Multi-working-condition optimization method for cross beam of multi-strategy gantry type automatic tape laying machine tool

Abstract

The invention provides a multi-working-condition optimization method for a cross beam of a multi-strategy gantry type automatic tape laying machine tool. The method comprises the steps that static and dynamic performance indexes of the cross beam under various typical working conditions are determined through a finite element analysis method; carrying out topological optimization on the cross beam according to the static performance indexes to obtain a conceptual model, and reconstructing to obtain an initial geometric model; sensitivity analysis is carried out, and a plurality of design parameters of the initial geometric model having great influence on the static performance index and the dynamic performance index are screened out as design variables; using the optimal Latin hypercube experiment to design sample points, and establishing a BP neural network as an agent model; an NSGA-III multi-objective optimization algorithm is adopted for solving, and a Pareto frontier solution set is obtained; and finally, assigning each target weight through an entropy weight TOPSIS method, sorting Pareto frontier solutions, and finally determining an optimal solution of the cross beam size parameters. In this way, topological optimization and size optimization strategies are combined, and static and dynamic performance indexes are improved while light weight of the cross beam is achieved.

Description

A Multi-Working Condition Optimization Method for the Crossbeam of a Multi-Strategy Gantry Automatic Tape Laying Machine Technical Field

[0001] This invention relates to the field of processing equipment technology, and more specifically, to a multi-condition optimization method for the crossbeam of a multi-strategy gantry-type automatic tape laying machine. Background Technology

[0002] Gantry-type tape layers are crucial core equipment in advanced composite material manufacturing, primarily used for the production and laying of large composite components such as fuselages and wings in the aerospace industry. Their working principle involves accurately laying prepreg tape onto the mold surface and shaping it according to a pre-set layup trajectory file. Unlike traditional gantry milling machines, tape layers prioritize layup accuracy and speed over traditional cutting forces and machining stability. Performance evaluation of tape layers mainly relies on indicators such as geometric accuracy, thermal error, and control system servo error. Due to the large span, high speed, and large size characteristics of gantry-type tape layers, their structural design faces more complex static and dynamic performance challenges. The crossbeam structure, in particular, as the main load-bearing component, has a profound impact on the overall rigidity, positioning accuracy, and dynamic characteristics of the machine tool. Therefore, how to comprehensively improve the static and dynamic performance of the crossbeam has become an urgent problem to be solved in the field of large machine tool manufacturing. Summary of the Invention

[0003] The present invention aims to at least solve the problem of poor static and dynamic performance of crossbeams in the prior art.

[0004] In view of this, one object of the present invention is to provide a multi-condition optimization method for the crossbeam of a multi-strategy gantry automatic tape laying machine.

[0005] To achieve the above objectives, the first aspect of the present invention provides a multi-condition optimization method for the crossbeam of a multi-strategy gantry-type automatic tape laying machine, comprising:

[0006] Step S1: Determine the static and dynamic performance indicators of the crossbeam under various typical working conditions using the finite element analysis method. The static performance indicators include the maximum total deformation of the crossbeam under various working conditions, and the dynamic performance indicators include the first natural frequency of the crossbeam.

[0007] Step S2: Based on the static performance indicators, perform topology optimization on the beam to obtain a conceptual model, and reconstruct the conceptual model to obtain the initial geometric model of the beam;

[0008] Step S3: Perform sensitivity analysis on the design parameters of the initial geometric model, and select several design parameters that have a significant impact on the static performance index and the dynamic performance index as design variables;

[0009] Step S4: Using the selected design variables as input and performance indicators as output, calculate the multiple sets of samples obtained from the optimal Latin hypercube experimental design, train the BP neural network model as a surrogate model, and use the NSGA-III multi-objective optimization algorithm to solve the Pareto front solution set.

[0010] Step S5: Assign weights to each objective using the entropy-weighted TOPSIS method and sort the Pareto front solutions to finally determine the optimal solution for the beam size parameters.

[0011] Optionally, step S4 specifically includes:

[0012] With the objectives of minimizing static performance indicators, maximizing dynamic performance indicators, and minimizing optimized quality, and constrained by the range of values ​​of the design variables, the NSGA-III algorithm is iterated.

[0013] In each iteration, the values ​​of the selected design variables are input into the trained neural network model for solving, so as to obtain the optimized quality, static performance index and dynamic performance index of the neural network model output.

[0014] After the algorithm converges, the Pareto front solution set of the design variables is obtained.

[0015] Optionally, step S5 includes:

[0016] The weights of each solution to the design variables are determined using the entropy weight method.

[0017] Based on the weights, calculate the proximity of each solution of the design variables to the ideal solution;

[0018] Based on the calculated proximity, the solutions for the design variables in the Pareto front solution set are sorted.

[0019] Optionally, the BP neural network model is trained in the following manner:

[0020] The optimal Latin hypercube experimental design was used to generate sample points within the range of design variables. The mass, maximum total deformation under various working conditions and first natural frequency of each sample point were obtained through finite element analysis.

[0021] The neural network model is trained based on sample data, where the input layer consists of design variables and the output layer consists of mass, maximum total deformation under various working conditions, and first-order natural frequency.

[0022] By combining topology optimization with size optimization, the above technical solutions achieve lightweighting of the crossbeam while significantly improving its static and dynamic performance indicators.

[0023] Additional aspects and advantages of the invention will become apparent in the following description or may be learned by practice of the invention. Attached Figure Description

[0024] Figure 1 is a flowchart of a multi-condition optimization method for the crossbeam of a multi-strategy gantry automatic tape laying machine according to an embodiment of the present invention;

[0025] Figure 2 is a schematic diagram of the crossbeam of a gantry-type automatic tape laying machine according to an embodiment of the present invention;

[0026] Figure 3 is a schematic diagram of the crossbeam of a gantry-type automatic tape laying machine according to an embodiment of the present invention;

[0027] Figure 4 is a schematic diagram of the crossbeam of a gantry-type automatic tape laying machine according to an embodiment of the present invention. Detailed Implementation

[0028] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0029] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0030] Some embodiments of the present invention are described below with reference to Figures 1 to 4.

[0031] Referring to Figure 1, this embodiment of the invention provides a multi-condition optimization method for the crossbeam of a multi-strategy gantry-type automatic tape laying machine, including:

[0032] Step S1: Determine the static and dynamic performance indicators of the crossbeam under various typical working conditions using the finite element analysis method. The static performance indicators include the maximum total deformation of the crossbeam under various working conditions, and the dynamic performance indicators include the first natural frequency of the crossbeam.

[0033] Step S2: Based on the static performance indicators, perform topology optimization on the beam to obtain a conceptual model, and reconstruct the conceptual model to obtain the initial geometric model of the beam.

[0034] Step S3: Perform sensitivity analysis on the design parameters of the initial geometric model, and select several design parameters that have a significant impact on the static performance index and the dynamic performance index as design variables;

[0035] Step S4: Using the selected design variables as input and performance indicators as output, calculate the multiple sets of samples obtained from the optimal Latin hypercube experimental design, train the BP neural network model as a surrogate model, and use the NSGA-III multi-objective optimization algorithm to solve the Pareto front solution set.

[0036] Step S5: Assign weights to each objective using the entropy-weighted TOPSIS method and sort the Pareto front solutions to finally determine the optimal solution for the beam size parameters.

[0037] In this way, topology optimization and size optimization can be combined to achieve lightweight beams while significantly improving their static and dynamic performance indicators.

[0038] In one possible implementation, step S4 specifically includes:

[0039] With the objectives of minimizing static performance indicators, maximizing dynamic performance indicators, and minimizing optimized quality, and constrained by the range of values ​​for design variables, the NSGA-III algorithm is iterated.

[0040] In each iteration, the values ​​of the selected design variables are input into the trained neural network model for solving, so as to obtain the optimized quality, static performance index and dynamic performance index of the neural network model output.

[0041] After the algorithm converges, the Pareto front solution set of the design variables is obtained.

[0042] In one possible implementation, step S5 includes:

[0043] The weights of each solution to the design variables are determined using the entropy weight method.

[0044] Based on the weights, calculate the proximity of each solution of the design variables to the ideal solution;

[0045] Based on the calculated proximity, the solutions for the design variables in the Pareto front solution set are sorted.

[0046] In one possible implementation, the BP neural network model is trained in the following way:

[0047] The optimal Latin hypercube experimental design was used to generate sample points within the range of design variables. The mass, maximum total deformation under various working conditions and first natural frequency of each sample point were obtained through finite element analysis.

[0048] The neural network model is trained based on sample data, where the input layer consists of design variables and the output layer consists of mass, maximum total deformation under various working conditions, and first-order natural frequency.

[0049] Specific Implementation

[0050] Step S1: Determine the static and dynamic performance indicators of the beam under various typical working conditions using the finite element analysis method. The static performance indicators include the maximum total deformation of the beam, and the dynamic performance indicators include the first natural frequency of the beam.

[0051] For example, in this embodiment, Solidworks software was used to create a 3D model of the beam. The beam has a length of 7500 mm, a width of 1190 mm, and a height of 1610 mm. Based on Saint Venant's Principle, the beam model was reasonably simplified by removing small details such as chamfers, bosses, and threaded holes that have little impact on the stress analysis. The simplified beam model is shown in Figure 2, and the simplified beam has a mass of 16043 kg.

[0052] The crossbeam is made of Q345 steel. The material parameters are detailed in Table 1, including key parameters such as elastic modulus, Poisson's ratio, and yield strength.

[0053] Table 1 Material setting

[0054]

[0055] The finite element static analysis method discretizes a complex structure into a finite number of simple elements, then performs mechanical analysis on each element, and finally obtains the stress, strain and displacement distribution of the entire structure.

[0056] During the operation of a gantry-type tape layer, the crossbeam is subjected to external forces, resulting in deformation and stress. Static analysis of the crossbeam can effectively assess its ability to resist deformation and failure. Based on the processing requirements of aerospace composite materials, this embodiment selects three representative working conditions to study the static characteristics of the crossbeam under different conditions: the crossbeam attachment at the left extreme position, the middle of the crossbeam, and the right extreme position. Through these three typical working condition settings, the structural performance of the crossbeam under different operating states can be comprehensively analyzed.

[0057] Step S2: Based on the static performance indicators and the fraction of the optimized mass to the initial mass, perform topology optimization on the beam to obtain the initial geometric model of the beam.

[0058] Topology optimization is an advanced design technique that uses mathematical methods to determine the optimal distribution of materials within a given design space. Its core objective is to achieve optimal structural performance with the least amount of material while meeting performance, constraint, and manufacturing requirements. Topology optimization can fundamentally change the topology of a structure, significantly reducing structural mass without sacrificing performance, and improving design efficiency and effectiveness. This embodiment of topology optimization mainly consists of the following steps:

[0059] First, this study uses a geometric reconstruction method to fill in empirical features such as weight reduction holes in the original model as continuous entities, thereby eliminating artificially preset geometric constraints and establishing an unbiased benchmark model for subsequent topology optimization.

[0060] Then, necessary constraints are imposed on the initial optimization model to form a constrained initial optimization mathematical model. Topology optimization is performed on the initial optimization model in ANSYS, and the material distribution is gradually adjusted through iterative calculations to finally obtain the conceptual model. This embodiment uses the minimum weighted strain energy under multiple working conditions as the optimization objective and the mass fraction of the optimized design domain relative to the initial design domain as a constraint to perform multi-objective topology optimization, resulting in a conceptual model. Its topology optimization design mathematical model is as follows:

[0061]

[0062] In the formula, C i (X) is the static strain energy of the i-th working condition, C i (X)=u T Ku; X is the design variable, representing the element density; u is the nodal displacement vector; ω i It is the weighting coefficient for the i-th working condition; N is the total number of units; M i (X) represents the quality of the optimized design domain; M0 represents the quality of the initial optimization model; and Δ represents the quality score.

[0063] Finally, the conceptual model is measured and reconstructed to transform it into a manufacturable geometric model.

[0064] Step S3: Perform sensitivity analysis on the initial geometric model based on multiple design parameters of the crossbeam, and select multiple design parameters that have a significant impact on static and dynamic performance indicators as design variables.

[0065] For example, referring to Figures 3 and 4, this embodiment initially selected a total of 9 design parameters: P1 and P2 are the thicknesses of the upper and lower wall panels, P3 and P4 are the thicknesses of the front and rear wall panels, P5 is the thickness of the intermediate stiffener, P6 is the thickness of the reinforcing rib, P7 and P8 are the upper and lower key angles of the intermediate stiffener, and P9 is the width of the reinforcing rib.

[0066] Sensitivity analysis is a method for assessing the influence of input variables on model output, aiming to determine which variables are most sensitive to the outcome. It quantifies the importance of each variable by changing the values ​​of the input variables and observing the changes in the output. Mathematically, sensitivity can be understood as: if a function y = f(x1, x2, ..., x...) is more sensitive to certain input variables than to others, it is more sensitive to the output. n If is differentiable, then its first-order sensitivity can be expressed as:

[0067]

[0068] Sensitivity analysis can determine which design parameters are sensitive to the objective function, and the complexity of the optimization problem can be reduced by ignoring insensitive parameters.

[0069] Step S4: Using the range of values ​​of the design variables as constraints, the NSGA-III algorithm is used to input the design variables into the trained neural network model for iterative solution to obtain the Pareto front solution set of the design variables.

[0070] NSGA-III (Non-dominated Sorting Genetic Algorithm III) is a multi-objective optimization algorithm based on genetic algorithms. This algorithm focuses on solving multi-objective optimization problems (MaOPs) in high-dimensional objective spaces and is applicable to complex optimization scenarios with three or more objective functions. This embodiment, based on the BP neural network model established in Section 3.2.3, uses the NSGA-III optimization algorithm to obtain the Pareto front solution. Combining the above research results, the objective function, constraints, and design space for the multi-objective optimization of the beam structure can be expressed as follows:

[0071]

[0072] In the formula, Y M The mass of the beam; These represent the maximum total deformation under the conditions of the left end, middle, and right end, respectively; Y f Y is the first-order natural frequency; Mo , Y fo These are the original beam mass, the maximum total deformation under each working condition, and the first natural frequency, respectively. These are the upper and lower limits for each design variable.

[0073] Step S5: Sort the design variables in the Pareto front solution set according to their proximity to the ideal solution, and determine the solution of the design variable with the highest proximity as the optimized design parameters of the beam.

[0074] To obtain the optimal solution for the beam structure optimization, this embodiment employs the entropy-based TOPSIS method to select the optimal solution from the Pareto front obtained in the previous section. The optimal solution selection strategy based on the entropy-based TOPSIS method is a method that combines objective weight determination with multi-criteria decision-making to select the optimal solution from the Pareto front. This method uses the entropy weight method to determine the weights of each objective, then uses the TOPSIS method to sort the Pareto solution set, and finally selects the solution closest to the ideal solution as the optimal solution. The steps of this method are as follows:

[0075] (1) Constructing the evaluation matrix. Assuming there are m evaluation objects and n evaluation indicators, the constructed evaluation matrix is ​​as follows:

[0076]

[0077] (2) Data standardization. Based on the attributes of the data evaluation indicators, they are divided into positive and negative objectives. The standardization of positive indicators is shown below.

[0078]

[0079] The negative indicators are standardized as shown below.

[0080]

[0081] In the formula, x ij r is the j-th evaluation index for the i-th evaluation object; ij This is standardized data.

[0082] (3) Calculate the probability matrix. Calculate the probability of the i-th evaluation object appearing under the j-th evaluation index, as shown below.

[0083]

[0084] (4) Calculate information entropy. The formula for calculating the entropy value of the j-th evaluation index is as follows:

[0085]

[0086] In the formula, k = 1 / lnm is the adjustment coefficient.

[0087] (5) Calculate the coefficient of difference. The coefficient of difference for the j-th evaluation indicator is shown below.

[0088] d j =1-e j (11)

[0089] (6) Calculate the weights. Calculate the weights of each evaluation indicator. The sum of the weights of all evaluation indicators is 1. The formula is as follows:

[0090]

[0091] (7) Weighted Standardization Matrix. The weighted standardization matrix is ​​obtained by multiplying the standardized objective function value by the weights determined by the entropy weight method, as follows:

[0092] Z ij =w j ·r ij (13)

[0093] (8) Determine the positive and negative ideal solutions. The positive ideal solution is the optimal value for each evaluation index, and the negative ideal solution is the worst value for each objective. The calculation formula is as follows:

[0094]

[0095] (9) Calculate the Euclidean distance between each index and the positive and negative ideal solutions. The calculation formula is as follows:

[0096]

[0097] (10) Calculate the proximity. The formula for calculating the proximity of each solution to the ideal solution is as follows:

[0098]

[0099] C i A larger value indicates that the evaluated object is closer to the ideal solution, the higher the approximation, and the better the overall value. The entropy-weighted TOPSIS method assigns more objective weights to the indicators, enabling rapid and effective selection of ideal solutions from the Pareto frontier.

[0100] The solution adopted in this embodiment:

[0101] (1) Finite element analysis was performed on the static and dynamic performance indicators of the crossbeam of the gantry-type tape laying machine under three typical working conditions. The static and dynamic performance parameters of the crossbeam structure before optimization were obtained. With the goal of minimizing the weighted static strain energy under multiple working conditions, the topology of the crossbeam structure was optimized, and the crossbeam structure used for size optimization was finally obtained.

[0102] (2) To improve the efficiency of beam structural parameter optimization, sensitivity analysis was used to screen out structural parameters that have a significant impact on beam mass and static and dynamic performance indicators as design variables. A surrogate model for beam mass and static and dynamic performance was established using a BP neural network, and combined with the NSGA-III multi-objective optimization algorithm and the entropy-weighted TOPSIS method, the complex optimization problem under multiple working conditions was effectively solved.

[0103] (3) The optimization results show that compared with the original design, the mass of the optimized beam is reduced by 20.21%, the maximum deformation under the three working conditions is significantly reduced, and the first natural frequency is improved. This fully verifies the effectiveness of the proposed method in improving the static and dynamic performance of the beam and lightweight design, and provides important theoretical support and application value for the structural optimization of large-span gantry machine tools.

[0104] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0105] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in one or more blocks of the flowchart illustrations and / or one or more blocks of the block diagrams.

[0106] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowcharts and / or one or more block diagrams.

[0107] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more block diagrams.

[0108] It should be noted that any reference signs placed between parentheses in the claims should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In a unit claim enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third, etc., does not indicate any order. These words can be interpreted as names.

Claims

1. A multi-condition optimization method for the crossbeam of a multi-strategy gantry-type automatic tape laying machine, characterized in that, Includes the following steps: Step S1: Determine the static and dynamic performance indicators of the crossbeam under various typical working conditions using the finite element analysis method. The static performance indicators include the maximum total deformation of the crossbeam under various working conditions, and the dynamic performance indicators include the first natural frequency of the crossbeam. Step S2: Based on the static performance indicators, perform topology optimization on the beam to obtain a conceptual model, and reconstruct the conceptual model to obtain the initial geometric model of the beam. Step S3: Perform sensitivity analysis on the design parameters of the initial geometric model, and select several design parameters that have a significant impact on the static and dynamic performance indicators as design variables. Step S4: Using the selected design variables as input and the performance indicators as output, calculate multiple sets of samples obtained from the optimal Latin hypercube experimental design, train a BP neural network model as a surrogate model, and solve the Pareto front solution set using the NSGA-III multi-objective optimization algorithm. Step S5: Assign weights to each objective and sort the Pareto front solutions using the entropy-weighted TOPSIS method, and finally determine the optimal solution for the beam size parameters.

2. The multi-condition optimization method according to claim 1, characterized in that, Step S4 specifically includes: taking the minimum static performance index, the maximum dynamic performance index, and the minimum optimized quality as objectives, and using the range of values ​​of the design variables as constraints, performing NSGA-III algorithm iterations; in each iteration, inputting the values ​​of the selected design variables into the trained neural network model for solving, to obtain the optimized quality, static performance index, and dynamic performance index output by the neural network model; after the algorithm converges, obtaining the Pareto front solution set of the design variables.

3. The multi-condition optimization method according to claim 1, characterized in that, Step S5 includes: determining the weight of each solution of the design variable using the entropy weight method; calculating the proximity of each solution of the design variable to the ideal solution based on the weight; and sorting the solutions of the design variable in the Pareto front solution set based on the calculated proximity.

4. The multi-condition composite optimization method according to claim 1, characterized in that, The BP neural network model is trained in the following way: the optimal Latin hypercube experimental design is used to generate sample points within the range of design variables, and the mass, maximum total deformation and first natural frequency of each sample point are obtained through finite element analysis. The neural network model is trained based on sample data, where the input layer consists of design variables and the output layer consists of mass, maximum total deformation under various working conditions, and first-order natural frequency.

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