Prediction algorithm

Abstract

The invention relates to the technical field of space optics, and provides a prediction algorithm, which is used for calculating the tensile rigidity of a large-aperture reflector side support flexible tangential rod, and comprises the following steps: dividing the flexible tangential rod into a plurality of areas according to the structure of the flexible tangential rod; respectively calculating the tensile deformation of each area of the flexible tangential rod according to the structure of each area of the flexible tangential rod; calculating the total tensile deformation of the flexible tangential rod based on the tensile deformation of each area of the flexible tangential rod; and calculating the tensile rigidity of the flexible tangential rod based on the total tensile deformation and the tensile force applied to the flexible tangential rod. According to the method, different deformation calculation formulas are specifically adopted for different structures, so that the tensile rigidity of the flexible tangential rod can be accurately obtained.

Description

Technical Field

[0001] The present application relates to the field of space optics technology, and in particular to a prediction algorithm for calculating the tensile stiffness of flexible tangential rods of side supports of large-aperture reflectors. Background Art

[0002] As the aperture of ground-based photoelectric telescopes continues to increase, the weight of the primary mirror and its support system is also increasing. In order to ensure that the primary mirror still has good surface accuracy and posture accuracy under the action of gravity, the primary mirror support system must be reasonably designed. In general, the primary mirror support system consists of two parts: axial support and lateral support. When the pitch angle of the telescope changes, the axial support and lateral support jointly bear the weight of the primary mirror. When the optical axis of the telescope points to the horizontal, the lateral support bears the entire weight of the primary mirror, which plays a decisive role in the surface accuracy and posture accuracy of the primary mirror. Therefore, the lateral support is an important part of the primary 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 the large-aperture reflector, it is very important to calculate the tensile stiffness of the lateral support rod according to the expected tensile force. The existing calculation method often cannot calculate the tensile stiffness in combination with the specific structure of the lateral support rod, resulting in a large calculation error of the tensile stiffness. Therefore, it is necessary to propose a new calculation method for the tensile stiffness of the lateral support rod of a large-aperture reflector to reduce the calculation error of the tensile stiffness of the lateral support rod. Summary of the invention

[0004] This application proposes a method for calculating the tensile stiffness of a flexible tangential rod of a large-aperture reflector side support, including: 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; Calculate the total tensile deformation of the flexible tangential rod based on the tensile deformation of each region of the flexible tangential rod ; Based on the total tensile deformation and the tension on the flexible tangential rod F Calculate the tensile stiffness of the flexible tangential rod , the tensile stiffness of the flexible tangential rod Satisfies the following relationship: .

[0005] In some embodiments, 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; Among them, 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.

[0006] In some embodiments, the tensile deformation of the first region Satisfies the following relationship: (1) in, E is the elastic modulus of the flexible tangential rod material, L 1 is the thickness of the first region along the x direction, is the thickness of the first region along the y direction, c1 is half of the thickness of the first region along the z direction; The tensile deformation of the second area Satisfies the following relationship: (2) in, is Poisson's ratio, is the thickness of the second region along the z direction.

[0007] In some embodiments, the tensile deformation of the third region Satisfies the following relationship: (3) in, L 3 is the thickness of the third region along the x direction, is the thickness of the third region along the z direction, is the thickness of the third region along the y direction.

[0008] In some embodiments, the tensile deformation of the fourth region Satisfies the following relationship: (4) in, is the thickness of the fourth region along the z direction and the y direction, is the width of the connecting portion between the fourth region and the third region along the y direction, L 4 is the thickness of the fourth region along the x direction.

[0009] In some embodiments, the tensile deformation of the fifth region Satisfies the following relationship: (5) in, is the thickness of the fifth region along the y direction, is the width of the fifth region along the z direction, L 5 is the thickness of the fifth region along the x direction.

[0010] In some embodiments, the tensile deformation of the sixth region is Satisfies the following relationship: (6) in, is the thickness of the sixth region along the y direction and the z direction, and r is the radius of the seventh region.

[0011] In some embodiments, the tensile deformation of the seventh region is Satisfies the following relationship: (7) in, is the thickness of the seventh region along the x direction.

[0012] In some embodiments, the tensile deformation of the eighth region is Satisfies the following relationship: (8) Tensile deformation of the ninth area Satisfies the following relationship: (9) in, is the thickness of the ninth region along the x direction, is the side length of the ninth region.

[0013] In some embodiments, the total tensile deformation of the flexible tangential rod is Satisfies the following relationship: .

[0014] Compared with the related art, the above solution of the embodiment of the present application has at least the following beneficial effects: 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

[0015] 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: Figure 1 A structural diagram of a flexible tangential rod assembly for side support of a large-aperture reflector provided in some embodiments of the present application; Figure 2 A flow chart of a method for calculating the tensile stiffness of flexible tangential rods of side supports of large-aperture reflectors provided in some embodiments of the present application.

[0016] Figure 3 A simplified structural diagram of a flexible tangential rod provided in some embodiments of the present application; Figure 4 for Figure 3 sectional view of; Figure 5 A structural diagram of the first region of a flexible tangential rod provided in some embodiments of the present application; Figure 6 A structural diagram of the second region of the flexible tangential rod provided in some embodiments of the present application; Figure 7 A third region structural diagram of a flexible tangential rod provided in some embodiments of the present application; Figure 8 A structural diagram of the fourth region of the flexible tangential rod provided in some embodiments of the present application; Fig. 9 A simplified structural diagram of the fourth region of the flexible tangential rod provided in some embodiments of the present application; Fig.10 A simulation diagram of the fourth region of the flexible tangential rod provided in some embodiments of the present application; Fig.11 A structural diagram of the fifth region of the flexible tangential rod provided in some embodiments of the present application; Fig.12 A sixth region structural diagram of a flexible tangential rod provided in some embodiments of the present application; Fig.13 A seventh region structural diagram of a flexible tangential rod provided in some embodiments of the present application; Fig.14 A structural diagram of the eighth region of the flexible tangential rod provided in some embodiments of the present application; Fig.15 Structural diagram of the ninth region of the flexible tangential rod provided in some embodiments of the present application.

[0017] Reference numerals: Adhesive pad 1, flexible tangential rod 2, support seat 3, first structure 201, second structure 202, third structure 203, fourth structure 204, fifth structure 205, first area 21, second area 22, third area 23, fourth area 24, fifth area 25, sixth area 26, seventh area 27, eighth area 28, and ninth area 29. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application will be further described in detail below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present application.

[0019] The terms used in the embodiments of the present application are only for the purpose of describing specific embodiments, and are not intended to limit the present application. The singular forms "a", "said" and "the" used in the embodiments of the present application and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings, and "multiple" generally includes at least two.

[0020] It should be understood that the term "and / or" used in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0021] It should be understood that although the terms first, second, third, etc. may be used to describe in the embodiments of the present application, 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 the present application, the first may also be referred to as the second, and similarly, the second may also be referred to as the first.

[0022] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a product or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such product or device. In the absence of more restrictions, the elements defined by the sentence "comprises a" do not exclude the presence of other identical elements in the product or device including the elements.

[0023] The present invention proposes a prediction algorithm for calculating the tensile stiffness of a flexible tangential rod for a side support of a large-aperture reflector, and mainly relates to a flexible tangential rod assembly for a side support of a large-aperture reflector. Figure 1 As shown, the flexible tangential rod assembly for the side support of the large-aperture reflector mainly includes a bonding pad 1, a flexible tangential rod 2, and a support seat 3. The bonding pad 1 is fixedly connected to the primary mirror, the support seat 3 is fixedly connected to the mirror chamber, and the two ends of the flexible tangential rod 2 are respectively connected to the bonding pad 1 and the support seat 3 to realize the side support of the primary mirror on the mirror chamber.

[0024] Among them, the flexible tangential rod 2 support has good support stiffness, and can realize thermal decoupling and static friction release between the adhesive pad 1 and the support seat 3. Therefore, the flexible tangential rod 2 is suitable for use in large-aperture telescope support systems. Generally, 3 or 6 sets of flexible tangential rods 2 are used, and the tensile stiffness of the flexible tangential rod 2 plays a decisive role in the support stiffness of the lateral support. The flexible tangential rod 2 is usually a variable-section rod. When calculating its tensile stiffness, the rod is divided into several sections according to the different cross-sections, and the tensile deformation formula is used to calculate the deformation of each section separately, and the total deformation is combined to calculate the total stiffness.

[0025] like Figure 2 As shown, some embodiments of the present application provide a method for calculating the tensile stiffness of a flexible tangential rod of a side support of a large-aperture reflector, comprising the following method steps: Step S10: dividing the flexible tangential rod into a plurality of regions according to its structure; Step S20: calculating the tensile deformation of each region of the flexible tangential rod according to the structure of each region of the flexible tangential rod; Step S30: Calculate the total tensile deformation of the flexible tangential rod based on the tensile deformation of each region of the flexible tangential rod ; Step S40: Based on the total tensile deformation and the tension on the flexible tangential rod F Calculate the tensile stiffness of the flexible tangential rod , the tensile stiffness of the flexible tangential rod Satisfies the following relationship: .

[0026] As a specific implementation of a flexible tangential rod, Figure 1 As shown, the present application is not limited to the flexible tangential rod of this structure. For a flexible tangential rod of any structure, the tensile stiffness of the flexible tangential rod can be accurately calculated by using the calculation method of the implementation steps described above.

[0027] In order 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 defining the following three mutually perpendicular axes: the lateral axis y, the anterior-posterior axis x, and the vertical axis z. The direction opposite to the arrow along the anterior-posterior axis x is marked as "forward", and the direction of the arrow along the anterior-posterior axis x is marked as "backward". The direction of the arrow along the lateral axis y is marked as "right side", and the opposite direction of the arrow along the lateral axis y is "left side". The direction of the arrow along the vertical axis z is "upper side", and the opposite direction of the arrow along the vertical axis z is "lower side".

[0028] As an embodiment, the flexible tangential rod 2 is a symmetrical structure, and one half thereof (such as Figure 1 The flexible tangential rod 2 includes a first structure 201, a second structure 202, a third structure 203, a fourth structure 204 and a fifth structure 205 in sequence along the x direction.

[0029] For the convenience of calculation, the simplified structure of the flexible tangential rod 2 of the present application is as follows: Figure 3 As shown, Figure 4 for Figure 3 Cross-sectional view. The flexible tangential rod 2 is symmetrical with respect to the symmetry line, and one side of the symmetry line is divided into 9 areas according to the different cross-sectional shapes in the x-direction of the front and rear axes. Among them, the first structure 201 is divided into the first area 21 and the second area 22, the second structure 202 is divided into the third area 23 and the fourth area 24, the third structure 203 is divided into the fifth area 25 and the sixth area 26, the fourth structure 204 is divided into the seventh area 27, and the fifth structure 205 is divided into the eighth area 28 and the ninth area 29. The eighth area 28 is solid as a whole, and the center circle of the ninth area 29 is hollow. The circle on the eighth area 28 represents the boundary with the center circle of the ninth area 29. The two ends of the flexible tangential rod 2 are subjected to a tensile force F, and the tensile force F is along the axial direction of the flexible tangential rod 2. The tensile length and tensile strength of each area are calculated separately, which can be combined into the total tensile length and tensile strength of the flexible tangential rod 2.

[0030] In some embodiments, Figure 5 As shown, the cross section of the first region 21 changes gradually, and the size is as follows Figure 5 As shown, the tensile deformation calculation method is adopted, and the tensile deformation of the first region 21 is obtained by integral summation. , the tensile deformation of the first region 21 Satisfies the following relationship: (1) in, E is the elastic modulus of the flexible tangential rod material, L 1 is the thickness of the first region 21 along the x direction, and is also the radius of the central semicircle, is the thickness of the first region 21 along the y direction, c1 is half of the thickness of the first region 21 along the z direction, is the thickness of the end surface of the first region 21 along the z direction.

[0031] The size of the second area 22 is Figure 6 As shown, is the thickness of the second region 22 along the z direction, is the thickness of the second region 22 along the x direction, is the thickness of the connecting portion between the second region 22 and the third region 23 along the y direction. Since the cross-sectional change between the second region 22 and the third region 23 is relatively large, the shear deformation is used to calculate the stretching length, where the shear stress Along the x direction, its size is:

[0032] Shear modulus for:

[0033] in, is Poisson's ratio. Due to the following relationship:

[0034] Then the shear strain is obtained :

[0035] The tensile deformation amount of the second region 22 Satisfies the following relationship: (2) In some embodiments, Figure 7 As shown, in the third area 23, is the thickness of the third region 23 along the z direction, L 3 is the thickness of the third region 23 along the x direction, is the thickness of the third region 23 along the y direction. Satisfies the following relationship: (3) In some embodiments, Figure 8 As shown, is the thickness of the fourth region 24 along the z-direction and the y-direction, is the width of the connecting portion between the fourth region 24 and the third region 23 along the y direction, L 4is the thickness of the fourth region 24 along the x direction. The deformation of the fourth region 24 is simplified to shear deformation and bending deformation at both ends. The shear deformation at one end satisfies the following relationship:

[0036] Calculate the average amount of stretch caused by the bending deformation at one end. Equivalent tensile force to a uniformly distributed load on the cantilever beam , due to the symmetry of the structure, we take one side of the model for analysis, such as Fig. 9 As shown. The model force is simplified to a uniformly distributed load Loading at length On the cantilever beam, Fig.10 As shown. Cantilever beam under uniform load The deflection curve equation is:

[0037]

[0038]

[0039] in, From 0 to The moment of inertia is between for:

[0040] The average elongation caused by bending deformation is obtained by integration:

[0041]

[0042] Since both ends are deformed, the deformation of the fourth region 24 is for:

[0043] Therefore, the tensile deformation amount of the fourth region 24 is Satisfies the following relationship: (4) In some embodiments, Fig.11 As shown, is the thickness of the fifth region along the y direction, is the width of the fifth region along the z direction, L 5 is the thickness of the fifth region along the x direction.

[0044] The tensile deformation of the fifth region 25 Satisfies the following relationship: (5) In some embodiments, Fig.12 As shown, its deformation is simplified to the shear deformation at both ends, where 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, is the width of the sixth region 26 along the z direction, L 6 is the thickness of the sixth region 26 along the x direction. The shear deformation on the left side of the sixth region 26 is:

[0045] The right side of the sixth region 26 is also calculated using the shear deformation principle, and the shear stress for:

[0046] Shear modulus for:

[0047] in, is Poisson's ratio. Due to the following relationship:

[0048] Then the shear strain is obtained :

[0049] Then the shear deformation on the right side of the sixth region 26 is for:

[0050] Then the deformation amount of the sixth region 26 is for:

[0051] Therefore, the tensile deformation amount of the sixth region 26 is Satisfies the following relationship: (6) In some embodiments, Fig.13 As shown, is the thickness of the seventh region along the x direction. The tensile deformation of the seventh region 27 Satisfies the following relationship: (7) In some embodiments, Fig.14 As shown, is the thickness of the eighth region along the x direction. Using the shear deformation calculation method, the shear stress along the x direction is for:

[0052] Shear modulus for:

[0053] in, is Poisson's ratio. Due to the following relationship:

[0054] Then the shear strain is obtained :

[0055] The tensile deformation of the eighth region 28 Satisfies the following relationship: (8) like Fig.15 As shown, the tensile deformation of the ninth region 29 Satisfies the following relationship: (9) in, is the thickness of the ninth region along the x direction, is the side length of the ninth region.

[0056] In some embodiments, the total tensile deformation of the flexible tangential rod is Satisfies the following relationship: (10) in

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] when , When , the tensile stiffness of the flexible tangential rod is simplified to: (11) The present invention proposes a method for calculating the tensile stiffness of a flexible tangential rod of a large-aperture reflector side support. For a portion with a gradually changing cross section, a tensile deformation formula is used, and the total deformation is solved by integration. For a portion with a relatively large cross section change, a shear deformation formula is used instead of a tensile deformation formula. For some special portions, the average deformation is calculated by combining the bending deformation formula and the shear deformation formula. By using different deformation calculation formulas for different portions in a targeted manner, the tensile deformation and tensile stiffness of the flexible tangential rod are obtained.

[0066] Finally, it should be noted that: each embodiment in this specification is described by way of example, and each embodiment focuses on the differences from other embodiments, and the same or similar parts between the embodiments can be referred to each other. For the system or device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0067] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A prediction algorithm for calculating the tensile stiffness of the flexible tangential rods of the side supports of large-aperture 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; Calculate the total tensile deformation of the flexible tangential rod based on the tensile deformation of each region of the flexible tangential rod ; Based on the total tensile deformation and the tension on the flexible tangential rod F Calculate the tensile stiffness of the flexible tangential rod , the tensile stiffness of the flexible tangential rod Satisfies the following relationship: 。 2. The prediction algorithm according to claim 1, characterized in that , 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; Among them, 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.

3. The prediction algorithm according to claim 2, characterized in that , The tensile deformation of the first area Satisfies the following relationship: （1） in, E is the elastic modulus of the flexible tangential rod material, L 1 is the thickness of the first region along the x direction, is the thickness of the first region along the y direction, c1 is half of the thickness of the first region along the z direction; The tensile deformation of the second area Satisfies the following relationship: （2） in, is Poisson's ratio, is the thickness of the second region along the z direction.

4. The prediction algorithm according to claim 2, characterized in that , The tensile deformation of the third area Satisfies the following relationship: （3） in, L 3 is the thickness of the third region along the x direction, is the thickness of the third region along the z direction, is the thickness of the third region along the y direction.

5. The prediction algorithm according to claim 2, characterized in that , Tensile deformation of the fourth area Satisfies the following relationship: （4） in, is the thickness of the fourth region along the z direction and the y direction, is the width of the connecting portion between the fourth region and the third region along the y direction, L 4 is the thickness of the fourth region along the x direction.

6. The prediction algorithm according to claim 2, characterized in that , Tensile deformation of the fifth area Satisfies the following relationship: （5） in, is the thickness of the fifth region along the y direction, is the width of the fifth region along the z direction, L 5 is the thickness of the fifth region along the x direction.

7. The prediction algorithm according to claim 2, characterized in that , Tensile deformation of the sixth region Satisfies the following relationship: （6） in, is the thickness of the sixth region along the y direction and the z direction, and r is the radius of the seventh region.

8. The prediction algorithm according to claim 2, characterized in that , Tensile deformation of the seventh area Satisfies the following relationship: （7） in, is the thickness of the seventh region along the x direction.

9. The prediction algorithm according to claim 2, characterized in that , Tensile deformation of the eighth region Satisfies the following relationship: （8） Tensile deformation of the ninth area Satisfies the following relationship: （9） in, is the thickness of the ninth region along the x direction, is the side length of the ninth region.

10. The prediction algorithm according to claim 2, characterized in that , the total tensile deformation of the flexible tangential rod Satisfies the following relationship: 。

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