IN EDGE ROLLER GEOMETRY

Cross Reference to Related Applications

[0001] This application claims the benefit of priority under 35 U.S.C. § 119 of U.S. Provisional Application Serial No.: 63/220,110, filed on July 9, 2021, the content of which is relied upon and incorporated herein by reference in its entirety.

Field

[0002] The present specification generally relates to apparatuses and methods for making glass ribbons.

Technical Background

[0003] Glass forming apparatuses are commonly used to form various glass products such as glass sheets used for LCD displays and the like. These glass sheets may be manufactured using a downdraw process by downwardly flowing molten glass over a forming wedge to form a continuous glass ribbon. In a downdraw process, various rollers may be used to provide a pulling force to the continuous glass ribbon, apply a tension to the ribbon, or to guide the glass ribbon. Edge rollers, for example, may pinch the edges of the continuous glass ribbon and guide the glass ribbon. Such edge rollers may be arranged in pairs to contact opposing surfaces of the glass ribbon. In the event that the edge rollers do not have corresponding shapes, a separation distance therebetween may vary as a function of time (e.g., as the edge rollers rotate), leading to thickness variations in glass sheets. Such thickness variations may lead to the glass sheets being unsuitable for certain applications, such as high definition displays.

SUMMARY

[0004] A first aspect of the present disclosure includes a method of manufacturing glass comprising: forming a glass ribbon from a quantity of molten material, the glass ribbon comprising a first surface and a second surface; contacting the first surface with a first edge roller and the second surface with a second edge roller; rotating the first edge roller at a first rotational velocity and rotating the second edge roller at a second rotational velocity ; generating a firsttorque signal representative of a torque appliedto the first edge roller and a second torque signal representative of a second torque applied to the second edge roller; generating a torque summation signal of the first torque signal and the second torque signal; and modulating the first rotational velocity and the second rotational velocity in a time-dependent manner to counteract variations in the torque summation signal.

[0005] A second aspect of the present disclosure includes a method according to the first aspect, wherein modulating the first rotational velocity and the second rotational velocity in a time dependent manner comprises periodically modulating the first rotational velocity and the second rotational velocity by computing a target rotational velocity co _T using an equation: w _t = A * sin + f) + w _N , wherein A is an amplitude of modulation, Q1 2 is an angular position of the first edge roller or the second edge roller, F is a phase of modulation, and CO _N is a target rotational velocity of the first edge roller and the second edge roller.

[0006] A third aspect of the present disclosure includes a method according to any of the first through the second aspects, further comprising determining the phase of modulation by: determining a time delay between a roll position signal representative of the angular position and the torque summation signal; and converting the time delay to a phase angle.

[0007] A fourth aspect of the present disclosure includes a method according to any of the firstthrough the third aspects, further comprising, prior to determiningthe phase of modulation, filtering the torque summation signal using a bandpass filter comprising an upper cut-off frequency and a lower cut-off frequency, wherein co _N is between the upper cut-off frequency and the lower cut-off frequency.

[0008] A fifth aspect of the present disclosure includes a method accordingto any of the first through the fourth aspects, further comprising: sensing a thickness of the glass ribbon downstream of the first edge roller and the second edge roller; and determining the amplitude of modulation A based on the thickness of the glass ribbon.

[0009] A sixth aspect of the present disclosure includes a method according to any of the first through the fifth aspects, wherein determining the amplitude of modulation A comprises: periodically modulating the first angular velocity and the second angular velocity using a first value for the amplitude of modulation A; determining if the first value resulted in a reduction of thickness variations in the glass ribbon; and if the first value resulted in a reduction of thickness variations in the glass ribbon, increasing the amplitude of modulation A until the reduction in thickness variations is no longer observed.

[0010] A seventh aspect of the present disclosure includes a method according to any of the first through the sixth aspects, wherein the first edge roller and the second edge roller comprise different cross-sectional shapes such that a separation distance b etween the first edge roller and the second edge roller periodically varies with rotation of the first edge roller and the second edge roller.

[0011] An eighth aspect of the present disclosure includes a method according to any of the first through the seventh aspects, wherein the torque summation signal serves as a proxy for the separation distance such that, when the torque summation signal is greater than an average torque value, the separation distance is greater than an average distance.

[0012] A ninth aspect of the present disclosure includes a method according to any of the first through the eighth aspects, wherein the modulating the first rotational velocity and the second rotational velocity to counteract changes in the torque summation signal comprises: decreasing at least one of the first rotational velocity and the second rotational velocity during periods of time when the separation distance is increasing; and increasing at least one of the first rotational velocity and the second rotational velocity during periods of time when the separation distance is decreasing.

[0013] A tenth aspect of the present disclosure includes a method according to any of the first through the ninth aspects, wherein the modulating the first rotational velocity and the second rotational velocity to counteract changes in the torque summation signal reduces a moving- window thickness range of the glass ribbon under that achieved when the first rotational velocity and the second rotational velocity are not modulated.

[0014] An eleventh aspect of the present disclosure includes a method of manufacturing glass comprising the steps of: forming a glass ribbon from a quantity of molten material, the glass ribbon comprising a first surface and a second surface; contacting the first surface with a first edge roller and the second surface with a second edge roller, wherein the first edge roller and the second edge roller comprise different cross-sectional shapes such that a separation distance between the first edge roller and the second edge roller periodically varies depending on velocities at which the first and second edge rollers are rotated; driving the first edge roller and the second edge roller at a first rotational velocity and a second rotational velocity, respectively, generating a torque summation signal representative of a total torque applied to the first edge roller and the second edge roller; determining a time delay between the torque summation signal and an electric roll position signal representative of one or more of the first rotational position and the second rotational position; and updating the first rotational velocity and the second rotational velocity based on the time delay, the first rotational position, and the second rotational position.

[0015] A twelfth aspect of the present disclosure includesa method accordingto the eleventh aspect, wherein the updating comprises modulating the first rotational velocity and the second rotational velocity in a time-dependent manner.

[0016] A thirteenth aspect of the present disclosure includes a method accordingto any of the eleventh through the thirteenth aspects, wherein the modulating comprises periodically modulatingthefirstrotational velocity and the second rotational velocity by computing a target rotational velocity CO _T using an equation: w _t = A * sin + f) + w _N , wherein A is an amplitude of modulation, Q1 2 is an angular position of the first edge roller or the second edge roller, F is a phase of modulation determined from the time delay, and co _N is a target rotational velocity of the first edge roller and the second edge roller.

[0017] A fourteenth aspect of the present disclosure includes a method accordingto any of the eleventh through the thirteenth aspects, further comprising: sensing a thickness of the glass ribbon downstream of the first edge roller and the second edge roller; and determining the amplitude of modulation A based on the thickness of the glass ribbon.

[0018] A fifteenth aspect of the present disclosure includes a method according to any of the eleventh through the fourteenth aspects, wherein determining the amplitude of modulation A comprises: periodically modulating the first angular velocity and the second angular velocity using a first value for the amplitude of modulation A; determining if the first value resulted in a reduction of thickness variations in the glass ribbon; and if the first value resulted in a reduction of thickness variations in the glass ribbon, increasing the amplitude of modulation A until the reduction in thickness variations is no longer observed.

[0019] A sixteenth aspect of the present disclosure includes a method according to any of the eleventh through the fifteenth aspects, wherein the torque summation signal serves as a proxy for the separation distance such that, when the torque summation signal is greater than an average torque value, the separation distance is greater than an average distance.

[0020] A seventeenth aspect of the present disclosure includes a method according to any of the eleventh through the sixteenth aspects, wherein the updating comprises increasing the first rotational velocity.

[0021] An eighteenth aspect of the present disclosure a glass manufacturing apparatus comprising: a forming body configured to form a glass ribbon from a quantity of molten material, the glass formingbody defining a draw pathway extending from the formingbody along which the glass ribbon may be formed; an edge roll assembly comprising a pair of edge rollers positioned on either side of the draw pathway, the pair of edge rollers comprising a first edge roller comprising a first cross-sectional shape and a second edge roller comprising a second cross-sectional shape, the first cross-sectional shape varying from the second cross- sectional shape such that the first edge roller and the second edge roller are separated from one another by a separation distance that varies depending on velocities at which the first edge roller and the second edge rollers are rotated; one or more drive units mechanically coupled to the first edge roller and the second edge roller and configured to cause the first edge roller to rotate at a first rotational velocity about a first rotational axis and the second edge roller to rotate at a second rotational velocity about a second rotational axis, the one or more drive units further configured to generate a first torque signal representative of a first torque applied to the first edge roller and a second torque signal representative of a second torque applied to the second edge roller; and a controller communicably coupled to the one or more drive units and operable to: generate a torque summation signal from the first torque signal and the second torque signal; and modulate the first rotational velocity and the second rotational velocity using the torque summation signal such that the first and second rotational velocities are inversely proportional to the variable separation distance.

[0022] A nineteenth aspect of the present disclosure includes an apparatus according to the eighteenth aspect, further comprising a thickness sensor configured to sense a thickness of the glass ribbon downstream of the first edge roller and the second edge roller, the controller operable to modulate the first rotational velocity and the second rotational velocity based on the thickness of the glass ribbon. [0023] A twentieth aspect of the present disclosure includes a method according to any of the eighteenth through the nineteenth aspects, wherein the controller is operable to periodically modulate the first rotational velocity and the second rotational velocity using a phase of modulation computed based on a time delay between the torque summation signal and an electric roll position signal generated by the one or more drive units, the electric roll position signal being representative of a rotational position of at least one of the first edge roller or the second edge roller.

[0024] Additional features and advantages of the apparatus and methods for making a glass ribbon and replaceable heating cartridge for use in such apparatus and methods will be set forth in the detailed description which follows, and in part will be readily apparent to those skilled in the art from that description or recognized by practicing the embodiments described herein, including the detailed description which follows the claims, as well as the appended drawings.

[0025] It is to be understood that both the foregoing general description and the following detailed description describe various embodiments and are intended to provide an overview or framework for understanding the nature and character of the claimed subject matter. The accompanying drawings are included to provide a further understanding of the various embodiments andareincorporatedinto and constitute a part of this specification. The drawings illustrate the various embodiments described herein, ad together with the description serve to explain the principles and operations of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] FIG. 1 schematically depicts an apparatus for makingglass, accordingto one ormore embodiments shown and described herein;

[0027] FIG. 2 schematically depicts the apparatus for making glass in cross-section through the line 2-2 of FIG. 1, accordingto one ormore embodiments described herein;

[0028] FIG. 3A schematically depicts the apparatus for making glass in cross-section through the line 3-3 of FIG. 2, accordingto one ormore embodiments described herein;

[0029] FIG. 3B schematically depicts a plot of a separation distance between edge rollers of an edge roller pair of the apparatus for makingglass depicted in FIGS. 1-3 A, accordingto one ormore embodiments described herein; [0030] FIG. 4A depicts a plot of a torque summation signal of torques provided to edge rollers of an edge roller pair of an apparatus for making glass, according to one or more embodiments described herein;

[0031] FIG. 4B depicts a period-domain transformation of the plot of the torque summation signal depicted in FIG. 4 A, according to one or more embodiments described herein;

[0032] FIG. 5A depicts a frequency-domain plot of low-pass filter portion of a bandpass filterusedto filtera torque summation signal, accordingto one ormore embodiments described herein;

[0033] FIG. 5B depicts a frequency-domain plot of a high-pass filter portion of a bandpass filterusedto filtera torque summation signal, accordingto one ormore embodiments described herein;

[0034] FIG. 6 A a plot of an unfiltered torque summation signal of torques provided to edge rollers of an edge roller pair of an apparatus for making glass, according to one or more embodiments described herein;

[0035] FIG. 6B depicts a plot of a filtered torque summation signal generated by filtering the torque summation signal of FIG. 6Ausingthe bandpass filter depictedin FIGS. 4Aand4B, accordingto one ormore embodiments described herein;

[0036] FIG. 7 depicts a plot including a torque summation signal overlaid onto an electric roller position signal, accordingto one ormore embodiments described herein;

[0037] FIG. 8 depicts a flow diagram of a method of modulating rotational velocities of edge rollers of an apparatus for making glass, accordingto one or more embodiments described herein;

[0038] FIG. 9 depicts a flow diagram of a method of determining a phase of modulation and an amplitude of modulation that may be used to modulate the rotational velocities during the method of FIG. 8, accordingto one ormore embodiments described herein;

[0039] FIG. 10 depicts a plot of a thickness flapping trend of a glass ribbon generated using a plurality of amplitudes of modulation to modulate rotational velocities of edge rollers, accordingto one ormore embodiments described herein; DETAILED DESCRIPTION

[0040] Reference will nowbe made in detail to embodiments oftheapparatusesand methods for making glass ribbon that modulate rotational velocities of edge rollers in a time-dependent manner to counteract changes in a torque summation signal associated with pairs of the edge rollers, examples of which are illustrated in the accompanying drawings. Whenever possible, the same reference numerals are used throughout the drawings to refer to the same or like parts. The apparatuses for making glass ribbon of the present disclosure may include a glass forming body to form a glass ribbon from a quantity of molten material and a plurality of edge rollers positioned downstream from the glass forming body. The plurality of edge rollers may comprise an edge roller pair comprising a first edge roller and a second edge roller positioned to contact opposite surfaces of the glass ribbon. One or more drive units may rotate the first and second edge rollers at first and second rotational velocities and generate torque signals representative of torques applied to the first and second edge rollers. The first edge roller may differ from the second edge roller in cross-sectional shape such that a separation distance between the first and second edge rollers may vary as a function of time, leading to the torque signals varying as a function of time. A controller may receive the torque signals and generate a torque summation signal. The controller may modulate the rotational velocities at which the first and second edge rollers are rotated by the one or more drive units to counteract variations in the torque summation signal. Such time-dependent modulation may reduce the variability of the separation distance between the first and second edge rollers and reduce thickness variations in the glass ribbon. As a result, glass sheets produced via the apparatuses described herein may comprise more uniform wall thicknesses than those produced without time- dependent roller velocity modulation.

[0041] As used herein, the term “thickness flapping” refers to a periodic thickness variation in a draw direction near the edge of a glass ribbon while the glass ribbon is being formed using a downdraw process (e.g., a fusion draw process, a slot draw process).

[0042] Referring now to FIG. 1, an embodiment of an apparatus 10 for making glass, such as a glass ribbon 12, is schematically depicted. The apparatus 10 generally includes a melting vessel 15 configured to receive batch material 16 from a storage bin 18. The batch material 16 can be introduced to the melting vessel 15 by a batch delivery device 20 powered by a motor 22. An optional controller 24 may be provided to activate the motor 22 and a molten glass level probe 28 can be used to measure the glass melt level within a standpipe 30 and communicate the measured information to the controller 24.

[0043] The apparatus 10 can also include a fining vessel 38, such as a fining tube, located downstream from the melting vessel 15 and coupled to the melting vessel 15 by way of a first connecting tube 36. A mixing vessel 42 can alsobe located downstream from the fining vessel 38. A delivery vessel 46may be located downstream from the mixingvessel 42. As depicted, a second connecting tube 40 couples the fining vessel 38 to the mixing vessel 42 and a third connecting tube 44 couples the mixing vessel 42 to the delivery vessel 46. As further illustrated, a downcomer 48 is positioned to deliver glass melt from the delivery vessel 46 to an inlet 50 of a forming vessel 60. In the embodiment schematically depicted in FIG. 1, the melting vessel 15, fining vessel 38, mixing vessel 42, delivery vessel 46, and forming vessel 60 are examples of various glass processing stations that may be located in series along the apparatus 10.

[0044] The melting vessel 15 is typically made from a refractory material, such as refractory (e.g., ceramic) brick. The apparatus 10 may further include components that are typically made from platinum or platinum-containing metals such as platinum-rhodium, platinum-iridium and combinations thereof, but which may also comprise such refractory metals such as molybdenum, palladium, rhenium, tantalum, titanium, tungsten, ruthenium, osmium, zirconium, and alloys thereof and/or zirconium dioxide. The platinum-containing components can include one or more of the first connecting tube 36, the fining vessel 38, the second connecting tube 40, the standpipe 30, the mixing vessel 42, the third connecting tube 44, the delivery vessel 46, the downcomer 48 and the inlet 50. The formingvessel 60 can also be made from a refractory material and is designed to form the glass melt into a glass ribbon 12.

[0045] FIG. 2 is a cross sectional perspective view of the apparatus 10 along line 2-2 of FIG. 1. As shown, the formingvessel 60 includes a forming wedge 62 comprising a pair of downwardly inclinedformingsurfaceportions66a, 66b thatextendbetween opposed ends 64a, 64b of the forming wedge 62. The downwardly inclined forming surface portions 66a, 66b converge along a draw direction 68 to form a bottom edge, hereinafter root 70. Molten glass 17 may fill a trough extending between the opposed ends 64a, 64b, extend downward over the downwardly inclined forming surface portions 66a, 66b, and converge at the root 70 to form a glass ribbon 12. A draw plane 72 extends through the root 70. The glass ribbon 12 may be drawn in the draw direction 68 along the draw plane 72. The draw plane 72 extends vertically through the root 70, bisectingthe forming vessel 60. However, it should be understood that the draw plane 72 may not extend vertically through the root 70 in alternative configurations. While FIGS. 1 and 2 generally depict one embodiment of a glass forming apparatus and a forming vessel, it should also be understood that aspects of the present disclosure may be used with various other forming vessel configurations.

[0046] Referring now to FIGS. 1-2, the apparatus 10 also includes at least one edge roller assembly for drawing glass ribbon from the root 70 of the forming vessel 60. For example, the apparatus 10 is depicted to include first and second edge roller assemblies 130a, 130b (see FIG. 1). The first edge roller assembly 130a includes a first pair of edge rollers 132 configured to engage a first edge of the glass ribbon 12 as the glass ribbon 12 is drawn from the root 70 of the forming wedge 62. The second edge roller assembly 130b includes a second pair of edge rollers 134 configured to engage another, second edge of the glass ribbon 12 as the glass ribbon 12 is drawn from the root 70 of the forming wedge 62. The first and second edge roller assemblies 130a, 130b aid in drawingthe glass ribbon 12 from the root 70 of the forming wedge 62. For example, the first and second edge roller assemblies 130a, 130b may provide the desired edge characteristics and proper fusion of the edge portions of the molten glass 17 being drawn off opposed surfaces of the downwardly inclined forming surface portions 66a, 66b. In certain embodiments, the first and second edge roller assemblies 130a, 130b can be located at various positions within the viscous region of the glass being drawn from the root 70. For instance, in some embodiments the first and second edge roller assemblies 130a, 130b can be located immediately below the root 70. In some embodiments, the first and second edge roller assemblies 130a, 130b are located a distance beneath the root 70 that may depend on the composition of the glass ribbon 60 and other factors (e.g., draw speed, glass ribbon thickness, etc.) of the production process.

[0047] FIGS. 2 and 3 A depict one embodiment of the first edge roller assembly 130a. The second edge roller assembly 130b (see FIG. 1) maybe substantially identical in structure to the first edge roller assembly 130a in some embodiments. As depicted in FIG. 2, the first edge roller assembly 130a comprises the first pair of edge rollers 132. The first pair of edge rollers 132 comprises a first edge roller 132a and a second edge roller 132b. The first and second edge rollers 132a, 132b are configured to simultaneously engage a first major surface 110a and a second major surface 110b, respectively, of the glass ribbon 12 as the glass ribbon 12 is drawn from the root 70 of the forming wedge 62. The first edge roller assembly 130a includes a first shaft 136 mechanically coupled to the first edge roller 132a and a second shaft 138 mechanically coupled to the second edge roller 132b. The first and second shafts 136, 138 are depicted in FIG. 2 to be substantially-cylindrical shaped and extend linearly between the first and second edge rollers 132a, 132b in a direction perpendicular to the draw direction 68 (e.g, in the x-direction of the coordinate axes depicted in FIG. 2). In embodiments, the first and second shafts 136, 138 may extendthrough a housing (not depicted) containingthe glass ribbon 12. The housing may shield components of the apparatus 10 (e.g., the one or more drive units 137, the controller 150 depicted in FIG. 1) and aid in maintaining a controlled environment around the glass ribbon. Alternative forms for the first and second shafts 136, 138 are contemplated and within the scope of the present disclosure. For example, in embodiments, the first and second shafts 136, 138 may at least partially extend in the draw direction 68 (e.g, at an angle to the x-axis depicted in FIG. 2).

[0048] In embodiments, the first and second shafts 136, 138 are rotatably driven by one or more drive units 137. The one or more drive units 137 may be mechanically coupled to the first and second edge rollers 132a, 132b to cause the first edge roller 132a to rotate at a first rotational velocity coi about a first rotation axis 140a and a second edge roller 132b to rotate at a second rotational velocity C02 about a second rotation axis 140b. In embodiments, the first and second rotational velocities wi, co ₂ are equal and opposite to one another (e.g. , the first edge roller 132a may rotate in a clockwise direction and the second edge roller 132b may rotate in a counterclockwise direction suchthatthe first edge roller assembly 130a guides the glass ribbon

12 in the draw direction 68). In embodiments, the first and second rotational velocities coi, o¾ are selected to correspond to a desired draw speed of the glass ribbon.

[0049] In embodiments, the one or more drive units 137 comprise a suitable drive mechanism (e.g., a suitable motor such as an electric or hydraulic motor, or other suitable actuator) configured to rotate the first and second edge rollers 132a, 132b aboutthe first and second rotation axes 140a, 140b. It should be understood that the one or more drive units 137 may take a variety of forms. For example, in embodiments, the first and second shafts 136,

138 are mechanically linked such that a single drive unit rotates both the first and second shafts 136, 138 with a single mechanical output, such as a rotating drive shaft. In embodiments, a transmission or the like may mechanically couple the mechanical output of the one or more drive units 137 to the first and second shafts 136, 138 to rotate the first and second shafts 136, 138 in a desired set of directions. The one or more drive units 137 may comprise a first drive unit mechanically coupled to the first shaft 136 and a second drive unit mechanically coupled to the second shaft 138. In such embodiments, each drive unit may individually rotate one of the first and second edge rollers 132a, 132b.

[0050] In embodiments, in addition to the first and second edge roller assemblies 130a, 130b, the apparatus 10 comprises one or more pull roller assemblies (not depicted). The one or more pull roller assemblies may contact first and second major surfaces 110a, 110b of the glass ribbon 12 to apply a tension to the glass in order to determine a thickness 166 of the glass ribbon 12. The first and second edge roller assemblies 130a, 130b may counteract variations in width (e.g., in the +/- X-direction depicted in the coordinate axis of FIG. 1) of the glass ribbon 12 caused by the tension applied by the pull roller assemblies. The first and second edge roller assemblies 130a, 130b may be cooled to a temperature beneath that of the glass ribbon 12 to cause the cool the edges of the glass ribbon 12 to aid in reducing lateral contraction thereof beneath the root 70. The first and second edge roller assemblies 130a. 130b may also aid in fusing the different flows of the molten glass 17 travelling over the inclined forming surface portions 66a, 66b. In embodiments, one or more edge rollers of the first and second edge roller assemblies 130a, 130b comprises a knurled surface to prevent slippage of the glass ribbon 12 and also potentially provide additional cooling.

[0051] Referring to FIGS. 1 and 2, in embodiments, the apparatus 10 can include a thickness sensor 160 oriented to sense a thickness 166 of the glass ribbon 12. While the thickness sensor 160 is depicted to be in alignment with a central portion of the glass ribbon 12 (e.g., lying between the first and second edge roller assemblies 130a, 130b), the thickness sensor 160 may be positioned to measure the thickness 166 at any location within the glass ribbon 12. For example, the thickness sensor 160 may be positioned to measure the thickness 166 at a location beneath the first edge roller assembly 130a in the downward draw direction (e.g., the -Z direction of the coordinate axes depicted in the figures). The thickness sensor 160 may be movable to measure the thickness 166 at a variety of locations on the glass ribbon 12.

[0052] The thickness sensor 160 may take a variety of forms, depending on the implementation. For example, the thickness sensor 160 can include solid probes that contact the first and second major surfaces 110a, 110b to measure the thickness 166. In other examples, the thickness sensor may employ fluid (e.g., gas) to sense the thickness 166 of the glass ribbon 12 based on feedback (e.g., pressure feedback) from fluid streams impacting the first and second major surfaces 110a, 110b. In still other examples, the thickness sensor 160 may include an acoustic sensor. In the depicted embodiment, the thickness sensor 160 is a laser sensor that emits a laser beam that is incident on the glass ribbon 12 at a measurement location 170. A first portion of the laser beam may reflect from the first major surface 110a and a second portion of the laser beam is transmitted through the glass ribbon and is reflected off the second major surface 110b. The reflected light may be detected by the thickness sensors and differences between the signals reflected off the first and second major surfaces 110a, 110b may be used to measure the thickness 166. While a single thickness sensor 160 is depicted in FIGS. 1 -2, certain embodiments of the apparatus 10 may include a plurality of thickness sensors for measuring the thickness 166 at a variety of locations simultaneously.

[0053] In embodiments, the thickness sensor 160 is communicably coupled to a controller 150 of the apparatus 10. As described herein, measurements of the thickness may be used to determine an amplitude of modulation A used by the controller 150 to modulate the first and second rotational velocities coi, C02 of the first and second edge rollers 132a, 132b. For example, measurements by the thickness sensor 160 can be used to determine whether a particular amplitude of modulation A results in variability of the thickness 166 decreasing over a predetermined measurement period (e.g., 10 minutes, 30 minutes, 60 minutes) to determine whether the amplitude of modulation A should be adjusted.

[0054] With reference to FIGS. 1, 3 A, and 3B, the first and second edge rollers 132a, 132b may differ from one another in cross-sectional shape. In the example depicted in FIG. 3 A, for illustrative purposes the first edge roller 132a is depicted as comprising a first cross-sectional shape 142a that is substantially elliptical in shape, whereas the second edge roller 132b is depicted to comprise a second cross-sectional shape 142b thatis substantially circular in shape. Such varying cross-sections may result from wear of the first and second edge rollers 132a, 132b and/or machining errors. As a result, the first and second edge rollers 132a, 132b may be separated from one another (in a direction perpendicular to the draw direction 68) by a variable separation distance 144 as the first and second edge rollers 132a, 132b rotate. The variable separation distance 144 may vary dependent on the rotational position of each of the first and second edge rollers 132a, 132b. For example, as the first and second edge rollers 132a, 132b are rotated about the first and second rotation axes 140a, 140b (see FIG. 2), the rotational position of each of the first and second edge rollers 132a, 132b varies as a function of time depending on the first and second rotational velocities coi, co ₂ . As the first and second edge rollers 132a, 132b rotate, the portions of first and second edge rollers 132a, 132b that are most proximate to one another in a direction perpendicular to the draw direction 68 (e.g., the +/- y directions depicted in FIG. 3) may change. If the first and second rotational velocities coi, G¾ are the same in magnitude, for example, the variable separation distance 144 may vary periodically as a function of the first and second rotational velocities coi, co ₂ . The depicted cross- sectional shapes of the first and second edge rollers 132a, 132b are only examples. Mechanical wear of the first and second edge rollers 132a, 132b, may result in rollers having complex surface profiles such that the variable separation distance 144 varies as a function of rotational position in a manner that differs from that depicted in FIG. 3B.

[0055] FIG. 3B depicts a plot 300 of the variable separation distance 144 in an example where the first and second edge rollers 132a, 132b are rotated atthe same rotational speed. The x-axis in FIG. 3B is a normalized time (e.g., as a ratio with a period of rotation), while the y- axis depicts a magnitude of the normalized variable separation distance. As shown, the variable separation distance 144 varies in accordance with a sinusoid having a period corresponding to the rotational speed of the first and second edge rollers 132a, 132b (e.g., determined by the one or more drive units 137). In an example, the variable separation distance 144 may vary when the first and second edge rollers 132a, 132b are rotated at the same speed in accordance with a function having a plurality of frequency components, with the frequency components varying in accordance with differences in radial dimension between the first and second edge rollers 132a, 132b at corresponding angular positions thereon (e.g., associated with how the first and second edge rollers 132a, 132b are initially aligned prior to being actuated by the one or more drive units 137).

[0056] Due to the variable separation distance 144, the volume of molten glass in the glass ribbon 12 per unit time traversing the first pair of edge rollers 132 may vary as a function of the magnitude of the variable separation distance 144. For example, during time intervals where the first and second edge rollers 132a, 132b are relatively close to one another (such as within the time interval 304 depicted in FIG. 3B), the flow of the molten glass 17 between the first and second edge rollers 132a, 132b may be impeded to a greater extent than when the first and second edge rollers 132a, 132b are relatively farther apart (such as within the time interval 302 depicted in FIG. 3B). Such non-constant flow of the molten glass 17 through the first pair of edge rollers 132 may lead to thickness variations in the glass ribbon 12. In the example described herein with respect to FIGS. 3A-3B, a thickness of the glass ribbon 12 proximate to the edge engaged by the first pair of edge rollers 132 may vary periodically in accordance with the sinusoid depicted in FIG. 3B. The thickness variations (thickness flapping) may lead to glass sheets cut from the glass ribbon 12 being unsuitable for certain applications, such as use in high definition displays. Out-of-roundness of any edge rollers in the apparatus 10 may ultimately lead to thickness flapping in the glass ribbon.

[0057] In view of the foregoing, the apparatus 10 comprises a controller 150 communicably coupled to the one or more drive units 137 to control rotation of the first and second edge rollers 132a, 132b. The controller 150may include computer readable instructions storedin a memory 152 and executed by a processor 154. The instructions may be accessible by the processor 154 in accordance with an addressing schemeto control operationof the first and second edge roller assemblies 130a, 130b in keeping with the methods described herein. The memory 152 may include one or more control modules configured to operate the first and second edge roller assemblies 130a, 130b using a feedback control scheme utilizing torque signals generated by the one or more drive units 137. For example, in embodiments where the one or more drive units 137 comprises a single drive unit configured to rotate both the first and second shafts 136, 138, the single drive unit may generate a torque signal representing a total torque generated and transferred to the first and second edge rollers 132a, 132b. In embodiments where the one or more drive units 137 includes a pair of drive units, with each drive unit being configured to individually rotate one of the first and second shafts 136, 138, each drive unit may generate a torque signal representing a torque generated and transferred to each of the first and second edge rollers 132a, 132b separately. The control modules stored in the memory 152 may cause the processor 154 to analyze the torque signals generated via the one or more drive units 137 and control the first and second angular velocities coi, co ₂ using the torque signals.

[0058] FIGS. 4 A-4B depict plots of a torque summation signal received by the controller 150 of the apparatus 10 described herein with respect to FIGS. 1-3B. FIG. 4 A depicts a time domain plot 400 of a torque summation signal (e.g., representing a summation of the torques applied to the first and second shafts 136, 138 via the one on or more drive units 137). FIG. 4B depicts a period-domain (in seconds) transformation plot 402 of the torque summation signal depicted in FIG. 4A. As shown in FIG. 4B, the torque summation signal includes a dominant period component 404 comprising a period of 12.5 seconds (s). The primary period component 404 in the torque summation signal matches a period of rotation of the first and second edge rollers 132a, 132b in this example. Without wishing to be bound by theory, it is believed thatthe periodicity in the torque summation signal is caused by the variable separation distance 144 (see FIG. 3 A). When the variable separation distance 144 is decreasing (or less than an average or median value), it is believed that relatively greater torque is applied to the first and second edge rollers 132a, 132b (e.g., as compared to when the variable separation distance 144 is at a minimum value) by the one or more drive units 137 to maintain the rotation of the first and second edge rollers 132a, 132b at a programmed speed due to friction with the glass ribbon 12. When the variable separation distance 144 is increasing (or greater than a median or average value), it is believed that a lesser torque is applied to the first and second edge rollers 132a, 132b (e.g., as compared to when the variable separation distance 144 is ata maximum value) than when the variable separation distance 144 is decreasing. The greater separation distance may reduce friction with the molten glass 17, requiring less torque to maintain a nominal rotational speed.

[0059] As such, the torque signals generated by the one or more drive units 137 provide a feedback signal that is a proxy for the magnitude of the variable separation distance 144. In view of this, with reference to FIG. 1, the controller 150 may receive the torque signals, generate a torque summation signal from the torque signals (e.g., in the event that separate torque signals associated with each edge roller are generated by the one or more drive units 137), and modulate the first and second rotational velocities coi, co ₂ in a time-dependent fashion to counteract changes in the torque summation signal. For example, the controller 150 may control operation of the one or more drive units 137 to rotate the first and second shafts 136, 138 at variable speeds to reduce the variability in the total pulled glass between the first and second edge rollers 132a and 132b, which may lead to a reduction in thickness flapping in the glass ribbon 12.

[0060] In embodiments, the controller 150 periodically modulates the first and second rotational velocities coi, co ₂ of the first and second edge rollers 132a, 132b. In embodiments, the controller 150 periodically modulates the first rotational velocity coi and the second rotational velocity co ₂ in accordance with where w _t is a target speed associated with the first rotational velocity coi and the second rotational velocity co ₂ , A is an amplitude of modulation, 0i ₂ is an angular position of the first edge roller 132a or the second edge roller 132b , F is a phase of modulation, and co _N is a nominal rotational velocity of the first edge roller 132a and the second edge roller 132b (e.g., associated with a draw speed of the glass ribbon 12).

[0061] In embodiments, the controller 150 is configured to receive roll position signals that are indicative of the values q _{1 2} in equation 1. For example, in embodiments, the one or more drive units 137 comprise encoders that output an electric roll position signal (e.g., a voltage, a current) that varies in proportion to the rotational position (e.g., ranging from 0° to just under 360°) of the first and second shafts 136, 138 relative to reference positions. The electric roll position signal generated by the encoders of the one or more drive units 137 may periodically vary as a function of the first and second rotational velocities coi, co ₂ . In embodiments, the first and second rotational velocities coi, co ₂ correspond to the nominal rotational velocity CO _N (e.g, prior to any modulation). The nominal rotational velocity co _N may be input to the controller 150 as a predetermined input associated with a desired draw speed of the glass ribbon 12.

[0062] The angular positions q _{1 2} of each of the first edge roller 132a and second edge roller 132b may determine a magnitude of the variable separation distance 144. That is, depending on the cross-sectional shapes of first and second edge rollers 132a, 132b, the angular positions q _{1 2} may determine the magnitude of the variable separation distance 144. However, accurate geometrical information regarding cross-sectional shapes of the first and second edge rollers 132a, 132b maybe unavailable (e.g., the first and second edge rollers 132a, 132b may change in shape overlong-term operation of the apparatus 10). As such, the electric roll position signal generated via the one or more drive units 137 may not be sufficient to determine the extent to which the variable separation distance 144 is varying with time in order to determine the extent to modulate co _N to counteract variations in the variable separation distance 144.

[0063] As described herein, with reference to FIGS. 1, 3 A, 3B, 4A, and 4B, the periodic variation of the torque summation signal generated via the one or more drive units 137 may serve as a proxy for the variable separation distance 144. The magnitude of the variable separation distance 144 may be estimated by the variation in the torque summation signal in reference to an average or median of the torque summation signal. As such, the torque summation signal may be used to determine an extent by which to modulate co _N in equation 1.

[0064] The phase of modulation F in equation 1 may determine a timing at which the controller 150 modulates the first and second angular velocities coi, co ₂ to a particular extent. Given that the magnitude of the variable separation distance 144 depends on the rotational positions q _{1 2} of the first and second edge rollers 132a, 132b, which, as discussed above, are related to the magnitude of the torque summation signal, the phase of modulation F may be determined based on a delay time between reference electronic roll position signal and the torque summation signal. For example, a time delay between starting points of corresponding periods of each of the torque summation signal and the electronic roll position signal may be used to determine the phase of modulation F in equation 1. An example of determining such a time delay is described herein with respect to FIG. 7.

[0065] As shown in FIGS. 4A and 4B, the torque summation signal representative of the torques applied to the first and second edge rollers 132a, 132b via the one or more drive units 137 comprises a plurality of frequency (or period) components, in addition to the dominant period component 404 at the period associated with the first and second rotational velocities coi, co ₂ . As shown, the torque summation signal also comprises a plurality of low period (or high frequency) components 406 and a plurality of high period (or low frequency) components 408.

[0066] In embodiments, the low period components 406 and the high period components 408 of the torque summation signal may not be present in the electric roll position signal generated by the encoders of the one or more drive units 137, as the electric roll position signal may be independent of the precise geometry of the first and second edge rollers 132a, 132b (and notinclude components stemmingfrom mechanical interactionsbetweenthe rollers). The low period components 406 and the high period components 408 may notbe attributed to radial variations in edge roller shape. In embodiments, the low period components 406 and the high period components 408 are attributed to mechanical and/or electrical noise. As such, the low period components 406 andthe high period components 408 may render estimation of the phase of modulation F described herein inaccurate, as a measured phase difference between the torque summation signal and the electric roll position signal may vary between successive periods of rotation. Accordingly, the controller 150 of the apparatus 10 (see FIG. 1) may include filtering logic to filter the torque summation signal generated by the one or more drive units 137. The filtering logic may implement a bandpass filter allowing a spectral band of interest around component 404, including targets for the first and second rotational velocities coi, co ₂ (e.g., corresponding to the nominal rotational velocity co _N of equation 1) to pass therethrough. [0067] FIGS. 5 A and 5B depict frequency domain plots of the low-pass filter portion 500 of a bandpass filter used to filter a torque summation signal and the high-pass filter portion 504 of the bandpass filter, in accordance with an example embodiment. The low-pass filter portion 500 and high-pass filter portion 504 may be used to filter out the plurality of low period components 406 and the high period components 408 of the torque summation signal depicted in FIGS. 4A-4B. In this example, the dominant period component404 (see FIG.4B) comprises a period of 12.5 s, corresponding to a frequency of 0.08 Hz. As depicted in FIG. 5 A, the low- pass filter portion 500 filters out signal components having frequencies above a cutoff frequency 502 of approximately 0.09 Hz. As depicted in FIG. 5B, the high-pass filter portion 504 filters out signal components having frequencies below a cutoff frequency 506 of approximately 0.02 Hz. As such, the frequency associated with the dominant period component404 (see FIG. 4B) lies between the cutoff frequencies 502and 506 ofthebandpass filter depicted in FIGS. 5A-5B.

[0068] In the example depicted in FIGS. 5 A-5B, the cutoff frequency 502 associated with the low-pass filter portion 500 is closer to the dominant period component 404 (e.g., a difference between the cutoff frequency 502 and the frequency of the dominant period component404 is 0.01 Hz in this example) than the cutoff frequency 506 of the high-pass filter portion 504 (e.g., a difference between the cutoff frequency 506 and the frequency of the dominant period component 404 is 0.06 Hz) in this example. That is, the bandpass filter is configured to filter out high frequency components having frequencies that are more than 0.01 Hz greater than the frequency associated with the dominant period component 404. Such a configuration may be beneficial because higher frequency components are closer to the dominant frequency component 404 and may also tend to reduce the accuracy of the phase of modulation F described herein to a greater extent than lower frequencies components. The cutoff frequencies 502, 506 are configurable parameters and may be chosen based on a desired speed for the first and second edge rollers 132a, 132b. In embodiments, the cutoff frequencies 502, 506 are determined by analyzing filtered torque summation signals to determine values for the cutoff frequencies 502, 506 that generate consistent results for determining the phase of modulation F described herein. The particular cutoff frequencies 502, 506 used may vary and have different relationships to the dominant period component 404 than that shown in FIGS. 5A-5B [0069] With reference to FIG. 1, in embodiments, filtering torque signals generated by the one or more drive units 137 using bandpass filters, such as the bandpass filter described herein with respect to FIGS. 5A-5B, may introduce a phase shift into the torque summation signal. Such a filter-induced phase shift may reduce the accuracy of the phase of modulation F generated using the methods described herein. Accordingly, in embodiments, the memory 152 may include filter compensation logic configured to phase shift filtered torque summation signals by an amount needed to compensate for the filter-induce phase shift associated with the bandpass filter. In embodiments, a plurality oftorque summation signals comprisinga plurality of different primary frequency components (e.g., at different frequencies) are filtered using the bandpass filter, and phase shifts for each of the torque summation signals are determined using established filtering theory algebraic expressions. Based on the frequency associated with the dominant period component 404 (see FIG. 4B), such a relation may be used to compute a phase shift that is used to process a filtered torque signal.

[0070] FIG. 6A depicts a time series plot 602 of a raw torque summation signal generated by the one or more drive units 137 (see FIG. 1A). FIG. 6B depicts a time series plot 604 of a filtered torque summation signal that represents the raw torque summation signal depicted in FIG. 6A filtered by the bandpass filter described herein with respect to FIGS. 5 A and 5B and subsequently phase shifted to compensate for the filter-induced phase shift. As shown, the filtered torque summation signal is a generally smooth, periodic signal having a period associated with the dominant period component 404 (see FIG. 4B). As shown in FIG. 6B, the amplitude of the filtered signal varies periodically with a lower frequency than that associated with the dominantperiodcomponent404. Withoutwishingtobeboundby theory, itisbelieved that such periodic variation in amplitude is the result of mechanical interactions between the first and second edge rollers 132a, 132b. The filtered torque summation signal depicted in FIG. 6B provides a baseline to establish a time delay with the electric roll position signals generated via the one or more drive units 137.

[0071] FIG. 7 depicts a time series plot 680 including an overlay of a raw torque summation signal 700 generated by the one or more drive units 137, a filtered torque summation signal 702, an electric roll position signal 704 generated via the one or more drive units 137, and a time delay 706 associated with corresponding portions of the filtered torque summation signal 702 and the electric roll position signal 704. As shown in FIG. 7, the electric roll position signal 704 comprises a saw tooth function where the amplitude of the signal varies from a minimum value when the rotational position of the one or more drive units 137 is at 0°, to a maximum value when the rotational position of the one or more drive units 137 is just less than 360°. Transitions between the maximum and minimum values (depicted as vertical lines in the electric roll position signal 704) represent points in time when one of the first and second edge rollers 132a, 132b (see FIG. 1) completes a rotation.

[0072] With reference to FIGS. 1 and 7, the raw torque summation signal 700 may represent a summation of torque signals generated by the one or more drive units 137 during rotation of the first and second edge rollers 132a, 132b. For example, the raw torque summation signal 700 may represent a summation of a first torque signal generated by a first drive unit rotating the first edge roller 132a about the first rotation axis 140a and a second torque signal generated by a second drive unit rotatingthe second edge roller 132b aboutthe second rotation axis 140b. The filtered torque summation signal 702 may be generated by processing the raw torque summation signal 700 using a bandpass filter like the bandpass filter described herein with respect to FIGS. 5 A and 5B. The raw torque summation signal 700 and filtered torque summation signal 702 are normalized relative to a reference value.

[0073] As shown in FIG. 7, a time delay 706 between the filtered torque summation signal 702 and the electric roll position signal 704 may be determined by calculating a difference between a first point in time where one of the first and second edge rollers 132a, 132b is completing a revolution (or period of rotation) and a second point in time where the filtered torque summation signal 702 starts a period of variation. In embodiments, the filtered torque summation signal 702 starts a period of variation when the filtered torque summation signal 702 comprises an average value about which the magnitude of the filtered torque summation signal 702 periodically oscillates. In embodiments, a value of the time delay 706 may be converted to the phase of modulation F described herein by multiplying the value of the time delay 706 with the dominant frequency of interest, as depictedby component404 in FIG. 4B.

[0074] In embodiments, values for the time delay 706 are computed for a plurality of successive periods of each of the electric roll position signal 704 and the filtered torque summation signal 702, and an average of the values is used to compute the phase of modulation F described herein. Averaging a plurality of values forthe time delay 706 over multiple cycles may beneficially resultin amore accurate estimate of the time delay, andtherefore computation of the phase of modulation F that reduces thickness flapping to a greater extent than embodiments relying on a single computation of the time delay 706 to compute the phase of modulation F. In embodiments, the controller 150 computes values for the time delay 706 automatically based on measurement times associated with the filtered torque summation signal 702 and the electric roll position signal 704 having particular values (e.g., times when the filtered torque summation signal 702 comprises an average or median value and when the electric roll position signal 704 comprises a maximum or minimum value).

[0075] FIG. 8 depicts a flow diagram of a method 800 of modulating rotational velocities of edge rollers of a glass forming apparatus using a torque summation signal. The method 800 may be performed by the controller 150 of the apparatus 10 described herein with respect to FIGS. 1 -3. Accordingly, reference will be made to various components depicted in FIGS. 1-3 to aid in the description of the method 800. Performance of the method 800 may result in the glass ribbon 12 having a more uniform thickness 166 than if the first and second edge roller assemblies 130a, 130b were operated at a constant rotational speed. While the first edge roller assembly 130a is referenced herein, the method 800 may be performed to control rotation of edge rollers in the second edge roller assembly 130b or any other edge roller assembly in the apparatus 10.

[0076] At block 802, the controller 150 receives torque signals associated with edge rollers disposed on either side of the glass ribbon 12. For example, the controller 150 may receive torque signals generated by the one or more drive units 137 used to rotate the first and second edge rollers 132a, 132b of the first edge roller assembly 130a described herein. In embodiments, the controller 150 may receive a single torque signal associated with a particular edge roller pair. For example, in embodiments, a single drive unit may be used to rotate both the first edge roller 132a and the second edge roller 132b such that a single torque signal (representing a torque summation signal) is received by the controller 150. In such embodiments, the controller may generate a torque summation signal by receiving the torque signal from the single drive unit.

[0077] At block 804, the controller 150 combines the torque signals received at block 802 into a torque summation signal. For example, in embodiments where separate drive units (e.g, separate motors) are used to rotate the first and second edge rollers 132a, 132b, a torque signal may be generated by each drive unit. Each individual torque signal may be received by the controller 150 and combined by the controller into a torque summation signal. The torque summation signal may be filtered using a bandpass filter as described herein with respect to FIGS. 5 A-5B to remove frequency components that are outside of a predetermined range of frequencies associated with a target rotational speed of the first and second edge rollers 132a, 132b (e.g., the target rotational speed may be based on a desired draw speedforthe glass ribbon 12). After filtering, the filtered torque summation signal may be phase shifted based on a predetermined filter-induced phase shift associated with the bandpass filter. The filtered and phase-shifted torque summation signal may then be used to determine a phase of modulation F, as described herein.

[0078] At block 806, the controller 150 modulates the first and second rotational velocities coi, C02 of the first and second edge rollers 132a, 132b in a time-dependent manner to counteract changes in the torque summation signal. As described herein, time intervals when the torque summation signal increases with time may indicate that the variable separation distance 144 (see FIG. 3 A) is decreasing. During such time intervals, the controller 150 may increase the rotational speed of the first and second edge rollers 132a, 132b (e.g., increase the first and second rotational velocities coi, C02) to maintain a rate at which the glass moves through the first edge roller assembly 130a. Time intervals when the torque summation signal decreases with time may indicate that the variable separation distance (see FIG. 3B) is increasing. During such time intervals, the controller 150 may decrease the rotational speed of the first and second edge rollers 132a, 132b (e.g., decrease the first and second rotational velocities coi, co ₂ ). In embodiments, the controller 150 may provide control signals that increase or decrease the first and second rotational velocities coi, co ₂ by predetermined amounts (e.g., stored in a lookup table) based on a trend in the torque summation signal. For instance, if the torque summation signal increases by a threshold magnitude over a predetermined period (e.g., approximately one quarter of a revolution period of the first and second edge rollers 132a, 132b), the controller 150 may increase the first and second rotational velocities coi, co ₂ until a decrease in amplitude of the torque summation signal is detected. The extent by which the first and second rotational velocities coi, co ₂ are modulated may vary in proportion to the extent of the increase or decrease in the torque summation signal. The modulation of the first and second rotational velocities coi, co ₂ may result in the variable separation distance 144 (see FIG. 3 A) having a lesser impact on the glass ribbon thickness over a period of rotation of the first and second edge rollers 132a, 132b. The modulation reduces effects of the first and second edge rollers 132a, 132b not being perfectly round in shape. [0079] In embodiments, the controller 150 periodically modulates the first and second rotational velocities coi, co _2. In such embodiments, when the torque signals are initially received by the controller 150 at block 802, the first and second edge rollers 132a, 132b may be rotating at the nominal target angular velocity co _N . The periodic modulation of the first and second rotational velocities coi, co ₂ may result in the first and second edge rollers 132a, 132b being rotated at a rate that is dependent on the angular positions thereof (e.g., as measured by the electric roll position signals generated by the one or more drive units 137 described herein). For example, in embodiments, the controller 150 causes the one or more drive units 137 to rotate at an angular speed that varies as a function of angular position of the first and second edge rollers 132a, 132b. Angular positions of the first and second edge rollers 132a, 132b where the torque summation signal is increasing above and decreasing below an average value may be identified, and, the first and second rotational velocities coi, co ₂ may be increased or decreased above or below the nominal target angular velocity co _N depending on the extent that the torque summation signal differs from the average value at a particular angular position.

[0080] In embodiments, the controller 150 periodically modulates the first and second rotational velocities coi, co ₂ periodically in accordance with equation 1 herein. In such embodiments, the controller 150 may perform the method 900 depicted in FIG. 9 to generate values for the amplitude of modulation A and the phase of modulation F parameters described herein. At block 902, the controller 150 may determine the phase of modulation F in equation 1 based on a time delay between an electric roll position signal and the torque summation signal. For example, the controller 150 may compute the time delay using a filtered and phase- shifted torque summation signal and the electric roll position signal generated via an encoder associated with the one or more drive units 137 using a procedure similar to that discussed above with respect to FIG. 7~(e.g., by determining a difference in time between when the electric roll position signal indicates a beginning of a period of rotation and when the torque summation signal is an average or median value). In embodiments, the controller 150 may include validation logic that validates the phase of modulation F computed as described herein. For example, using an estimated phase of modulation F, the controller may phase shift a previously measured torque summation signal usingthe estimated phase of modulation F. The controller 150 may compare the phase-shifted torque summation signal to an electric roll position signal to determine whether the estimated phase of modulation F meets a tolerance. If the tolerance is not met, the phase of modulation F may be re-estimated by measuring additional cycles of the torque summation signal and the electric roll position signal. [0081] At block 904 the controller 150 may determine the amplitude of modulation A in equation 1. The amplitude ofmodulation Amay be determinedusingatrial and errortechnique that incrementally increases the amplitude of modulation A. During periods of time that the amplitude of modulation A is held constant, the controller 150 may monitor the thickness 166 (e.g., using measurements from the thickness sensor 160). For example, the controller 150 may continuously monitor the thickness 166 and determine a thickness range of the glass ribbon 12 over a predetermined measurement period (e.g., 5 seconds, 10 seconds, 30 seconds, 1 minute, 3, minutes, 5 minutes, 10 minutes, 30 minutes, 1 hour, 2 hours). The measured thickness range may be compared to a previously measured value associated with a previous amplitude of modulation A. If a decrease in the thickness range is measured, the controller A may increase the amplitude of modulation A by a predetermined increment (e.g., 0.1, 0.2, 0.3, 0.4) and determine whether the increased amplitude of modulation A results in a further reduction in the thickness range. If a particular value for the amplitude of modulation A results in an increase in the thickness range being observed, the controller 150 may decrease the amplitude of modulation A to a previous value (e.g., the last value for the amplitude of modulation A where a decrease in the thickness range was observed). The controller 150 may incrementally increase the amplitude of modulation A using fixed or variable increments until a reduction in thickness variation (or range) is no longer observed. The increment used by the controller 150 to update the amplitude of modulation A may vary depending on the extent of the reduction in thickness variation observed.

Examples

[0082] The embodiments described herein will be further clarified by the following examples. FIG. 10 depicts a plot 1000 of experimental results while modulating the rotational velocities of edge rollers using equation 1 herein. The experimental results were achieved during fabrication of CorningLotus®NXT Glass. _The phase of modulation F was determined using the method described herein with respect to FIG. 7. A line 1002 in the plot 1000 represents a moving window range of a measured thickness of a glass ribbon. The vertical lines 1006, 1008, 1010, 1012, 1014, 1016, 1018, and 1020 represent points in time when the amplitude of modulation A was increased in accordance with the method 900 described herein with respect to FIG. 9. [0083] During the period of time to the left of the vertical line 1006, the rotational velocities of the edge rollers was not modulated. As shown, for substantially the entirety of this period, the moving window range of the thickness was greater than or equal to 4 micrometers (pm). Between the vertical line 1006 and the vertical line 1008, the amplitude of modulation A was set to 0.3. As a result, the moving window range of the thickness was less than 4 pm within this time window. Accordingly, the amplitude of modulation A was increased to 0.5 at the vertical line 1008, which resulted in a further reduction in the moving window range of the thickness. Such reductions in the moving window range of the thickness continued to be observed until the amplitude of modulation was set to 0.9 after the vertical line 1012. Between the vertical lines 0.9 and 1.1, the moving window range of the thickness was measured to be less than 3.0 pm, representing a substantial improvement over the un-modulated case. Once the amplitude of modulation A was increased to 1.1 at the vertical line 1014, the moving window range of the thickness increased over what the moving window range of the thickness was when the amplitude of modulation A was 0.9. A further increase in the amplitude of modulation Ato 1.3 atthe vertical line 1016 resulted in a further increase in the movingwindow range of the thickness. Accordingly, at the vertical line 1018, the amplitude of modulation A was decreased to 1.1, where a reduction of the moving window range of the thickness was again observed as compared to when the amplitude of modulation A was 1.3. Accordingly, the amplitude of modulation A was further decreased to 0.9, where an initial minimum moving window range of the thickness was observed. The preceding example demonstrates how the amplitude of modulation A may be determined to result in a substantial reduction in thickness variations of the glass ribbon.

[0084] In view of the foregoing, methods of operating drive units of edge rollers of glass manufacturing apparatuses have been shown and described. Modulating rotational velocities of the edge rollers in a time-dependent manner to counteract variations observed in a torque summation signal has been shown to substantially reduce thickness flapping caused by edge rollers having differing cross-sectional shapes. The torque summation signal beneficially serves as a proxy for the variable separation distance between the edge rollers resulting from their varying cross-sectional shapes, indicating time periods when rotational velocities of the edge rollers may be increased or decreased above a nominal target velocity to maintain flow of glass through the edge rollers, thereby leading to reductions in thickness variations in the glass ribbon and glass sheets having more uniform thicknesses. [0085] It will be apparent to those skilled in the art that various modifications and variations can be made to the embodiments described herein without departing from the spirit and scope of the claimed subject matter. Thus, it is intended that the specification cover the modifications and variations of the various embodiments described herein provided such modification and variations come within the scope of the appended claims and their equivalents.