Mechanism-data fusion method for predicting machining deformation of thin-walled blade

Abstract

The patent application is a mechanism-guided data-driven method for thin-walled blade machining deformation prediction, mainly including the following steps: 1. Establishing a milling force model based on the spindle power of the machine tool; 2. Establishing a thin-walled blade machining deformation mechanism model; 3. Data set construction of the data-driven model of thin-walled blade machining deformation; 4. Data enhancement based on the Monte Carlo simulation method; 5. Mechanism-guided data-driven thin-walled blade machining deformation prediction.

Description

Technical Field

[0001] This invention belongs to the field of precision machining and manufacturing technology for complex thin-walled parts, specifically relating to a data-driven method for predicting deformation during the machining of thin-walled blades. Background Technology

[0002] Thin-walled blades are crucial components in high-end equipment such as aero-engines and nuclear power turbines, and their machining quality directly impacts equipment performance. Thin-walled blades inherently possess low rigidity, making them prone to elastic deformation during milling, leading to machining errors. Therefore, predicting machining deformation is necessary before compensation. Traditional prediction methods, such as mechanistic model-based methods for predicting machining deformation in thin-walled parts, suffer from approximation errors due to the coupling of multiple factors during milling and the inconsistency between theoretical and actual coordinate systems, affecting the accuracy of deformation prediction. Furthermore, data-driven model prediction methods suffer from convergence issues. Therefore, leveraging the learning capabilities of data-driven models and the theoretical support of mechanistic models, a mechanistic-data fusion method for predicting machining deformation in thin-walled blades is adopted to improve the accuracy and efficiency of deformation prediction.

[0003] The paper "Prediction of Elastic Deformation and Optimization of Process Parameters in Milling Aero-engine Blades" proposes a mechanism-guided data-driven method for predicting machining deformation. This method establishes a blade milling mechanism model based on the Deform and ABAQUS platforms, collects blade elastic deformation data, and combines genetic algorithms and BP neural networks to predict the elastic deformation, thus improving the problem of out-of-tolerance machining accuracy in the semi-finish milling process of aero-engine blades. However, the accuracy of the aforementioned mechanism model based on finite element method is limited by process parameter settings and computer performance, and insufficient data collection affects the training accuracy of its data-driven model, resulting in limitations in the efficiency and accuracy of deformation prediction for thin-walled parts. Summary of the Invention

[0004] This invention addresses the limitations of existing mechanism-guided data-driven deformation prediction methods for thin-walled blade machining. It improves the efficiency and accuracy of deformation prediction by modeling milling forces, the deformation mechanism of blade milling, and mechanism-guided data-driven modeling during thin-walled blade machining, thus providing theoretical guidance for deformation control in the machining process. The specific steps are as follows:

[0005] Step 1: Establish a milling force model based on machine tool spindle power. Calibrate the spindle power model based on milling force through experiments and solve for the inverse function. Obtain a milling force model based on spindle power.

[0006] Step 2: Establish a deformation mechanism model for thin-walled blades. Based on the finite element method, the stiffness and elastic deformation distribution of the thin-walled blades are calculated. A mid-arc surface model and measurement point normals are established using the UG secondary development program. The stiffness and elastic deformation distribution of the blade model are obtained. The residual stress state during thin-plate milling is analyzed, and a blade mechanism model for elastic deformation and machining residual stress deformation is established.

[0007] Step 3: Establish a data-driven model dataset for the machining deformation of thin-walled blades. The input dataset is used to solve for stiffness values ​​and normal vectors at selected sample points on the blade. The output dataset is obtained by calculating the minimum distance from the measured data to the blade back surface using a UG secondary development program, thus yielding the machining deformation at the measurement points.

[0008] Step 4: Perform data augmentation based on Monte Carlo simulation method, divide the processing deformation data, train the model using simulated data, and test the model using measured data. This division ensures that there is enough data for data-driven model training, and also allows observation of the performance of the trained model on real datasets.

[0009] Step 5: Establish a prediction model for the machining deformation of thin-walled blades using the Extreme Learning Machine. Optimize the parameters of the prediction model using the Sparrow Search algorithm. Combine this with the deformation mechanism model of thin-walled blades to predict the machining deformation of thin-walled blades, so that the predicted machining deformation of thin-walled blades has high accuracy and efficiency.

[0010] This invention addresses the problems of low efficiency, low accuracy, and limitations in predicting the deformation of thin-walled blades for aero-engines. It proposes a mechanism-guided, data-driven method for predicting the machining deformation of thin-walled blades, which offers the following advantages:

[0011] 1. In this prediction method, the stiffness calculation and blade elastic deformation distribution calculation of the finite element method are used to establish the mid-arc surface to obtain the blade stiffness and elastic deformation distribution, which improves the calculation efficiency.

[0012] 2. In this prediction method, data augmentation of the output samples is performed based on the Monte Carlo method, which realizes the establishment of a data-driven model based on small samples and reduces the workload of data collection in actual production.

[0013] 3. This prediction method combines the advantages of data-driven model learning capabilities and mechanistic model theoretical support, giving the prediction model a comprehensive advantage in terms of accuracy and efficiency. Its RMSE is reduced by 30.5% compared to the original model, and the model training speed is fast, making it suitable for engineering applications. Attached Figure Description

[0014] Figure 1 This is a diagram of the milling force model for the present invention.

[0015] Figure 2This is a projection relationship diagram of the milling force in this invention patent.

[0016] Figure 3 This is a mesh generation diagram of the arc surface model of the blade in this invention patent.

[0017] Figure 4 This is a diagram illustrating the equivalent bending moment effect of residual stress during processing, as per the patent of this invention.

[0018] Figure 5 This is a schematic diagram of the elastic deformation and residual stress deformation of the thin-walled blade in this invention patent.

[0019] Figure 6 The probability density function and distribution of the processing deformation simulation data of this invention patent

[0020] Figure 7 Loss using different activation function models for this invention patent

[0021] Figure 8 This is a flowchart of the SSA optimization ELM parameter flowchart for this invention patent.

[0022] Figure 9 This is a flowchart illustrating the overall process of predicting thin-walled blade deformation using a mechanism-guided data-driven model, as described in this invention patent. Detailed Implementation

[0023] The following describes the specific implementation of this invention using nuclear power turbine blades as the research object. Step 1: Establish a milling force model based on machine tool spindle power.

[0024] When modeling the milling power of a machine tool, a milling force model is first established. Since the cutting tool used for machining thin-walled blades is a ring cutter, the milling force model is referenced. Figure 1 .

[0025] First, based on the rotational motion of the machine tool spindle, the cutting edge is discretized into infinitesimal elements. The rotational power consumed by each infinitesimal element in the radial, axial, and tangential directions is as follows:

[0026]

[0027] Where: dP R,r dP R,a dP R,t The differential milling power of the cutting edge element in the radial, axial, and tangential directions; dF t,i,s Let be the tangential component of the cutting force in the tool coordinate system; v is the instantaneous milling speed of the cutting edge element, in m / min. Based on the above analysis, the power of the cutting edge of the tool element rotating to remove material is:

[0028] dP R =dP R,t =v c dF t,i,s(2)

[0029] Based on the feed motion of the feed servo system, the feed cutting power consumed by each cutting edge micro-element in the radial, axial, and tangential directions is:

[0030]

[0031] Where: v f For feed rate; Let be the instantaneous immersion angle of the milling cutting edge element. Based on the above analysis, the power of material removal by the cutting edge of the tool element is:

[0032]

[0033] Based on the above modeling and analysis of the power components consumed by the rotational motion and feed motion of the micro-element cutting edge, it can be seen that the two constitute the total power consumed by the micro-element cutting edge in the cutting process:

[0034]

[0035] By transforming coordinates, the instantaneous cutting force of the infinitesimal cutting edge can be converted to the machine tool coordinate system. Therefore, the instantaneous cutting components of the infinitesimal element in the x, y, and z directions can be obtained as follows:

[0036]

[0037] The above derivation and analysis yields the instantaneous cutting power model for the infinitesimal cutting edge as follows:

[0038]

[0039] Reference Figure 2 The projection relationship of milling force is calculated by integrating the cutting tooth portion along the axial depth of cut. Given the extremely short tool rotation cycle in actual cutting, average power is more practical than instantaneous power. The average cutting power of one tool rotation cycle can be expressed as:

[0040]

[0041] Through milling experiments, the obtained milling force and power data were linearly fitted to obtain the milling power P. Cut Regarding the cutting force F x F y F z The prediction model is:

[0042]

[0043] Step 2: Establish a model of the deformation mechanism during thin-walled blade processing.

[0044] First, the stiffness of the blade model is calculated using the finite element method. Unit forces are applied to each discrete point in the x, y, and z directions to obtain the unit elastic deformation distribution. Then, the unit normal elastic deformation distribution of the blade is obtained by multiplying this force by the normal vector of the discrete point. Finally, the curved surfaces in the blade model are extracted using secondary development with UG software. The steps are as follows:

[0045] (a) Open the UG software and execute the .dll program to read the air profile section line data points;

[0046] (b) Fit the data points to obtain the leaf section line, and extract the middle arc line of the section line;

[0047] (c) Fit all the mid-arc lines to obtain the mid-arc surface of the blade.

[0048] Reference Figure 3 The mid-arc surface model of the blade is divided into four-node curved shell elements. Boundary conditions are set according to the solid element model. The stiffness of the mid-arc surface model is extracted using ABAQUS secondary development to realize the assembly of the overall stiffness matrix.

[0049] Next, the blade back profile is selected to calculate the overall elastic deformation distribution of the thin-walled blade. The stiffness matrices in the X, Y, and Z directions are solved respectively. The compliance matrix is ​​obtained by inversion. Then, unit forces in the X, Y, and Z directions are applied to the compliance matrices in the X, Y, and Z directions respectively. The normal elastic deformation distribution is obtained by multiplying them with the normal vector.

[0050]

[0051] in: F represents the compliance matrix of the model in the X, Y, and Z directions; x,i F y,j F z,k This represents the normal projection of the milling force in the X, Y, and Z directions of the model, where i, j, and k are the normal vectors of the model surface. Here, the surface selected is the blade back profile. The normal vectors of the nodes on the blade back profile are calculated using the UG software's internal API function library, following these steps:

[0052] (a) Open the UG software, execute the .dll program, and read the spatial X, Y, and Z coordinates of the nodes;

[0053] (b) Select the surface where the node is located, which is the back surface of the leaf in this case, and calculate the normal vector of the node on the surface;

[0054] (c) Write the extracted node normal vectors to an external file for output.

[0055] Finally, the finite element method was used to analyze the residual stress and deformation during blade machining. Figure 4 Considering the small deformation of the thin plate, the curvature and surface deflection of the thin plate in the X and Y directions of the coordinate system after deformation can be obtained as follows:

[0056]

[0057]

[0058] Substituting equation (11) into equation (12), we get:

[0059]

[0060] To give the model a certain degree of fundamentality and generalizability, equation (13) is simplified to a theoretical model of residual stress deformation during thin-walled blade processing:

[0061] w(x,y)=αx 2 +βy 2 (14)

[0062] Where α and β are model coefficients.

[0063] according to Figure 5 It can be analyzed that the deformation at a certain moment during the milling process of thin-walled blades is affected by the superposition of elastic deformation and deformation due to machining residual stress. A deformation mechanism model for thin-walled blades can be established as follows:

[0064]

[0065] Where: α1~α3, b are model coefficients; ε is the error caused by uncertainties in the processing.

[0066] Step 3: Construction of the data-driven model dataset for thin-walled blade processing deformation.

[0067] Input dataset construction, let equation (15) h(y) = y 2 h(z)=z 2 Equation (15) can be rewritten as:

[0068] f(x,y,z)=α1g(x,y)+α2h(z)+α3h(y)+ε (16)

[0069] Mechanism-guided data-driven model input is X i = (g(x,y),h(y),h(z)), 266 sample points are selected on the blade back surface. The stiffness values ​​in the X and Y directions of the sample points are calculated using the stiffness calculation method in step 2, and the normal vector in the X and Y directions of the sample points are calculated using the normal vector solution method to construct the input dataset.

[0070] The raw data is measured from the production site using a coordinate measuring machine (CMM). The machining deformation values ​​at the measured points are calculated, and an output dataset is constructed. The steps are as follows:

[0071] (a) Open the UG software, execute the .dll program, and import the coordinate measuring data points of the sample points;

[0072] (b) Select the surface where the sample point is located, i.e. the back surface of the thin-walled blade, and calculate the minimum distance from the measurement data point to the back surface and the coordinates of the minimum distance point;

[0073] (c) Subtract the radius of the coordinate measuring probe from the calculated minimum distance to obtain the machining deformation of the sample point;

[0074] (d) Output the calculated machining deformation of the measurement point and the coordinates of the minimum distance point to an external file.

[0075] Step 4: Perform data augmentation based on Monte Carlo simulation methods.

[0076] Because the output of the data-driven model established in step 3 is limited by actual production conditions and the amount of data is too small, it is necessary to expand the sample size using statistical simulation methods, namely Monte Carlo simulation. The steps are as follows:

[0077] (a) Solve for the probability density distribution function of the actual collected processing deformation data;

[0078] (b) Using probability distribution sampling, the values ​​of random variables that conform to the probability density distribution of the processing deformation data are obtained by calculation;

[0079] (c) The calculated random variable values ​​are the output processing deformation data simulation quantities.

[0080] When generating new data, the number of data points generated will be close to the expected value. For the data requiring augmentation, the interval size for generating data is selected as 0.001, and the expected number of data points generated is 266. A total of 20 sets of data are generated, each with 266 data points. Figure 6 It can be seen that the probability density function fitting result of the generated data is highly similar to the estimated probability density of the original data. The model is trained using simulated data and tested using measured data, which reduces the workload of actual data collection, improves efficiency and saves resources.

[0081] Step 5: Mechanism-guided data-driven prediction of deformation during thin-walled blade processing.

[0082] First, a machining deformation prediction model is designed based on Extreme Learning Machine (ELM). The ELM consists of one hidden layer, an input layer, two hidden layers, and an output layer. During training, only the connection weights between the hidden and output layers need to be calculated. The mean absolute error (MAE) loss function is chosen during ELM training.

[0083]

[0084] Where: yi is the true value to be predicted; is the predicted value of the integrative neural network; n is the number of values ​​to be predicted. The activation function of the ELM is determined by comparing the prediction results of the Sigmoid, Sine, and Hardlim function models, and a double-loop optimization algorithm is used to determine the number of neurons in the hidden layer. The algorithm steps are as follows:

[0085] (a) Input samples, set the number of hidden layer neurons from 1 to 150 for iterative training, and calculate the MAE of the test set.

[0086] (b) Calculate the MAE of the test set 10 times in a loop;

[0087] (c) Select the number of neurons with the smallest average value of the test set MAE as the optimal number of neurons.

[0088] The most suitable activation function can be determined by the mean absolute error of the test set in the algorithm. Figure 6 The optimization range was determined to be between 1 and 150. The Sigmoid activation function with the minimum loss on the test set was selected, and the optimal number of hidden layer nodes in the network was determined to be 145.

[0089] Secondly, the parameters of the trained processing deformation prediction modality are optimized based on the Sparrow Search Algorithm (SSA). SSA is combined with ELM, using SSA to optimize the mesh parameters and find the optimal combination of network parameters. The optimization process is described in [reference needed]. Figure 8 .

[0090] Finally, the dataset from step 3 and the enhanced simulation dataset from step 4 were fed into the mechanism-guided sparrow-optimized extreme learning machine model for predicting deformation in thin-walled blade processing. The sparrow-optimized model reduced the RMSE by 30.50% and the training time was 61 seconds. Figure 8 This is a flowchart illustrating the overall process for predicting the deformation during the machining of thin-walled blades according to the present invention.

Claims

1. A mechanism-data fusion-based method for predicting deformation during thin-walled blade processing, comprising the following steps: Step 1: Establish a milling force model based on machine tool spindle power; Step 2: Establish a model for the deformation mechanism of thin-walled blades during processing; the steps for establishing the model for the deformation mechanism of thin-walled blades during processing are as follows: The stiffness of the blade model is calculated based on the finite element method. Unit forces in the x, y, and z directions are applied to each discrete point to obtain the unit elastic deformation distribution. Then, the unit normal elastic deformation distribution of the blade is obtained by multiplying it with the normal vector of the discrete point. The arc surface in the blade model is extracted by secondary development using UG software. The mid-arc surface model of the blade is divided into four-node curved shell elements. Boundary conditions are set according to the solid element model. The stiffness of the mid-arc surface model is extracted using ABAQUS secondary development to realize the assembly of the overall stiffness matrix. The overall elastic deformation distribution of the thin-walled blade is calculated by selecting the blade back profile. The stiffness matrices in the X, Y, and Z directions are solved separately. The compliance matrix is ​​obtained by inverting the matrices. Then, unit forces in the X, Y, and Z directions are applied to the compliance matrices respectively, and the normal elastic deformation distribution is obtained by multiplying them by the normal vector. In the formula, , , The model's compliance matrices in the X, Y, and Z directions; , , Let X be the normal projection of the milling force in the X, Y, and Z directions of the model, where... , , The normal vector for the model surface is used here; the surface selected here is the back of the leaf. The normal vector of the node on the blade back surface is calculated by calling the internal API function library of UG software; The residual stress deformation of the blade during machining was analyzed using the finite element method. The curvature and surface deflection in the X and Y directions of the coordinate system after the thin plate deformation were obtained as follows: From the curvature formula and the deflection formula, we can obtain: Simplified theoretical model of residual stress and deformation during thin-walled blade processing: in, α and β are model coefficients; Based on the fact that the deformation at a certain moment during the milling of thin-walled blades is affected by the superposition of elastic deformation and deformation due to residual stress during machining, a deformation mechanism model for thin-walled blade machining is established as follows: in: , , These are the model coefficients; Errors caused by uncertainties in the processing; Step 3: Construction of the model dataset driven by the data of thin-walled blade processing deformation; Step 4: Perform data augmentation based on Monte Carlo simulation methods; Step 5: Mechanism-guided data-driven prediction of thin-walled blade machining deformation: Design a machining deformation prediction model based on extreme learning machine; optimize the parameters of the trained machining deformation prediction model based on sparrow search algorithm (SSA); use the dataset and the enhanced simulation dataset to feed the mechanism-guided sparrow optimization extreme learning machine thin-walled blade machining deformation prediction model to perform thin-walled blade machining deformation prediction.

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