Bolt connection local contact stiffness sudden change threshold prediction method

Abstract

The invention relates to a bolted connection local contact stiffness sudden change threshold prediction method, which comprises the following steps of: 1, constructing a three-dimensional model of a bolted connection composite board, and performing finite element simulation analysis on the three-dimensional model; 2, performing preliminary screening and normalization on data obtained by modal analysis and harmonic response analysis; 3, constructing a machine learning prediction model by using the training set; 4, the precision of the machine learning prediction model is tested and verified through the test set, and evaluation is carried out through the evaluation indexes. According to the method, the time cost and complexity of manual testing are reduced, the dynamic overhaul period can be formulated according to the predicted threshold value cycle index, and the monitoring efficiency and the production efficiency are improved.

Description

Technical Field

[0001] The invention relates to a method for predicting a threshold value of a sudden change in local contact stiffness of a bolt connection, and belongs to the technical field of bolt detection. Background Art

[0002] Bolted connections are one of the most important connection methods because they are easy to assemble, disassemble, and maintain. They are a core part of mechanical assembly and are very common in mechanical structures, such as bridges, airplanes, and automobiles. However, bolted composite structures are often in a vibrating environment during use, which can easily cause bolts to loosen, resulting in a reduction in local bolt preload and bolt connection stiffness, thereby affecting the integrity of the bolted structure and causing structural instability or fatigue failure. Traditional methods for detecting bolt loosening have significant limitations, such as: relying on manual inspection and being unable to obtain data in real time; the detection method is greatly affected by the environment; the high price of the detection equipment, etc., which brings great inconvenience to the detection. How to quickly and accurately monitor bolt loosening in real time is currently a major problem in many workplaces.

[0003] Finite element simulation uses parametric modeling to simulate the various contact processes in bolted connections (friction, slip, and preload attenuation), revealing the physical mechanisms of stiffness mutations. A neural network, leveraging the extensive data generated by the simulation, establishes a model capable of monitoring bolt loosening and determining its mutation threshold, overcoming the challenges of traditional modeling and low prediction efficiency.

[0004] Recent research has seen numerous examples of machine learning being applied to structural inspection, such as using support vector machines (SVMs) to identify loose bolts. The neural networks employed excel at solving complex nonlinear problems. In vibrating environments such as wind turbine bolts and high-speed rail bogies, real-time monitoring of the vibration spectrum can predict stiffness degradation, triggering preload compensation. Dynamic maintenance cycles can also be established based on predicted threshold cycles. Summary of the Invention

[0005] The threshold value of local contact stiffness mutation of bolted connections is difficult to measure under current vibration environment. The present invention provides a method for predicting the threshold value of local contact stiffness mutation of bolted connections based on finite element simulation and BP neural network, aiming to reduce the time cost and complexity of manual testing.

[0006] A method for predicting a threshold value of a sudden change in local contact stiffness of a bolted connection comprises the following steps:

[0007] Step 1: Construct a three-dimensional model of the bolted composite plate, perform finite element analysis on it, and simultaneously perform modal analysis and harmonic response analysis to obtain the natural frequency and frequency response function of the composite plate and identify the law of resonant frequency shift;

[0008] Step 2: Perform preliminary screening and normalization on the data, and divide the data in the simulated data set into training set, cross-training set and test set;

[0009] Step 3: Use the training set to construct a machine learning prediction model of a BP neural network with physical constraints. The input layer receives vibration frequency, amplitude, preload force, and surface roughness parameters, and the output layer predicts the critical stiffness mutation point and stiffness attenuation rate ΔK / K0. The accuracy of the BP neural network prediction model is evaluated using evaluation indicators, and the prediction accuracy of the BP neural network is evaluated using data from the cross-validation set.

[0010] Step 4: Use the test set to test the accuracy of the machine learning prediction model. When the accuracy meets the standard, the neural network prediction model is successfully output. If the accuracy does not meet the standard, repeat step 4 until the accuracy meets the standard. After the accuracy meets the standard, the BP neural network prediction model is output, which is the prediction model for the local contact stiffness mutation threshold of the bolted connection.

[0011] The three-dimensional model of the bolted composite plate is constructed in step 1, and the finite element analysis thereof specifically includes:

[0012] S1.1: Key part: Since the research focuses on the relationship between bolts and plates, a parametric modeling method is used to construct a simplified model of bolt-connected composite plates, ignoring non-critical process features such as fillets and small holes to ensure computational efficiency. Specifically, SOLIDWORKS is used to construct a simplified model of bolt-connected composite plates (bolts, nuts, upper and lower composite plates).

[0013] S1.2: Define key parameters such as bolt preload, friction coefficient, contact surface dimensions, and material properties (default is structural steel). Define the contact surface, plate-bolt, plate-nut, bolt-nut, and plate-plate friction contact, set the friction coefficient (recommended 0.1-0.3), use bound contact to simulate the initial preload state, apply axial preload through the preload loading module, perform finite element simulation, and locally refine the mesh in the contact area (around the bolt hole) to ensure the accuracy of stress gradient capture; the mesh in other areas can be relatively sparse; constrain the sides of the composite plate to fixed supports.

[0014] Specifically, the model was imported using ANSYS, a finite element simulation software, and the corresponding material properties were assigned to the bolts and composite plate. The mesh was then refined locally in the contact area (around the bolt hole), while the mesh in other areas was allowed to be sparse to ensure the accuracy of the simulation results.

[0015] S1.3: Perform "modal analysis" to extract the natural frequencies and vibration modes of the first six stages, record the impact of the bolt connection stiffness on the overall dynamic characteristics, apply a swept frequency vibration load (e.g., 0-2000 Hz), obtain the frequency response function of the composite plate through "harmonic response analysis", identify the pattern of resonant frequency offset, gradually reduce the preload, simulate the loosening process (simulate the loosening process), repeat the modal and harmonic response analysis, record the curve of the natural frequency changing with the preload, and determine the contact stiffness threshold through the slope mutation point.

[0016] Specifically: Using finite element simulation and "modal analysis", extract the natural frequencies and vibration modes of the first six stages, and record the impact of the bolt connection stiffness on the overall dynamic characteristics. Apply a sweep vibration load (such as 0-2000Hz), obtain the frequency response function of the composite plate through "harmonic response analysis", and identify the law of resonant frequency offset. Finally, the preload force can be gradually reduced (simulating the loosening process) and the modal and harmonic response analysis can be repeated. Record the curve of the natural frequency changing with the preload force, and determine the contact stiffness threshold through the slope mutation point.

[0017] The data set in step 2 specifically includes:

[0018] The dataset consists of the following parameters: a bolted composite plate with four matching bolts and nuts, and two composite plates. The default material is structural steel. The input layer receives the vibration frequency, amplitude, preload, and surface roughness parameters, and the output layer predicts the critical stiffness mutation point and stiffness decay rate ΔK / K0.

[0019] The second step specifically includes:

[0020] The data were preliminarily screened and normalized, and the data with vibration displacement less than 2 mm were retained. The retained data were normalized according to formula (1), and the data in the simulated data set were divided into training set, cross-validation set and test set in a ratio of 8:1:1;

[0021]

[0022] Where: y i is the normalized data, x i is the original data, x min is the minimum value of each dimension in the original data, x max is the maximum value of each dimension in the original data.

[0023] The evaluation index in step 3 is one or more of the correlation coefficient R, mean absolute error MAE, and relative error RAE;

[0024] The calculation formula of the correlation coefficient R is:

[0025]

[0026] The calculation formula for the mean absolute error MAE is:

[0027]

[0028] Relative error RAE calculation formula:

[0029]

[0030] Where N is the total number of samples, y ai and y pi represent the true value and the predicted value respectively. represents the average of all the values ​​of the simulation, The average of all values ​​representing the predicted value.

[0031] When constructing a machine learning prediction model using the training set, a BP neural network was used as the machine learning method. Frequency f, amplitude A, preload force F, friction coefficient μ, roughness Ra, elastic modulus E, and Poisson's ratio ν were used as input layers, with eight layers and two output layers representing the stiffness mutation point and stiffness attenuation, respectively. The hidden layer was set to two, with the number of neurons ranging from 16 to 8, respectively. A stiffness calculation formula was introduced before the output layer to provide physical constraints, ensuring that the prediction results conformed to basic physical principles.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] The present invention performs preliminary screening and normalization on the data obtained from simulation through finite element analysis of bolts and composite plates, and divides the data into a training set, a test set and a cross-validation set; uses the training set to construct a BP neural network prediction model, and uses cross-validation to evaluate the accuracy of the BP neural network prediction model; uses the test set to test the accuracy of the BP neural network prediction model and perform index evaluation.

[0034] The present invention reduces the time cost and complexity of manual testing, and can also formulate dynamic maintenance cycles based on the predicted threshold cycle number, thereby improving monitoring efficiency and production efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0036] Figure 1 This is a flow chart of the method for predicting the threshold value of the sudden change of local contact stiffness of a bolted connection according to the present invention.

[0037] Figure 2 This is a neural network structure diagram of the BP neural network in the method for predicting the mutation threshold value of local contact stiffness of bolted connections of the present invention.

[0038] Figure 3 This is the result obtained by the finite element simulation modal analysis of the present invention.

[0039] Figure 4 This is the result (1) obtained by the finite element harmonic response analysis of the present invention.

[0040] Figure 5 This is the result (2) obtained by the finite element harmonic response analysis of the present invention.

[0041] Figure 6 This is the result (3) obtained by the finite element harmonic response analysis of the present invention.

[0042] Figure 7 This is a three-dimensional model of the bolted composite plate of the present invention. DETAILED DESCRIPTION

[0043] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0044] Reference Figure 1 A method for predicting the threshold value of sudden change of local contact stiffness of a bolted connection comprises the following steps:

[0045] Step 1: Construct a three-dimensional model of the bolted composite plate, perform finite element analysis on it, and simultaneously perform modal analysis and harmonic response analysis to obtain the natural frequency and frequency response function of the composite plate and identify the law of resonant frequency shift;

[0046] Step 2: Perform preliminary screening and normalization on the data, and divide the data in the simulated data set into training set, cross-training set and test set;

[0047] The three-dimensional model of the bolted composite plate is constructed in step 1, and the finite element analysis thereof specifically includes:

[0048] S1.1: Pre-critical part: Since the research focuses on the relationship between bolts and plates, a parametric modeling method is used to construct a simplified model of bolted composite plates, ignoring non-critical process features such as fillets and small holes to ensure computational efficiency;

[0049] Reference Figure 7Specifically: Use SOLIDWORKS to build a bolt-connected composite plate model. The two composite plates are 200 mm long, 100 mm wide, and 12 mm thick, with four through holes with a diameter of 12.1 mm, four M12 hexagonal head bolts, and their four matching nuts.

[0050] S1.2: Define key parameters such as bolt preload, friction coefficient, contact surface dimensions, and material properties (default is structural steel). Define the contact surface, plate-bolt, plate-nut, bolt-nut, and plate-plate friction contact, set the friction coefficient (recommended 0.1-0.3), use bound contact to simulate the initial preload state, apply axial preload through the preload loading module, perform finite element simulation, and locally refine the mesh in the contact area (around the bolt hole) to ensure the accuracy of stress gradient capture; the mesh in other areas can be relatively sparse; constrain the sides of the composite plate to fixed supports.

[0051] Specifically, the finite element software ANSYS Workbench was used to import the geometric model and material properties (default structural steel), perform meshing, and perform local mesh encryption in the contact area (around the bolt hole) to ensure the accuracy of stress gradient capture; the mesh in other parts can be relatively sparse. Set the friction contact between the connection states plate-bolt, plate-nut, bolt-nut, and plate-plate, and set the friction coefficient (recommended 0.1-0.3). Use binding contact to simulate the initial preload state, and apply axial preload through the preload loading module. Constrain the composite plate to fixed supports on all sides.

[0052] S1.3: Perform "modal analysis" to extract the natural frequencies and vibration modes of the first six stages, record the impact of the bolt connection stiffness on the overall dynamic characteristics, apply a swept frequency vibration load (e.g., 0-2000 Hz), obtain the frequency response function of the composite plate through "harmonic response analysis", identify the pattern of resonant frequency offset, gradually reduce the preload, simulate the loosening process (simulate the loosening process), repeat the modal and harmonic response analysis, record the curve of the natural frequency changing with the preload, and determine the contact stiffness threshold through the slope mutation point.

[0053] Reference Figure 3-6 Specifically, perform a modal analysis, extract the first six natural frequencies and mode shapes, and record the impact of the bolted joint stiffness on the overall dynamic characteristics. Apply a swept-frequency vibration load and, through harmonic response analysis, obtain the frequency response function of the composite plate and identify the pattern of resonant frequency shifts. Repeat the modal and harmonic response analysis with decreasing preload. Record the curve of the natural frequency versus preload, and determine the contact stiffness threshold by observing the slope mutation point.

[0054] The data were preliminarily screened and normalized, and the data with vibration displacement less than 2 mm were retained. The retained data were normalized according to formula (1), and the data in the simulated data set were divided into training set, cross-validation set and test set in a ratio of 8:1:1;

[0055]

[0056] Where: y i is the normalized data, x i is the original data, x min is the minimum value of each dimension in the original data, x max is the maximum value of each dimension in the original data.

[0057] Step 3: Use the training set to construct a machine learning prediction model of a BP neural network with physical constraints. The input layer receives vibration frequency, amplitude, preload force, and surface roughness parameters, and the output layer predicts the critical stiffness mutation point and stiffness attenuation rate ΔK / K0. The accuracy of the BP neural network prediction model is evaluated using evaluation indicators, and the prediction accuracy of the BP neural network is evaluated using data from the cross-validation set.

[0058] Reference Figure 2 When constructing a machine learning prediction model using the training set, a BP neural network was used. Frequency f, amplitude A, preload F, friction coefficient μ, roughness Ra, elastic modulus E, and Poisson's ratio ν were used as input layers, with eight layers and two output layers representing the stiffness mutation point and stiffness attenuation, respectively. The hidden layer was set to two, with the number of neurons ranging from 16 to 8, respectively. A stiffness calculation formula was introduced before the output layer to provide physical constraints, ensuring that the prediction results conformed to basic physical principles.

[0059] Residual connection of the physical constraint stiffness calculation formula:

[0060]

[0061] Where: K0 is the lower limit of theoretical stiffness, E is the elastic modulus of the material, d e is the equivalent diameter of the thread stress section, i.e. the effective diameter of the bolt, and L is the total thickness of the connected parts.

[0062] The evaluation index in step 3 is one or more of the correlation coefficient R, mean absolute error MAE, and relative error RAE;

[0063] The calculation formula of the correlation coefficient R is:

[0064]

[0065] The calculation formula for the mean absolute error MAE is:

[0066]

[0067] Relative error RAE calculation formula:

[0068]

[0069] Where N is the total number of samples, y ai and y pi represent the true value and the predicted value respectively. represents the average of all the values ​​of the simulation, The average of all values ​​representing the predicted value.

[0070] Step 4: Use the test set to test the accuracy of the machine learning prediction model. When the accuracy meets the standard, the neural network prediction model is successfully output. If the accuracy does not meet the standard, repeat step 4 until the accuracy meets the standard. After the accuracy meets the standard, the BP neural network prediction model is output, which is the prediction model for the local contact stiffness mutation threshold of the bolted connection.

[0071] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. It is apparent to those skilled in the art that various changes, modifications, substitutions, and variations to these embodiments may be made without departing from the principles and spirit of the present invention, and these changes and modifications still fall within the scope of protection of the present invention.

Claims

1. A method for predicting the threshold value of sudden change in local contact stiffness of a bolted connection, characterized by: The following steps are involved: Step 1: Construct a three-dimensional model of the bolted composite plate, perform finite element analysis on it, and simultaneously perform modal analysis and harmonic response analysis to obtain the natural frequency and frequency response function of the composite plate and identify the law of resonant frequency shift; Step 2: Perform preliminary screening and normalization on the data, and divide the data in the simulated data set into training set, cross-training set and test set; Step 3: Use the training set to construct a machine learning prediction model of a BP neural network with physical constraints. The input layer receives vibration frequency, amplitude, preload force, and surface roughness parameters, and the output layer predicts the critical stiffness mutation point and stiffness attenuation rate ΔK / K0. The accuracy of the BP neural network prediction model is evaluated using evaluation indicators, and the prediction accuracy of the BP neural network is evaluated using data from the cross-validation set. Step 4: Use the test set to test the accuracy of the machine learning prediction model. When the accuracy meets the standard, the neural network prediction model is successfully output. If the accuracy does not meet the standard, repeat step 4 until the accuracy meets the standard. After the accuracy meets the standard, the BP neural network prediction model is output, which is the prediction model for the local contact stiffness mutation threshold of the bolted connection.

2. The method for predicting the threshold value of sudden change in local contact stiffness of a bolted connection according to claim 1, characterized in that: In the step 1, a three-dimensional model of the bolted composite plate is constructed and a finite element analysis is performed on the model, specifically including: S1.1: Use parametric modeling to construct a simplified model of bolted composite plates, ignoring non-critical process features such as fillets and small holes to ensure computational efficiency; S1.2: Define key parameters for bolt preload, friction coefficient, contact surface dimensions, and material properties. Define the contact surface, plate-bolt, plate-nut, bolt-nut, and plate-plate friction contacts, set the friction coefficient, use bound contact to simulate the initial preload state, apply axial preload through the preload loading module, perform finite element simulation, and perform local mesh refinement in the contact area to ensure the accuracy of stress gradient capture; constrain the sides of the composite plate to fixed supports. S1.3: Perform modal analysis to extract the natural frequencies and vibration modes of the first six stages, record the effect of bolt connection stiffness on the overall dynamic characteristics, apply a swept-frequency vibration load, and obtain the frequency response function of the composite plate through harmonic response analysis to identify the pattern of resonant frequency shifts. Gradually reduce the preload force to simulate the loosening process, repeat the modal and harmonic response analysis, and record the curve of the natural frequency versus preload force. Determine the contact stiffness threshold based on the slope mutation point.

3. The method for predicting the threshold value of sudden change of local contact stiffness of bolted connection according to claim 1, characterized in that: The data set in step 2 specifically includes: The dataset consists of the following parameters: a bolted composite plate with four matching bolts and nuts, and two composite plates. The default material is structural steel. The input layer receives the vibration frequency, amplitude, preload, and surface roughness parameters, and the output layer predicts the critical stiffness mutation point and stiffness decay rate ΔK / K0.

4. The method for predicting the threshold value of sudden change of local contact stiffness of bolted connection according to claim 3, characterized in that: The second step specifically includes: The data were preliminarily screened and normalized, and the data with vibration displacement less than 2 mm were retained. The retained data were normalized according to formula (1), and the data in the simulated data set were divided into training set, cross-validation set and test set in a ratio of 8:1:1; Where: y i is the normalized data, x i is the original data, x min is the minimum value of each dimension in the original data, x max is the maximum value of each dimension in the original data.

5. The method for predicting the threshold value of sudden change of local contact stiffness of bolted connection according to claim 1, characterized in that: The evaluation index in step 3 is one or more of the correlation coefficient R, mean absolute error MAE, and relative error RAE; The calculation formula of the correlation coefficient R is: The calculation formula for the mean absolute error MAE is: Relative error RAE calculation formula: Where N is the total number of samples, y ai and y pi represent the true value and the predicted value respectively. represents the average of all the values ​​of the simulation, The average of all values ​​representing the predicted value.

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