A prediction method

Abstract

The present application relates to the field of space optical technology. The present application provides a prediction method for calculating the tensile stiffness of a flexible tangential rod with side support for a large-aperture reflector, including: dividing the flexible tangential rod into multiple regions according to its structure; calculating the tensile deformation amounts of the respective regions of the flexible tangential rod according to the structures of the respective regions of the flexible tangential rod; calculating the total tensile deformation amount of the flexible tangential rod based on the tensile deformation amounts of the respective regions of the flexible tangential rod; calculating the tensile stiffness of the flexible tangential rod based on the total tensile deformation amount and the tensile force received by the flexible tangential rod. By specifically adopting different deformation calculation formulas for different structures, the present application can accurately obtain the tensile stiffness of the flexible tangential rod.

Description

Technical Field

[0001] The present application relates to the field of space optical technology. Specifically, it relates to a prediction method for calculating the tensile stiffness of flexible tangential rods for lateral support of large-aperture mirrors. Background Art

[0002] As the aperture of ground-based optoelectronic telescopes continues to increase, the weight of the mirror and its support system also becomes larger and larger. To ensure that the mirror still has good surface accuracy and pose accuracy under the action of gravity, it is necessary to reasonably design the mirror support system. Generally, the mirror support system consists of two parts: axial support and lateral support. When the telescope's pitch angle changes, the axial support and the lateral support jointly bear the weight of the mirror. When the telescope's optical axis points horizontally, the lateral support bears the entire weight of the mirror, which plays a decisive role in the surface accuracy and pose accuracy of the mirror. Therefore, the lateral support is an important part of the mirror support system. Traditional lateral support methods generally include steel belt support, mercury bag support, radial cosine push-pull support, vertical push-pull support, etc.

[0003] Therefore, in order to ensure the stable support and rotation of large-aperture mirrors, it is very important to calculate the tensile stiffness of the lateral support rods according to the predicted tensile force. Existing calculation methods often cannot calculate the tensile stiffness in combination with the specific structure of the lateral support rods, resulting in relatively large calculation errors for the tensile stiffness. Therefore, it is necessary to propose a new calculation method for the tensile stiffness of the lateral support rods of large-aperture mirrors to reduce the calculation error of the tensile stiffness of the lateral support rods. Summary of the Invention

[0004] The present application proposes a calculation method for the tensile stiffness of flexible tangential rods for lateral support of large-aperture mirrors, including:

[0005] Dividing the flexible tangential rod into multiple regions according to its structure;

[0006] Calculating the tensile deformation of each region of the flexible tangential rod according to the structure of each region of the flexible tangential rod;

[0007] Calculating the total tensile deformation ΔL of the flexible tangential rod based on the tensile deformation of each region of the flexible tangential rod;

[0008] Calculating the tensile stiffness k of the flexible tangential rod based on the total tensile deformation ΔL and the tensile force F applied to the flexible tangential rod. The tensile stiffness k of the flexible tangential rod satisfies the following relationship:

[0009]

[0010] In some embodiments, dividing the flexible tangential rod into multiple regions according to its structure includes:

[0011] The flexible tangential rod successively includes a first structure, a second structure, a third structure, a fourth structure, and a fifth structure along the x direction;

[0012] Among them, the first structure is divided into a first region and a second region, the second structure is divided into a third region and a fourth region, the third structure is divided into a fifth region and a sixth region, the fourth structure is divided into a seventh region, and the fifth structure is divided into an eighth region and a ninth region.

[0013] In some embodiments, the tensile deformation amount ΔL1 of the first region satisfies the following relationship:

[0014]

[0015] Among them, E is the elastic modulus of the material of the flexible tangential rod, L1 is the thickness of the first region along the x direction, a1 is the thickness of the first region along the y direction, and c1 is half of the thickness of the first region along the z direction;

[0016] The tensile deformation amount ΔL2 of the second region satisfies the following relationship:

[0017]

[0018] Among them, μ is the Poisson's ratio, and a2 is the thickness of the second region along the z direction.

[0019] In some embodiments, the tensile deformation amount ΔL3 of the third region satisfies the following relationship:

[0020]

[0021] Among them, L3 is the thickness of the third region along the x direction, a3 is the thickness of the third region along the z direction, and h3 is the thickness of the third region along the y direction.

[0022] In some embodiments, the tensile deformation amount ΔL4 of the fourth region satisfies the following relationship:

[0023]

[0024] Among them, a4 is the thickness of the fourth region along the z direction and the y direction, h4 is the width of the connection part between the fourth region and the third region along the y direction, and L4 is the thickness of the fourth region along the x direction.

[0025] In some embodiments, the tensile deformation amount ΔL5 of the fifth region satisfies the following relationship:

[0026]

[0027] Among them, a5 is the thickness of the fifth region along the y direction, h5 is the width of the fifth region along the z direction, and L5 is the thickness of the fifth region along the x direction.

[0028] In some embodiments, the tensile deformation amount ΔL6 of the sixth region satisfies the following relationship:

[0029]

[0030] Wherein, a6 is the thickness of the sixth region along the y direction and the z direction, and r is the radius of the seventh region.

[0031] In some embodiments, the tensile deformation amount ΔL7 of the seventh region satisfies the following relationship:

[0032]

[0033] Wherein, L7 is the thickness of the seventh region along the x direction.

[0034] In some embodiments, the tensile deformation amount ΔL8 of the eighth region satisfies the following relationship:

[0035]

[0036] The tensile deformation ΔL9 of the ninth region satisfies the following relationship:

[0037]

[0038] Wherein, L9 is the thickness of the ninth region along the x direction, and d9 is the side length of the ninth region.

[0039] In some embodiments, the total tensile deformation ΔL of the flexible tangential rod satisfies the following relationship:

[0040] ΔL=ΔL1+ΔL2+ΔL3+ΔL4+ΔL5+ΔL6+ΔL7+ΔL8+ΔL9.

[0041] Compared with the related art, the above solution of the embodiment of the present application has at least the following beneficial effects:

[0042] The present invention proposes a method for calculating the tensile stiffness of the flexible tangential rod of the side support of a large-aperture reflector. By splitting the specific structures of different parts, the split structures are divided into multiple calculation areas, and different deformation calculation methods are used in a targeted manner, and finally the tensile deformation and tensile stiffness of the flexible tangential rod are obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the present application, and together with the specification, are used to explain the principles of the present application. Obviously, the drawings described below are only some embodiments of the present application, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0044] Figure 1 Structural diagram of the flexible tangential rod assembly for the side support of a large-aperture mirror provided in some embodiments of the present application;

[0045] Figure 2 Flowchart of the calculation method for the tensile stiffness of the flexible tangential rod for the side support of a large-aperture mirror provided in some embodiments of the present application.

[0046] Figure 3 Simplified structural diagram of the flexible tangential rod provided in some embodiments of the present application;

[0047] Figure 4 For Figure 3 Cross-sectional view;

[0048] Figure 5 Structural diagram of the first region of the flexible tangential rod provided in some embodiments of the present application;

[0049] Figure 6 Structural diagram of the second region of the flexible tangential rod provided in some embodiments of the present application;

[0050] Figure 7 Structural diagram of the third region of the flexible tangential rod provided in some embodiments of the present application;

[0051] Figure 8 Structural diagram of the fourth region of the flexible tangential rod provided in some embodiments of the present application;

[0052] Figure 9 Simplified structural diagram of the fourth region of the flexible tangential rod provided in some embodiments of the present application;

[0053] Figure 10 Simulation diagram of the fourth region of the flexible tangential rod provided in some embodiments of the present application;

[0054] Figure 11 Structural diagram of the fifth region of the flexible tangential rod provided in some embodiments of the present application;

[0055] Figure 12 Structural diagram of the sixth region of the flexible tangential rod provided in some embodiments of the present application;

[0056] Figure 13 Structural diagram of the seventh region of the flexible tangential rod provided in some embodiments of the present application;

[0057] Figure 14 Structural diagram of the eighth region of the flexible tangential rod provided in some embodiments of the present application;

[0058] Figure 15 Structural diagram of the ninth region of the flexible tangential rod provided in some embodiments of the present application.

[0059] Reference Signs:

[0060] Adhesive pad 1, flexible tangential rod 2, support base 3, first structure 201, second structure 202, third structure 203, fourth structure 204, fifth structure 205, first region 21, second region 22, third region 23, fourth region 24, fifth region 25, sixth region 26, seventh region 27, eighth region 28, ninth region 29. Detailed Implementation Manner

[0061] In order to make the objectives, technical solutions, and advantages of this application clearer, the following will further describe this application in detail with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, rather than all the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of this application.

[0062] The terms used in the embodiments of this application are only for the purpose of describing specific embodiments, and are not intended to limit this application. The singular forms "a", "the", and "said" used in the embodiments of this application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise. "Plural" generally includes at least two.

[0063] It should be understood that the term "and / or" used herein is only a description of the associated relationship of the associated objects, indicating that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " herein generally represents an "or" relationship between the associated objects before and after.

[0064] It should be understood that although the terms first, second, third, etc. may be used in the embodiments of this application to describe, these should not be limited to these terms. These terms are only used to distinguish. For example, without departing from the scope of the embodiments of this application, the first may also be referred to as the second, and similarly, the second may also be referred to as the first.

[0065] It should also be noted that the term "comprising", "including" or any other variant thereof is intended to cover a non-exclusive inclusion, so that a commodity or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or further includes elements inherent to such a commodity or device. Without more limitations, the element defined by the statement "including one" does not exclude the existence of another identical element in the commodity or device including the said element.

[0066] A prediction algorithm proposed by the present invention is used for calculating the tensile stiffness of the flexible tangential rods for the side support of a large-aperture mirror, and mainly relates to a flexible tangential rod assembly for the side support of a large-aperture mirror. As Figure 1 shown, the flexible tangential rod assembly for the side support of a large-aperture mirror mainly includes an adhesive pad 1, a flexible tangential rod 2, and a support base 3. The adhesive pad 1 is fixedly connected to the mirror, the support base 3 is fixedly connected to the mirror chamber, and both ends of the flexible tangential rod 2 are respectively connected to the adhesive pad 1 and the support base 3 to realize the side support of the mirror on the mirror chamber.

[0067] Among them, the flexible tangential rod 2 has good support stiffness, and at the same time can realize the thermal decoupling and static friction release between the adhesive pad 1 and the support base 3. Therefore, the flexible tangential rod 2 is suitable for application in the support system of a large-aperture telescope. Generally, 3 sets or 6 sets of flexible tangential rods 2 are adopted, and the tensile stiffness of the flexible tangential rod 2 plays a decisive role in the support stiffness of the side support. The flexible tangential rod 2 is usually a variable cross-section rod. When calculating its tensile stiffness, the rod is divided into several segments according to different cross-sections, and the deformation amount of each segment is calculated respectively by using the tensile deformation formula, and then merged into the total deformation amount to calculate the total stiffness.

[0068] As Figure 2 shown, some embodiments of the present application provide a method for calculating the tensile stiffness of the flexible tangential rods for the side support of a large-aperture mirror, including the following method steps:

[0069] Step S10: Divide the flexible tangential rod into multiple regions according to its structure;

[0070] Step S20: Calculate the tensile deformation amount of each region of the flexible tangential rod according to the structure of each region of the flexible tangential rod;

[0071] Step S30: Calculate the total tensile deformation amount ΔL of the flexible tangential rod based on the tensile deformation amounts of each region of the flexible tangential rod;

[0072] Step S40: Calculate the tensile stiffness k of the flexible tangential rod based on the total tensile deformation amount ΔL and the tensile force F received by the flexible tangential rod. The tensile stiffness k of the flexible tangential rod satisfies the following relationship:

[0073]

[0074] As a specific implementation manner of the flexible tangential rod, as Figure 1 shown, but the present application is not limited to the flexible tangential rod with this structure. For flexible tangential rods with any structure, the above-described implementation steps can accurately calculate the tensile stiffness of the flexible tangential rod.

[0075] To more clearly describe the behavior of the flexible tangential rod, the following direction definitions are made: The flexible tangential rod can be calibrated by traveling along three mutually perpendicular axes defined as follows: the transverse axis y, the front-back axis x, and the vertical axis z. The direction opposite to the arrow along the front-back axis x is marked as "forward", and the direction along the arrow of the front-back axis x is marked as "backward". The direction of the arrow of the transverse axis y is marked as "right side", and the direction opposite to the arrow along the transverse axis y is "left side". The direction of the arrow of the vertical axis z is "upper side", and the direction opposite to the arrow along the vertical axis z is "lower side".

[0076] As an implementation, the flexible tangential rod 2 has a symmetric structure. Select half of it (as Figure 1 shown by the dashed box) for analysis and calculation. The flexible tangential rod 2 sequentially includes a first structure 201, a second structure 202, a third structure 203, a fourth structure 204, and a fifth structure 205 along the x direction.

[0077] For the convenience of calculation, the simplified structure of the flexible tangential rod 2 of the present application is as Figure 3 shown. Figure 4 is Figure 3 a cross-sectional view. The flexible tangential rod 2 is symmetric about the symmetry line. The side of the symmetry line is divided into 9 regions according to the different cross-sectional shapes in the x direction of the front-back axis. Among them, the first structure 201 is divided into a first region 21 and a second region 22, the second structure 202 is divided into a third region 23 and a fourth region 24, the third structure 203 is divided into a fifth region 25 and a sixth region 26, the fourth structure 204 is divided into a seventh region 27, the fifth structure 205 is divided into an eighth region 28 and a ninth region 29. The entire eighth region 28 is solid, and the central circle of the ninth region 29 is hollow. The circle on the eighth region 28 represents the boundary with the central circle of the ninth region 29. Tensile forces F are applied to both ends of the flexible tangential rod 2, and the tensile force F is along the axial direction of the flexible tangential rod 2. By calculating the tensile length and tensile strength for each region respectively, the total tensile length and tensile strength of the flexible tangential rod 2 can be synthesized.

[0078] In some embodiments, as Figure 5 shown, the cross-section of the first region 21 gradually changes, and the dimensions are as Figure 5 shown. Using the tensile deformation calculation method and integrating and summing, the tensile deformation amount ΔL1 of the first region 21 is obtained. The tensile deformation amount ΔL1 of the first region 21 satisfies the following relationship:

[0079]

[0080] Among them, E is the elastic modulus of the flexible tangential rod material, L1 is the thickness of the first region 21 in the x direction, which is also the radius of the central semi-circle, a1 is the thickness of the first region 21 in the y direction, c1 is half of the thickness of the first region 21 in the z direction, and b1 is the thickness of the end face of the first region 21 in the z direction.

[0081] The dimensions of the second region 22 are as Figure 6 shown. a2 is the thickness of the second region 22 in the z direction, L2 is the thickness of the second region 22 in the x direction, and h2 is the thickness of the connection part between the second region 22 and the third region 23 in the y direction. Since the cross-sectional change between the second region 22 and the third region 23 is relatively large, shear deformation is used to calculate the tensile length. Among them, the shear stress τ is in the x direction, and its magnitude is:

[0082]

[0083] The shear modulus G is:

[0084]

[0085] Among them, μ is the Poisson's ratio. Due to the following relationship:

[0086] τ = G×γ

[0087] Then the shear strain γ is obtained:

[0088]

[0089] The tensile deformation amount ΔL2 of the second region 22 satisfies the following relationship:

[0090]

[0091] In some embodiments, as Figure 7 shown, in the third region 23, a3 is the thickness of the third region 23 in the z direction, L3 is the thickness of the third region 23 in the x direction, and h3 is the thickness of the third region 23 in the y direction. The tensile deformation amount ΔL3 of the third region 23 satisfies the following relationship:

[0092]

[0093] In some embodiments, as Figure 8 shown, a4 is the thickness of the fourth region 24 in the z direction and y direction, h4 is the width of the connection part between the fourth region 24 and the third region 23 in the y direction, and L4 is the thickness of the fourth region 24 in the x direction. The deformation of the fourth region 24 is simplified to shear deformation and bending deformation at both ends. The shear deformation amount at one end satisfies the following relationship:

[0094]

[0095] Calculate the average value of the tensile amount caused by the bending deformation at one end. Equivalent the tensile force to the uniformly distributed load q on the cantilever beam. Due to the structural symmetry, take the model on one side for analysis, as Figure 9 shown. Simplify the force on the model to a uniformly distributed load q applied on a cantilever beam with a length of l, as Figure 10 shown. The deflection curve equation of the cantilever beam under the uniformly distributed load q is:

[0096]

[0097] l = (a4 - h4) / 2

[0098] q = F / a4

[0099] where x takes values between 0 and l, and the moment of inertia I is:

[0100]

[0101] Use integration to obtain the average elongation caused by the bending deformation:

[0102]

[0103] Since there is deformation at both ends, the deformation amount ΔL4 of the fourth region 24 is:

[0104] ΔL4 = 2(ΔL 41 + ΔL 42 )

[0105] Therefore, the tensile deformation amount ΔL4 of the fourth region 24 satisfies the following relationship:

[0106]

[0107] In some embodiments, as Figure 11 shown, where a5 is the thickness of the fifth region along the y direction, h5 is the width of the fifth region along the z direction, and L5 is the thickness of the fifth region along the x direction.

[0108] The tensile deformation amount ΔL5 of the fifth region 25 satisfies the following relationship:

[0109]

[0110] In some embodiments, as Figure 12 shown, its deformation is simplified to the shear deformation at both ends, where a6 is the thickness of the sixth region 26 along the y direction and the z direction, r is the radius of the seventh region 27, h6 is the width of the sixth region 26 along the z direction, and L6 is the thickness of the sixth region 26 along the x direction. The shear deformation amount on the left side of the sixth region 26 is:

[0111]

[0112] On the right side of the sixth region 26, the shear deformation principle is also used for calculation, and the shear stress τ is:

[0113]

[0114] The shear modulus G is:

[0115]

[0116] where μ is the Poisson's ratio. Due to the following relationship:

[0117] τ = G×γ

[0118] Then the shear strain γ is obtained:

[0119]

[0120] Then the shear deformation amount ΔL of the right side of the sixth region 26 62 is:

[0121]

[0122] Then the deformation amount ΔL6 of the sixth region 26 is:

[0123] ΔL6 = ΔL 61 +ΔL 62

[0124] Therefore, the tensile deformation amount ΔL6 of the sixth region 26 satisfies the following relationship:

[0125]

[0126] In some embodiments, as Figure 13 shown, where L7 is the thickness of the seventh region in the x direction. The tensile deformation amount ΔL7 of the seventh region 27 satisfies the following relationship:

[0127]

[0128] In some embodiments, as Figure 14 shown, L8 is the thickness of the eighth region in the x direction. Using the shear deformation calculation method, the shear stress τ in the x direction is:

[0129]

[0130] The shear modulus G is:

[0131]

[0132] where μ is the Poisson's ratio. Due to the following relationship:

[0133] τ = G×γ

[0134] Then the shear strain γ is obtained as follows:

[0135]

[0136] The tensile deformation amount ΔL8 of the eighth region 28 satisfies the following relationship:

[0137]

[0138] As Figure 15 shown, the tensile deformation amount ΔL9 of the ninth region 29 satisfies the following relationship:

[0139]

[0140] where L9 is the thickness of the ninth region in the x - direction, and d9 is the side length of the ninth region.

[0141] In some embodiments, the total tensile deformation amount ΔL of the flexible tangential rod satisfies the following relationship:

[0142]

[0143] where

[0144]

[0145]

[0146] When a1 = a2 = a3 = a4 = a5 = a6 = a, and h3 = h4 = h5 = h, the tensile stiffness of the flexible tangential rod is simplified to:

[0147]

[0148] The present invention proposes a calculation method for the tensile stiffness of a flexible tangential rod for side - supporting a large - aperture mirror. For the part with gradually changing cross - section, the tensile deformation formula is adopted, and the total deformation is solved by integration. For the part with a relatively large change in cross - section, the shear deformation formula is used instead of the tensile deformation formula. For some special parts, the average deformation amount is calculated by combining the bending deformation formula and the shear deformation formula. By adopting different deformation calculation formulas for different parts, the tensile deformation amount and tensile stiffness of the flexible tangential rod are obtained.

[0149] Finally, it should be noted that: the various embodiments in this specification are described by way of example. Each embodiment focuses on the differences from other embodiments. The same or similar parts among the various embodiments can be referred to each other. For the systems or devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0150] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit it; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A prediction method for calculating the tensile stiffness of the flexible tangential rods of the side supports of large-diameter reflectors, characterized in that ,include: Dividing the flexible tangential rod into a plurality of regions according to its structure; Calculating the tensile deformation of each region of the flexible tangential rod according to the structure of each region of the flexible tangential rod; Calculating a total tensile deformation ΔL of the flexible tangential rod based on the tensile deformation of each region of the flexible tangential rod; The tensile stiffness k of the flexible tangential rod is calculated based on the total tensile deformation ΔL and the tensile force F applied to the flexible tangential rod. The tensile stiffness k of the flexible tangential rod satisfies the following relationship: The flexible tangential rod is divided into a plurality of regions according to its structure, including: The flexible tangential rod includes a first structure, a second structure, a third structure, a fourth structure and a fifth structure in sequence along the x direction; The first structure is divided into a first area and a second area, the second structure is divided into a third area and a fourth area, the third structure is divided into a fifth area and a sixth area, the fourth structure is divided into a seventh area, and the fifth structure is divided into an eighth area and a ninth area; The tensile deformation ΔL1 of the first region satisfies the following relationship: Wherein, E is the elastic modulus of the material of the flexible tangential rod, L1 is the thickness of the first region along the x direction, a1 is the thickness of the first region along the y direction, and c1 is half of the thickness of the first region along the z direction; The tensile deformation ΔL2 of the second region satisfies the following relationship: Wherein, μ is Poisson's ratio, a2 is the thickness of the second region along the z direction; The tensile deformation amount ΔL4 of the fourth region satisfies the following relationship: Wherein, a4 is the thickness of the fourth region along the z direction and the y direction, h4 is the width of the connecting portion between the fourth region and the third region along the y direction, and L4 is the thickness of the fourth region along the x direction.

2. The prediction method according to claim 1, characterized in that , The tensile deformation ΔL3 of the third region satisfies the following relationship: Wherein, L3 is the thickness of the third region along the x direction, a3 is the thickness of the third region along the z direction, and h3 is the thickness of the third region along the y direction.

3. The prediction method according to claim 1, characterized in that , The tensile deformation ΔL5 of the fifth region satisfies the following relationship: Wherein, a5 is the thickness of the fifth region along the y direction, h5 is the width of the fifth region along the z direction, and L5 is the thickness of the fifth region along the x direction.

4. The prediction method according to claim 1, characterized in that , The tensile deformation ΔL6 of the sixth region satisfies the following relationship: Wherein, a6 is the thickness of the sixth region along the y direction and the z direction, and r is the radius of the seventh region.

5. The prediction method according to claim 1, characterized in that , The tensile deformation ΔL7 of the seventh region satisfies the following relationship: Wherein, L7 is the thickness of the seventh region along the x direction.

6. The prediction method according to claim 1, characterized in that , The tensile deformation ΔL8 of the eighth region satisfies the following relationship: The tensile deformation ΔL9 of the ninth region satisfies the following relationship: Wherein, L9 is the thickness of the ninth region along the x direction, and d9 is the side length of the ninth region.

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