Improved elastic interaction-based polymer material flange bolt tightening optimization method and system

Abstract

This invention relates to the field of bolt preload optimization technology, specifically a method and system for optimizing bolt tightening in polymer flanges based on improved elastic interactions. By combining the traditional elastic interaction coefficient method with a material viscoelastic relaxation model, a unified description model of spatial coupling and temporal evolution is established, enabling precise control of residual preload in polymer flange connection systems under long-term service conditions. This overcomes the limitation of the traditional elastic interaction coefficient method, which is only applicable to linear elastic materials, and can be directly applied to flange connection structures made of viscoelastic polymer materials such as PTFE. Simultaneously, a reverse optimization approach is employed to automatically calculate the optimal initial preload based on the long-term target residual preload, achieving pre-compensation control. After optimization, the stress distribution on the flange surface is more uniform, effectively reducing local stress concentration and improving sealing performance and connection reliability.

Description

Technical Field

[0001] This invention relates to the field of bolt preload optimization technology, specifically to a method and system for optimizing the tightening of polymer flange bolts based on improved elastic interaction. Background Technology

[0002] In semiconductor manufacturing equipment, chemical pipelines, and pressure vessels, multi-bolt flange connections are the most common type of mechanical connection. Traditionally, bolts are tightened one by one in a predetermined sequence during assembly. However, due to the elastic deformation of the connecting components, when preload is applied to subsequent bolts, the preload of the already tightened bolts is redistributed, resulting in an elastic interaction. This spatial coupling leads to significant differences in the residual preload of each bolt, affecting the uniformity of stress and sealing reliability of the connection structure.

[0003] To address the aforementioned issues, the traditional Elastic Interaction Coefficient Method (EICM) can deduce an optimized initial preload distribution scheme by establishing an interaction matrix between bolts, resulting in a more uniform preload after assembly. However, this method is based on the assumption of linear elastic materials and is suitable for materials such as metal flanges. Its applicability to polymeric materials with significant viscoelastic properties, such as polytetrafluoroethylene (PTFE), is considerably limited.

[0004] Traditional elastic interaction coefficient methods are mainly applicable to isotropic linear elastic materials such as metals. However, for polymer fasteners such as PTFE, which exhibit significant viscoelastic characteristics, the preload decays nonlinearly over time after tightening. Therefore, there is an urgent need to develop a novel preload optimization method that can simultaneously consider the spatial elastic interaction between bolts and the time-dependent stress relaxation of polymer materials, so that flange connections maintain a uniform and stable preload state after long-term service. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide an optimized method and system for tightening polymer flange bolts based on improved elastic interactions.

[0006] The technical solution adopted by this invention to solve its technical problem is:

[0007] An optimized method for tightening polymer flange bolts based on improved elastic interactions includes the following steps:

[0008] S1. Obtain input parameters, including flange connection structure parameters, number of bolts, tightening sequence, target residual preload vector, viscoelastic parameters of polymer material, and ambient temperature;

[0009] S2. Establish a three-dimensional finite element simulation model of the polymer material flange connection structure based on the input parameters, and set the evaluation time and the given initial preload vector as the initial value for iteration;

[0010] S3. Using the initial preload vector as input, perform the tightening process simulation according to the tightening sequence, and continue to simulate relaxation until the evaluation time after tightening is completed, extracting the preload change data of each bolt throughout the simulation process;

[0011] S4. Based on the simulation data of the tightening process, establish a spatial elastic interaction model of the bolt tightening process and obtain the total spatial influence matrix; at the same time, based on the simulation data of continuous relaxation to the evaluation time, combined with the viscoelastic parameters of the polymer material corresponding to the ambient temperature, establish a time-dependent stress relaxation model and obtain the time-domain evolution matrix at the evaluation time.

[0012] S5. The coefficient of variation is used as the evaluation index of the dispersion of residual preload. The current coefficient of variation is calculated based on the simulation data of residual preload at the evaluation time.

[0013] S6. Determine whether the current coefficient of variation is not greater than the preset threshold;

[0014] If satisfied, the current initial preload vector is taken as the optimization result, and the iteration is terminated;

[0015] If the conditions are not met, the total spatial influence matrix is ​​coupled with the temporal evolution matrix to establish a unified spatiotemporal prediction model for residual preload. Using the set target residual preload vector as a constraint, the new initial preload vector is solved in reverse using the spatiotemporal prediction model for residual preload, and the process returns to S3 for the next iteration until the preset threshold is met.

[0016] As a preferred embodiment, a further technical solution of the present invention is:

[0017] Preferably, the establishment of the spatial elastic interaction model in S4 specifically includes:

[0018] Define the instantaneous influence matrix of the j-th tightening operation in the tightening sequence as follows: :

[0019] ;

[0020] Among them, the j-th column element This represents the interaction coefficient between the j-th tightening operation and the preload of the i-th bolt. Indicates the increment of preload applied during the j-th tightening operation. This represents the change in preload of the i-th bolt caused by the j-th tightening operation;

[0021] After completing the entire tightening sequence according to the tightening order, the total spatial influence matrix is ​​obtained by right-multiplying and accumulating the instantaneous influence matrices of each step. :

[0022] ;

[0023] Where n is the total number of tightening steps, corresponding to the total number of bolts;

[0024] The instantaneous preload vector at the completion of bolt tightening is obtained based on the total spatial influence matrix. :

[0025] ;

[0026] in, This represents the initial preload of the nth bolt.

[0027] Preferably, the establishment of the time-dependent stress relaxation model in S4 specifically includes:

[0028] To address the viscoelastic relaxation effect, the normalized relaxation kernel function of polymer bolts is described using Prony series based on linear viscoelastic theory. :

[0029] ;

[0030] Where k represents the bolt number; t represents the relaxation time from the moment the tightening is completed to the moment the timer starts; and N is the order of the Prony series. The dimensionless relaxation amplitude represents the relaxation order of the k-th bolt at the m-th relaxation level. This represents the relaxation time of the k-th bolt at the m-th relaxation stage; This represents the long-term residual stiffness coefficient of the k-th bolt;

[0031] A time-domain evolution matrix in diagonal form is constructed based on a normalized relaxed kernel function. This describes the independent preload decay process of each bolt:

[0032] ;

[0033] Among them, diagonal elements , ... These represent the normalized relaxation kernel functions of bolts 1 to n at time t, respectively. The off-diagonal elements are 0, indicating that the relaxation processes of each bolt are independent.

[0034] Preferably, in S6, a unified spatiotemporal prediction model for residual preload is established. Using the set target residual preload vector as a constraint, the process of inversely solving for the new initial preload vector using the spatiotemporal prediction model for residual preload includes:

[0035] The residual preload vector distribution at any service time is represented by the following spatiotemporal prediction model for residual preload:

[0036] ;

[0037] in, This represents the residual preload vector of each bolt after a relaxation time t. This represents the time-domain evolution matrix after relaxation time t. Represents the total spatial influence matrix. Indicates the initial preload vector;

[0038] To assess the time Target residual preload vector To constrain the equations, a system of nonlinear equations is established and expanded:

[0039] ;

[0040] The established nonlinear equations are solved in reverse to obtain the new initial preload vector. .

[0041] Preferably, the coefficient of variation in S5 is calculated as follows:

[0042] ;

[0043] in, Indicates the coefficient of variation; Indicates the time of evaluation of the i-th bolt. The residual preload value; This represents the average value of the residual preload of all bolts at the time of evaluation.

[0044] This invention also discloses an optimized system for tightening polymer flange bolts based on improved elastic interactions, specifically comprising:

[0045] The acquisition module is used to acquire input parameters, including flange connection structure parameters, number of bolts, tightening sequence, target residual preload vector, viscoelastic parameters of polymer materials, and ambient temperature.

[0046] The simulation module is used to build a three-dimensional finite element simulation model of the polymer material flange connection structure based on the input parameters, and to set the evaluation time and the given initial preload vector as the initial value for iteration.

[0047] The simulation module is used to simulate the tightening process according to the tightening sequence, with the initial preload vector as input, and to continuously simulate the relaxation until the evaluation time after tightening, and to extract the preload change data of each bolt throughout the simulation process;

[0048] The evaluation module is used to establish a spatial elastic interaction model of the bolt tightening process based on the simulation data of the tightening process and obtain the total spatial influence matrix; at the same time, based on the simulation data of continuous relaxation to the evaluation time and combined with the viscoelastic parameters of the polymer material corresponding to the ambient temperature, a time-dependent stress relaxation model is established to obtain the time-domain evolution matrix at the evaluation time.

[0049] The calculation module is used to use the coefficient of variation as an evaluation index of the dispersion of residual preload, and calculates the current coefficient of variation based on the simulation data of residual preload at the evaluation time.

[0050] The judgment module is used to determine whether the current coefficient of variation is not greater than a preset threshold.

[0051] If satisfied, the current initial preload vector is taken as the optimization result, and the iteration is terminated;

[0052] If the conditions are not met, the total spatial influence matrix and the temporal evolution matrix are coupled to establish a unified spatiotemporal prediction model for residual preload. The new initial preload vector is solved in reverse using the residual preload spatiotemporal prediction model, and the simulation module is triggered until the preset threshold is met.

[0053] In another aspect of the present invention, an electronic device is also provided, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0054] Memory is used to store processor-executable instructions;

[0055] When the processor executes the instructions stored in the memory, it implements the above-mentioned optimized method for tightening polymer flange bolts based on improved elastic interactions.

[0056] The present invention, which adopts the above technical solution, has the following prominent features compared with the prior art:

[0057] Breaking through the limitation of traditional elastic interaction coefficient methods, which are only applicable to linear elastic materials, this method can be directly applied to flange connection structures made of viscoelastic polymers such as PTFE. Simultaneously, employing a reverse optimization approach, it automatically calculates the optimal initial preload based on the long-term target residual preload, achieving pre-compensation control. The optimized flange surface exhibits a more uniform stress distribution, effectively reducing local stress concentration and improving sealing performance and connection reliability.

[0058] It is not only suitable for different ambient temperatures and different target preload conditions, but also adaptable to complex flange connection systems composed of different tightening sequences and different numbers of bolts, and has good versatility and engineering application value. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of the method flow in an embodiment of the present invention;

[0060] Figure 2 This is a schematic diagram of a three-dimensional finite element simulation model in an embodiment of the present invention, wherein (a) is a PTFE flange connector model, (b) is the flange bolt distribution, and (c) is the flange connector dimensions;

[0061] Figure 3 These are schematic diagrams illustrating the optimized tightening effect of PTFE flanges at different temperatures in embodiments of the present invention, wherein: (a) before optimization at 25℃; (b) after optimization at 25℃; (c) before optimization at 40℃; (d) after optimization at 40℃; (e) before optimization at 60℃; (f) after optimization at 60℃; (g) before optimization at 80℃; (h) after optimization at 80℃.

[0062] Figure 4 This is a schematic diagram of the system architecture in an embodiment of the present invention;

[0063] Figure 5 This is a schematic diagram of the electronic device structure in an embodiment of the present invention. Detailed Implementation

[0064] The present invention will be further illustrated below with reference to specific embodiments. The purpose of this illustration is solely to provide a better understanding of the invention. Therefore, the examples given do not limit the scope of protection of the present invention.

[0065] like Figure 1 As shown in the figure, this embodiment presents an optimized method for tightening polymer flange bolts based on improved elastic interactions, specifically including the following steps:

[0066] S1. Obtain input parameters, including flange connection structure parameters, number of bolts, tightening sequence, target residual preload vector, viscoelastic parameters of polymer material, and ambient temperature.

[0067] S2. Establish a three-dimensional finite element simulation model of the polymer material flange connection structure based on the input parameters, and set the evaluation time and the given initial preload vector as the initial value for iteration.

[0068] S3. Using the initial preload vector as input, simulate the tightening process according to the tightening sequence, and continue to simulate relaxation until the evaluation time after tightening is completed, extracting the change data of preload of each bolt throughout the simulation process.

[0069] S4. Based on the simulation data of the tightening process, establish a spatial elastic interaction model of the bolt tightening process and obtain the total spatial influence matrix; at the same time, based on the simulation data of continuous relaxation to the evaluation time, combined with the viscoelastic parameters of the polymer material corresponding to the ambient temperature, establish a time-dependent stress relaxation model and obtain the time-domain evolution matrix at the evaluation time.

[0070] S5. The coefficient of variation is used as the evaluation index for the dispersion of residual preload. The current coefficient of variation is calculated based on the simulation data of residual preload at the evaluation time.

[0071] S6. Determine whether the current coefficient of variation is not greater than the preset threshold;

[0072] If satisfied, the current initial preload vector is taken as the optimization result, and the iteration is terminated;

[0073] If the conditions are not met, the total spatial influence matrix is ​​coupled with the temporal evolution matrix to establish a unified spatiotemporal prediction model for residual preload. Using the set target residual preload vector as a constraint, the new initial preload vector is solved in reverse using the spatiotemporal prediction model for residual preload, and the process returns to S3 for the next iteration until the preset threshold is met.

[0074] In practice, establishing a space elastic interaction model specifically includes:

[0075] Define the instantaneous influence matrix of the j-th tightening operation in the tightening sequence as follows: :

[0076] ; (1)

[0077] Among them, the j-th column element This represents the interaction coefficient between the j-th tightening operation and the preload of the i-th bolt. Indicates the increment of preload applied during the j-th tightening operation. This represents the change in preload of the i-th bolt caused by the j-th tightening operation;

[0078] After completing the entire tightening sequence according to the tightening order, the total spatial influence matrix is ​​obtained by right-multiplying and accumulating the instantaneous influence matrices of each step. :

[0079] ; (2)

[0080] Where n is the total number of tightening steps, corresponding to the total number of bolts;

[0081] The instantaneous preload vector at the completion of bolt tightening is obtained based on the total spatial influence matrix. :

[0082] ; (3)

[0083] in, This represents the initial preload of the nth bolt.

[0084] Establishing a time-dependent stress relaxation model specifically includes:

[0085] To address the viscoelastic relaxation effect, the normalized relaxation kernel function of polymer bolts is described using Prony series based on linear viscoelastic theory. :

[0086] ; (4)

[0087] Where k represents the bolt number; t represents the relaxation time from the moment the tightening is completed to the moment the timer starts; and N is the order of the Prony series. The dimensionless relaxation amplitude represents the relaxation order of the k-th bolt at the m-th relaxation level. This represents the relaxation time of the k-th bolt at the m-th relaxation stage; This represents the long-term residual stiffness coefficient of the k-th bolt;

[0088] A time-domain evolution matrix in diagonal form is constructed based on a normalized relaxed kernel function. This describes the independent preload decay process of each bolt:

[0089] ; (5)

[0090] Among them, diagonal elements , ... These represent the normalized relaxation kernel functions of bolts 1 to n at time t, respectively. The off-diagonal elements are 0, indicating that the relaxation processes of each bolt are independent.

[0091] The process of establishing a unified spatiotemporal prediction model for residual preload, using a set target residual preload vector as a constraint, and then inversely solving for a new initial preload vector using the spatiotemporal prediction model for residual preload includes:

[0092] The residual preload vector distribution at any service time is represented by the following spatiotemporal prediction model for residual preload:

[0093] ; (6)

[0094] in, This represents the residual preload vector of each bolt after a relaxation time t. This represents the time-domain evolution matrix after relaxation time t. Represents the total spatial influence matrix. Indicates the initial preload vector;

[0095] To assess the time Target residual preload vector To constrain the equations, a system of nonlinear equations is established and expanded:

[0096] (7)

[0097] The established nonlinear equations are solved in reverse to obtain the new initial preload vector. .

[0098] The coefficient of variation is calculated as follows:

[0099] ; (8)

[0100] in, Indicates the coefficient of variation; Indicates the time of evaluation of the i-th bolt. The residual preload value; This represents the average value of the residual preload of all bolts at the time of evaluation.

[0101] Example

[0102] A three-dimensional finite element simulation model of the flange bolt connection system was constructed using ABAQUS software. This model fully includes the PTFE raised face flange, bolts, and nuts. Figure 2 As shown in the diagram. For mesh generation, a high-precision mesh model was used for the bolt and nut assemblies; the flange components were discretized using eight-node linear hexahedral volumetric elements (C3D8), with mesh refinement implemented in the contact area to accurately capture complex interfacial stress gradients. Secondly, contact properties were defined. The model employed a surface-to-surface contact algorithm, with normal behavior following a hard contact criterion to suppress over-closure, and tangential behavior using a penalized friction model with a friction coefficient set to 0.13. During the boundary conditions and load application phase, rigid body displacement was eliminated by applying fully fixed constraints to both ends of the flange tube, and the actual bolt preload application process was simulated using the software's "Bolt load" function. Finally, the flange material was set as a thermo-viscoelastic constitutive model, enabling accurate simulation of the load relaxation behavior of the flange bolts over time under tightening loads.

[0103] At a normal temperature of 25℃, each bolt in the bolt group was preloaded with a force of 100N using a sequential tightening method (1-2-3-4). After all bolts were preloaded, they were kept in a relaxed state for one hour. Simulation results show that the preload of the tightened bolts fluctuated significantly due to the continuous compression of the connector caused by subsequent bolt loading. After entering the relaxation stage, the preload of each bolt decreased rapidly, eventually resulting in a large difference in residual preload, indicating that the traditional uniform loading method cannot guarantee long-term uniform stress.

[0104] The total spatial influence matrix between bolts is extracted based on the tightening process, and a corresponding time-domain evolution matrix is ​​established based on the relaxation characteristics of PTFE material. After coupling the two, the target preload after 1 hour of relaxation is used as the optimization objective, and different initial preload distribution schemes for each bolt are calculated in reverse.

[0105] Specifically, the target preload is achieved after 1 hour of relaxation. With the core guiding principle, the initial preload is first set. The tightening process and the state after 1 hour of relaxation were simulated using the established three-dimensional finite element simulation model, and the simulation data of residual preload were extracted. Then, the coefficient of variation (CV) is calculated using formula (8) as an evaluation index, and 3% is set as a preset threshold. If CV ≤ 3%, the current initial preload vector is accepted. Otherwise, if it is not satisfied, the simulation data of the whole process is extracted and the residual preload spatiotemporal prediction model is used to solve the new initial preload vector in reverse until the initial preload vector that satisfies the preset threshold is obtained.

[0106] Based on simulation data, the data of the tightening stage are calculated according to equation (2) to obtain the total spatial influence matrix. This is used to represent the elastic interaction during the bolt tightening process, thereby reflecting the degree of spatial coupling between bolts. Furthermore, by combining equations (4) and (5), the residual strength coefficient after 1 hour of relaxation is calculated, and the time-domain evolution matrix of the relaxation process is constructed. This reflects the difference in stress relaxation caused by the viscoelasticity of PTFE material. Finally, according to equation (7), the optimized initial preload for bolts 1 to 4 were calculated to be 152.508 N, 158.170 N, 165.595 N, and 172.564 N, respectively. The optimized results show that although different initial preloads were applied to each bolt, after tightening and relaxation for 1 hour, the residual preload tended to be highly consistent, the flange contact stress distribution was more uniform, and the problems of local stress concentration and uneven sealing that existed in the traditional method were significantly improved.

[0107] See Figure 3 Further verification was conducted at different ambient temperatures of 40℃, 60℃, and 80℃. The results showed that the proposed method could effectively compensate for the relaxation effect caused by temperature changes, maintaining a high consistency in residual preload. Simultaneously, tests were conducted on different tightening sequences (clockwise, cross, and Z-shaped), different target preloads, and four-bolt, six-bolt, and eight-bolt structures, all achieving good optimization results and verifying the stability and universality of the method.

[0108] See Figure 4 This invention also discloses an optimized system for tightening polymer flange bolts based on improved elastic interactions, specifically comprising:

[0109] The acquisition module is used to acquire input parameters, including flange connection structure parameters, number of bolts, tightening sequence, target residual preload vector, viscoelastic parameters of polymer materials, and ambient temperature.

[0110] The simulation module is used to build a three-dimensional finite element simulation model of the polymer material flange connection structure based on the input parameters, and to set the evaluation time and the given initial preload vector as the initial value for iteration.

[0111] The simulation module is used to simulate the tightening process according to the tightening sequence, with the initial preload vector as input, and to continuously simulate the relaxation until the evaluation time after tightening, and to extract the preload change data of each bolt throughout the simulation process;

[0112] The evaluation module is used to establish a spatial elastic interaction model of the bolt tightening process based on the simulation data of the tightening process and obtain the total spatial influence matrix; at the same time, based on the simulation data of continuous relaxation to the evaluation time and combined with the viscoelastic parameters of the polymer material corresponding to the ambient temperature, a time-dependent stress relaxation model is established to obtain the time-domain evolution matrix at the evaluation time.

[0113] The calculation module is used to use the coefficient of variation as an evaluation index of the dispersion of residual preload, and calculates the current coefficient of variation based on the simulation data of residual preload at the evaluation time.

[0114] The judgment module is used to determine whether the current coefficient of variation is not greater than a preset threshold.

[0115] If satisfied, the current initial preload vector is taken as the optimization result, and the iteration is terminated;

[0116] If the conditions are not met, the total spatial influence matrix and the temporal evolution matrix are coupled to establish a unified spatiotemporal prediction model for residual preload. The new initial preload vector is solved in reverse using the residual preload spatiotemporal prediction model, and the simulation module is triggered until the preset threshold is met.

[0117] The evaluation module is specifically used to define the instantaneous influence matrix under the j-th tightening operation in the tightening sequence. :

[0118] ;

[0119] Among them, the j-th column element This represents the interaction coefficient between the j-th tightening operation and the preload of the i-th bolt. Indicates the increment of preload applied during the j-th tightening operation. This represents the change in preload of the i-th bolt caused by the j-th tightening operation;

[0120] After completing the entire tightening sequence according to the tightening order, the total spatial influence matrix is ​​obtained by right-multiplying and accumulating the instantaneous influence matrices of each step. :

[0121] ;

[0122] Where n is the total number of tightening steps, corresponding to the total number of bolts;

[0123] The instantaneous preload vector at the completion of bolt tightening is obtained based on the total spatial influence matrix. :

[0124] ;

[0125] in, This represents the initial preload of the nth bolt.

[0126] The evaluation module is also used to describe the normalized relaxation kernel function of polymer bolts based on the Prony series, using linear viscoelastic theory, for viscoelastic relaxation effects. :

[0127] ;

[0128] Where k represents the bolt number; t represents the relaxation time from the moment the tightening is completed to the moment the timer starts; and N is the order of the Prony series. The dimensionless relaxation amplitude represents the relaxation order of the k-th bolt at the m-th relaxation level. This represents the relaxation time of the k-th bolt at the m-th relaxation stage; This represents the long-term residual stiffness coefficient of the k-th bolt;

[0129] A time-domain evolution matrix in diagonal form is constructed based on a normalized relaxed kernel function. This describes the independent preload decay process of each bolt:

[0130] ;

[0131] Among them, diagonal elements , ... These represent the normalized relaxation kernel functions of bolts 1 to n at time t, respectively. The off-diagonal elements are 0, indicating that the relaxation processes of each bolt are independent.

[0132] The judgment module, specifically used for the residual preload vector distribution at any service moment, is represented by the following spatiotemporal prediction model of residual preload:

[0133] ;

[0134] in, This represents the residual preload vector of each bolt after a relaxation time t. This represents the time-domain evolution matrix after relaxation time t. Represents the total spatial influence matrix. Indicates the initial preload vector;

[0135] To assess the time Target residual preload vector To constrain the equations, a system of nonlinear equations is established and expanded:

[0136] ;

[0137] The established nonlinear equations are solved in reverse to obtain the new initial preload vector. .

[0138] The coefficient of variation is calculated as follows:

[0139] ;

[0140] in, Indicates the coefficient of variation; Indicates the time of evaluation of the i-th bolt. The residual preload value; This represents the average value of the residual preload of all bolts at the time of evaluation.

[0141] This invention also provides an electronic device, such as... Figure 5 As shown, it includes a processor 001, a communication interface 002, a memory 003, and a communication bus 004. The processor 001, communication interface 002, and memory 003 communicate with each other via the communication bus 004.

[0142] Memory 003 is used to store computer programs;

[0143] When processor 001 executes the program stored in memory 003, it implements the above-mentioned optimized method for tightening polymer flange bolts based on improved elastic interactions, including:

[0144] S1. Obtain input parameters, including flange connection structure parameters, number of bolts, tightening sequence, target residual preload vector, viscoelastic parameters of polymer material, and ambient temperature;

[0145] S2. Establish a three-dimensional finite element simulation model of the polymer material flange connection structure based on the input parameters, and set the evaluation time and the given initial preload vector as the initial value for iteration;

[0146] S3. Using the initial preload vector as input, perform the tightening process simulation according to the tightening sequence, and continue to simulate relaxation until the evaluation time after tightening is completed, extracting the preload change data of each bolt throughout the simulation process;

[0147] S4. Based on the simulation data of the tightening process, establish a spatial elastic interaction model of the bolt tightening process and obtain the total spatial influence matrix; at the same time, based on the simulation data of continuous relaxation to the evaluation time, combined with the viscoelastic parameters of the polymer material corresponding to the ambient temperature, establish a time-dependent stress relaxation model and obtain the time-domain evolution matrix at the evaluation time.

[0148] S5. The coefficient of variation is used as the evaluation index of the dispersion of residual preload. The current coefficient of variation is calculated based on the simulation data of residual preload at the evaluation time.

[0149] S6. Determine whether the current coefficient of variation is not greater than the preset threshold;

[0150] If satisfied, the current initial preload vector is taken as the optimization result, and the iteration is terminated;

[0151] If the conditions are not met, the total spatial influence matrix is ​​coupled with the temporal evolution matrix to establish a unified spatiotemporal prediction model for residual preload. Using the set target residual preload vector as a constraint, the new initial preload vector is solved in reverse using the spatiotemporal prediction model for residual preload, and the process returns to S3 for the next iteration until the preset threshold is met.

[0152] The communication bus mentioned in the above electronic devices can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc. For ease of illustration, only one thick line is used to represent it in the diagram, but this does not mean that there is only one bus or one type of bus.

[0153] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0154] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0155] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0156] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0157] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0158] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system and electronic device embodiments are basically similar to the method embodiments, so the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0159] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for optimizing the tightening of polymer flange bolts based on improved elastic interactions, characterized in that, Specifically, the following steps are included: S1. Obtain input parameters, including flange connection structure parameters, number of bolts, tightening sequence, target residual preload vector, viscoelastic parameters of polymer material, and ambient temperature; S2. Establish a three-dimensional finite element simulation model of the polymer material flange connection structure based on the input parameters, and set the evaluation time and the given initial preload vector as the initial value for iteration; S3. Using the initial preload vector as input, perform the tightening process simulation according to the tightening sequence, and continue to simulate relaxation until the evaluation time after tightening is completed, extracting the preload change data of each bolt throughout the simulation process; S4. Based on the simulation data of the tightening process, establish a spatial elastic interaction model of the bolt tightening process and obtain the total spatial influence matrix; at the same time, based on the simulation data of continuous relaxation to the evaluation time, combined with the viscoelastic parameters of the polymer material corresponding to the ambient temperature, establish a time-dependent stress relaxation model and obtain the time-domain evolution matrix at the evaluation time. S5. The coefficient of variation is used as the evaluation index of the dispersion of residual preload. The current coefficient of variation is calculated based on the simulation data of residual preload at the evaluation time. S6. Determine whether the current coefficient of variation is not greater than the preset threshold; If satisfied, the current initial preload vector is taken as the optimization result, and the iteration is terminated; If the conditions are not met, the total spatial influence matrix is ​​coupled with the temporal evolution matrix to establish a unified spatiotemporal prediction model for residual preload. Using the set target residual preload vector as a constraint, the new initial preload vector is solved in reverse using the spatiotemporal prediction model for residual preload, and the process returns to S3 for the next iteration until the preset threshold is met.

2. The optimized method for tightening polymer flange bolts based on improved elastic interactions according to claim 1, characterized in that, The specific steps involved in establishing the spatial elastic interaction model in S4 are as follows: Define the instantaneous influence matrix of the j-th tightening operation in the tightening sequence as follows: : ； Among them, the j-th column element This represents the interaction coefficient between the j-th tightening operation and the preload of the i-th bolt. Indicates the increment of preload applied during the j-th tightening operation. This represents the change in preload of the i-th bolt caused by the j-th tightening operation; After completing the entire tightening sequence according to the tightening order, the total spatial influence matrix is ​​obtained by right-multiplying and accumulating the instantaneous influence matrices of each step. : ； Where n is the total number of tightening steps, corresponding to the total number of bolts; The instantaneous preload vector at the completion of bolt tightening is obtained based on the total spatial influence matrix. : ； in, This represents the initial preload of the nth bolt.

3. The optimized method for tightening polymer flange bolts based on improved elastic interactions according to claim 2, characterized in that, The establishment of a time-dependent stress relaxation model in S4 specifically includes: To address the viscoelastic relaxation effect, the normalized relaxation kernel function of polymer bolts is described using Prony series based on linear viscoelastic theory. : ； Where k represents the bolt number; t represents the relaxation time from the moment the tightening is completed to the moment the timer starts; and N is the order of the Prony series. The dimensionless relaxation amplitude represents the relaxation order of the k-th bolt at the m-th relaxation level. This represents the relaxation time of the k-th bolt at the m-th relaxation stage; This represents the long-term residual stiffness coefficient of the k-th bolt; A time-domain evolution matrix in diagonal form is constructed based on a normalized relaxed kernel function. This describes the independent preload decay process of each bolt: ； Among them, diagonal elements , ... These represent the normalized relaxation kernel functions of bolts 1 to n at time t, respectively. The off-diagonal elements are 0, indicating that the relaxation processes of each bolt are independent.

4. The optimized method for tightening polymer flange bolts based on improved elastic interactions according to claim 3, characterized in that, In S6, a unified spatiotemporal prediction model for residual preload is established. Using the set target residual preload vector as a constraint, the process of inversely solving for the new initial preload vector using this model includes: The residual preload vector distribution at any service time is represented by the following spatiotemporal prediction model for residual preload: ； in, This represents the residual preload vector of each bolt after a relaxation time t. This represents the time-domain evolution matrix after relaxation time t. Represents the total spatial influence matrix. Indicates the initial preload vector; To assess the time Target residual preload vector To constrain the equations, a system of nonlinear equations is established and expanded: ； The established nonlinear equations are solved in reverse to obtain the new initial preload vector. .

5. The optimized method for tightening polymer flange bolts based on improved elastic interactions according to claim 4, characterized in that, The coefficient of variation in S5 is calculated as follows: ； in, Indicates the coefficient of variation; Indicates the time of evaluation of the i-th bolt. The residual preload value; This represents the average value of the residual preload of all bolts at the time of evaluation.

6. A polymer flange bolt tightening optimization system based on improved elastic interaction, characterized in that, The method described in any one of claims 1 to 5 is applied, specifically including: The acquisition module is used to acquire input parameters, including flange connection structure parameters, number of bolts, tightening sequence, target residual preload vector, viscoelastic parameters of polymer materials, and ambient temperature. The simulation module is used to build a three-dimensional finite element simulation model of the polymer material flange connection structure based on the input parameters, and to set the evaluation time and the given initial preload vector as the initial value for iteration. The simulation module is used to simulate the tightening process according to the tightening sequence, with the initial preload vector as input, and to continuously simulate the relaxation until the evaluation time after tightening, and to extract the preload change data of each bolt throughout the simulation process; The evaluation module is used to establish a spatial elastic interaction model of the bolt tightening process based on the simulation data of the tightening process and obtain the total spatial influence matrix; at the same time, based on the simulation data of continuous relaxation to the evaluation time and combined with the viscoelastic parameters of the polymer material corresponding to the ambient temperature, a time-dependent stress relaxation model is established to obtain the time-domain evolution matrix at the evaluation time. The calculation module is used to use the coefficient of variation as an evaluation index of the dispersion of residual preload, and calculates the current coefficient of variation based on the simulation data of residual preload at the evaluation time. The judgment module is used to determine whether the current coefficient of variation is not greater than a preset threshold. If satisfied, the current initial preload vector is taken as the optimization result, and the iteration is terminated; If the conditions are not met, the total spatial influence matrix and the temporal evolution matrix are coupled to establish a unified spatiotemporal prediction model for residual preload. The new initial preload vector is solved in reverse using the residual preload spatiotemporal prediction model, and the simulation module is triggered until the preset threshold is met.

7. The optimized polymer flange bolt tightening system based on improved elastic interaction according to claim 6, characterized in that, The evaluation module is specifically used to define the instantaneous influence matrix under the j-th tightening operation in the tightening sequence. : ； Among them, the j-th column element This represents the interaction coefficient between the j-th tightening operation and the preload of the i-th bolt. Indicates the increment of preload applied during the j-th tightening operation. This represents the change in preload of the i-th bolt caused by the j-th tightening operation; After completing the entire tightening sequence according to the tightening order, the total spatial influence matrix is ​​obtained by right-multiplying and accumulating the instantaneous influence matrices of each step. : ； Where n is the total number of tightening steps, corresponding to the total number of bolts; The instantaneous preload vector at the completion of bolt tightening is obtained based on the total spatial influence matrix. : ； in, This represents the initial preload of the nth bolt.

8. The optimized polymer flange bolt tightening system based on improved elastic interaction according to claim 7, characterized in that, The evaluation module is also used to describe the normalized relaxation kernel function of polymer bolts based on the Prony series, using linear viscoelastic theory, for viscoelastic relaxation effects. : ； Where k represents the bolt number; t represents the relaxation time from the moment the tightening is completed to the moment the timer starts; and N is the order of the Prony series. The dimensionless relaxation amplitude represents the relaxation order of the k-th bolt at the m-th relaxation level. This represents the relaxation time of the k-th bolt at the m-th relaxation stage; This represents the long-term residual stiffness coefficient of the k-th bolt; A time-domain evolution matrix in diagonal form is constructed based on a normalized relaxed kernel function. This describes the independent preload decay process of each bolt: ； Among them, diagonal elements , ... These represent the normalized relaxation kernel functions of bolts 1 to n at time t, respectively. The off-diagonal elements are 0, indicating that the relaxation processes of each bolt are independent.

9. The optimized system for tightening polymer flange bolts based on improved elastic interactions according to claim 8, characterized in that, The judgment module, specifically used for the residual preload vector distribution at any service moment, is represented by the following spatiotemporal prediction model for residual preload: ； in, This represents the residual preload vector of each bolt after a relaxation time t. This represents the time-domain evolution matrix after relaxation time t. Represents the total spatial influence matrix. Indicates the initial preload vector; To assess the time Target residual preload vector To constrain the equations, a system of nonlinear equations is established and expanded: ； The established nonlinear equations are solved in reverse to obtain the new initial preload vector. .

10. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory is used to store processor-executable instructions; The processor, when executing instructions stored in memory, implements the optimized method for tightening polymer flange bolts based on improved elastic interactions as described in any one of claims 1-5.

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