A method for predicting residual stress on a grinding surface

Abstract

The present invention belongs to the technical field of grinding processing, and discloses a method for predicting grinding surface residual stress. By inferring the probability distribution of model parameters using experimental data, the generalization and interpretability of the physical model can be ensured in a data hybrid-driven manner. That is, the existing physical model and experimental data are combined in an organized way. On the one hand, some initial guiding information can be provided, which can be defined as prior knowledge; on the other hand, real grinding experiments provide additional information about the true residual stress of external cylindrical grinding, and this information can be propagated into the model parameters through the physical model. Therefore, the present invention can accurately obtain the corresponding relationship between the workpiece grinding process parameters and their surface residual stress under corresponding processing conditions using small sample data, realize the accurate prediction of grinding surface residual stress, and further improve the high mechanical and physical properties such as corrosion resistance, fatigue resistance and wear resistance of parts.

Description

Technical Field

[0001] The present invention belongs to the technical field of grinding processing, and particularly relates to a method for predicting grinding surface residual stress. Background Art

[0002] The grinding process is widely used in the applications of key parts such as crankshafts, camshafts, bearings and gears. The thermal process and mechanical process in grinding will cause the elastic-plastic deformation of the internal material of the parts, and then residual stress is generated. In order to control the residual stress of the ground parts and improve the high mechanical and physical properties such as corrosion resistance, fatigue resistance and wear resistance of the parts, it is necessary to predict the residual stress generated by the material under different grinding processes.

[0003] At present, there are few methods for predicting grinding surface residual stress in the prior art. The existing methods for predicting the residual stress on the grinding surface mainly include physical-based analytical methods, finite element methods and empirical model methods, which require a large amount of calibration and verification data. For example, the physical-based analytical method has the problem of inaccurate model parameters; the finite element method has the disadvantages of long calculation time, low prediction efficiency, and poor model interchangeability under different input parameter conditions; while the data-based empirical model method lacks generality and physical interpretability. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a method for predicting grinding surface residual stress, which combines a physical-based analytical method and a data-based machine learning method to achieve accurate prediction of grinding residual stress through physical processes such as complex geometry / kinematics and data driving.

[0005] The present invention is realized by the following technical solutions:

[0006] A method for predicting grinding surface residual stress, which is carried out according to the following steps:

[0007] (1) Conduct grinding tests on multiple workpieces; and measure the initial residual stress of the workpiece before each grinding test and the final residual stress of the workpiece after each grinding test;

[0008] (2) Form a database with the material parameters, grinding wheel parameters, process parameters of each grinding test and the final residual stress obtained in step (1), and divide the data in the database into a training set and a test set;

[0009] (3) Normalize the training set;

[0010] (4) Establish a neural network and set the initial conditions of the neural network;

[0011] (5) Train the neural network to obtain the predicted residual stress output by the neural network and calculate the deviation of the neural network;

[0012] (6) Convert the predicted residual stress output by the neural network into the strain of the workpiece in the plastic deformation stage through the J-C constitutive model;

[0013] (7) Obtain the deviation equation of the analytical residual stress based on the Merwin and Johnson boundary conditions and the Prandtl-Reuss incremental relationship;

[0014] (8) Express the deviation equation in the form of a partial differential equation through Hooke's law and the von Mises flow rule, and use the partial differential equation as the boundary constraint equation for physical analysis;

[0015] (9) Establish the loss function of the physical analysis combined with the neural network prediction model according to the neural network algorithm and the boundary constraint equation, and obtain the maximum deviation L of the physical analysis combined with the neural network prediction model max ;

[0016] (10) Set the allowable maximum error value according to the process requirements, compare the maximum deviation of the physical analysis combined with the neural network prediction model with the allowable maximum error value. If the maximum deviation is less than or equal to the allowable maximum error value, go to step (12); if the maximum deviation is greater than the allowable maximum error value, go to step (11);

[0017] (11) Update the connection weights and thresholds of the neural network, go to step (5), and repeat steps (5)-(10);

[0018] (12) Save the physical analysis combined with the neural network prediction model and output the predicted residual stress.

[0019] Further, the material parameters in step (2) include the elastic modulus E and Poisson's ratio v of the material; the grinding wheel parameters include the grinding wheel grain size M, the grinding wheel grain concentration V g and the grinding wheel hardness H; the process parameters include the grinding wheel dressing feed rate f d , the grinding wheel linear velocity v s , the workpiece linear velocity v w , the feed rate f r and the grinding depth a p .

[0020] Further, the normalized training set in step (3) is specifically as follows:

[0021]

[0022] Among them, is the average value of the data corresponding to each column in the parameter matrix, x is the original data, and x' is the normalized data; specifically, the parameter matrix in the training set is the material parameter [S]' = (E, v), the grinding wheel parameter [W]' = (M, V g , H), and the process parameter [T]' = (f d , v s , v w , f r , a p ).

[0023] Furthermore, in step (4), the normalized data obtained in step (3) in the training set is used as the input parameter of the neural network. According to the input parameter, the number of input layer neurons e is set, and the final residual stress is used as the output parameter. According to the output parameter, the number of output layer neurons g is set. The initial number of hidden layer neurons b is determined according to the following formula:

[0024]

[0025] where b is the initial number of hidden layer neurons of the neural network, e is the number of input layer neurons of the neural network, and g is the number of output layer neurons of the neural network.

[0026] Furthermore, in step (5), the gradient descent optimization method is used to train the neural network, and the activation function is selected as the adaptive activation function; the deviation E of the neural network is determined by the following formula:

[0027]

[0028] where l is the number of outputs of the neural network, m is the number of training examples, is the jth predicted residual stress of the kth training example, is the jth final residual stress of the kth training example;

[0029] Furthermore, in step (6), the relationship between strain and stress in the plastic deformation stage described by the J-C constitutive model is as follows:

[0030]

[0031] where ε p is the strain of the workpiece, is the equivalent strain rate of the workpiece, is the reference strain rate of the workpiece, T is the temperature, and A, B, n, C, m are plastic parameters that can be obtained by querying the J-C constitutive database; according to this formula, the difference between the predicted residual stress and the initial residual stress in different directions of the workpiece is used as the stress and substituted into to obtain the strain ε p of the workpiece in different directions;

[0032] Furthermore, in step (7), the boundary conditions described by Merwin and Johnson are as follows:

[0033]

[0034]

[0035] where x, y, z represent the coordinate axes, are the strains in the i, j directions, are the stresses in the i, j directions, i, j ∈ {x, y, z}, f 1，2，3，4 (z) represents a non-zero quantity related to the coordinate value z;

[0036] Furthermore, the stress and strain deviations are obtained through the Prandtl-Reuss incremental relationship:

[0037]

[0038]

[0039] In the formula, s i and e i are the stress components and strain components respectively, σ i and ∈ i are the principal stress and strain respectively.

[0040] Furthermore, in step (8), the boundary constraint equation is expressed as the following partial differential equation:

[0041]

[0042] where is the rate of irreversible energy dissipation, governed by Hooke's law, J2 is the second invariant of the stress deviation tensor in the von Mises flow rule, and G is the shear modulus.

[0043] Furthermore, in step (9), the loss function is constructed as follows:

[0044]

[0045] This formula is the loss function of the physical analysis combined with the neural algorithm prediction model, is the loss function of the initial conditions, is the loss function of the boundary conditions, is the loss function of the overall model, enabling the solution of the neural network to satisfy the boundary condition equation constraints, is the difference between the solution predicted by the neural network and the true value. λ ic 、λ bc 、λr , λ g is a preset coefficient representing the weight of each loss, generally between 0 and 1. Solving the maximum value gives the maximum deviation L max .

[0046] The beneficial effects of the present invention are as follows:

[0047] The present invention infers the probability distribution of model parameters using experimental data, enabling the generalization and interpretability of physical models to be guaranteed in a data hybrid-driven manner. That is, the existing physical models and experimental data are combined in an organized way. On the one hand, it can provide some initial guiding information, which can be defined as prior knowledge; on the other hand, real grinding experiments provide additional information about the true residual stress in external cylindrical grinding, and this information can be propagated into the model parameters through the physical model. Therefore, the present invention can accurately obtain the corresponding relationship between the workpiece grinding process parameters and its surface residual stress under corresponding processing conditions using small sample data, achieving accurate prediction of grinding surface residual stress, and further improving high mechanical and physical properties such as corrosion resistance, fatigue resistance, and wear resistance of parts. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a flowchart of a method for predicting grinding surface residual stress provided by the present invention;

[0049] Figure 2 is a prediction model diagram of a method for predicting grinding surface residual stress provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0050] The present invention will be further described in detail below through specific embodiments. The following embodiments can enable those skilled in the art to understand the present invention more comprehensively, but do not limit the present invention in any way.

[0051] As Figure 1 and Figure 2 shown, this embodiment provides a method for predicting grinding surface residual stress, which is carried out according to the following steps:

[0052] (1) Conduct grinding tests on multiple workpieces; and measure the initial residual stress of the workpiece before each grinding test and the final residual stress of the workpiece after each grinding test;

[0053] (2) Form a database with the material parameters, grinding wheel parameters, process parameters of each grinding test and the final residual stress obtained in step (1), and divide the data in the database into a training set and a test set.

[0054] Among them, the material parameters include the elastic modulus E and Poisson's ratio v of the material, which are determined according to the workpiece material used in the grinding test; the grinding wheel parameters include the grinding wheel grit size M, the grinding wheel abrasive concentration V g and the grinding wheel hardness H, which are determined according to the grinding wheel used in the grinding test; the process parameters include the dressing feed rate f of the grinding wheel d , the grinding wheel linear speed v s , the workpiece linear speed v w , the feed rate f r and the grinding depth a p , which are determined according to the process parameters used during the grinding test.

[0055] (3) Normalized training set.

[0056] As a preferred implementation, the normalized training set is specifically as follows:

[0057]

[0058] Among them, is the average value of the data corresponding to each column in the parameter matrix, x is the original data, and x' is the normalized data; specifically, the parameter matrix in the training set is the material parameter [S]' = (E, v), the grinding wheel parameter [W]' = (M, V g , H), and the process parameter [T]' = (f d , v s , v w , f r , a p ).

[0059] (4) Establish a neural network and set the initial conditions of the neural network.

[0060] As a preferred implementation, the neural network includes an input layer, a hidden layer, and an output layer. Randomly initialize all connection weights and thresholds in the neural network in the range (0, 1). Use the normalized data in the training set obtained in step (3) as the input parameters of the neural network. Set the number of neurons in the input layer e according to the input parameters, use the final residual stress as the output parameter, and set the number of neurons in the output layer g according to the output parameter. Determine the initial number of neurons b in the hidden layer according to the following formula:

[0061]

[0062] Among them, b is the initial number of neurons in the hidden layer of the neural network, e is the number of neurons in the input layer of the neural network, and g is the number of neurons in the output layer of the neural network.

[0063] (5) Train the neural network to obtain the predicted residual stress output by the neural network and calculate the deviation of the neural network.

[0064] As a preferred embodiment, the neural network is trained using the optimization method of gradient descent, and the activation function is selected as the adaptive activation function. The specific optimization method is mini-batch SGD (stochastic gradient descent). The deviation E of the neural network is determined by the following formula:

[0065]

[0066] where l is the number of outputs of the neural network, m is the number of training examples, is the j-th predicted residual stress of the k-th training example, is the j-th final residual stress of the k-th training example;

[0067] (6) Convert the predicted residual stress output by the neural network into the strain of the workpiece in the plastic deformation stage through the J-C constitutive model.

[0068] As a preferred embodiment, the relationship between the strain and stress in the plastic deformation stage described by the J-C constitutive model is as follows:

[0069]

[0070] where ε p is the strain of the workpiece, is the equivalent strain rate of the workpiece, is the reference strain rate of the workpiece, T is the temperature, and A, B, n, C, m are plastic parameters that can be obtained by querying the J-C constitutive database; according to this formula, the difference between the predicted residual stress and the initial residual stress in different directions of the workpiece is used as the stress and substituted into to obtain the strain ε p of the workpiece in different directions;

[0071] (7) Obtain the deviation equation of the analytical residual stress based on the Merwin and Johnson boundary conditions and the Prandtl-Reuss incremental relationship.

[0072] Furthermore, the boundary conditions described by Merwin and Johnson are as follows:

[0073]

[0074]

[0075] where x, y, z represent the coordinate axes, is the strain in the i, j directions, is the stress in the i, j directions, i, j ∈ {x, y, z}, and f 1，2，3，4 (z) represents a non-zero quantity related to the coordinate value z;

[0076] Furthermore, the stress and strain deviations are obtained through the Prandtl-Reuss incremental relationship:

[0077]

[0078]

[0079] where s i and e i are the stress component and strain component respectively, σ i and ∈ i are the principal stress and strain respectively.

[0080] (8) The deviation equation is expressed in the form of a partial differential equation through Hooke's law and the von Mises flow rule, and the partial differential equation is used as the boundary constraint equation for physical analysis.

[0081] Furthermore, the boundary constraint equation is expressed as the following partial differential equation:

[0082]

[0083] where is the rate of irreversible energy dissipation, governed by Hooke's law, J2 is the second invariant of the stress deviation tensor in the von Mises flow rule, and G is the shear modulus.

[0084] (9) According to the neural network algorithm and the boundary constraint equation, the loss function of the physical analysis combined with the neural network prediction model is established, and the maximum deviation L max ;

[0085] Furthermore, the loss function is constructed as follows:

[0086]

[0087] This formula is the loss function of the physical analysis combined with the neural algorithm prediction model, is the loss function of the initial conditions, is the loss function of the boundary conditions, is the loss function of the overall model, enabling the solution of the neural network to satisfy the boundary condition equation constraints, is the difference between the solution predicted by the neural network and the true value. λ ic , λ bc , n r , λ g are preset coefficients, representing the weights of each loss, generally between 0 and 1. Solving for the maximum value gives the maximum deviation L max .

[0088] (10) Set the maximum allowable error value according to the process requirements, compare the maximum deviation of the physical analysis combined with the neural network prediction model with the maximum allowable error value. If the maximum deviation is less than or equal to the maximum allowable error value, go to step (12); if the maximum deviation is greater than the maximum allowable error value, go to step (11).

[0089] (11) Update the connection weights and thresholds of the neural network, go to step (5), and repeat steps (5)-(10).

[0090] (12) Save the physical analysis combined with the neural network prediction model and output the predicted residual stress.

[0091] For example:

[0092] Conduct grinding tests on 25 workpieces: Use 45# steel workpieces, E = 210 GPa, v = 0.33; Use a grinding wheel with a grit size of 100 mesh, a grit concentration of 53%, and a hardness of L; Adopt plunge external cylindrical grinding, a p is 40 μm, and other process parameters are as follows in the table:

[0093]

[0094]

[0095] Adopt the grinding surface residual stress prediction method of the present invention for plunge external cylindrical grinding. The grinding wheel and the workpiece are the same as those in the above test, and the process parameters are f d is 60 mm / min, f r is 0.06 mm / min, v s is 27 m / s, v w is 1.75 m / s, a p is 40 μm for prediction of the grinding test. The final residual stress of the workpiece measured is -303 MPa, and the predicted residual stress output is -319 MPa.

[0096] Although the preferred embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many specific transformations in form without departing from the spirit of the invention and the scope protected by the claims. All of these fall within the protection scope of the present invention.

Claims

1. A method for predicting the residual stress on a grinding surface, characterized in that, The method is carried out according to the following steps: (1) Conduct grinding tests on multiple workpieces; and measure the initial residual stress of the workpiece before each grinding test, and measure the final residual stress of the workpiece after each grinding test; (2) Form a database with the material parameters, grinding wheel parameters, process parameters of each grinding test and the final residual stress obtained in step (1), and divide the data in the database into a training set and a test set; (3) Normalize the training set; (4) Establish a neural network and set the initial conditions of the neural network; (5) Train the neural network to obtain the predicted residual stress output by the neural network, and calculate the deviation of the neural network; (6) Convert the predicted residual stress output by the neural network into the strain of the workpiece in the plastic deformation stage through the J-C constitutive model; (7) Obtain the deviation equation of the analytical residual stress based on the Merwin and Johnson boundary conditions and the Prandtl-Reuss incremental relationship; (8) Express the deviation equation in the form of a partial differential equation through Hooke's law and the von Mises flow rule, and use the partial differential equation as the boundary constraint equation for physical analysis; (9) Establish the loss function of the physical analysis combined with the neural network prediction model according to the neural network algorithm and the boundary constraint equation, and obtain the maximum deviation L of the physical analysis combined with the neural network prediction model max ; (10) Set the allowable maximum error value according to the process requirements, compare the maximum deviation of the physical analysis combined with the neural network prediction model with the allowable maximum error value. If the maximum deviation is less than or equal to the allowable maximum error value, go to step (12); if the maximum deviation is greater than the allowable maximum error value, go to step (11); (11) Update the connection weights and thresholds of the neural network, go to step (5), and repeat steps (5)-(10); (12) Save the physical analysis combined with the neural network prediction model and output the predicted residual stress.

2. The method for predicting residual stress on a grinding surface according to claim 1, wherein The material parameters in step (2) include the elastic modulus E and Poisson's ratio v of the material; the grinding wheel parameters include the grinding wheel grit size M, the grinding wheel abrasive concentration V g and the grinding wheel hardness H; the process parameters include the grinding wheel dressing feed rate f d , the grinding wheel linear velocity v s , the workpiece linear velocity v w , the feed rate f r and the grinding depth a p .

3. A method for predicting the residual stress on a grinding surface according to claim 1, characterized in that The specific normalization of the training set in step (3) is as follows: Among them, is the average value of the data corresponding to each column in the parameter matrix, x is the original data, and x′ is the normalized data; specifically, the parameter matrix in the training set is the material parameter [S]′ = (E, v), the grinding wheel parameter [W]′ = (M, V g , H), and the process parameter [T]′ = (f d , v s , v w , f r , a p ).

4. A method for predicting residual stress on a grinding surface according to claim 1, characterized in that, In step (4), the normalized data in the training set obtained in step (3) is used as the input parameter of the neural network. According to the input parameter, the number of neurons e in the input layer is set. The final residual stress is used as the output parameter, and the number of neurons g in the output layer is set according to the output parameter. The initial number of neurons b in the hidden layer is determined according to the following formula: where b is the initial number of neurons in the hidden layer of the neural network, e is the number of neurons in the input layer of the neural network, and g is the number of neurons in the output layer of the neural network.

5. A method for predicting residual stress on a grinding surface according to claim 1, characterized in that, In step (5), the neural network is trained using the optimization method of gradient descent, and the activation function is selected as the adaptive activation function; the deviation E of the neural network is determined by the following formula: where 1 is the number of outputs of the neural network, m is the number of training examples, is the j-th predicted residual stress of the k-th training example, is the j-th final residual stress of the k-th training example.

6. A method for predicting the residual stress on a grinding surface according to claim 1, characterized in that, In step (6), the relationship between strain and stress in the plastic deformation stage described by the J-C constitutive model is as follows: where ε p is the strain of the workpiece, is the equivalent strain rate of the workpiece, is the reference strain rate of the workpiece, T is the temperature, and A, B, n, C, m are plastic parameters that can be obtained by querying from the J-C constitutive database; according to this formula, the difference between the predicted residual stress and the initial residual stress in different directions of the workpiece is used as the stress and substituted into to obtain the strain ε of the workpiece in different directions p。 7. A method for predicting the residual stress on a grinding surface according to claim 1, characterized in that In step (7), the boundary conditions described by Merwin and Johnson are as follows: where x, y, and z represent the coordinate axes, are the strains in the i and j directions, are the stresses in the i and j directions, where i, j ∈ {x, y, z}, and f 1，2，3，4 (z) represents a non-zero quantity related to the coordinate value z; Furthermore, the stress and strain deviations are obtained through the Prandtl-Reuss incremental relationship: S i = σ i -s e i = ∈ i -e where s i and e i are stress component and strain component respectively, and σ i and ∈ i are principal stress and strain respectively.

8. A method for predicting grinding surface residual stress according to claim 1, characterized in that In step (8), the boundary constraint equation is expressed as the following partial differential equation: where is the rate of irreversible energy dissipation, governed by Hooke's law, J2 is the second invariant of the stress deviator tensor in the von Mises flow rule, and G is the shear modulus.

9. A method for predicting residual stress on a grinding surface according to claim 1, characterized in that In step (9), the loss function is constructed as follows: This formula is the loss function of the physical analysis combined with the neural algorithm prediction model, which is the loss function of the initial conditions, which is the loss function of the boundary conditions, which is the loss function of the overall model, enabling the solution of the neural network to satisfy the boundary condition equation constraints, which is the difference between the solution predicted by the neural network and the true value, λ ic 、λ bc 、λ r 、λ g are preset coefficients, representing the weights of each loss, between 0 and 1. Solving for its maximum value gives the maximum deviation L max .

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