A method for designing a damping structure of a wall-beam joint of an air jet loom

Abstract

The application relates to the field of air-jet loom design, and proposes a damping structure design method for the wall plate-beam connection of an air-jet loom. First, a parameterized dynamic model is established, with the minimum vibration transmissibility and the maximum modal loss factor as the targets. A nonlinear viscoelastic constitutive model of a composite damping material is adopted, the damping structure is composed of a base layer, a viscoelastic damping layer, a friction sliding layer and a constraint layer, and the interface mechanical coupling relationship between the layers of the damping structure is determined. The system equation and the finite element model are constructed by integrating the above models, and the parameters such as the damping layer distribution and the friction coefficient are iteratively optimized. The model is calibrated by comparing the theoretical solution with the simulation result, and a complete design system is formed. Finally, based on multiple regression analysis, a standardized adaptation formula of key design parameters and loom working conditions is derived. The method solves the problems of traditional design blindness, inefficiency and slow adaptation, and realizes the efficient design of the damping structure with predictability and rapid adaptation.

Description

Technical Field

[0001] This application relates to the field of air jet loom design, and more particularly to a damping structure design method for the connection between the wall panel and the crossbeam of an air jet loom. Background Technology

[0002] As a core piece of equipment in the textile industry, vibration control during high-speed operation of air-jet looms is crucial to weaving quality and equipment reliability. The main operating frequency range of air-jet looms is typically 10-20Hz, and the operating temperature range covers a wide range from -40℃ to 80℃. During high-speed operation, the connection between the wall panel and the crossbeam becomes a critical node for vibration transmission and amplification. Harmonic excitation forces generated by weft insertion force and airflow impact induce strong vibrations at this point. If this vibration is not effectively suppressed, it will be transmitted to the entire machine through the connection structure, severely affecting the surface finish and uniformity of the woven fabric, accelerating wear and fatigue of various components, shortening equipment lifespan, increasing maintenance costs, and reducing overall production efficiency.

[0003] Currently, existing technologies for vibration reduction at the wall panel-beam connection of air-jet looms mostly employ rigid connections or simple single-layer damping structures. Rigid connections offer almost no vibration reduction capability, resulting in extremely high vibration transmission efficiency, which fails to meet the stability requirements of high-speed looms. Simple single-layer damping structures have a single energy dissipation mechanism, typically providing limited attenuation for vibrations in specific directions or narrow frequency bands. This structure cannot fully adapt to the wide frequency range of 10-20Hz and the wide temperature range of -40℃ to 80℃ experienced by air-jet looms in actual operation. Its vibration reduction performance degrades significantly or even fails under temperature and frequency changes, making it difficult to achieve stable and efficient vibration reduction under all operating conditions.

[0004] A deeper problem lies in the lack of a systematic and targeted design methodology in current technologies. Existing damping structure designs often rely on experience or trial and error, failing to develop a complete theoretical model and design process specifically for the unique dynamic characteristics of the wall panel-beam connection in air-jet looms (such as axial and radial coupled vibrations). The design process is highly unpredictable, unable to accurately quantify the correlation between the energy dissipation performance of the damping structure and the final vibration reduction effect, leading to a disconnect between design and effect, and an inability to achieve precise vibration reduction. Furthermore, due to the lack of a systematic design methodology, the damping structure often needs to be redesigned for different models and operating conditions of air-jet looms, making it neither universal nor replicable, resulting in long design cycles and high R&D and modification costs.

[0005] Therefore, an innovative damping structure design method is urgently needed for the connection between the wall panel and crossbeam of an air-jet loom. This method not only requires conceiving an efficient damping structure form adaptable to wide frequency and temperature range operating conditions, but more importantly, it must provide a complete and systematic design framework from theoretical modeling, parameter quantification, performance prediction to engineering adaptation. This is to overcome the fundamental defects of existing technologies, such as blind design, poor results, and inability to be generalized, thereby achieving predictable, reproducible, and applicable precise vibration reduction design for different loom models. Summary of the Invention

[0006] In view of this, this application proposes a damping structure design method for the connection between the wall panel and the crossbeam of an air-jet loom, aiming to solve the technical problem that the existing damping structures at the connection between the wall panel and the crossbeam of an air-jet loom have poor vibration reduction effect and cannot be universally adapted due to the lack of systematic and targeted design.

[0007] The technical solution of this application is implemented as follows: This application discloses a damping structure design method for the connection between the wall panel and the crossbeam of an air-jet loom, including the following steps: S1. Obtain the geometric and material parameters of the wall panel-beam connection structure of the target model air jet loom, establish a parameterized dynamic model of the connection structure accordingly, and set the optimization objectives as minimizing vibration transmissibility and maximizing modal loss factor. S2. Determine the composite damping material for the damping structure used in the connection structure. Based on the working frequency domain and temperature domain of the air jet loom, obtain the nonlinear viscoelastic constitutive relationship of the composite damping material. The damping structure includes a base layer, a viscoelastic damping layer, a friction slip layer and a constraint layer arranged sequentially from the inside to the outside. S3. Based on the aforementioned nonlinear viscoelastic constitutive relation, determine the interfacial mechanical coupling relationship between the layers of the damping structure; S4. Integrate the parametric dynamic model, nonlinear viscoelastic constitutive relation, and interfacial mechanical coupling relation to form a systematic coupling equation characterizing the overall dynamic characteristics of the connection structure and the damping structure; S5. Based on the system coupling equation, establish a finite element model of the connection structure and the damping structure as a whole, and iteratively optimize the key design parameters of the damping structure with the optimization objective. The key design parameters include the coverage area of ​​the viscoelastic damping layer, the friction coefficient of the interface between the viscoelastic damping layer and the friction slip layer, and the connection preload. S6. Substitute the key design parameters obtained by iterative optimization into the systematic coupling equation to calculate the theoretical solution. Compare the calculated theoretical solution with the simulation prediction results of the finite element model, and correct the parameters in the interface mechanical coupling relationship based on error analysis to update the finite element model and form a corrected finite element model. Based on the corrected finite element model, input the working condition parameters of the air jet loom, and output the key design parameters of the damping structure that are adapted through simulation calculation.

[0008] This application has the following advantages over the prior art: (1) The damping structure design method for the connection between the wall panel and the crossbeam of the air-jet loom disclosed in this application constructs a complete technical chain of data input and target setting → determination of material and interface relationship → system model integration → numerical optimization → model verification and calibration → rapid design application. It systematically transforms the damping structure design from an experience-based trial-and-error mode to a quantifiable and reproducible mode based on theoretical prediction, numerical optimization and closed-loop verification. This method not only obtains a highly reliable corrected finite element model through iterative optimization and calibration, but also realizes rapid design parameter output for new working conditions through this model. It fundamentally solves the technical problems of blindness, inefficiency and inability to quickly adapt to different machine models in traditional design, and provides a complete solution for achieving efficient, accurate and rapid vibration reduction design of air-jet loom connection nodes.

[0009] (2) By establishing precise mechanical relationships based on material constitutive parameters for the interfaces between layers of the damping structure, and specifically defining the mechanical coupling relationship between the viscoelastic damping layer and the friction slip layer as a piecewise function relationship that adapts to the vibration load, a precise quantitative description of the microscopic energy dissipation mechanism inside the structure is achieved. This scheme transforms the synergistic effect of the two energy dissipation mechanisms, viscoelastic shear and friction slip, from an abstract concept into a calculable and predictable mathematical model, thereby providing a key, adaptive interface behavior criterion for the entire design system under wide working conditions. It is the core theoretical foundation for ensuring that the final damping structure achieves efficient and intelligent vibration reduction.

[0010] (3) The piecewise calculation model for total energy consumption provided in this embodiment is the direct integration and quantification output of the piecewise function interface relationship at the system-level performance level. This model not only clearly reveals the two-stage energy consumption mechanism of the adaptive switching and coordination of viscoelastic energy consumption and frictional energy consumption of the damping structure with different working conditions, but more importantly, it establishes a precise and calculable quantitative relationship between material parameters, key design variables and the final vibration reduction performance index (modal loss factor). This model can be directly used as the embedded objective function or evaluation function in the optimization process of step S5, so that the iterative optimization process guided by maximizing the modal loss factor has a specific and efficient calculation basis, which is a key theoretical tool for realizing accurate and predictable design of damping structures.

[0011] (4) The standardized adaptation formula defined in this application is the key to the leap from precise but cumbersome case design to rapid and reliable generalized application of this design method. It extracts the complex nonlinear relationships implicit in the complete design theory system into concise and clear linear empirical formulas within a specific engineering parameter space, which greatly reduces the application threshold of this method, improves design efficiency, and fundamentally solves the industrial problems of existing technologies that cannot be universally applied and replicated, and have long design cycles and high costs. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a schematic diagram of the damping structure at the connection between the wall panel and the crossbeam of the air-jet loom disclosed in an embodiment of this application; Figure 2 This is a flowchart illustrating the damping structure design method for the connection between the wall panel and the crossbeam of an air-jet loom, as disclosed in an embodiment of this application. Figure label: 100, wall panel; 200, beam; 300, damping structure; 310, base layer; 320, viscoelastic damping layer; 330, friction slip layer; 340, restraint layer. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0015] like Figure 1 As shown, combined with Figure 2 This application discloses a damping structure design method for the connection between the wall panel and the crossbeam of an air-jet loom, including the following steps: Step S1: Obtain the geometric and material parameters of the wall panel-beam connection structure of the target model air jet loom, establish a parameterized dynamic model of the connection structure accordingly, and set the optimization objectives as minimizing vibration transmissibility and maximizing modal loss factor.

[0016] This step serves as the starting point for data input, the theoretical foundation, and the direction setting for the entire design process. It involves obtaining the geometric and material parameters of the wall panel-beam connection structure for the target model of the air-jet loom. Specifically, this is achieved by collecting fundamental information such as the dimensions, shape, mass, and elastic modulus of the physical objects of the wall panel and beam, providing precise input data for subsequent quantitative modeling. Based on this, a parametric dynamic model of the connection structure is established. This model uses mechanical principles and mathematical equations to abstract and describe the dynamic behavior of the connection under vibration excitation. The matrices or parameters included in the model, such as mass, stiffness, and damping, are all designed as adjustable variables, thus enabling their correlation with the damping structure parameters to be designed later.

[0017] Setting the optimization objectives as minimizing vibration transmissibility and maximizing modal loss factor establishes clear and quantifiable performance goals for the entire design process. Vibration transmissibility directly measures the efficiency of vibration energy transfer from the excitation source to other parts of the structure through the connecting structure; minimizing it means pursuing the best vibration isolation effect. Modal loss factor characterizes the system's ability to dissipate mechanical energy under specific vibration modes; maximizing it means pursuing the strongest inherent vibration reduction capability. These two objectives together constitute the core criteria for evaluating the quality of the final design, guiding all subsequent optimization work.

[0018] Step S2: Determine the composite damping material for the damping structure of the connection structure. Based on the working frequency and temperature domains of the air jet loom, obtain the nonlinear viscoelastic constitutive relationship of the composite damping material. The damping structure includes a base layer, a viscoelastic damping layer, a friction slip layer, and a constraint layer arranged sequentially from the inside to the outside.

[0019] This step clarifies the material composition and key material properties of the design object. Determining the composite damping material for the damping structure involves selecting or preparing polymer-based materials with specific viscoelastic properties. Based on the unique operating frequency of 10-20Hz and wide operating temperature range of -40℃ to 80℃ of the air-jet loom, the nonlinear viscoelastic constitutive relationship of the composite damping material is obtained. This is to accurately characterize the complex changes in key mechanical parameters of the material, such as storage modulus and loss modulus, with vibration frequency and operating temperature. This relationship is fundamental to ensuring the predictable performance of the damping structure under complex actual working conditions. The defined damping structure adopts a four-layer configuration from the inside out: a base layer, a viscoelastic damping layer, a friction slip layer, and a constraint layer. The base layer is usually connected to the wall panel, serving as the structural foundation; the viscoelastic damping layer is the main body providing frictional energy dissipation from the internal molecular chains of the material; the friction slip layer is in close contact with the viscoelastic damping layer, providing conditions for interfacial slip frictional energy dissipation; the constraint layer is used to constrain the shear deformation of the viscoelastic layer and is connected to the beam body, thereby enhancing its energy dissipation efficiency. These four layers together constitute the physical carrier for realizing the composite energy consumption mechanism.

[0020] Step S3: Based on the nonlinear viscoelastic constitutive relation, determine the interfacial mechanical coupling relationship between the layers of the damping structure.

[0021] This step is crucial for refining the micromechanical behavior of the damping structure, with the three interfaces being the core regions where energy transfer and dissipation occur. Based on the material parameters provided by the nonlinear viscoelastic constitutive relation obtained in step S2, the interfacial mechanical coupling relationships between the layers of the damping structure are determined. This essentially establishes a mathematical relationship between the shear stress generated under vibration at these three interfaces: between the base layer and the viscoelastic layer, between the viscoelastic layer and the friction slip layer, and between the friction slip layer and the constraint layer, and the parameters in the nonlinear viscoelastic constitutive relation.

[0022] Step S4: Integrate the parameterized dynamic model, nonlinear viscoelastic constitutive relation, and interfacial mechanical coupling relation to form a systematic coupling equation characterizing the overall dynamic properties of the connecting structure and the damping structure.

[0023] This step integrates the scattered local relationships into a unified system model. Integrating the parametric dynamic model, nonlinear viscoelastic constitutive relations, and interfacial mechanical coupling relations established in the preceding steps is a comprehensive technical process. Its core is to derive the overall effect exhibited by the entire damping structure at the connection structure based on the aforementioned interfacial mechanical coupling relations, i.e., equivalent dynamic parameters, such as equivalent stiffness parameters and equivalent damping parameters. These equivalent dynamic parameters comprehensively reflect the contribution of the composite structure to the overall dynamic characteristics of the system. Subsequently, these equivalent dynamic parameters are integrated into the parametric dynamic model established in step S1, which describes the dynamics of the basic connection structure, in a linear superposition manner.

[0024] Specifically, the equivalent stiffness contribution is added to the system's total stiffness matrix, and the equivalent damping contribution is added to the system's total damping matrix. This results in a completely new, solvable systemic coupled equation. This equation fully encompasses the dynamic characteristics of both the foundation connection structure and the damping structure, and the coefficients in the equation are directly related to the design parameters of the damping structure, serving as a theoretical bridge connecting microscopic design variables and macroscopic system responses.

[0025] Step S5: Based on the system coupling equation, establish a finite element model of the connection structure and the damping structure as a whole, and iteratively optimize the key design parameters of the damping structure with the optimization objective. The key design parameters include the coverage area of ​​the viscoelastic damping layer, the friction coefficient of the interface between the viscoelastic damping layer and the friction slip layer, and the connection preload.

[0026] This step involves automatic optimization using numerical tools under theoretical guidance. Based on the physical relationships revealed by the systematic coupling equations formed in step S4, a finite element model of the connection structure and damping structure as a whole is established in the finite element analysis software. The establishment of this finite element model essentially transforms the physical laws described by the systematic coupling equations into a computer-recognizable numerical model, ensuring the theoretical consistency of the simulation. Then, guided by the optimization objectives of minimizing vibration transmissibility and maximizing modal loss factor set in step S1, an optimization process is set up. Using the coverage area of ​​the viscoelastic damping layer, the friction coefficient of the interface between the viscoelastic damping layer and the friction slip layer, and the preload of the connecting bolts as adjustable key design parameters, iterative optimization calculations are initiated in the finite element software. This process automatically tries countless parameter combinations, and by comparing the objective function values ​​under each combination, it ultimately finds the optimal set of design parameters that minimizes vibration transmissibility and maximizes modal loss factor.

[0027] Step S6: Substitute the key design parameters obtained by iterative optimization into the systematic coupling equation to calculate the theoretical solution. Compare the calculated theoretical solution with the simulation prediction results of the finite element model. Based on error analysis, correct the parameters in the nonlinear viscoelastic constitutive relationship and the interface mechanical coupling relationship to form a corrected complete design theory system.

[0028] This step constitutes a crucial closed loop of theory-simulation verification, model calibration, and rapid design application. First, the optimal key design parameters obtained through iterative optimization in step S5 are substituted into the systemic coupled equations generated in step S4. The theoretical solutions for vibration transmissibility and modal loss factor are then obtained directly through mathematical analysis or numerical methods. Simultaneously, these same parameters are also used in simulation calculations within the finite element model established in step S5 to obtain the corresponding simulation prediction results.

[0029] The theoretical solution is compared with the simulation prediction results, and the relative error between the two is calculated. Based on this error analysis, the parameters in the interfacial mechanical coupling relationship determined in step S3 are corrected, such as calibrating the friction coefficient of key interfaces (e.g., between the viscoelastic damping layer and the friction slip layer). After correction, the interface properties in the finite element model are updated accordingly. After this calibration process, a corrected finite element model with reliable prediction accuracy is finally formed.

[0030] More importantly, the modified finite element model itself becomes a powerful design tool. Based on this model, by inputting the operating parameters of the target jet loom (such as the main operating frequency and weft insertion force), the model can be directly driven to perform simulation calculations and output optimized key design parameters of the damping structure (such as the coverage area of ​​the viscoelastic damping layer, the interface friction coefficient, and the connection preload), thereby realizing a fast and accurate design process from "operating condition input" to "design parameter output".

[0031] The damping structure design method for the wall panel-beam connection of an air-jet loom disclosed in this application systematically transforms damping structure design from an experience-based trial-and-error mode to a quantifiable and reproducible mode based on theoretical prediction, numerical optimization, and closed-loop verification. This method not only obtains a highly reliable corrected finite element model through iterative optimization and calibration, but also enables rapid output of design parameters for new working conditions. It fundamentally solves the technical problems of blindness, inefficiency, and inability to quickly adapt to different loom models in traditional design, providing a complete solution for efficient, accurate, and rapid vibration reduction design of air-jet loom connection nodes. This involves constructing a complete technical chain: data input and target setting → material and interface relationship determination → system model integration → numerical optimization → model verification and calibration → rapid design application.

[0032] In some embodiments, the specific process of establishing the parameterized dynamic model in step S1 includes: establishing a two-degree-of-freedom dynamic model for axial and radial vibrations based on the geometric and material properties of the wall panel-beam connection structure. The core of this limitation lies in simplifying the complex vibrations of the connection structure into a precisely analyzable two-degree-of-freedom system. The vibrations of the connection node between the air-jet loom wall panel and the beam are mainly manifested as axial vibrations along the connecting bolts and radial vibrations perpendicular to the axial direction. Establishing a two-degree-of-freedom model for these two main directions effectively captures the core dynamic characteristics of the node, ensuring the accuracy of the model while avoiding the analytical complexity caused by excessive freedom, thus laying a simple yet reliable theoretical foundation for subsequent system design.

[0033] The equations of the two-degree-of-freedom dynamic model are expressed as follows: .

[0034] In this equation, [M] is the mass matrix, [ C ] is the damping matrix, [ K ] is the stiffness matrix, { x} is the displacement vector. For velocity vectors, Let { be the acceleration vector, { F} represents the simple harmonic excitation force vector when the air-jet loom is working.

[0035] The mass matrix [M] reflects the inertial characteristics of the connecting nodes in both the axial and radial degrees of freedom. According to a specific embodiment, its expression is: .in, m 1 represents the equivalent mass corresponding to axial vibration. m 2 represents the equivalent mass corresponding to radial vibration. The form of this diagonal matrix indicates that axial and radial inertial coupling is ignored in the modeling, which is consistent with the conventional treatment for simplifying the principal direction analysis of this type of structure.

[0036] Stiffness matrix [ K This describes the elastic recovery characteristics of the connection structure in the axial and radial directions, as well as the possible coupling stiffness. Its specific expression is: In the formula, k 11 and k 22 These represent the direct stiffness in the axial and radial directions, respectively. k 12 and k 21 These represent the coupling stiffness between axial and radial vibrations. These stiffness coefficients are determined by the material and geometric properties of the wall panels, beams, and connecting components.

[0037] Damping matrix [ C This characterizes the energy dissipation characteristics of the system. The initial value is set based on the damping characteristics of the main material and will be corrected in conjunction with the parameters of the damping structure.

[0038] The harmonic excitation force vector {F} during the operation of an air-jet loom represents the external excitation acting on the connection node. In the air-jet loom's operating scenario, the main excitation sources, such as weft insertion and airflow impact, can be modeled as harmonic excitations. Therefore, this excitation force vector has the following form: ,in F 0 For the amplitude of the excitation force, oh This is the excitation angular frequency, corresponding to a main operating frequency of 10~20Hz. t For time, j The imaginary unit, e is the base of the natural logarithm.

[0039] Displacement vector { x}, velocity vector acceleration vector These are the displacement, velocity, and acceleration response column vectors corresponding to the two degrees of freedom, respectively.

[0040] By introducing a well-structured and physically meaningful two-degree-of-freedom dynamic equation, the complex vibration problem of engineering structures is transformed into a standard form that can be mathematically analyzed and numerically analyzed. This model not only quantitatively characterizes the mass, stiffness, damping, and external excitation characteristics of the connection nodes, but more importantly, it provides the initial, parameterized dynamic description of the system for the entire design process. All subsequent design and optimization of damping materials and interface models will ultimately change the dynamic response of the system by influencing the stiffness matrix [K] and damping matrix [C] in this equation, thereby achieving the optimization goals of minimizing vibration transmissibility and maximizing modal loss factor.

[0041] In some embodiments, the optimization objective is based on the vibration transmissibility. T and modal loss factor or m As a core performance indicator, it is expressed as the vibration transmissibility. T Minimize and modal loss factor or m maximize.

[0042] In this embodiment, vibration transmissibility T Vibration transmissibility is a key indicator for evaluating the vibration isolation effect of a system. It is defined as the ratio of the output vibration response to the input excitation amplitude, directly reflecting the efficiency of vibration energy transfer through the wall panel-beam connection node. To ensure the design has theoretical predictive power, its calculation formula needs to be clearly defined. Based on the forced vibration theory of single-degree-of-freedom systems and applicable to the equivalent model of the connection structure, the vibration transmissibility... T This can be expressed as the frequency ratio. r Damping ratio x Functions: .

[0043] Among them, frequency ratio r The relative relationship between the operating frequency of the air-jet loom and the system's natural frequency is defined as: . oh This refers to the operating angular frequency of the air-jet loom, corresponding to a main frequency of 10~20Hz. oh 0 The natural angular frequency of the connection structure is, specifically, the natural angular frequency of the beam. , K For equivalent stiffness, m 2 Represents the equivalent mass corresponding to radial vibration. Frequency ratio. r This determines whether the system operates in the ideal vibration isolation zone. When the operating frequency is within the effective vibration isolation zone, T < 1, thus achieving effective vibration isolation.

[0044] System damping ratio xThe contribution of overall system damping to vibration attenuation is characterized by its ability to dissipate vibration energy; its expression is: Where c is the equivalent damping, which characterizes the system's ability to dissipate vibrational energy. The system damping ratio... x The larger the value, the faster the system vibration decays and the more significant the vibration reduction effect.

[0045] Establish vibration transmissibility T Minimization means optimizing the design to reduce the value of the transmissibility function as much as possible within the target operating frequency domain, thereby achieving efficient vibration isolation.

[0046] Vibration isolation efficiency Derived from vibration transmissibility, and used to quantify the actual vibration reduction effect of the structure, the expression is: ,Will Substituting into the previous expression, we get the following expression: , The larger the value, the more effective the structure is at suppressing vibration.

[0047] Modal loss factor or m Used to measure the energy dissipation capacity of a system at a certain mode, reflecting the efficiency of energy dissipation through damping mechanisms within the vibration period of a structure. Its definition is: .in, This represents the total energy dissipated by the structure within a single cycle. This represents the maximum elastic strain energy of the structure. Elastic strain energy satisfy Modal loss factor or m The larger the value, the higher the structural energy dissipation efficiency and the stronger the ability to suppress resonance conditions. This invention will... or m As a key optimization indicator, it is essential to ensure that the system meets the requirements for resonance suppression and efficient vibration reduction within the mainstream operating frequency domain of the jet loom.

[0048] By vibration transmissivity T Minimize and modal loss factor or m Maximizing performance was established as the core of parallel optimization, achieving synergistic improvement and precise quantification of the system's vibration isolation and energy dissipation performance, and pursuing... T Minimizing vibration energy directly aims to suppress the transmission of vibration energy from the excitation source to the structure, thereby enhancing vibration isolation; while pursuing... or mMaximizing this involves enhancing the structure's inherent ability to dissipate mechanical energy as heat, thereby strengthening damping efficiency. These two aspects complement each other, guiding all subsequent modeling, simulation, and parameter optimization work. This systematically drives the design results to simultaneously meet the stringent requirements of external vibration isolation and internal vibration dissipation, ultimately ensuring that the designed damping structure achieves optimal comprehensive vibration reduction performance under the wide frequency and temperature range conditions of the jet loom.

[0049] In some embodiments, the damping structure comprises, from the inside out: a base layer made of metal, a viscoelastic damping layer, a friction slip layer with a low coefficient of friction, and a rigid constraint layer; wherein the viscoelastic damping layer is made of rubber and the friction slip layer is made of polymer.

[0050] This definition clarifies the specific material composition of the damping structure for achieving an efficient composite energy dissipation mechanism. The base layer, made of metal, such as A6061 aluminum alloy, serves as the mechanical foundation for a reliable connection between the entire damping structure and the wall panel or beam, providing necessary structural stiffness. The viscoelastic damping layer, made of rubber, such as nitrile rubber, is the core functional layer for achieving viscoelastic shear energy dissipation over a wide temperature range. Its polymer chains generate internal friction under alternating stress, converting vibrational mechanical energy into heat energy. The friction slip layer, with a low coefficient of friction, is made of polymer, such as polytetrafluoroethylene (PTFE), which is in close contact with the rubber layer, forming an interface capable of relative slippage. When vibration is strong, this interface undergoes micro-slippage after reaching the slip triggering condition, dissipating a large amount of energy through Coulomb friction. The rigid constraint layer, such as Q235 steel, constrains the internal viscoelastic damping layer, forcing it to primarily undergo shear deformation during vibration, thereby significantly improving the energy dissipation efficiency of this layer. The clear distinction and coordinated design of these four layers in terms of materials and functions are the physical carrier for achieving segmented coupling of viscoelastic energy dissipation and frictional slip energy dissipation in this application.

[0051] The nonlinear viscoelastic constitutive relation was obtained in the following way: based on the WLF temperature frequency shift principle, a description of the modulus of the composite damping material as a function of temperature was established. T With frequency f The relationship between the changes was determined; and through parameter inversion analysis, the parameter ranges of the energy storage modulus and loss modulus of the composite damping material in the operating frequency domain and temperature domain were determined.

[0052] The above scheme limits the technical means for accurately adapting the material model to the specific working conditions of the air-jet loom. Since the air-jet loom operates in a wide temperature range from -40°C to 80°C, temperature changes significantly affect the viscoelastic properties of the composite damping material, leading to changes in the material's storage modulus and loss modulus, thus affecting the vibration reduction effect. Therefore, based on the WLF temperature frequency shift principle, a nonlinear viscoelastic constitutive relation is established to correct the influence of temperature on material properties. The expression for the nonlinear viscoelastic constitutive relation is: .

[0053] In the formula, C1 and C2 are material property constants; T is the actual working temperature of the air-jet loom (°C), ranging from -40°C to 80°C, covering working environments in different regions and seasons; T0 is the reference temperature, set at 25°C (normal operating conditions), serving as the benchmark for temperature correction.

[0054] However, merely establishing a model framework is insufficient; the specific parameters within the model must be obtained. Determining the material parameter range through parameter inversion analysis is a crucial step in making the theoretical model practically applicable in engineering. In practice, dynamic thermomechanical analysis and other tests are required on the composite damping material samples to obtain experimental data on its storage modulus G' and loss modulus G'' at several temperature points and within a certain frequency range. Subsequently, using the WLF equation as the core, an optimization algorithm is employed to globally fit the experimental data, inverting the optimal model parameters C1 and C2, as well as the master curves of G' and G'' at the reference temperature T0. Finally, the value range (parameter range) of the storage modulus G' and loss modulus G'' of the material in the 10~20Hz operating frequency domain and -40℃~80℃ operating temperature domain of an air-jet loom is determined. This calibrated and quantifiable material constitutive model provides reliable input for subsequent accurate calculations of the damping layer's stiffness and damping contribution, and predictions of interfacial mechanical behavior, fundamentally ensuring the accuracy and adaptability of the design method under a wide range of operating conditions.

[0055] In order to obtain accurate nonlinear viscoelastic constitutive relations and parameter ranges, this embodiment provides the following specific implementation methods.

[0056] 1) Sample preparation and dynamic thermomechanical analysis and testing.

[0057] First, according to national standards (such as GB / T 9870.1) or international standards (such as ASTM D4065), the composite damping material (e.g., nitrile rubber) is prepared into standard-sized specimens. Subsequently, testing is performed using a dynamic thermomechanical analyzer. The test should be conducted in shear mode to simulate the actual stress state of the damping layer. The temperature scan range is set from -40℃ to 80℃, fully covering the operating temperature range of the air-jet loom. At each set temperature point, for example, every 10℃ or 20℃, a frequency scan test is performed. The frequency range should be appropriately wider than the operating frequency domain, for example, 0.1Hz to 100Hz, to obtain sufficient frequency domain data for constructing the master curve. During the test, the strain amplitude must be controlled within the linear viscoelastic range to ensure the validity of the data. Through this test, the strain of the material at different temperature points is directly obtained. T i and frequency point f i Energy storage modulus below and loss modulus Original experimental data matrix.

[0058] 2) Time-temperature superposition and parameter inversion based on WLF equations.

[0059] After obtaining the experimental data, time-temperature superposition analysis was performed based on the WLF temperature frequency shift principle to construct the master curve at a reference temperature T0. T0 = 25℃ was selected as the reference temperature. For each test temperature... T i Based on the modulus-frequency data, the horizontal frequency shift factor relative to the reference temperature T0 was calculated using the WLF equation. .

[0060] Initially, C1 and C2 are parameters to be determined. Using manual or computer-aided curve translation techniques, the parameters at different temperatures are... and The experimental curves were shifted along the frequency axis until they were at... T 0 The two curves overlap to form a smooth main curve covering an extremely wide frequency range; the translation amount is... .

[0061] Subsequently, the least squares method was used to perform global automated fitting and inversion of the above process, with the material constants C1 and C2 and the reference temperature as the optimization variables. T 0 Below and The main curve itself, the optimization objective is to minimize all experimental points ( T i , f i , , The overall error between G' and the predicted values ​​from the WLF equation and the principal curve is calculated. Through iterative solutions, the optimal model parameters C1 and C2 are finally derived, along with a mathematical expression describing G' and G'' as a function of the reduced frequency. The equation of the changing principal curve.

[0062] 3) Determine the parameter range of the working domain.

[0063] Based on the calibrated WLF equations, the performance parameters of the material under specific working conditions of an air-jet loom are calculated. The operating temperature range (-40℃~80℃) and operating frequency range (10Hz~20Hz) are substituted into the model.

[0064] For any given operating temperature T, the corresponding WLF equation can be used to calculate... , operating frequency domain Convert to refracted frequency domain You can query or calculate the corresponding G' and G'' values ​​within the reduced frequency range on the main curve.

[0065] By traversing the entire operating temperature range, the complete surfaces of the energy storage modulus G' and loss modulus G'' as a function of operating conditions can be obtained, thereby determining their parameter ranges under the operating conditions of 10~20Hz and -40℃~80℃. For example, the range of values ​​for the energy storage modulus G' is... MPa, the range of values ​​for loss modulus G'' is MPa.

[0066] In some embodiments, the interfacial mechanical coupling relationship is achieved by establishing mathematical relationships between the interfacial shear stress and the parameters in the nonlinear viscoelastic constitutive relation for each layer of the damping structure.

[0067] In this embodiment, based on the material parameters provided by the nonlinear viscoelastic constitutive relation determined in step S2, particularly the storage modulus G' and loss modulus G'', a precise mathematical description of the micromechanical behavior of each interface is established. Specifically, this involves establishing the alternating shear stress of each interface. t With shear strain c The constitutive relation equation between the macroscopic material properties and the microscopic interfacial mechanical response makes the interfacial behavior predictable and calculable.

[0068] The interfacial mechanical coupling relationship between the base layer and the viscoelastic damping layer, and the interfacial mechanical coupling relationship between the friction slip layer and the constraint layer, are both continuous functions of shear stress and shear strain.

[0069] For ease of description, the interface between the base layer and the viscoelastic damping layer is defined as the first interface, the interface between the viscoelastic damping layer and the friction slip layer is defined as the second interface, and the interface between the friction slip layer and the constraint layer is defined as the third interface.

[0070] For the first interface, namely the interface between the base layer and the viscoelastic damping layer, its mechanical behavior is mainly manifested as pure shear deformation of the viscoelastic damping layer. The interfacial mechanical coupling relationship is a constitutive relation describing the pure viscoelastic shear behavior, which is a continuous function. Specifically, its shear stress... t 1 is represented as: .

[0071] in, The shear strain amplitude at the first interface. The frequency of vibration. t For time, j The imaginary unit, e is the base of the natural logarithm.

[0072] According to the principle of strain compatibility constraints, the shear strain amplitude γ at the first interface 10 The overall shear strain amplitude γ0 of the composite damping layer is equal to that of the composite damping layer, i.e., γ 10 =γ0. The basic definition of the shear strain amplitude γ0 is the sum of the wall panel vibration amplitude A and the thickness of the composite damping layer. The ratio, its expression is: Substituting the above-mentioned strain compatibility relationship and the definition of shear strain amplitude into the mechanical coupling relationship formula of the first interface, a simplified expression for the shear stress of the first interface can be further derived: .

[0073] This formula shows that there is no relative slip at the first interface, and energy is dissipated solely through the shear deformation of the composite damping material. With vibration amplitude Proportional The larger the value, the greater the shear stress and the more energy is consumed.

[0074] Furthermore, the mechanical coupling relationship at the first interface indicates that the stress response at the first interface is entirely determined by the sum of the storage modulus G' and the loss modulus G'' of the viscoelastic material, with the storage modulus G' contributing the elastic restoring force. Both contribute to viscous dissipation capacity, and together they dissipate vibrational energy in a continuous manner.

[0075] The mechanical coupling relationship of the second interface is a piecewise function relationship of shear stress and shear strain. The specific form of the piecewise function relationship is based on the comparison result of the vibration bending moment and the slip trigger threshold of the second interface.

[0076] The second interface, the one between the viscoelastic damping layer and the friction slip layer, is the key location where coordinated energy dissipation occurs. The mechanical coupling relationship at this second interface is not a single continuous function, but a piecewise function. The piecewise division is based on the vibration bending moment borne by the second interface. M With a predefined slip trigger threshold The comparison results.

[0077] When vibration bending moment M Less than the slip trigger threshold At this time, the load on the second interface is relatively small, insufficient to overcome the static friction and induce macroscopic slippage. The mechanical behavior of the second interface is similar to that of the first interface, exhibiting pure viscoelastic shear, and its constitutive relation is a continuous function: .

[0078] in, The value represents the shear strain amplitude at the second interface. At this point, energy dissipation mainly depends on the internal friction of the viscoelastic material.

[0079] When vibration bending moment M Reaching or exceeding the slip trigger threshold At this point, if the load on the second interface is sufficiently large, it triggers relative slip between the frictional slip layer and the viscoelastic layer. The mechanical behavior of the second interface undergoes a sudden change, and the constitutive relation becomes a different function. Its shear stress... In addition to the viscoelastic shear stress, a frictional stress term determined by Coulomb's law of friction is added. .

[0080] in, Let be the coefficient of friction of the second interface. This refers to the additional normal pressure caused by vibration. This represents the frictional energy dissipation caused by interface slip, which is independent of velocity. At this point, the energy dissipation mechanism becomes a coupled superposition of viscoelastic energy dissipation and frictional slip energy dissipation, resulting in a significant improvement in energy dissipation efficiency.

[0081] First, the vibration bending moment M is analyzed. It originates from the simple harmonic excitation force during the operation of the air-jet loom. Its magnitude is determined by both the amplitude of the simple harmonic excitation force and the length of the lever arm. The calculation formula is as follows: In the formula, The distance from the point of application of the weft force to the connecting node. F a For the amplitude of the harmonic excitation force, M Follow F a Changes, resonance of the jet loom M To reach the maximum value, it is necessary to ensure that at this time... This causes friction to consume energy.

[0082] The slip trigger threshold in this embodiment The slip-triggered bending moment threshold. It is a key parameter for initiating frictional slip energy dissipation, and needs to be derived from interfacial friction characteristics, vibration-induced additional normal pressure, and structural dimensions. Its calculation formula is as follows: .

[0083] In the formula, The preload of the connecting bolts, h The lever arm length is determined based on the bolt distribution. The additional normal pressure from the vibration is involved. This is the additional normal force generated by the vibration inertia of the connection node during vibration. Its magnitude is closely related to the equivalent mass of the connection node, the vibration angular frequency, and the vibration amplitude of the wall panel. The calculation method is as follows: .

[0084] In the above calculation formula, Let A be the equivalent mass of the connecting node, and let A be the vibration amplitude of the wall panel. The vibration angular frequency is the additional normal pressure applied during vibration. It increases with increasing vibration intensity to ensure high vibration levels. Lowering the friction makes it easier to initiate frictional slip.

[0085] In the above calculation formula, the lever arm length is determined based on the bolt distribution. h The definition of is: In the formula, The center distance (m) of the high-strength bolts. The value of directly affects The size is adjusted by... Precise control This ensures that it matches the resonant bending moment of the jet loom.

[0086] According to the principle of strain compatibility, in order to ensure consistent deformation between the first and second interfaces and avoid stress concentration due to deformation differences, the shear strain amplitude of the second interface is... The shear strain amplitude of the first interface needs to be compared with that of the second interface. To maintain equality, the constraints are: This constraint effectively ensures the deformation consistency of the two-layer structure, avoids damage to the damping layer structure caused by stress concentration, and maintains the overall stability of the four-layer damping structure.

[0087] For the third interface, namely the interface between the friction slip layer and the constraint layer, its mechanical behavior is mainly elastic shear, without any energy dissipation. Its core function is to transfer loads, compress the damping structures of each layer, and ensure the fit and overall stability of the four-layer damping structure. The mechanical coupling relationship of the third interface is the constitutive relation describing the elastic shear behavior, which is also a continuous function. Specifically, its shear stress... t 3 Represented as .

[0088] in, The shear strain amplitude at the third interface can be obtained from the shear stress at the second interface. t 2 Shear modulus of the constraint layer material G S The derivation yields the following formula: .

[0089] Due to the shear modulus of the constraint layer material The shear strain amplitude γ at the third interface is much larger than the storage modulus G' of the composite damping material. 30 The deformation is extremely small and can be approximated as negligible. This characteristic ensures that the third interface hardly deforms during vibration, serving only as a load transfer carrier. It ensures that the constraint layer can effectively compress each layer of damping structure, maintaining the integrity and stress stability of the four-layer damping structure, and providing a guarantee for the efficient energy dissipation of the first and second interfaces.

[0090] By establishing precise mechanical relationships based on material constitutive parameters for the interfaces between layers of the damping structure, and specifically defining the mechanical coupling relationship between the viscoelastic damping layer and the friction slip layer as a piecewise function that adapts to vibration loads, a precise quantitative description of the microscopic energy dissipation mechanism within the structure is achieved. This scheme transforms the synergistic effect of viscoelastic shear and friction slip energy dissipation mechanisms from abstract concepts into a calculable and predictable mathematical model. This provides a crucial, adaptive interface behavior criterion for the entire design system, adaptable to a wide range of operating conditions, and forms the core theoretical foundation for ensuring efficient and intelligent vibration reduction in the final damping structure.

[0091] In some embodiments, single-cycle energy dissipation is a core indicator for measuring the energy dissipation capacity of each interface and a key basis for quantifying the energy dissipation efficiency of the entire damping structure. The total energy dissipation is the sum of the single-cycle energy dissipation of the first, second, and third interfaces. Their mechanical coupling relationship needs to be derived by considering the interface energy dissipation characteristics under different vibration conditions, based on the vibration bending moment. With slip-triggered bending moment threshold The magnitude relationship can be described in two cases, and the specific coupling equations are as follows:

[0092]

[0093] in, This represents the total energy consumption per cycle. The single-cycle energy consumption of the first, second, and third interfaces are shown below. The single-cycle energy consumption and related key parameters of each interface are further derived and explained in detail.

[0094] For the first interface, its energy dissipation is solely based on viscoelastic shear deformation. Combining this with the general law of single-cycle shear energy dissipation for viscoelastic materials, the formula for calculating its single-cycle energy dissipation W1 can be derived as follows: In this formula, π is a constant, and G'' is the loss modulus of the composite damping material. For the effective volume of the composite damping layer, γ 10 The shear strain amplitude of the first interface directly reflects the basic energy consumption contribution of the first interface.

[0095] For the second interface, its energy consumption mode changes with the vibration condition, and is divided into two cases: low vibration condition and high vibration condition. Energy is dissipated solely through viscoelastic shear deformation, and its single-cycle energy dissipation W2 is consistent with the J1 interface form, i.e. High vibration conditions The frictional slip energy consumption is initiated, and the energy consumption per cycle is the sum of the viscoelastic shear energy consumption and the frictional slip energy consumption, i.e. .

[0096] For the third interface, since it only undergoes elastic shear deformation and does not generate energy dissipation, its single-cycle energy consumption W3 is 0, i.e. .

[0097] Effective volume of viscoelastic damping layer These are fundamental parameters for calculating viscoelastic shear energy dissipation. Their magnitude is determined by the effective contact area between the viscoelastic damping layer and each interface, as well as the thickness of the viscoelastic damping layer. The calculation formula is as follows:

[0098] In the formula, This represents the effective contact area between the viscoelastic damping layer and each interface. This refers to the thickness of the viscoelastic damping layer. From the perspective of energy dissipation principles, The larger the volume, the greater the potential for viscoelastic shear energy dissipation of the composite damping material. However, in actual design, it is necessary to combine engineering costs and structural space, and reasonably control the coverage area ratio of the damping material to achieve a balance between energy dissipation performance and material cost.

[0099] The unidirectional microslip amplitude of the second interface under high vibration conditions s 0 is the core parameter for calculating the energy dissipation of frictional slip. Its magnitude is related to the vibration bending moment, slip trigger threshold, slip coefficient, and slip equivalent stiffness. The derivation formula is as follows:

[0100] In the formula, k The slip coefficient, This represents the slip-equivalent stiffness. Wherein, the slip coefficient... k coefficient of friction with the second interface m 2. Related, its calculation formula is:

[0101]

[0102] This formula reflects the relationship between the slip coefficient and the friction coefficient. m The larger the value of 2, the greater the slip coefficient. k The smaller the value, the smaller the corresponding unidirectional microslip amplitude. s The smaller the value of 0, the better it is at avoiding structural damage caused by excessive slippage and ensuring the long-term durability of the damping structure.

[0103] Slip equivalent stiffness It is a key parameter for controlling the amplitude of unidirectional microslip. Its magnitude is determined by the shear modulus of the constraint layer material, the effective contact area, and the thickness of the friction slip layer. The calculation formula is as follows:

[0104] In the formula, The thickness of the friction slip layer, The shear modulus of the constraint layer material. This can be achieved through reasonable adjustment. The value of [value] ensures the amplitude of unidirectional micro-slip. s The slippage should be controlled within a reasonable range to avoid excessive slippage affecting structural stability, while ensuring the high efficiency of energy dissipation through frictional slippage.

[0105] Under high vibration conditions, the frictional slip energy dissipation at the second interface is the main source of the total energy dissipation of the entire damping structure, and its frictional energy dissipation... The calculation formula is:

[0106] The coefficient 4 in the formula originates from the reciprocating slip process within the vibration cycle: within a complete vibration cycle, the second interface will undergo positive slip. s 0 → Reverse Slide s The reciprocating motion of 0 has a total sliding distance of 4. s Therefore, a coefficient of 4 is introduced to ensure the accuracy of friction energy consumption. This part of friction energy consumption accounts for the vast majority of the total energy consumption under high vibration conditions. It is the core support for achieving efficient energy consumption of high-frequency vibration in air-jet looms and is also the key advantage of the dual energy consumption mechanism.

[0107] The piecewise calculation model for the total energy dissipation Wd provided in this embodiment is a direct integration and quantification output of the piecewise function interface relationship at the system-level performance level. This model not only clearly reveals the two-stage energy dissipation mechanism of the adaptive switching and synergistic interaction between viscoelastic and frictional energy dissipation in damped structures under varying operating conditions, but more importantly, it establishes a precise and calculable quantitative relationship between material parameters, key design variables, and the final vibration reduction performance index (modal loss factor). This model can be directly used as an embedded objective function or evaluation function in the optimization process of step S5, providing a concrete and efficient calculation basis for the iterative optimization process guided by maximizing the modal loss factor. It is a key theoretical tool for achieving accurate and predictable design of damped structures.

[0108] In some embodiments, the specific method for forming the systemic coupling equations is as follows: the equivalent stiffness contribution and equivalent damping contribution of the damping structure are linearly superimposed into the parameterized dynamic model in the form of stiffness matrix and damping matrix, respectively, to obtain the integrated total stiffness matrix and total damping matrix, thereby constituting the systemic theoretical equations.

[0109] The above scheme clarifies the core mathematical operations for integrating the equivalent parameters of the subsystems into the overall system equations. The equivalent dynamic parameters of the damping structure derived from the aforementioned steps essentially quantify the influence of this four-layer structure on the overall dynamic characteristics of the connecting node system. Expressing the equivalent stiffness contribution and equivalent damping contribution as stiffness and damping matrices, respectively, is a standard and necessary mathematical form for system integration using structural dynamics theory. This process ensures that the characteristics of the subsystems can be accurately incorporated into the analytical framework of a multi-degree-of-freedom system.

[0110] As some embodiments, this application provides a specific implementation method for linearly superimposing the equivalent stiffness contribution and equivalent damping contribution of the damping structure into a parametric dynamic model in the form of a stiffness matrix and a damping matrix. This is a systematic transformation and integration process from a physical model to a mathematical representation, and its detailed steps are as follows: The first step is to derive the equivalent stiffness and damping coefficient from the interface mechanics model.

[0111] Based on the contact mechanics model constructed in step S3, the overall force-displacement relationship and energy dissipation relationship of the damping structure under macroscopic vibration are calculated, thereby obtaining its equivalent stiffness coefficient and damping coefficient.

[0112] First, regarding the equivalent stiffness coefficient Derivation: Equivalent stiffness reflects the ability of a damping structure to provide elastic restoring force under small deformations. It is obtained by analyzing the maximum elastic potential energy stored in the damping structure (especially its core viscoelastic damping layer) over one vibration cycle. Using the constitutive relations of the first and second interfaces in step S3, the total elastic strain energy of the structure at a given strain amplitude can be calculated. Equivalent stiffness coefficient It can be obtained through the principle of energy equivalence and the macroscopic deformation geometry of the structure. For example, for a damping layer whose deformation is mainly shear, its equivalent shear stiffness can be calculated using the principle of energy equivalence and the relationship between macroscopic deformation and geometry. This can be expressed as the material's storage modulus G' and effective area. A 0 and thickness h c Related functions: The material storage modulus G' here is given by the constitutive model determined in step S2 at the target frequency and temperature.

[0113] Secondly, regarding the equivalent damping coefficient Derivation: Equivalent damping reflects the ability of a damped structure to dissipate energy within one vibration cycle. This directly corresponds to the total periodic energy dissipation calculated in the aforementioned embodiment. According to the principles of damping mechanics, for a viscous damped system subjected to harmonic excitation, its energy dissipation per cycle is... With equivalent viscous damping coefficient The strain amplitude γ satisfies the following relationship: .

[0114] Therefore, the equivalent damping coefficient of the damping structure under specific working conditions can be derived from the segmented energy dissipation formula. This coefficient combines the combined contributions of internal friction and interfacial slip friction in viscoelastic materials, and is related to the vibration amplitude (which determines M). Variables related to the relationship.

[0115] The second step is to construct the contribution matrix from the equivalent coefficients. and .

[0116] The equivalent stiffness coefficient obtained in the first step and equivalent damping coefficient Based on the position and connection relationships of the damping structure in the parameterized dynamic model established in step S1, a contribution matrix to the stiffness matrix and damping matrix of the entire system is mapped and constructed. and .

[0117] The two-degree-of-freedom dynamic model established in step S1 typically corresponds to the main motion directions (such as axial and radial) at the connection nodes. It is necessary to analyze how the deformation of the damping structure (four-layer structure) affects these degrees of freedom. For example, the shear deformation of the damping layers directly couples to the radial displacement of the connection nodes.

[0118] Based on mechanical principles and the finite element method, the equivalent stiffness coefficient is... and equivalent damping coefficient It is placed in the corresponding position in the system matrix. For example, if the damping structure mainly affects the first... i If there are 1 degree of freedom, then its contribution to the system stiffness matrix is... It will be a matrix with most elements being zero, only when... There is a value at the position If the damping structure is coupled with the first i and the j If there are degrees of freedom, then the contribution will appear at the corresponding positions (i,i), (j,j), (i,j), (j,i), etc. Matrix The construction method is exactly the same as that, using The dimensions of these contribution matrices are exactly the same as the dimensions of the [K] and [C] matrices of the basic model in step S1.

[0119] The third step is to perform linear superposition to construct the systematic theoretical equations.

[0120] Linear superposition into the parameterized dynamic model is a specific technical means to complete system integration. The parameterized dynamic model established in step S1 has the following general matrix form: .

[0121] in, and Initially, the stiffness and damping characteristics of the main connecting structures, such as wall panels and beams, are primarily characterized. The equivalent stiffness contribution matrix of the damping structure is shown. The equivalent damping contribution matrix is ​​denoted as The second step yields the following result: by linear superposition, these two contribution matrices are directly added to the corresponding matrix of the base model. , .

[0122] Here, and Each element in the matrix has a functional relationship with the key design parameters to be optimized in step S5 (such as the distribution of the damping layer and the friction coefficient of the second interface). Therefore, changes in the design parameters will directly lead to... and The changes.

[0123] Obtain the integrated total stiffness matrix With the total damping matrix Then, substituting it back into the original dynamic equation framework, we obtain the aforementioned systematic theoretical equation: .

[0124] This new equation is the final output of step S4. It has the same form as the initial equation, but its underlying meaning has fundamentally changed: its system matrix... and It fully encompasses all the dynamic characteristics of the basic connection structure and the designed damping structure.

[0125] In some embodiments, the key design parameters of the damping structure are iteratively optimized based on the optimization objective, and the constraints satisfied include: the coverage area of ​​the viscoelastic damping layer accounts for 40% to 60% of the total projected area of ​​the contact region of the connection structure, and the stiffness of the connection structure in the vertical direction after optimization is not less than 25.1 × 10⁻⁶. 4 N / m, and the maximum slip of the interface between the viscoelastic damping layer and the friction slip layer after optimization does not exceed 100μm in one vibration cycle.

[0126] The area ratio constraint aims to balance damping performance and structural connection strength. The coverage area of ​​the viscoelastic damping layer is limited to between 40% and 60% of the total projected area of ​​the contact region of the connected structure, based on in-depth engineering trade-offs. If the ratio is too low, there will be insufficient effective energy-dissipating material, making it difficult to achieve a significant vibration reduction effect; if the ratio is too high, it will excessively encroach on the metal contact area used for high-strength bolt connections or welding in the connection region, potentially weakening the overall load-bearing capacity and reliability of the connection node. This ratio range ensures that the effective coverage of the damping material is maximized while maintaining sufficient mechanical connection strength, representing a key design boundary for achieving engineering feasibility.

[0127] Regarding the vertical stiffness constraint, this constraint is to ensure that the basic mechanical properties of the connection node are not excessively weakened after the introduction of the damping structure. The vertical stiffness of the connection structure refers to its ability to resist deformation in the direction perpendicular to the connection surface (i.e., the main load-bearing direction). The optimized connection structure stiffness must be no less than 25.1 × 10⁻⁶. 4 The threshold is defined as Newton-meters per meter (N / m). This threshold is determined through stress analysis and stability requirements of the air-jet loom wall panel-beam connection node. It ensures that the static and dynamic deformation of the overall structure under major working loads such as weft insertion force remains within permissible limits, avoiding sacrificing the necessary rigidity of the main structure for excessive vibration reduction. During the optimization process, any combination of design parameters that causes the stiffness value in this direction to fall below this threshold will be excluded.

[0128] Regarding the maximum slip constraint, this constraint is directly related to the energy dissipation mechanism of frictional slip at the second interface, aiming to control the amplitude of frictional slip to balance efficient energy dissipation and long-term durability. The optimized maximum slip of the second interface within one vibration cycle is the unidirectional micro-slip amplitude s0 in the formula described in the aforementioned embodiment. Limiting s0 to no more than 100 micrometers is based on two considerations: firstly, sufficient slip is a prerequisite for significant frictional energy dissipation; secondly, excessive slip amplitude can lead to accelerated interface wear, potentially affecting long-term operational stability and lifespan. This upper limit ensures that frictional slip energy dissipation remains within a highly efficient and safe range. In this embodiment, the magnitude of s0 is determined by the formula... Calculation, where k The slip coefficient, K s This is the equivalent stiffness for slippage. This is achieved through reasonable design of interface parameters (friction coefficient μ2, slip layer thickness). h slip (etc.) to regulate k and K s This ensures that when slippage is triggered under high vibration conditions, s0 is actively controlled within 100 μm, thereby achieving controllable and efficient friction energy dissipation.

[0129] In some embodiments, in step S6, the step of correcting the parameters in the interface mechanical coupling relationship based on error analysis specifically involves: calculating the relative error ε between the theoretical solution and the simulation prediction result; if ε > 5%, then correcting the material parameters in the nonlinear viscoelastic constitutive relationship and the friction coefficient of the second interface, and repeating steps S5 and S6 until ε ≤ 5%.

[0130] The theoretical solution and simulation prediction results here refer to the core performance index values ​​calculated under the set of key design parameters obtained after optimization in step S5, namely, the vibration transmissibility. T and modal loss factor or m The relative error ε is calculated separately or in combination for these two indicators. One specific implementation method is to select... or m As a representative verification index, its theoretical solution is calculated. Compared with simulation predictions The relative percentage error between them is calculated using the following formula: .

[0131] Setting ε > 5% as the trigger condition for correction is based on a balance between engineering accuracy requirements and computational efficiency. If ε is greater than this threshold, it indicates that the parameter settings in the currently used theoretical model (including the material constitutive model and the interface contact model) deviate significantly from the actual physical behavior, and its prediction results are unreliable and cannot be used as the basis for subsequent standardized formula derivation. If ε ≤ 5%, the theoretical model is considered to have been effectively calibrated, and its prediction accuracy is within an acceptable range for engineering. The design theory formed by this model system has high credibility. This threshold ensures the reliability of the final complete design theory system.

[0132] When the error exceeds the limit, the parameter that needs to be corrected specifically points to the friction coefficient of the second interface.

[0133] The key parameter in the second interface contact mechanics model—the coefficient of friction. , Directly affects the slip trigger threshold The energy dissipated by friction under high vibration conditions is highly sensitive to the system's damping characteristics. Since the interfacial friction coefficient is affected by various factors such as surface condition and lubrication, the theoretical preset value may differ from the actual situation, making it a key target for calibration.

[0134] The iterative correction process is as follows: If ε > 5%, then correct the friction coefficient in the interface mechanical coupling relationship. Then, repeat steps S5 and S6, i.e., using the corrected parameters, re-establish the finite element simulation model and perform a new round of iterative optimization to obtain new key design parameters. Then, calculate the new theoretical solution and simulation results, and compare the errors. This process is repeated until the calculated relative error ε satisfies the condition ε ≤ 5%.

[0135] When ε ≤ 5%, it means that the calibrated theoretical relationship and the high-fidelity finite element simulation model achieve a high degree of consistency in performance prediction. At this point, the systemic coupling equations, the corrected nonlinear viscoelastic constitutive relation, the corrected interfacial mechanical coupling relation, and the accompanying verified optimization design parameter library together constitute a corrected and complete design theory system. This system is internally self-consistent and predictively accurate, laying a solid theoretical and practical foundation for the reliable derivation of the universal standardized adaptation formula in step S7.

[0136] In some embodiments, step S7 is further included: based on the modified finite element model, multiple sets of different air-jet loom operating condition parameters and their corresponding key optimization design parameters are obtained to form sample data; multiple linear regression analysis is performed on the sample data to obtain a standardized adaptation formula between the key design parameters and the air-jet loom operating condition parameters; the standardized adaptation formula is a multiple linear equation about the air-jet loom operating condition parameters; the air-jet loom operating condition parameters include the main operating frequency of the air-jet loom.f , and the strength of the weft F and the length of the wall panel-beam connection surface L The standardized adaptation formula is used to calculate at least one of the optimized key design parameters, and the standardized adaptation formula is as follows: ,in, For the optimized key design parameters, k 1, k 2, k 3 represents the fit coefficients determined through multiple linear regression analysis.

[0137] Step S7 elevates the design process from model-based case studies to a rapid, formulaic adaptation applicable to a wide range of looms. Specifically, based on the modified finite element model obtained in step S6, a series of pairing data of operating parameters and optimal key design parameters can be efficiently generated by inputting multiple representative combinations of different operating conditions, thus constructing a sample dataset for regression analysis. Subsequently, multiple linear regression analysis is used to fit this dataset, uncovering the inherent statistical regularity between key design parameters and operating conditions. Finally, a standardized adaptation formula with operating conditions as independent variables is derived for each key design parameter, which is expressed as the aforementioned multiple linear equation. This establishes a clear standardized design path: when designing damping structures for new looms or new operating conditions, designers do not need to repeatedly perform complex modeling, optimization, and verification processes. They only need to input the operating conditions of the target loom, and the recommended values ​​of all key design parameters can be directly calculated through the corresponding standardized adaptation formula, thereby completing the adaptation design quickly and efficiently.

[0138] The standardized adaptation formula defined in this embodiment is linear, simple, intuitive, and easy for engineers to understand, remember, and apply. The operating parameters include: operating frequency. f , and the strength of the weft F The length L of the connecting surface is a key, easily obtainable, and measurable parameter characterizing the core working conditions and connecting structure dimensions of different types of air-jet looms. Together, they determine the excitation characteristics of the system and the dynamic boundary conditions of the connecting nodes. (Formula) A model was established to map these three input operating parameters to a specific output design parameter. The direct mathematical mapping of .

[0139] The key design parameters here are the variables defined in steps S1 and S5 that need to be determined through optimization. Specifically, these include: the coverage area of ​​the viscoelastic damping layer, the friction coefficient μ2 of the second interface, and the preload F0 of the connecting bolts. It is important to emphasize that for these three different types of key design parameters, three different standardized fitting formulas will be obtained through independent multiple regression analysis, each formula having its own set of fitting coefficients. k1, k 2, k 3).

[0140] For example, the formula used to output the optimal friction coefficient is: .

[0141] The formula for outputting the optimal preload is: .

[0142] The formula for outputting the optimal viscoelastic damping layer coverage area is: .

[0143] Adaptability coefficient k 1, k 2, k 3 was determined using the statistical method of multiple linear regression analysis. The specific implementation steps are as follows:

[0144] 1) Based on the complete design theory system modified in step S6, select... n Group( n It needs to be large enough, such as n >20) Representative combinations of operating parameters for air-jet looms covering a range of common models ( f i , F i , L i For each set of working conditions ( f i , F i , L i Each step (S5) is executed completely once to obtain the optimal set of key design parameter values ​​corresponding to that working condition, including... , , And so on. n There are 10 sample data points, each containing input variables ( f , F , L and output variables X opt .

[0145] 2) Optimized values ​​of a certain type of key design parameters X opt As the dependent variable, with operating condition parameters f , F , L Using [variable name] as the independent variable, a multiple linear regression analysis was performed. Algorithms such as least squares were used to fit the result that best reflects [variable name]. X opt and f, F , L The coefficient of the linear relationship between them k 1, k 2, k 3 ， Make the formula The regression analysis minimizes the sum of prediction errors for all sample data. It also provides an index to measure the goodness of fit of the formula, thus assessing the reliability of the linear model.

[0146] 3) For each type of key design parameter, repeat the above regression analysis to obtain their respective adaptation coefficients, thereby forming a complete set of working condition parameter-design parameter mapping formula library.

[0147] Finally, by integrating all the obtained standardized adaptation formulas and their usage conditions, an engineering application path is established that outputs optimized design parameters based on input operating parameters. When designing this damping structure for a new air-jet loom, designers only need to input the basic operating parameters of that model. f , F , L The recommended values ​​of all key design parameters can be calculated directly using the corresponding standardized adaptation formulas, without the need for complex modeling, simulation, and optimization iterations.

[0148] The standardized adaptation formula defined in this application is key to the leap of this design method from precise but cumbersome case-specific design to rapid and reliable generalized application. It extracts the complex nonlinear relationships implicit in the complete design theory system into concise and clear linear empirical formulas within a specific engineering parameter space, greatly reducing the application threshold of this method, improving design efficiency, and fundamentally solving the industry problems of existing technologies being unable to be universally applied and replicated, resulting in long design cycles and high costs.

[0149] This application also provides an electronic device. It includes a processor and a memory; the memory stores a computer program, wherein the computer program, when executed by the processor, implements the aforementioned damping structure design method for the connection between the air jet loom wall panel and the crossbeam.

[0150] Specifically, the processor may include, for example, a general-purpose microprocessor, an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor may also include onboard memory for caching purposes. The processor may be a single processing unit or multiple processing units for performing different actions of the method flow according to embodiments of this application.

[0151] Memory can be any medium capable of containing, storing, transmitting, propagating, or transmitting instructions. For example, memory can include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, instruments, or propagation media. Specific examples of memory include: magnetic storage devices such as magnetic tape or hard disk drives (HDDs); optical storage devices such as optical discs (CD-ROMs); and also random access memory (RAM) or flash memory; and / or wired / wireless communication links.

[0152] This application also provides a computer-readable medium storing a computer program that, when executed by a processor, implements the damping structure design method for the connection between the wall panel and crossbeam of a jet loom described above. This computer-readable medium may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into that device / apparatus / system. The aforementioned computer-readable medium carries one or more programs, which, when executed, implement the method according to the embodiments of this application.

[0153] According to embodiments of this application, a computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0154] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A damping structure design method for the connection between the wall panel and the crossbeam of an air-jet loom, characterized in that, The steps include the following: S1. Obtain the geometric and material parameters of the wall panel-beam connection structure of the target model air jet loom, establish a parameterized dynamic model of the connection structure accordingly, and set the optimization objectives as minimizing vibration transmissibility and maximizing modal loss factor. S2. Determine the composite damping material for the damping structure used in the connection structure. Based on the working frequency domain and temperature domain of the air jet loom, obtain the nonlinear viscoelastic constitutive relationship of the composite damping material. The damping structure includes a base layer, a viscoelastic damping layer, a friction slip layer and a constraint layer arranged sequentially from the inside to the outside. S3. Based on the aforementioned nonlinear viscoelastic constitutive relation, determine the interfacial mechanical coupling relationship between the layers of the damping structure; S4. Integrate the parametric dynamic model, nonlinear viscoelastic constitutive relation, and interfacial mechanical coupling relation to form a systematic coupling equation characterizing the overall dynamic characteristics of the connection structure and the damping structure; S5. Based on the system coupling equation, establish a finite element model of the connection structure and the damping structure as a whole, and iteratively optimize the key design parameters of the damping structure with the optimization objective. The key design parameters include the coverage area of ​​the viscoelastic damping layer, the friction coefficient of the interface between the viscoelastic damping layer and the friction slip layer, and the connection preload. S6. Substitute the key design parameters obtained by iterative optimization into the systematic coupling equation to calculate the theoretical solution. Compare the calculated theoretical solution with the simulation prediction results of the finite element model, and correct the parameters in the interface mechanical coupling relationship based on error analysis to update the finite element model and form a corrected finite element model. Based on the corrected finite element model, input the working condition parameters of the air jet loom, and output the key design parameters of the damping structure that are adapted through simulation calculation.

2. The damping structure design method at the connection between the wall panel and crossbeam of the air-jet loom as described in claim 1, characterized in that, In step S1, the parameterized dynamic model is a two-degree-of-freedom dynamic model for the axial and radial vibrations of the connection structure. The equations of the two-degree-of-freedom dynamic model are expressed as follows: Where [M] is the mass matrix, [ C ] is the damping matrix, [ K ] is the stiffness matrix, { x } is the displacement vector. For velocity vectors, Let { be the acceleration vector, { F } represents the simple harmonic excitation force vector when the air-jet loom is working.

3. The damping structure design method at the connection between the wall panel and crossbeam of the air-jet loom as described in claim 1, characterized in that, In step S2, the damping structure comprises, from the inside out: a base layer made of metal, a viscoelastic damping layer, a friction slip layer with a low coefficient of friction, and a rigid constraint layer; wherein, the viscoelastic damping layer is made of rubber and the friction slip layer is made of polymer. Obtaining the nonlinear viscoelastic constitutive relation includes: Based on the WLF temperature frequency shift principle, a model describing the modulus of the composite damping material as a function of temperature is established. T With frequency f The changing relationship: ; in, This is the temperature correction factor. C 1 , C 2 For material constants, T 0 For reference temperature; The energy storage modulus of the composite damping material in the operating frequency and temperature domains was determined through parameter inversion analysis. With loss modulus The parameter range.

4. The damping structure design method at the connection between the wall panel and the crossbeam of the air-jet loom as described in claim 3, characterized in that, In step S3, the interfacial mechanical coupling relationship is achieved by establishing a mathematical relationship between the interfacial shear stress and the parameters in the nonlinear viscoelastic constitutive relation between the interfaces of each layer of the damping structure. The interfacial mechanical coupling relationship between the base layer and the viscoelastic damping layer, and the interfacial mechanical coupling relationship between the friction slip layer and the constraint layer, are both continuous functions of shear stress and shear strain. The interfacial mechanical coupling relationship between the viscoelastic damping layer and the friction slip layer is a piecewise function relationship of shear stress and shear strain. The specific form of the piecewise function relationship is based on the comparison result of the vibration bending moment and the slip trigger threshold at the interface between the viscoelastic damping layer and the friction slip layer.

5. The damping structure design method for the connection between the wall panel and crossbeam of the air-jet loom as described in claim 4, characterized in that, In step S3, the piecewise function expression of the interfacial mechanical coupling relationship between the viscoelastic damping layer and the friction slip layer is as follows: The vibration bending moment at the interface between the viscoelastic damping layer and the friction slip layer At that time, the shear stress at the interface between the viscoelastic damping layer and the friction slip layer τ 2 satisfy: ; The vibration bending moment at the interface between the viscoelastic damping layer and the friction slip layer At that time, the shear stress at the interface between the viscoelastic damping layer and the friction slip layer τ 2 satisfy: ; in, The energy storage modulus of the composite damping material is given. The loss modulus of the composite damping material is given. This represents the shear strain amplitude at the interface between the viscoelastic damping layer and the friction slip layer. The frequency of vibration. t For time, This is the additional normal pressure caused by vibration; j The imaginary unit, e is the base of the natural logarithm; The slip trigger threshold is the slip trigger bending moment threshold. It is determined by the following formula: ,in, The coefficient of friction is the coefficient of friction at the interface between the viscoelastic damping layer and the friction slip layer. The preload of the connecting bolts, h The lever arm length is determined based on the bolt distribution.

6. The damping structure design method at the connection between the wall panel and crossbeam of the air-jet loom as described in claim 5, characterized in that, Based on the interfacial mechanical coupling relationship between the viscoelastic damping layer and the friction slip layer, the total energy dissipated by the damping structure within one vibration cycle W d Determined by the following piecewise equation: ； in, This represents the total energy consumption per cycle. The effective volume of the viscoelastic damping layer is... This represents the shear strain amplitude at the interface between the base layer and the viscoelastic damping layer. It represents the unidirectional microslip amplitude at the interface between the viscoelastic damping layer and the friction slip layer.

7. The damping structure design method for the connection between the wall panel and crossbeam of the air-jet loom as described in claim 2, characterized in that, In step S4, the specific method for forming the systematic coupling equations is as follows: The equivalent stiffness contribution and equivalent damping contribution of the damping structure are linearly superimposed into the parameterized dynamic model in the form of stiffness matrix and damping matrix, respectively, to obtain the integrated total stiffness matrix and total damping matrix, which constitute the system theoretical equation.

8. The damping structure design method for the connection between the wall panel and crossbeam of the air-jet loom as described in claim 1, characterized in that, In step S5, the key design parameters of the damping structure are iteratively optimized based on the optimization objective. The constraints include: the coverage area of ​​the viscoelastic damping layer accounts for 40% to 60% of the total projected area of ​​the contact region of the connection structure; and the stiffness of the connection structure in the vertical direction after optimization is not less than 25.1 × 10⁻⁶. 4 N / m, and the maximum slip of the interface between the viscoelastic damping layer and the friction slip layer after optimization does not exceed 100μm in one vibration cycle.

9. The damping structure design method for the connection between the wall panel and the crossbeam of the air-jet loom as described in claim 4, characterized in that, In step S6, the parameters in the nonlinear viscoelastic constitutive relation and the interface mechanical coupling relation based on error analysis are specifically: the relative error ε between the theoretical solution and the simulation prediction result is calculated. If ε > 5%, the friction coefficient of the interface between the viscoelastic damping layer and the friction slip layer is corrected, and steps S5 and S6 are repeated until ε ≤ 5%.

10. The damping structure design method at the connection between the wall panel and the crossbeam of the air-jet loom as described in claim 1, characterized in that, The method also includes step S7: Based on the modified finite element model, multiple sets of different air-jet loom operating condition parameters and their corresponding key optimization design parameters are obtained to form sample data. Multiple linear regression analysis is performed on the sample data to obtain a standardized adaptation formula between the key design parameters and the air-jet loom operating condition parameters. The standardized adaptation formula is a multiple linear equation relating the air-jet loom operating condition parameters. The air-jet loom operating condition parameters include the main operating frequency of the air-jet loom. f , and the strength of the weft F and the length of the wall panel-beam connection surface L The standardized adaptation formula is used to calculate at least one of the optimized key design parameters, and the standardized adaptation formula is as follows: ,in, For the optimized key design parameters, k 1, k 2, k 3 represents the fit coefficients determined through multiple linear regression analysis.

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