阅读说明：本技术 用于估计材料片形状的方法及设备 (Method and apparatus for estimating shape of material sheet ) 是由 约翰·S·阿博特三世 郑哲明 于 2020-03-27 设计创作，主要内容包括：本案提供用于获取玻璃片的无重力形状、及固有形状、及热应变的方法及设备,并使用此等方法及设备改善玻璃制造技术。(Methods and apparatus for obtaining a gravity-free shape, and intrinsic shape, and thermal strain of a glass sheet are provided, and glass manufacturing techniques are improved using such methods and apparatus.)

1. A method, comprising:

obtaining a respective first initial weight measurement on each of a plurality of force sensors of a gauge in response to a first application glass sheet when all of the plurality of force sensors are at a constant initial height (flat); and

estimating a first intrinsic shape of the first glass sheet from the respective first initial weight measurements.

2. The method of claim 1, wherein the meter comprises a plurality of height adjustable pins, each height adjustable pin associated with one of the plurality of force sensors.

3. The method of claim 1, wherein estimating the first intrinsic shape of the first glass sheet comprises:

calculating, for each force sensor of the plurality of force sensors, a respective secondary height away from the constant initial height from the respective first initial weight measurement, wherein the calculation is based on a recursive algorithm for moving the height adjustable latch to estimate a gravity-free shape of the first glass sheet; and

estimating said first intrinsic shape from said respective minor heights thereof.

4. The method of claim 1, wherein estimating the first intrinsic shape of the first glass sheet from the respective first initial weight measurements is represented as:

wherein w₀In the form of the first intrinsic shape,is the bending stiffness of the first glass sheet, h is the thickness of the first glass sheet, ρ is the density of the first glass sheet, g is the gravity constant, E is the Young's modulus of the first glass sheet, ν is the Poisson's ratio of the first glass sheet, and f_iIs the respective first initial weight measurement.

5. The method of claim 1, further comprising estimating a first embedded thermal strain of the first glass sheet.

6. The method of claim 5, further comprising estimating the first embedded thermal strain of the first glass sheet by:

obtaining a measured stress in the first glass sheet as the first glass sheet is pressed flat; and

estimating the first embedded thermal strain from the measured stress and the first intrinsic shape.

7. The method of claim 6, wherein:

a stress function obtained from the measured stress may be represented according to the first intrinsic shape as follows:

whereinAs a function of the stress, EK_G(w₀) Is the first inherent shape w₀A Gaussian curve of, andis the number of terms based on the first embedding thermal strain, at; and

obtaining the estimate of the thermal strain by solving for a.

8. The method of claim 5, further comprising estimating a gravity-free shape of the first glass sheet based on the first intrinsic shape and the first embedded thermal strain of the first glass sheet.

9. The method of claim 8, further comprising:

(a) comparing the measured gravity-free shape of the glass sheet to the estimated value of the gravity-free shape to obtain an indication of the accuracy of the estimated first embedded thermal strain of the first glass sheet;

(b) correcting the estimated first embedded thermal strain and re-estimating the gravity-free shape of the first glass sheet based on the first intrinsic shape of the first glass sheet and the corrected first embedded thermal strain when the comparison indicates that the precision of the estimated first embedded thermal strain is below a minimum value; and

(c) repeating steps (a) and (b) until the comparison result indicates the accuracy with which the estimated first embedding thermal strain is equal to or higher than the minimum value.

10. The method of claim 1, further comprising:

estimating a plurality of local gravity-free shapes for each of a respective section of the plurality of sections of the first glass sheet if the first glass sheet is cut into the plurality of sections,

wherein each of the local gravity-free shapes is estimated from the first inherent shape, an

Wherein each local gravity-free shape of the plurality of local gravity-free shapes is estimated by subtracting a respective local average plane of the plurality of local average planes from the first eigen shape.

11. The method of claim 1, further comprising:

(a) obtaining a respective second initial weight measurement on each of the plurality of force sensors in response to a second application glass sheet when all of the plurality of force sensors of the gauge are set to the constant initial height;

(b) estimating a second intrinsic shape of the second glass sheet from the respective second initial weight measurements; and

(c) repeating steps (a) and (b) for each application glass sheet of a plurality of application glass sheets to obtain a plurality of intrinsic shapes of the plurality of application glass sheets, wherein the plurality of application glass sheets includes at least the first application glass sheet and the second application glass sheet.

12. The method of claim 11, further comprising:

applying a stitching procedure to obtain an estimate of a combined intrinsic shape comprising each intrinsic shape of the plurality of intrinsic shapes of the plurality of application glass sheets that matches at an edge of the plurality of application glass sheets;

estimating an embedded thermal strain of a combined glass sheet, wherein the combined glass sheet is estimated using a stitching procedure to combine the plurality of application glass sheets matched at respective edges of the plurality of application glass sheets; and

estimating a gravity-free shape of the combined glass sheet from the combined intrinsic shape and the embedded thermal strain.

13. The method of claim 12, wherein said estimate of said embedded thermal strain of said assembled glass sheet is obtained by:

estimating a respective embedded thermal strain for each of the plurality of applied glass sheets; and

averaging the respective embedded thermal strains of each of the plurality of applied glass sheets to obtain the embedded thermal strain of the combined glass sheet.

14. The method of claim 12, wherein said estimate of said embedded thermal strain of said assembled glass sheet is obtained by:

cutting a subsection from a representative glass sheet, wherein the representative glass sheet is representative of the feature of the combined glass sheet and has a larger square area than any one of the plurality of application glass sheets;

applying the subsections of the representative glass sheet to a plurality of force sensors of the gauge;

obtaining a respective initial weight measurement on each force sensor of the plurality of force sensors in response to the subsection of the representative glass sheet when all of the plurality of force sensors are set to a constant initial height;

estimating an intrinsic shape of the subsection of the representative glass sheet from the initial weight measurement;

obtaining a measured stress in the subsection of the representative glass sheet while the subsection of the representative glass sheet is in progress; and

estimating the embedded thermal strain of the combined glass sheet from the measured stress and the intrinsic shape of the sub-section of the representative glass sheet.

Technical Field

The disclosed embodiments relate to methods and apparatus for measuring and estimating the shape of a sheet of material, such as a relatively large sheet of glass, particularly a large and thin sheet of glass.

Background

Producing commercial products (e.g., Liquid Crystal Displays (LCDs), other display glass, etc.) from larger pristine glass sheets involves a number of challenges. For example, it is important to understand and control the behavior of the glass sheet during the process used to form the large glass sheet (e.g., the downdraw fusion process) and downstream processes (e.g., the behavior of the glass sheet when it is held in place on a flat surface by a vacuum chuck, cut, etc.). Such challenges are described in U.S. Pat. No. 7,509,218 and international patent publication No. WO2009/108302, the entire disclosures of which are incorporated herein by reference.

To better control the glass forming and manufacturing process, it is of great value to gain knowledge about the gravity-free shape of large glass sheets, which are themselves flexible objects. Determining the gravity-free shape of large glass sheets has become particularly challenging. As glass manufacturing processes advance, the original glass sheets become larger and thinner. Indeed, in the past, a typical pristine glass sheet may be about 1500 mm x1800 mm; however, the prior art allows for pristine glass sheets on the order of about (e.g., measuring 2880 mm x3130 mm) 9 square meters, and in the near future, even larger glass sheets are contemplated. These glass sheets have a thickness of about 0.7 mm, and thus the demand for thinner glass sheets is increasing.

Conventional methods of determining a gravity-free shape employ bed of nails (BON) techniques, for example, as described in detail in U.S. patent No. 7,509,218 and U.S. patent No. 9,031,813, the entire disclosures of which are incorporated herein by reference. The BON technology involves an apparatus having an array (e.g., about 100) of height adjustable pins and force sensor combinations. Any of a number of recursive algorithms may be employed to adjust the respective height adjustable latch in response to the measured force applied to the force sensor through the glass sheet. When the recursive algorithm causes the corresponding height of the height adjustable latch to be relatively constant by the force sensor for the measured target weight, then the corresponding height of the latch will produce a gravity-free shape of the glass sheet.

One of the limitations of BON technology is the array size of the height adjustable pin and force sensor combination. In fact, as the size of the raw glass sheet increases, the available area on the BON equipment becomes too small to accommodate the raw glass sheet.

Disclosure of Invention

In accordance with one or more aspects of the disclosed embodiments, new techniques are employed to provide a more complete understanding of the shape of a flexible object, such as a glass sheet, not only with respect to gravity-free shapes, but also with respect to the characteristics of the inherent shape and associated thermal strain.

One or more embodiments herein may address how to estimate both the gravity-free shape and the intrinsic shape of a glass sheet from one or more measurements taken during a BON technique that measures the gravity-free shape.

One or more embodiments herein can address how to estimate the shape and warp characteristics of a glass sheet (and of a smaller piece of glass sheet cut from the glass sheet) from the gravity-free shape of the glass sheet, the inherent shape of the glass sheet, and/or from the thermal strain of the glass sheet.

One or more embodiments herein address how to estimate the gravity-free shape of a large glass sheet that is too large to fit on available BON equipment based on the corresponding intrinsic shape and thermal strain of many smaller pieces of the glass sheet that are cut from the large glass sheet.

Other aspects, features, and advantages will be apparent to one skilled in the art from the description herein taken in conjunction with the accompanying drawings.

Drawings

For the purposes of illustration, there are forms shown in the drawings that are presently preferred, it being understood, however, that the embodiments disclosed and described herein are not limited to the precise arrangements and instrumentalities shown.

FIG. 1A is a schematic representation of a glass sheet placed on a BON apparatus, particularly in an initial pass where all height adjustable pins of the BON apparatus are at a constant height (flat);

FIG. 1B is a schematic illustration of the glass sheet of FIG. 1A placed on a BON apparatus, particularly in a final iteration of the algorithm where all height adjustable pins of the BON apparatus indicate a gravity-free shape of the glass sheet;

fig. 2A, 2B, 2C, and 2D illustrate respective stages in the splicing process to cut a large piece of glass sheet into small pieces, obtain respective gravity-free shapes, and estimate an estimate of the gravity-free shape of the pristine glass sheet.

FIG. 3A is a representative graph of recursion (X-axis) versus pin height (Y-axis) variation in a BON device;

FIG. 3B is a representative graph of recursion (X-axis) versus weight error (Y-axis) in the BON device of FIG. 3A;

FIG. 4A is a schematic representation of a representative shading of an actual gravity-free shape of a dome-shaped glass sheet;

FIG. 4B is a simplified schematic representation of a shading of an estimated intrinsic shape of a glass sheet;

FIG. 4C is a simplified schematic representation of shading of an estimated thermal strain of a glass sheet; and

FIG. 4D is a simplified schematic representation of shading of a gravity-free shape of the glass sheet of FIG. 4A calculated based on the estimated intrinsic shape of FIG. 4B and the estimated thermal strain of FIG. 4C.

Detailed Description

Referring to the drawings, wherein like numerals indicate like elements, there is shown in fig. 1A schematic view of a glass sheet 10 placed on a BON apparatus 100, particularly in an initial iteration where all height adjustable pins 102 of the BON apparatus 100 are at a constant height (i.e., flat). As previously described, each height adjustable pin 102 is associated with a corresponding force sensor 104, which are arranged in an X-Y array (e.g., a 9X 11 array). The corresponding height of the height adjustable latch 102 is measured in the Z direction (e.g., typically in millimeters).

Fig. 1B is a schematic diagram of the glass sheet 10 on the BON apparatus 100 of fig. 1A, particularly where all of the height adjustable pins 102 of the BON apparatus 100 indicate a gravity-free shape of the glass sheet 10 in the final iteration of the algorithm.

The BON process involves calculating/estimating a set of target weights (e.g., constants) that the glass sheet 10 will exert on the force sensor 104 if the glass sheet 10 is perfectly flat (i.e., has a perfectly flat, gravity-free shape) and if the array of height-adjustable pins 102 is perfectly flat. Since the glass sheet 10 is not perfectly flat, the actual initial weight measured at the initial recursion (fig. 1) of all height adjustable pins 102 of the BON apparatus 100 in the constant (i.e., flat) case does not match the target weight. Thus, in order to match the actual measured weight on the force sensor 104 to the target weight, the corresponding height of the height adjustable pin 102 of the BON device 100 cannot be constant (and must be changed).

Any of a number of recursive algorithms may be employed to calculate the change in the respective height of the height adjustable bolt 102 based on the measured weight on each recursive force sensor. A recursive algorithm is employed to converge on the final set of respective heights of the height adjustable bolt 102 such that the actual measured weight on the force sensor 104 matches the target weight. The resulting set of corresponding heights reflects the (non-flat) gravity-free shape of glass sheet 10. The determined gravity-free shape may be confirmed or tested by flipping the glass sheet 10 to the other side and performing the BON process again. If both BON processes result in substantially the same gravity-free shape, the gravity-free shape is confirmed.

As discussed above, one of the limitations of a given BON apparatus 100 is the limited size of the height adjustable pins 102 and associated array of force sensors 104. In the case of the embodiment shown in fig. 1A, 1B, the arrangement of the 9 × 11 array is capable of measuring glass sheets on the order of about 1500 mm × 1800 mm. Therefore, it is not possible to directly measure the gravity-free shape of a larger glass sheet (e.g., about 2880 mm × 3130 mm) by placing the entire glass sheet on the BON apparatus 100 shown in fig. 1A, 1B.

With reference to fig. 2A, 2B, 2C, and 2D, a discussion of a conventional attempt to solve the above-mentioned problems will be presented. The power of the attempted solution: (i) cutting larger glass sheets into smaller pieces; (ii) measuring the gravity-free shape of each smaller piece on the BON device 100; (iii) the gravity-free shape of each smaller piece is mathematically stitched together to estimate the gravity-free shape of the larger glass sheet (if uncut). Fig. 2A, 2B, 2C, and 2D illustrate respective stages in the splicing process whereby glass sheet 20 (larger than the available area of BON apparatus 100) is cut into smaller pieces 20A, 20B, 20C, 20D. Fig. 2A illustrates the respective gravity-free shape of each block acquired separately using the BON device 100. Fig. 2A illustrates a top view (shaded) of a corresponding gravity-free shape, while fig. 2B is a representative perspective view of the gravity-free shape of the smaller pieces 20A, 20B, 20C, 20D. Fig. 2A and 2B show that the gravity-free shape of each smaller piece 20A, 20B, 20C, 20D is generally saddle-shaped.

Fig. 2C illustrates the final estimation operation of the gravity-free shape of the larger glass sheet 20 using the mathematical procedure of a conventional splicing process (or procedure) where each respective gravity-free shape of the nubs 20A, 20B, 20C, 20D matches at the respective edges of the nubs 20A, 20B, 20C, 20D. Although the result in fig. 2C is interesting, it does not match the actual gravity-free shape of glass sheet 20 in fig. 2D, and is typically dome-shaped.

It has been found that for some types of glass sheets, the relatively large glass sheet 20 typically exhibits a dome-shaped, gravity-free shape; however, when cut into small pieces, each piece typically has a saddle-shaped, gravity-free shape. It is believed that these characteristics are due to the fusion draw process during the manufacture of glass sheet 20. Thus, when small pieces of glass are cut from a larger sheet of glass 20 (that has been fusion drawn) for commercial applications, the glass pieces tend to exhibit a saddle shape unless changes are made to the fusion drawing process. Notably, however, this is not apparent from the gravity-free (dome) shape of the larger glass sheet 20.

It is noted that the shape estimated in fig. 2C has some similarities to another feature (i.e., the intrinsic shape) of glass sheet 20. The intrinsic shape is the shape determined by cutting the glass sheet into a plurality of smaller pieces, measuring the gravity-free shapes of these pieces, and mathematically splicing the gravity-free shapes together (using the splicing procedure described above). However, it has been found that the inherent shape of the glass sheet can be estimated without cutting the glass sheet into pieces. This finding is based in part on the representative graphs of fig. 3A and 3B.

FIG. 3A is a representative graph of the variation in height of the insert pins in a BON device (the absolute variation in height plotted along the Y-axis) as a function of the number of recursions (plotted along the X-axis). The data are the results of the recursive algorithm described above performed on glass sheet 10 measuring 1500 mm x1850 mm x1.0 mm on the BON apparatus shown in fig. 1A and 1B. The curve 300 is a graph of the absolute value of the maximum height change of the one or more height adjustable pins 102 according to the number of recursions. Curve 302 is a graph of the absolute value of the change in height of a given pin (e.g., pin #1) in the adjustable pin 102 based on the number of recursions. Curve 304 is a graph of the absolute value of the change in height of another designated pin (e.g., pin #30) in the height adjustable pins 102 according to the number of recursions.

Fig. 3B is a representative graph of weight error in a BON device (grams plotted along the Y-axis) as a function of recursion times (plotted along the X-axis) (corresponding to the experiment performed in conjunction with fig. 3A). Curve 306 is a plot of the maximum weight error of one or more force sensors 104 as a function of the number of recursions. Curve 308 is a plot of the median weight error of one or more force sensors 104 as a function of the number of recursions.

Looking at the circled portions of FIGS. 3A and 3B, some interesting information about the recursive algorithm employed by the BON technique can be ascertained. Special attention is paid to the latter case, in which the secondary height of the height adjustable bolt is estimated based on the measured weight at each recursion, and any weight error is tried to be zeroed. As can be seen in fig. 3A and 3B, the error initially decreases rapidly (indicating that the shape is converging) so that the smallest error occurs near the recursions 100 through 200. The error then increases and then decreases again to an earlier error size around the recursion 800. This demonstrates that the initial estimate of the height adjustable pin 102 will respond to the weight distribution when the height adjustable pin 102 is generally horizontal (flat). In this orientation, the embedded thermal strain of the glass sheet 10 (in-plane stress/strain) has little effect on the normal force (weight) on the height adjustable latch 102. Thus, the initial estimate of the motion of the height adjustable pin 102 converges on an inherent shape (not a gravity-free shape) when the height adjustable pin 102 is generally flat. Once the recursive algorithm estimates that the next height of the height adjustable latch 102 is sufficiently out of plane (sufficiently far from flat, e.g., greater than the thickness of the glass sheet), the embedded stress of the glass sheet 10 has an increased effect on the normal force (weight) on the force sensor 104. This results in a process where the recursive algorithm converges in the other direction, i.e., eventually into a gravity-free shape of the glass sheet 10. Thus, the gravity-free shape can be determined from the inherent shape of glass sheet 10 and the embedded thermal strain.

As previously mentioned, when the glass sheet 10 is placed on an array of relatively flat height adjustable pins 102, the recursive algorithm measures the weight distribution and then attempts to move the pins 102 to a position where the weight will match the target weight. At zero recursion, the initial weight measurement provides a solution to the inherent shape of glass sheet 10. Applying a recursive algorithm in the BON apparatus 100, once the glass sheet 10 is moved out of plane (after calculating and moving the height adjustable pin 102 using the initial weight measurements), the weight on the height adjustable pin 102 will reflect both the intrinsic shape and reflect the in-plane stress. Thus, the height adjustable latch 102 will converge to the gravity-free shape of the glass sheet 10 rather than to the inherent shape of the glass sheet 10.

According to one or more embodiments herein, such methods and apparatus provide: (i) acquiring a respective initial weight measurement on each of the plurality of force sensors in response to applying the glass sheet 10 while the plurality of force sensors of the gauge are all at a constant initial height (flat); and (ii) estimating the intrinsic shape of the glass sheet from the respective initial weight measurements.

Generally, the gauge need not include a height adjustable pin 102 (e.g., in BON equipment) because only one initial weight measurement is necessary at a minimum. Of course, the meter may be a BON device, wherein the meter includes a plurality of height adjustable pins 102, each associated with one of the plurality of force sensors 104 as previously described.

The operation of estimating the intrinsic shape of glass sheet 10 may be accomplished by: (i) calculating, for each height-adjustable bolt of the plurality of height-adjustable bolts 102 (and/or each force sensor 104 of the plurality of force sensors), a respective secondary height away from the constant initial height from the respective initial weight measurement, wherein the calculating step estimates the gravity-free shape of the glass sheet 10 based on a recursive algorithm for moving the adjustable bolt 102; and (ii) estimating the intrinsic shape of glass sheet 10 based on the respective minor heights.

Another way of estimating the inherent shape of the glass sheet 10 from the corresponding initial weight measurements is as follows:

wherein w₀In the form of a first inherent shape,is the bending stiffness of the glass sheet, h is the thickness of the glass sheet, ρ is the density of the glass sheet, g is the gravity constant, E is the Young's modulus of the glass sheet, v is the Poisson's ratio of the glass sheet, and f_iAre corresponding initial weight measurements.

The intrinsic shape can be verified by modeling. The information provided by BON technologies corporation is the measured weight on the height adjustable pin and the predicted height relative to the inherent shape of the average horizontal plane. The software can be implemented in commercially available software products such as,or similar software, when a horizontal planar sheet of the correct size, thickness, and glass properties (density, young's modulus, poisson's ratio, etc.) is deformed by moving the pin (in the model) to the position predicted by the BON technique, the modeling force on the pin is inferred. The modeled reaction force on the pin should be consistent with the measurement data of the BON, and indeed.

In some cases, the BON technique may use a matrix that is derived for a different sheet thickness than the actual sheet in the experiment. In such a case, ANSYS analysis will show that the difference in reaction force is the ratio of [ (thickness 1)/(thickness 2) ] × 2. The intrinsic shape can thus be corrected and if thickness 1 and thickness 2 are known, the correction can be made without ANSYS analysis.

The intrinsic shape can also be more directly estimated by applying a measured force error (relative to a flat horizontal plate) at the pin position and estimating the shape change, by using COMSOL, ANSYS, or similar model estimation.

The characteristic of the glass sheet associated with the intrinsic shape and gravity shape characteristics is the embedded thermal strain. Embedded thermal strain of the glass sheet occurs when different portions of the glass sheet crystallize (or freeze) at different times, and this characteristic affects the shape of the glass sheet. According to one or more embodiments herein, such methods and apparatus provide for estimating the embedded thermal strain of a glass sheet. By way of example, the embedded thermal strain of a glass sheet can be estimated by: (i) obtaining a measured stress in the glass sheet as the glass sheet is pressed flat; and (ii) estimating the embedded thermal strain based on the measured stress and the intrinsic shape.

In connection with the above, the stress function obtained from the measured stress can be expressed in terms of the intrinsic shape, as follows:

whereinAs a function of stress, EK_G(w₀) Is of an intrinsic shape w₀A Gaussian curve of, andis the number of terms based on embedded thermal strain, α T; and obtaining an estimated value of the thermal strain by solving alpha. In the above stress function, the only way for the thermal strain to affect the yield result is through the second orderDerivative of(also referred to as "Del-Squares alpha T"). Therefore, to estimate the effect of thermal strain, only "Del ^2alpha T" needs to be estimated. Referring to fig. 4C, Alpha-T is used which is uniform in the vertical direction and varies only in the horizontal direction due to the formation of glass sheet flowing down from the draw (i.e., the variation under the draw is less than the variation across the draw). Importantly, Del ^ of the function is effectively constant, and many other functions will also result in a constant.

The estimated thermal strain may be tested and improved according to the following methods and apparatus: (a) comparing the measured gravity-free shape of the glass sheet to the estimated value of the gravity-free shape to obtain an indication of the accuracy of the estimated embedded thermal strain of the glass sheet; (b) when the comparison result indicates that the accuracy of the estimated embedded thermal strain is lower than the minimum value, correcting the estimated embedded thermal strain, and re-estimating the gravity-free shape of the glass sheet according to the inherent shape of the glass sheet and the corrected embedded thermal strain; and (c) repeating steps (a) and (b) until the comparison result indicates a precision with which the first embedded thermal strain is estimated to be equal to or higher than the minimum value.

Referring to fig. 4A, 4B, 4C, and 4D, the methods and apparatus disclosed herein may provide functionality for estimating the gravity-free shape of glass sheet 10 based on the inherent shape of glass sheet 10 and the embedded thermal strain. Fig. 4A is a schematic diagram of a representative shading of an actual gravity-free shape of dome-shaped glass sheet 10. Without actually measuring the gravity-free shape of glass sheet 10, and using the techniques discussed above, the intrinsic shape of glass sheet 10 (fig. 4B) can be estimated and used in a manner related to the estimate of the thermal strain of the glass sheet (fig. 4C) to estimate the gravity-free shape of glass sheet 10 (fig. 4D), which is also dome-shaped.

With the discoveries set forth above, advantageous results may be obtained, including methods and apparatus for estimating the respective local gravity-free shape of a smaller piece of a larger glass sheet without cutting the larger glass sheet. In particular, such methods and apparatus provide for estimating the corresponding local gravity-free shape based on the inherent shape of the glass sheet. For example, each local gravity-free shape of the plurality of local gravity-free shapes may be estimated by subtracting a respective local average plane of the plurality of local average planes from the intrinsic shape.

Advantageous results may be obtained using the findings discussed above, particularly when the gravity-free shape of large glass sheet 20 cannot be directly measured by a BON apparatus (as described above). In this regard, a single, relatively large glass sheet 20 is considered to comprise a plurality of glass sheets (if cut into smaller pieces), wherein the plurality of glass sheets comprises a first applied glass sheet, a second applied glass sheet, and the like.

The methods and apparatus herein provide for: (i) obtaining a respective first initial weight measurement on each of the plurality of force sensors in response to the first application glass sheet when all of the plurality of force sensors of the gauge are at a constant initial height (flat); and (ii) estimating a first intrinsic shape of the first glass sheet from the respective first initial weight measurements.

Such methods and apparatus further provide: (a) obtaining a respective second initial weight measurement on each of the plurality of force sensors in response to the second application glass sheet when all of the plurality of force sensors are set to a constant initial height; (b) estimating a second intrinsic shape of the second glass sheet from the respective second initial weight measurements; and (c) repeating steps (a) and (b) for each of the plurality of application glass sheets to obtain a plurality of intrinsic shapes for the plurality of application glass sheets.

Such methods and apparatus further provide: (a) applying a stitching procedure to obtain an estimate of a combined intrinsic shape, the combined intrinsic shape comprising each intrinsic shape that matches a plurality of intrinsic shapes of a plurality of application glass sheets at edges of the plurality of application glass sheets; (b) estimating an embedded thermal strain of the combined glass sheet, wherein the combined glass sheet is estimated using a stitching procedure to combine a plurality of applied glass sheets matched at respective edges of the plurality of applied glass sheets; and (c) estimating the gravity-free shape of the composite glass sheet based on the composite intrinsic shape and the embedded thermal strain.

Such methods and apparatus further provide: by obtaining an estimate of the embedded thermal strain of the combined glass sheet: (a) estimating a respective embedded thermal strain for each of the plurality of applied glass sheets; and (b) averaging the respective embedded thermal strains of each of the plurality of applied glass sheets to obtain an embedded thermal strain for the combined glass sheet.

Additionally or alternatively, such methods and apparatus further provide for: obtaining an estimate of embedded thermal strain of the assembled glass sheet by: (a) cutting a subsection from a representative glass sheet, wherein the representative glass sheet is representative of a feature of the combination glass sheet and has a larger square area than any one of the plurality of application glass sheets; (b) applying sub-segments of a representative glass sheet to a plurality of force sensors of a meter; (c) obtaining a respective initial weight measurement on each of the plurality of force sensors in response to the subsection of the representative glass sheet when all of the plurality of force sensors are set to a constant initial height; (d) estimating an intrinsic shape of a subsection of the representative glass sheet from the initial weight measurement; (e) obtaining a measured stress in a subsection of a representative glass sheet as the subsection of the representative glass sheet; and (f) estimating the embedded thermal strain of the combined glass sheet based on the measured stress and the intrinsic shape of the sub-section of the representative glass sheet.

Although the present disclosure has been described in connection with particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the embodiments herein. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present description.