Friction coefficient calculation model, method for constructing same, and use for simulation of rotary friction welding

Abstract

This invention discloses a friction coefficient calculation model, its construction method, and its application in rotational friction welding simulation. The model calculates the real-time friction coefficient between two test pieces during rotational friction welding, where ε is the pressure at the contact surface of the two test pieces, ε is the relative linear velocity, and ε is the interface temperature. e is a natural constant, and a, b, c, d, and f are all constants. The friction coefficient calculation model uses machine learning to decouple the friction coefficient calculation, constructing a friction coefficient prediction model adaptable to the entire temperature range. Based on this friction coefficient calculation model, inertial friction welding simulation can provide technical support for inertial friction welding process optimization and industrial applications.

Description

Technical Field

[0001] This invention belongs to the field of welding simulation technology, specifically relating to a method for constructing a friction coefficient prediction model based on machine learning-enhanced friction constitutive model. Background Technology

[0002] Friction welding is a solid-state joining technology that avoids solidification defects generated during fusion welding and has been widely used for joining various metallic materials. Inertial friction welding (IFW), a type of friction welding, offers advantages such as high production efficiency, minimal joint deformation, and complete weld joints, and is commonly used for welding disc and shaft components. During IFW, the kinetic energy stored in the flywheel is converted into interfacial heat energy through friction between the workpieces in a short time, softening and plasticizing the interfacial material. This softened and plasticized material is then extruded outwards under axial pressure to form flash, thus creating the weld joint. IFW provides stable weld quality and high structural integrity, playing a crucial role in the manufacturing of aero-engine rotor components.

[0003] As the requirements for material performance in aerospace equipment continue to increase, novel nickel-based superalloys with high γ' phase volume fraction are gradually becoming key materials for aerospace engines. These alloys contain high concentrations of Ti and Al, with a γ' precipitate volume fraction exceeding 40%, exhibiting extremely high high-temperature strength. However, with the continuous improvement in material strength, the welding process window for inertial friction welding is gradually narrowing. Its application in new structures and materials still heavily relies on experience, and extensive process optimization experiments inevitably lead to material waste and long development cycles.

[0004] To address the aforementioned issues, numerical simulation-assisted analysis of the inertial friction welding process has become an effective and economical approach. Therefore, developing a simulation model with high fidelity and strong generalization ability is crucial. The friction coefficient is a key parameter affecting the accuracy of friction welding simulations; however, experimentally measuring the friction coefficient under extreme conditions is extremely challenging, and the strong coupling between key variables (such as interface temperature and relative linear velocity) makes it difficult to decompose their individual effects. Therefore, most existing studies employ simplified friction models. Inevitably, this simplification reduces the accuracy of numerical simulations, leading to insufficient simulation precision and significantly weakening the model's generalization ability. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a friction coefficient calculation model that has high simulation accuracy and generalization ability, thereby achieving the goal of rapid process screening.

[0006] Another objective of this invention is to provide an application of a friction coefficient calculation model in the simulation of rotary friction welding.

[0007] A friction coefficient calculation model, which is This friction coefficient calculation model calculates the real-time friction coefficient between two test pieces during rotary friction welding. , The coefficient of friction between two test pieces during rotary friction welding. This refers to the real-time pressure at the contact surface of the two test pieces during rotary friction welding. The relative linear velocity of the two test pieces during rotational friction welding is given in real time. The real-time interface temperature of the contact surfaces of the two test pieces during rotary friction welding; e is the natural constant, and a, b, c, d, and f are all constants;

[0008] The methods for calculating a, b, c, d, and f include:

[0009] Step 1: Prepare two tubular specimens: the first tubular specimen and the second tubular specimen. The two specimens to be tested are the first specimen to be tested and the second specimen to be tested. The material of the first tubular specimen is the same as that of the first specimen to be tested, and the material of the second tubular specimen is the same as that of the second specimen to be tested.

[0010] Step 2: Fix the first tubular specimen to the fixture and the second tubular specimen to the spindle, and perform rotational friction welding on the two tubular specimens coaxially opposite each other. During the rotational friction welding process, v, P, T and M of the two tubular specimens are obtained at time intervals of less than 0.5s.

[0011] P represents the real-time pressure at the contact surface during the rotary friction welding process of the two tubular specimens.

[0012] The relative linear velocity in real time during the rotational friction welding process of two tubular specimens;

[0013] The real-time interface temperature between two tubular specimens during the rotary friction welding process;

[0014] M represents the real-time spindle torque during the rotary friction welding process of the two tubular specimens;

[0015] Step 3: Take ln(P), v, T, and T² from the same moment of rotary friction welding as a preprocessed sample. Arrange all preprocessed samples row-wise to obtain the feature matrix. Perform standardization on each element in the feature matrix according to the standardization formula to obtain the standardized matrix. The standardization formula is as follows:

[0016] In the formula, Let be the element in the i-th row and j-th column of the characteristic matrix. Let i be the element in the i-th row and j-th column of the normalized matrix. Let be the mean of the elements in the j-th column of the characteristic matrix. Let $\frac{j}{j}$ be the standard deviation of the elements in the $j$-th column of the characteristic matrix

[0017] Step 4: Each row in the normalization matrix represents a sample, and each column in the normalization matrix corresponds to a feature. Calculate the friction coefficient μ of each sample based on M and P obtained at the same moment during rotary friction welding.

[0018] Step 5: Calculate the logarithmic value of the friction coefficient based on the friction coefficient μ of each sample. As a label for this sample;

[0019] Step 6: Use the standardized matrix as the modeling dataset. Substitute the modeling dataset and all its corresponding labels into the ridge regression model for training, resulting in the trained ridge regression model. The linear regression equation of the trained ridge regression model is: ,in, The weight coefficients of the features are obtained after standardization with ln(P). The weight coefficients of the features are obtained after standardization of v. The weight coefficients of the features are obtained after T² standardization. The weight coefficients of the features are obtained after T is standardized. The intercept of the linear regression equation is denoted as . The output of the trained ridge regression model;

[0020] Step 7, according to , , , , mean mean mean mean , , , and Calculate a, b, c, d, and f. The formulas for calculating a, b, c, d, and f are as follows:

[0021]

[0022]

[0023]

[0024]

[0025] .

[0026] In the above technical solution, the training method of substituting the modeling dataset and all the labels corresponding to the modeling dataset into the ridge regression model for training includes:

[0027] S1, in the logarithmic interval to Generate multiple logarithmically spaced values, each value serving as a separate unit. traverse each And perform the following operations:

[0028] Will the current As a regularization parameter in the loss function of the ridge regression model, the modeling dataset is divided into five subsets using five-fold cross-validation. Four subsets are selected as the training set in each round of five-fold cross-validation, and the remaining subset is used as the validation set. In each round of five-fold cross-validation, the training set and its corresponding labels are substituted into the ridge regression model to obtain the trained model. Then, the validation set from the current round is substituted into the trained model, and the MSE value of the validation set is calculated based on the validation set and its corresponding labels. After the five-fold cross-validation is completed, the average of the five MSE values ​​obtained by five-fold cross-validation is calculated as the cross-validation average MSE.

[0029] S2, select the trained model with the smallest cross-validation mean MSE as the trained ridge regression model.

[0030] In the above technical solution, the loss function of the ridge regression model Represented as:

[0031] Where S is the total number of samples in the current training set, and yᵢ is the label of the i-th sample in the training set. Let the feature value of the j-th feature of the i-th sample in the training set be _____. for The weight coefficients corresponding to the features, where λ is the regularization parameter.

[0032] In the above technical solution, the rotary friction welding corresponding to the friction coefficient calculation model is either inertial friction welding or continuous driving friction welding, and the rotary friction welding in step 2 is either inertial friction welding or continuous driving friction welding.

[0033] In the above technical solutions, the interface temperature is directly measured based on thermocouples or infrared thermal imagers.

[0034] In the above technical solution, v is the real-time linear velocity of the middle position of the second tubular specimen in the wall thickness direction during the rotary friction welding process.

[0035] In the above technical solutions, ,in, In the formula, M0 is the system loss torque, and D is the outer diameter of the tubular specimen. The inner diameter is the diameter of the tubular specimen.

[0036] The above-mentioned friction coefficient calculation model is used in the simulation of rotary friction welding. The friction coefficient calculation model is embedded into the numerical simulation model of inertial friction welding for simulation.

[0037] The rotary friction welding in the friction coefficient calculation model can be the same as or different from the rotary friction welding in step 2. For example, the rotary friction welding in step 2 is continuous-drive friction welding. The friction coefficient calculation model is obtained from the modeling dataset obtained through continuous-drive friction welding. The friction coefficient calculation model can simulate inertial friction welding of two test pieces. The beneficial effects of this invention are as follows:

[0038] 1. The friction coefficient calculation model of the present invention decouples the calculation of friction coefficient through machine learning, constructs a friction coefficient prediction model that is adapted to the entire temperature range, and forms a "machine learning-enhanced friction constitutive model".

[0039] 2. By embedding the friction coefficient calculation model into the numerical simulation model of inertial friction welding, the interface friction coefficient can be dynamically and adaptively updated with temperature, contact pressure, etc., which can more accurately describe the frictional heat generation, high-temperature softening of materials and plastic flow behavior. This significantly improves the prediction accuracy of key physical quantities such as welding temperature field, axial shortening, and interface stress distribution, making the simulation results closer to the actual welding process and providing more reliable numerical basis for the optimization of inertial friction welding process parameters and mechanism analysis.

[0040] Based on this friction coefficient calculation model, inertial friction welding simulation was conducted. Since the machine learning-enhanced friction constitutive model can well describe the friction behavior of the interface during the welding process, the friction coefficient calculation model can significantly improve the simulation calculation efficiency while ensuring high-precision prediction capability. It also has good generalization ability for inertial friction welding with different welding parameters and geometric dimensions, and can provide technical support for inertial friction welding process optimization and industrial application. Attached Figure Description

[0041] Figure 1 Here are (a) a structural diagram and (b) a magnified view of two test pieces;

[0042] Figure 2 The simulation results and physical photos of the outer part of the boss are shown. (a) is a small tubular specimen and (b) is a large tubular specimen.

[0043] Figure 3 Let (a) be the relative error and (b) be the root mean square relative error. Detailed Implementation

[0044] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0045] Example 1

[0046] A friction coefficient calculation model, which is The friction coefficient calculation model calculates the real-time friction coefficient between two test pieces (in this embodiment, both test pieces are made of nickel-based high-temperature alloy, model GH4065A) during rotary friction welding. (Rotational friction welding is either inertial friction welding or continuous drive friction welding.) The coefficient of friction between two test pieces during rotary friction welding. This refers to the real-time pressure at the contact surface of the two test pieces during rotary friction welding. The relative linear velocity of the two test pieces during rotational friction welding is given in real time. The interface temperature is the real-time temperature of the contact surface of the two test pieces during rotary friction welding. The interface temperature is directly measured based on a thermocouple or an infrared thermal imager; e is the natural constant (e≈2.718281828459), and a, b, c, d and f are all constants.

[0047] The methods for calculating a, b, c, d, and f include:

[0048] Step 1: Prepare two tubular specimens: the first tubular specimen and the second tubular specimen (the two tubular specimens have the same cross-section). The two test pieces are the first test piece and the second test piece. The material of the first tubular specimen is the same as that of the first test piece, and the material of the second tubular specimen is the same as that of the second test piece.

[0049] Step 2: Fix the first tubular specimen to the fixture (the fixture is used to fix the first tubular specimen), and fix the second tubular specimen to the spindle, so that the two tubular specimens are coaxial and opposite but not in contact. Control the rotation of the second tubular specimen on the spindle. After the spindle reaches the specified speed n, control the spindle to move towards the first tubular specimen at a feed speed V (axial feed movement of the tubular specimen), so that the end faces of the two tubular specimens gradually contact and perform rotary friction welding (rotary friction welding is inertial friction welding or continuous drive friction welding. In step 2 of this embodiment, it is continuous drive friction welding). Maintain the rotary friction welding until the feed distance reaches 3.5 mm, and end the rotary friction welding. During the rotary friction welding process, v, P, T, and M of the two tubular specimens are obtained at time intervals of less than 0.5 s. The rotational speed of the second tubular specimen relative to the first tubular specimen during rotary friction welding is n (the first tubular specimen remains stationary, and the rotational speed n is the spindle speed).

[0050] P represents the real-time pressure at the contact surface during the rotary friction welding process of the two tubular specimens.

[0051] The relative linear velocity in real time during the rotational friction welding process of two tubular specimens;

[0052] The interface temperature between two tubular specimens during the rotary friction welding process is measured in real time using a thermocouple or an infrared thermal imager.

[0053] M represents the real-time spindle torque during the rotary friction welding process of the two tubular specimens;

[0054] v is the real-time linear velocity at the midpoint of the wall thickness direction of the second tubular specimen during the rotary friction welding process. v is calculated based on the rotational speed n and the average diameter D1 of the tubular specimen.

[0055] (n is in revolutions per minute) D is the outer diameter of the tubular specimen. The inner diameter of the tubular specimen;

[0056] Step 3: Calculate ln(P) based on P and T² based on T. Take ln(P), v, T, and T² from the same moment of rotational friction welding as a preprocessed sample. Arrange all preprocessed samples by row to obtain the feature matrix. Perform standardization processing on each element in the feature matrix according to the standardization formula (to eliminate the differences in dimensions and numerical magnitudes between different columns, ensuring that the contribution of each column of data to the subsequent ridge regression model training is of the same order of magnitude), to obtain the standardized matrix. The standardization formula is as follows:

[0057] In the formula, Let be the element in the i-th row and j-th column of the characteristic matrix. Let i be the element in the i-th row and j-th column of the normalized matrix. Let be the mean of the elements in the j-th column of the characteristic matrix. Let $\frac{j}{j}$ be the standard deviation of the elements in the $j$-th column of the characteristic matrix

[0058] Step 4: Each row in the normalization matrix represents a sample, and each column in the normalization matrix corresponds to a feature. Calculate the friction coefficient μ of each sample based on M and P obtained at the same moment during rotary friction welding.

[0059] ,in, This represents the real-time shear stress at the contact surface of two tubular specimens during rotary friction welding. ;

[0060] In the formula, M0 is the system loss torque. M0 is obtained by rotating the second tubular specimen without contacting the first tubular specimen, and the spindle torque at this time is the system loss torque.

[0061] Step 5: Calculate the logarithmic value of the friction coefficient based on the friction coefficient μ of each sample. As a label for this sample;

[0062] Step 6: Use the standardized matrix as the modeling dataset. Substitute the modeling dataset and all its corresponding labels into the ridge regression model for training, resulting in the trained ridge regression model. The linear regression equation of the trained ridge regression model is: ,in, The weight coefficients of the feature (j=1) are obtained after standardization with ln(P). The weight coefficients of the feature (j=2) are obtained after standardization of v. The weight coefficients of the feature (j=3) are obtained after T² standardization. The weight coefficients of the feature (j=4) are obtained after T standardization. The intercept of the linear regression equation is denoted as . The output of the trained ridge regression model ( (predicted value);

[0063] Calculate the mean based on the feature matrix. mean mean mean , , , and , where the mean In the characteristic matrix Mean of the column containing the element, mean In the characteristic matrix Mean of the column containing the element, mean In the characteristic matrix Mean of the column containing the element, mean In the characteristic matrix The mean of the column containing the element. In the characteristic matrix The standard deviation of the elements in the column In the characteristic matrix The standard deviation of the elements in the column In the characteristic matrix The standard deviation of the elements in the column In the characteristic matrix The standard deviation of the elements in the column;

[0064] Step 7, according to , , , , mean mean mean mean , , , and Calculate a, b, c, d, and f. The formulas for calculating a, b, c, d, and f are as follows:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] To calculate e Power of 1.

[0071] Example 2

[0072] Based on Example 1, D is 20 mm, d is 12 mm, the length of each tubular specimen is 30 mm, and the wall thickness is 4 mm.

[0073] The rotational speed n and feed rate V for obtaining v, P, T, and M during the rotary friction welding process of two tubular specimens are shown in Table 1 (i.e., 8 rotary friction welding operations were performed, and the rotational speed n and feed rate V were not exactly the same for the 8 rotary friction welding operations). In each rotary friction welding operation, v, P, T, and M of the two tubular specimens were obtained at time intervals of 0.03s.

[0074] Table 1

[0075]

[0076] Following steps 2 to 5 in Example 1, a total of 380 samples were obtained based on the 8 rotational friction welding operations in Table 1, with each sample corresponding to a label. 80% of these 380 samples were used as the modeling dataset in Example 1, and the remaining 20% ​​were used as the prediction set.

[0077] In step 6 of Example 1, the training method for substituting the modeling dataset and all the corresponding labels into the ridge regression model includes:

[0078] S1, in the logarithmic interval to Generate 100 logarithmically spaced values, each value serving as a separate unit. traverse 100 Each of them and perform the following operations:

[0079] Will the current As a regularization parameter in the loss function of the ridge regression model, the modeling dataset is divided into 5 subsets using a five-fold cross-validation method. Four subsets are selected as the training set (244 samples) each time, and the remaining subset is used as the validation set (60 samples). In each round of the five-fold cross-validation, the training set and its corresponding labels are substituted into the ridge regression model to obtain the trained model. Then, the validation set from the current round is substituted into the trained model, and the MSE value of the validation set is calculated based on the validation set and its corresponding labels. After the five-fold cross-validation is completed, the average of the five MSE values ​​obtained in this round is calculated as the cross-validation average MSE.

[0080] Loss function of ridge regression model Represented as:

[0081] Where S is the total number of samples in the current training set, and yᵢ is the label of the i-th sample in the training set (i.e., the logarithmic value of the friction coefficient ln( )), Let the feature value of the j-th feature of the i-th sample in the training set be _____. for The weight coefficients of the corresponding features, λ is the regularization parameter (in this embodiment, the ridge regression model is called with the Ridge and RidgeCV classes of the sklearn library. For details of the ridge regression model, see: Sun Donglei, Sun Yi, Liu Rui, et al. Prediction method of distributed photovoltaic absorption capacity of distribution network based on ridge regression [J]. Journal of Shandong University (Engineering Science), 2025, 55(03):149-157+164.).

[0082] S2. Among the 100 cross-validation average MSEs obtained in S1, the trained model with the smallest cross-validation average MSE is selected as the trained ridge regression model.

[0083] In this embodiment, the regularization parameter of the trained ridge regression model is 0.0643, that is, when λ=0.0643, the trained ridge regression model can achieve the best fitting performance.

[0084] The prediction set was substituted into the trained ridge regression model for prediction. The average MSE of the trained ridge regression model on the prediction set was 0.001365, and the coefficient of determination (R²) was [missing information]. 2 The value is 0.92.

[0085] The ridge regression model after training , , , , as follows:

[0086] , , =-0.973、 , -1.901, thus obtaining: a=10.966, b=0.781, c=0.706, d=945.367, f=706.240;

[0087] Therefore, the friction coefficient calculation model for the two test pieces is as follows:

[0088] .

[0089] Example 3

[0090] Based on Example 2, the structures of the two test pieces are as follows: Figure 1 As shown, both the second and first test specimens are tubular. A ring-shaped boss is formed on the bottom ring surface of the second test specimen, and a ring-shaped boss is formed on the top ring surface of the first test specimen. The cross-section of the bosses along the axial direction of the test specimens is square. The two test specimens are two small-sized tubular specimens, and the dimensions of the small-sized tubular specimens are shown in Table 2.

[0091] Inertial Friction Welding Simulation Group: The friction coefficient calculation model from Example 2 was embedded into the inertial friction welding numerical simulation model constructed using Abaqus software via the Fric subroutine. Simulation analysis was conducted on the second and first test pieces, and the simulation results for the outer part of the boss were obtained as follows: Figure 2 As shown in “Simulation” in (a), the axial shortening can be obtained as 4.47 mm through simulation.

[0092] Inertial friction welding experimental group: The second test piece is positioned directly above the first test piece. The first test piece is fixed to the fixture, and the second test piece is fixed to the spindle, making the two test pieces coaxial. At this time, the bosses of the second test piece and the first test piece are opposite each other. The second test piece is rotated on the spindle and rotates with the first test piece to perform inertial friction welding. The parameters of inertial friction welding are shown in Table 3 "Small-sized tubular specimens" (interface temperature is directly measured based on thermocouples or infrared thermal imagers), where the relative linear velocity is the linear velocity at the midpoint of the wall thickness direction of the test piece. A photograph of the outer part of the boss after inertial friction welding is shown below. Figure 2 As shown in “Actual” in (a), the axial shortening is 4.49 mm, as can be seen from the actual photograph.

[0093] Depend on Figure 2 As shown in (a), the axial shortening obtained after simulation of the small-sized tubular specimen is 4.47 mm, while the actual measured axial shortening is 4.49 mm, with an error of only 0.45%.

[0094] Example 4

[0095] The procedure is essentially the same as in Example 3, with the only difference being that the two test specimens are two large-sized tubular specimens, the dimensions of which are shown in Table 2 under "Large-sized Tubular Specimens". The parameters for inertial friction welding are shown in Table 3 under "Large-sized Tubular Specimens".

[0096] The simulation results of the inertial friction welding simulation group in this embodiment are as follows: Figure 2 As shown in "Simulation" in (b), the axial shortening is 2.88 mm, obtained through simulation. The actual photograph of the outer part of the boss obtained from the inertial friction welding experimental group in this embodiment is shown below. Figure 2 As shown in (b) "Actual", the axial shortening is 3.02 mm, and the error of the axial shortening is 4.64%.

[0097] Table 2

[0098]

[0099] Table 3

[0100]

[0101] As can be seen from Examples 3 and 4, the friction coefficient calculation model (MLF model) of the present invention, when applied to the simulation of inertial friction welding, has an error of less than 6% in predicting the axial shortening; this indicates that the friction coefficient calculation model of the present invention has good generalization ability, can adapt to changes in welding parameters and changes in the geometry of the welding specimen, and can achieve high-precision simulation of inertial friction welding.

[0102] Example 5

[0103] Small-sized tubular specimen group: basically the same as Example 3, the only difference is that the parameters of inertial friction welding are one of 1#~6# in Table 4.

[0104] Large-size tubular specimen group: basically the same as Example 4, the only difference is that the parameters of inertial friction welding are one of 1#~3# in Table 5.

[0105] Table 4

[0106]

[0107] Table 5

[0108]

[0109] The relative error (MRE) and root mean square relative error (RMSRE) of axial shortening for each parameter in both the large-size and small-size tubular specimen groups were calculated using parameters for friction welding with different inertia. The average value of the relative errors (MRE) of the nine axial shortening parameters for both groups was then obtained. Figure 3 The MLF in (a) is shown; the average value of the root mean square relative error (RMSRE) of the total nine axial shortenings for both the large-size tubular specimen group and the small-size tubular specimen group is obtained, as shown in Figure (a). Figure 3 The MLF is shown in (b).

[0110] Comparative Example 1

[0111] The method is essentially the same as in Example 5, except that the friction coefficient calculation model is replaced with a constant friction coefficient model (CF model), which sets the friction coefficient to 0.05. For details on the constant friction coefficient model, see: My Nu, HT, Le, TT, Minh, LP, & Loc, NH (2019). A study on rotary friction welding of titanium alloy (Ti6Al4V). Advances in Materials Science and Engineering, 2019(1), 4728213.

[0112] The average of the relative errors (MRE) of the nine axial shortening measurements in both the large-size tubular specimen group and the small-size tubular specimen group is as follows: Figure 3 As shown in CF in (a), the root mean square relative error (RMSRE) of the total nine axial shortenings in both the large-size tubular specimen group and the small-size tubular specimen group is as follows: Figure 3As shown in CF in (b).

[0113] Comparative Example 2

[0114] It is basically the same as Example 5, except that the friction coefficient calculation model is replaced with a temperature-based friction coefficient model (TF model):

[0115] .

[0116] For a temperature-based friction coefficient model, see: Khosrowshahi, JH, Sadeghi, MH, & Rasti, A. (2020). Numerical simulation of plastic deformation in direct-drive friction welding of AISI 4140 and ASTM A106 steel tubes. Archives of Civil and Mechanical Engineering, 20(4), 116.

[0117] The average of the relative errors (MRE) of the nine axial shortening measurements in both the large-size tubular specimen group and the small-size tubular specimen group is as follows: Figure 3 As shown in TF in (a), the root mean square relative error (RMSRE) of the total nine axial shortenings in both the large-size tubular specimen group and the small-size tubular specimen group is as follows: Figure 3 TF is shown in (b).

[0118] Comparative Example 3

[0119] The model is basically the same as in Example 5, except that the friction coefficient calculation model is replaced with a friction constitutive model (LSF model):

[0120]

[0121] The friction constitutive model was obtained by directly fitting the friction test data using the traditional least squares method.

[0122] The average of the relative errors (MRE) of the nine axial shortening measurements in both the large-size tubular specimen group and the small-size tubular specimen group is as follows: Figure 3 As shown in LSF in (a), the root mean square relative error (RMSRE) of the total nine axial shortenings in both the large-size tubular specimen group and the small-size tubular specimen group is as follows: Figure 3 The LSF in (b) is shown.

[0123] Depend on Figure 3As can be seen, the friction coefficient calculation model of this invention has a mean relative error (MRE) of only 5.29% and a root mean square relative error (RMSRE) of 5.91%, both lower than the constant friction coefficient model, the temperature-based friction coefficient model, and the friction constitutive model. When applied to simulation, the friction coefficient calculation model (MLF) of this invention exhibits the highest simulation prediction accuracy and the best stability, demonstrating excellent simulation capabilities for different welding conditions and providing guidance for selecting actual welding process windows.

[0124] The present invention has been described above by way of example. It should be noted that any simple modifications, alterations or other equivalent substitutions that can be made by those skilled in the art without creative effort without departing from the core of the present invention fall within the protection scope of the present invention.

Claims

1. A friction coefficient calculation model, characterized in that, It is This friction coefficient calculation model calculates the real-time friction coefficient between two test pieces during rotary friction welding. , This represents the real-time pressure at the contact surface of the two test pieces during rotary friction welding. The real-time relative linear velocity of the two test pieces during rotary friction welding. The real-time interface temperature of the contact surfaces of the two test pieces during rotary friction welding; e is the natural constant. a , b , c , d and f All are constants; calculate a , b , c , d and f The methods include: Step 1: Prepare two tubular specimens: the first tubular specimen and the second tubular specimen. The two specimens to be tested are the first specimen to be tested and the second specimen to be tested. The material of the first tubular specimen is the same as that of the first specimen to be tested, and the material of the second tubular specimen is the same as that of the second specimen to be tested. Step 2: Perform rotational friction welding on two tubular specimens coaxially facing each other. During the rotational friction welding process, obtain images of the two tubular specimens at time intervals of less than 0.5 seconds. v P, T and M ; P The pressure at the contact surface during the rotational friction welding process of two tubular specimens is measured in real time. v The relative linear velocity in real time during the rotational friction welding process of two tubular specimens; T The real-time interface temperature between two tubular specimens during the rotary friction welding process; M The real-time spindle torque during the rotary friction welding process of two tubular specimens; Step 3, combine ln(P) from the same moment of rotary friction welding. v、 T and T² are used as preprocessed samples. All preprocessed samples are arranged row-wise to obtain the feature matrix. Each element in the feature matrix is ​​then standardized according to the standardization formula to obtain the standardized matrix. The standardization formula is as follows: In the formula, Let be the element in the i-th row and j-th column of the characteristic matrix. Let i be the element in the i-th row and j-th column of the normalized matrix. Let be the mean of the elements in the j-th column of the characteristic matrix. Let $\frac{j}{j}$ be the standard deviation of the elements in the $j$-th column of the characteristic matrix Step 4: Each row in the normalization matrix represents a sample, and each column corresponds to a feature. This is based on the data obtained at the same moment during the rotational friction welding process for each sample. M and P Calculate the friction coefficient of this sample. μ ; Step 5, based on the friction coefficient of each sample μ Calculate the logarithmic value of the friction coefficient As a label for this sample; Step 6: Use the standardized matrix as the modeling dataset. Substitute the modeling dataset and all its corresponding labels into the ridge regression model for training, resulting in the trained ridge regression model. The linear regression equation of the trained ridge regression model is: ,in, The weight coefficients of the features are obtained after standardization with ln(P). for v The standardization process yields the feature weight coefficients. The weight coefficients of the features are obtained after T² standardization. The weight coefficients of the features are obtained after T is standardized. The intercept of the linear regression equation is denoted as . The output of the trained ridge regression model; Step 7, according to mean mean mean mean , , , and calculate a , b , c , d and f, a , b , c , d and f The calculation formula is as follows: ； ； ； ； 。 2. The friction coefficient calculation model according to claim 1, characterized in that, Training methods that substitute the modeling dataset and all its corresponding labels into the ridge regression model include: S1, in the logarithmic interval to Generate multiple logarithmically spaced values, each value serving as a separate unit. traverse each And perform the following operations: Will the current As a regularization parameter in the loss function of the ridge regression model, the modeling dataset is divided into five subsets using five-fold cross-validation. Four subsets are selected as the training set in each round of five-fold cross-validation, and the remaining subset is used as the validation set. In each round of five-fold cross-validation, the training set and its corresponding labels are substituted into the ridge regression model to obtain the trained model. Then, the validation set from the current round is substituted into the trained model, and the MSE value of the validation set is calculated based on the validation set and its corresponding labels. After the five-fold cross-validation is completed, the average of the five MSE values ​​obtained by five-fold cross-validation is calculated as the cross-validation average MSE. S2, select the trained model with the smallest cross-validation mean MSE as the trained ridge regression model.

3. The friction coefficient calculation model according to claim 2, characterized in that, Loss function of ridge regression model Represented as: ， Where S is the total number of samples in the current training set. y ᵢ represents the label of the i-th sample in the training set. Let the feature value of the j-th feature of the i-th sample in the training set be _____. for The weight coefficients corresponding to the features, where λ is the regularization parameter.

4. The friction coefficient calculation model according to claim 1, characterized in that, The corresponding rotary friction welding in the friction coefficient calculation model is either inertial friction welding or continuous driving friction welding. In step 2, the rotary friction welding is either inertial friction welding or continuous driving friction welding.

5. The friction coefficient calculation model according to claim 1, characterized in that, The interface temperature is measured directly using a thermocouple or an infrared thermal imager.

6. The friction coefficient calculation model according to claim 1, characterized in that, v The linear velocity at the midpoint of the second tubular specimen in the wall thickness direction during the rotary friction welding process.

7. The friction coefficient calculation model according to claim 1, characterized in that, ,in, In the formula, M0 is the system loss torque, D is the outer diameter of the tubular specimen, and d is the inner diameter of the tubular specimen.

8. The application of the friction coefficient calculation model as described in any one of claims 1 to 7 in the simulation of rotary friction welding, characterized in that, The friction coefficient calculation model was embedded into the numerical simulation model of inertial friction welding for simulation.

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