A method for measuring flow stress of thin-walled metal tube based on free bulging

Abstract

The application discloses a kind of based on free bulging thin-walled pipe flow stress measurement method, including establishing database, writing depth learning algorithm, bulging test;The database is established by using ABAQUS finite element software to establish thin-walled pipe free bulging model, different flow stress curves are constructed based on Swift flow stress mathematical model and input into model, gather pipe material bulging height curve, and establish the database of corresponding relationship;The depth learning algorithm is written by using Python programming language as model algorithm platform, and the neural network structure is established, the data is forwardly transmitted and the reverse transmission is carried out by using error back propagation method, and the depth learning algorithm is gradually improved by continuously learning data;The bulging test is carried out by bulging test to pipe material, and the flow stress of pipe material is obtained by using depth learning algorithm;The application can improve the simplicity of pipe material flow stress measurement method.

Description

Technical Field

[0001] The invention belongs to the technical field of flow stress measurement of metal pipes, in particular to a flow stress measurement method of a thin-walled metal pipe based on free expansion. Background Art

[0002] Currently, thin-walled metal tubes are a key lightweight component used in a wide range of fields, including automobiles, aircraft, aerospace, and military equipment. Their mechanical properties are crucial for determining whether these equipment meet the requirements. Designers need to select and design parameters such as the size of these thin-walled tubes based on their mechanical properties. Manufacturers also need to optimize their processing technology based on these mechanical properties. Flow stress is one of the most important parameters in the mechanical properties of tubes.

[0003] However, in the past, the flow stress of pipes was measured by directly using solid cylindrical specimens made of the corresponding materials for uniaxial tensile tests, and the stress-strain curve obtained was used as the flow stress of the pipe, which had a large error from the actual situation. Later, people used the prepared pipes to directly conduct uniaxial tensile tests, or cut rectangular specimens of the pipes along the axial or circumferential direction for uniaxial tensile tests, which would produce a certain degree of work hardening. During operation, high-pressure fluid is usually passed through the inside of the pipe, and these measurement methods cannot simulate actual working conditions. Later, researchers used pipes to directly conduct hydraulic bulging tests. By measuring the curvature radius of the bulge in the bulging area, wall thickness and other data, theoretical analysis was performed to obtain the flow stress of the pipe. This method cannot accurately measure the curvature radius and wall thickness, and the measurement process is not simple and time-consuming. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for measuring the flow stress of a thin-walled metal pipe based on free expansion, so as to improve the simplicity of the method for measuring the flow stress of a thin-walled pipe.

[0005] The technical solutions for achieving the purpose of the present invention are:

[0006] A method for measuring flow stress of a thin-walled metal tube based on free expansion, comprising:

[0007] (1) Establishing a database: Using finite element software to establish a free bulging model of the pipe, by collecting the change curves of the bulging height under the hydraulic bulging state of the pipe with different flow stresses, a database of the corresponding relationship between the flow stress of the pipe and the change of the bulging height is established;

[0008] (2) Establishing a neural network model: Using a programming language, a three-layer neural network structure is established, including an input layer, a hidden layer, and an output layer. Each layer has a certain number of neurons, each neuron represents a coordinate point, and an activation function sigmoid layer is set in the middle of the hidden layer.

[0009] (3) Training the neural network model: First, the error back propagation method based on the computational graph is used to calculate the derivative gradient of each layer of neurons, and then the neural network model is trained using the training data;

[0010] (4) Conducting bulging tests to obtain experimental results: The pipe is hydraulically bulged using a pipe hydraulic bulging device, and the bulging height change curve of the pipe bulging area is collected in real time. The flow stress of the pipe is obtained using a neural network model.

[0011] Compared with the prior art, the present invention has the following significant advantages:

[0012] (1) The present invention is simple to obtain the required measurement data: the present invention only needs to add a bulging height displacement sensor to the pipe hydraulic bulging equipment to measure the bulging height, avoiding the measurement of complex pipe bulging area contour curvature radius and wall thickness data.

[0013] (2) The measuring method of the present invention has good versatility: it is suitable for measuring the flow stress of thin-walled metal pipes with a certain range of thickness-to-diameter ratios and has high efficiency.

[0014] The present invention is further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is an overall flow chart of the flow stress measurement method of the present invention;

[0016] Figure 2 Schematic diagram of the tube bulging device

[0017] Figure 3 Schematic diagram of the backward transfer of deep learning algorithms.

[0018] Figure 4 Deep learning neural network structure diagram

[0019] Figure 5 This is the hydraulic bulging height curve of low carbon steel S235 pipe

[0020] Figure 6 The flow stress and actual flow stress curve of low carbon steel S235 pipe obtained by this method DETAILED DESCRIPTION

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0022] Combine Figure 1 The present embodiment provides a method for measuring flow stress of a thin-walled metal pipe based on free expansion, comprising the following steps:

[0023] Step 1, a finite element model for free bulging of thin-walled tube is established by using ABAQUS finite element software: there are two components in the finite element model, one component is the tube, and the other component is the pressure head, which is a hollow cylinder, and is placed at both ends of the tube to limit the radial displacement change of the tube, and the middle region of the tube is the free bulging region, and a two-dimensional axisymmetric finite element model is established.

[0024] Step 2, the Swift flow stress mathematical model is used to construct the flow stress curve of the tube, and the equation of the Swift model is as follows:

[0025] σ=K(ε0+ε) n (1)

[0026] In the formula, K is the strength factor; n is the strain hardening index of the material; ε0 is the yield strain of the material; σ is the flow stress of the material; and ε is the strain of the material. The strength factor K is respectively 250, 500, 750 and 1000, the yield strain ε0 of the material is respectively 0.1, 0.2, 0.3 and 0.4, and the strain hardening index n of the material is respectively 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6, which are combined into 96 different flow stress curves.

[0027] Step 3, the obtained tube flow stress curve is input into the tube bulging finite element model, and the bulging height H of the middle point of the tube wall outer surface of the tube bulging region is obtained through finite element analysis. out The bulging height and bulging pressure change curve of the tube is obtained by the following formula.

[0028] H=r0+H out (2)

[0029] In the formula, H out is the bulging height of the highest point of the tube wall outer surface of the tube; r0 is the initial radius of the tube; and H is the bulging height of the tube. Each tube flow stress curve corresponds to a tube bulging height change curve.

[0030] Step 4, a deep learning model based on error back propagation method is established:

[0031] 4.1, the deep learning network structure is designed, including input layer, hidden layer and output layer, and the hidden layer is divided into first layer hidden layer and second layer hidden layer. There are 40 neurons in the input layer, respectively representing 40 coordinate points of the input curve; there are 10 neurons in the output layer, respectively representing 10 coordinate points of the output curve; there are 20 neurons in the first layer hidden layer; and there are 10 neurons in the second layer hidden layer, as shown in Figure 4 .

[0032] 4.2. In the deep learning model, the hidden layer output activation function is set to the sigmoid function, as shown in the following formula (3); during the reverse transfer, the sigmoid function needs to be differentiated, and the derivative formula is shown in formula (4), which is expressed as formula (5) using the sigmoid function.

[0033]

[0034] Where f(x) is the result calculated by the sigmoid function formula; e is the Napier constant 2.71820…; x is the number at the coordinate point; is the derivative of f(x) with respect to x.

[0035] 4.3. In the neural network, after the data is forward-transferred, it deviates from the training data. The mean square error (MSE) is used to calculate the loss function, as shown in formula (6).

[0036]

[0037] Where MSE is the mean square error between the output value of the neural network and the training data; N is the number of coordinate point values ​​in the neural network; t is the sequence number of the coordinate point values ​​in the neural network; y t The output value of the neural network; m t is the actual value of the training data.

[0038] 4.4. The error back propagation method is used to calculate the gradient of each layer. The specific gradient derivative formula is as follows Figure 3 As shown. Combined Figure 3 , The following details the gradient derivation process of the error back propagation method in the deep learning model. First, the result Y2 of the output layer is differentiated, and the derivative is 1; continue to forward back propagation, and encounter matrix addition and multiplication operations. In the error back propagation method, in the derivation process of the addition operation, the upstream value is actually passed to the downstream intact. For the multiplication operation, the derivative value of a downstream matrix is ​​the upstream input signal multiplied by the transpose of another downstream matrix. At this time, the gradient of the bias coefficient B2 and the weight coefficient W2 of the second hidden layer is obtained; continue forward propagation, it is a sigmoid function, and the sigmoid function is differentiated; continue forward propagation, encounter matrix addition and multiplication operations, and in the same way as the second step, in the error back propagation method, for the addition operation, the upstream value is passed to the downstream intact. For the multiplication operation, the derivative value of a downstream matrix is ​​the upstream input signal multiplied by the transpose of another downstream matrix. At this time, the gradient of the bias coefficient B1 and the weight coefficient W1 of the first hidden layer is obtained.

[0039] Step 5: Initialize the parameters of the neurons in each layer of the neural network, and use the random function random of the numpy module in the Python language to generate multiple sets of random values ​​that conform to the standard normal distribution for the weight coefficient matrix W1 and bias coefficient matrix B1 of the first hidden layer and the weight coefficient matrix W2 and bias coefficient matrix B2 of the second hidden layer.

[0040] Step 6: Convert the obtained bulging height curve into a bulging coefficient curve according to formula (7), and perform maximum and minimum processing on the coordinate points on the curve according to formulas (8) and (9).

[0041]

[0042] X scaled =X std *(max-min)+min (9)

[0043] Where K is the expansion coefficient of the tube; H is the expansion height of the middle point of the tube expansion area; r0 is the initial radius of the tube; X std is the normalized result of the coordinate point; X is the value of the horizontal or vertical axis of the coordinate point; X min The minimum value of the horizontal or vertical axis of all coordinate points; X max The maximum value of the horizontal or vertical axis of all coordinate points; max is the maximum value of the coordinate point that needs to be scaled to a certain range, the default is 1; min is the minimum value of the coordinate point that needs to be scaled to a certain range, the default is 0; X scaled is the preprocessing result of the coordinate point.

[0044] Step 7: The neural network performs forward transfer calculations. The matrix (2, 40) composed of the processed 40 coordinate point data on the tube bulging height change curve is multiplied by the weight coefficient matrix W1 of the first hidden layer and then added to the bias coefficient matrix B1. The result is calculated according to the activation function formula (3); the second hidden layer operation is performed, and the weight coefficient matrix W2 is multiplied and then added to the bias coefficient matrix B2; finally, it reaches the output layer intact.

[0045] Step 8: Calculate the loss function of the neural network according to formula (6)

[0046] Step 9. Set the hyperparameter learning rate to 0.7 (multiple tests found that a learning rate of 0.7 can more effectively reduce the error).

[0047] Step 10: Multiply the learning rate set in step 9 by the gradient of each layer of the neural network obtained in step 4.4 to obtain the deviation of each layer, and then update the weight coefficient and bias coefficient of each layer accordingly.

[0048] Step 11: Determine whether the mean square error obtained by formula (6) meets the set error accuracy requirements. If not, restart the forward and backward transfer of training data until the requirements are met, indicating that the deep learning model training is completed.

[0049] Step 12: Conduct hydraulic bulging test on the pipe. Figure 2 Schematic diagram of a hydraulic bulging device for pipes. A thin-walled metal pipe is fixed in the hydraulic bulging device. Figure 3 shows the pipe pressure head, which presses on both ends of the pipe to limit the radial displacement of the pipe at both ends. High-pressure liquid is passed into the pipe through pipe 1. A pressure sensor inside pipe 1 measures the pipe bulging pressure. A displacement sensor is placed in the middle of the pipe bulging area (Figure 2). As the bulging pressure increases, the displacement sensor measures the bulging height in the middle of the bulging area.

[0050] Step 13: Based on the tube bulging pressure and tube bulging height data collected in step 12, a curve showing the change of bulging height with pressure is formed. 40 coordinate points are evenly intercepted and input into the deep learning model to obtain the tube flow stress curve.

[0051] This example uses the data of tube bulging height obtained by Temim Zribi, Ali Khalfallah and Hedi BelHadjSalah in the literature "Experimental characterization and inverse constitutive parameters identification of tubular materials for tube hydroforming process" to conduct a free bulging test on a low carbon steel S235 tube using a new independently developed tube hydraulic bulging equipment. The outer diameter of the tube is 50 mm, the initial wall thickness is 1.07 mm, the length of the middle bulging area is 60 mm, and the tube bulging height curve is as follows: Figure 5 As shown. Input it into the deep learning model to obtain the flow stress curve of low carbon steel S235 pipe, as shown Figure 6 As shown, it is found that the degree of agreement is higher than that of the actual flow stress. The present invention does not need to measure the complicated data of the curvature radius and wall thickness change of the pipe bulging area, which greatly reduces the workload, improves the efficiency, and ensures the accuracy of measuring the pipe flow stress.

Claims

1. A method for measuring flow stress of a thin-walled metal tube based on free expansion, characterized in that: include: (1) Establishing a database: Using finite element software to establish a free bulging model of the pipe, by collecting the change curves of the bulging height under the hydraulic bulging state of the pipe with different flow stresses, a database of the corresponding relationship between the flow stress of the pipe and the change of the bulging height is established; H=r0+H out Where H out is the bulging height of the outer surface of the tube wall at the highest point of bulging; r0 is the initial radius of the tube; H is the bulging height of the tube; each tube flow stress curve corresponds to a tube bulging height change curve; (2) Establishing a neural network model: Using a programming language, a three-layer neural network structure is established, including an input layer, a hidden layer, and an output layer. Each layer has a certain number of neurons, each neuron represents a coordinate point, and an activation function sigmoid layer is set in the middle of the hidden layer. Building a neural network model and training the neural network model include the following steps: Step 1: Establish a three-layer neural network structure, including an input layer, two hidden layers and an output layer. A sigmoid activation function layer is set between the two hidden layers. Each layer has several neurons, and the neurons between layers are interconnected. Step 2: Use the random function of the numpy module in Python language to initialize the parameters of each neuron in the neural network layer; Step 3: Convert the obtained tube bulging height curve into a tube bulging coefficient curve, and perform maximum and minimum processing on the coordinate points on the tube bulging coefficient curve to obtain a two-dimensional array; The conversion of the tube expansion coefficient curve is carried out as follows: X scaled =X std *(max-min)+min (9) Where K is the expansion coefficient of the tube; H is the expansion height of the middle point of the tube expansion area; r0 is the initial radius of the tube; X std is the normalized result of the coordinate point; X is the value of the horizontal or vertical axis of the coordinate point; X min The minimum value of the horizontal or vertical axis of all coordinate points; X max The maximum value of the horizontal or vertical axis of all coordinate points; X scaled is the preprocessing result of the coordinate point; Step 4: Start forward propagation of the two-dimensional array in the deep learning model to perform matrix operations; Step 5: Compare the calculated value through forward transfer with the actual value to calculate the loss function of the neural network model; Step 6: Set the hyperparameter learning rate. Step 7: Subtract the result of the forward pass calculation of the two-dimensional array from the multiplication result of the learning rate and the gradient of each layer of the neural network structure to update the weight coefficient and bias coefficient of each layer; Step 8: Determine whether the error meets the requirements. If not, restart the training data until the requirements are met. (3) Training the neural network model: First, the error back propagation method based on the computational graph is used to calculate the derivative gradient of each layer of neurons, and then the neural network model is trained using the training data; (4) Conducting bulging tests to obtain experimental results: The pipe is hydraulically bulged using a pipe hydraulic bulging device, and the bulging height change curve of the pipe bulging area is collected in real time. The flow stress of the pipe is obtained using a neural network model.

2. The method for measuring flow stress of a thin-walled metal tube based on free expansion according to claim 1, characterized in that: Building a database involves the following steps: Step 1: Use ABAQUS finite element software to establish a two-dimensional axisymmetric finite element model for the free bulging process of thin-walled metal tubes. The finite element model has two components: one is the tube, and the other is the indenter, which is a hollow cylinder placed at both ends of the tube to limit the radial displacement of the tube at both ends. The middle area of ​​the tube is the free bulging area; Step 2: Using the Swift flow stress mathematical model, different flow stress curves of the pipe are constructed by changing the values ​​of the intensity factor, yield strain, and strain hardening exponent; Step 3: Input the obtained pipe flow stress curve into the pipe bulging finite element model, obtain the bulging height and bulging pressure change curve at the middle point of the pipe bulging area through finite element analysis, and establish a database with corresponding relationships.

3. The method for measuring flow stress of a thin-walled metal tube based on free expansion according to claim 1, characterized in that: The loss function is calculated as follows: Where MSE is the mean square error between the output value of the neural network and the training data; N is the number of coordinate point values ​​in the neural network; t is the sequence number of the coordinate point values ​​in the neural network; y t The output value of the neural network; m t is the actual value of the training data.

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