An optimization method for irregular capillary head models used in additive manufacturing

Abstract

This invention discloses an optimization method for a shaped capillary head model used in additive manufacturing. The method includes establishing a capillary shape compensation formula for the capillary forming angle; establishing a head flow resistance formula for the capillary diameter and surface roughness; determining the capillary diameter and surface roughness based on the head flow resistance formula and the desired flow resistance; determining the number of capillaries, capillary distribution, capillary forming angle, and capillary length based on the capillary shape compensation formula and the desired thermal resistance; and optimizing the 3D head model using the determined capillary diameter, surface roughness, number of capillaries, capillary distribution, forming angle, and length. This invention enables the control of flow resistance and thermal resistance in the head of shaped capillary structures manufactured using additive manufacturing, achieving integrated design and manufacturing of the shaped capillary head structure.

Description

Technical Field

[0001] This invention belongs to the field of additive manufacturing technology, and relates to an optimization method for an irregular capillary head model used in additive manufacturing, particularly to a method for controlling the flow resistance and thermal resistance of an irregular capillary head in additive manufacturing of a liquid rocket engine. Background Technology

[0002] The head section is a core component in the liquid rocket attitude control engine's gas generator and thrust chamber, responsible for propellant guidance and distribution, ensuring uniform propellant distribution within the decomposition chamber. It contains numerous spatially irregularly shaped, twisted capillary structures with diameters of 0.6mm–0.8mm and wall thicknesses of 0.1mm–0.2mm. Traditional manufacturing processes for attitude control engine heads, involving separate parts and brazing, suffer from drawbacks such as long processing times, low efficiency, high scrap rates, reliance on worker skill levels, and high costs, hindering the stable and reliable mass production of irregularly shaped capillary structures and their components. Additive manufacturing technology, as one of the latest and most advanced manufacturing technologies, features integrated CAD / CAM and highly efficient manufacturing, enabling the integral manufacturing of irregularly shaped capillary structure attitude control engine heads.

[0003] Due to limitations in additive manufacturing processes, two prominent issues exist in the design and fabrication of additively manufactured capillary heads: First, the surface roughness of additively manufactured surfaces is higher than that of machined surfaces. Based on the surface state of additively manufactured surfaces, there is no database corresponding to the relationship between capillary structure, surface quality, and fluid pressure drop, resulting in a lack of methods for controlling the flow resistance of additively manufactured capillary heads. Second, additively manufactured capillary heads integrate independently distributed capillaries into a heat-insulating frame, leading to lower thermal resistance than traditional designs. This poses a risk of thermal backflow causing generator ablation, and currently, there is no method for controlling the thermal resistance of additively manufactured capillary heads. These two issues hinder the engineering application of additively manufactured heads. To address these problems, a systematic approach to controlling the flow resistance and thermal resistance of additively manufactured capillary heads is needed. Summary of the Invention

[0004] The purpose of this invention is to overcome the above-mentioned defects and provide an optimization method for the head model of irregular capillary structures used in additive manufacturing. This invention solves the technical problem that the lack of flow resistance and thermal resistance control technology for the head of additively manufactured capillary structures hinders its mass engineering application. This invention proposes a method for controlling the flow resistance and thermal resistance of the head of irregular capillary structures in additive manufacturing.

[0005] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0006] An optimization method for an irregular capillary head model used in additive manufacturing includes:

[0007] Establish a capillary shape compensation formula for the capillary forming angle;

[0008] Establish a head flow resistance formula for capillary diameter and capillary surface roughness;

[0009] Based on the head flow resistance formula, the capillary diameter and capillary surface roughness are determined according to the expected flow resistance of the head.

[0010] Based on the capillary shape compensation formula, the number of capillaries, capillary distribution, capillary forming angle and capillary length are determined according to the expected thermal resistance of the head.

[0011] The head 3D model is optimized by using the determined capillary diameter, capillary surface roughness, number of capillaries, capillary distribution, capillary forming angle, and capillary length.

[0012] Furthermore, the method for establishing the capillary shape compensation formula regarding the capillary forming angle is as follows:

[0013] Design a series of capillaries with equally spaced forming angles in the range of 0° to 60° and equally spaced tube diameters in the range of 0.4 to 1 mm, and use a series of head 3D models containing the series of capillaries for laser selective melting forming.

[0014] The collapse information of the capillary overhang at each forming angle and pipe diameter was statistically analyzed, and the capillary shape compensation formula for the capillary forming angle was obtained by fitting.

[0015] The forming angle is the angle between the inner surface of the capillary and the horizontal plane.

[0016] Furthermore, in the method for establishing a capillary shape compensation formula regarding the capillary forming angle, a series of capillary forming angles are 0°, 20°, 30°, 40°, and 50°, and the tube diameter is in the range of 0.4 mm to 1 mm with an interval of 0.1 mm.

[0017] Furthermore, the capillary shape compensation formula is as follows:

[0018]

[0019] Where θ is the capillary forming angle and d0 is the diameter compensation value of the capillary overhang.

[0020] Furthermore, the method for establishing the head flow resistance formula regarding capillary diameter and capillary surface roughness is as follows:

[0021] Design a series of capillaries with equally spaced diameters in the range of 0.4 to 1 mm, and use a series of head three-dimensional models containing the series of capillaries to perform laser selective melting to form a series of heads with different capillary diameters.

[0022] Chemical polishing was performed on heads with the same capillary diameter for different durations until chemical polishing of heads with different capillary diameters was completed.

[0023] The surface roughness of capillaries under different chemical polishing times was measured using a three-dimensional digital microscope.

[0024] The pressure drop and uniformity of the liquid flow at each head with different pipe diameters and surface roughness were measured, and the flow resistance formula for the head with respect to the capillary diameter and capillary surface roughness was obtained after fitting.

[0025] Furthermore, in the method for establishing the head flow resistance formula for capillary diameter and capillary surface roughness, a series of capillary tubes with diameters increasing by 0.1 mm in the range of 0.4 to 1 mm are first designed. The heads with the same capillary diameter are chemically polished for 0.5 min, 1 min, 2 min, and 3 min, and the head flow resistance formula for capillary diameter and capillary surface roughness is initially obtained.

[0026] A series of capillaries with diameters increasing by 0.1 mm in the range of 0.4 to 1 mm were designed. The heads of the capillaries with the same diameter were chemically polished for 1 mm, 1.5 min, 2.5 min, 2 min, and 3 min. The head flow resistance formulas for the capillary diameter and capillary surface roughness were modified to obtain the head flow resistance formulas for the capillary diameter and capillary surface roughness.

[0027] Furthermore, the formulas for head flow resistance regarding capillary diameter and capillary surface roughness are as follows:

[0028]

[0029] In the formula, P is the pressure drop, d is the capillary diameter, and R is the capillary surface roughness.

[0030] Furthermore, the chemical polishing method involves using an electric pump to uniformly flow the polishing solution within the capillary at a pressure of 0.7 MPa and a speed of 50-60 mm / s.

[0031] The chemical polishing solution is a mixed solution containing hydrochloric acid, nitric acid and hydrofluoric acid, with a volume ratio of 4:3:1.

[0032] The amount of material removed during polishing at different polishing times is ≤0.05mm.

[0033] Furthermore, the number of capillaries determined based on the desired flow resistance of the head is 30 to 100. The number of capillaries is distributed in multiple concentric rings. Each capillary includes a vertical section and an inclined section. The inclined sections of capillaries distributed in the same concentric ring have the same forming angle. The inclined sections of capillaries distributed in different concentric rings have the forming angle increasing from the outside to the inside. The length of capillaries distributed in different concentric rings decreases from the outside to the inside. The diameter of the inclined section of the capillary is optimized based on the capillary shape compensation formula.

[0034] Furthermore, there are a total of 39 capillaries, which are concentrated inside the insulation frame;

[0035] Capillaries are classified into four categories: A, B, C, and D. All four categories of irregularly shaped capillaries are distributed in a ring shape. Category A capillaries are distributed in the outermost ring, totaling 18, with a total length of 160 mm and a capillary forming angle of 20° at the inclined point. Category B, C, and D capillaries are distributed towards the center in sequence. Category B capillaries consist of 12, with a total length of 150 mm and a capillary forming angle of 23° at the inclined point. Category C capillaries consist of 6, with a total length of 140 mm and a capillary forming angle of 26° at the inclined point. Category D capillaries consist of 3, with a total length of 120 mm and a capillary forming angle of 28° at the inclined point.

[0036] Compared with the prior art, the present invention has at least one of the following advantages:

[0037] (1) This invention creatively proposes an optimization method for a shaped capillary head model for additive manufacturing. Through the iterative optimization design route of head capillary diameter-surface quality-fluid flow pressure drop, a method for controlling the fluid flow resistance of the head in additive manufacturing is obtained. That is, the flow resistance of the head is controlled by adjusting the capillary diameter and surface quality.

[0038] (2) This invention obtains a method for controlling the thermal resistance of the head in additive manufacturing by using the iterative optimization design technology route of capillary quantity / distribution / length-thermal resistance. That is, the thermal resistance of the head is controlled by adjusting the diameter, quantity and distribution of capillary tubes.

[0039] (3) Based on the additive manufacturing head flow group and thermal resistance control method, this invention obtains the diameter, quantity, length and distribution of the additive manufacturing head capillary structure that meet the design requirements, realizes the integrated design and manufacturing of the irregular capillary head structure, and integrates the manufacturing of more than 30 parts in the traditional "machining + bending + chemical milling + brazing + fusion welding" process, solving the problems of multiple welds that are not inspectable or measurable, insufficient reliability, long processing cycle and many processes in the traditional processing process;

[0040] (4) This invention takes into account a variety of influencing factors and gives several relevant formulas that can achieve thermal resistance control and flow resistance control. It has universality and can effectively improve product design efficiency and optimize the thermal resistance and flow resistance performance of the product.

[0041] (5) The present invention proposes a shape compensation method for the inclined section of the capillary, which can effectively avoid the occurrence of collapse and improve product quality;

[0042] (6) This invention achieves uniform and efficient polishing of additive manufacturing capillary tubes through the design of circulating flow chemical polishing fixtures and the control of polishing process parameters. On the one hand, it ensures the pressure drop requirements of the liquid flow at the head, and on the other hand, it removes the powder adhering to the capillary tube at the head, thus ensuring product reliability. Attached Figure Description

[0043] Figure 1 It is a typical capillary configuration;

[0044] Figure 2 This is the shape of the inclined portion of the capillary tube in this invention;

[0045] Figure 3 This is an optimized 3D model of the capillary head of the present invention. Detailed Implementation

[0046] The features and advantages of the present invention will become clearer and more apparent from the following detailed description.

[0047] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0048] This invention discloses an optimization method for an additive manufacturing irregular capillary structure head model, which is actually a method for controlling the flow resistance and thermal resistance of an additive manufacturing irregular capillary structure head for liquid rocket engines. The method mainly includes the following steps:

[0049] S1 establishes a capillary shape compensation formula regarding the capillary forming angle; a typical capillary configuration is as follows: Figure 1 As shown;

[0050] S2 establishes the head flow resistance formula for capillary diameter and capillary surface roughness;

[0051] Based on the head flow resistance formula, the capillary diameter and capillary surface roughness are determined according to the expected flow resistance of the head.

[0052] S3 is based on the capillary shape compensation formula, which determines the number of capillaries, capillary distribution, capillary forming angle and capillary length according to the expected thermal resistance of the head.

[0053] S4 optimizes the 3D head model by using the determined capillary diameter, capillary surface roughness, number of capillary tubes, capillary distribution, capillary forming angle, and capillary length.

[0054] Step S1, which optimizes shape accuracy, mainly includes two steps: First, design a series of capillary structures with forming angles of 0°, 20°, 30°, 40°, and 50°, and diameters ranging from 0.4mm to 1mm, increasing in 0.1mm increments. Perform laser selective melting to form these structures. The forming angle refers to the angle between the inner surface of the capillary and the horizontal plane. Second, statistically analyze the collapse distance and shape of the suspended portion of the capillary at each forming angle and diameter, and fit the results to obtain shape compensation formulas for different diameters and forming angles.

[0055]

[0056] In the formula, θ is the capillary forming angle, and d0 is the diameter compensation value of the capillary overhang. The overhang is the upper semicircle of the cross-section of the inclined section of the capillary.

[0057] In steps S2 to S5, the process / design collaborative optimization design, and the control of head flow resistance and thermal resistance, mainly refer to the iterative design of capillary diameter, quantity, and distribution based on the overall head design, to form a method for controlling head fluid flow resistance and thermal resistance. Finally, based on the flow resistance and thermal resistance control method, an integrated design model of head structure and function is obtained. The head flow resistance control technology route is an iterative optimization design of head capillary diameter-surface quality-fluid flow pressure drop, and the head thermal resistance control technology route is an iterative optimization design of capillary quantity / distribution / length-thermal resistance.

[0058] Step S2 involves iterative optimization of the capillary diameter, surface quality, and fluid pressure drop at the head.

[0059] The iterative optimization method for capillary head diameter-surface quality-fluid flow pressure drop mainly includes three steps: First, design a series of capillary head structures with diameters ranging from 0.4mm to 1mm, increasing in increments of 0.1mm; Second, perform chemical polishing on each head with different diameters for different times (0.5min, 1min, 2min, 3min), and measure the capillary surface roughness under different chemical polishing times using a three-dimensional digital microscope; Third, measure the fluid flow pressure drop and pressure drop uniformity in different regions of heads with different diameters and surface roughness, summarize and analyze the data, and preliminarily fit and determine the correspondence between capillary head diameter, surface roughness, and fluid flow pressure drop. Step 4: Design a series of capillary heads with diameters ranging from 0.4mm to 1mm, increasing in 0.05mm increments. Perform chemical polishing with different process parameters (1mm, 1.5min, 2.5min, 2min, 3min), and conduct liquid flow pressure drop and uniformity tests. Correct and verify the formula for the correspondence between capillary diameter, surface roughness, and liquid flow pressure drop fitted in Step 3, and finally determine the formula for calculating the liquid flow pressure drop of the head.

[0060]

[0061] In the formula, P is the pressure drop, d is the pipe diameter, and R is the roughness.

[0062] Based on the above formula for calculating the pressure drop of the head fluid flow, and according to the design pressure drop requirements of the head, the capillary diameter and surface roughness are calculated to obtain the capillary size and surface condition, wherein the diameter is 0.4 mm and the chemical polishing time is 3 min.

[0063] The capillary chemical polishing process for the head is hampered by the capillary structure and solution flow resistance, resulting in weak solution exchange within the capillary. After a certain polishing time, the concentration of the chemical solution is low, and concentration differences exist between different parts, leading to incomplete or uneven chemical milling polishing. To ensure uniform capillary polishing, a solution circulation flow chemical milling finishing fixture—a flow-guiding plate-shaped fixture—is designed. (The fixture has a hole in the central area with a diameter matching the upper diameter of the head, and threaded holes with a diameter of 5mm at each of the four corners. The fixture is sealed to the upper end of the head with bolts, and a pump is connected to the head through a pipe.) An electric pump is used to uniformly fill the capillary with the polishing solution at a certain pressure and speed, ensuring the uniformity of chemical solution exchange. The pump pressure is 0.7 MPa, and the solution flow rate is 50-60 mm / s. The chemical polishing solution is a mixture of hydrochloric acid, nitric acid, and hydrofluoric acid in a ratio of 4:3:1. The polishing removal amount at polishing times of 0.5 min, 1 min, 2 min, and 3 min is ≤0.05 mm, which does not affect the head strength.

[0064] Step S3 involves iterative optimization design of capillary number / distribution / length-thermal resistance.

[0065] The additively manufactured capillary head integrates the independently distributed capillaries of traditional designs into a heat-insulating frame, resulting in lower thermal resistance. Through a design featuring high flow rate, high integration, and high aspect ratio, cooling is enhanced, the heat return area is reduced, and the heat conduction distance is increased, thereby improving the thermal resistance of the additively manufactured capillary head. After multiple rounds of iterative design based on the number, distribution, length, and thermal resistance of capillaries, for high-flow-rate heads ≥200g / s, information on the number, distribution, and length of capillaries meeting the thermal resistance requirements was obtained. Specifically, there are 39 capillaries, concentrated within the heat-insulating frame, categorized into four types: A, B, C, and D. Four types of irregularly shaped capillaries, A, B, C, and D, are arranged in a ring. Type A capillaries are located on the outermost ring, totaling 18, with a total unfolded length of 160 mm and a capillary formation angle of 20° at the inclined section. Types B, C, and D capillaries are distributed sequentially towards the center. Type B capillaries number 12, with an unfolded length of 150 mm and a capillary formation angle of 23° at the inclined section; Type C capillaries number 6, with an unfolded length of 140 mm and a capillary formation angle of 26° at the inclined section; and Type D capillaries number 3, with an unfolded length of 120 mm and a capillary formation angle of 28° at the inclined section. (See...) Figure 1 Based on the capillary shape compensation parabola formula in step (3), the shapes of the inclined sections of capillary tubes with diameters A, B, C, and D are calculated, see... Figure 2 .

[0066] Through iterative optimization of capillary diameter, surface quality, and fluid pressure drop, as well as iterative optimization of capillary number / distribution / length and thermal resistance, the final optimized 3D model of the capillary head structure was determined, such as... Figure 3 As shown.

[0067] Based on the above process, the present invention utilizes the following steps to achieve additive manufacturing of the irregular capillary structure head of a liquid rocket engine:

[0068] (1) Establish an integrated three-dimensional head model based on additive manufacturing.

[0069] (2) Based on the stress distribution and support configuration of the integrated model obtained in step (1) during the forming process, the growth direction of the head is determined according to the principle of minimum stress, minimum support and removability.

[0070] (3) Based on the growth direction of step (2), extract the typical structural features of the capillary in the model, optimize the capillary structure accuracy and surface quality, and obtain high-precision, high-surface-quality capillary process parameters and scanning path.

[0071] (4) Iterative optimization of process and design, adjustment of head flow resistance and thermal resistance, and obtaining an optimized three-dimensional model.

[0072] (5) Based on the three-dimensional model determined in step (4) and the growth direction determined in step (2), design the process support and process powder cleaning port to obtain the three-dimensional process model of the head.

[0073] (6) Using the process parameters and scanning speed obtained in step (3), the process three-dimensional model obtained in step (5) is segmented to obtain the laser scanning path parameters of each slice layer and laser additive manufacturing is performed.

[0074] (7) Remove the metal powder in the head capillary structure obtained in step (6), and remove the process support after heat treatment.

[0075] (8) After chemical polishing the head obtained in step (7), a liquid flow test is performed.

[0076] (9) Perform microfocus CT foreign matter detection on the capillary head obtained in step (8).

[0077] In step (8), the head flow control method is adopted, namely the chemical polishing parameters and circulation flow channel tooling determined by the capillary diameter-surface quality-fluid flow pressure drop iterative optimization design process, to chemically polish the entire head. After polishing, the fluid flow test is performed.

[0078] The present invention has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and embodiments of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims.

[0079] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. An optimization method for an irregular capillary head model used in additive manufacturing, characterized in that, include: Establish a capillary shape compensation formula for the capillary forming angle; Establish a head flow resistance formula for capillary diameter and capillary surface roughness; Based on the head flow resistance formula, the capillary diameter and capillary surface roughness are determined according to the expected flow resistance of the head. Based on the capillary shape compensation formula, the number of capillaries, capillary distribution, capillary forming angle and capillary length are determined according to the expected thermal resistance of the head. The head 3D model is optimized by using the determined capillary diameter, capillary surface roughness, number of capillaries, capillary distribution, capillary forming angle, and capillary length. The method for establishing the capillary shape compensation formula regarding the capillary forming angle is as follows: Design a series of capillaries with equally spaced forming angles in the range of 0° to 60° and equally spaced tube diameters in the range of 0.4 to 1 mm, and use a series of head 3D models containing the series of capillaries for laser selective melting forming. The collapse information of the capillary overhang at various forming angles and diameters was statistically analyzed, and the capillary shape compensation formula for the capillary forming angle was obtained by fitting. The forming angle is the angle between the inner surface of the capillary and the horizontal plane; The method for establishing the head flow resistance formulas for capillary diameter and capillary surface roughness is as follows: Design a series of capillaries with equally spaced diameters in the range of 0.4~1mm, and use a series of head three-dimensional models containing the series of capillaries to perform laser selective melting to form a series of heads with different capillary diameters. Chemical polishing was performed on heads with the same capillary diameter for different durations until chemical polishing of heads with different capillary diameters was completed. The surface roughness of capillaries under different chemical polishing times was measured using a three-dimensional digital microscope. The pressure drop and uniformity of the liquid flow at each head with different pipe diameters and surface roughness were measured, and the flow resistance formula for the head with respect to the capillary diameter and capillary surface roughness was obtained after fitting.

2. The optimization method for an irregular capillary head model used in additive manufacturing according to claim 1, characterized in that, In the method for establishing a capillary shape compensation formula for the capillary forming angle, a series of capillary forming angles are 0°, 20°, 30°, 40°, and 50°, and the tube diameter is in the range of 0.4 mm to 1 mm with an interval of 0.1 mm.

3. The optimization method for an irregular capillary head model used in additive manufacturing according to claim 2, characterized in that, The capillary shape compensation formula is: ； in, θ For capillary forming angle, This is the capillary tube diameter compensation value.

4. The optimization method for an irregular capillary head model used in additive manufacturing according to claim 1, characterized in that, In the method for establishing the head flow resistance formula for capillary diameter and capillary surface roughness, a series of capillary tubes with diameters increasing by 0.1 mm in the range of 0.4~1 mm are first designed. The heads with the same capillary diameter are chemically polished for 0.5 min, 1 min, 2 min and 3 min, and the head flow resistance formula for capillary diameter and capillary surface roughness is initially obtained. A series of capillaries with diameters increasing by 0.1 mm in the range of 0.4 to 1 mm were designed. The heads of the capillaries with the same diameter were chemically polished for 1 mm, 1.5 min, 2.5 min, 2 min, and 3 min. The head flow resistance formulas for the capillary diameter and capillary surface roughness were modified to obtain the head flow resistance formulas for the capillary diameter and capillary surface roughness.

5. The optimization method for an irregular capillary head model used in additive manufacturing according to claim 4, characterized in that, The formula for head flow resistance regarding capillary diameter and capillary surface roughness is as follows: In the formula, P For pressure drop, d The diameter of the capillary tube. R This refers to the surface roughness of the capillary.

6. The optimization method for an irregular capillary head model used in additive manufacturing according to claim 4, characterized in that, The chemical polishing method involves using an electric pump to uniformly flow the polishing solution into the capillary at a pressure of 0.7 MPa and a speed of 50-60 mm / s. The chemical polishing solution is a mixed solution containing hydrochloric acid, nitric acid and hydrofluoric acid, with a volume ratio of 4:3:

1. The amount of material removed during polishing at different polishing times is ≤0.05mm.

7. The optimization method for an irregular capillary head model used in additive manufacturing according to claim 1, characterized in that, The number of capillaries, determined by the desired flow resistance at the head, is 30 to 100. The capillaries are distributed in multiple concentric rings. Each capillary includes a vertical section and an inclined section. The inclined sections of capillaries distributed in the same concentric ring have the same forming angle. The inclined sections of capillaries distributed in different concentric rings have an increasing forming angle from the outside to the inside. The length of capillaries distributed in different concentric rings decreases from the outside to the inside. The diameter of the inclined section of the capillary is optimized based on the capillary shape compensation formula.

8. The optimization method for an irregular capillary head model used in additive manufacturing according to claim 7, characterized in that, There are a total of 39 capillaries, which are concentrated inside the insulation frame; Capillaries are classified into four categories: A, B, C, and D. All four categories of irregularly shaped capillaries are distributed in a ring shape. Category A capillaries are distributed in the outermost ring, totaling 18, with a total length of 160 mm and a capillary forming angle of 20° at the inclined point. Category B, C, and D capillaries are distributed towards the center in sequence. Category B capillaries consist of 12, with a total length of 150 mm and a capillary forming angle of 23° at the inclined point; Category C capillaries consist of 6, with a total length of 140 mm and a capillary forming angle of 26° at the inclined point; and Category D capillaries consist of 3, with a total length of 120 mm and a capillary forming angle of 28° at the inclined point.

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