CN102007370A - 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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- CN102007370A CN102007370A CN200980114488.8A CN200980114488A CN102007370A CN 102007370 A CN102007370 A CN 102007370A CN 200980114488 A CN200980114488 A CN 200980114488A CN 102007370 A CN102007370 A CN 102007370A
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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
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 the method for the plate of material of arbitrary shape with respect to 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 the 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 LCD (LCD) is to depend on the passive flat panel displays that external light source is used to throw light on.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 the electrochemical conditions that it experienced in the display process).First type is intrinsic matrix addressing, based on the threshold value character of liquid crystal material.Second kind 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 large-scale electron device such as display or luminous plaque is carried out this plate of processing request comply with plane form.This is undertaken by the plate vacuum is clamped on the flat surfaces usually.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 to flatten (purely developable) shape purely, if especially area supported itself and on-plane surface, then could this thing happens.
Summary of the invention
One wide in range aspect in, the method of a kind of definite glass plate with respect to the compliance on surface described, this 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, from these a plurality of Gaussian curvature magnitude differences, select Gaussian curvature magnitude maximum for this plate poor, this maximum Gaussian curvature magnitude difference and the max-thresholds that is predetermined are compared, if this maximum Gaussian curvature magnitude difference is equal to or less than this max-thresholds, then this plate is classified as acceptable, if perhaps this maximum Gaussian curvature magnitude difference then classifies as this plate unacceptable greater than this max-thresholds.
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 on for example adjustable pin of adjustable support bed.
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 conspicuous, 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 subjected 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 with laser instrument sealed glass material seal.
Fig. 3 is the side cross-sectional view of equipment that is used for measuring at neutral density " agravic " environment the shape of plate or material (as glass plate).
Fig. 4 utilizes " nail bed " to measure the side cross-sectional view of equipment of the gravity-free shape of plate of material (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 described plate of material representative with projection 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 take place that flattens, and makes this hemisphere shape to 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 a glass plate.
Figure 10 is the skeleton view that moves " window " that is used for the Gaussian curvature of exosyndrome material plate (as glass plate), and this plate of material has the distortion of low magnitude on width.
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 symmetry 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 unrestricted purpose for explanation proposes to have 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 description, thereby it is unclear to be unlikely to make that the description of this invention thickens about well-known device, method and material.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 the 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 basic vertical forming surface portion 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, and the glass tape that is used to regulate shaping leaves the speed that converges profiled surface, thereby determines 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 the glass edge part that contacts with carry-over pinch rolls subsequently 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 on molecular level.By to finish machinery required and electrochemical conditions from liquid or viscous state to the transformation of solid or elastic stage carry out exquisite balance careful temperature range or the distribution of selecting, realized being about to thickness the variation of 0.5 millimeter rigid strip from the glop form of the wedge shape part root that for example is shaped.Some place in the elasticity temperature province 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 technology, 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 by mobile the causing 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 uneven surface equally.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 technology that depends on dimensional stability, for example deposits circuit on substrate, for example situation about finding in LCD is made.For example, in the manufacturing of LCD, the big 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 to be eliminated or stress distributes again, make alteration of form subsequently.Therefore, though 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 of desired design can accurately be measured 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, go up one or more layers organic material 54 of deposition at first glass plate 56 (as substrate 56).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 sensitivity, 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, 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.Though bonding agent applies easily and uses, its shortcoming is, must exist sealing to show the commercial life-span reliably 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 the frit paste encapsulant of distribution coil or wire frame form heats the cover plate with frit then, 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.The heating glass material 60 then, for example use laser instrument 64 emission of lasering beam 66, make frit softening and form gas-tight seal between backboard 56 and cover plate 58.
Can imagine 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 accurately to align.Usually it is smooth requiring substrate in these forming processes.For example, the smooth area supported that often backboard substrate vacuum pressing will be used to process.
A kind of measure of flatness that is used to characterize the glass plate of substantially flat at present is a maximum " warpage " of measuring this glass.That is, a kind of method of the distance (or deviation) with respect to the last a plurality of points in reference surfaces assay plate surface, the deviation of distance has been represented the gap of this plate shape and true planar, the i.e. warpage of this plate.Can use not too accurately the weigh mode of maximum warpage then as this plate shape (for example flatness of this plate).
Fig. 3 illustrates a kind of method of determining the shape of glassware such as glass plate according to the embodiment of the present invention.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 average density that is predetermined and the mean refractive index that is predetermined.This fluid also has average density that is predetermined and the mean refractive index that is predetermined.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 a neutral density with respect to glass plate 48, claim that glass plate has neutral buoyancy, because glass plate should not have to keep appointed positions under the condition of mechanical support in fluid 74, 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 refractive index match liquid, steeping liq, optically-coupled liquid, refractometer liquid and other special liquid.The advantage of these liquid is that they are normally atoxic, and these density of liquid are regulated easily, for example increases or reduces concentration by evaporation and regulate.Thereby can also realize the required potpourri average density that is predetermined by mixing two or more fluids, finish the adjusting of convection cell density with different densities.For example, the Eagle 2000 of Corning Incorporated (Corning Incorporated) manufacturing
TMThe average density of glass is about 2.37 gram/cubic centimetres.Can mix some fluids, for example average density is the first fluid of 2.35 gram/cubic centimetres and second fluid that average density is 2.45 gram/cubic centimetres, and their combined amount can effectively obtain the three-fluid that average density equals 2.37 gram/cubic centimetres 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 first side 78 (sensors sides) and the second right side 80 of non-sensor cover in the face of sensor 76.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.Tolerance between the mean refractive index of the factor decision fluid of sensitivity by sensor 76 and so on and the mean refractive index of 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 on the surface of glass plate 70, apply 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 is bonded on the 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 excellent results.But any coating that the difference between its refractive index and the fluid refracting rate can detect all is an 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 this is coated with any stress that course glass plate 70 applies and all is not enough to the distortion that causes this glass plate amount outer.Therefore, can be by discontinuous mode, for example, coating is applied on the glass plate with the form of the point, line or other shapes that become series.The optional thickness that can also measure this glass plate as the variable format of position on the 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 t=d thus
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, and wherein the energy to induction carries out timing as the acoustic energy that has known speed in fluid.For example a kind of right sensors is the LT8110 confocal laser device displacement transducer that U.S. Keyence company (Keyence Corporation of America) makes.Though sensor 76 can be positioned at the flow surface top, preferred sensor contacts with fluid, therefore can advantageously eliminate the air-fluid interface in flow surface 82.Sensor 76 can be immersed in the fluid fully.
The so-called nail bed of the method employing of another kind of definite gravity-free shape (bed-of-nails, BoN) measuring system, as shown in Figure 4.In the BoN measuring system, usefulness pin in groups is from following support plate.These pins can vertical moving, can measure the supporting role power of plate.Can also measure moving of each pin.
Height that can metering needle, the target weight that makes 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 support target weight at once, then when the height on another pin changed, the weight size of being carried will change.If this system of manual adjustments will expend the plenty of time and regulate these pins.If regulate this system automatically, then need a kind of algorithm to regulate these pins.
But in the system of former manual adjustments, each pin of independent regulation.The height of regulating each pin is up to realizing target weight.This independent adjusting action is once carried out a pin, from first pin to a last pin.But, because being regulated the load that makes on the every other pin, a pin changes, so must constantly repeat this process again and again, each cycle all proofreaies and correct the little deviation of introducing in last 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 warpage 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.Up to all pins being regulated just needs assessment pin acting force.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, promptly a pin is regulated and is had influence on every other pin.So, in every kind of situation almost, all realized on all pins, realizing the advantage of target pin acting force.
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 tabular object as measuring object 140, depict glass substrate 140 in the figure 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, and each pin 110 carrying specified wt.Each pin 110 comprises the specified wt of load measurement element (load cell) 112 with surveyingpin 110 supportings.Load measurement element 112 can be installed on the top of height adjuster 114, this height adjuster is the device by the height of known way metering needle 110, preferably motor driven.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 processor 130 carries out a kind of algorithm then, 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 promptly algorithm is good more, and it is fast more 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, can change the load on all pins 110 usually.If use N pin 110 in the measurer 100, then purpose is to find such pin height, makes that the acting force on each pin 110 is a particular value.For example, for the substrate 140 of the substantially flat with average relatively thickness and density, estimation can have roughly mass distribution uniformly, 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 to be maintained fixed.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, the variation of pin height is related with the variation of pin load-bearing by N-3 equation with N-3 unknown quantity.With the definite reference surfaces of 3 fixing pins with respect to described equation association.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 another moment sum.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,, then will carry out rigid motion, but this is disadvantageous if do not fix this 3 pins.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 separating.Therefore, need fix 3 pins, make and have only one to separate when finding the solution the pin height regulates system of equations.
The simple performance of the pattern that above-mentioned warpage measurement is a 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 (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.Second plate 206 comprises depression (concavity) 208 (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, 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 second example board comply with desktop, will cause this plate distortion or tears.
Can flatten the surface is the surface that can convert flat surfaces by the variation that keeps angle and distance to.When flattening the surface when being 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 that set point is gone up on the surface
1And k
2Product.That is K=k,
1k
2From physics meaning, Gaussian curvature is described the extent of deviation of 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,, then should be equal to (being equivalent to) flat surfaces at this some place in the surface if Gaussian curvature is zero.Just this difference can be described by simple experiment.Leg-of-mutton each angle sum of drawing on spherome surface (positive gauss curvature) is greater than 180 °, and similar leg-of-mutton each angle sum of drawing on right cylinder (Gaussian curvature=0) is necessary for 180 °.Can flatten the surface and have zero Gaussian curvature, can under the situation that does not stretch, compresses or tear, be transformed into flat surfaces.If can make surperficial graduation under 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 the compliance of glass plate with respect to 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 near mating.If reference surfaces is the plane, then in order accurately to comply with this reference (as supporting) surface, the lip-deep each point of this plate should have null Gaussian curvature.Magnitude difference between the corresponding Gaussian curvature is big more, and the resistance that this plate shows complying with is big more.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 is predetermined
Plate|-| K
Supporting||≤G, wherein G is the maximal value that is predetermined, G often depends on the application of this plate, can be determined by experiment, or determine by simulation).Corresponding point are meant, 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 subjected 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 (as flat surfaces) as shown in Figure 6 or the Gaussian curvature magnitude of paddy can not cause big 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 bigger acting force this plate is flattened.As mentioned above, this can cause increasing harmful effect (bending, stress etc.) that may influence concrete manufacture process.On the contrary, the magnitude of Gaussian curvature is big more, makes the plate required acting force that flattens big more.The bending of plate at first takes place 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 represented with flattening shape, 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 action 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,, produce big membrane interaction power and moment along with planarization application power increases.For the singular point (singularity) of big Gaussian curvature magnitude, apply more weak acting force in the time of (as having only gravity), the Gaussian curvature magnitude that can estimate 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.Though 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, just can determine the Gaussian curvature of this plate at the each point place by adopting agravic plate to form the distance that measuring method is determined at a plurality of some places and reference plane.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
2Be equation 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 parabolic closely 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 to plate carries 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 difference between the respective regions of this zone of plate and area supported is bigger) situation beyond, this plate can comprise a kind of so bigger zone, this zone even have relevant less but limited Δ K.In this case, the big zone with lower magnitude is flattened to this big zone summation, cause identical ill-effect equally.Consider the big zone that level Δ K in a small amount is associated, can in this lip-deep mobile window, carry out integration by the absolute value to Δ K, with the result with respect to integral area normalization.Can use the K integrated value (K that obtains then
Integration) as tolerance to this plate shape.That is,
This situation as shown in Figure 10, wherein integral area S moves 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 the magnitude of this plate in the Gaussian curvature at each point place simply on this plate.Δ K be can easily determine then, 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 the half width of bubble along 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 flatten the bubble (for example b＞＞bubble of a) of elongation to flatten than the symmetry bubble (a=b) that makes equal height and want much simple, because the maximum Gaussian curvature of bubble becomes lower.Figure 13 is the diameter of symmetry bubble and the graph of a relation of height, and the Gaussian curvature of this symmetry bubble is 1 * 10
-8Millimeter
-2Highly-bubble that diameter Relationship is positioned at the curve right side tends to show good clamping behavior (can be clamped in the enterprising parallel planesization of smooth supporting mass by vacuum), 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 the single maximal value of warpage with the relation that glass plate clamps behavior.
● 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 under 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, though 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 subjected to the protection of following claim.
Claims (8)
1. the method for the compliance on a definite glass plate and a surface, this method may further comprise the steps:
Determine the shape of this 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 the Gaussian curvature magnitude of this plate, determine on this plate that the Gaussian curvature magnitude of each point is poor in a plurality of points;
From a plurality of Gaussian curvature magnitude differences, select the maximum Gaussian curvature magnitude of this plate poor;
This maximum Gaussian curvature magnitude difference and the max-thresholds that is predetermined compared and
If this maximum Gaussian curvature magnitude is equal to or less than this threshold value, then this plate is classified as acceptable, if this maximum Gaussian curvature magnitude greater than this max-thresholds, then classifies as this 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 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 plate is bearing on a plurality of adjustable pins that these pins are suitable for applying the acting force that is predetermined to this plate.
5. the method for claim 1 is characterized in that, described method also is included on this 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, described max-thresholds is less than or equal to about 1 * 10
-8Millimeter
-2
8. the method for claim 1 is characterized in that, a plurality of points on the described plate are represented the subclass of all putting on the whole plate, and the subclass 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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|---|---|
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| CN102007370B 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 |
Country Status (5)
| Country | Link |
|---|---|
| JP (1) | JP5416143B2 (en) |
| KR (1) | KR101543053B1 (en) |
| CN (1) | CN102007370B (en) |
| TW (1) | TWI392846B (en) |
| WO (1) | WO2009108302A1 (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109641774A (en) * | 2016-05-23 | 2019-04-16 | 康宁股份有限公司 | Predict the method for the gravity-free shape of glass plate and the method based on gravity-free shape management glass plate quality |
| CN113468782A (en) * | 2021-06-21 | 2021-10-01 | 上汽大众汽车有限公司 | Laminated glass finite element modeling method for vehicle collision assessment |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
Family Cites Families (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| RU1791703C (en) * | 1987-10-30 | 1993-01-30 | Центральный научно-исследовательский геологоразведочный институт цветных и благородных металлов | Method of checking state of long-measure object |
| 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 |
| JP3937212B2 (en) * | 1997-04-25 | 2007-06-27 | 独立行政法人理化学研究所 | Method for discriminating shape error of free-form surface |
| JP3418819B2 (en) * | 1998-01-13 | 2003-06-23 | 東芝セラミックス株式会社 | Plate flatness measuring device |
| JP3344649B2 (en) * | 1998-08-19 | 2002-11-11 | 理化学研究所 | Evaluation method for shape error of free-form surface |
| 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 KR KR1020107021506A patent/KR101543053B1/en active IP Right Grant
- 2009-02-25 CN CN200980114488.8A patent/CN102007370B/en not_active Expired - Fee Related
- 2009-02-25 JP JP2010548704A patent/JP5416143B2/en not_active Expired - Fee Related
- 2009-02-25 WO PCT/US2009/001166 patent/WO2009108302A1/en active Application Filing
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109641774A (en) * | 2016-05-23 | 2019-04-16 | 康宁股份有限公司 | Predict the method for the gravity-free shape of glass plate and the method based on gravity-free shape management glass plate quality |
| CN109641774B (en) * | 2016-05-23 | 2022-02-18 | 康宁股份有限公司 | Method for predicting gravity-free shape of glass sheet and method for managing quality of glass sheet based on gravity-free shape |
| US11614323B2 (en) | 2016-05-23 | 2023-03-28 | Corning Incorporated | Method of predicting gravity-free shape of glass sheet and method of managing quality of glass sheet based on gravity-free shape |
| CN113468782A (en) * | 2021-06-21 | 2021-10-01 | 上汽大众汽车有限公司 | Laminated glass finite element modeling method for vehicle collision assessment |
Also Published As
| Publication number | Publication date |
|---|---|
| JP2011513727A (en) | 2011-04-28 |
| KR101543053B1 (en) | 2015-08-07 |
| TWI392846B (en) | 2013-04-11 |
| CN102007370B (en) | 2013-03-13 |
| WO2009108302A1 (en) | 2009-09-03 |
| KR20100138971A (en) | 2010-12-31 |
| TW201003036A (en) | 2010-01-16 |
| JP5416143B2 (en) | 2014-02-12 |
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