A method for optimizing the surface structure of a wind tunnel vane to reduce noise and a vane

Abstract

The application belongs to the technical field of aerospace engineering, and particularly discloses a wind tunnel guide vane surface structure optimization noise reduction method and a guide vane, which comprises the following steps: a plurality of inner recesses are formed in the guide vane, and a protruding part is formed between adjacent inner recesses; the inner wall included angle of the inner recess is designed to determine the size of the cross section of the inner recess; the protruding part and the inner recess are respectively extended along the flow direction of the airflow on the circular arc windward surface, and the cross sections of the protruding part and the inner recess are respectively equal along the extending direction, and a protruding belt and an inner recess belt are formed; the method has the following advantages: the inner recess with the groove structure formed in the guide vane can effectively reduce the resistance generated when the airflow impacts the guide vane, effectively reduce the noise generated by the airflow, and improve the overall performance of the aeroacoustic wind tunnel; the simple inner recess with the groove structure is repeatedly generated on the surface of the guide vane, and the single size is fixed, part of the material is cut off, the mass of the single guide vane is light, the single guide vane is easy to mill, and the processing is convenient.

Description

Technical Field

[0001] This invention relates to the field of aerospace engineering technology, and more specifically, to a method for optimizing the surface structure of a wind tunnel guide vane and a wind tunnel guide vane for noise reduction. Background Technology

[0002] Wind tunnels are the primary experimental equipment for aerodynamic research. They provide various test data under simulated relative motion between aircraft and air, serving as the basis for engineers' design and development. They are an indispensable and crucial infrastructure in my country's aerospace industry. With the development of aircraft themselves and the increasing demands for energy conservation and environmental protection, military and civilian aircraft are facing increasingly stringent restrictions and requirements regarding aerodynamic noise. For example, the International Civil Aviation Organization (ICAO) has established increasingly stringent noise control standards; aircraft and helicopters must meet these standards before they can be sold, and aircraft already in operation that do not meet the standards are grounded. Acoustic wind tunnels, as experimental platforms for aerodynamic noise research, are an essential foundational experimental equipment.

[0003] In a recirculating wind tunnel, such as Figure 4 Airflow needs to pass through multiple corners, and the guide vanes at the corners can reduce drag losses at the corner sections and improve the airflow characteristics at the corner exits. In single-return wind tunnels with conventional guide vanes installed, the losses caused by the guide vanes at the corners typically account for 10-20% of the total wind tunnel losses, and in some cases can be as high as 40%. In addition to generating losses, the guide vanes also produce noise, which affects the accuracy of the test.

[0004] To address these issues, a method for optimizing the surface structure of wind tunnel guide vanes and a corresponding noise reduction method are proposed. Summary of the Invention

[0005] The present invention aims to provide a method for optimizing the surface structure of a wind tunnel guide vane and a wind tunnel guide vane for noise reduction, so as to solve or improve at least one of the above-mentioned technical problems.

[0006] In view of this, the first aspect of the present invention is to provide a method for noise reduction by optimizing the surface structure of wind tunnel guide vanes.

[0007] A second aspect of the present invention is to provide a flow guide plate.

[0008] The first aspect of the present invention provides a method for noise reduction by optimizing the surface structure of a wind tunnel guide vane, comprising the following steps: considering the separation and vortex formation when airflow impacts the surface of the guide vane, multiple concave portions are formed on the arc-shaped windward surface of the guide vane, and protrusions are formed between adjacent concave portions, so that when the airflow generates flow vortices in the concave portions, small flow vortices capable of suppressing flow direction are simultaneously formed at the top of the protrusions; considering the bottom width of the concave portions, the size of the guide vane and the distance between the center points of adjacent concave portions are designed, and the included angle of the inner wall of the concave portions is designed to determine the cross-sectional size of the concave portions; the protrusions and concave portions are extended along the flow direction of the airflow on the arc-shaped windward surface, and the cross-sections of the protrusions and concave portions are equal along the extension direction, forming protrusion bands and concave bands, so that the airflow continuously generates small flow vortices while flowing on the guide vane, thereby reducing the airflow resistance and noise during flow.

[0009] This invention provides a method for optimizing the surface structure of a wind tunnel guide vane to reduce noise. When airflow passes through the surface of the guide vane with a concave portion, a bottom-level flow vortex is generated at the bottom of the concave portion. Under its influence, a small flow vortex is induced near the tip of the protrusion. This small flow vortex weakens the bottom-level flow vortex associated with the bottom of the concave portion and retains low-speed fluid in the bottom of the concave portion, limiting the spanwise motion of the bottom-level flow vortex perpendicular to the extension direction of the concave zone. This allows the airflow to move orderly along the extension direction of the concave portion, reducing the friction between the airflow and the wall, weakening the turbulence of the boundary layer between the airflow and the guide vane surface, reducing the exchange of kinetic energy and energy, reducing the amplitude of the airflow, reducing the shear stress of the boundary layer, and reducing drag and noise.

[0010] By creating a grooved recess in the guide vane, the resistance generated when the airflow impacts the guide vane can be effectively reduced, and the noise generated by the airflow can be effectively reduced, which improves the overall performance of the aeroacoustic wind tunnel.

[0011] The simple concave part of the groove structure is repeatedly generated on the surface of the guide plate with a fixed size. By removing part of the material, the individual guide plate can be made lightweight, easy to mill, and convenient to process.

[0012] In addition, the technical solutions provided by embodiments of the present invention may also have the following additional technical features:

[0013] In any of the above technical solutions, the guide plate is an arc plate, and the arc-shaped windward surface is the concave surface of the guide plate; a windward end and an air-supplying end are determined perpendicular to the direction of extension along the flow direction of the airflow on the guide plate, and the head of the air-supplying end is sharper than the head of the windward end; the tails of the windward end and the air-supplying end are tangent to the concave surface and the outer concave surface of the guide plate, respectively; wherein, the arc plate is a quarter-circle arc structure.

[0014] In this technical solution, the guide vane is set as an arc plate so that it can be set at the corner of the recirculation wind tunnel to guide the airflow. An air supply end and a windward end are respectively set at the head and the end of the guide vane along the flow direction of the airflow. The head of the air supply end is set as sharp, and the head of the windward end is set as a rounded head that is blunter than the head of the air supply end.

[0015] The tails of the air outlet and the air supply outlet are tangent to the inner and outer concave surfaces of the guide vane, respectively, which makes the surface of the guide vane smoother, reduces sharp edges, and helps the airflow flow on the surface of the guide vane.

[0016] In any of the above technical solutions, the step of designing the bottom width of the concave portion and the bottom width of the protruding portion along the radial direction of the guide plate, taking into account the length, width, and height of the guide plate, specifically includes: obtaining the thickness h and length L of the guide plate, the bottom width Lb of the concave portion, the distance Lv between the center points of adjacent concave portions, and the width Ld between the concave portion and the two sides of the guide plate; and respectively designing the correlation between the thickness h of the guide plate, the length L of the guide plate, the bottom width Lb of the concave portion, the width Ld between the concave portion and the two sides of the guide plate, and the distance Lv between the center points of adjacent concave portions.

[0017] In this technical solution, the thickness and length of the guide plate are obtained in advance, and the correlation between the distance between the center points of the adjacent concave portions and the distance between the center points of the concave portions and the distance between the center points of the adjacent concave portions is set. The distance between the center points of the adjacent concave portions and the width of the concave portions and the sides of the guide plate, as well as the bottom width of the concave portions, are then set to obtain the width of the sides of the guide plate and the bottom width of the concave portions. Finally, the size and arrangement spacing of the concave portions on the surface of the guide plate are obtained.

[0018] In any of the above technical solutions, the relevance includes:

[0019] L / Lv=100~200, Lb / Lv=0~0.5, Ld / Lv=0.5~2, h / Lv>3.

[0020] In this technical solution, the correlation between known and unknown quantities is determined by specific numerical ratios, and the solution for the determined dimensions is obtained to ensure that the final value is within a reasonable range.

[0021] In any of the above technical solutions, the included angle between the two side walls of the concave portion is α, and the design range is: α = 60° to 75°.

[0022] In this technical solution, the acceptable range of unknown quantities is determined by specific numerical ratios, and the size is solved to ensure that the final value is within a reasonable range. For α = 60° to 75°, the parameter h ≈ Lv has the best drag reduction and noise reduction effect.

[0023] In any of the above technical solutions, the inner and outer concave surfaces of the guide vane are both arc surfaces, and the radius of the inner concave surface is R1 and the radius of the outer concave surface is R2, then the following correlation is satisfied: The centers of the arcs of the inner and outer concave surfaces are located at the same point.

[0024] In this technical solution, in different recirculation wind tunnels, the guide vanes need to have different sizes of concave inner surface radius and concave outer surface radius. By defining the ratio of the two radii and the correlation between the concave inner surface radius and thickness and the concave outer surface radius, the thickness of the guide vane is determined, and the spacing of the concave portions is further determined, so that the concave portions of the guide vanes used in the wind tunnel can be set according to the size of the wind tunnel, thereby increasing the range of wind tunnel sizes that this method can be used in.

[0025] In any of the above technical solutions, the top of the protrusion is set as a apex angle, and the apex angle is located within the arc-shaped windward surface of the guide vane, so as to determine the depth of the concave portion along the radial direction of the guide vane.

[0026] In this technical solution, the apex angle of the protrusion formed between adjacent concave portions is limited to within the arc surface of the concave portion, so that the airflow will not generate convection when flowing between adjacent concave portions, thus ensuring the stable flow of low-speed fluid.

[0027] A second aspect of the present invention provides a flow guide plate, comprising a plate body having an arc-shaped structure and a circular arc windward surface; a concave portion disposed on the circular arc windward surface of the plate body, and the circular arc windward surface extending in the circumferential direction; a protrusion formed between adjacent concave portions; wherein the included angle α between the two side walls of the concave portion is in the range of: α = 60° to 75°, and the correlation between the thickness h of the flow guide plate, the length L of the flow guide plate, the bottom width Lb of the concave portion, the width Ld of the concave portion and the two sides of the flow guide plate and the distance Lv between the center points of the adjacent concave portions is included, and the correlation includes: Lv / L = 100 to 200, Lb / Lv = 0 to 0.5, Ld / Lv = 0.5 to 2, and h / Lv > 3.

[0028] The present invention provides a flow guide plate. When a concave portion is formed on a plate body with an inner surface, the extension direction of the concave portion is limited by taking into account the direction of airflow. This ensures that the flow guide plate can obtain the gain brought by the concave portion after contacting the airflow, that is, reduce the airflow resistance and noise.

[0029] Furthermore, since the guide vane is determined by the wind tunnel guide vane surface structure optimization and noise reduction method defined in the above embodiments, the guide vane proposed in this embodiment possesses all the beneficial effects of the wind tunnel guide vane surface structure optimization and noise reduction method defined in the above embodiments, which will not be elaborated further here.

[0030] The beneficial effects of this invention compared to the prior art are as follows:

[0031] By creating a grooved recess in the guide vane, the resistance generated when the airflow impacts the guide vane can be effectively reduced, and the noise generated by the airflow can be effectively reduced, which improves the overall performance of the aeroacoustic wind tunnel.

[0032] The simple concave part of the groove structure is repeatedly generated on the surface of the guide plate with a fixed size. By removing part of the material, the individual guide plate can be made lightweight, easy to mill, and convenient to process.

[0033] Additional aspects and advantages of embodiments of the invention will become apparent in the following description or may be learned by practice of embodiments of the invention. Attached Figure Description

[0034] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0035] Figure 1 This is a flowchart of the method of the present invention;

[0036] Figure 2 This is a schematic diagram of the aeroacoustic wind tunnel noise reduction guide plate of the present invention;

[0037] Figure 3 This is a dimensional diagram of the concave surface structure of the guide vane of the present invention;

[0038] Figure 4 This is a cross-sectional view and a schematic diagram of the dimensions of the aeroacoustic wind tunnel noise reduction guide plate of the present invention;

[0039] Figure 5 This is a schematic diagram of the guide vane and the installation wind tunnel of the present invention.

[0040] in, Figure 1-5 The correspondence between the reference numerals and component names in the attached drawings is as follows:

[0041] 1. Leading edge of the guide vane; 2. Groove structure; 3. Trailing edge of the guide vane. Detailed Implementation

[0042] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0043] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0044] Please see Figure 1-5 The following describes a method for optimizing the surface structure of a wind tunnel guide vane and a wind tunnel guide vane according to some embodiments of the present invention.

[0045] An embodiment of the first aspect of the present invention proposes a method for noise reduction through optimization of the surface structure of wind tunnel guide vanes. In some embodiments of the present invention, such as... Figure 1 As shown, a method for noise reduction by optimizing the surface structure of a wind tunnel guide vane is provided. This method includes the following steps:

[0046] Considering that the airflow separates and forms vortices when it impacts the surface of the guide vane, multiple concave sections are opened on the arc-shaped windward side of the guide vane, and protrusions are formed between adjacent concave sections. This allows the airflow to generate directional vortices in the concave sections, while simultaneously forming small directional vortices at the top of the protrusions that can suppress the flow direction.

[0047] The dimensions of the guide vane and the distance between the center points of adjacent concave parts are designed based on the bottom width of the concave part, and the included angle of the inner wall of the concave part is designed to determine the dimensions of the cross-section of the concave part.

[0048] The protrusion and concave portion extend along the flow direction of the airflow on the arc-shaped windward surface, and the cross-sections of the protrusion and concave portion are equal along the extension direction, forming a protruding band and a concave band, so that the airflow continuously generates small vortices in the direction of flow while flowing on the guide vane, and reduces the airflow resistance and noise during flow.

[0049] This invention provides a method for optimizing the surface structure of a wind tunnel guide vane to reduce noise. When airflow passes through the surface of the guide vane with a concave portion, a bottom-level flow vortex is generated at the bottom of the concave portion. Under its influence, a small flow vortex is induced near the tip of the protrusion. This small flow vortex weakens the bottom-level flow vortex associated with the bottom of the concave portion and retains low-speed fluid in the bottom of the concave portion, limiting the spanwise motion of the bottom-level flow vortex perpendicular to the extension direction of the concave zone. This allows the airflow to move orderly along the extension direction of the concave portion, reducing the friction between the airflow and the wall, weakening the turbulence of the boundary layer between the airflow and the guide vane surface, reducing the exchange of kinetic energy and energy, reducing the amplitude of the airflow, reducing the shear stress of the boundary layer, and reducing drag and noise.

[0050] By creating a grooved recess in the guide vane, the resistance generated when the airflow impacts the guide vane can be effectively reduced, and the noise generated by the airflow can be effectively reduced, which improves the overall performance of the aeroacoustic wind tunnel.

[0051] The simple concave part of the groove structure is repeatedly generated on the surface of the guide plate with a fixed size. By removing part of the material, the individual guide plate can be made lightweight, easy to mill, and convenient to process.

[0052] In some embodiments, the guide vane is an arc plate, and the arc-shaped windward surface is the concave surface of the guide vane; a windward end and an air-supplying end are defined perpendicular to the direction of extension along the flow direction of the airflow on the guide vane, and the head of the air-supplying end is sharper than the head of the windward end; the tails of the windward end and the air-supplying end are tangent to the concave surface and the concave surface of the guide vane, respectively; wherein, the arc plate is a quarter-circle arc structure.

[0053] In this embodiment, the guide vane is set as an arc plate so that it can be set at the corner of the recirculation wind tunnel to guide the airflow. An air supply end and a windward end are respectively set at the first end and the last end of the guide vane along the flow direction of the airflow. The head of the air supply end is set to be sharp, and the head of the windward end is set to be a rounded head that is blunter than the head of the air supply end, which is beneficial for rectification and reduces pressure loss.

[0054] The tails of the air outlet and the air supply outlet are tangent to the inner and outer concave surfaces of the guide vane, respectively, which makes the surface of the guide vane smoother, reduces sharp edges, and helps the airflow flow on the surface of the guide vane.

[0055] In some embodiments, the bottom width of the concave portion and the bottom width of the protruding portion are designed considering the length, width, and height of the guide vane. Specifically, this includes: obtaining the thickness h and length L of the guide vane, the bottom width Lb of the concave portion, the distance Lv between the center points of adjacent concave portions, and the width Ld between the concave portion and the sides of the guide vane; and designing the correlation between the thickness h of the guide vane, the length L of the guide vane, the bottom width Lb of the concave portion, the width Ld between the concave portion and the sides of the guide vane, and the distance Lv between the center points of adjacent concave portions.

[0056] In this embodiment, by pre-observing the thickness and length of the guide plate and setting the correlation between the distance between the center points of adjacent concave portions and the center points of adjacent concave portions, the required distance between the center points of adjacent concave portions on the guide plate is calculated. Furthermore, by setting the correlation between the distance between the center points of adjacent concave portions and the width of the concave portions and the sides of the guide plate, and the bottom width of the concave portions, the width of the sides of the guide plate and the bottom width of the concave portions are obtained, and finally the size and arrangement spacing of the concave portions on the surface of the guide plate are obtained.

[0057] In some embodiments, relevance includes:

[0058] L / Lv=100~200, Lb / Lv=0~0.5, Ld / Lv=0.5~2, h / Lv>3.

[0059] In this embodiment, the correlation between known and unknown quantities is determined by specific numerical ratios, and the solution for the determined size is obtained to ensure that the final value is within a reasonable range.

[0060] In some embodiments, the included angle between the two side walls of the concave portion is α, and the design range is: α = 60° to 75°.

[0061] In this embodiment, the acceptable range of unknown quantities is determined by specific numerical ratios, and the solution for the determined size is performed to ensure that the final value is within a reasonable range. According to the literature, α = 60° to 75° should make the parameter h ≈ Lv to achieve the best drag reduction and noise reduction effect.

[0062] In some embodiments, both the inner and outer concave surfaces of the guide vane are arc surfaces, and the radius of the inner concave surface is R1 and the radius of the outer concave surface is R2, then the following correlation is satisfied: The centers of the arcs of the inner and outer concave surfaces are located at the same point.

[0063] In this embodiment, in different recirculation wind tunnels, the guide vanes need to have different sizes of concave inner surface radius and concave outer surface radius. By defining the ratio of the two radii and the correlation between the concave inner surface radius and thickness and the concave outer surface radius, the thickness of the guide vane is determined, and the spacing of the concave portions is further determined, so that the concave portions of the guide vanes used in the wind tunnel can be set according to the size of the wind tunnel, thereby increasing the range of wind tunnel sizes that this method can be used in.

[0064] In some embodiments, the top of the protrusion is set as a apex, and the apex is located within the arcuate windward surface of the guide vane to determine the depth of the recess along the radial direction of the guide vane.

[0065] In this embodiment, the apex angle of the protrusion formed between adjacent concave portions is limited to within the arc surface of the concave portion, so that the airflow does not generate convection when flowing between adjacent concave portions, thus ensuring the stable flow of low-speed fluid.

[0066] A second aspect of the invention provides a flow guide plate. In some embodiments of the invention, such as... Figure 2-5 As shown, a flow guide is provided, which includes the following:

[0067] The sheet body has an arc-shaped structure and a rounded windward surface;

[0068] The concave portion is located on the arc-shaped windward surface of the sheet body, and extends in the circumferential direction of the arc-shaped windward surface;

[0069] A protrusion is formed between adjacent concave portions;

[0070] The included angle α between the two side walls of the concave portion is in the range of α = 60° to 75°. The correlation between the thickness h of the guide plate, the length L of the guide plate, the bottom width Lb of the concave portion, the width Ld of the concave portion and the two sides of the guide plate and the distance Lv between the center points of the adjacent concave portions is as follows: Lv / L = 100 to 200, Lb / Lv = 0 to 0.5, Ld / Lv = 0.5 to 2, and h / Lv > 3.

[0071] An embodiment of the second aspect of the present invention provides a flow guide plate in which, when a recess is formed on a plate having an inner surface, the direction of extension of the recess is limited by considering the direction of airflow, thereby ensuring that the flow guide plate can obtain the gain brought by the recess after contacting the airflow, that is, reducing the airflow resistance and noise.

[0072] Furthermore, since the guide vane is determined by the wind tunnel guide vane surface structure optimization and noise reduction method defined in the above embodiments, the guide vane proposed in this embodiment possesses all the beneficial effects of the wind tunnel guide vane surface structure optimization and noise reduction method defined in the above embodiments, which will not be elaborated further here.

[0073] Specifically, the concave zone formed by the extension of the concave part along the arc-shaped windward surface is the groove structure 2, and the protruding zone formed between adjacent groove structures 2 is the rib structure, the windward part is the leading edge 1 of the guide vane, and the air supply part is the trailing edge 3 of the guide vane.

[0074] The two outermost groove structures are 50mm apart from the end of the nearest side of the guide vane. The bottom width of the groove structure is 10mm, the spacing between the groove structures is 50mm, and the sharp angle of the groove structure is 60°.

[0075] The guide vane has a circular arc transition section consisting of concentric quarter-circles with radii of 2000mm and 2200mm, and a thickness of 200mm.

[0076] The guide vane requires 119 grooves, and the regular arrangement of the grooves can be machined by CNC or conventional milling machines.

[0077] Furthermore, the trench structure 2 is a V-shaped trench.

[0078] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this invention, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0079] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for optimizing the surface structure of a wind tunnel fence to reduce noise, characterized in that, It comprises the following steps: Considering the separation of the airflow hitting the surface of the guide vane to form a vortex, a plurality of concave portions are arranged on the circular arc windward surface of the guide vane, and a protruding portion is formed between adjacent concave portions, so that when the airflow generates a flow direction vortex in the concave portion, a flow direction small vortex capable of inhibiting the flow direction is formed on the top of the protruding portion; The size of the guide vane is considered to design the bottom width of the concave portion and the distance between the center points of adjacent concave portions, and the inner wall angle of the concave portion is designed to determine the size of the cross section of the concave portion; The protruding portion and the concave portion extend along the circumferential direction of the circular arc windward surface, and the cross section of the protruding portion is equal and the cross section of the concave portion is equal in the extending direction, and a protruding band and a concave band are formed, so that the airflow continuously generates a flow direction small vortex when flowing on the guide vane, and the resistance of the airflow and the noise during flowing are reduced; The guide vane is a circular arc plate, and the circular arc windward surface is the concave surface of the guide vane; The windward end and the air supply end perpendicular to the extending direction are determined along the flowing direction of the airflow on the guide vane, and the head of the air supply end is sharper than the head of the windward end; The tail of the windward end and the tail of the air supply end are tangent to the concave surface and the outer concave surface of the guide vane, respectively; The circular arc plate is a quarter circular arc structure; The length, width and height of the guide vane are considered to design the bottom width of the concave portion along the radial direction of the guide vane and the bottom width of the protruding portion, which specifically includes: The thickness h of the guide vane, the length L of the guide vane, the bottom width Lb of the concave portion, the width Ld of the concave portion and the guide vane on both sides, and the correlation of the distance Lv between the center points of adjacent concave portions are designed respectively; The correlation includes: Lv / L=100~200, Lb / Lv=0~0.5, Ld / Lv=0.5~2, h / Lv>3; The angle between the two side walls of the concave portion is α, and the designed range is: α=60°~75°; The top of the protruding portion is provided with a top angle, and the top angle is located in the circular arc windward surface of the guide vane to determine the depth of the concave portion along the radial direction of the guide vane; the top angle of the protruding portion formed between adjacent concave portions is limited in the circular arc surface of the concave portion, so that the airflow flowing in the adjacent concave portions does not produce convection, ensuring the stable flow of low-speed fluid.

2. The method according to claim 1, wherein, The inner concave surface and the outer concave surface of the guide vane are both circular arc surfaces, and the radius of the inner concave surface is , and the radius of the outer concave surface is , and the following correlation is satisfied: ； The centers of the concave surface and the outer concave surface are located at the same point.

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