A BESO-based method for optimizing the frame structure of air-jet looms

Abstract

The present invention proposes a method for optimizing the frame structure of an air jet loom based on the BESO method, which relates to the field of air jet loom design and includes the following steps: S1. Establishing a three-dimensional model of the air jet loom frame, setting material parameters, meshing, applying loads, and boundary conditions; S2. Setting the objective function, BESO parameters, and volume constraints; S3. Performing finite element stress analysis to identify weak areas in the air jet loom frame structure; S4. Constructing a weight distribution model to divide the optimization regions; S5. Iterating BESO optimization based on the weight distribution model; S6. When the preset optimization objectives and constraints are met, the optimization process stops, resulting in the final air jet loom frame optimization model. By constructing a directional flexibility objective function to prioritize stiffness in a specific direction and combining the weight distribution model to divide the optimization regions, the method achieves coordinated optimization of the air jet loom frame structure's efficient lightweighting and dynamic stability, thereby improving the stiffness, weight, and stability of the air jet loom frame.

Description

Technical Field

[0001] The invention relates to the field of air jet loom design, and in particular to a frame structure optimization method of an air jet loom based on a BESO method. Background Art

[0002] As core equipment in the modern textile industry, air-jet looms require a frame structure that maintains high rigidity and dynamic stability despite high-frequency weft beating impacts, alternating loads from the shedding mechanism, and complex vibration conditions. As textile machinery advances toward higher speeds, the frame must simultaneously meet the complex demands of lightweighting, high rigidity, and assembly stability. Its lightweight design requires maximizing the removal of redundant material while ensuring assembly accuracy and dynamic rigidity. Traditional empirical design methods achieve localized reinforcement through the placement of uniformly thickened ribs, but this often results in excessive overall weight, making it difficult to meet the energy efficiency requirements of modern textile equipment.

[0003] Although the bidirectional evolutionary structural optimization (BESO) algorithm can achieve lightweighting by iteratively removing inefficient materials, it suffers from a fundamental flaw in the frame optimization: the failure of dynamic protection of key assembly areas. First, the uniform sensitivity calculation easily misjudges key assembly areas such as bolt mounting holes and guide rail positioning surfaces as inefficient areas, resulting in loss of assembly accuracy after optimization; second, the single-direction stiffness design cannot suppress the lateral vibration caused by high-speed weft beating, and although the static protection zone setting can prevent the removal of key areas, it causes sudden changes in interface stress and limits the weight reduction efficiency. Summary of the Invention

[0004] In view of this, this application proposes a method for optimizing the frame structure of an air-jet loom based on the BESO method, aiming to solve the problem that traditional methods are unable to accurately distinguish between key structures that must be retained and redundant materials that can be optimized and removed under dynamic working conditions, resulting in the optimization results being difficult to meet the dual requirements of high-precision assembly and high weight reduction rate of air-jet looms.

[0005] The technical solution of this application is achieved as follows:

[0006] This application discloses a method for optimizing the frame structure of an air-jet loom based on the BESO method, comprising the following steps:

[0007] S1. Build a 3D model of the air jet loom frame, define material physical parameters and divide the mesh into units, and apply assembly loads and boundary conditions.

[0008] S2. Construct the directional flexibility objective function based on vibration modal analysis, set the volume constraint threshold and the evolution rate parameter of the BESO algorithm;

[0009] S3. Identify weak areas of the rack through finite element stress analysis, and extract the geometric coordinates of key assembly areas within the weak areas based on the rack assembly functional requirements as a core assembly feature point set;

[0010] S4. Construct a weight allocation model to calculate the three-dimensional distances from all elements in the weak area to the nearest core feature point, divide the design domain into a prohibited optimization area, a transition optimization area, and a free optimization area according to a preset distance threshold, and allocate element optimization weights based on the distances;

[0011] S5. Perform regional BESO optimization iterations: Calculate element sensitivity based on the directional flexibility objective function, adjust the sensitivity value according to the weight, and update the element density according to the following strategy: lock the element density to 1.0 in the prohibited optimization area, adjust the density by interpolation according to the weight ratio in the transition optimization area, and remove inefficient elements in the free optimization area according to the adjusted sensitivity; calculate the remaining material volume and directional weighted flexibility change rate of the current iteration;

[0012] S6. If the remaining material volume does not reach the volume constraint threshold, or the directional weighted flexibility change rate does not meet the preset convergence condition, return to S5 to continue iteration. If both the volume constraint and the flexibility convergence condition are met, the topology optimized frame model is output.

[0013] Based on the above technical solution, preferably, identifying the weak area of ​​the frame in step S3 includes: determining the stress concentration area through finite element stress analysis, marking it as a weak area when the local stress value exceeds a preset proportion of the allowable stress of the material, and visually locating it through a three-dimensional stress cloud map.

[0014] Based on the above technical solution, preferably, the directional flexibility objective function in step S2 is defined as: ,in, is the flexibility in the X direction, is the X-direction weight, is the flexibility in the Y direction, is the Y direction weight, K is the structural stiffness matrix, calculated by the finite element method, and the weight coefficient satisfies To suppress the lateral vibration of the air jet loom.

[0015] Based on the above technical solution, preferably, the method of constructing the weight distribution model in step S4 includes the following steps:

[0016] S41, calculating the three-dimensional distance between the unit and the core feature point;

[0017] ,in, x a , y a , z a For unit The spatial coordinates of x Oi ,y Oi , z Oi for No. i Core assembly feature points O i The spatial coordinates of

[0018] S42, optimizing the weight according to the distance allocation unit, wherein the weight function is selected from any one of the following: the inverse model is , the exponential model is ,in L i is the distance from the unit to the nearest core point, p is the penalty factor, l is the attenuation coefficient, is the smoothing constant, oh i is the initial weight, Optimize weights for units;

[0019] S43. Divide the design domain into a prohibited optimization area, a transition optimization area, and a free optimization area based on the distance threshold.

[0020] Based on the above technical solution, preferably, the cell density update strategy of the regional BESO optimization iteration in step S5 is: the cell density of the prohibited optimization area is forced to be locked to r i =1.0; the cell density in the transition optimization area is adjusted by weight interpolation, and the interpolation formula is: , in or is the relaxation factor, is the intermediate density variable; the free optimization region removes inefficient units according to the adjusted sensitivity ranking.

[0021] On the basis of the above technical solution, preferably, the unit sensitivity calculation in step S5 includes superposition of multiple load conditions, and the comprehensive sensitivity calculation is the weighted sum of each load type: ,in is the weight coefficient of the mth type of load, In order to correspond to the sensitivity of the load, the load types include at least the beating force, the shedding mechanism force and the inertia force.

[0022] On the basis of the above technical solution, preferably, the weight distribution model integrates a stress protection mechanism, including applying a weight amplification factor to the units in the high stress area, which is defined as: ,in, k is the stress amplification factor, 0.5≤ k ≤2.0, s i is the unit stress, s yield is the yield strength of the material; the stress gradient of adjacent elements is constrained to satisfy: ,in, s j 、 s i is the stress of adjacent elements, L ij is the unit spacing, Δ s max is the maximum allowable stress difference, and Δ s max ≤0.2 s yield , Δ L is the unit characteristic size.

[0023] Based on the above technical solution, preferably, the convergence judgment criterion in step S6 is: the rate of change of the directional weighted flexibility objective function satisfies: ,in, For the k The weighted flexibility value of the iteration, The convergence threshold is preset. If the above conditions are not met for multiple consecutive iterations, it will return to the historical optimal solution and reduce the material removal rate.

[0024] On the basis of the above technical solution, preferably, the protection of the key assembly area in step S3 includes: defining a protection zone with the assembly positioning point as the center, and the protection radius meets R ≥ R min And it is positively correlated with the assembly size tolerance; the unit density in the protection zone is forced to be locked to r i =1; the protection zone element stiffness matrix is ​​modified to K ′= K + αK 0, where K is the current stiffness matrix, K 0 is the initial stiffness matrix, α is the reinforcement coefficient; the units outside the protected area are optimized according to the weight distribution model.

[0025] On the basis of the above technical solution, preferably, the volume constraint in step S6 is achieved by controlling the material volume fraction, including the steps of: limiting the material volume fraction in the optimization process to ,in V T =∑ i v i is the total volume of the design domain, v i is the unit volume,f is the preset material volume fraction; the cell density is updated by the Lagrange multiplier method or sensitivity screening strategy to satisfy ; The sensitivity screening strategy includes removing inefficient materials according to unit sensitivity ranking and dynamically adjusting the removal threshold to match the target volume.

[0026] The present invention has the following beneficial effects compared to the prior art:

[0027] (1) The air-jet loom frame structure optimization method disclosed in this application strengthens the priority of stiffness in a specific direction by constructing a directional flexibility objective function, and divides the prohibited optimization area, transition area and free area into two areas by combining a dynamic weight distribution model, thereby achieving efficient lightweighting and dynamic stability coordinated optimization of the air-jet loom frame structure. This method accurately protects key assembly areas such as bolt holes and guide rail surfaces, suppresses lateral vibration, and improves material utilization through a regional gradient optimization strategy. At the same time, the use of multi-condition load superposition and dual convergence criteria ensures the stability of the optimization results under actual complex loads, significantly solving the technical problems of assembly failure, excessive vibration and low weight reduction efficiency in traditional methods.

[0028] (2) Through the innovative design of the directional flexibility objective function, the dynamic stability requirements (suppression of lateral vibration) of the air-jet loom frame are deeply combined with the lightweight goal (efficient weight reduction). Furthermore, through differentiated weight distribution, multi-directional stiffness collaborative optimization, and precise adaptation to actual working conditions, the limitations of the traditional BESO method in multi-directional load-bearing scenarios are overcome, providing a highly reliable and high-precision structural optimization method for high-speed textile equipment.

[0029] (3) By protecting the key assembly areas, the assembly accuracy and structural stability of the key areas of the air-jet loom frame are effectively guaranteed during the optimization process. At the same time, during the optimization of the non-protected areas, the material can still be fully utilized to improve the overall structural performance. This ensures that the optimized structure still has high strength and high performance while meeting the assembly accuracy.

[0030] (4) The weight distribution model based on three-dimensional distance and area division can effectively optimize the structural performance of the air-jet loom frame, ensure the integrity of key parts, and simultaneously achieve weight reduction, improve material utilization, and enhance the efficiency and accuracy of the optimization process. This solution can maximize the effect of design optimization while ensuring the functionality of the frame.

[0031] (5) Through a regional density update strategy (locking prohibited areas, interpolating transition areas, and sorting and removing free areas), a coordinated improvement of "assembly protection, stress smoothing, and weight reduction efficiency" in the optimization of air-jet loom frames was achieved. Its technical solution precisely addresses the three major defects of traditional BESO. Through dynamic weight allocation and gradient transition mechanisms, it provides a highly reliable and high-precision lightweight design method for high-speed textile equipment.

[0032] (6) Through the sensitivity calculation mechanism of superimposing multiple load conditions, the problem of insufficient adaptability of the traditional BESO method in complex load scenarios is solved. Its technical solution significantly improves the multi-condition performance stability and fatigue life of the air-jet loom frame through differentiated weight distribution, global stress equilibrium optimization and accurate modeling of the actual load spectrum, providing a high-reliability solution for the lightweight design of high-speed textile equipment.

[0033] (7) Through the dual mechanisms of weight amplification in high-stress areas and stress gradient constraints, the traditional BESO method systematically solves the problems of misremoval, stress mutation, and dynamic instability in high-stress area optimization. Its technical solution significantly improves the structural safety, fatigue life, and adaptability to multiple working conditions of the frame through dynamic protection and global stress balancing, providing an innovative solution for the reliability design of high-speed textile equipment.

[0034] (8) By setting a convergence criterion based on the weighted flexibility change rate, it is possible to accurately determine whether the optimization process has stabilized. This ensures the reliability and stability of the optimization results, making the structure perform better in practical applications. When the convergence conditions are not met for multiple consecutive iterations, returning to the historical optimal solution can effectively prevent the optimization process from falling into the local optimal solution, thereby increasing the possibility of global optimization. The strategy of reducing the material removal rate makes the optimization process more flexible and adaptable. When the convergence conditions are not met, by reducing the material removal rate, the optimization can be carried out more cautiously to ensure that the structural performance is not negatively affected by excessive material removal. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0036] Figure 1 This is a flow chart of the air jet loom frame structure optimization method disclosed in this application;

[0037] Figure 2 Schematic diagram of the force applied to the vibration mode experimental test of the air jet loom frame disclosed in this application;

[0038] Figure 3 This is a schematic diagram of the three-dimensional structure of the air-jet loom frame disclosed in this application;

[0039] Figure 4 This is the local area to be optimized of the wall panel in the air-jet loom frame disclosed in this application;

[0040] Figure 5 This is a schematic diagram of the weight distribution model disclosed in this application. DETAILED DESCRIPTION

[0041] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0042] like Figure 1-5 As shown, the embodiment of the present invention discloses a method for optimizing the frame structure of an air jet loom based on the BESO method, comprising the following steps:

[0043] S1. Build a 3D model of the air jet loom frame, define the material physical parameters and divide the mesh elements, and apply assembly loads and boundary conditions.

[0044] Specifically, in step S1, a three-dimensional model can be constructed using three-dimensional software to ensure that the size and shape of the model accurately reflect the structural characteristics of the actual frame. In order to perform finite element analysis, the frame model needs to be divided into a finite number of units (for example, tetrahedral or hexahedral units) and the material physical properties of each unit, such as elastic modulus, Poisson's ratio, density, etc., need to be specified. The choice of material should be consistent with the material used in the actual frame (such as steel, aluminum alloy, etc.). At the same time, appropriate loads and boundary conditions must be applied to the model to simulate the external forces and constraints that the frame is subjected to when the loom is operating. According to the actual working conditions and application requirements, appropriate assembly loads (such as bolt preload, weft beating impact load, opening mechanism load) and boundary conditions (such as fixed constraints, supports, etc.) should be applied.

[0045] Through geometric modeling and meshing, the machine frame's structural characteristics are accurately characterized, providing a foundation for optimization. Assembly loads (such as bolt preload) and dynamic loads (beating force) are introduced to simulate actual working conditions, avoiding bias in single-load optimization. Fixed constraints are set to meet the actual machine frame installation conditions, ensuring the authenticity of the mechanical analysis.

[0046] S2. Construct the directional flexibility objective function based on vibration modal analysis, set the volume constraint threshold and the evolution rate parameter of the BESO algorithm.

[0047] In this step, vibration modal analysis is used to determine the structural flexibility in various directions (flexibility is the inverse of stiffness). A directional flexibility objective function is constructed based on the vibration characteristics in different directions, reflecting the dynamic performance of the frame in these directions. For example, differentiated X / Y weightings guide the optimization process to prioritize enhancing stiffness in specific directions. A volume constraint threshold limits the total amount of material removed to prevent stiffness failure due to excessive weight reduction. The BESO algorithm's evolution rate parameters are dynamically adjusted, such as high-speed removal in the early stages and low-speed optimization in the later stages, to balance convergence speed and accuracy.

[0048] The directional flexibility objective function ensures that the dynamic performance of the structure in all directions is considered during the optimization process, improving the overall dynamic stability of the frame. The volume constraint threshold and evolution rate parameters are set to ensure the convergence of the optimization process and the weight reduction effect.

[0049] S3. Identify the weak areas of the rack through finite element stress, and extract the geometric coordinates of the key assembly areas in the weak areas determined based on the rack assembly function requirements as the core assembly feature point set.

[0050] In this step, finite element analysis is performed to simulate the stresses on the frame under various operating conditions. The purpose of this analysis is to identify potential weaknesses in the frame, such as areas of stress concentration, areas of excessive deformation, or areas at risk of failure. Using FEM (finite element method) calculations, the stress, strain, and displacement distributions of the frame under various loads are determined. Identifying weak points provides a foundation for subsequent optimization design.

[0051] Once a weak area is identified, it means that the weak area of ​​the rack needs structural optimization. Within the weak area, the geometric coordinates of the key assembly areas (such as bolt mounting holes and guide rail positioning surfaces) are determined according to the assembly function requirements of the rack, and these points are extracted as the core assembly feature point set. The core feature point set defines that these key assembly areas need to be protected and optimization is prohibited to prevent hole deformation or benchmark loss.

[0052] S4. Construct a weight allocation model to calculate the three-dimensional distances from all units in the weak area to the nearest core feature point. Divide the design domain into prohibited optimization areas, transition optimization areas, and free optimization areas according to the preset distance threshold, and allocate unit optimization weights based on the distance.

[0053] In this step, a dynamic weight allocation model is constructed based on the results of vibration modal analysis and weak area identification. This model assigns different optimization weights to different areas of the rack based on their importance and stress conditions.

[0054] Specifically, the model divides the frame into a prohibited optimization zone, a transition zone, and a free zone. The prohibited optimization zone typically includes critical assembly areas such as bolt holes and guide rail surfaces. These areas must remain intact during the optimization process, with no material removal or reduction. The transition zone, the intermediate area between the weak area and the free zone, undergoes appropriate optimization to balance overall structural performance. The free zone is an area that can be significantly optimized, achieving weight reduction by removing excess material.

[0055] The technical benefits of building a weight distribution model are reflected in the protection of critical areas and the improvement of overall structural performance during the optimization process. By clearly defining the areas and assigning their weights, the optimization process focuses on structural weaknesses and critical assembly areas, avoiding assembly failures and structural weakening caused by optimization, thereby maintaining the rigidity and stability of the frame.

[0056] Optimization weights are assigned to units based on distance, with closer distances giving higher weights and vice versa. Distance calculation and design domain division ensure the protection of critical assembly areas during the optimization process while improving weight reduction efficiency. The construction of a weight allocation model allows for a more refined and regionalized optimization process, enhancing optimization effectiveness.

[0057] S5. Perform regional BESO optimization iterations: Calculate element sensitivity based on the directional flexibility objective function, reflecting the element's contribution to overall flexibility. Adjust sensitivity values ​​based on weights, and update element density according to the following strategy: Lock element density at 1.0 in the prohibited optimization zone, maintaining the original state. In the transition optimization zone, adjust density by interpolation based on weight proportions, performing partial optimization. In the free optimization zone, remove inefficient elements based on adjusted sensitivity. Calculate the remaining material volume and directional weighted flexibility change rate for the current iteration.

[0058] In this step, the bidirectional evolutionary structural optimization (BESO) method is used for iterative optimization of each region. BESO is a method that gradually optimizes the structural topology by adding or removing material in each iteration, gradually approaching the optimal structural design.

[0059] Regional optimization involves applying different optimization strategies to different regions, based on the regions defined in step S4. The prohibited optimization region remains unchanged, the transition region undergoes appropriate optimization, and the free region undergoes a more substantial optimization. During the iterative optimization process, material additions and removals in each region are adjusted based on their weights in the weight distribution model. Furthermore, a multi-condition load superposition method is employed, which considers the load conditions of the rack under various operating conditions during the optimization process, ensuring the stability and effectiveness of the optimization results under various operating conditions.

[0060] The technical benefit of regional BESO optimization iteration lies in achieving a coordinated optimization of the frame's efficient lightweighting and dynamic stability. Through a refined regional optimization strategy, the accuracy and efficiency of the optimization process are improved, ensuring structural performance in key areas while achieving overall weight reduction. Furthermore, the superposition of multiple load conditions ensures the reliability of the optimization results under different operating conditions, avoiding the limitations of optimizing under a single operating condition.

[0061] S6. If the remaining material volume does not reach the volume constraint threshold, or the directional weighted flexibility change rate does not meet the preset convergence condition, return to S5 to continue iteration. If both the volume constraint and the flexibility convergence condition are met, the topology optimized frame model is output.

[0062] In this step, strict convergence criteria are set to ensure that the optimization process gradually approaches the optimal solution within a reasonable calculation range. Dual convergence criteria typically include convergence of material change rate and convergence of structural performance indicators. Material change rate convergence refers to the fact that the amount of material added or removed from the optimization area is less than a preset threshold over several consecutive iterations. Structural performance indicator convergence refers to the fact that the changes in key performance indicators such as the structure's stiffness and vibration characteristics are less than a preset threshold over several consecutive iterations.

[0063] The technical effect of strict convergence judgment is to ensure the stability and reliability of the optimization process, avoiding over-optimization or failure to achieve the optimization goal. Through the dual convergence criteria, the final optimization result can be guaranteed to have a high weight reduction rate while maintaining sufficient structural rigidity and stability, thus demonstrating excellent performance in practical applications.

[0064] The air-jet loom frame structure optimization method disclosed in this application strengthens the priority of stiffness in a specific direction by constructing a directional flexibility objective function, and divides the prohibited optimization area, transition area, and free area into a dynamic weight distribution model, thereby achieving efficient lightweighting and dynamic stability coordinated optimization of the air-jet loom frame structure. This method accurately protects key assembly areas such as bolt holes and guide rail surfaces, suppresses lateral vibration, and improves material utilization through a regional gradient optimization strategy. At the same time, the use of multi-condition load superposition and dual convergence criteria ensures the stability of the optimization results under actual complex loads, significantly solving the technical problems of assembly failure, excessive vibration, and low weight reduction efficiency in traditional methods.

[0065] In some embodiments, identifying the weak area of ​​the frame in step S3 includes: determining the stress concentration area through finite element stress analysis, marking it as a weak area when the local stress value exceeds a preset proportion of the material allowable stress, and visually locating it through a three-dimensional stress cloud map.

[0066] Stress analysis can pinpoint weak areas within the rack due to poor structural design, uneven material distribution, or significant exposure to external loads. These areas often experience significant stress concentrations, potentially leading to structural fatigue, damage, or vibration. Focusing optimization efforts on these weak areas is crucial for improving overall rack performance.

[0067] By setting a preset ratio for the material's allowable stress, designers can be provided with a scientific standard to ensure that the identified weak areas are mechanically reasonable and not too broad or too narrow. This allows the optimization process to focus more on areas that truly need strengthening, avoiding ineffective optimization or missing critical areas.

[0068] By identifying weak areas and performing targeted optimization, designers can clearly determine which areas require reinforcement and which areas can be moderately weighted, thereby providing a more targeted and efficient optimization solution. This scientific area division and identification method provides the foundation for subsequent BESO optimization, making the optimization process more guided and efficient.

[0069] In step S3, a protection zone is defined around the assembly location point. Specifically, the protection zone is centered around the assembly location point and has a certain protection radius. The protection radius satisfies the following conditions:

[0070] Protection radius meets R ≥ R min， Protection radius R Must be greater than or equal to the minimum protection radius R min， The protection radius is positively correlated with the assembly size tolerance, that is, during the actual assembly process, the size of the protection zone should be adjusted according to the actual tolerance requirements to ensure the structural stability and accuracy of the critical assembly area.

[0071] In the protected area, in order to ensure assembly accuracy and structural integrity, the unit density is forced to be locked to r i = 1. This means that all cells within the protected areas must maintain full density (i.e. no material is allowed to be removed or weakened), thus ensuring that these areas do not change during the optimization process and the structure remains stable.

[0072] In the protection zone, the element stiffness matrix will be modified. The modified stiffness matrix is: K ′= K + αK 0, where K is the current stiffness matrix, K 0 is the initial stiffness matrix, α is the reinforcement coefficient.

[0073] The purpose of this correction is to ensure that these critical areas maintain their structural strength and stability during the optimization process by strengthening the stiffness of the units in the protection zone, thereby avoiding insufficient strength caused by optimization.

[0074] Units outside the protected area are optimized according to a weight distribution model. Specifically, units outside the protected area are optimized with appropriate weights based on their role and importance in the overall structure to ensure the overall performance and efficiency of the optimization results.

[0075] By protecting critical assembly areas, the air-jet loom frame structure maintains assembly accuracy and structural stability in key areas during optimization. Furthermore, during optimization of unprotected areas, full material utilization can be achieved, improving overall structural performance. This ensures that the optimized structure maintains high strength and performance while maintaining assembly accuracy.

[0076] As some preferred implementations, the method of constructing the weight distribution model in step S4 includes the following steps:

[0077] S41. Calculate the three-dimensional distance from the unit to the core feature point.

[0078] Refer to the attached Figure 5 As shown in Figure 2, in this step, the three-dimensional distance between each design unit and one or more core feature points is first calculated, and the Euclidean distance formula is used to quantify the spatial relationship between the unit and these key points:

[0079] ,in, x a , y a , z a For unit The spatial coordinates of x Oi , y Oi , z Oi for No. i Core assembly feature points O i The spatial coordinates of .

[0080] Core feature points can include key assembly points, connection points, and stress concentration locations of the rack, such as bolt holes and guide rail surfaces. The result of this calculation is the distance of each unit relative to the key structural points.

[0081] This calculation determines the relative position of each unit, providing basic data for subsequent optimization weight allocation. It also accurately assesses the spatial relationship between the unit and the core structural area, providing a more accurate basis for regional division for optimization.

[0082] S42. Assign unit optimization weights based on distance. This step is the key to the weight assignment model. Its purpose is to assign optimization weights based on the distance between the unit and the core feature point. Different weight assignment functions will affect the removal or retention of units during the optimization process.

[0083] In this embodiment, the weight function is selected from any one of the following: , the exponential model is ,in L i For unit i The distance to the nearest core point, p is a penalty factor used to control the effect of distance on weight. l is the attenuation coefficient, is the smoothing constant, oh i is the initial weight, Optimize weights for units.

[0084] The logic of the reciprocal model: When the unit is closer to the core feature point ( L i →0), weight oh i ′ is larger (closer to ), the material retention priority is the highest; with distance L i As the value increases, the weight value decays rapidly (with The remote unit is removed first.

[0085] Applicable scenarios: 1. Steep gradient protection, the core assembly area (such as around bolt holes) must be strictly protected to prevent any accidental removal; 2. Efficient weight reduction, fast removal of redundant materials away from the core area (such as free zone).

[0086] About the logic of the exponential model: weight increases with distance L i The increase decays exponentially, and the change trend is smooth;

[0087] The near end is weighted highly (preserving material) and the far end is weighted less (allowing removal), but the rate of decay is controlled by λ.

[0088] Applicable scenarios: 1. Smooth transition requirements: Sudden changes in interface stress need to be avoided (such as around the guide rail installation surface);

[0089] 2. Gradual optimization: Achieve continuous gradual change of material distribution in the transition zone to reduce the risk of stress concentration.

[0090] The inverse model focuses on ensuring assembly accuracy, while the exponential model emphasizes weight reduction efficiency and stress control. Combining the two overcomes the limitations of traditional static protection zones. By selecting a weighted model, designers can dynamically adjust optimization strategies based on actual needs (such as weight reduction targets and vibration suppression priorities), enhancing design flexibility.

[0091] S43. Divide the design domain into a prohibited optimization area, a transition optimization area, and a free optimization area based on the distance threshold.

[0092] Among them, the prohibited optimization zone is located in the area very close to the core feature point (such as around the bolt hole), and the elements in these areas are not allowed to be removed or optimized. The transition optimization zone is the area at a medium distance from the core feature point, and these areas can be optimized to a certain extent. The free optimization zone is the area far from the core feature point, and these areas can significantly remove material to achieve the weight reduction target.

[0093] By dividing the design domain into different optimization zones, optimization intensity can be appropriately distributed based on the distance between elements and core feature points, avoiding over-optimization in critical areas. The prohibited optimization zone prevents unnecessary optimization of critical structural parts (such as mounting holes and connection surfaces), thereby maintaining the functionality and stability of the structure. The free optimization zone allows for the removal of sufficient material to achieve weight reduction goals. This zone division allows for greater flexibility and precision in the optimization process, allowing optimization zones to be adjusted according to actual needs, avoiding indiscriminate material removal.

[0094] A weight distribution model based on three-dimensional distance and regional division can effectively optimize the structural performance of air-jet loom frames, ensuring the integrity of key components while reducing weight, improving material utilization, and enhancing the efficiency and accuracy of the optimization process. This solution maximizes the effectiveness of design optimization while maintaining frame functionality.

[0095] As some implementation methods, the unit density update strategy of the regional BESO optimization iteration in step S5 is:

[0096] The cell density in the prohibited optimization area is forced to be locked r i =1.0, the prohibited optimization areas are usually located in key structural parts, such as assembly holes, connection points, etc. These areas must maintain their original density to ensure the integrity of structural strength and assembly function.

[0097] The cell density in the transition optimization area is adjusted by weight interpolation. The interpolation formula is: , in, It is k The cell density after +1 iteration, or is the relaxation factor, which controls the weight ratio of the new and old density values. is the intermediate density variable.

[0098] The cell density update strategy in the transition optimization zone combines the intermediate density variable of the current iteration and the density value of the previous iteration, and uses the relaxation factor or Through progressive density adjustment, large fluctuations in element density during the iteration process can be avoided, a smooth transition of material distribution can be achieved, sudden changes in interface stress can be avoided, and the stability and convergence of the optimization process can be improved.

[0099] Free optimization zones remove inefficient elements based on adjusted sensitivity. These zones are located in areas farther from the core feature points, where material removal can be maximized to achieve weight reduction. Removing inefficient elements based on adjusted sensitivity ensures that the optimization process focuses on removing material in areas that have less impact on structural performance, thereby achieving optimal weight reduction.

[0100] Through the regional density update strategy, some problems existing in the traditional BESO method in rack optimization are systematically solved.

[0101] 1) Traditional methods fail to consider assembly functional requirements in global sensitivity calculations, and are prone to misjudging key areas such as bolt holes and guide rail mounting surfaces as inefficient areas, leading to incorrect material removal, deformation of assembly interfaces, or failure of positioning benchmarks.

[0102] Solution: This application implements mandatory locking of unit density in prohibited optimization areas, completely retaining materials in key areas and avoiding the risk of erroneous removal at the algorithm level.

[0103] Technical effect: Ensure the geometric accuracy of the assembly interface, avoid assembly function failure due to optimization, and improve the matching reliability between the rack and external components.

[0104] 2) Due to the sudden change in material distribution at the rigid boundary between the traditional static protection zone and the free optimization zone, local stress concentration is caused, which significantly increases the risk of fatigue cracking.

[0105] Solution strategy: This application introduces a density interpolation adjustment mechanism in the transition optimization area, achieves a smooth transition of material distribution through progressive weight distribution, and eliminates interface mutations.

[0106] Technical effect: After optimization, the structural stress distribution is continuous and smooth, which significantly reduces the risk of fatigue failure and extends the service life of the frame.

[0107] 3) Traditional methods tend to remove excessive materials when pursuing weight reduction, resulting in reduced structural stiffness or oscillations in the optimization process, making it difficult to balance efficiency and stability.

[0108] Solution strategy: In the free optimization zone, inefficient materials are accurately removed by sensitivity sorting. At the same time, optimization oscillations are suppressed through interpolation in the transition zone, and the iterative stability is controlled by combining the dual convergence criterion.

[0109] Technical effect: Maintaining structural rigidity while efficiently reducing weight, the optimization process converges quickly, and the results are reliable and directly applicable in engineering.

[0110] By leveraging a regional density update strategy (locking prohibited areas, interpolating transition areas, and sorting and removing free areas), this approach achieves a synergistic improvement in "assembly protection, stress smoothing, and weight reduction efficiency" for air-jet loom frame optimization. This technical solution precisely addresses the three major flaws of traditional BESO. Through dynamic weight allocation and a gradient transition mechanism, it provides a highly reliable and precise lightweight design approach for high-speed textile equipment.

[0111] In some implementations, the directional flexibility objective function in step S2 is defined as: .

[0112] in, C x is the flexibility in the X direction, defined as , is the X-direction weight, C y is the Y-direction flexibility, defined as , is the Y direction weight, K is the structural stiffness matrix, calculated by the finite element method, F x is the load vector in the X direction (such as the impact force of weft beating), F y is the load vector in the Y direction (such as lateral vibration inertia force).

[0113] Flexibility is the inverse of stiffness. Specifically, the smaller the flexibility, the greater the stiffness. The directional flexibility objective function increases the stiffness in a specific direction by reducing the flexibility in that direction. The structural stiffness matrix can be calculated using the finite element method. K . Using the inverse matrix of the stiffness matrix , can be combined with the external force vector F x and F y Calculate X and Y Directional flexibility.

[0114] like Figure 3 As shown in the figure, according to the modal vibration results of the air-jet loom, a directional weight is set for the flexibility of the structural optimization area. The vibration vibration shapes in the left and right X directions are more obvious, so we set directional weighting coefficients in the X and Y directions, and calculate and analyze the flexibility in each direction during the optimization process.

[0115] In order to suppress the lateral ( Y direction) vibration, need to increase X Directional rigidity to prevent the impact of beating-up from being transmitted to Y direction. Therefore, the weight coefficient satisfies . In this way, when optimizing the objective function C total middle, X Directional flexibility C x is given a larger weight, the optimization process will tend to reduce X The flexibility in the X direction is increased, thereby increasing the rigidity in the X direction and reducing the lateral vibration of the air jet loom.

[0116] Specifically, by setting The optimization process prioritizes reducing X-direction flexibility, which increases X-direction stiffness, effectively reducing deformation in the X direction caused by the impact force during the beating-up process. Increasing X-direction stiffness reduces deformation in the X direction, indirectly reducing the transmission of impact force to the Y direction, thereby suppressing lateral vibration.

[0117] Through the innovative design of a directional flexibility objective function, the dynamic stability requirements (suppressing lateral vibration) of the air-jet loom frame are deeply integrated with the lightweight goal (efficient weight reduction). Furthermore, through differentiated weight allocation, multi-directional stiffness collaborative optimization, and precise adaptation to actual working conditions, the limitations of the traditional BESO method in multi-directional load-bearing scenarios are overcome, providing a highly reliable and precise structural optimization method for high-speed textile equipment.

[0118] The goal of calculating the unit sensitivity in step S5 is to determine the sensitivity of each unit under different loads by comprehensively considering multiple load conditions. The calculation formula for the comprehensive sensitivity is: .

[0119] in, It is i The combined sensitivity of each unit, is the weight coefficient of the mth type of load, is the sensitivity of the corresponding load, M is the total number of load types.

[0120] The load types include at least beating force, shedding mechanism force and inertia force.

[0121] Among them, the inertial force is the acceleration load of the high-speed moving parts and is defined as the external load. The sensitivity calculation formula is: .

[0122] in is the weight ratio of the external load, is the penalty factor, is the average flexibility of the structure, For the The stiffness matrix of each element, For the The displacement vector of each unit, For the The transposed matrix of the displacement vector of each element.

[0123] The beating force is generated by the impact force during the beating process. If the applied load is the beating force load, the sensitivity calculation formula is: .

[0124] in is the tension of the weft yarn, It is the insertion force required by the textile machine or air jet device to overcome the warp tension when inserting the weft yarn. For the The volume of a unit, is the initial density, is the direction matrix of the force.

[0125] The opening mechanism force is the force generated during the operation of the opening mechanism. If the applied load is the opening mechanism load, the sensitivity calculation formula is:

[0126] .

[0127] in It is the opening angle when the opening mechanism moves, that is, the angle between the warp yarns or the inclination angle of the opening device.

[0128] In the above embodiment, the beating force weight ( c 1) Usually the highest (e.g. c 1=0.6), because it has the greatest impact on the dynamic stability of the frame; the opening mechanism force weight ( c 2) Second (e.g. c 2=0.3), reflecting the periodic load demand of the heald frame movement; the inertia force weight ( c 3) Lower (e.g. c 3=0.1), which is used to balance the additional stress caused by acceleration.

[0129] The traditional BESO method only optimizes a single load (such as the static beating force) in frame optimization, ignoring the actual multi-load coupling effect. This leads to performance degradation of the optimization results under real working conditions (such as insufficient dynamic stiffness). This application's comprehensive sensitivity calculation covers the synergistic effects of the beating force, shedding mechanism force, and inertia force, ensuring that the optimization results match the actual load spectrum.

[0130] By superimposing multiple load cases, the sensitivity calculation mechanism addresses the limited adaptability of traditional BESO methods in complex load scenarios. Through differentiated weight allocation, global stress equilibrium optimization, and precise modeling of actual load spectra, this technical solution significantly improves the multi-condition performance stability and fatigue life of air-jet loom frames, providing a highly reliable solution for the lightweight design of high-speed textile equipment.

[0131] As some implementation methods, the embodiments of the present application further integrate a stress protection mechanism based on the weight distribution model, and systematically solve the technical defects of the traditional BESO method in the optimization of high stress areas through dynamic weight adjustment and stress gradient constraints.

[0132] Specifically, the weight distribution model integrates a stress protection mechanism, which includes applying a weight amplification factor to the elements in the high stress area, defined as:

[0133]

[0134] in, k is the stress amplification factor, 0.5≤ k ≤2.0, s i For the i The unit stress, s yield is the yield strength of the material; oh i is the initial weight, oh i ′ is the element weight after stress protection is applied.

[0135] In this way, when the element stress s i When approaching the yield strength, the weight oh i ′ is significantly amplified, and the optimization process prioritizes retaining materials in high stress areas to avoid structural failure caused by accidental removal, thereby giving priority to structural strengthening in these areas during the optimization process.

[0136] In order to avoid stress concentration during the optimization process, the stress protection mechanism also constrains the stress gradient of adjacent elements. The stress gradient constraint is defined as:

[0137] ,in, s j 、 s i is the stress of adjacent elements, L ij is the unit spacing, Δ s max is the maximum allowable stress difference, and Δ smax ≤0.2 s yield , Δ L is the unit characteristic size.

[0138] This constraint ensures that the stress distribution in the structure does not exhibit excessive gradients, thereby avoiding stress concentrations and potential structural failure.

[0139] By applying a weighted amplification factor to high-stress areas, the optimization process places greater emphasis on structural reinforcement in these areas, thereby improving the overall structure's stress resistance. This effectively reduces stress levels in high-stress areas and mitigates the risk of fatigue failure. Stress gradient constraints ensure that stress differences between adjacent elements are not excessive, thereby avoiding stress concentration and improving the overall reliability and durability of the structure. Through weighted amplification and stress gradient constraints, the optimization results can better reflect the structural performance under actual operating conditions, ensuring that the optimized structure has higher reliability and safety during actual use.

[0140] By leveraging the dual mechanisms of weight amplification in high-stress regions and stress gradient constraints, this approach systematically addresses the issues of misremoval, stress mutation, and dynamic instability inherent in traditional BESO optimization methods. Through dynamic protection and global stress balancing, this technical solution significantly improves the structural safety, fatigue life, and adaptability to multiple operating conditions of the frame, providing an innovative solution for the reliability design of high-speed textile equipment.

[0141] Based on the directional flexibility objective function, this application also defines a dual convergence criterion and a dynamic backoff mechanism. The core of this mechanism is to improve the algorithm convergence stability and the reliability of the optimization results by monitoring the flexibility change rate and adaptively adjusting the optimization strategy. The convergence criterion based on the change rate of the directional weighted flexibility objective function is as follows:

[0142] The convergence criterion is based on the rate of change of the directional weighted flexibility objective function, and the specific formula is as follows:

[0143] ,in, For the k The weighted flexibility value of the iteration, This formula indicates that if the change rate of the weighted flexibility value of the current iteration and the weighted flexibility value of the previous iteration is less than the preset threshold , the optimization process is considered to have converged and reached a stable state.

[0144] If the above conditions are not met for multiple consecutive iterations, the system will perform the following processing steps:

[0145] Roll back to the best solution in the past: The optimization process will roll back to the best solution obtained in the previous iteration. This avoids getting stuck in a local optimum or a bad solution during the optimization process. Reduce the material removal rate: By reducing the material removal rate, the optimization process becomes more conservative, avoiding structural instability caused by removing material too quickly.

[0146] By setting a convergence criterion based on the weighted flexibility change rate, it is possible to accurately determine whether the optimization process has stabilized. This ensures the reliability and stability of the optimization results, resulting in better performance of the structure in practical applications. When the convergence conditions are not met after multiple consecutive iterations, reverting to the historical optimal solution can effectively prevent the optimization process from falling into a local optimal solution, thereby increasing the possibility of global optimization. The strategy of reducing the material removal rate makes the optimization process more flexible and adaptable. When the convergence conditions are not met, by reducing the material removal rate, the optimization can be carried out more cautiously to ensure that the structural performance is not negatively affected by excessive material removal.

[0147] In step S6, the volume constraint is achieved by controlling the material volume fraction, including the steps of:

[0148] Limit the material volume fraction during optimization to ,in V T =∑ i v i is the total volume of the design domain, v i is the unit volume, f This limit ensures that the total amount of material will not exceed the preset volume fraction during the optimization process. f , thereby achieving effective control of the total volume.

[0149] To satisfy the material volume constraints, the cell density is updated as follows:

[0150] Update the cell density by Lagrange multiplier method or sensitivity screening strategy so that ; By introducing Lagrange multipliers, the volume constraint problem can be transformed into an unconstrained optimization problem, thereby solving the optimal unit density distribution.

[0151] The sensitivity screening strategy involves removing inefficient materials based on unit sensitivity ranking and dynamically adjusting the removal threshold to match the target volume. Specifically, the sensitivity value of each unit is first calculated and ranked according to the sensitivity value; secondly, based on the ranking results, the material units with low sensitivity are removed; in order to match the target volume, the material removal threshold is dynamically adjusted to ensure that the material volume gradually approaches the preset volume fraction during the optimization process. .

[0152] A volume constraint method based on material volume fraction control effectively constrains the total volume of the design domain. Simultaneously, the Lagrange multiplier method and sensitivity screening strategy optimize the unit density distribution, resulting in more efficient material utilization and improved structural performance. This approach not only ensures that the air-jet loom frame structure meets volume constraints, but also significantly enhances its mechanical properties and stability.

[0153] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing the frame structure of an air jet loom based on the BESO method, characterized in that: The steps include: S1. Build a 3D model of the air jet loom frame, define the material physical parameters and divide the mesh units, and apply assembly loads and boundary conditions. S2. Construct the directional flexibility objective function based on vibration modal analysis, set the volume constraint threshold and the evolution rate parameter of the BESO algorithm; S3. Identify weak areas of the rack through finite element stress analysis, and extract the geometric coordinates of key assembly areas within the weak areas based on the rack assembly functional requirements as a core assembly feature point set; S4. Construct a weight allocation model to calculate the three-dimensional distances from all elements in the weak area to the nearest core feature point, divide the design domain into a prohibited optimization area, a transition optimization area, and a free optimization area according to a preset distance threshold, and allocate element optimization weights based on the distances; S5. Perform regional BESO optimization iterations: Calculate element sensitivity based on the directional flexibility objective function, adjust the sensitivity value according to the weight, and update the element density according to the following strategy: lock the element density to 1.0 in the prohibited optimization area, adjust the density by interpolation according to the weight ratio in the transition optimization area, and remove inefficient elements in the free optimization area according to the adjusted sensitivity; calculate the remaining material volume and directional weighted flexibility change rate of the current iteration; S6. If the remaining material volume does not reach the volume constraint threshold, or the directional weighted flexibility change rate does not meet the preset convergence condition, return to S5 to continue iteration. If both the volume constraint and the flexibility convergence condition are met, the topology optimized frame model is output.

2. The air jet loom frame structure optimization method based on the BESO method according to claim 1, characterized in that: Identifying the weak area of ​​the frame in step S3 includes: determining the stress concentration area through finite element stress analysis, marking the weak area when the local stress value exceeds a preset ratio of the material allowable stress, and visually locating it through a three-dimensional stress cloud map.

3. The air jet loom frame structure optimization method based on the BESO method according to claim 1, characterized in that: The directional flexibility objective function in step S2 is defined as: ,in, is the flexibility in the X direction, is the X-direction weight, is the flexibility in the Y direction, is the Y direction weight, K is the structural stiffness matrix, calculated by the finite element method, and the weight coefficient satisfies To suppress the lateral vibration of the air jet loom.

4. The air jet loom frame structure optimization method based on the BESO method according to claim 1, characterized in that: The method of constructing the weight distribution model in step S4 includes the following steps: S41, calculating the three-dimensional distance between the unit and the core feature point; ,in, x a , y a , z a For unit The spatial coordinates of x Oi , y Oi , z Oi for No. i Core assembly feature points O i The spatial coordinates of S42, according to the distance allocation unit optimization weight, the weight function is selected from any one of the following: the inverse model is , the exponential model is ,in L i is the distance from the unit to the nearest core point, p is the penalty factor, λ is the attenuation coefficient, is the smoothing constant, ω i is the initial weight, Optimize weights for units; S43. Divide the design domain into a prohibited optimization area, a transition optimization area, and a free optimization area based on the distance threshold.

5. The air jet loom frame structure optimization method based on the BESO method according to claim 4, characterized in that: The cell density update strategy of the regional BESO optimization iteration in step S5 is: the cell density of the prohibited optimization area is forced to be locked to ρ i =1.0; the cell density in the transition optimization area is adjusted by weight interpolation, and the interpolation formula is: , in η is the relaxation factor, is the intermediate density variable; the free optimization region removes inefficient units according to the adjusted sensitivity ranking.

6. The air jet loom frame structure optimization method based on the BESO method according to claim 3, characterized in that: The unit sensitivity calculation in step S5 includes the superposition of multiple load conditions, and the comprehensive sensitivity calculation is the weighted sum of each load type: ,in is the weight coefficient of the mth type of load, In order to correspond to the sensitivity of the load, the load types include at least the beating force, the shedding mechanism force and the inertia force.

7. The air jet loom frame structure optimization method based on the BESO method according to claim 4, characterized in that: The weight distribution model integrates a stress protection mechanism, which includes applying a weight amplification factor to elements in high stress areas, defined as: ,in, k is the stress amplification factor, 0.5≤ k ≤2.0, σ i is the unit stress, σ yield is the yield strength of the material; the stress gradient of adjacent elements is constrained to satisfy: ,in, σ j 、 σ i is the stress of adjacent elements, L ij is the unit spacing, Δ σ max is the maximum allowable stress difference, and Δ σ max ≤0.2 σ yield , Δ L is the unit characteristic size.

8. The air jet loom frame structure optimization method based on the BESO method according to claim 3, characterized in that: The convergence criterion in step S6 is: the rate of change of the directional weighted flexibility objective function satisfies: ,in, For the k The weighted flexibility value of the iteration, The convergence threshold is preset. If the above conditions are not met for multiple consecutive iterations, it will return to the historical optimal solution and reduce the material removal rate.

9. The air jet loom frame structure optimization method based on the BESO method according to claim 2, characterized in that: The protection of the key assembly area in step S3 includes defining a protection zone with the assembly positioning point as the center, and the protection radius meets R ≥ R min And it is positively correlated with the assembly size tolerance; the unit density in the protection zone is forced to be locked to ρ i =1; the protection zone element stiffness matrix is ​​modified to K ′= K + αK 0, where K is the current stiffness matrix, K 0 is the initial stiffness matrix, α is the reinforcement coefficient; the units outside the protected area are optimized according to the weight distribution model.

10. The air jet loom frame structure optimization method based on the BESO method according to claim 1, characterized in that: The volume constraint in step S6 is achieved by controlling the material volume fraction, including the steps of limiting the material volume fraction in the optimization process to ,in V T =∑ i v i is the total volume of the design domain, v i is the unit volume, f is the preset material volume fraction; Update the cell density by Lagrange multiplier method or sensitivity screening strategy so that ; The sensitivity screening strategy includes removing inefficient materials according to unit sensitivity ranking and dynamically adjusting the removal threshold to match the target volume.

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