacceptable. According to the method of claim 1, wherein the step of determining the shape comprises determining the shape without gravity. The method of claim 2, wherein the step of determining the shape without gravity comprises immersing the glass sheet in a medium density fluid. According to the method of claim 2, the step of determining the shape without gravity includes supporting the glass sheet on a plurality of adjustable pins, the plurality of adjustable pins being adapted to apply a predetermined force to the glass sheet. According to the method of claim 1, further comprising the step of forming a film device on the glass sheet. The method of claim 1, wherein the Gaussian curvature value of the support surface is substantially zero everywhere. The method of claim 1, wherein the maximum low limit is less than or equal to 1 x 10 ^-8 /mm ² . The method of claim 1, wherein the plurality of points on the glass sheet represent a subset of the total number of points on the entire glass sheet, and the subset of points can be varied to produce a multi-point moving window.