A clamping force layout optimization method for toothed siding considering curing deformation

Abstract

The present invention discloses a method for optimizing the clamping force layout of a toothed wall panel taking curing deformation into consideration, and belongs to the technical field of aircraft assembly; the specific method is: obtaining the curing deformation distribution of a toothed composite skin; based on the curing deformation distribution of the toothed composite skin, combined with the N‑2‑1 positioning principle, establishing a composite toothed wall panel assembly simulation model taking curing deformation into consideration, calculating the warping angle of the toothed area and the absolute average deformation value of the toothed wall panel surface, and establishing a composite toothed wall panel clamping layout optimization mathematical model; taking the warping angle of the toothed area and the absolute average deformation value of the toothed wall panel surface as optimization targets, adopting a multi-objective grey wolf optimization algorithm, and obtaining the optimal layout of the clamping force distribution of the composite toothed wall panel taking curing deformation into consideration. The present invention solves the problems that the prior art has difficulty in ensuring the spatial accuracy of the wall panel when producing composite toothed wall panels, and is prone to secondary deformation and out-of-tolerance.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft assembly, and in particular relates to a method for optimizing the clamping force layout of a toothed wall panel taking solidification deformation into consideration. Background Art

[0002] At present, most of the research on aircraft panel assembly deformation focuses on product deformation caused by assembly conditions during the assembly process, and there are few studies that comprehensively consider curing deformation and assembly deformation. For example, the disclosed large-scale composite fuselage panel assembly clamping layout optimization method considers panel deformation, internal stress level and tooling cost to perform multi-objective optimization on discrete clamping layout, so as to achieve high-precision, high-performance and low-cost assembly clamping positioning of large composite fuselage panels; the combined prediction method for aircraft panel assembly deviation, this method uses Adam optimized BP neural network prediction model and substructure technology, and realizes the full consideration of the deviation caused by assembly relationship, assembly process, etc. under the condition of considering the initial error of parts, and accurately predicts the panel assembly deformation; the aircraft large component pre-connection layout and multi-constraint action sequence optimization method, this method establishes a large component pre-connection assembly quality prediction model based on different pre-connection layouts and sequences through finite element analysis and neural network, and establishes a multi-constraint action sequence optimization model based on this model, so as to achieve rapid search for the optimization of aircraft large component pre-connection and sequence, thereby improving assembly efficiency, reducing assembly gaps, and improving assembly quality.

[0003] The above methods and related technologies do not involve the influence of curing deformation on the assembly of wall panels, nor do they study thin-walled parts with specific shape characteristics, and there are still deficiencies in guiding the production process of toothed wall panels. Therefore, designing a suitable clamping force layout under the condition of considering curing deformation is of great significance to improving the assembly accuracy of composite toothed wall panels.

[0004] At present, a large number of toothed wall panels are used in advanced stealth aircraft to achieve better stealth performance. However, due to the large size of the toothed wall panels and their weak overall rigidity, they are easily affected by assembly conditions (gravity field, clamping layout, clamping error and clamping force, etc.) during the assembly stage, resulting in assembly deformation, causing gaps and step differences between the wall panels after assembly with the fuselage, which in turn affects the aerodynamic shape and stealth performance of the aircraft surface. On the other hand, the proportion of composite materials used in aircraft structures continues to increase, but there is little research on the forming and assembly process of composite toothed wall panels: traditional toothed wall panels are metal parts, and the serrated edges are obtained by cutting with a five-axis machine tool after the skin is stretched and formed; while composite toothed wall panels are prepregs with toothed edges produced during the blanking process. During the subsequent curing process, the wall panel edge shape changes dramatically and the internal interaction of the materials is significantly different, resulting in large deformation of the wall panel after curing and poor shape accuracy.

[0005] For composite toothed wall panels, production units are still in an empirical production mode, obtaining empirical data through repeated trials and then performing deformation compensation. In the subsequent assembly process, the curing deformation of the wall panels in their initial state is rarely considered. The fixtures manufactured according to the design data are difficult to ensure the spatial accuracy of the wall panels, and are prone to secondary deformation and out-of-tolerance problems. Summary of the invention

[0006] Technical issues to be solved:

[0007] In order to avoid the shortcomings of the prior art, the present invention provides a method for optimizing the clamping force layout of toothed wall panels taking curing deformation into consideration, taking composite toothed wall panels as the object, starting from the process flow of composite toothed wall panels, taking curing deformation and assembly process into consideration, and establishing a toothed wall panel assembly deformation simulation model based on the "N-2-1" positioning layout principle; taking the overall deformation of the toothed wall panels and the warping angle deformation of the toothed area as the optimization targets. The present invention solves the problems that the prior art has difficulty in ensuring the spatial accuracy of the wall panels when producing composite toothed wall panels, and is prone to secondary deformation and out-of-tolerance.

[0008] The technical solution of the present invention is: a method for optimizing the clamping force layout of a toothed wall panel considering solidification deformation, and the specific steps are as follows:

[0009] Obtaining the curing deformation distribution of the composite toothed skin;

[0010] Based on the curing deformation distribution of composite toothed skin and combined with the N-2-1 positioning principle, a composite toothed panel assembly simulation model considering curing deformation is established, the warping angle of the toothed area and the absolute average deformation value of the toothed panel surface are calculated, and a mathematical model for optimizing the clamping layout of composite toothed panel is established.

[0011] Taking the warping angle of the toothed area and the absolute average deformation value of the toothed panel surface as optimization targets, a multi-objective grey wolf optimization algorithm is used to obtain the optimal layout of the clamping force distribution of the composite toothed panel considering the curing deformation.

[0012] A further technical solution of the present invention is: the method for obtaining the curing deformation distribution of the composite material toothed skin is:

[0013] Based on the sequential coupling modeling method of composite materials, a temperature-curing degree simulation model of the composite tooth-shaped skin is first established to obtain the curing degree and temperature of the nodes during the curing process; then a curing deformation simulation model of the composite tooth-shaped skin is established; then, the curing degree and temperature are used as boundary conditions to import the curing deformation simulation model of the composite tooth-shaped skin, and the curing deformation distribution of the composite tooth-shaped skin is calculated.

[0014] A further technical solution of the present invention is: the modeling method for obtaining the curing deformation distribution of the composite material toothed skin is:

[0015] The curing kinetic equation of the composite material is constructed and the expression is as follows:

[0016]

[0017] Wherein, α is the degree of curing; t is the reaction time; dα / dt is the curing rate; is the curing degree function; T is temperature; is the reaction rate function;

[0018] The thermal-chemical model of composite material curing is constructed, and the expression is as follows:

[0019]

[0020] In the formula, , , represent the thermal conductivity of the composite material in the x, y, and z directions, respectively; represents the density of the composite material,

[0021] represents the specific heat capacity of the composite material; Indicates the heat release rate of the resin curing reaction;

[0022] Based on the composite material curing kinetic equation and composite material curing thermal-chemical model, a composite material tooth-shaped skin temperature-curing degree simulation model is established to obtain the curing degree and temperature of the nodes during the composite material tooth-shaped skin curing process;

[0023] The time-varying evolution model of composite materials is constructed, and the expression is as follows:

[0024]

[0025] In the formula, Er represents the elastic modulus of the resin, the superscripts 0 and 1 represent the uncured and cured states of the resin, respectively; α represents the degree of curing, Indicates the degree of cure at the gel point; ;

[0026] Construct a residual stress calculation model for composite materials, and the expression is as follows:

[0027]

[0028] Where C is the stiffness matrix of the composite material; ε is the total strain; ε t is the thermal strain; ε c is the chemical strain; ΔT is the curing temperature difference; β is the thermal expansion coefficient of the resin; γ is the chemical shrinkage coefficient; Δα is the change in the degree of curing;

[0029] Based on the composite material time-varying evolution model and composite material residual stress calculation model, a composite material tooth-shaped skin curing deformation simulation model is established;

[0030] The curing degree and temperature of the nodes during the curing process of the composite toothed skin are taken as boundary conditions, and the curing deformation simulation model of the composite toothed skin is introduced to calculate the curing deformation distribution of the composite toothed skin.

[0031] A further technical solution of the present invention is: the method for establishing a composite material toothed wall panel assembly simulation model taking into account curing deformation is:

[0032] The composite toothed skin after curing deformation is calculated based on the composite toothed skin curing deformation simulation model, and the composite toothed skin after curing deformation is imported into the finite element software as the initial state of the positioning and clamping stage;

[0033] Based on the composite toothed skin after solidification and deformation, a toothed wall panel assembly simulation model of the long stringer, the pallet and the skin is established in the finite element software;

[0034] Combining the N-2-1 positioning principle and the skin-long stringer assembly process, the boundary conditions and loads of the composite toothed panel assembly simulation model considering the curing deformation are determined.

[0035] A further technical solution of the present invention is: the boundary conditions and loads of the composite material toothed wall panel assembly simulation model considering curing deformation are:

[0036] Boundary condition settings for the composite toothed skin: limit the displacement of the composite toothed skin in the X direction, limit the displacement of the bottom surface of the composite toothed skin in the Y direction, and limit the rotation of the composite toothed skin in the Z direction;

[0037] Boundary condition settings of the inner pallet in the pallet: the inner pallet is set as a rigid body, the reference point is bound and set to be completely fixed;

[0038] Setting boundary conditions for the long stringer: limit the displacement in the X and Y directions at both ends of the long stringer;

[0039] The clamping force applied to the composite toothed skin is set, M reference points are established on the outer surface of the composite toothed skin, the M reference points are bound to the shape of the composite toothed skin, and concentrated force loads are applied to the reference points in the positive direction of the Z axis.

[0040] A further technical solution of the present invention is: the method for establishing a composite material toothed wall panel clamping layout optimization mathematical model is:

[0041] The clamping layout of the composite toothed wall panel is established as the design variable, and the coordinates of each clamping point are used to represent the clamping layout. The expression is as follows:

[0042]

[0043] In the formula, X is the design variable, represents the position coordinates of the i-th clamping point, N Indicates the number of clamping points;

[0044] The optimization objective function is constructed with the warping angle of the toothed area and the absolute average deformation value of the toothed wall panel surface as the optimization targets; the functional expression of the warping angle of the toothed area is:

[0045]

[0046]

[0047] In the formula, is the angle between the theoretical plane and the best fitting plane; is the warping angle value of the i'th tooth shape area; H is the number of toothed areas in the toothed skin; n1 is the normal vector of the best fitting plane, and n2 is the normal vector of the theoretical plane;

[0048] The function expression of the absolute average deformation value of the toothed wall panel surface is:

[0049]

[0050] In the formula, K is the number of unit nodes of the composite toothed skin finite element model; is the i"th unit node in the composite toothed skin after assembly deformation Coordinate value; is the i"th unit node in the non-deformed composite toothed skin Coordinate value;

[0051] The constraint conditions for clamping layout optimization are established, and the expression is:

[0052]

[0053]

[0054]

[0055]

[0056] In the formula, p irepresents the position coordinates of the i-th clamping point, p j represents the position coordinates of the jth clamping point; Ω represents the feasible domain of the clamping point layout; L represents the interference distance; N represents the number of clamping points; M represents the maximum number of clamping points provided by the tooling; SDVi(X) It represents the failure criterion of the internal unit of the composite toothed skin;

[0057] According to the design variables, optimization objective function and constraint condition analytical expressions, a mathematical model for optimizing the clamping layout of composite material toothed wall panels is established, and its expression is:

[0058]

[0059]

[0060]

[0061] A further technical solution of the present invention is: the multi-objective grey wolf optimization algorithm includes the following operations:

[0062] A patching algorithm is introduced on the basis of the original multi-objective grey wolf optimization algorithm. When an infeasible solution appears during the iteration process, the infeasible solution is transformed into a feasible solution through patching to ensure the feasibility of the clamping force layout.

[0063] The clamping force is arranged in a set area. The repair algorithm traverses the clamping force position and checks it. When an interfering solution appears during the iteration process, that is, the clamping force position does not meet the constraint conditions, the interfering solution is repaired so that the clamping force position is randomly distributed to the set area, so that it is converted into a feasible solution and invalid iteration is avoided.

[0064] A further technical solution of the present invention is: the method of using the multi-objective grey wolf optimization algorithm to obtain the optimal layout of the clamping force distribution of the composite material toothed wall panel considering the curing deformation is as follows:

[0065] Write the multi-objective gray wolf optimization algorithm, set the gray wolf population size, maximum number of iterations, archive size, number of dimensional grids, leader selection pressure parameter, archive member deletion pressure parameter, clamping force value area range, and maximum number of clamping points;

[0066] Within the feasible region of the clamping point, the Latin hypercube sampling method LHS is used to generate the initial population and initialize the coefficient vector ;

[0067] Based on the layout of the generated parent population, the position of the clamping force is updated in the composite toothed wall panel assembly simulation model considering curing deformation, and the corresponding absolute average deformation of the toothed wall panel surface and the warping angle of the toothed area under different clamping layouts in the parent population are obtained through simulation analysis, and the non-dominated Pareto optimal solution is found and archived;

[0068] Determine whether the population in the archive exceeds the archive size. If so, it needs to be adjusted according to the adaptive grid rules;

[0069] Select the positions of alpha gray wolf, beta gray wolf, and delta gray wolf from the population, and based on the positions of the three gray wolves, determine the position of omega gray wolf and update the coefficient vector ;

[0070] Repeat the above steps until the maximum number of iterations is reached, the optimization is completed, and the Pareto frontier set is obtained;

[0071] Select the most appropriate Pareto optimal solution based on the obtained Pareto frontier set and actual engineering needs.

[0072] Beneficial Effects

[0073] The beneficial effects of the present invention are as follows: based on the curing deformation simulation calculation results of the composite material toothed skin, the present invention establishes a finite element model of the toothed wall panel assembly clamping layout taking into account the curing deformation; then establishes a toothed wall panel clamping layout optimization method based on the multi-objective grey wolf optimization algorithm, describes the entire optimization process, and carries out optimization analysis in combination with the finite element model of the toothed wall panel clamping layout taking into account the curing deformation and the multi-objective grey wolf optimization algorithm; finally, selects the most appropriate Pareto optimal solution according to the actual needs of the project.

[0074] Different from the traditional empirical trial and error method, the method of the present invention utilizes technologies such as finite element analysis and numerical optimization to find a more optimal clamping force layout through theoretical calculations, so as to avoid the cost waste caused by repeated experiments and trials and achieve lower calculation costs. By comparing with the conventional layout, the clamping force layout obtained by this method can obtain a smaller absolute average deformation value of the wall panel surface and a smaller angular warping angle value of the toothed area, which indicates that the deformation of the wall panel is effectively controlled, thereby improving the effect and quality of the assembly process of the composite toothed wall panel. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 This is a flow chart of a method for optimizing the clamping force layout of a toothed wall panel taking into account solidification deformation according to an embodiment of the present invention;

[0076] Figure 2 is a node temperature distribution cloud diagram calculated by a composite material tooth-shaped skin temperature-curing degree simulation model in an embodiment of the present invention;

[0077] Figure 3 is a deformation distribution cloud diagram calculated by the curing deformation simulation model in the embodiment of the present invention;

[0078] Figure 4 Schematic diagram of a composite material toothed wall panel assembly simulation model according to an embodiment of the present invention;

[0079] Figure 5 is a schematic diagram of a feasible domain of the clamping point layout in an embodiment of the present invention;

[0080] Figure 6 Schematic diagram of the Pareto frontier set obtained by iterative optimization of the multi-objective grey wolf optimization algorithm in an embodiment of the present invention;

[0081] Figure 7 is a schematic diagram of the clamping layout distribution corresponding to the Pareto solution in an embodiment of the present invention;

[0082] Figure 8 is a wall panel assembly deformation cloud diagram after optimization by the multi-objective grey wolf optimization algorithm in an embodiment of the present invention (relative to the assembly deformation in the curing stage);

[0083] Fig. 9 It is the conventional layout wall panel assembly deformation cloud diagram (relative to the assembly deformation in the curing stage);

[0084] Fig.10 It is a comparison cloud diagram of the actual assembly deformation of the wall panels before and after the multi-objective Grey Wolf optimization algorithm is optimized in the embodiment of the present invention. DETAILED DESCRIPTION

[0085] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0086] Based on the existing technology, composite toothed wall panels are still in an empirical production mode, and empirical data are obtained through repeated trial production before deformation compensation. In the subsequent assembly process, the curing deformation of the wall panels in the initial state is rarely considered. The fixture manufactured according to the design data is difficult to ensure the spatial accuracy of the wall panels, and secondary deformation and out-of-tolerance problems are easily generated. The present invention provides a method for optimizing the clamping force layout of toothed wall panels considering curing deformation, and the specific steps are as follows:

[0087] Step 1: Obtain the curing deformation distribution of the composite toothed skin;

[0088] Based on the composite material sequential coupling modeling method, a composite material tooth-shaped skin temperature-curing degree simulation model is first established to obtain the curing degree and temperature of the nodes during the curing process; then a composite material tooth-shaped skin curing deformation simulation model is established; then the curing degree and temperature are used as boundary conditions, and the composite material tooth-shaped skin curing deformation simulation model is imported to calculate the curing deformation distribution of the composite material tooth-shaped skin;

[0089] Step 2: Based on the curing deformation distribution of the composite toothed skin and combined with the N-2-1 positioning principle, a composite toothed panel assembly simulation model considering curing deformation is established, the warping angle of the toothed area and the absolute average deformation value of the toothed panel surface are calculated, and a mathematical model for optimizing the clamping layout of the composite toothed panel is established;

[0090] Step 3: Taking the warping angle of the toothed area and the absolute average deformation value of the toothed wall panel surface as optimization targets, a multi-objective grey wolf optimization algorithm is used to obtain the optimal layout of the clamping force distribution of the composite material toothed wall panel considering the curing deformation.

[0091] The following is combined with Figure 1-10 The technical solution of the present invention is described in further detail.

[0092] This embodiment provides a method for optimizing the clamping force layout of a toothed wall panel taking into account solidification deformation, such as Figure 1 As shown, the optimization method comprises the following steps:

[0093] S1: Based on the composite material sequential coupling modeling method, a composite material tooth-shaped skin temperature-curing degree simulation model is first established to obtain the curing degree and temperature of the nodes during the curing process; the node curing degree and temperature are used as boundary conditions and passed to the composite material tooth-shaped skin curing deformation simulation model to obtain the curing deformation distribution of the composite material tooth-shaped skin;

[0094] The specific steps of step S1 are:

[0095] S101: Based on the phenomenological model, a composite material curing kinetic equation is established, and its mathematical expression is:

[0096]

[0097] Wherein, α is the degree of curing; t is the reaction time; dα / dt is the curing rate; is the curing degree function; T is the temperature; is the reaction rate function;

[0098] In this example, the reaction rate function Following the Arrhenius criterion, the formula is:

[0099]

[0100] In the formula, A is the frequency factor, ΔE is the reaction activation energy; R is the universal gas constant, its value is 8.3145 J / (mol·K);

[0101] In this embodiment, the curing degree function The autocatalytic curing kinetic model is adopted, and the formula is:

[0102]

[0103] In the formula, m and n are the reaction orders;

[0104] S102: Based on Fourier's heat conduction law and energy balance principle, a thermal-chemical model for composite material curing is established, and its formula is:

[0105]

[0106] In the formula, , , represent the thermal conductivity of the composite material in the x, y, and z directions, respectively; represents the density of the composite material,

[0107] represents the specific heat capacity of the composite material; Indicates the heat release rate of the resin curing reaction;

[0108] In this embodiment, the heat release rate Q of the resin curing reaction is expressed as:

[0109]

[0110] In the formula, Indicates resin density; represents the fiber volume fraction; It indicates the heat released by the resin curing reaction per unit mass.

[0111] S103: Based on the curing kinetics equation and the thermo-chemical model, the USDFLD, DISP, FILM and HETVAL subroutines are written using the secondary development function of ABAQUS software to establish a composite tooth-shaped skin temperature-curing degree simulation model, and finally the temperature and curing degree of each node of the composite tooth-shaped skin after curing are obtained;

[0112] In this embodiment, the composite toothed skin is composed of a rectangular area and a toothed area, the left and right teeth are symmetrical, and the upper and lower teeth are of different sizes. Its specific dimensions are: long tooth distance 906mm, short tooth distance 846mm, width 342mm, thickness 2.4mm, a total of 16 layers, and a single layer thickness of 0.15mm;

[0113] In this embodiment, the dimensions of the flat plate mold established are: 1000 mm long, 700 mm wide, and 10 mm thick;

[0114] In this embodiment, the composite toothed skin is made of T700 / 7901 carbon fiber reinforced epoxy resin composite material, and the ply method is [45 / 0 / -45 / 90]2s. Its thermochemical performance parameters are shown in Table 1, and the curing kinetic parameters of 7901 epoxy resin are shown in Table 2. The flat mold material is 6061 aluminum alloy, and its thermochemical performance parameters are shown in Table 3;

[0115] Table 1 Thermochemical properties of T700 / 7901 composites

[0116]

[0117] Table 2 Curing kinetic parameters of 7901 epoxy resin

[0118]

[0119] Table 3 Thermochemical properties of 6061 aluminum alloy

[0120]

[0121] In this embodiment, the temperature results calculated by the composite material tooth-shaped skin temperature-curing degree simulation model are as follows: Figure 2 As shown;

[0122] S104: Establish a composite material time-varying evolution model, the formula of which is:

[0123]

[0124] In the formula, Er represents the elastic modulus of the resin, the superscripts 0 and 1 represent the uncured and cured states of the resin, respectively; α represents the degree of curing. In this embodiment, the degree of curing at the gel point is determined to be 0.35, that is, ; The calculation formula of αmod is: ;

[0125] S105: Considering the chemical shrinkage reaction and thermal expansion effect during the curing process, the chemical shrinkage coefficient and thermal expansion coefficient of the resin are determined, and a residual stress calculation model for the composite material is established.

[0126] In this example, only the chemical shrinkage reaction after the gel point is considered, and the chemical shrinkage of the 7901 resin from the gel point to the glassy state is determined to be 0.6%;

[0127] In this embodiment, considering that the thermal expansion coefficient of the resin in the rubber state and the viscous flow state is 2.5 times that in the glass state, the thermal expansion coefficient of the resin can be expressed as:

[0128]

[0129] In the formula, is the thermal expansion coefficient of the resin, and the superscripts 0 and 1 represent the rubbery and glassy states; represents the longitudinal and transverse thermal expansion coefficient of the fiber, E represents the elastic modulus, represents Poisson's ratio; subscript r represents resin, subscript f represents fiber, subscript 1 represents parallel to the fiber direction, and subscript 2 represents perpendicular to the fiber direction;

[0130] The residual stress calculation model of composite materials is as follows:

[0131]

[0132] Where C is the stiffness matrix of the composite material; ε is the total strain; ε t is the thermal strain; ε c is the chemical strain; Δ T is the curing temperature difference; β is the thermal expansion coefficient of the resin; γ is the chemical shrinkage coefficient; Δα is the change in the degree of curing;

[0133] S106: Based on the composite material time-varying evolution model and residual stress calculation model, ABAQUS software secondary development function is used to write UMAT and UEXPAN subroutines to establish a composite material tooth-shaped skin curing deformation simulation model;

[0134] In this embodiment, the mechanical property parameters of T700 / 7901 are shown in Table 4 and Table 5:

[0135] Table 4 Properties of T700 fiber

[0136]

[0137] Table 5 Properties of 7901 resin

[0138]

[0139] S107: Import the result of the temperature-curing degree model as a predefined field into the curing deformation model, add corresponding boundary conditions, interactions and loads, and calculate the tooth-shaped skin deformation distribution cloud map;

[0140] In this embodiment, the calculated maximum deformation is 3.163 mm, and the deformation distribution cloud diagram is as follows: Figure 3 shown.

[0141] S2: Based on the curing deformation distribution of the composite toothed skin and combined with the N-2-1 positioning principle, a composite toothed panel assembly simulation model considering curing deformation is established, the warping angle of the toothed area and the absolute average deformation value of the toothed panel surface are calculated, and a mathematical model for optimizing the clamping layout of the composite toothed panel is established;

[0142] The specific steps of step S2 are:

[0143] S201: importing the composite toothed skin obtained by calculating the composite toothed wall panel curing deformation simulation model into ABAQUS as the initial state of the positioning and clamping stage;

[0144] S202: Establishing a toothed wall panel assembly model including a long stringer, a card plate and a skin, and determining the boundary conditions and loads of the assembly simulation model in combination with the N-2-1 positioning principle and the skin-long stringer assembly process;

[0145] In this embodiment, the length of the long stringer is , inner card board size The skin presser, positioning block, outer clamp, etc. are set in the form of load and boundary conditions. The toothed wall panel assembly simulation model established is as follows: Figure 4 As shown;

[0146] In this embodiment, the toothed skin is made of T700 / 7901 CFRP composite material, and the long stringer and the pallet are made of aluminum alloy material, and their material properties are shown in Table 6 and Table 7;

[0147] Table 6 Material properties of T700 / 7901 unidirectional laminates

[0148]

[0149] Table 7 Material properties of aluminum alloy

[0150]

[0151] In this embodiment, the boundary conditions and loads of the assembly simulation model are set as follows:

[0152] Boundary condition setting for composite toothed skin: limit the displacement of the left side of the skin in the U1 direction (i.e. constrain its movement in the X direction), limit the displacement of the bottom surface of the skin in the U2 direction and the rotation in the U3 direction (i.e. constrain its movement in the Y direction and rotation in the Z direction). Boundary condition setting for the inner plate: the inner plate is set as a rigid body, and the reference points are bound and set to be completely fixed. Boundary condition setting for the long stringer: limit the displacement of the two ends of the long stringer in the U1 and U2 directions. In the LOAD module, set the clamping force applied to the composite toothed skin, establish M reference points on the outer surface of the skin (M does not exceed 16, that is, the maximum number of clamps that the outer plate can provide), bind the M reference points to the skin shape, apply concentrated force loads to the reference points, and the direction is along the positive direction of the Z axis; the clamping force is set to 50N. S203: Establish the clamping layout as a design variable. The clamping layout is represented by the coordinates of each clamping point, and its mathematical expression is:

[0153]

[0154] In the formula, X represents the design variable, represents the position coordinates of the i-th clamping point, N Indicates that there are a total of N Clamping point;

[0155] S204: Taking the warping angle of the toothed area and the absolute average deformation value of the toothed wall panel surface as the optimization target, an optimization objective function is constructed; the function expression of the warping angle of the toothed area is:

[0156]

[0157]

[0158] In the formula, represents the angle between the theoretical plane and the best fit plane; represents the warping angle value of the i'th tooth shape area; H represents the number of toothed areas in the toothed skin; n1 represents the normal vector of the best fitting plane, and n2 represents the normal vector of the theoretical plane;

[0159] In this embodiment, the least square method is used to perform the best plane fitting on the spatial nodes of the toothed area in the finite element model of the toothed wall panel. 1 , n 2 The calculation method is as follows:

[0160] The general expression for the plane equation is: , where A, B, C, and D are the coefficients corresponding to the plane equation. Generally, A, B, and C are not all 0;

[0161] As ordered , then the above plane method can be transformed into:

[0162]

[0163] make , , , but:

[0164]

[0165] Obtain , , The value of can be used to calculate the best fitting plane equation. The formula is as follows:

[0166]

[0167]

[0168] In the formula, X' is a data matrix, a row represents a data point, and a column represents an independent variable; is the spatial coordinate value of the tooth area node after deformation in the finite element; Y' is the observation value vector; D is the coefficient vector to be solved;

[0169] Then the normal vector of the best fitting plane can be obtained , assuming the theoretical plane normal vector , then the angle between the two planes is calculated as follows:

[0170]

[0171]

[0172] The function expression of the absolute average deformation value of the toothed wall panel surface is:

[0173]

[0174] In the formula, is the number of unit nodes of the composite toothed skin finite element model; is the i"th unit node in the composite toothed skin after assembly deformation Coordinate value; is the i"th unit node in the non-deformed composite toothed skin Coordinate value.

[0175] S205: Establishing the constraint condition for clamping layout optimization, the expression is:

[0176]

[0177]

[0178]

[0179]

[0180] In the formula, p i represents the position coordinates of the i-th clamping point, p j represents the position coordinates of the jth clamping point; Ω represents the feasible domain of the clamping point layout; L represents the interference distance; N represents the number of clamping points; M represents the maximum number of clamping points provided by the tooling; SDVi(X) It represents the failure criterion of the internal unit of the composite toothed skin;

[0181] In this embodiment, the feasible domain of the clamping point layout is as follows: Figure 5 As shown;

[0182] In this embodiment, SDVi(X) The 3D Hashin criterion is selected, and its formula is:

[0183]

[0184] In the formula, They are the damage onset criteria for fiber tensile failure, fiber compression failure, matrix tensile failure and matrix compression failure respectively. They are the principal stress and shear stress along the fiber direction (direction 1), the perpendicular fiber direction (direction 2), the ply direction (direction 3) and the corresponding tangent plane. are longitudinal tensile and compressive strength, respectively. are the transverse tensile and compressive strengths, They are the shear strength along the 3 directions, 2 directions and 1 direction in the plane respectively.

[0185] S206: According to the design variables, objective function, and constraint condition analytical expressions, a mathematical model for optimizing the clamping layout of toothed wall panels is established, and its expression is:

[0186]

[0187]

[0188]

[0189] S3: Taking the warping angle of the toothed area and the absolute average deformation of the toothed wall panel surface as optimization targets, a multi-objective grey wolf optimization algorithm is used to obtain the optimal layout of the clamping force distribution.

[0190] The specific steps of step S3 are:

[0191] S301: Import the composite tooth-shaped skin after solidification and deformation and establish an assembly finite element model, write a multi-objective gray wolf optimization algorithm, set the gray wolf population size N', the maximum number of iterations MaxIt, the archive size ArchiveSize, the number of dimensional grids nGrid, the leader selection pressure parameter beta', the archive member deletion pressure parameter gamma, the clamping force value range Ω, and the maximum number of clamping points M;

[0192] In this embodiment, the parameter settings of the multi-objective gray wolf optimization algorithm are shown in Table 8:

[0193] Table 8 Multi-objective grey wolf optimization algorithm parameters

[0194]

[0195] S302: In the feasible region of the clamping point, Latin hypercube sampling (LHS) is used to generate the initial population and initialize ;

[0196] S303: Based on the layout of the generated parent population, the position of the clamping force is updated in the finite element model, and the absolute average deformation of the toothed wall panel surface and the warping angle of the toothed area corresponding to different clamping layouts in the parent population are obtained through simulation analysis, and the non-dominated Pareto optimal solution is found and archived;

[0197] S304: Determine whether the population Archive in the archive exceeds the archive size ArchiveSize, if so, it needs to be adjusted according to the adaptive grid rule;

[0198] S305: Select the positions of alpha gray wolf, beta gray wolf, and delta gray wolf (i.e., optimal solution, good solution, and suboptimal solution) from the Archive population, and based on their positions, determine the position of omega gray wolf (i.e., candidate solution), and update ;

[0199] In this embodiment, the selection method of alpha gray wolf, beta gray wolf and delta gray wolf is as follows:

[0200] In the archive, through the roulette method, one is selected as the alpha wolf, beta wolf, and delta wolf in the least crowded area of ​​the search space. The probability calculation formula for each individual in the archive to be selected as the leader is:

[0201]

[0202] In the formula, c is a constant greater than 1, N i is the total number of individuals in the population to which the individual belongs.

[0203] In this embodiment, the position calculation method of the omega gray wolf is as follows:

[0204]

[0205]

[0206]

[0207] In the formula, are the distance vectors between the omega wolf and the leader alpha wolf, beta wolf, and delta wolf respectively; is the position vector of alpha wolf, beta wolf, and delta wolf; is the position vector of the omega gray wolf in the tth iteration, is the position vector of the omega gray wolf in the t+1th iteration.

[0208] In this embodiment, the coefficient vector The calculation method is as follows:

[0209]

[0210] In the formula, It decreases linearly from 2 to 0 during the iteration. is a random vector between 0 and 1;

[0211] S306: Repeat S303 to S305 until the maximum number of iterations MaxIt is reached, the optimization is completed, and the Pareto frontier set is obtained;

[0212] S307: Based on the obtained Pareto frontier set, select the most appropriate Pareto optimal solution according to the actual needs of this project.

[0213] In this embodiment, the Pareto frontier set obtained by optimizing the iteration through the multi-objective grey wolf optimization algorithm is as follows: Figure 6 As shown in the figure, it can be seen that the two optimization goals of absolute average deformation value and warping angle of tooth-shaped area cannot be optimal at the same time. In this embodiment, the warping angle of tooth-shaped area is given priority while ensuring that the average absolute deformation value of the wall panel surface is small. The solution with an absolute average deformation value of 0.1218 mm and a warping angle of 0.1688° in the tooth-shaped area is selected. The clamping layout distribution corresponding to this solution is shown in the figure below. Figure 7 As shown, the assembly deformation cloud diagram is as follows Figure 8 As shown;

[0214] In this embodiment, a set of conventional clamping layouts is set as a comparison. A clamping force of 50N is applied to the wall panel every 300mm, and 4 clamping points are arranged in the toothed area. The assembly deformation results obtained by the conventional layout are as follows: Fig. 9 As shown;

[0215] Compare the assembly deformation results of the conventional layout and the optimized layout. The actual deformation comparison cloud diagram is as follows: Fig.10 As shown. It can be seen that the overall deformation of the optimized wall panel is small, the deformation value of 90% of the area is less than 0.2mm, the maximum deformation is 0.6mm, which occurs at the right tooth tip, and the overall deformation distribution of the four tooth-shaped areas is relatively uniform, indicating that the warping angle of the tooth-shaped area is small. However, the overall deformation value of the wall panel in the conventional layout is unevenly distributed, with the maximum deformation of 1.6mm, which occurs at the left tooth tip, and the deformation distribution of the four tooth-shaped areas is uneven, indicating that the warping angle of the tooth-shaped area is large; the absolute average deformation value of the conventional layout is 0.2158mm, and the warping angle of the tooth-shaped area is 0.5417°. Compared with the conventional layout, the optimized layout reduces the two deformation measurement indicators by 43.56% and 68.84% respectively, which proves the effectiveness of the optimization method proposed in the present invention.

[0216] In summary, the present invention establishes a finite element model of the assembly clamping layout of the toothed wall panel considering the curing deformation based on the simulation calculation results of the curing deformation of the toothed skin of the composite material; then establishes a toothed wall panel clamping layout optimization method based on the multi-objective grey wolf optimization algorithm, describes the entire optimization process, and combines the finite element model of the clamping layout of the toothed wall panel considering the curing deformation and the multi-objective grey wolf optimization algorithm to carry out optimization analysis; finally, the most appropriate Pareto optimal solution is selected according to the actual needs of the project. Different from the traditional empirical trial and error method, the method of the present invention uses finite element analysis and numerical optimization techniques to find a better clamping force layout through theoretical calculation, avoiding the cost waste caused by repeated experimental trials and achieving a lower calculation cost; by comparing with the conventional layout, the clamping force layout obtained by this method can obtain a smaller absolute average deformation value of the wall panel surface and a smaller angle warping angle value of the toothed area, which shows that the wall panel deformation is effectively controlled and the effect and quality of the composite material toothed wall panel assembly process are improved.

[0217] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A method for optimizing the clamping force layout of toothed wall panels considering curing deformation, characterized in that The specific steps are as follows: Obtaining the curing deformation distribution of the composite toothed skin; Based on the curing deformation distribution of composite toothed skin and combined with the N-2-1 positioning principle, a composite toothed panel assembly simulation model considering curing deformation is established, the warping angle of the toothed area and the absolute average deformation value of the toothed panel surface are calculated, and a mathematical model for optimizing the clamping layout of composite toothed panel is established. Taking the warping angle of the toothed area and the absolute average deformation value of the toothed wall panel surface as optimization targets, a multi-objective grey wolf optimization algorithm is used to obtain the optimal layout of the clamping force distribution of the composite toothed wall panel considering the curing deformation; The method for establishing the optimized mathematical model for the clamping layout of the composite material toothed wall panel is as follows: The clamping layout of the composite toothed wall panel is established as the design variable, and the coordinates of each clamping point are used to represent the clamping layout. The expression is as follows: In the formula, X is the design variable, represents the position coordinates of the i-th clamping point, N Indicates the number of clamping points; The optimization objective function is constructed with the warping angle of the toothed area and the absolute average deformation value of the toothed wall panel surface as the optimization targets; the functional expression of the warping angle of the toothed area is: In the formula, is the angle between the theoretical plane and the best fitting plane; is the warping angle value of the i'th tooth shape area; H is the number of toothed areas in the toothed skin; n1 is the normal vector of the best fitting plane, and n2 is the normal vector of the theoretical plane; The function expression of the absolute average deformation value of the toothed wall panel surface is: In the formula, K is the number of unit nodes of the composite toothed skin finite element model; is the i"th unit node in the composite toothed skin after assembly deformation Coordinate value; is the i"th unit node in the non-deformed composite toothed skin Coordinate value; The constraint conditions for clamping layout optimization are established, and the expression is: In the formula, p i represents the position coordinates of the i-th clamping point, p j represents the position coordinates of the jth clamping point; Ω represents the feasible domain of the clamping point layout; L represents the interference distance; N represents the number of clamping points; M represents the maximum number of clamping points provided by the tooling; SDVi(X) It represents the failure criterion of the internal unit of the composite toothed skin; According to the design variables, optimization objective function and constraint condition analytical expressions, a mathematical model for optimizing the clamping layout of composite material toothed wall panels is established, and its expression is: 。 2. According to claim 1, a method for optimizing the clamping force layout of a toothed wall panel taking curing deformation into consideration is characterized in that: The method for obtaining the curing deformation distribution of the composite tooth-shaped skin is as follows: based on the composite sequential coupling modeling method, firstly, a composite tooth-shaped skin temperature-curing degree simulation model is established to obtain the curing degree and temperature of the node during the curing process; Then, a simulation model of the curing deformation of the composite toothed skin is established; then, the curing degree and temperature are used as boundary conditions, the simulation model of the curing deformation of the composite toothed skin is imported, and the curing deformation distribution of the composite toothed skin is calculated.

3. According to claim 2, a method for optimizing the clamping force layout of a toothed wall panel taking curing deformation into consideration is characterized in that: The modeling method for obtaining the curing deformation distribution of the composite material toothed skin is: The curing kinetic equation of the composite material is constructed and the expression is as follows: Wherein, α is the degree of curing; t is the reaction time; dα / dt is the curing rate; is the curing degree function; T is temperature; is the reaction rate function; The thermal-chemical model of composite material curing is constructed, and the expression is as follows: In the formula, , , represent the thermal conductivity of the composite material in the x, y, and z directions, respectively; represents the density of the composite material, represents the specific heat capacity of the composite material; Indicates the heat release rate of the resin curing reaction; Based on the composite material curing kinetic equation and composite material curing thermal-chemical model, a composite material tooth-shaped skin temperature-curing degree simulation model is established to obtain the curing degree and temperature of the nodes during the composite material tooth-shaped skin curing process; The time-varying evolution model of composite materials is constructed, and the expression is as follows: In the formula, Er represents the elastic modulus of the resin, the superscripts 0 and 1 represent the uncured and cured states of the resin, respectively; α represents the degree of curing, Indicates the degree of cure at the gel point; ; Construct a residual stress calculation model for composite materials, and the expression is as follows: Where C is the stiffness matrix of the composite material; ε is the total strain; ε t is the thermal strain; ε c is the chemical strain; Δ T is the curing temperature difference; β is the thermal expansion coefficient of the resin; γ is the chemical shrinkage coefficient; Δα is the change in degree of curing; Based on the composite material time-varying evolution model and composite material residual stress calculation model, a composite material tooth-shaped skin curing deformation simulation model is established; The curing degree and temperature of the nodes during the curing process of the composite toothed skin are taken as boundary conditions, and the curing deformation simulation model of the composite toothed skin is introduced to calculate the curing deformation distribution of the composite toothed skin.

4. The method for optimizing the clamping force layout of a toothed wall panel considering solidification deformation according to claim 3, characterized in that: The method for establishing a composite material toothed wall panel assembly simulation model taking into account curing deformation is: The composite toothed skin after curing deformation is calculated based on the composite toothed skin curing deformation simulation model, and the composite toothed skin after curing deformation is imported into the finite element software as the initial state of the positioning and clamping stage; Based on the composite toothed skin after solidification and deformation, a toothed wall panel assembly simulation model of the long stringer, the pallet and the skin is established in the finite element software; Combining the N-2-1 positioning principle and the skin-long stringer assembly process, the boundary conditions and loads of the composite toothed panel assembly simulation model considering the curing deformation are determined.

5. The method for optimizing the clamping force layout of a toothed wall panel considering solidification deformation according to claim 4, characterized in that: The boundary conditions and loads of the composite material toothed wall panel assembly simulation model considering curing deformation are: Boundary condition settings for the composite toothed skin: limit the displacement of the composite toothed skin in the X direction, limit the displacement of the bottom surface of the composite toothed skin in the Y direction, and limit the rotation of the composite toothed skin in the Z direction; Boundary condition settings of the inner pallet in the pallet: the inner pallet is set as a rigid body, the reference point is bound and set to be completely fixed; Setting boundary conditions for the long stringer: limit the displacement in the X and Y directions at both ends of the long stringer; The clamping force applied to the composite toothed skin is set, M reference points are established on the outer surface of the composite toothed skin, the M reference points are bound to the shape of the composite toothed skin, and concentrated force loads are applied to the reference points in the positive direction of the Z axis.

6. A method for optimizing the clamping force layout of a toothed wall panel taking curing deformation into consideration according to claim 5, characterized in that: The multi-objective grey wolf optimization algorithm includes the following operations: A patching algorithm is introduced on the basis of the original multi-objective grey wolf optimization algorithm. When an infeasible solution appears during the iteration process, the infeasible solution is transformed into a feasible solution through patching to ensure the feasibility of the clamping force layout. The clamping force is arranged in a set area. The repair algorithm traverses the clamping force position and checks it. When an interfering solution appears during the iteration process, that is, the clamping force position does not meet the constraint conditions, the interfering solution is repaired so that the clamping force position is randomly distributed to the set area, so that it is converted into a feasible solution and invalid iteration is avoided.

7. A method for optimizing the clamping force layout of a toothed wall panel taking solidification deformation into consideration according to claim 6, characterized in that: The method of using the multi-objective grey wolf optimization algorithm to obtain the optimal layout of the clamping force distribution of the composite toothed wall panel considering the curing deformation is as follows: Write the multi-objective gray wolf optimization algorithm, set the gray wolf population size, maximum number of iterations, archive size, number of dimensional grids, leader selection pressure parameter, archive member deletion pressure parameter, clamping force value area range, and maximum number of clamping points; Within the feasible region of the clamping point, the Latin hypercube sampling method LHS is used to generate the initial population and initialize the coefficient vector ; Based on the layout of the generated parent population, the position of the clamping force is updated in the composite toothed wall panel assembly simulation model considering curing deformation, and the corresponding absolute average deformation of the toothed wall panel surface and the warping angle of the toothed area under different clamping layouts in the parent population are obtained through simulation analysis, and the non-dominated Pareto optimal solution is found and archived; Determine whether the population in the archive exceeds the archive size. If so, it needs to be adjusted according to the adaptive grid rules; Select the positions of alpha gray wolf, beta gray wolf, and delta gray wolf from the population, and based on the positions of the three gray wolves, determine the position of omega gray wolf and update the coefficient vector ; Repeat the above steps until the maximum number of iterations is reached, the optimization is completed, and the Pareto frontier set is obtained; Select the most appropriate Pareto optimal solution based on the obtained Pareto frontier set and actual engineering needs.

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