Device and method for adjusting width of glass liquid outlet at overflow port of kiln

By using high-temperature resistant stainless steel plates and lined material blocking devices in photovoltaic glass production, combined with adjustment arms and scale calculations, the problem of quickly determining and adjusting the width of the glass liquid outlet at the furnace overflow port was solved, thereby improving production safety and efficiency.

CN116986793BActive Publication Date: 2025-09-19HENAN ANCAI HI-TECH +1
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Patent Information

Application Number
CN202310815973.X
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-07-05
Publication Date
2025-09-19
Estimated Expiration
2043-07-05

AI Technical Summary

Technical Problem

In photovoltaic glass production, determining and adjusting the width of the glass liquid outlet at the kiln overflow port is difficult and labor-intensive, and the existing material blocking device is fragile, affecting production safety and efficiency.

Method used

A material blocking device including a high-temperature resistant stainless steel plate shell, an inner lining and a high-temperature resistant filler is used, combined with an adjustment arm and an adjustment base. The glass liquid outlet width is quickly determined and accurately adjusted through scale and traction rate calculation.

Benefits of technology

The rapid and accurate adjustment of the glass liquid outlet width of the kiln overflow port is achieved, the labor intensity is reduced, the brittle breakage of the material blocking device is avoided, and the safety and efficiency of production are improved.

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Abstract

The present invention discloses a device and method for adjusting the width of the glass liquid outlet of the overflow port of a kiln. A high-temperature resistant stainless steel plate is used as the outer shell of the material retaining device, and is assisted by an inner lining and filled with a special high-temperature resistant filler. This not only overcomes the brittleness and easy cracking of the original material retaining device and the negative effects on production caused by it, but also has heat preservation properties and meets the production requirements. By utilizing this device and the related process methods developed, the determination and adjustment of the width of the glass liquid outlet of the overflow port of the kiln can be made quick and accurate. Not only can the initial value of the width of the glass liquid outlet of the overflow port of the kiln be quickly determined when the equipment is installed or before the machine is changed and started, but also the glass liquid outlet width can be quickly determined and quickly and accurately adjusted when the width specifications of the glass plate change during normal production.
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Description

Technical Field

[0001] The present invention belongs to the technical field of photovoltaic glass equipment, and in particular relates to a device and method for adjusting the width of a glass liquid outlet at an overflow port of a kiln. Background Art

[0002] With the development of modern industry, the global energy crisis and air pollution are becoming increasingly prominent. Solar energy, as an ideal renewable clean energy source, is gaining significant attention. Photovoltaic cells, which utilize the photovoltaic effect to convert solar energy into electricity, are seeing a gradual expansion in the market, and photovoltaic glass, used as a cover for photovoltaic cells, has also seen widespread development. Different users require different widths of photovoltaic glass panels, making determining and adjusting the width of the furnace overflow outlet a frequent task in daily production. During operation, the temperature of the molten glass at the overflow outlet ranges from 1100 to 1200°C, generating significant heat radiation. Operators must wear cumbersome labor protection equipment, resulting in high labor intensity. Furthermore, the overflow retaining bricks are made of brittle, common silicate materials. These bricks can break easily during adjustment, potentially damaging the calendering rollers and severely compromising production.

[0003] During the production of photovoltaic rolled glass, the rolling machine and lip tiles are replaced approximately every three months. This requires the replacement of two retaining devices mounted above the lip tiles. Because their positions have changed during previous production processes, and the width of the glass sheets produced after startup is not constant, precise initial positioning of the two newly installed retaining devices is crucial. Traditionally, a rough estimate of the position was used, followed by adjustments later. However, this adjustment was laborious due to the high ambient temperature.

[0004] How can the initial width of the furnace overflow outlet be determined during installation or before startup to ease subsequent operations? How can the potential risk of breakage during adjustment of overflow retaining bricks made of common silicate materials be avoided? If the required width of the glass sheet product changes during production, how can the overflow outlet width be quickly determined and adjusted? Solving these problems has become a pressing research topic for the photovoltaic glass industry. Summary of the Invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and to provide a device and method for adjusting the width of the glass liquid outlet at the overflow port of a kiln, so as to realize rapid determination and adjustment of the width of the glass liquid outlet.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A device for adjusting the width of a glass melt outlet at an overflow port of a furnace comprises a material retaining device and an adjusting device disposed at the front end of a calendering roller at the overflow port. The material retaining device comprises an outer shell, an inner lining, and a high-temperature resistant filler. The inner lining is disposed within the outer shell, and the inner end surface of the inner lining smoothly connects with the inner end surface of the outer shell and is configured as an arcuate surface corresponding to the outer circumference of the calendering roller. The high-temperature resistant filler is disposed within a cavity enclosed by the outer shell and the inner lining.

[0008] The adjusting device includes an adjusting arm and an adjusting base for adjusting and placing the adjusting arm, and an adjusting vertical plate is fixedly provided at the end of the adjusting arm and is connected to the shell through the adjusting vertical plate to push the blocking device to move forward and backward.

[0009] The shell includes an inner baffle and a front baffle fixedly connected thereto, and the inner end surface and bottom end surface of the inner baffle are both configured as arc surfaces, and the inner end surface and bottom end surface of the lining are correspondingly and smoothly matched with the arc surface of the inner baffle.

[0010] The adjustment base includes a base frame and fastening screw holes vertically provided on the base frame, and a frame groove is provided on the lower end surface of the base frame, and the frame groove is matched with the outer end surface of the adjustment arm;

[0011] During assembly, the head end of the adjusting arm passes through the base frame in the transverse direction, and the provided fastening bolt passes through the fastening thread hole and directly reaches the upper end surface of the adjusting arm to limit and fix it.

[0012] The high-temperature resistant filler comprises 75% to 85% by weight of silicate refractory clay material, 3% to 5% of fine wood powder, 3% to 5% of sodium metasilicate adhesive, 0.6% to 0.8% of hemp silk, and 10.5% to 11.5% of water.

[0013] A tightening and fixing plate is also provided between the lining and the adjusting vertical plate.

[0014] The adjusting vertical plate is provided with a long fastening hole for adjusting the height of the adjusting arm, and the outer shell is provided with a corresponding shell fastening hole.

[0015] An adjustment scale is also provided on the horizontal side of the adjustment arm.

[0016] A method for adjusting a width adjustment device for a glass melt outlet at an overflow port of a furnace, comprising the following steps:

[0017] (1) Connection between the material blocking device and the adjusting arm

[0018] The adjusting arm is connected to the outer shell of the material blocking device through the adjusting vertical plate, and a tightening fixing plate is placed between the lining and the adjusting vertical plate, and the tightening fixing plate is fastened to the lining by a fastening wire passing through the adjusting vertical plate;

[0019] (2) Preliminary installation of the material blocking device and adjustment device on both sides of the overflow port

[0020] First, fix the base frame of the adjustment base on the lip bricks on both sides of the overflow outlet of the calender, and pass the head end of the adjustment arm through the base frame horizontally, and fit the adjustment arm tightly into the groove of the frame;

[0021] Then, fasten the bolt through the fastening thread hole to fix the adjustment arm, and use the fastening long hole of the adjustment vertical plate to smoothly place the material blocking device and the adjustment device;

[0022] (3) Assume that the width of the glass initially produced is A0, and it is divided into two pieces during cutting, so the total width is 2A0. The clear edge width of each side is B, and the total width of the cold end glass plate is C0 = 2 (A0 + B);

[0023] (4) The change of the pulling rate k, that is, the change of the linear speed of the conveying roller and the calendering roller of the annealing furnace, will cause the width of the glass sheet to change by x. Then the initial width of the glass liquid outlet at the furnace overflow port is A = C0 + kx;

[0024] (5) Based on the initial width A calculated in step (4), loosen the fastening bolts and push the adjustment arm forward or backward so that the distance between the two shells is A.

[0025] The pulling rate described in step (4):

[0026] k=100*(a-b) / b

[0027] Wherein, a is the linear speed of the annealing furnace conveyor roller, and b is the linear speed of the calendering roller.

[0028] When the glass sheet thickness is 2.8 mm or 3.2 mm, k changes by 1, and the width change x is correspondingly 5;

[0029] When the thickness of the glass plate is 2.0 mm or 2.5 mm, k changes by 1, and the width change x is correspondingly 3.

[0030] The beneficial effects of the present invention are:

[0031] (1) The device and method for adjusting the width of the glass liquid outlet at the overflow port of the kiln disclosed in the present invention use a high-temperature resistant stainless steel plate as the outer shell of the material retaining device, and are assisted by an inner lining and filled with a special high-temperature resistant filler. This not only overcomes the brittleness and easy cracking of the original material retaining device and the negative effects on production, but also has heat preservation properties and meets the production requirements. By using this device and the related process methods developed, the determination and adjustment of the width of the glass liquid outlet at the overflow port of the kiln can be made quick and accurate. Not only can the initial value of the width of the glass liquid outlet at the overflow port of the kiln be determined quickly when the equipment is installed or before the machine is changed and started, but also the glass liquid outlet width can be quickly determined and quickly and accurately adjusted when the width specifications of the glass plate change during normal production.

[0032] (2) When adjusting the width, the initial position of the overflow stopper can be determined when the overflow stopper is initially installed, based on the required glass plate width specifications and edge cleaning amount, the linear speed ratio of the annealing furnace conveyor roller and the calendering roller drive, and the corresponding plate width retraction and expansion amount. When the width specifications are changed, the requirements can be met by adjusting the device to retract and expand according to the linear speed ratio of the annealing furnace conveyor roller and the calendering roller drive and the corresponding plate width retraction and expansion amount. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 1. It is a structural diagram of the outer shell of the material blocking device;

[0034] Figure 2 It is a structural diagram of the inner lining of the material retaining device;

[0035] Figure 3 It is a schematic diagram of the assembly structure of the shell and the lining;

[0036] Figure 4 It is a structural diagram of the regulating arm;

[0037] Figure 5 It is a structural diagram of the tightening fixing plate;

[0038] Figure 6 It is a structural diagram of the adjustment base;

[0039] Figure 7 It is a schematic diagram of the overall assembly structure of the present invention. DETAILED DESCRIPTION

[0040] The following describes the implementation of the present invention through specific embodiments. People skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification.

[0041] The present invention provides a device and method for adjusting the width of a glass melt outlet at a furnace overflow port. Figures 1 to 7 shown.

[0042] A device for adjusting the width of a glass liquid outlet at an overflow port of a kiln comprises a material blocking device and an adjusting device arranged at the front end of a calendering roller at the overflow port, and the material blocking device comprises an outer shell 1, an inner lining 2 and a high-temperature resistant filler 206, the inner lining 2 being placed in the outer shell 1, and the inner end surface of the inner lining 2 being smoothly connected to the inner end surface of the outer shell 1 and both being arranged as arc-shaped surfaces corresponding to the outer peripheral surface of the calendering roller 9, and the high-temperature resistant filler 206 being placed in a cavity surrounded by the outer shell 1 and the inner lining 2.

[0043] The adjusting device includes an adjusting arm and an adjusting base for adjusting and placing the adjusting arm, and an adjusting vertical plate 301 is fixedly provided at the end of the adjusting arm and is connected to the housing 1 through the adjusting vertical plate 301 to push the blocking device to move forward and backward.

[0044] The shell 1 includes an inner baffle 103 and a front baffle 101 fixedly connected thereto, and the inner end surface and bottom end surface of the inner baffle 103 are both set as arc surfaces, and the inner end surface and bottom end surface of the lining 2 are correspondingly smooth and consistent with the arc surface of the inner baffle 103.

[0045] The adjustment base includes a base frame 501 and fastening holes 505 vertically provided on the base frame 501. A frame groove 504 is provided on the lower end surface of the base frame 501, and the frame groove 504 is matched with the outer end surface of the adjustment arm.

[0046] During assembly, the head end of the adjustment arm passes through the base frame 501 in the horizontal direction, and the provided fastening bolt 506 passes through the fastening thread hole 505 and directly reaches the upper end surface of the adjustment arm to limit and fix it.

[0047] The high-temperature resistant filler comprises 75% to 85% by weight of silicate refractory clay material, 3% to 5% of fine wood powder, 3% to 5% of sodium metasilicate adhesive, 0.6% to 0.8% of hemp silk, and 10.5% to 11.5% of water.

[0048] A tightening and fixing plate 4 is further provided between the inner lining and the adjusting vertical plate.

[0049] The adjusting vertical plate 301 is provided with a long fastening hole 302 for adjusting the height of the adjusting arm, and the housing 1 is provided with a corresponding housing fastening hole 102 .

[0050] An adjustment scale 305 is also provided on the horizontal side of the adjustment arm.

[0051] The adjustment method of the glass melt outlet width adjustment device of the kiln overflow port comprises the following steps:

[0052] (1) Connection between the material blocking device and the adjusting arm

[0053] The adjusting arm is connected to the outer shell 1 of the material blocking device through the adjusting vertical plate 301, and a tightening fixing plate 4 is placed between the lining 2 and the adjusting vertical plate 301, and the tightening fixing plate 4 is fastened to the lining 2 by a fastening wire passing through the adjusting vertical plate 301;

[0054] (2) Preliminary installation of the material blocking device and adjustment device on both sides of the overflow port

[0055] First, fix the base frame 501 of the adjustment base on the lip bricks on both sides of the overflow outlet of the calender, and then pass the head end of the adjustment arm through the base frame 501 horizontally, and fit the adjustment arm tightly into the frame groove 504;

[0056] Then, fasten the bolt through the fastening thread hole 505 to fix the adjustment arm, and use the fastening long hole of the adjustment vertical plate 301 to smoothly place the material blocking device and the adjustment device;

[0057] (3) Assume that the width of the glass initially produced is A0, and it is divided into two pieces during cutting, so the total width is 2A0. The clear edge width of each side is B, and the total width of the cold end glass plate is C0 = 2 (A0 + B);

[0058] (4) The change of the pulling rate k, that is, the change of the linear speed of the conveying roller and the calendering roller of the annealing furnace, will cause the width of the glass sheet to change by x. Then the initial width of the glass liquid outlet at the furnace overflow port is A = C0 + kx;

[0059] The traction rate

[0060] k=100*(a-b) / b

[0061] Wherein, a is the linear speed of the annealing furnace conveying roller 12, and b is the linear speed of the calendering roller 9.

[0062] Changes in the traction rate k will cause changes in the width of the glass plate. Experimental or empirical data can also provide a corresponding relationship between the change in k and the change in plate width: when the glass plate thickness is 2.8mm or 3.2mm, k changes by 1, and the width change x corresponds to 5; when the glass plate thickness is 2.0mm or 2.5mm, k changes by 1, and the width change x corresponds to 3.

[0063] (5) Based on the initial width A calculated in step (4), loosen the fastening bolt 506 and push the adjustment arm forward or backward so that the distance between the two shells is A.

[0064] The specific embodiments are as follows:

[0065] Production and installation of material blocking device:

[0066] The outer shell 1 and the inner lining 2 of the material blocking device are arranged in accordance with Figure 3 Weld together. It should be noted that the upper arc surface 202 of the lining 2 should be smoothly matched with the upper arc surface 104 of the inner baffle of the outer shell 1, and the inner bottom plate arc surface 203 should be smoothly matched with the lower arc surface 105 of the inner baffle, and each weld should be tightly fitted. After welding, an inner cavity is formed between the outer shell 1 and the inner lining 2 of the material stopper device, which is filled with a high-temperature resistant filler 206. The high-temperature resistant filler 206 includes a silicate refractory material of 75% to 85%, fine wood powder of 3% to 5%, sodium metasilicate adhesive of 3% to 5%, hemp silk of 0.6% to 0.8%, and water of 10.5% to 11.5%. It is manufactured according to the following method:

[0067] 1) Weigh various materials according to the required amount, first mix the silicate refractory clay and fine wood chips to obtain a mixture;

[0068] 2) Dilute the sodium metasilicate binder with water and pour it into the mixture, and stir the mixed materials to make them into a moist loose soil;

[0069] 3) Fill the loose soil mixture into the inner lining, tamp it, smooth it, and dry it in the shade.

[0070] The material blocking device is connected to the adjusting arm:

[0071] Two elongated holes 302 for height adjustment on the adjustment arm's adjustment plate 301 align with the two housing fastening holes 102 on the housing's front baffle 101 and are secured with fastening wires. A clamping plate 4 is placed vertically between the retaining device's liner 2 and the adjustment plate 301. Two jacking wire holes 304 are provided on the adjustment plate 301, through which jacking wires are inserted to secure the clamping plate 4 against the retaining device's liner 2, preventing the high-temperature-resistant filler 206 from falling out of the liner cavity if it breaks.

[0072] Preliminary installation of the material blocking device and the adjustment device on both sides of the overflow port:

[0073] First, fix the two adjustment bases on the lip bricks on both sides of the overflow outlet using the base positioning holes 502 and fastening wires 503 at the lower end of the base frame 501, pass the adjustment arm through the base frame 501, and fit the adjustment handle 303 at the end of the adjustment arm tightly against the frame groove 504, and fasten the adjustment handle 303 using the fastening wire hole 505 and the fastening bolt 506. Finally, use the two fastening long holes 302 on the adjustment plate 301 to place the entire material blocking device and adjustment device flat.

[0074] After the whole material blocking device and adjustment device are installed, they should be installed together with the relevant equipment. Figure 7 As shown, the direction indicated by the arrow is the flow direction 6 of the glass liquid, and the transfer brick 7 is correspondingly arranged at the front end of the blocking device.

[0075] When adjusting the outlet width adjustment device, assume that the width of the initially produced glass is A0, and it is divided into two pieces during cutting, so the total width is 2A0, and the edge clearance width on each side is B, which is usually 70mm. The total width of the cold end glass plate is C0=2(A0+70);

[0076] The thickness of the commonly processed glass plate is 2.8mm or 3.2mm, and the traction rate k value of the glass plate is 30, so the total change kx=30*5=150mm.

[0077] Then the width of the two material stop devices is A=C0+150=2*(A0+70)+150=2A0+290.

[0078] Therefore, if you want to produce a glass plate with a width of A0=1050mm, the width of the material blocking device is 2390mm, and it can be placed symmetrically with the middle axis, and so on.

[0079] This method can more accurately determine the initial positions of the two material blocking devices and achieve digital operation.

[0080] As the processing steps progress, when it is necessary to produce glass sheets of different widths, the width of the glass liquid outlet at the furnace overflow port is adjusted as follows:

[0081] First calculate the width difference △C between the front and rear processed glass plates, and then adjust the two stoppers forward or backward by △C respectively; specifically, loosen the handle fastening wire 506, and adjust the handle 303 forward or backward to adjust the position of the two stoppers, thereby achieving width adjustment.

[0082] In the present invention, a high-temperature resistant stainless steel plate is used as the outer shell of the material blocking device, and is assisted by an inner lining and filled with a special high-temperature resistant filler. This not only overcomes the brittleness and easy cracking of the original material blocking device and the negative effects on production, but also has heat preservation properties and meets production requirements. By using this device and the related process methods developed, the width of the glass liquid outlet of the kiln overflow port can be determined and adjusted quickly and accurately.

[0083] The width adjustment method is to determine the initial position of the overflow port material retaining device during initial installation based on the required glass plate width specifications and edge cleaning amount, the linear speed ratio of the annealing furnace conveying roller and the calendering roller transmission, and the corresponding plate width retraction and expansion. When the width specifications are changed, the device can be adjusted to meet the requirements based on the linear speed ratio of the annealing furnace conveying roller and the calendering roller transmission and the corresponding plate width retraction and expansion.

[0084] If the terms "first" and "second" are used in this patent to limit components, those skilled in the art should know that the use of "first" and "second" is only for the convenience of describing the present invention and simplifying the description, and the above terms have no special meaning.

[0085] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications are possible without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the claimed invention. The scope of the present invention is defined by the appended claims and their equivalents.

[0086] In the description of the present invention, it should be understood that the terms "front", "rear", "left", "right", "center", etc., indicating directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction. Therefore, they cannot be understood as limiting the protection content of the present invention.

Claims

1. A method for adjusting the width of a glass melt outlet at a furnace overflow port, characterized in that: The device comprises a material blocking device and an adjusting device provided at the front end of the calendering roller at the overflow port, and the material blocking device comprises an outer shell, an inner lining and a high-temperature resistant filler. The inner lining is placed in the outer shell, and the outer shell is made of a high-temperature resistant stainless steel plate. The inner end surface of the inner lining is smoothly connected to the inner end surface of the outer shell and both are set to be arc-shaped surfaces corresponding to the outer circumference of the calendering roller, and the high-temperature resistant filler is placed in a cavity surrounded by the outer shell and the inner lining. The adjusting device includes an adjusting arm and an adjusting base for adjusting the adjusting arm, and an adjusting vertical plate is fixed to the end of the adjusting arm and is connected to the housing through the adjusting vertical plate to push the blocking device to move forward and backward; The adjusting plate is provided with a long fastening hole for adjusting the height of the adjusting arm, and the shell is provided with a corresponding shell fastening hole; The outer shell includes an inner baffle and a front baffle fixedly connected thereto, wherein the inner end surface and the bottom end surface of the inner baffle are both configured as arc-shaped surfaces, and the inner end surface and the bottom end surface of the lining are correspondingly smooth and consistent with the arc-shaped surface of the inner baffle; The adjustment base includes a base frame and fastening screw holes vertically provided on the base frame, and a frame groove is provided on the lower end surface of the base frame, and the frame groove is matched with the outer end surface of the adjustment arm; During assembly, the head end of the adjusting arm passes through the base frame in the horizontal direction, and the fastening bolt passes through the fastening thread hole and directly reaches the upper end of the adjusting arm to limit and fix it; The adjustment method includes the following steps: (1) Connection between the material blocking device and the adjusting arm The adjusting arm is connected to the outer shell of the material blocking device through the adjusting vertical plate, and a tightening fixing plate is placed between the lining and the adjusting vertical plate, and the tightening fixing plate is fastened to the lining by a fastening wire passing through the adjusting vertical plate; (2) Preliminary installation of the material blocking device and adjustment device on both sides of the overflow port First, fix the base frame of the adjustment base on the lip bricks on both sides of the overflow outlet of the calender, and pass the head end of the adjustment arm through the base frame horizontally, and fit the adjustment arm tightly into the groove of the frame; Then, fasten the bolts through the fastening holes to fix the adjustment arm, and use the fastening long holes of the adjustment vertical plate to smoothly place the blocking device and the adjustment device; (3) Assume that the width of the glass initially produced is A0, and it is divided into two pieces during cutting, so the total width is 2A0. The clear edge width of each side is B, and the total width of the cold end glass plate is C0 = 2 (A0 + B); (4) The change of the pulling rate k, that is, the change of the linear speed of the conveying roller and the calendering roller of the annealing furnace, will cause the width of the glass sheet to change by x. Then the initial width of the glass liquid outlet at the furnace overflow port is A = C0 + kx; traction rate k=100*(a-b) / b Wherein, a is the linear speed of the annealing furnace conveyor roller, and b is the linear speed of the calendering roller; (5) Based on the initial width A calculated in step (4), loosen the fastening bolts and push the adjustment arm forward or backward so that the distance between the two shells is A.

2. The method for adjusting the width of a furnace overflow glass outlet according to claim 1, characterized in that: The high-temperature resistant filler includes 75% to 85% by weight of silicate refractory clay material, 3% to 5% of fine wood powder, 3% to 5% of sodium metasilicate adhesive, 0.6% to 0.8% of hemp silk, and 10.5% to 11.5% of water, and the total amount of the above components is 100%.

3. The method for adjusting the width of a furnace overflow glass outlet according to claim 1, characterized in that: An adjustment scale is also provided on the horizontal side of the adjustment arm.

4. The method for adjusting the width of a furnace overflow glass outlet according to claim 1, characterized in that: When the glass sheet thickness is 2.8 mm or 3.2 mm, k changes by 1, and the width change x is correspondingly 5; When the thickness of the glass plate is 2.0 mm or 2.5 mm, k changes by 1, and the width change x is correspondingly 3.

Citation Information

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