Method for determining a control range of a bolt pre-tightening force

Abstract

The application discloses a method for determining the control range of bolt connection pre-tightening force, which comprises the following steps: firstly, establishing a finite element model of bolt connection under the condition of applying pre-tightening force; calculating the maximum equivalent stress of the connection area under different pre-tightening force conditions; constructing a radial basis function proxy model based on the pre-tightening force and the equivalent stress; considering the uncertainty of the pre-tightening force, obtaining a plurality of groups of sample points of the pre-tightening force, and calculating the corresponding equivalent stress through the radial basis function proxy model; calculating the reliability confidence factor of the equivalent stress, and taking the bolt pre-tightening force when the reliability confidence factor is greater than 1 as the control applied pre-tightening force range. Starting from the essence of the uncertainty of the pre-tightening force, the uncertainty of the pre-tightening force is described through the mean value and the multiple relationship of the pre-tightening force, the safe working range of the structure is determined according to the reliability confidence factor of the equivalent stress, the pre-tightening force control range is obtained, the traditional pre-tightening force control is expanded from a single deterministic value to a range interval, and the reliability requirement of the structure in the range is ensured.

Description

Technical Field

[0001] This invention relates to the reliability of bolted connections, specifically to a method for determining the control range of bolted connection preload. Background Technology

[0002] Bolted connections, as a primary connection method in complex engineering structures, serve functions such as connecting components, sealing, and transferring loads. The preload of bolted connections plays a decisive role in the performance and safe operation of bolted structures. However, there are no clear indicators for controlling the preload during the assembly of bolted structures. Furthermore, as a connection unit within a structure, bolted connections are a major source of structural uncertainty. Therefore, controlling the preload during the assembly of bolted connections in complex structures is crucial to ensuring safe structural operation. Summary of the Invention

[0003] Purpose of the invention: To address the above-mentioned shortcomings, the present invention provides a method for determining the bolt preload control range to ensure the reliability of bolted connections.

[0004] Technical solution: To solve the above problems, the present invention adopts a method for determining the control range of bolt connection preload, including the following steps:

[0005] (1) Establish a finite element model of the bolted connection structure under the condition of applying preload;

[0006] (2) Based on the established finite element model, calculate the maximum equivalent stress in the bolt connection area under different preloads applied to the bolt;

[0007] (3) Construct a radial basis function surrogate model based on the applied preload and the calculated equivalent stress;

[0008] (4) Considering the uncertainty of preload, within the range of the mean value of preload and the multiple relationship between the standard deviation of preload and the mean value, a nested random sampling method is used to obtain several sets of mean values ​​of preload and multiple relationships between the standard deviation of preload and the mean value. These are combined to obtain several sets of sample points of applied preload. The equivalent stress corresponding to each set of preload sample points is calculated through the radial basis function surrogate model to obtain the probability distribution, mean and standard deviation of each set of equivalent stress.

[0009] (5) The performance threshold for the maximum equivalent stress in the bolt connection area and the confidence level of the equivalent stress probability distribution;

[0010] (6) Obtain the upper quantile of the equivalent stress probability distribution based on the preset confidence level, calculate the difference M between the performance threshold and the upper quantile, and the difference U between the upper quantile and the mean of the equivalent stress.

[0011] (7) The bolt preload when M is greater than U is used as the range of preload to control the applied preload.

[0012] Furthermore, in step (4), the uncertainty of the preload is described by the mean of the preload and the multiple relationship between the standard deviation of the preload and the mean. It is assumed that the mean of the applied preload and the multiple relationship between the standard deviation of the preload and the mean both follow a uniform distribution. Then the preload follows a normal distribution composed of the two distributions. Several sets of preload sample points are generated by random sampling. According to the fact that the preload follows a normal distribution, each set of preload sample points includes twice the number of preload sample points of the sampled preload mean. The obtained preload sample points are used to calculate the maximum equivalent stress in the connection area through the radial basis function surrogate model.

[0013] Furthermore, in step (1), when establishing the finite element model, the bolt connection structure is meshed, the bolt thread is ignored, and the bolt and nut are integrated. Considering that the bolt connection is in service in the deep sea long-term high-pressure ultra-deep environment, the external pressure load of the working face is set.

[0014] Furthermore, in step (2), several bolt preload values ​​are randomly generated by Latin hypercube random sampling, and the generated bolt preload values ​​are substituted into the finite element model to calculate the equivalent stress in the bolt connection area.

[0015] Furthermore, based on the mechanical properties of the materials and parts, the performance threshold for the maximum equivalent stress in the bolt connection area of ​​the deep-sea pressure-resistant structure was set to 450 MPa, and the confidence level of the equivalent stress probability distribution was set to 99%.

[0016] Beneficial effects: Compared with the prior art, the significant advantage of this invention is that it starts from the nature of the uncertainty of preload and describes the uncertainty of preload by the mean value of preload and the multiple relationship between the standard deviation of preload and the mean value. Based on the relationship between the performance threshold and the equivalent stress characteristics of the bolt connection area, the safe working range of the structure is determined, and the preload control range is obtained. This expands the traditional preload control from a single deterministic value to a range interval, ensuring that the structure meets the reliability requirements within this range. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the bolt connection structure in this invention;

[0018] Figure 2 This is a schematic diagram of the finite element model of the bolt connection structure in this invention;

[0019] Figure 3 This is a cumulative probability distribution diagram of equivalent stress in the bolted connection area of ​​this invention;

[0020] Figure 4This is a surrogate model diagram of the equivalent stress radial basis function in the bolted connection area of ​​this invention;

[0021] Figure 5 This is a contour map showing the equivalent stress confidence factor of the bolted connection area in this invention.

[0022] Figure 6 This is a diagram showing the control range of the preload force for bolt connections in this invention. Detailed Implementation

[0023] like Figures 1 to 6 As shown, this embodiment describes a method for determining the control range of bolt connection preload. In engineering, the preload control of bolt connections primarily relies on torque sensors. However, during assembly, the state of the connection interface corresponding to the same torque value exhibits significant uncertainty, leading to substantial differences in stress at the connection interface. This is particularly true for deep-sea pressure-resistant structures, where the fluctuating loads and corrosion at ultra-deep depths exacerbate the uncertainty of bolt connection preload. Therefore, this embodiment addresses the more complex situation of bolt connections in deep-sea pressure-resistant shells. Considering the uncertainty in bolt preload tightening, especially in the complex deep-sea pressure-resistant structure, the design dimensions of deep-sea pressure-resistant structures need to be customized according to actual requirements. A scaled-down model using a custom approach is employed, such as... Figure 1 As shown, the determination method includes the following steps:

[0024] Step (1): Establish a finite element model of the bolted connection structure under preload conditions; according to the structural design scheme, mesh the bolted connection of the deep-sea pressure-resistant structure using finite element preprocessing software. The end caps, cylinder, and bolts are all described using three-dimensional solid elements, ignoring the bolt threads, and the bolts and nuts are treated as a single unit. All parts are set to contact relationships, and a preload is applied to the bolts using the Bolt preload method. Furthermore, to save computational costs, only an eighth of the model is used, and the boundary conditions and loads of the structure are set in an axisymmetric manner. The simulation model is as follows: Figure 2 As shown. Considering the bolted connection in the long-term high-pressure ultra-deep environment of the deep sea, in this embodiment, it is assumed that the external pressure load on the working surface of the structure is 45MPa, and this load is perpendicular to the outer surface of the structure.

[0025] Step (2): Based on the established finite element model, calculate the maximum equivalent stress in the bolt connection area under different preload conditions. 1000 bolt preload values ​​are randomly generated using the Latin hypercube random sampling method and substituted into the finite element model. The equivalent stress in the connection area under load is calculated using finite element software. The focus here is on the maximum equivalent stress; that is, the maximum equivalent stress in the area is extracted after the calculation. Simultaneously, to verify the accuracy of the proxy model, another 100 bolt preload values ​​are generated using the Latin hypercube random sampling method as a test sample. The equivalent stress calculation and maximum equivalent stress extraction are also performed in this way.

[0026] Step (3): Construct a radial basis function surrogate model based on the applied preload and the calculated equivalent stress; there are various forms of radial basis functions, among which the most common Gaussian radial basis function is shown in equation (1):

[0027]

[0028] In the formula: Let x be a radial basis function, and x be an input variable. k Let ||xx| be the spatial vector of the kth placement point. k || represents the Euclidean norm, and d represents the Gaussian radial basis function. A radial basis function surrogate model is established by fitting the preload and the corresponding equivalent stress in the connection region, and the model is then determined using the coefficient of determination R0. 2 The relative mean square error (RMSE) is used to test the accuracy of the radial basis function surrogate model, which requires that the surrogate model established here has sufficient reproducibility and predictive ability.

[0029] Step (4): Considering the uncertainty of the preload, the uncertainty of the preload is described by the mean of the preload and the multiple relationship between the standard deviation of the preload and the mean. The mean of the applied preload is set to follow a uniform distribution. In this embodiment, the mean of the preload is set to be uniformly distributed within the range [8000, 12000]N. The multiple relationship between the standard deviation of the preload and the mean is set to follow a uniform distribution. In this embodiment, the multiple relationship is set to be uniformly distributed within the range [0.01, 0.1]. The preload follows a normal distribution formed by the combination of the two distributions. In this embodiment, a nested random sampling method is used to obtain 1000 preload mean values ​​and the multiple relationship between the preload standard deviation and the mean value. Based on the sampling preload mean and multiple relationship, 1000 sets of preload values ​​are obtained. Assuming that the preload follows a normal distribution, each set of preload values ​​includes 2000 preload sample points. The maximum equivalent stress corresponding to each set of preload sample points is calculated using a radial basis function surrogate model, and the probability distribution, mean, and standard deviation of each set of equivalent stress are obtained.

[0030] Step (5): Preset the performance threshold for the maximum equivalent stress in the bolted connection area and the confidence level of the equivalent stress probability distribution. Based on the mechanical properties of the material and parts, the performance threshold for the maximum equivalent stress in the bolted connection area of ​​the deep-sea pressure-resistant structure is set to 450 MPa; and the confidence level of the equivalent stress probability distribution is preset to 99%.

[0031] Step (6): Obtain the upper quantile of the equivalent stress probability distribution based on the preset 99% confidence level. Calculate the difference between the performance threshold and the upper quantile of the equivalent stress probability distribution under the 99% confidence level, denoted as M, and the difference between the upper quantile and the mean of the equivalent stress probability distribution, denoted as U. Define the ratio of M and U as the reliability confidence factor of the bolted connection of the deep-sea pressure-resistant structure. For the convenience of determining the bolt preload in subsequent steps, a method similar to steps (2) and (3) is adopted here. The confidence factor is used as the output quantity, and the relationship between the mean and standard deviation of the bolt preload and the multiple of the mean is used as the input quantity to establish the radial basis function model of the confidence factor.

[0032] Step (7): In engineering, it is assumed that the structure can work safely when the performance margin M is greater than the performance index uncertainty U. Based on the surrogate model relationship between the confidence factor and the statistical characteristics of bolt preload established in step (6), a surface plot of the equivalent stress confidence factor in the bolt connection area and the corresponding contour plot are established, such as... Figure 4 and Figure 5 As shown in the figure, based on the phenomenon shown, find the curve with a contour line equal to 1 in the figure. The mean value and corresponding standard deviation range of the preload working that can ensure the safe service of the structure can be obtained. That is, the range of preload that should be controlled during the installation of the structure, that is, the bolt preload when M is greater than U is taken as the range of preload to be applied.

Claims

1. A method for determining the control range of preload force in a bolt connection, characterized in that, Includes the following steps: (1) Establish a finite element model of the bolted connection structure under the condition of applying preload; (2) Based on the established finite element model, calculate the maximum equivalent stress in the bolt connection area under different preloads applied to the bolt; (3) Construct a radial basis function surrogate model based on the applied preload and the calculated equivalent stress; (4) Considering the uncertainty of preload, within the range of the mean value of preload and the multiple relationship between the standard deviation of preload and the mean value, a nested random sampling method is used to obtain several mean values ​​of preload and multiple relationships between the standard deviation of preload and the mean value. These are combined to obtain several groups of sample points of applied preload. The equivalent stress corresponding to each group of preload sample points is calculated through the radial basis function surrogate model to obtain the probability distribution, mean and standard deviation of each group of equivalent stress. (5) Set the performance threshold for the maximum equivalent stress in the bolted connection area and the confidence level of the equivalent stress probability distribution; (6) Obtain the upper quantile of the equivalent stress probability distribution based on the set confidence level, calculate the difference M between the performance threshold and the upper quantile, and the difference U between the upper quantile and the mean of the equivalent stress. (7) The bolt preload when M is greater than U is used as the range of preload to control the applied preload.

2. The method for determining the control range of bolt connection preload according to claim 1, characterized in that, In step (4), the uncertainty of the preload is described by the mean of the preload and the multiple relationship between the standard deviation of the preload and the mean. It is assumed that the mean of the applied preload and the multiple relationship between the standard deviation of the preload and the mean both follow a uniform distribution. Then the preload follows a normal distribution composed of the two distributions. Several sets of sample points of the mean of the preload and the multiple relationship between the standard deviation of the preload and the mean are generated by random sampling. According to the fact that the preload follows a normal distribution, each set of preload sample points is obtained. The maximum equivalent stress of the connection area is calculated by the radial basis function surrogate model of the obtained preload sample points.

3. The method for determining the control range of bolt connection preload according to claim 1, characterized in that, In step (1), when establishing the finite element model, the bolt connection structure is meshed, the bolt thread is ignored, and the bolt and nut are integrated. Considering that the bolt connection is in service in the deep sea long-term high-pressure ultra-deep environment, the external pressure load of the working face is set.

4. The method for determining the control range of bolt connection preload according to claim 1, characterized in that, In step (2), several bolt preload values ​​are randomly generated by Latin hypercube random sampling. The generated bolt preload values ​​are substituted into the finite element model to calculate the maximum equivalent stress in the bolt connection area.

5. The method for determining the control range of bolt connection preload according to claim 1, characterized in that, In step (5), the performance threshold of the maximum equivalent stress in the bolt connection area of ​​the deep-sea pressure-resistant structure is set to 450 MPa based on the mechanical properties of the materials and parts, and the confidence level of the equivalent stress probability distribution is set to 99%.

6. The method for determining the control range of bolt connection preload according to claim 1, characterized in that, In step (6), the ratio of M to U is defined as the confidence factor of the bolt connection, and a radial basis function surrogate model is established between the mean of several preloads obtained in step (4) and the multiple relationship between the standard deviation of the preload and the mean, and the corresponding calculated confidence factor.

7. The method for determining the control range of bolt connection preload according to claim 6, characterized in that, In step (7), a contour map is established based on the mean value of the preload and the multiple relationship between the standard deviation of the preload and the mean value. The range of bolt preload when the confidence factor is greater than 1 is obtained through the contour map.

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