A method for designing a mold profile for a carbon fiber composite reflector

Abstract

The present application relates to a kind of carbon fiber composite reflector mould surface new design method, belong to satellite antenna field;For the thermal deformation in the curing process of reflector, chemical shrinkage deformation and the deformation problem caused by mould, consider the thermal deformation influence of carbon fiber resin matrix composite material from rubber state to glass state whole cycle process, and according to the mould surface compensation of thermal deformation analysis result is carried out.Formation of reflector three-dimensional analysis model;The reflector is according to the rubber state and glass state of corresponding solidification process Double-state whole solidification cycle thermal deformation analysis is carried out, and three-point boundary constraint analysis method is proposed, and it is consistent with the working condition of reflector curing;In the solidification cycle of reflector, the interfacial stress of mould to reflector is extracted, and it is superimposed into reflector thermal deformation and is compensated jointly, through the thermal deformation joint compensation of reflector and mould, the mould surface design for high-precision composite material reflector manufacturing is realized, meet the need of high-precision antenna reflector to surface precision.

Description

Technical Field

[0001] This invention belongs to the field of satellite antennas and relates to a method for designing the mold surface of a carbon fiber composite reflector. Background Technology

[0002] The surface accuracy error of high-precision reflectors is mainly caused by curing deformation. From the perspective of the causes of deformation, curing deformation can be divided into thermal deformation, chemical shrinkage deformation, and deformation caused by the mold. Thermal deformation is a reflector deformation phenomenon caused by the thermal expansion effect of the material itself. Composite material reflectors have different coefficients of thermal expansion in different principal axis directions, giving the reflector anisotropic thermal expansion characteristics. Chemical shrinkage deformation is closely related to the resin system of high-precision reflectors. After the composite material reflector gels during the curing process, that is, after the transformation from a rubber state to a glass state, the volume of the matrix resin can still change due to the continued curing chemical reaction, resulting in changes in the shape of the reflector. This is one of the key factors causing surface accuracy errors in high-precision reflectors. The thermal expansion coefficients of the mold and the reflector are inconsistent and significantly different. They will change with different expansion and contraction rates, generating curing stress in the reflector. Deformation caused by the mold is another key factor causing surface accuracy errors in high-precision reflectors and cannot be ignored. These factors cause the reflector, which is cured and formed in close contact with the mold, to be inconsistent with the theoretical surface of the reflector, resulting in a deterioration in the surface accuracy of the reflector. Therefore, how to comprehensively consider thermal deformation, chemical shrinkage deformation and mold deformation, and compensate for the mold surface is the bottleneck technology in manufacturing high-precision reflectors.

[0003] Currently available methods for compensating for thermal deformation of reflector molds include:

[0004] 1) Experimental method: Based on experience and experiments, the mold surface is repeatedly adjusted and compensated by repeated trials to offset the deformation of the mold. However, this method is rarely used for reflectors produced in single pieces, and it is time-consuming, material-intensive and costly.

[0005] 2) Formula Derivation Method: Ignoring the curing deformation of the reflector, and focusing only on the mold, it is assumed that the expansion deformation between any two points on the mold is ΔL = L·CTE·ΔT. In the formula, ΔL is the deformation; CTE is the mold expansion coefficient; ΔT is the temperature difference; and L is the straight-line distance between the two points, which is independent of the path from one point to the other.

[0006] For a standard parabola:

[0007] X 2 +Y 2 =4FZ (1)

[0008] The shape of the parabola at the curing temperature becomes:

[0009] X 2+Y 2 =4F(1+CTE·ΔT)Z (2)

[0010] Therefore, the surface after mold shape compensation is:

[0011]

[0012] 3) Finite element simulation method:

[0013] Currently, finite element simulation methods can be categorized as follows:

[0014] Method ①: Without considering the curing deformation of the reflector, only the mold is studied. After the mold is meshed according to the volume element or shell element to establish a finite element model, the mold is subjected to thermal deformation analysis based on the homogeneous material and uniform temperature field, with the six degrees of freedom of the center point of the mold finite element model as the boundary constraints. The theoretical surface of the reflector after shrinking and deforming from the curing temperature to room temperature is used as the compensated mold surface, and the reflector is cured and formed on this mold surface.

[0015] Method ②: Based on method ①, combined with experimental methods, the mold surface is further corrected according to the measured results of the product processed after mold surface compensation. Although this method considers the actual thermal deformation of the reflector component, the forming process of the reflector component is discrete. This reverse compensation method requires a large number of samples to improve the reliability of mold surface compensation, and it is also expensive. Summary of the Invention

[0016] The technical problem solved by this invention is to overcome the shortcomings of existing technologies and propose a novel design method for the mold surface of carbon fiber composite reflectors. This method achieves mold surface design for high-precision composite material reflector manufacturing through joint compensation for thermal deformation of the reflector and mold, thus meeting the surface accuracy requirements of high-precision antenna reflectors.

[0017] The solution of the present invention is:

[0018] A novel design method for the mold surface of a carbon fiber composite reflector includes the following steps:

[0019] Create physical models of the reflector and the mold; the reflector's reflective surface is parabolic in shape; the reflector's reflective surface is placed vertically downwards, and the mold is placed at the bottom of the reflector, with the upper surface of the mold fitting against the reflector's reflective surface;

[0020] Establish a finite element model of the reflector and establish a reference coordinate system O-XYZ in the finite element model of the reflector; obtain the initial coordinate matrix δ0 of all n nodes of the finite element model of the reflector; and determine the m nodes in the n nodes of the finite element model of the reflector that are in contact with the upper surface of the mold based on the physical models of the reflector and the mold.

[0021] Extract the coordinates of m nodes; establish the finite element model of the mold, set the coordinate values ​​of the surface nodes on the upper surface of the mold to be consistent with the coordinates of the m nodes, and establish m spring elements to correspond one-to-one with the m nodes of the reflector;

[0022] Set the Young's modulus, shear modulus, Poisson's ratio, and coefficient of thermal expansion of the reflector finite element model along the X, Y, and Z directions; set the Young's modulus, shear modulus, Poisson's ratio, and coefficient of thermal expansion of the mold finite element model; set the spring stiffness of the spring element.

[0023] In the finite element model of the reflector, take the center node and define it as point A; take the intersection of the edge of the finite element model of the reflector and the +X axis and define it as point B; the intersection of the axis parallel to +Y passing through the center point A and the edge of the reflector is defined as point C; set constraints for the three points A, B, and C;

[0024] The finite element model of the reflector and the finite element model of the mold are heated to the temperature at which the finite element model of the reflector solidifies into a glassy state. The coordinates δ1 of n nodes of the finite element model of the reflector in the X, Y, and Z directions in the reference coordinate system, the coordinates δ2 of m nodes of the finite element model of the reflector in contact with the finite element model of the mold in the X, Y, and Z directions, and the coordinates δ3 of m nodes of the finite element model of the mold in the X, Y, and Z directions are obtained by finite element analysis.

[0025] Calculate the interface displacement Δδ of the mold finite element model to the reflector finite element model, calculate the deformation δ4 of the reflector finite element model caused by heating, and calculate the comprehensive deformation δ5 of the reflector finite element model when the temperature reaches the curing temperature.

[0026] After the reflector finite element model is kept at the curing temperature for 2-2.5 hours, the deformed coordinates ε1 of n nodes of the reflector finite element model in the X, Y, and Z directions in the reference coordinate system, the deformed coordinates ε2 of m nodes of the reflector finite element model in contact with the mold finite element model in the X, Y, and Z directions, and the deformed coordinates ε3 of m nodes of the mold finite element model in the X, Y, and Z directions are obtained by finite element analysis.

[0027] Calculate the interface displacement Δε of the mold finite element model and the deformation ε4 of the reflector finite element model caused by thermal insulation.

[0028] Since the temperature does not change during the heat preservation process at the curing temperature of the finite element model of the reflector, i.e., δ3=ε3, calculate the comprehensive deformation ε5 of the finite element model of the reflector in the glassy state.

[0029] Calculate the coordinate values ​​P0 of each node in the finite element model of the reflector in the glassy state;

[0030] The finite element models of the reflector and the mold were cooled to room temperature. The deformed coordinates of n nodes of the reflector finite element model in the X, Y, and Z directions in the reference coordinate system were then obtained through finite element analysis. The coordinates of m nodes at contact between the finite element model of the reflector and the finite element model of the mold after deformation in the X, Y, and Z directions.

[0031] Calculate the coordinates P1 of each node in the finite element model of the reflector after it returns to room temperature;

[0032] Calculate the coordinate values ​​D′ of the nodes after surface compensation in the finite element model of the mold;

[0033] The coordinates of m nodes in contact between the reflector finite element model and the mold finite element model are extracted from the coordinate value D′. The surface is then fitted in reverse to obtain the compensated geometric model of the mold finite element model.

[0034] In the above-mentioned novel design method for the mold surface of a carbon fiber composite reflector, the method for establishing the reference coordinate system O-XYZ is as follows:

[0035] The origin O is the vertex of the parabolic surface of the finite element model of the reflector; the X direction is the direction of the axis of symmetry of the parabolic surface of the finite element model of the reflector; the Z axis is the direction that coincides with the focal axis of the parabolic surface of the finite element model of the reflector and points towards the focal point of the parabolic surface; the Y axis conforms to the right-hand rule.

[0036] In the aforementioned novel design method for the mold surface of a carbon fiber composite reflector, the finite element model of the reflector is meshed using hexahedral elements to obtain the initial coordinate matrix δ0 of n nodes:

[0037]

[0038] In the formula, x 0i Let be the coordinates of the i-th node in the X direction;

[0039] y 0i Let be the Y-coordinate of the i-th node;

[0040] z 0i Let be the coordinates of the i-th node in the Z direction.

[0041] In the above-mentioned novel design method for carbon fiber composite reflector mold surface, the finite element model of the mold is meshed using triangular shell elements.

[0042] In the above-mentioned novel design method for carbon fiber composite reflector mold surface, the finite element model of the reflector is set as a carbon fiber resin matrix composite material.

[0043] The finite element model of the reflector is set in the glassy state, with Young's modulus of 50 GPa, shear modulus of 3.4 GPa, Poisson's ratio of 0.3, and coefficient of thermal expansion of 2.6 × 10⁻⁶ in the X direction. -6 / ℃; Young's modulus in the Y direction is 50 GPa, shear modulus is 3.4 GPa, Poisson's ratio is 0.3, and coefficient of thermal expansion is 2.6 × 10⁻⁶. -6 / ℃; Young's modulus in the Z direction is 8.5 GPa, shear modulus is 7 GPa, Poisson's ratio is 0.25, and coefficient of thermal expansion is 5 × 10⁻⁶. -5 / ℃;

[0044] In its rubbery state, the reflector has a Young's modulus of 50 GPa, a shear modulus of 3.4 GPa, a Poisson's ratio of 0.3, and a coefficient of thermal expansion of 1 × 10⁻⁶ in the X direction. -8 / ℃; Young's modulus in the Y direction is 50 GPa, shear modulus is 3.4 GPa, Poisson's ratio is 0.3, and coefficient of thermal expansion is 1×10⁻⁶. -8 / ℃; Young's modulus in the Z direction is 8.5 GPa, shear modulus is 7 GPa, Poisson's ratio is 0.25, and coefficient of thermal expansion is 1×10⁻⁶. -8 / ℃;

[0045] The finite element model of the mold is set with Young's modulus of 170 GPa, shear modulus of 65.4 GPa, Poisson's ratio of 0.3, and coefficient of thermal expansion of 1 × 10⁻⁶. -5 / ℃;

[0046] The spring stiffness of the spring unit is set to 0.1 N / mm.

[0047] In the above-mentioned novel design method for the mold surface of a carbon fiber composite reflector, the displacements in the X, Y, and Z directions of point A are all constrained; the displacements in the Y and Z directions of point B are constrained; and the displacement in the Z direction of point C is constrained.

[0048] In the above-mentioned novel design method for carbon fiber composite reflector mold surface, the heating process for the reflector finite element model and the mold finite element model is as follows:

[0049] At room temperature, the finite element model of the reflector is in a rubber state. The finite element model of the reflector is heated from room temperature (20℃) at a heating rate of 0.5-2℃ / min. When the temperature reaches 70℃-80℃, it is held for 30 minutes. Then, the temperature is increased at a rate of 0.5-2℃ / min until the temperature at which the finite element model of the reflector solidifies into a glassy state is reached. The solidification temperature is 125℃.

[0050] In the above-mentioned novel design method for carbon fiber composite reflector mold surface, the coordinate δ1 after deformation is:

[0051]

[0052] In the formula, x 1i Let X be the coordinate of the i-th node in the X direction among the n nodes after heating.

[0053] y 1i Let be the Y-coordinate of the i-th node out of n nodes after heating;

[0054] z 1i Let Z be the coordinate of the i-th node among the n nodes after heating.

[0055] The coordinates δ2 after deformation are:

[0056]

[0057] In the formula, x 2j Let J be the coordinate of the j-th node in the m-th node of the finite element model of the reflector after heating.

[0058] y 2j Let be the Y-coordinate of the j-th node among the m nodes in the finite element model of the reflector after heating.

[0059] z 2j Here are the coordinates of the j-th node in the m-th node of the finite element model of the reflector after heating; the coordinates δ3 after deformation are:

[0060]

[0061] In the formula, x 3k Let X be the coordinate of the k-th node in the m-th node of the mold finite element model after heating.

[0062] y 3k Let Y be the coordinate of the k-th node in the m-th node of the finite element model of the mold after heating.

[0063] z 3k Let Z be the coordinate of the kth node in the Z-direction among the m nodes of the finite element model of the mold after heating.

[0064] In the novel design method for the mold surface of a carbon fiber composite reflector described above, the interface displacement Δδ is:

[0065] Δδ=δ3-δ2

[0066] The deformation δ4 is:

[0067] δ4=K n×m ·K m×m ·Δδ

[0068] In the formula, K n×m Here is the stiffness matrix of the finite element model of the reflector;

[0069] Km×m The stiffness matrix of the spring element at the interface between the mold finite element model and the reflector finite element model;

[0070] The total deformation δ5 is:

[0071] δ5 = δ1 + δ4.

[0072] In the novel design method for the mold surface of a carbon fiber composite reflector described above, the interface displacement Δε is:

[0073] Δε=ε3-ε2

[0074] The deformation ε4 is:

[0075] ε4=K n×m ·K m×m ·Δε

[0076] In the formula, K n×m Here is the stiffness matrix of the finite element model of the reflector;

[0077] K m×m This is the stiffness matrix of the spring element at the interface between the mold finite element model and the reflector finite element model.

[0078] In the above-mentioned novel design method for carbon fiber composite reflector mold surface, the comprehensive deformation ε5 of the reflector finite element model in the glassy state is:

[0079] ε5=ε1+ε4+δ1

[0080] The coordinate value P0 is:

[0081] P0 = δ0 + ε1 + ε4 + δ1.

[0082] In the novel design method for the mold surface of a carbon fiber composite reflector described above, the specific method for cooling is as follows:

[0083] The temperature was reduced from the curing temperature of 125°C to room temperature (20°C) at a cooling rate of 1°C / min.

[0084] In the above-mentioned novel design method for carbon fiber composite reflector mold surface, coordinate P1 is:

[0085]

[0086] The coordinate value D′ is:

[0087]

[0088] The beneficial effects of this invention compared to the prior art are:

[0089] (1) Based on the structural characteristics of carbon fiber resin-based composite material reflectors and combined with the mechanical and thermal performance parameters of composite materials in two states (rubber state / glass state), the present invention establishes a three-dimensional analysis model of the reflector. The model is accurate and the subsequent analysis is highly accurate.

[0090] (2) This invention performs dual-state full-curing cycle thermal deformation analysis on the reflector according to the rubber state and glass state corresponding to the curing process, and innovates the method of thermal deformation analysis of reflector curing.

[0091] (3) When applying boundary constraints, the present invention proposes a three-point boundary constraint analysis method that matches the working conditions during reflector curing; during the reflector curing cycle, the stress of the mold on the reflector interface is extracted and superimposed into the reflector thermal deformation for joint compensation, thereby improving the accuracy of reflector thermal deformation calculation and mold design method. Attached Figure Description

[0092] Figure 1 This is a schematic diagram of the reflector and mold model of the present invention;

[0093] Figure 2 This is a schematic diagram of the finite element model of the reflector of the present invention;

[0094] Figure 3 This is a schematic diagram of the temperature control of the reflector and mold in this invention;

[0095] Figure 4 A schematic diagram showing the positions of points A, B, and C in the finite element model of the reflector of this invention. Detailed Implementation

[0096] The present invention will be further described below with reference to the embodiments.

[0097] This invention provides a novel design method for the mold surface of a carbon fiber composite reflector. It addresses the issues of thermal deformation, chemical shrinkage deformation, and deformation caused by the mold during the curing process of the reflector. The method combines the analysis of thermal deformation of the reflector components and the mold during the heating and cooling process, considers the influence of thermal deformation of the carbon fiber resin-based composite material throughout the entire curing process from the rubber state to the glass state, and compensates for the mold surface based on the results of the thermal deformation analysis.

[0098] A novel design method for carbon fiber composite reflector mold surface includes the following steps:

[0099] First, physical models of the reflector and mold are created based on the actual situation; the reflector's reflecting surface is parabolic in shape; the reflector's reflecting surface is placed vertically downwards, and the mold is placed at the bottom of the reflector, with the upper surface of the mold fitting flush with the reflector's reflecting surface, such as... Figure 1 As shown.

[0100] Establish a finite element model of the reflector, such as Figure 2 As shown, a reference coordinate system O-XYZ is established in the finite element model of the reflector. The method for establishing the reference coordinate system O-XYZ is as follows: the origin O is the vertex of the parabolic surface of the finite element model of the reflector; the X direction is the direction of the axis of symmetry of the parabolic surface of the finite element model of the reflector; the Z axis is the direction that coincides with the focal axis of the parabolic surface of the finite element model of the reflector and points to the focal point of the parabolic surface; the Y axis conforms to the right-hand rule.

[0101] The finite element model of the reflector is meshed using hexahedral elements, and the initial coordinate matrix δ0 of n nodes is obtained as follows:

[0102]

[0103] In the formula, x 0i Let be the coordinates of the i-th node in the X direction;

[0104] y 0i Let be the Y-coordinate of the i-th node;

[0105] z 0i Let be the coordinates of the i-th node in the Z direction.

[0106] Based on the physical models of the reflector and the mold, determine the m nodes that are in contact with the upper surface of the mold out of the n nodes in the finite element model of the reflector.

[0107] Extract the coordinates of m nodes. Establish a finite element model of the mold, and mesh the mold finite element model using triangular shell elements, ensuring that the number of nodes and node coordinates on the mold surface are consistent with the number of nodes and coordinates of the m nodes in contact with the mold surface. Then, establish m spring elements to correspond one-to-one with the m nodes of the reflector.

[0108] Set the Young's modulus, shear modulus, Poisson's ratio, and coefficient of thermal expansion of the reflector finite element model along the X, Y, and Z directions; set the Young's modulus, shear modulus, Poisson's ratio, and coefficient of thermal expansion of the mold finite element model; set the spring stiffness of the spring element. Specifically, set as follows:

[0109] The finite element model of the reflector is set as a carbon fiber resin matrix composite material;

[0110] The finite element model of the reflector is set in the glassy state, with Young's modulus of 50 GPa, shear modulus of 3.4 GPa, Poisson's ratio of 0.3, and coefficient of thermal expansion of 2.6 × 10⁻⁶ in the X direction. -6 / ℃; Young's modulus in the Y direction is 50 GPa, shear modulus is 3.4 GPa, Poisson's ratio is 0.3, and coefficient of thermal expansion is 2.6 × 10⁻⁶. -6 / ℃; Young's modulus in the Z direction is 8.5 GPa, shear modulus is 7 GPa, Poisson's ratio is 0.25, and coefficient of thermal expansion is 5 × 10⁻⁶.-5 / ℃; In its rubbery state, the reflector has a Young's modulus of 50 GPa, a shear modulus of 3.4 GPa, a Poisson's ratio of 0.3, and a coefficient of thermal expansion of 1×10⁻⁶ in the X direction. -8 / ℃; Young's modulus in the Y direction is 50 GPa, shear modulus is 3.4 GPa, Poisson's ratio is 0.3, and coefficient of thermal expansion is 1×10⁻⁶. -8 / ℃; Young's modulus in the Z direction is 8.5 GPa, shear modulus is 7 GPa, Poisson's ratio is 0.25, and coefficient of thermal expansion is 1×10⁻⁶. -8 / ℃, see Table 1 for details.

[0111] The finite element model of the mold is set with Young's modulus of 170 GPa, shear modulus of 65.4 GPa, Poisson's ratio of 0.3, and coefficient of thermal expansion of 1 × 10⁻⁶. -5 / ℃, see Table 2 for details.

[0112] The spring stiffness of the spring unit is set to 0.1 N / mm, as detailed in Table 3.

[0113] Table 1

[0114]

[0115]

[0116] Table 2

[0117] parameter value Young's modulus E 170GPa Shear modulus G 65.4 GPa Poisson's ratio v 0.3 Coefficient of thermal expansion (CTE) <![CDATA[1×10 -5 / ℃]]>

[0118] Table 3

[0119] parameter value Spring stiffness K 0.1N / mm

[0120] In the finite element model of the reflector, the center node is defined as point A; the intersection of the edge of the reflector finite element model and the +X axis is defined as point B; the intersection of the axis parallel to +Y passing through the center point A and the edge of the reflector is defined as point C. Figure 4 As shown. Constraints are set for three points A, B, and C; the displacements of point A in the X, Y, and Z directions are all constrained, and are represented as (0, 0, 0) in the finite element model. The displacements of point B in the Y and Z directions are constrained, and are represented as (, 0, 0) in the finite element model; the displacement of point C in the Z direction is constrained, and is represented as (, , 0).

[0121] Compared to the constraint center point with three displacements and three rotations, the three-point constraint method can not only establish fixed constraints for the finite element model, but also truly reflect the boundary constraints of the reflector.

[0122] The finite element models of the reflector and the mold were subjected to heating treatment, such as... Figure 3As shown, the process of heating the finite element model of the reflector and the finite element model of the mold is as follows:

[0123] At room temperature, the finite element model of the reflector is in a rubber state. The finite element model of the reflector is heated from room temperature (20℃) at a heating rate of 0.5-2℃ / min. When the temperature reaches 70℃-80℃, it is held for 30 minutes. Then, the temperature is increased at a rate of 0.5-2℃ / min until the temperature at which the finite element model of the reflector solidifies into a glassy state is reached. The solidification temperature is 125℃.

[0124] The temperature is raised to the solidified glass state temperature of the reflector finite element model; the deformed coordinates δ1 of n nodes of the reflector finite element model in the X, Y, and Z directions in the reference coordinate system, the deformed coordinates δ2 of m nodes of the reflector finite element model in contact with the mold finite element model in the X, Y, and Z directions, and the deformed coordinates δ3 of m nodes of the mold finite element model in the X, Y, and Z directions are obtained through finite element analysis.

[0125] The coordinates δ1 after deformation are:

[0126]

[0127] In the formula, x 1i Let X be the coordinate of the i-th node in the X direction among the n nodes after heating.

[0128] y 1i Let be the Y-coordinate of the i-th node out of n nodes after heating;

[0129] z 1i Let Z be the coordinate of the i-th node among the n nodes after heating.

[0130] The coordinates δ2 after deformation are:

[0131]

[0132] In the formula, x 2j Let J be the coordinate of the j-th node in the m-th node of the finite element model of the reflector after heating.

[0133] y 2j Let be the Y-coordinate of the j-th node among the m nodes in the finite element model of the reflector after heating.

[0134] z 2j Let J be the coordinate of the j-th node in the Z-direction among the m nodes of the finite element model of the reflector after heating.

[0135] The deformed coordinate δ3 is:

[0136]

[0137] In the formula, x3k Let X be the coordinate of the k-th node in the m-th node of the mold finite element model after heating.

[0138] y 3k Let Y be the coordinate of the k-th node in the m-th node of the finite element model of the mold after heating.

[0139] z 3k Let Z be the coordinate of the kth node in the Z-direction among the m nodes of the finite element model of the mold after heating.

[0140] Calculate the interface displacement Δδ of the mold finite element model to the reflector finite element model, calculate the deformation δ4 of the reflector finite element model caused by heating, and calculate the comprehensive deformation δ5 of the reflector finite element model when the temperature reaches the curing temperature.

[0141] The interface displacement Δδ is:

[0142] Δδ=δ3-δ2

[0143] The deformation δ4 is:

[0144] δ4=K n×m ·K m×m ·Δδ

[0145] In the formula, K n×m Here is the stiffness matrix of the finite element model of the reflector;

[0146] K m×m The stiffness matrix of the spring element at the interface between the mold finite element model and the reflector finite element model;

[0147] The total deformation δ5 is:

[0148] δ5 = δ1 + δ4.

[0149] Hold the finite element model of the reflector at its curing temperature for 2-2.5 hours. Figure 3 As shown. The coordinates ε1 of the n nodes of the reflector finite element model in the X, Y, and Z directions in the reference coordinate system after deformation, the coordinates ε2 of the m nodes of the reflector finite element model in contact with the mold finite element model in the X, Y, and Z directions after deformation, and the coordinates ε3 of the m nodes of the mold finite element model in the X, Y, and Z directions after deformation are obtained by finite element analysis.

[0150] Calculate the interface displacement Δε of the mold finite element model and the deformation ε4 of the reflector finite element model caused by thermal insulation.

[0151] The interface displacement Δε is:

[0152] Δε=ε3-ε2

[0153] The deformation ε4 is:

[0154] ε4=K n×m ·K m×m ·Δε

[0155] In the formula, K n×m Here is the stiffness matrix of the finite element model of the reflector;

[0156] K m×m This is the stiffness matrix of the spring element at the interface between the mold finite element model and the reflector finite element model.

[0157] Since the temperature does not change during the heat preservation process at the curing temperature of the finite element model of the reflector, i.e., δ3 = ε3, the comprehensive deformation ε5 of the finite element model of the reflector in the glassy state is calculated. The comprehensive deformation ε5 of the finite element model of the reflector in the glassy state is:

[0158] ε5=ε1+ε4+δ1

[0159] Calculate the coordinate values ​​P0 of each node in the finite element model of the reflector in the glassy state. The coordinate values ​​P0 are:

[0160] P0 = δ0 + ε1 + ε4 + δ1.

[0161] The finite element models of the reflector and mold were cooled to room temperature. The specific cooling method was to reduce the temperature from the curing temperature of 125℃ to room temperature (20℃) at a cooling rate of 1℃ / min. The deformed coordinates of n nodes of the reflector finite element model in the X, Y, and Z directions in the reference coordinate system were obtained through finite element analysis. The coordinates of m nodes at contact between the finite element model of the reflector and the finite element model of the mold after deformation in the X, Y, and Z directions.

[0162] Calculate the coordinates P1 of each node in the finite element model of the reflector after returning to room temperature; coordinates P1 are:

[0163]

[0164] Calculate the coordinate values ​​D′ of the nodes in the finite element model of the mold after surface compensation. The coordinate values ​​D′ are:

[0165]

[0166] The coordinates of m nodes in contact between the reflector finite element model and the mold finite element model are extracted from the coordinate value D′. The surface is then fitted in reverse to obtain the compensated geometric model of the mold finite element model.

[0167] The working principle of this invention is as follows:

[0168] To meet the manufacturing requirements of high-precision composite material reflectors, this study jointly analyzes the thermal deformation of reflector components and molds during heating and cooling processes. The influence of thermal deformation on the carbon fiber resin matrix composite material during the entire curing process, from the rubber state to the glass state, is considered, and the mold surface is compensated based on the thermal deformation analysis results. Considering the structural characteristics of the reflector components and the mechanical and thermal performance parameters of the composite material in both states (rubber / glass), a three-dimensional model is created to improve modeling and analysis accuracy. The composite material reflector undergoes a dual-state, full-cycle thermal deformation analysis according to the rubber and glass states corresponding to the curing process, innovating the method for analyzing reflector curing thermal deformation. When applying boundary constraints, a novel three-point boundary constraint analysis method is proposed, which matches the working conditions during reflector curing. During the curing cycle of the reflector components, the interfacial stress of the mold on the reflector components is extracted and superimposed into the reflector's thermal deformation for joint compensation, improving the accuracy of reflector thermal deformation calculation and mold design methods.

[0169] The mold surface material in this invention is low-cost ductile iron, which is readily available in China, thus improving the competitiveness of high-precision reflector products in both international and domestic markets.

[0170] In this invention, the surface accuracy of the reflector manufactured using a cast iron mold, achieved through joint analysis and comprehensive compensation of thermal deformation of the high-precision composite material reflector and the mold, reaches 100µm RMS. This is superior to the surface accuracy of the reflector manufactured using a cast iron mold without surface compensation, and reaches the surface accuracy level of reflectors manufactured using high thermal stability composite material molds and Invar molds. Further surface compensation of the high thermal stability composite material molds and Invar molds will further improve the surface accuracy of the reflector manufacturing.

[0171] This invention addresses the structural characteristics of carbon fiber resin-based composite material reflectors and, combined with the mechanical and thermal performance requirements of the composite material in two states (rubber state / glass state), establishes a three-dimensional analysis model of the reflector. It innovates the method for analyzing the thermal deformation of reflectors during curing by performing a dual-state full-curing cycle thermal deformation analysis of the reflector according to the rubber and glass states corresponding to the curing process. When applying boundary constraints, a three-point boundary constraint analysis method is proposed, which matches the working conditions during reflector curing. During the reflector curing cycle, the stress on the reflector interface from the mold is extracted and superimposed into the reflector's thermal deformation for joint compensation, improving the accuracy of reflector thermal deformation calculation and mold design methods.

[0172] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for designing the mold surface of a carbon fiber composite reflector, characterized in that: Includes the following steps: Establish physical models of reflector (1) and mold (2); the reflective surface of reflector (1) is parabolic in shape; the reflective surface of reflector (1) is placed vertically downward, and mold (2) is set at the bottom of reflector (1), and the upper surface of mold (2) is in contact with the reflective surface of reflector (1); Establish a finite element model of reflector (1), and establish a reference coordinate system O-XYZ in the finite element model of reflector (1); obtain the initial coordinate matrix of all n nodes of the finite element model of reflector (1). ; Based on the physical models of the reflector (1) and the mold (2), determine the m nodes in the n nodes of the finite element model of the reflector (1) that are in contact with the upper surface of the mold (2); Extract the coordinates of m nodes; establish the finite element model of the mold (2), set the coordinate values ​​of the surface nodes on the upper surface of the mold (2) to be consistent with the coordinates of the m nodes, and establish m spring elements corresponding one-to-one with the m nodes of the reflector (1); Set the Young's modulus, shear modulus, Poisson's ratio and coefficient of thermal expansion of the reflector (1) finite element model along the X, Y and Z directions respectively; set the Young's modulus, shear modulus, Poisson's ratio and coefficient of thermal expansion of the mold (2) finite element model; set the spring stiffness of the spring element; In the finite element model of reflector (1), take the center node and define it as point A; take the intersection of the edge of the finite element model of reflector (1) and the +X axis and define it as point B; the intersection of the axis parallel to +Y through the center point A and the edge of the reflector is defined as point C; set the constraints of the three points A, B and C; The finite element model of the reflector (1) and the finite element model of the mold (2) were heated to the temperature at which the finite element model of the reflector (1) solidified into a glassy state. The coordinates of the n nodes of the reflector (1) finite element model after deformation in the X, Y, and Z directions in the reference coordinate system were obtained by finite element analysis. The coordinates of m nodes in contact between the reflector (1) and the mold (2) in the X, Y, and Z directions after deformation. Coordinates of the m nodes of the mold (2) finite element model after deformation in the X, Y, and Z directions ; Calculate the interface displacement of the mold (2) finite element model on the reflector (1) finite element model.

1. Calculate the deformation of the reflector caused by temperature rise (1) Finite element model Calculate the overall deformation of the finite element model of the reflector (1) when the temperature rises to the curing temperature. ; After the reflector (1) finite element model was kept at the curing temperature for 2-2.5h, the deformed coordinates of n nodes of the reflector (1) finite element model in the X, Y, and Z directions in the reference coordinate system were obtained by finite element analysis. The coordinates of m nodes in contact between the reflector (1) and the mold (2) in the X, Y, and Z directions after deformation. Coordinates of the m nodes of the mold (2) finite element model after deformation in the X, Y, and Z directions ; Calculate the interface displacement of the finite element model of the mold (2) 1. Calculate the deformation of the reflector (1) finite element model caused by thermal insulation. ; Since the temperature does not change during the heat preservation process at the curing temperature of the finite element model of the reflector (1), that is... Calculate the overall deformation of the finite element model of the reflector (1) in the glassy state. ; Calculate the coordinate values ​​of each node of the finite element model of the reflector (1) in the glassy state. ; The finite element models of reflector (1) and mold (2) were cooled to room temperature. The coordinates of the n nodes of the finite element model of reflector (1) in the XYZ directions in the reference coordinate system were obtained by finite element analysis. The coordinates of m nodes in contact between the reflector (1) and the mold (2) in the X, Y, and Z directions after deformation. ; Calculate the coordinates of each node of the reflector (1) after the finite element model returns to room temperature. ; Calculate the coordinate values ​​of the nodes of the mold (2) after surface compensation in the finite element model. ; From coordinate values Extract the coordinates of m nodes in the contact between the reflector (1) finite element model and the mold (2) finite element model, and backfit the surface to obtain the geometric model of the mold (2) finite element model after compensation.

2. The method for designing the mold surface of a carbon fiber composite reflector according to claim 1, characterized in that: The method for establishing the reference coordinate system O-XYZ is as follows: The origin O is the vertex of the parabolic surface of the finite element model of the reflector (1); the X direction is the direction of the axis of symmetry of the parabolic surface of the finite element model of the reflector (1); the Z axis is the direction that coincides with the focal axis of the parabolic surface of the finite element model of the reflector (1) and points towards the focal point of the parabolic surface; the Y axis conforms to the right-hand rule.

3. The method for designing the mold surface of a carbon fiber composite reflector according to claim 1, characterized in that: The finite element model of the reflector (1) is meshed using hexahedral elements to obtain an initial coordinate matrix of n nodes. for: In the formula, For the first The coordinates of each node in the X direction; For the first The coordinates of each node in the Y direction; For the first The coordinates of each node in the Z direction.

4. The method for designing the mold surface of a carbon fiber composite reflector according to claim 1, characterized in that: The finite element model of the mold (2) is meshed using triangular shell elements.

5. The method for designing the mold surface of a carbon fiber composite reflector according to claim 1, characterized in that: The finite element model of the reflector (1) is set as a carbon fiber resin matrix composite material; The finite element model of the reflector (1) is divided into a glass state and a rubber state. The Young's modulus, shear modulus, Poisson's ratio and thermal expansion coefficient of the finite element model of the reflector (1) in the glass state are set along the X, Y and Z directions. The Young's modulus, shear modulus, Poisson's ratio and thermal expansion coefficient of the finite element model of the reflector (1) in the rubber state are also set.

6. The method for designing the mold surface of a carbon fiber composite reflector according to claim 5, characterized in that: The finite element model of the reflector (1) is set in the glassy state with Young's modulus of 50 GPa, shear modulus of 3.4 GPa, Poisson's ratio of 0.3, and coefficient of thermal expansion of _____. × / ℃; Young's modulus in the Y direction is 50 GPa, shear modulus is 3.4 GPa, Poisson's ratio is 0.3, and coefficient of thermal expansion is × / ℃; Young's modulus in the Z direction is 8.5 GPa, shear modulus is 7 GPa, Poisson's ratio is 0.25, and coefficient of thermal expansion is × / ℃; The reflector (1) in its rubber state has a Young's modulus of 50 GPa in the X direction, a shear modulus of 3.4 GPa, a Poisson's ratio of 0.3, and a coefficient of thermal expansion of _____. × / ℃; Young's modulus in the Y direction is 50 GPa, shear modulus is 3.4 GPa, Poisson's ratio is 0.3, and coefficient of thermal expansion is × / ℃; Young's modulus in the Z direction is 8.5 GPa, shear modulus is 7 GPa, Poisson's ratio is 0.25, and coefficient of thermal expansion is × / ℃; The finite element model of mold (2) is set with Young's modulus of 170 GPa, shear modulus of 65.4 GPa, Poisson's ratio of 0.3, and coefficient of thermal expansion of _____. × / ℃; The spring stiffness of the spring unit is set to 0.1 N / mm.

7. The method for designing the mold surface of a carbon fiber composite reflector according to claim 1, characterized in that: Constraints are set for the X, Y, and Z displacements of point A; constraints are set for the Y and Z displacements of point B; and constraints are set for the Z displacement of point C.

8. The method for designing the mold surface of a carbon fiber composite reflector according to claim 5, characterized in that: The process of heating the finite element model of the reflector (1) and the finite element model of the mold (2) is as follows: At room temperature, the finite element model of reflector (1) is in a rubber state; the finite element model of reflector (1) is heated from room temperature of 20℃ at a heating rate of 0.5-2℃ / min, and when the temperature reaches 70℃-80℃, it is held for 30min, and then the heating rate continues to be increased at 0.5-2℃ / min until the temperature at which the finite element model of reflector (1) is solidified into a glass state is reached.

9. The method for designing the mold surface of a carbon fiber composite reflector according to claim 1, characterized in that: Coordinates after deformation for: In the formula, For the n nodes after heating, the th node is... The coordinates of each node in the X direction; For the n nodes after heating, the th node is... The coordinates of each node in the Y direction; For the n nodes after heating, the th node is... The coordinates of each node in the Z direction; Coordinates after deformation for: In the formula, For the finite element model of the reflector (1) after heating, the m-th node is... The coordinates of each node in the X direction; For the finite element model of the reflector (1) after heating, the m-th node is... The coordinates of each node in the Y direction; For the finite element model of the reflector (1) after heating, the m-th node is... The coordinates of each node in the Z direction; Coordinates after deformation for: In the formula, For the mold (2) after heating, the m-th node in the finite element model is... The coordinates of each node in the X direction; For the mold (2) after heating, the m-th node in the finite element model is... The coordinates of each node in the Y direction; For the mold (2) after heating, the m-th node in the finite element model is... The coordinates of each node in the Z direction.

10. The method for designing the mold surface of a carbon fiber composite reflector according to claim 1, characterized in that: Interface displacement for: Deformation for: In the formula, The stiffness matrix of the finite element model of the reflector (1); The stiffness matrix of the spring element at the interface of the mold (2) finite element model and the reflector (1) finite element model; Comprehensive deformation for: 。 11. The method for designing the mold surface of a carbon fiber composite reflector according to claim 1, characterized in that: Interface displacement for: Deformation for: In the formula, The stiffness matrix of the finite element model of the reflector (1); The stiffness matrix of the spring element at the interface of the mold (2) finite element model and the reflector (1) finite element model.

12. The method for designing the mold surface of a carbon fiber composite reflector according to claim 1, characterized in that: The overall deformation of the finite element model of the reflector in the glassy state (1) for: coordinates for: 。 13. The method for designing the mold surface of a carbon fiber composite reflector according to claim 6, characterized in that: The specific methods for cooling down are as follows: From the curing temperature, the temperature was reduced to room temperature (20°C) at a cooling rate of 1°C / min.

14. The method for designing the mold surface of a carbon fiber composite reflector according to claim 1, characterized in that: coordinate for: ； coordinates for: 。

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