Ultra-large polygonal quartz tube tailor-welding method and quartz tube

Abstract

The invention provides a tailor-welding method for an oversized polygonal quartz tube and the quartz tube. The quartz tube is formed by welding and splicing a plurality of quartz plates, the cross section of the quartz tube is of a regular polygon structure of which the diameter of an inscribed circle is not less than 600mm, and the size limitation of a traditional centrifugal tube expanding process is broken through. The tailor-welding method comprises the steps of blanking and cutting, edge treatment, positioning and assembling, high-temperature welding and annealing treatment. The invention further relates to a special clamp which comprises a center base, a rotating platform and a plurality of radial adjusting supporting arm assemblies, and accurate indexing rotation is achieved through the angle scale locking device. According to the method, a traditional tube expanding process is abandoned, the production cost is reduced by more than half, and the prepared quartz tube has better deformation resistance and is particularly suitable for large-size semiconductor process equipment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of quartz tube, in particular to a super-large-size polygonal quartz tube splicing and welding method and a quartz tube. BACKGROUND

[0002] At present, the quartz tube in the semiconductor industry is generally produced by continuous melting method to produce a circular quartz glass mother tube, and then expanded by centrifugal force generated by high-speed rotation of a glass lathe. The process is controlled by the physical limit of the equipment, and the maximum expanded tube diameter is usually not more than 500 mm. With the development of 450 mm and above large-size silicon wafer technology, the existing quartz tube is difficult to meet the size requirements of the high-temperature diffusion, oxidation and other process equipment. If the traditional expansion process is used to produce quartz tubes with a diameter of more than 600 mm, not only the technical difficulty is extremely great, but also the production cost is extremely high. SUMMARY

[0003] Therefore, the present application provides a super-large-size polygonal quartz tube splicing and welding method and a quartz tube, which can break through the size limit of traditional processing to produce super-large-size polygonal quartz tubes.

[0004] To solve the above problems, the present application provides a super-large-size polygonal quartz tube splicing and welding method, which comprises the following steps: S1: cutting and cutting the quartz plate into a plurality of rectangular plate pieces of a predetermined size; S2: edge processing, bevel processing and polishing of the splicing edge of the plurality of rectangular plate pieces; S3: positioning and assembling, using a special clamp to position and assemble the processed plate pieces into a regular polygonal cylindrical structure; S4: high-temperature welding, using a hydrogen-oxygen flame welding equipment to segmentally weld each splicing joint to form a closed tube body; S5: annealing treatment, annealing the welded tube body at 1080-1150 DEG C to eliminate internal stress.

[0005] Compared with the prior art, the technical effects achieved by the technical scheme are as follows: the physical limit problem existing in the traditional centrifugal expansion process is innovatively solved by the systematic splicing and welding process, the method adopts cutting, processing, assembling, welding and annealing procedures in steps, breaks through the technical bottleneck of the maximum diameter of the traditional process, and makes it possible to produce quartz tubes with a diameter of more than 600 mm. At the same time, since standard quartz plate is used as raw material, the dependence on expensive special expansion equipment is avoided, the production cost is greatly reduced, and the method is particularly suitable for the research and development verification stage of large-size semiconductor process equipment, and provides key process equipment support for the development of silicon wafer technology.

[0006] In one example of the present application, in step S3, the special clamp comprises: a center base provided with a rotating shaft; a rotating platform connected to the center base for rotation around the rotating shaft; and a plurality of radial adjustment support arm assemblies uniformly distributed on the rotating platform.

[0007] Compared with the prior art, the technical effects achieved by adopting the technical scheme are: the implementation precision and stability of the splicing welding process are ensured through the special fixture structure, a stable foundation is provided by the center base, the precise angle adjustment is realized by the rotating platform, and the full-range support is provided by the uniform distribution of the plurality of radial adjustment support arm assemblies, the three-dimensional positioning system can effectively ensure the relative position precision of the quartz plate materials in the assembly process, and displacement deformation caused by gravity or improper operation is prevented, and meanwhile, the modular design enables the same fixture to adapt to quartz tube production of different size specifications, and the utilization rate of the equipment and the flexibility of the production process are significantly improved.

[0008] In an example of the present application, the special fixture further comprises: an angle scale locking device comprising a worm gear mechanism and a low-speed motor driving the worm gear mechanism, and used for realizing automatic indexing rotation of the rotating platform.

[0009] Compared with the prior art, the technical effects achieved by adopting the technical scheme are: the precise control and automation improvement of the process are realized through the integrated angle scale locking device and automatic indexing system, the indexing precision of the rotating platform reaches the leading level in the industry through the cooperation of the worm gear mechanism and the low-speed motor driving, and the one-degree angle scale provides an intuitive positioning reference for the operator, and this design not only eliminates the errors caused by manual measurement and positioning, but also greatly improves the production efficiency, especially in the manufacturing process of the polygonal quartz tube with a large number of edges, the angle consistency of each splicing edge can be ensured, and a solid foundation is provided for the subsequent welding quality.

[0010] In an example of the present application, the number of the plurality of radial adjustment support arms is at least twice the number n of edges of the regular polygonal cylindrical structure.

[0011] Compared with the prior art, the technical effects achieved by adopting the technical scheme are: the stability and reliability of the assembly process are ensured through the scientific determination of the proportional relationship between the number of support arms and the number of edges of the polygon, the design scheme of setting the number of support arms to be at least twice the number of edges of the polygon can provide a plurality of support points for each plate, effectively dispersing the self-weight of the plate and the thermal stress generated in the welding process, and this configuration is particularly suitable for the manufacturing of large-size quartz tubes, and can prevent plate deformation or splicing misplacement caused by insufficient support, and at the same time, the increase in support density reduces the local stress concentration phenomenon, and provides an important guarantee for preparing high-quality quartz tube products.

[0012] In an example of the present application, each radial adjustment support arm assembly further comprises: a radial slide rail fixed to the rotating platform; and a sliding block base slidably arranged on the radial slide rail and used for abutting against the plate.

[0013] Compared with existing technologies, the technical effects achieved by this solution are as follows: the precise fit between the radial slide rail and the slider base enables precise fine-tuning of the support arm position. This design allows operators to precisely adjust the radial position of each support arm according to the diameter of the target quartz tube, ensuring accurate alignment when all plates are spliced. The linear guide rail ensures movement accuracy, and the lead screw drive provides stable positioning and holding force. This combination not only improves assembly accuracy but also enables the same fixture to adapt to the manufacturing of products with a wider diameter range, significantly enhancing the equipment's usability and economy.

[0014] In one embodiment of the present invention, the special fixture further includes a scale, which is disposed on the central base and is used to read the position of the plate.

[0015] Compared with existing technologies, the technical effects achieved by this solution are as follows: By setting up a precision ruler system, the position of the board material can be read intuitively and accurately positioned. The ruler is directly set on the central base and works in conjunction with the rotating platform and support arm system to provide operators with accurate position feedback. This eliminates the uncertainty of traditional experience-based estimation and ensures that each board material can be accurately positioned according to design requirements. Especially in large-scale production, it can guarantee the consistency and stability of product dimensions and provide a reliable technical means for quality control.

[0016] In one embodiment of the present invention, the special fixture further includes a plate guide, which is disposed on the rotating platform and abuts against the plate.

[0017] Compared with existing technologies, the technical effects achieved by this solution are as follows: the straightedge directly contacts the plate and provides reliable lateral support, effectively preventing the plate from tipping over during assembly and adjustment. This not only improves operational safety but also ensures the reliability of temporary fixation of the plate before final positioning, reducing the risk of displacement due to accidental collisions or vibrations. At the same time, the adjustable design of the straightedge allows it to adapt to quartz plates of different thicknesses, improving the versatility and practicality of the clamp.

[0018] The present invention also provides a quartz tube, which is adapted to any of the above-mentioned ultra-large polygonal quartz tube welding methods. The quartz tube includes: the quartz tube is formed by welding together multiple processed plates, and its cross-section is a regular polygonal cylindrical structure with an inscribed circle diameter of not less than 600 mm.

[0019] Compared with existing technologies, the technical effects achieved by this solution are as follows: the use of multiple quartz plates welded together to form a regular polygonal structure enables the manufacture of quartz tubes with diameters ranging from 600 to 1200 mm, fully meeting the requirements of large-size silicon wafer process equipment. The polygonal structure has better resistance to deformation and stability compared to the traditional circular structure. At the same time, this design allows for the direct integration of functional structures such as flanges and domes onto the tube body, significantly improving the overall integrity and performance of the product, and providing key process equipment support for the semiconductor industry to develop towards larger sizes.

[0020] In one embodiment of the present invention, the side length 'a' of the regular polygonal cylindrical structure is 200 mm to 300 mm.

[0021] Compared with existing technologies, the technical effects achieved by adopting this technical solution are as follows: by optimizing the design of polygon side length parameters within the range of 200-300mm, the best economy is achieved while ensuring structural strength and process feasibility. This size range has been verified by a large number of experiments, which can ensure that a single quartz plate has sufficient structural rigidity and is not easily deformed during handling and assembly, while not increasing the processing difficulty due to excessive size.

[0022] In one embodiment of the present invention, the number of sides n of the regular polygonal cylindrical structure is determined by the following formula: n = 180° / arctan(a / D); where a is the side length and D is the diameter of the inscribed circle.

[0023] Compared with existing technologies, the technical effects achieved by adopting this technical solution are as follows: The optimal number of polygon sides is determined through scientific mathematical modeling and calculation formulas. This formula is based on geometric principles and can accurately calculate the required number of sides according to the diameter of the target inscribed circle and the length of a single side. This ensures that the polygon is as close as possible to the characteristics of a circular flow channel while meeting structural requirements. It provides a theoretical basis for the design of quartz tubes of different sizes and specifications, ensuring the scientific and rational nature of product design. At the same time, by optimizing the selection of the number of sides, the structural stability and manufacturing economy are maximized while ensuring fluid performance.

[0024] By adopting the technical solution of the present invention, the following technical effects can be achieved: (1) The method innovatively solves the physical limit problem of traditional centrifugal tube expansion process through a systematic welding process. The method adopts a step-by-step cutting, processing, assembly, welding and annealing process, which breaks through the technical bottleneck of the maximum diameter of traditional process, enabling the production of quartz tubes with a diameter of more than 600 mm. At the same time, since standard quartz plates are used as raw materials, the dependence on expensive special tube expansion equipment is avoided, and the production cost is greatly reduced. It is particularly suitable for the research and development verification stage of large-size semiconductor process equipment, and provides key process equipment support for the development of silicon wafer technology. (2) The special fixture structure ensures the implementation accuracy and stability of the welding process. The central base provides a stable foundation, the rotating platform realizes precise angle adjustment, and multiple radial adjustment support arm components are evenly distributed to provide all-round support. This three-dimensional positioning system can effectively ensure the relative position accuracy of each quartz plate during the assembly process and prevent displacement deformation caused by gravity or improper operation. At the same time, its modular design allows the same fixture to adapt to the production of quartz tubes of different sizes and specifications, which significantly improves the utilization rate of the equipment and the flexibility of the production process. (3) The regular polygonal structure formed by welding multiple quartz plates has enabled the manufacture of quartz tubes with diameters ranging from 600 to 1200 mm, which fully meets the needs of large-size silicon wafer process equipment. Compared with the traditional circular structure, the polygonal structure has better resistance to deformation and stability. At the same time, this design allows for the direct integration of functional structures such as flanges and domes on the tube body, which greatly improves the overall performance and usability of the product, and provides key process equipment support for the semiconductor industry to develop towards larger sizes. Attached Figure Description

[0025] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings to be used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Figure 1 A schematic flowchart illustrating a method for welding ultra-large polygonal quartz tubes according to an embodiment of the present invention; Figure 2 This is one of the structural schematic diagrams of the special clamp provided in the embodiment of the present invention when it is used with a quartz tube; Figure 3 The second schematic diagram shows the structure of the special clamp provided in this embodiment of the invention when it is used with a quartz tube; Figure 4 This is the third schematic diagram of the structure of the special clamp provided in this embodiment of the invention when it is used with a quartz tube; Figure 5 for Figure 4 A magnified view of region A in the middle.

[0026] Explanation of reference numerals in the attached figures: 110. Center base; 120. Rotating shaft; 130. Rotating platform; 140. Radial adjustment support arm assembly; 141. Radial slide rail; 142. Slider base; 150. Plate straightedge; 200. Quartz tube. Detailed Implementation

[0027] To make the above-mentioned objectives, features, and advantages of the present invention more apparent and understandable, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] [First Embodiment] See Figure 1 This invention provides a method for welding ultra-large polygonal quartz tubes, comprising: S1: Cutting: Cutting the quartz slab into multiple rectangular pieces of a predetermined size; S2: Edge treatment, beveling and polishing the splicing edges of multiple rectangular plates; S3: Positioning and assembly, using special fixtures to position and assemble the processed plates into a regular polygonal cylindrical structure; S4: High-temperature welding, using oxyhydrogen flame welding equipment to weld each joint in sections to form a closed tube; S5: Annealing treatment, the welded pipe body is annealed at 1080℃~1150℃ to eliminate internal stress.

[0029] Preferably, the systematic welding process innovatively solves the physical limitations of traditional centrifugal tube expansion technology. This method uses a step-by-step process of cutting, processing, assembly, welding and annealing to break through the technical bottleneck of the maximum diameter of traditional processes, enabling the production of quartz tubes with a diameter of 600mm or more. At the same time, by using standard quartz plates as raw materials, it avoids dependence on expensive special tube expansion equipment, significantly reducing production costs. It is particularly suitable for the research and development verification stage of large-size semiconductor process equipment, providing key process equipment support for the development of silicon wafer technology.

[0030] See Figures 2-5 Specifically, in step S3, the special fixture includes: a central base 110, which is provided with a rotating shaft 120; a rotating platform 130, which is rotatably connected to the central base 110 around the rotating shaft 120; and multiple radially adjustable support arm assemblies 140, which are evenly distributed on the rotating platform 130.

[0031] Specifically, this specialized assembly fixture is an adjustable ring-shaped support and positioning system. Its core design concept is to provide precise and stable support for the splicing of polygonal quartz tubes 200, while adapting to the product requirements of different diameters and numbers of sides. The main body of the fixture is made of high-temperature resistant alloy steel (310S stainless steel) to withstand the radiant heat near the quartz during welding. All parts in contact with the quartz glass are made of high-temperature resistant non-metallic materials (graphite) to prevent hard scratches or cold cracks on the surface of the quartz tube 200.

[0032] Furthermore, the central base 110 is a robust, reinforced circular steel platform, connected to the rotating platform 130 at its bottom via large crossed roller bearings. It serves as the base for the entire fixture. Its core function is to allow the entire upper fixture to rotate precisely around its central axis. The rotating platform 130 has precise angle markings (one degree increment) along its edges and is equipped with a worm gear mechanism to precisely lock the platform to the next calculated angular position after each edge is welded (e.g., 36° precise rotation for a decagon). Drive: Automatic indexing is achieved via a low-speed motor. Number of radially adjustable support arms (modular units): At least twice the number of sides n of the target polygon (20 sets or more for a decagon), evenly distributed on the rotating platform 130. Each support arm is an independent unit, containing: Radial slide rail 141: A high-precision linear guide rail fixed to the rotating platform 130, strictly oriented towards the center. Slider base 142: Mounted on a slide rail, driven by a precision lead screw, its radial distance relative to the center is precisely controlled to accommodate different tube diameters (D value). The base has a scale for visually reading the position. Sheet metal guide 150: Used to secure the sheet metal and prevent tipping.

[0033] Preferably, the special fixture structure ensures the accuracy and stability of the welding process. The central base 110 provides a stable foundation, the rotating platform 130 enables precise angle adjustment, and multiple radially adjustable support arm assemblies 140 are evenly distributed to provide all-round support. This three-dimensional positioning system can effectively ensure the relative position accuracy of each quartz plate during the assembly process and prevent displacement and deformation caused by gravity or improper operation. At the same time, its modular design allows the same fixture to adapt to the production of quartz tubes 200 of different sizes and specifications, which significantly improves the utilization rate of the equipment and the flexibility of the production process.

[0034] Specifically, the special fixture also includes: an angle scale locking device, including a worm gear mechanism and a low-speed motor that drives the worm gear mechanism, used to realize the automatic indexing rotation of the rotary platform 130°.

[0035] Preferably, the integrated angle scale locking device and automatic indexing system achieve precise control and automation of the process. The worm gear mechanism, combined with the low-speed motor drive, ensures that the 130-degree indexing accuracy of the rotary platform reaches the industry-leading level. The angle scale, with each degree increment, provides operators with an intuitive positioning reference. This design not only eliminates the errors that may be caused by manual measurement and positioning, but also greatly improves production efficiency. Especially in the manufacturing process of polygonal quartz tubes 200 with a large number of sides, it can ensure the angular consistency of each splicing edge, providing a solid foundation for the subsequent welding quality.

[0036] Specifically, the number of radially adjustable support arms is at least twice the number of sides n of the regular polygonal cylindrical structure.

[0037] Preferably, by scientifically determining the ratio between the number of support arms and the number of polygon sides, the stability and reliability of the assembly process are ensured. The design scheme of setting the number of support arms to at least twice the number of polygon sides can provide multiple support points for each plate, effectively dispersing the self-weight of the plate and the thermal stress generated during welding. This configuration is particularly suitable for the manufacture of large-size quartz tubes 200, which can prevent plate deformation or splicing misalignment due to insufficient support. At the same time, by increasing the support density, the phenomenon of local stress concentration is reduced, which provides an important guarantee for the production of high-quality quartz tube 200 products.

[0038] Specifically, each radial adjustment support arm assembly 140 further includes: a radial slide rail 141, which is fixed to the rotating platform 130; and a slider base 142, which is slidably disposed on the radial slide rail 141 and is used to abut against the plate.

[0039] Preferably, the precise fit between the radial slide rail 141 and the slider base 142 enables precise fine-tuning of the support arm position. This design allows the operator to precisely adjust the radial position of each support arm according to the diameter of the target quartz tube 200, ensuring accurate alignment when all plates are spliced. The linear guide rail ensures movement accuracy, and the lead screw drive provides stable positioning and holding force. This combination not only improves assembly accuracy but also enables the same fixture to adapt to the manufacturing of products with a wider diameter range, significantly enhancing the use value and economy of the equipment.

[0040] Specifically, the special fixture also includes a ruler, which is located on the central base 110 and is used to read the position of the plate.

[0041] Preferably, a precision ruler system is set up to enable intuitive reading and accurate positioning of the board material. The ruler is directly set on the central base 110 and works in conjunction with the rotating platform 130 and the support arm system to provide accurate position feedback to the operator. This eliminates the uncertainty of traditional experience-based estimation and ensures that each board material can be accurately positioned according to the design requirements. Especially in large-scale production, this can ensure the consistency and stability of product dimensions and provide a reliable technical means for quality control.

[0042] Specifically, the special fixture also includes: a plate straightedge 150, which is located on the rotating platform 130 and abuts against the plate.

[0043] Preferably, the straightedge directly contacts the plate and provides reliable lateral support, effectively preventing the plate from tipping over during assembly and adjustment. This not only improves operational safety but also ensures the reliability of temporary fixation of the plate before final positioning, reducing the risk of displacement due to accidental collisions or vibrations. At the same time, the adjustable design of the straightedge allows it to adapt to quartz plates of different thicknesses, enhancing the versatility and practicality of the clamp.

[0044] The present invention also provides a quartz tube 200, which is adapted to any of the above-mentioned methods for welding ultra-large polygonal quartz tubes 200. The quartz tube 200 includes: the quartz tube 200 is formed by welding together multiple processed plates, and its cross-section is a regular polygonal cylindrical structure with an inscribed circle diameter of not less than 600 mm.

[0045] Preferably, the use of a regular polygonal structure formed by welding multiple quartz plates enables the manufacture of quartz tubes 200 with diameters ranging from 600 to 1200 mm, fully meeting the requirements of large-size silicon wafer process equipment. Compared with the traditional circular structure, the polygonal structure has better resistance to deformation and stability. At the same time, this design allows for the direct integration of functional structures such as flanges and domes on the tube body, greatly improving the overall integrity and performance of the product, and providing key process equipment support for the semiconductor industry to develop towards larger sizes.

[0046] Specifically, the side length 'a' of the regular polygonal cylindrical structure is 200mm to 300mm.

[0047] Specifically, 250mm is preferred.

[0048] Preferably, by optimizing the design of the polygon side length parameters within the range of 200-300mm, the best economy is achieved while ensuring structural strength and process feasibility. This size range has been verified by a large number of experiments, which can ensure that a single quartz plate has sufficient structural rigidity and is not easily deformed during handling and assembly, while not increasing the processing difficulty due to excessive size.

[0049] Specifically, the number of sides n of the regular polygonal cylindrical structure is determined by the following formula: n = 180° / arctan(a / D); where a is the side length and D is the diameter of the inscribed circle.

[0050] Preferably, the optimal number of sides of the polygon was determined through scientific mathematical modeling and calculation formulas. This formula is based on geometric principles and can accurately calculate the required number of sides according to the diameter of the target inscribed circle and the length of a single side. This ensures that the polygon is as close as possible to the characteristics of a circular flow channel while meeting structural requirements. This provides a theoretical basis for the design of quartz tubes 200 of different sizes and specifications, ensuring the scientific and rational nature of the product design. At the same time, by optimizing the selection of the number of sides, the structural stability and manufacturing economy are maximized while ensuring fluid performance.

[0051] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of splicing ultra-large size polygonal quartz tubes, characterized by, The method comprises the following steps: S1: cutting, cutting quartz plates into multiple rectangular pieces of predetermined size; S2: edge processing, beveling and polishing the splicing edges of the multiple rectangular pieces; S3: positioning and assembling, using a special fixture to position and assemble the processed pieces into a regular polygonal cylindrical structure; S4: high-temperature welding, using a hydrogen-oxygen flame welding device to segmentally weld each splicing joint to form a closed pipe body; S5: annealing treatment, annealing the welded pipe body at 1080-1150°C to eliminate internal stress.

2. The method of claim 1, wherein the super-size polygonal quartz tube is a tube having a cross-section in the shape of a polygon with at least 5 sides. In step S3, the special fixture comprises: a center base provided with a rotating shaft; a rotating platform connected to the center base for rotation around the rotating shaft; a plurality of radial adjustment support arm assemblies uniformly distributed on the rotating platform.

3. The method of claim 2, wherein the method further comprises: The special fixture further comprises: an angle scale locking device comprising a worm and gear mechanism and a low-speed motor driving the worm and gear mechanism, for realizing automatic indexing rotation of the rotating platform.

4. The method of claim 2, wherein: the number of the plurality of radial adjustment support arms is at least twice the number n of sides of the regular polygonal cylindrical structure.

5. The method of claim 2, wherein the super-size polygonal quartz tube is formed by welding a plurality of quartz tubes. Each radial adjustment support arm assembly further comprises: a radial slide rail fixed to the rotating platform; a slide block base slidingly arranged on the radial slide rail and used for abutting against the pieces.

6. The method of claim 2, wherein the method further comprises: The special fixture further comprises: a scale arranged on the center base, used for reading the position of the pieces.

7. The method of claim 2, wherein the method further comprises, The special fixture further comprises: a piece abutting scale arranged on the rotating platform and abutting against the pieces.

8. A quartz tube adapted to the method of splicing a large-size polygonal quartz tube according to any one of claims 1 to 7, characterized in that, The quartz pipe comprises: the quartz pipe is made of multiple processed pieces by welding, and has a regular polygonal cylindrical structure with an inscribed circle diameter of not less than 600 mm.

9. The quartz tube of claim 6, wherein, The side length a of the regular polygonal cylindrical structure is 200-300 mm.

10. The quartz pipe of claim 7, wherein: the number n of sides of the regular polygonal cylindrical structure is determined by the following formula: n = 180° / arctan(a / D); wherein a is the side length and D is the inscribed circle diameter.

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