CN102007370B - Method for predicting conformability of a sheet of material to a reference surface - Google Patents
Method for predicting conformability of a sheet of material to a reference surface Download PDFInfo
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- CN102007370B CN102007370B CN200980114488.8A CN200980114488A CN102007370B CN 102007370 B CN102007370 B CN 102007370B CN 200980114488 A CN200980114488 A CN 200980114488A CN 102007370 B CN102007370 B CN 102007370B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
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Abstract
A method of predicting the confopnability of a free form shape, such as a sheet of glass, to a surface is described. The method uses a gravity free measurement method to first determine a shape of the sheet, after which the magnitude of the Gaussian curvature of the sheet is made. The Gaussian curvature of the sheet is compared to a predetermined maximum, and a decision is made whether to pass or fail the sheet based on the results of the comparison.
Description
Invention field
The present invention relates to predict that the plate of material of arbitrary shape is with respect to the method for the compliance of reference surfaces.More particularly, the present invention relates to predict that glass plate complies with the method for the ability of the area supported that uses when this plate of processing as being suitable for glass plate in the flat-panel monitor.
Technical background
The glass-encapsulated that can have benefited from using gas-tight seal to many electronics or the photonic device of environment sensitive.These devices comprise photovoltaic device, Organic Light Emitting Diode (OLED) display, OLED luminous plaque, plasma scope, surface-conduction-electron emission display (SED) and Field Emission Display (FED) etc.For example liquid crystal display (LCD) is to depend on the passive flat panel displays that external light source is used for illumination.They are usually as segmented display or with a kind of manufacturing in two kinds of essential structures.The substrate that these two kinds of matrix-type need is different (except transparent and can bear in the display process its electrochemical conditions that experiences).The first type is intrinsic matrix addressing, take the threshold value character of liquid crystal material as the basis.The second is external matrix or active matrix (AM) addressing, and wherein the array of diode, metal-insulator-metal type (MIM) device or thin film transistor (TFT) (TFT) switches for each pixel provides electronics.In the both of these case kind, two glass plates form display device structure.Distance between these two plates is the critical gap dimension, is the 5-10 micron.The thickness of independent glass substrate is usually less than about 0.7 millimeter.
The glass plate that is used for electronic device such as display or luminous plaque is carried out this plate of processing request comply with plane form.This is usually by carrying out the plate vacuum clamping at flat surfaces.Although have strict manufacturing process and standard, these may be not to be perfect plane to the glass plate that is equal to or greater than 10 square metres greatly.Therefore, when forcing its compliant support surface, may produce clamp error, cause these plates ideally not remain in the plane.If the shape of plate is not purely to flatten (purely developable) shape, if especially area supported itself and on-plane surface, then could this thing happens.
Summary of the invention
One wide in range aspect in, a kind of definite glass plate has been described with respect to the method for the compliance on surface, the method comprises the shape of determining plate, use this shape to calculate the Gaussian curvature magnitude of a plurality of points on this plate, from the corresponding Gaussian curvature magnitude of area supported, deduct these a plurality of Gaussian curvature magnitudes to determine that a plurality of somes Gaussian curvature magnitude separately is poor on this plate, the Gaussian curvature magnitude of selection maximum for this plate is poor from these a plurality of Gaussian curvature magnitudes are poor, compare with max-thresholds that predetermine this maximum Gaussian curvature magnitude is poor, if poor this max-thresholds that is equal to or less than of this maximum Gaussian curvature magnitude, then this plate is classified as acceptable, if perhaps this maximum Gaussian curvature magnitude is poor greater than this max-thresholds, then classify as this plate unacceptable.
In some embodiments, the shape of plate can characterize by weightless approach, for example plate is placed the neutral density fluid, perhaps plate is bearing in adjustable support bed for example on the adjustable needle.
Describe also with reference to the accompanying drawings by following illustrative, can more easily understand the present invention, other purposes of the present invention, feature, details and advantage will be more apparent, and following illustrative is described and limited never in any form.All these spare systems that comprise in this instructions, method characteristic and advantage all are subject to the protection of appended claims all within the scope of the present invention.
Accompanying drawing is briefly described
Fig. 1 is the partial cross section skeleton view that is used to form the fusion pull-down device of sheets of glass.
Fig. 2 is the side cross-sectional view of glass combination part, and this glass combination part comprises the glass frit seal with the laser instrument sealing.
Fig. 3 is the side cross-sectional view for the equipment of the shape of measuring plate or material (such as glass plate) at neutral density " agravic " environment.
Fig. 4 utilizes " nail bed " to measure the side cross-sectional view of equipment of the gravity-free shape of plate of material (such as glass plate).
Fig. 5 is the skeleton view that is positioned at the plate of material of smooth reference surfaces top, and this plate of material comprises vertical projection, and the bossed plate of material representative of described tool can flatten surface (developable surface).
Fig. 6 is the skeleton view that is positioned at the plate of material of smooth reference surfaces top, and this plate of material comprises central peak or bubble, and described plate of material representative with peak or bubble can not flatten surface (non-developable surface).
Fig. 7 A and 7B are skeleton views, and the flattened cylindrical surface of Fig. 7 A can launch to form smooth (plane) surface among Fig. 7 B.
Fig. 8 A is the skeleton view that can not flatten spheroid.
Fig. 8 B makes the spheroid of Fig. 8 A half (hemisphere) smooth the skeleton view of tearing that must occur that flattens, so that this hemisphere shape can not flatten.
Fig. 9 makes the plate of material that can flatten flatten smooth required acting force with respect to the qualitative figure that makes the plate of material that can not flatten and flatten smooth required acting force, and this plate of material for example is glass plate.
Figure 10 is that this plate of material has the distortion of low magnitude at width for the skeleton view of the movement " window " of the Gaussian curvature of exosyndrome material plate (such as glass plate).
Figure 11 comprises z axle peak, is the three-dimensional plot of the plate of material on plane in other respects.
Figure 12 is the three-dimensional plot of the Gaussian curvature on Fig. 9 surface.
Figure 13 shows the height of symmetric bubble in the glass plate and the figure of the relation between the transverse dimensions (diameter), and this bubble has 1 * 10
-8Millimeter
-2The maximum Gaussian curvature magnitude.
Detailed Description Of The Invention
In the following detailed description, the unrestriced purpose in order to illustrate, proposition has disclosed the example embodiment of detail, provides complete understanding of the present invention.But, it will be obvious to those skilled in the art that by this instructions, can implement the present invention by other embodiments that are different from detail disclosed herein.And, omitted the description about well-known device, method and material, thereby be unlikely to so that the description of this invention thickens unclear.At last, as possible, similar key element like the Reference numeral representation class.
A kind of method of making glass plate is so-called fusion pulldown method.In being used to form the fusion overflow downdraw of glass tape, as shown in fig. 1, overflow groove element shaping wedge shape part 20 is included in the passage of upwards opening 22 that its vertical side is limited by wall part 24, and the top of these wall parts is in overflow peristoma or 26 places, the weir termination of relative longitudinal extension.Weir 26 is communicated with the relative external belt profiled surface of wedge-shaped element 20.As shown in the figure, wedge-shaped element 20 has a pair of substantially vertical profiled surface part 28, this is communicated with weir 26 the profiled surface part, this wedge-shaped element also provides a pair of downward-sloping surface portion 30 that converges, this forms straight glass draught line to converging surface portion summit or root 32 places termination below basic horizontal.Should be appreciated that surface portion 28,30 is provided on each vertical side of wedge shape part 20.
By the delivery path 36 that is communicated with passage 22 melten glass 34 is sent in the passage 22.The charging of sending into passage 22 can be single-ended, can be both-end when perhaps needing.Above overflow weir 26, provide a pair of restriction dam 38, adjacent with each end of passage 22, with the guiding melten glass 34 Free Surface 40 on overflow weir 26 as the logistics overflow that separates, arrive root 32 downwards along relative profiled surface part 28,30, these logistics that separate with chain line (chain line) expression converge at root, form the glass tape 42 of initial surface.Carry-over pinch rolls 44 are arranged on the downstream of the root 32 of wedge-shaped element 20, are used for regulating the glass tape that is shaped and leave the speed that converges profiled surface, thereby determine the nominal thickness of this glass tape.
The outer edge that carry-over pinch rolls are preferably designed at glass tape is in contact with it, and specifically, is in the medial region of the pearl that thickens that the edge of glass tape exists.Discard subsequently the glass edge part that contacts with carry-over pinch rolls in the slave plate.Each edge at band provides a pair of relative counter-rotational carry-over pinch rolls.
Along with the drawing of glass tape 42 along equipment partly moves downward, the complicated structural change of this glass tape experience not only changes in physical dimension but also at molecular level.By to finish the machinery required from liquid or viscous state to the transformation of solid or elastic stage and electrochemical conditions carry out exquisite balance temperature range or the distribution carefully selected, realized being about to thickness from the glop form of the wedge shape part root that for example is shaped the variation of 0.5 millimeter rigid strip.Some place in the elastic temperature zone in line of cut 48 place's cutting belt, forms glass plate or sheet 50.
Although glass manufacturer has been carried out strict production control for forming glass plate, for example to control by above technique, still there is gap in the shape of these plates with perfect plane.For example, in above-mentioned fusion process, the roller of the marginal portion by a contact zones provides the chance of the middle body generation warpage of band from shaping wedge shape part drawing glassribbons.This warpage may be caused by the movement of band, and perhaps the interaction by the various thermal stress that show in the band causes.For example, the vibration of introducing in the band by the downstream cutting technique can upwards propagate in the viscoelasticity zone of band, is frozen in the plate, shows as the deviation of the planarity of elastic webbing.The deviation that the width of band and/or the temperature difference on the length also can cause planarity.In fact, when cutting independent glass plate from band when, the stress that is frozen in the band can obtain the part elimination, causes equally uneven surface.In brief, the shape of the glass plate that obtains from band depends on band by the thermal history in the transition process the viscoelasticity zone, and this thermal history can change.The variation of this stress and/or shape is harmful to the technique that depends on dimensional stability, for example deposits circuit at substrate, situation about for example finding in liquid crystal display is made.For example, in the manufacturing of liquid crystal display, the large glass plate itself that cuts from the band that draws can cut into many less sheets.Therefore, cut apart at every turn and all cause stress elimination or stress redistribution, make subsequently alteration of form.Therefore, although can think that generally the plate that obtains is smooth, in fact this plate may show Gu Hefeng in its surface, and in processing subsequently, this may disturb the graduation operation to plate.Therefore, a kind of method energy of desired design Accurate Measurement is from the shape of the glass plate of band cutting.Can adopt thus obtained information to change the thermal history of the glass tape that is drawing.
Display manufacturer is accepted sheets of glass from glass manufacturer, further processes this plate and forms display equipment, perhaps other the device that comprises glass plate.For example, in the manufacturing of organic light emitting diode display shown in Figure 2 52, at one or more layers organic material 54 of the first glass plate 56 (such as substrate 56) deposition.Often this first glass plate is called backboard (backplane).Backboard 56 can also comprise thin film transistor (TFT) (TFT) and the electrode (not shown) is used for electric current is delivered to organic layer, makes these organic layers luminous.But, because 56 pairs of various environmental factors of organic material such as moisture and oxygen are responsive, so must be with organic layer and the airtight isolation of environment.Therefore, organic layer is sealed in the glass big envelope, this big envelope is by forming with lower member: backboard 56, the second glass plate 58 (sometimes being called cover plate or cover plate) and be arranged on encapsulant 60 between backboard and the cover plate.
Can adopt multiple encapsulating method that backboard is linked to each other with cover plate, comprise the use bonding agent.Although bonding agent applies easily and uses, its shortcoming is, must exist sealing to show the commercial reliably life-span to guarantee this device before losing efficacy.That is, moisture and/or oxygen finally may see through adhesive seal, cause organic layer and performance in display devices variation.
The more feasible approach of a kind of variation is that formation is frit-sealed between backboard and cover plate.According to this approach, on the cover board then the frit paste encapsulant of distribution coil or wire frame form heats the cover plate with frit, makes glass frit adhesion on the cover board.Then cover plate 58 is placed on the backboard 56, makes frit 60 (and organic layer 54) between cover plate and backboard.Then heat frit 60, for example use laser instrument 64 Emission Lasers bundles 66, make frit softening and between backboard 56 and cover plate 58, form gas-tight seal.
Can be imagined by above simple description, in the various deposition process of organic layer and TFT, and in the process that glass plate (substrate) is connected and seal, require backboard and/or cover plate Accurate align.Usually it is smooth requiring substrate in these forming processes.For example, often will be with backboard substrate vacuum pressing at the smooth area supported that is used for processing.
A kind of measure of the flatness of present glass plate for characterizing substantially flat is the maximum " warpage " of measuring this glass.That is, a kind of method of the distance (or deviation) with respect to the upper a plurality of points in reference surfaces assay plate surface, the deviation of distance has represented the gap of this plate shape and true planar, the i.e. warpage of this plate.Then can use maximum warpage as the mode of weighing not too accurately of this plate shape (for example flatness of this plate).
Fig. 3 illustrates a kind of method of determining according to the embodiment of the present invention the shape of glassware such as glass plate.According to the embodiment of Fig. 3, represent with Reference numeral 68 that generally glass plate 70 is arranged in the container 72 that comprises fluid 74.Glass plate 70 can be positioned on the flow surface, perhaps is immersed in the fluid, as described in more detail below.This glass plate has the average density that predetermines and the mean refractive index that predetermines.This fluid also has the average density that predetermines and the mean refractive index that predetermines.The average density of preferred this fluid be at least about this glass plate average density 85%; More preferably be at least about 90%; More preferably be at least about 95%.When the average density of fluid be at least about glass plate average density 85% the time, claim that fluid 74 is neutral density with respect to glass plate 48, claim that glass plate has neutral buoyancy, because glass plate should not have under the condition of mechanical support in the position of fluid 74 interior maintenance appointments, the time of maintenance is enough to finish the measurement of appointment.For example, suitable fluid can obtain from Cargille company (Cargille Inc.), and the said firm makes index matching liquid, steeping liq, optically-coupled liquid, refractometer liquid and other special liquid.The advantage of these liquid is that they are normally atoxic, and the density of these liquid is regulated easily, for example increases or reduces concentration by evaporation and regulate.Thereby can also realize the required potpourri average density that predetermines by mixing two or more fluids with different densities, finish the adjusting of convection cell density.For example, the Eagle 2000 of Corning Incorporated (Corning Incorporated) manufacturing
TMThe average density of glass is about 2.37 g/ccs.Can mix some fluids, for example average density is the second fluid that 2.35 g/ccs first fluid and average density are 2.45 g/ccs, and their combined amount can effectively obtain the 3rd fluid that average density equals 2.37 g/ccs substantially.It will be recognized by those of ordinary skills, can use any one or more fluids with essential density characteristics.
Continuation is used the distance of sensor 76 measurements from the sensor to the glass pane surface referring to Fig. 3.Glass plate 70 comprises the first side 78 (sensors sides) in the face of sensor 76, and the second right side 80 of non-sensor cover.In the present embodiment, sensors sides 78 can be called top side face 78, non-sensors sides 80 is called bottom side 80.Guarantee that glass surface can detect by sensor 76, the mean refractive index of expectation fluid 74 is different from the mean refractive index of glass plate 70, and this difference can detect.The factor of sensitivity by sensor 76 and so on determines the tolerance between the mean refractive index of the mean refractive index of fluid and glass.Perhaps, when the sensor of appointment can not be distinguished difference between the mean refractive index of the mean refractive index of glass plate and fluid, can apply on the surface of glass plate 70 a kind of film or coating (not shown), preferably be applied on the bottom side 80 of this plate, thus can survey sensor and glass-coating interface between distance.To the measurement of coating itself, for example when coating adhesion is on top side face 78 (sensors sides), can causes wrong the measurement, thereby cause measuring the surface of film rather than the surface of glass.Preferred this coating is opaque, but also nonessential like this, this coating can comprise for example paint, printing ink or dyestuff.The coating that has been found that White-opalescent obtains good result.But any coating that the difference between its refractive index and the fluid refractive index can detect all is acceptable.For example, this coating can comprise polymer film, and wherein the difference between the mean refractive index of the mean refractive index of this polymkeric substance and fluid can detect.Expect that any stress that this coating applies to glass plate 70 all is not enough to cause the distortion outside this glass plate amount.Therefore, can be by discontinuous mode, for example with the form of the point, line or other shapes that become series, coating is applied on the glass plate.The optional thickness that can also measure as the variable format of position on the glass plate this glass plate with film-glass interface range data combination, produces the surperficial contour map of the sensors sides of this glass plate.
According to this embodiment, in case glass plate 70 is arranged in the fluid 74 distance that just can use sensor 76 to measure from this sensor to this glass pane surface.Can use sensor 76 measure between these sensors and the glass plate top surface 78 apart from d
1, perhaps can use sensor 76 measure between these sensors and the glass plate basal surface 80 apart from d
2Can use sensor 76 to measure d
1And d
2, press thus t=d
2-d
1Determine the thickness t at any specific place of glass plate.For example, sensor 76 can comprise the laser instrument displacement transducer.But sensor 76 can comprise other devices that become known for measuring distance in this area, for example acoustic sensor.Laser device can comprise simple laser ranging system, perhaps more ingenious device, for example Mike's Ademilson interferometer (Michelson interferometer).Sensor can be based on the time, wherein the energy of induction is carried out timing such as the acoustic energy that has known speed in fluid.For example a kind of suitable sensor is the LT8110 confocal laser device displacement transducer that U.S. Keyence company (Keyence Corporation of America) makes.Although sensor 76 can be positioned at the flow surface top, therefore preferred sensor and fluid contact can advantageously eliminate the air-fluid interface in flow surface 82.Sensor 76 can be immersed in the fluid fully.
The another kind of so-called nail bed of method employing (bed-of-nails, BoN) measuring system of determining gravity-free shape, as shown in Figure 4.In the BoN measuring system, usefulness pin in groups is from following support plate.These pins can vertically move, and can measure the supporting role power of plate.Can also measure the movement of each pin.
Height that can metering needle is so that the target weight of each pin supporting appointment.For example, for the even and smooth substrate on being placed on the pin that is evenly distributed, its target weight can be the aliquot of this substrate overall weight.But each target weight may differ from one another, and can use according to the stress analysis of finite element analysis and determine target weight.When all pins all supported its specified wt, they were just supporting the particular substrate with its zero gravity shape.Support in its gravity-free positions by the pin that uses into array, can measure gravity-free shape by scanning substrate between these pins surface and the optical mode of measuring the height on whole surface.
Use a problem of BoN measurer to be, the height that changes an independent pin may change the weight on every other pin.For example, thereby in the extreme example more than an independent pin being lifted to the top that enough height are lifted to substrate on a plurality of pins, described a plurality of pins no longer carry any weight because they not with substrate contacts.Therefore, if thereby the height on the pin regulated at once support target weight, then when the height on another pin changed, the weight size of carrying will change.If this system of manual adjustments will expend the plenty of time and regulate these pins.If automatically regulate this system, then need a kind of algorithm to regulate these pins.
But in the system of former manual adjustments, each pin of independent regulation.Regulate the height of each pin until realize target weight.This independent adjusting action is once carried out a pin, from the first pin to last pin.But because a pin is regulated so that the load on the every other pin changes, so must constantly repeat this process again and again, each cycle proofreaies and correct the little deviation of introducing in upper one-period.
According to one or more embodiments, thereby comprised that some height that are used for metering needle can support the method for target weight simultaneously to all pins.Specifically, provide the method that the pin that becomes array is carried out system-computed and carries out suitable pin height adjusting.When all pins all supported its specified wt, their height was the gravity-free height of concrete substrate.The array that is in the pin of gravity-free height provides the measurement to gravity-free shape, and to the measurement of the potential shape distortion that may exist.The height adjuster of pin can also follow needle height, do not need extra height measuring device, for example optical scanner.
But all pins can be regulated simultaneously.Just need to assessment pin acting force until all pins are regulated.The pin acting force is the upwards acting force of pin, if pin is not among the motion, then this acting force equals the downward acting force by the pin supporting.By regulating pin in groups, this procedure declaration is following true, namely a pin is regulated and is had influence on every other pin.So, in every kind of situation almost, all realized the advantage of realize target pin acting force on all pins.
Referring to Fig. 4, the example bed of nails shape measurement measurer 100 of block diagram illustrations one or more embodiments according to the present invention.BoN measurer 100 comprises a plurality of pins 110, and at least 3 pins 110 are arranged, measurer pedestal 120, and processor 130.Use flexible plate-shaped body as measuring object 140, depict in the figure glass substrate 140 as.Glass substrate 140 is placed on the top of a plurality of pins 110, along with measuring object 140 bends under Action of Gravity Field, and each pin 110 carrying specified wt.Each pin 110 comprises that load measurement element (load cell) 112 is with the specified wt of surveyingpin 110 supportings.Load measurement element 112 can be installed on the top of height adjuster 114, and this height adjuster is the device of the height of metering needle 110 in a known manner, and preferably motor drives.Other configurations it is contemplated that for example have below load measurement element 112, and consider the weight of measuring height regulator 114.
Each load measurement element 112 can be transferred to processor 130 with the measuring-signal 132 relevant with the pin acting force that records by circuit 116, and then processor 130 carries out a kind of algorithm, and the height that calculating each pin 110 needs is regulated.Processor 130 can be transferred to each height adjuster 114 with conditioning signal 134 by circuit 116, and the height that calculates is regulated.Such situation is often arranged, and namely algorithm is better, and it is faster that load measurement element 112 reads target load.
The present invention has benefited from the following fact,, changes the pin height of an independent pin 110 that is, usually can change the load on all pins 110.If use N pin 110 in the measurer 100, then purpose is to find such pin height, so that the acting force on each pin 110 is a particular value.For example, for the substrate 140 of the substantially flat with relatively average thickness and density, estimation can have roughly uniformly mass distribution, so the value of specified wt equals the 1/N of substrate weight, provides the even distribution of these N pin 110.
According to a kind of embodiment, 3 pins 110 are not regulated, so they are fixed for each regulating cycle.These 3 locking pins 110 have been set a reference surfaces, so these 3 pins 110 should be not point-blank.For each cycle, there are 3 pins will keep fixing.In the cycle subsequently, will regulate these 3 pins.Then, regulate remaining all N-3 pin 110 according to following calculating, with this specified wt of same supporting.
The calculating that the pin height of N-3 pin 110 of residue is regulated can be considered to one group of simultaneous equations, with N-3 unknown quantity that the variation of pin height is related with the variation of pin load-bearing by N-3 equation.With the definite reference surfaces with respect to described equation association of 3 fixing pins.From the physics angle, the acting force sum, three equatioies that must satisfy have been represented around the moment sum of an axle and around the moment sum of another axle.Fix this 3 pins, the target weight of this needle system will be met by other pins are regulated, and the target weight of other pins also will be met.From the geometry angle, if do not fix this 3 pins, then will carry out rigid motion, but this is disadvantageous.Rigid motion can make the substrate translation, and it is rotated around two different axles, finds the solution when the pin height is regulated system of equations and will provide more than one solution.Therefore, need to fix 3 pins, only have a solution when pin height is regulated system of equations so that find the solution.
The simple performance of the pattern that above-mentioned warpage measurement is plate is for example plate to be pressed in a kind of bad index that forces the ability that this plate flattens on the smooth desktop by vacuum.For example, plate of material 200 (such as sheets of glass) is comprised along " length " of this plate extend, for example be parallel to vertical oncus 202 of an edge extension of this plate, the ultimate range of this oncus and smooth reference surfaces 204 is L+ δ, as shown in Figure 6.Suppose to comprise the part right cylinder in the shape of this oncus.The second plate 206 comprises depression (concavity) 208 (such as peak or bubble) in the plate surface, should depression also be L+ δ with the ultimate range of identical reference surfaces 204 wherein.These two plates will show identical maximum warpage (δ).But, can flatten because comprise the plate 200 (Fig. 5) of cylindrical oncus, make its easy degree that flattens greater than the easy degree that plate 206 with depression is flattened.
Can flatten the surface is not need to stretch, compress or tear the surface that the surface just can flatten.For example, with right cylinder discussed above, it comprises deployable surface shown in Fig. 7 A, just can be by launching that this periphery is shakeout because do not need to stretch or tear surface (Fig. 7 B).On the other hand, spherome surface (Fig. 8 A) can not flatten.Shakeout the part of spheroid, such as hemisphere, must stretch or tear hemisphere along a plurality of borders makes it comply with (Fig. 8 B).Therefore, in example before, the plate with cylindrical oncus can be flattened on smooth desktop, plate can not deform, and will make the second example board comply with desktop, will cause this plate distortion or tears.
Can flatten the surface is the surface that can convert by the variation that keeps angle and distance flat surfaces to.In the time can flattening the surface and be varied to flat surfaces, can in this surface, not introduce strain.Perhaps, can flatten the surface is not need to stretch, compress or tear the surface that the surface just can be formed by flat surfaces.Obviously, with the maximum warpage of glass plate it being characterized is enough to point out that this plate is not smooth, but still is not enough to measure the easy degree that forces this plate to form planar structure.
The Gaussian curvature K on surface is the intrinsic geometric properties on surface, is defined as the principal curvatures k of the upper set point in surface
1And k
2Product.That is, K=k
1k
2From physics meaning, the extent of deviation of Gaussian curvature description surface and flat surfaces.The mathematical derivation of Gaussian curvature is well-known, broadly is not included within this paper.The physical meaning of considering Gaussian curvature is more enlightening property.At first, how from the teeth outwards Gaussian curvature only depends on measuring distance and angle.For example, if the Gaussian curvature on surface then should comprise projection or peak at this some place in the surface for just; If Gaussian curvature is for negative, then this surface comprises the saddle depression points.But, if Gaussian curvature is zero, then should be equal to (being equivalent to) flat surfaces at this some place in the surface.Just this difference can be described by simple experiment.Leg-of-mutton each angle sum of drawing at spherome surface (positive gauss curvature) is greater than 180 °, and is necessary for 180 ° in similar leg-of-mutton each angle sum that right cylinder (Gaussian curvature=0) is drawn.Can flatten the surface and have zero Gaussian curvature, can in the situation that does not stretch, compresses or tear, be transformed into flat surfaces.If can make surperficial graduation in the situation that does not cause strain, then Gaussian curvature keeps constant.Therefore, the magnitude of understanding the Gaussian curvature on surface is complied with another surperficial degree and is had enlightenment understanding this surface.
According to one embodiment of the present invention, can adopt Gaussian curvature to characterize glass plate with respect to the compliance of reference surfaces, this reference surfaces for example is the surface of this plate of supporting.Preferred this plate can basic compliant support surface, this means the magnitude coupling of magnitude and the Gaussian curvature of area supported each point of the Gaussian curvature of this plate each point, perhaps approaches and mates.If reference surfaces is the plane, then in order accurately to comply with this reference (such as supporting) surface, the lip-deep each point of this plate should have null Gaussian curvature.Magnitude between the corresponding Gaussian curvature is poor larger, and the resistance that this plate shows complying with is larger.In other words, on the plate on each point and the area supported difference between the Gaussian curvature magnitude of corresponding point should be equal to or less than poor (the Δ K=||K of the maximum that predetermines
Plate|-| K
Supporting||≤G, wherein G is the maximal value that predetermines, G often depends on the application of this plate, can be determined by experiment, or determine by simulation).Corresponding point refer to, when plate is pressed on the area supported, on the plate with area supported on the overlapping point of point.If Δ K is greater than G, then this plate can't be complied with this area supported fully.When this plate was flattened, the strain energy that produces in the plate may for example cause the birefringence that appearance bends or strain causes in the glass.
By above content as can be known, suppose that this plate only is subject to the reacting force of gravity and desktop, estimate that then the independent peak that shows in the glass plate on being positioned over area supported (such as flat surfaces) as shown in Figure 6 or the Gaussian curvature magnitude of paddy can not cause large variation.It is especially true when the magnitude of Gaussian curvature increases.Along with the magnitude increase of Gaussian curvature, the resistance that this plate resists complanation increases, and must apply larger acting force this plate is flattened.As mentioned above, this can cause increasing harmful effect (bending, stress etc.) that may affect concrete manufacture process.On the contrary, the magnitude of Gaussian curvature is larger, makes the plate required acting force that flattens larger.Bending of plate at first occurs in having the zone that can flatten shape, because energy that these zones need are less than the energy that can not flattened region needs.As shown in Figure 9, the planarity of the qualitative display board of this figure and in order to realize the relation between the acting force that corresponding flatness applies.The surface in vertical dotted line left side is with can flattening shape representation, and this line right lateral surface is characterised in that to have not deployable shape.As shown in the drawing, in the zone 210 of the curve of drawing, use less acting force just can easily make can to open up the surface to flatten, unique resistance of complanation is come from this surperficial rigidity.On the other hand, can not open up the surface and need significant acting force.In the zone 212 of the curve of drawing, the surface bending appears easily, in zone 214, along with planarization application power increases, produce large membrane interaction force and moment.For the singular point (singularity) of large Gaussian curvature magnitude, apply weak acting force in the time of (as only having gravity), can estimate that the Gaussian curvature magnitude of this singular point is with unaffected.
Utilize Gaussian curvature, preferably can understand the gravity-free shape of plate.That is, the shape under agravic condition, taked of plate.Although can't in terrestrial environment, realize true null-gravity state, can be roughly near agravic condition.For example, can adopt the neutral density system.
In case determine the shape of plate, for example by adopting agravic plate to form the distance that measuring method is determined at a plurality of some places and reference plane, just can determine that this plate is in the Gaussian curvature at each point place.For example, can adopt the Gaussian curvature of regional area on the close parabolic method assay plate.Parabolic 2z=ax
2+ bxy+cy
2Gaussian curvature K at its place, summit equals ac-b
2, mean curvature H equals (a+c)/2.Parabolic and the intersection of normal plane at P place, its summit are para-curve, this para-curve in the curvature at P place by k
n=k
1Cos
2θ+k
2Sin
2θ provides, wherein k
1And k
2Equation k
2The root of-2Hk+K=0, θ are given and k
nReach the angle between the face of its maximal value (or minimum value).K
nExtreme value k
1And k
2It is previously described principal curvatures.It is well-known adopting closely parabolic mensuration Gaussian curvature, and this paper is not further elaborated.
Perhaps, can with continuous function f for example z=f (x, y) part or the whole plate of plate carried out match.The Gaussian curvature of arbitrfary point is on the plate:
K＝(f
xxf
yy-f
2 xy)/(1+f
2 x+f
2 y)
2
1
Wherein
Except plate comprises singular point (very little zone, but the Gaussian curvature between the respective regions of this zone of plate and area supported is poor larger) situation beyond, this plate can comprise a kind of so larger zone, this zone even have relevant less but limited Δ K.In this case, the larger zone with lower magnitude is flattened to this larger zone summation, cause equally identical ill-effect.Consider the larger zone that level Δ K in a small amount is associated, can in this lip-deep Moving Window, carry out integration by the absolute value to Δ K, with the result with respect to integral area normalization.Then can use the K integrated value (K that obtains
Integration) as the tolerance to this plate shape.That is,
This situation as shown in Figure 10, wherein integral area S is mobile on the plate surface.
Obviously, if known area supported is smooth (K everywhere is 0), when then determining the Gaussian curvature of plate, the Δ K of each point is exactly that this plate is in the magnitude of the Gaussian curvature at each point place simply on this plate.Then Δ K be can easily determine, point and the correspondence of putting between this plate and this supporting mass surface do not needed to consider.For example when display was with deposition TFT in the panel, this thing happens for possibility.The supporting mass that is used for this depositing operation may weigh several tons, becomes smooth by machine work, has very high tolerance.
If the supporting mass surface is not smooth, then must carry out similar supporting mass surface analysis, determining the Gaussian curvature of each point on the supporting mass surface, supporting mass lip-deep these corresponding to the each point on the plate of measuring Gaussian curvature.
Be the three-dimensional simulation figure of another kind of planar plate shown in Figure 11, this planar plate comprises the bubble (peak) by following equation definition:
Wherein c is the height of bubble, and x and y are respectively that bubble is along the half width of x and y axle.For the purpose of this embodiment, selecting a is 150 millimeters, and b is 50 millimeters, and c is 30 millimeters.Figure 12 shows the Gaussian curvature of the bubble of Figure 11.The maximum Gaussian curvature magnitude is expressed from the next:
Above equation 4 proofs, the bubble (for example b＞＞bubble of a) of elongation is flattened flatten than the symmetric bubble that makes equal height (a=b) simply too much because the maximum Gaussian curvature of bubble becomes lower.Figure 13 is the diameter of symmetric bubble and the graph of a relation of height, and the Gaussian curvature of this symmetric bubble is 1 * 10
-8Millimeter
-2Highly-bubble that diameter Relationship is positioned at the curve right side tends to show good clamping behavior (can by vacuum clamping at the enterprising parallel planes of smooth supporting mass), and height-diameter Relationship is positioned at the bubble in curve left side and tends to show bad clamping behavior (for example vacuum leak, complanation is incomplete etc.).Figure 13 shows that for given diameter, bubble should be lower than a certain height, thereby carries out effective complanation.Experimental work proves 1 * 10
-8Millimeter
-2The maximum Gaussian curvature magnitude be display with the practical upper limit of the maximum Gaussian curvature magnitude of sheets of glass (thickness is less than about 1 micron).
The elastic material board of compliance, especially sheets of glass and so on by adopting Gaussian curvature exosyndrome material plate has following purposes:
● the distortion of quantitative description sheets of glass becomes the ability of any given shape.This method is not limited to smooth and supporting mass structure level.
● help to understand the clamping behavior of plate, help to optimize the clamping scheme, because when sheets of glass being divided on smooth desktop, this plate is placed on major part on the zone that can flatten, and its Gaussian curvature is known.
● help to produce the shape standard of plate, this standard is closer than warpage single largest value with the relation that glass plate clamps behavior.
● the strain when helping to estimate to clamp and resultant pitch change.
What should highlight is, the embodiment of the invention described above, and especially any " preferably " embodiment only is possible embodiment, proposes these embodiments and only understands principle of the present invention for clear.Can in the situation that does not depart from the present invention's spirit and principle, carry out many variations and modification to the invention described above embodiment.For example, although example embodiment as herein described shows that with vertical stratification the present invention is effective equally for the structure of horizontal alignment.All such modifications and variation comprise all that within the scope of the present invention the present invention is subject to the protection of following claim.
Claims (8)
1. the method for the compliance of a definite glass plate and an area supported, the method may further comprise the steps:
Determine the shape of this glass plate;
Use this shape to calculate the Gaussian curvature magnitude of a plurality of points on this glass plate, described Gaussian curvature magnitude is the size of the value of Gaussian curvature;
From the corresponding Gaussian curvature magnitude of area supported, deduct the Gaussian curvature magnitude of this glass plate, determine on this glass plate the poor absolute value of Gaussian curvature magnitude of each point in a plurality of points;
From the poor absolute value of a plurality of Gaussian curvature magnitudes, select the maximum Gaussian curvature magnitude of this glass plate poor;
Compare with max-thresholds that predetermine this maximum Gaussian curvature magnitude is poor, and
Be equal to or less than the max-thresholds that this predetermines if this maximum Gaussian curvature magnitude is poor, then this glass plate classified as acceptablely, if this maximum Gaussian curvature magnitude is poor greater than this max-thresholds that predetermines, then classify as this glass plate unacceptable.
2. the method for claim 1 is characterized in that, the step of described definite shape comprises definite gravity-free shape.
3. method as claimed in claim 2 is characterized in that, the step of described definite gravity-free shape comprises this glass plate is immersed in the neutral density fluid.
4. method as claimed in claim 2 is characterized in that, the step of described definite gravity-free shape comprises this glass plate is bearing on a plurality of adjustable pins that these pins are suitable for applying the acting force that predetermines to this glass plate.
5. the method for claim 1 is characterized in that, described method also is included on this glass plate and forms thin-film device.
6. the method for claim 1 is characterized in that, the Gaussian curvature magnitude of described area supported all is zero throughout substantially.
7. the method for claim 1 is characterized in that, the described max-thresholds that predetermines is less than or equal to 1 * 10
-8Millimeter
-2
8. the method for claim 1 is characterized in that, a plurality of points on the described glass plate represent the subset of all putting on the whole glass plate, and the subset of described point changes, thereby produces the moving window of point.
Applications Claiming Priority (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US6741008P | 2008-02-28 | 2008-02-28 | |
| US61/067,410 | 2008-02-28 | ||
| PCT/US2009/001166 WO2009108302A1 (en) | 2008-02-28 | 2009-02-25 | Method for predicting conformability of a sheet of material to a reference surface |
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| CN102007370B true CN102007370B (en) | 2013-03-13 |
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| CN200980114488.8A Expired - Fee Related CN102007370B (en) | 2008-02-28 | 2009-02-25 | Method for predicting conformability of a sheet of material to a reference surface |
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| Country | Link |
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| JP (1) | JP5416143B2 (en) |
| KR (1) | KR101543053B1 (en) |
| CN (1) | CN102007370B (en) |
| TW (1) | TWI392846B (en) |
| WO (1) | WO2009108302A1 (en) |
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| US9031813B2 (en) * | 2010-08-27 | 2015-05-12 | Corning Incorporated | Methods and apparatus for estimating gravity-free shapes |
| US8973402B2 (en) * | 2010-10-29 | 2015-03-10 | Corning Incorporated | Overflow down-draw with improved glass melt velocity and thickness distribution |
| KR102035859B1 (en) * | 2014-05-28 | 2019-10-25 | 주식회사 펨토바이오메드 | Process for Measuring Viscosity |
| KR102499831B1 (en) | 2016-05-23 | 2023-02-14 | 코닝 인코포레이티드 | Method of predicting gravity-free shape of glass sheet and method of managing quality of a glass sheet based on gravity-free shape |
| CN113468782B (en) * | 2021-06-21 | 2023-04-07 | 上汽大众汽车有限公司 | Finite element modeling method for laminated glass for vehicle collision assessment |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1033101A (en) * | 1987-10-30 | 1989-05-24 | 中央地质研究院有色金属及贵重金属研究所 | Detect the method for condition of three-dimensional case |
| EP0977009A1 (en) * | 1997-04-25 | 2000-02-02 | Riken | Method of discriminating shape errors of free-form curved surface |
| EP1030162A1 (en) * | 1998-08-19 | 2000-08-23 | Riken | Method for evaluating error in shape of free curved surface |
Family Cites Families (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5573446A (en) * | 1995-02-16 | 1996-11-12 | Eastman Kodak Company | Abrasive air spray shaping of optical surfaces |
| JPH10269260A (en) * | 1997-03-24 | 1998-10-09 | Honda Motor Co Ltd | Shape data verifying method |
| JP3418819B2 (en) * | 1998-01-13 | 2003-06-23 | 東芝セラミックス株式会社 | Plate flatness measuring device |
| US6727864B1 (en) | 2000-07-13 | 2004-04-27 | Honeywell International Inc. | Method and apparatus for an optical function generator for seamless tiled displays |
| JP2004145674A (en) * | 2002-10-25 | 2004-05-20 | Nippon Sheet Glass Co Ltd | Method for designing mold surface of press bending form block |
| JP4773713B2 (en) | 2004-11-17 | 2011-09-14 | 三菱重工業株式会社 | Shape determination method of mold model |
| US7225665B2 (en) * | 2005-07-27 | 2007-06-05 | Corning Incorporated | Process and apparatus for measuring the shape of an article |
-
2009
- 2009-02-25 CN CN200980114488.8A patent/CN102007370B/en not_active Expired - Fee Related
- 2009-02-25 WO PCT/US2009/001166 patent/WO2009108302A1/en active Application Filing
- 2009-02-25 JP JP2010548704A patent/JP5416143B2/en not_active Expired - Fee Related
- 2009-02-25 KR KR1020107021506A patent/KR101543053B1/en active IP Right Grant
- 2009-02-26 TW TW98106291A patent/TWI392846B/en not_active IP Right Cessation
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1033101A (en) * | 1987-10-30 | 1989-05-24 | 中央地质研究院有色金属及贵重金属研究所 | Detect the method for condition of three-dimensional case |
| EP0977009A1 (en) * | 1997-04-25 | 2000-02-02 | Riken | Method of discriminating shape errors of free-form curved surface |
| EP1030162A1 (en) * | 1998-08-19 | 2000-08-23 | Riken | Method for evaluating error in shape of free curved surface |
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| Publication number | Publication date |
|---|---|
| TW201003036A (en) | 2010-01-16 |
| JP5416143B2 (en) | 2014-02-12 |
| TWI392846B (en) | 2013-04-11 |
| JP2011513727A (en) | 2011-04-28 |
| WO2009108302A1 (en) | 2009-09-03 |
| KR20100138971A (en) | 2010-12-31 |
| KR101543053B1 (en) | 2015-08-07 |
| CN102007370A (en) | 2011-04-06 |
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