Calculation method of three-dimensional residual stress distribution in thin-walled structure milling considering elastic deformation

Abstract

The present invention discloses a method for calculating the three-dimensional distribution of residual stress in milling of a thin-walled structure considering elastic deformation, comprising the following contents: step 1, constructing a mechanical model of multi-axis milling of a ball-end milling cutter; step 2, obtaining the actual milling depth of different tool positions of a titanium alloy thin-walled structure on a tool path line; step 3, constructing a gradient distribution prediction model for residual stress of a multi-axis milling titanium alloy, and predicting the prediction model coefficients of any set of milling process parameters through an RBF neural network; wherein the milling depth is the actual milling depth obtained in step 2; step 4, predicting the prediction model coefficients of different tool positions of the titanium alloy thin-walled structure one by one; and obtaining a three-dimensional distribution model of residual stress in milling of a thin-walled structure considering elastic deformation through a multivariate linear regression method. This method solves the problem of poor residual stress prediction accuracy in the case of elastic deformation in the processing of complex thin-walled structures of titanium alloys.

Description

Technical Field

[0001] The invention belongs to the technical field of residual stress prediction during multi-axis milling of titanium alloy thin-walled structures, and in particular relates to a method for calculating three-dimensional distribution of residual stress during milling of thin-walled structures taking elastic deformation into consideration. Background Art

[0002] There are a large number of complex titanium alloy thin-walled structures in aero-engines. The weak rigidity of titanium alloy thin-walled structures makes it very easy for elastic deformation of the cutter caused by milling force to occur during machining, and it also shows position dependence. This makes the actual milling depth of the titanium alloy thin-walled structure fine machining vary with the machining trajectory, resulting in uneven distribution of milling residual stress on the surface, and also showing position dependence. Therefore, the residual stress of multi-axis machining of titanium alloy thin-walled structures is a three-dimensional spatial distribution problem. Machining residual stress is highly sensitive to process parameters, and the randomness of the process can easily cause the randomness of residual stress distribution. The weak rigidity of titanium alloy thin-walled structures often causes deviations between actual process parameters and nominal process parameters, increasing the uncertainty of residual stress distribution on the surface of titanium alloy thin-walled structures. Under the same process parameters, the stiffness of different machining positions is different, and the residual stress induced by milling also changes accordingly.

[0003] The milling process involves physical phenomena such as the shearing effect between the blade and the milling layer material, as well as the friction between the front tool face and the chip, and the back tool face and the machined surface. The surface residual stress distribution state of the titanium alloy thin-walled structure has an important influence on its deformation. When the residual stress distribution is uneven or there is a large stress concentration, it will cause local plastic deformation of the titanium alloy thin-walled structure, resulting in distortion or expansion of the titanium alloy thin-walled structure. At the same time, the change of the residual stress distribution state will affect the deformation direction and amplitude of the titanium alloy thin-walled structure. Different stress distribution states will cause the titanium alloy thin-walled structure to deform in different directions, and the deformation amplitude may also change with the change of the stress distribution state. The titanium alloy thin-walled structure is elastically deformed by the milling force during the milling process, which changes the nominal milling depth, thereby causing the error between the residual stress prediction model and the actual measurement value to increase.

[0004] At present, although relevant research at home and abroad has recognized the high sensitivity of the external dimensions of titanium alloy thin-walled structures to residual stress, the prediction of processing residual stress mainly focuses on two aspects: surface residual stress and single-dimensional residual stress gradient distribution prediction. How to consider the influence of structural stiffness on the distribution law of processing residual stress in three-dimensional space and improve the prediction accuracy of residual stress under elastic deformation of titanium alloy thin-walled structures is a key problem that needs to be solved urgently in the current thin-walled parts processing deformation control. Summary of the invention

[0005] The purpose of the present invention is to provide a method for calculating the three-dimensional distribution of residual stress in thin-walled structure milling taking elastic deformation into consideration, so as to solve the problem of poor residual stress prediction accuracy in the case of elastic deformation in the processing of complex thin-walled structures of titanium alloy.

[0006] The technical solution adopted by the present invention is a method for calculating the three-dimensional distribution of residual stress in thin-walled structure milling considering elastic deformation, which includes the following contents:

[0007] Step 1: Use a ball-end milling cutter to multi-axis mill a titanium alloy thin-wall structure, construct a mechanical model of multi-axis milling with a ball-end milling cutter, calculate the three-dimensional milling force, and convert the three-dimensional milling force from the tool coordinate system to the workpiece coordinate system;

[0008] Step 2: According to the mechanical model of multi-axis milling of the ball-end milling cutter, the elastic deformation of each tool position of the titanium alloy thin-walled structure is calculated, and the milling depth is iteratively solved to obtain the actual milling depth of the titanium alloy thin-walled structure at different tool positions on the tool path line;

[0009] Step 3, using the hyperbolic tangent function to construct a gradient distribution prediction model for residual stress of titanium alloy during multi-axis milling; inputting sample data of residual stress of titanium alloy into the gradient distribution prediction model, and obtaining the optimal value of the prediction model coefficient of the gradient distribution prediction model through the firefly algorithm fitting; using the RBF neural network to establish the correlation between the optimal value of the milling process parameters and the prediction model coefficient; the output result obtained by the RBF neural network prediction is the prediction model coefficient corresponding to any set of milling process parameters in the design parameter domain;

[0010] The design parameter domain includes four milling process parameters: milling speed, feed speed, tilt angle, and milling depth. The milling depth is the actual milling depth obtained in step 2.

[0011] Step 4, repeat the method of step 3 to obtain the prediction model coefficient of each tool position of the titanium alloy thin-walled structure;

[0012] The relationship between the prediction model coefficient of each cutting position and the position of each cutting position is constructed by the multivariate linear regression method, and the prediction model coefficient is obtained as the cutting position changes. Direction and The three-dimensional model coefficients in the direction are substituted into the gradient distribution prediction model to obtain the three-dimensional distribution model of the residual stress of the thin-walled structure milling considering the elastic deformation;

[0013] in, Direction is the tool feed direction, The direction is perpendicular to the tool feed direction of the machining surface.

[0014] Furthermore, the specific method of step 2 includes the following contents:

[0015] Firstly, the three-dimensional average milling force is calculated based on the mechanical model of multi-axis milling with ball-end milling cutter.

[0016] Secondly, the three-dimensional average milling force is substituted into the Abaqus finite element model for deformation simulation, and the elastic deformation of the corresponding tool position is calculated;

[0017] Then, according to the elastic deformation, the milling depth of the titanium alloy thin-walled structure after each iteration is calculated, and the milling depth value in the ball-end milling cutter multi-axis milling mechanical model is updated, and the iterative calculation is repeated; when the difference between two adjacent calculated milling depths is within the set range, the iteration is exited, and the output of the last iteration is the actual milling depth of the titanium alloy thin-walled structure at the tool position.

[0018] Furthermore, step 3 is specifically as follows:

[0019] Firstly, a gradient distribution prediction model is constructed, the sample data of residual stress of titanium alloy is substituted into the gradient distribution prediction model as training samples, and the prediction model coefficients are initialized;

[0020] Secondly, initialize the firefly algorithm and perform fitting calculation on the prediction model coefficients to obtain the fitting accuracy;

[0021] When the fitting accuracy is ≤0.8, the prediction model coefficients are updated and the fitting calculation is performed again;

[0022] When the fitting accuracy is greater than 0.8, the prediction model coefficient at this time is the optimal value of the prediction model coefficient;

[0023] Then, the RBF neural network is used to establish the correlation between the milling process parameters and the optimal values ​​of the prediction model coefficients. Any set of milling process parameters in the design parameter domain is used as the input of the RBF neural network, and the RBF neural network is initialized; the optimal value of the prediction model coefficient is used as the target parameter; the milling depth is the actual milling depth of the corresponding tool position obtained according to the elastic deformation;

[0024] Calculate and judge the prediction error of RBF neural network;

[0025] When the prediction error is ≥ 0.1, the prediction model coefficients are recalculated and the error evaluation is performed again;

[0026] When the prediction error is less than 0.1, the prediction model coefficients of any set of milling process parameters input into the RBF neural network can be obtained.

[0027] Furthermore, the gradient distribution prediction model in step 3 is:

[0028] ,

[0029] In the formula, for Milling residual stress in the direction of is the corresponding depth value of the residual stress influence layer in the milling of titanium alloy thin-walled structure, and are the prediction model coefficients of the gradient distribution prediction model, and is a constant.

[0030] Furthermore, the three-dimensional distribution model established in step 4 is:

[0031] ;

[0032] in, and Both The three-dimensional model coefficients of the three-dimensional distribution model in the direction, and Both The three-dimensional model coefficients of the three-dimensional distribution model in the direction, and is a constant, Indicates the corresponding depth value of the residual stress influence layer of titanium alloy thin-walled structure milling. for Milling residual stress in the direction.

[0033] The beneficial effects of the present invention are as follows: due to the different stiffness of different processing positions of titanium alloy thin-walled structures, the residual stress induced by milling is unevenly distributed, and the existing residual stress prediction model cannot accurately predict this uneven distribution phenomenon. The present invention establishes an iterative relationship between milling force and elastic deformation, realizes the iterative solution of the milling depth of titanium alloy thin-walled structures, and thus obtains the actual milling depth of different tool positions. This iterative relationship solves the problem of deviation between actual process parameters and nominal process parameters caused by the weak rigidity of complex thin-walled structures of titanium alloys, and provides a basis for the accurate prediction of residual stress in complex thin-walled structures.

[0034] Although existing research has recognized the high sensitivity of thin-walled structure dimensions to residual stress, the research on residual stress distribution is still limited to the dimensions of surface residual stress and depth. The present invention combines the iterative relationship between milling force and elastic deformation with a one-dimensional gradient distribution prediction model of titanium alloy residual stress, obtains the residual stress gradient distribution at different tool positions of titanium alloy thin-walled structures, realizes the three-dimensional distribution prediction of milling residual stress of titanium alloy thin-walled structures, and obtains a three-dimensional distribution calculation method for milling residual stress of thin-walled structures considering elastic deformation. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a specific process flow chart of step 1 of the present invention;

[0036] Figure 2 It is a specific process flow chart of step 2 of the present invention;

[0037] Figure 3 It is a specific process flow chart of step 3 of the present invention;

[0038] Figure 4 Graph showing the change in milling depth versus iteration number for fine milling of a titanium alloy thin-wall structure in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] The present invention provides a method for calculating the three-dimensional distribution of residual stress in thin-walled structure milling considering elastic deformation, which includes the following contents:

[0041] Step 1: Use a ball-end milling cutter to mill titanium alloy thin-walled structures through multi-axis milling, build a mechanical model of multi-axis milling with a ball-end milling cutter, calculate the three-dimensional milling force, and convert the three-dimensional milling force from the tool coordinate system to the workpiece coordinate system. The construction process of the mechanical model of multi-axis milling with a ball-end milling cutter mainly includes three parts: inputting relevant data, solving the milling contact area between the tool and the titanium alloy thin-walled structure, and calculating the final milling force.

[0042] like Figure 1 As shown in the figure, the specific process of constructing the mechanical model of multi-axis milling with a ball-end milling cutter is as follows:

[0043] Step 1.1, input basic data, which are milling process parameters, tool geometry parameters and workpiece geometry parameters; the workpiece is a titanium alloy thin-walled structure, and the workpiece geometry parameters are the geometric dimensions of the titanium alloy thin-walled structure; the selection of milling process parameters must be consistent with the parameters used when generating the tool path file, and the milling process parameters are milling speed, feed speed, tilt angle and milling depth, and the tool is a ball-end milling cutter;

[0044] Step 1.2, based on the basic data in step 1.1, calculate the cutting-in and cutting-out angles between the tool and the titanium alloy thin-walled structure at each milling position; at the same time, by calculating the instantaneous undeformed milling thickness at any time point during the milling process, further determine the specific area of ​​contact between the tool and the titanium alloy thin-walled structure;

[0045] Step 1.3, substitute the milling force coefficient, traverse all the tooth micro-elements of the ball-end milling cutter; and calculate the milling force for each tooth micro-element; then perform the rotation angle integral cycle and the axial position angle integral cycle to solve the total milling force of the tool in the milling area;

[0046] and The milling force coefficients representing the tangential shear force and the cutting edge force, respectively; and The milling force coefficients represent the radial shear force and the cutting edge force respectively; and are the milling force coefficients of axial shear force and cutting edge force, respectively;

[0047] Step 1.4: Perform coordinate rotation transformation between the tool and the workpiece, calculate the three-dimensional milling force in the workpiece coordinate system and output the milling force data and waveform.

[0048] Among them, the mechanical model of multi-axis milling of ball-end milling cutter is:

[0049] ,

[0050] In the formula, is the tangential micro-element force, is the radial micro-element force, is the axial micro-element force, Represents the milling edge length of each microelement, and represents the undeformed chip thickness and undeformed milling width, is the radial immersion angle, is the axial immersion angle, is the main axis angle, is the discrete element thickness.

[0051] Step 2: According to the mechanical model of multi-axis milling of ball-end milling cutter, the elastic deformation of each tool position of titanium alloy thin-walled structure is calculated, and the milling depth of titanium alloy thin-walled structure is iteratively solved to obtain the actual milling depth of titanium alloy thin-walled structure at different tool positions on the tool path line. Different tool positions can be obtained by discretizing the tool path line along the tool feed direction.

[0052] Step 3, using the hyperbolic tangent function to construct a gradient distribution prediction model for residual stress of titanium alloy in multi-axis milling; inputting sample data of residual stress of titanium alloy into the gradient distribution prediction model, and obtaining the optimal value of the prediction model coefficient of the gradient distribution prediction model through firefly algorithm fitting; using the RBF neural network to establish the correlation between the milling process parameters and the optimal value of the prediction model coefficient;

[0053] The output result obtained by RBF neural network prediction is the prediction model coefficient corresponding to any set of milling process parameters in the design parameter domain;

[0054] Among them, the design parameter domain includes four milling process parameters: milling speed, feed speed, tilt angle and milling depth. The milling depth is the actual milling depth of the corresponding tool position obtained according to the elastic deformation;

[0055] The design parameter domain ranges from 20 to 180 m / min of milling speed, 0.01 to 0.09 mm / z of feed rate, 35 to 75° of inclination angle, and 0.1 to 0.3 mm of milling depth.

[0056] When titanium alloy is milled with a ball end mill, the mechanical effect has a significant impact on the machining process, while the thermal effect has a smaller impact. In addition, the distribution of residual stress caused by ball end milling has a certain regularity. In order to better understand and describe this distribution pattern, the hyperbolic tangent function is used to characterize the residual stress gradient distribution curve of multi-axis milling titanium alloy.

[0057] Step 4, repeat the method of step 3 to obtain the prediction model coefficient of each tool position of the titanium alloy thin-walled structure;

[0058] The relationship between the prediction model coefficient of each cutting position and the position of each cutting position is constructed by the multivariate linear regression method, and the prediction model coefficient is obtained as the cutting position changes. Direction and The three-dimensional model coefficients in the direction are substituted into the gradient distribution prediction model to obtain the three-dimensional distribution model of the milling residual stress of the thin-walled structure of titanium alloy considering elastic deformation;

[0059] in, Direction is the tool feed direction, The direction is perpendicular to the tool feed direction of the machining surface.

[0060] In some embodiments, Figure 2 As shown, the specific method of step 2 includes the following contents:

[0061] Firstly, the three-dimensional average milling force is calculated based on the mechanical model of multi-axis milling with ball-end milling cutter.

[0062] Secondly, the three-dimensional average milling force is substituted into the Abaqus finite element model for deformation simulation, and the elastic deformation of the corresponding tool position is calculated; the Abaqus finite element model is a tool for simulating and analyzing the performance of complex mechanical systems;

[0063] Then, according to the elastic deformation, the milling depth of the titanium alloy thin-walled structure after each iteration is calculated, and the milling depth value in the ball-end milling cutter multi-axis milling mechanical model is updated, and the iterative calculation is repeated; when the difference between the milling depths of two consecutive calculations is within the set range, the iteration is jumped out, and the output of the last iteration is the actual milling depth of the titanium alloy thin-walled structure at the tool position. The setting range is selected according to the processing accuracy, such as 0.005mm.

[0064] Titanium alloy thin-walled structures will undergo elastic deformation during the milling process, and this deformation will further lead to changes in the milling force. Therefore, there is a close interaction between the milling force and the elastic deformation. In order to achieve accurate prediction of the elastic deformation behavior of titanium alloy thin-walled structures, it is crucial to construct an appropriate iterative relationship between the milling force and the elastic deformation. Therefore, the present invention is based on the ball-end milling cutter multi-axis milling mechanical mechanics model, and uses the elastic deformation as a feedback variable to iteratively solve the milling depth. As the titanium alloy thin-walled structure undergoes elastic deformation under the action of the milling force, the corrected milling depth becomes smaller, which in turn causes the milling force to become smaller. Since the milling force is positively correlated with the elastic deformation, the elastic deformation also decreases accordingly. The milling force, the elastic deformation and the actual milling depth influence each other and fluctuate within a certain range, and eventually reach a state of equilibrium.

[0065] The formula for calculating the actual milling depth is:

[0066] ,

[0067] in, For the The actual milling depth after the iteration calculation; is the theoretical nominal milling depth; For the After the first iterative calculation, the normal elastic deformation of the titanium alloy thin-walled structure in the contact area between the tool ball head and the titanium alloy machined parts.

[0068] In some embodiments, Figure 3 As shown, step 3 is specifically as follows:

[0069] Firstly, a gradient distribution prediction model is constructed, the sample data of residual stress of titanium alloy is substituted into the gradient distribution prediction model as training samples, and the prediction model coefficients are initialized;

[0070] Secondly, initialize the firefly algorithm and perform fitting calculation on the prediction model coefficients to obtain the fitting accuracy;

[0071] When the fitting accuracy is ≤0.8, the prediction model coefficients are updated and the fitting calculation is performed again;

[0072] When the fitting accuracy is greater than 0.8, the prediction model coefficient at this time is the optimal value of the prediction model coefficient;

[0073] Then, the RBF neural network is used to establish the correlation between the milling process parameters and the optimal values ​​of the prediction model coefficients. Any set of milling process parameters in the design parameter domain is used as the input of the RBF neural network, and the RBF neural network is initialized; the optimal value of the prediction model coefficient is used as the target parameter; the milling depth is the actual milling depth of the corresponding tool position obtained according to the elastic deformation; the RBF neural network is a radial basis function neural network, which is a feedforward neural network;

[0074] Calculate and judge the prediction error of RBF neural network;

[0075] When the prediction error is ≥ 0.1, the prediction model coefficients are recalculated and the error evaluation is performed again;

[0076] When the prediction error is less than 0.1, the prediction model coefficients of any set of milling process parameters input into the RBF neural network can be obtained.

[0077] After the gradient distribution prediction model is built, it is experimentally verified. According to the experimental design, the structure of the RBF neural network includes four neurons in the input layer and two neurons in the output layer. As the RBF neural network is trained, the nodes in the hidden layer will automatically increase until the fitting accuracy meets the error requirements.

[0078] Matlab platform is a high-performance numerical computing environment and fourth-generation programming language. RBF neural network was developed on the Matlab platform. The extended parameter was set to 0.53. At least 100 groups of residual stress sample data obtained by experiments and simulations were used as training samples to train the RBF neural network and obtain the optimal RBF neural network structure. Finally, a verification experiment was carried out within the design parameter domain. The preset parameter range was milling speed 20~180m / min, feed speed 0.01~0.09mm / z, tilt angle 35~75° and milling depth 0.1~0.3mm. The residual stress value of the residual stress influence layer on the machined surface of the workpiece was measured, and the verification of the residual stress gradient distribution prediction model of multi-axis milling titanium alloy was completed. The verification results show that the proposed multi-axis milling titanium alloy residual stress gradient distribution prediction model has high prediction accuracy and can effectively predict the distribution of residual stress of titanium alloy.

[0079] In some embodiments, the gradient distribution prediction model in step 3 is:

[0080] ,

[0081] In the formula, for Milling residual stress in the direction of is the corresponding depth value of the residual stress influence layer in the milling of titanium alloy thin-walled structure, and are the prediction model coefficients of the gradient distribution prediction model, and is a constant.

[0082] In some embodiments, the three-dimensional distribution model established in step 4 is:

[0083] ;

[0084] in, and Both The three-dimensional model coefficients of the three-dimensional distribution model in the direction, and Both The three-dimensional model coefficients of the three-dimensional distribution model in the direction, and is a constant, Indicates the corresponding depth value of the residual stress influence layer of titanium alloy thin-walled structure milling. for Milling residual stress in the direction.

[0085] Embodiment: The three-dimensional distribution calculation method of residual stress in milling of thin-walled structure considering elastic deformation of the present invention is used to process Ti-6Al-4V titanium alloy thin-walled structure.

[0086] Step 1: Use a ball-end milling cutter to multi-axis mill a thin-walled structure of Ti-6Al-4V titanium alloy, construct a mechanical model of multi-axis milling with a ball-end milling cutter, calculate the three-dimensional milling force, and convert the three-dimensional milling force from the tool coordinate system to the workpiece coordinate system;

[0087] Step 2: The material of the titanium alloy thin-walled structure processed in this embodiment is Ti-6Al-4V titanium alloy, and its density is , the elastic modulus is 114GPa, and the Poisson's ratio is 0.34. The mesh type of the titanium alloy thin-walled structure is the three-dimensional stress eight-node linear hexahedral unit C3D8R, and the initial mesh size is 1mm. The simulated three-dimensional average milling force is applied to the corresponding tool position points respectively, and the elastic deformation of the tool milling at different positions is simulated by changing the reference point coordinates. The milling process parameters are obtained from actual engineering. Specifically, the inclination angle is 55°, the spindle speed is 118m / min, the feed speed is 0.046mm / z, and the milling depth is 0.2mm. The length of the titanium alloy thin-walled structure is 70mm, the height is 72mm, the minimum thickness is 1.27mm, the maximum thickness is 2.76mm, and the thickness varies uniformly. The tool feed direction of the titanium alloy thin-walled structure during milling is defined as The tool feed direction is the length direction of the titanium alloy thin-wall structure. The vertical feed direction of the machined surface is The vertical feed direction of the machined surface is the height direction of the titanium alloy thin-walled structure. Set the entry point of the tool to start milling the titanium alloy thin-walled structure as the origin. The positions of all tool positions on the machined surface of the titanium alloy thin-walled structure can be obtained by and The tool trajectory is planned along the tool feed direction of the titanium alloy thin-walled structure. Eight tool positions are selected on each tool trajectory to calculate the actual milling depth of the corresponding position. A total of 10 tool position trajectories are selected. The three-dimensional average milling force is calculated by Matlab software, and the Abaqus finite element model is called by Python script to solve the elastic deformation of each tool position. According to the elastic deformation, the milling depth of the titanium alloy thin-walled structure after each iteration is calculated, and the milling depth value in the ball-end milling cutter multi-axis milling mechanical model is updated, and the iterative calculation is repeated. The calculation is stopped when the difference between the two iterative calculations of the milling depth is less than 0.005mm.

[0088] Figure 4 : is a graph showing the milling depth of a titanium alloy thin-wall structure at a tool position in the embodiment of the present invention as a function of the number of iterations. Figure 4 It can be seen that after 5 iterations, the difference in milling depths obtained from two adjacent iterations is less than 0.005 mm, and the iteration stops. The output value of the last iteration is the actual milling depth of the tool position.

[0089] According to this iterative method, the actual milling depths of all tool positions are calculated and listed in Table 1.

[0090] Table 1 Titanium alloy thin-walled structure Direction and Simulation value of actual milling depth at each tool position in the direction

[0091]

[0092] Step 3: Use the hyperbolic tangent function to construct a gradient distribution prediction model for residual stress in multi-axis milling of titanium alloy; input the sample data into the gradient distribution prediction model, and obtain the optimal value of the prediction model coefficient through firefly algorithm fitting; then use the RBF neural network to establish the correlation between the milling process parameters and the optimal value of the prediction model coefficient.

[0093] In order to verify the accuracy of the gradient distribution prediction model, a rectangular block of 60mm×40mm×25mm was selected as the experimental object, and the following experiments were carried out:

[0094] Five groups of milling process parameters were selected within the design parameter domain consisting of milling speed of 20-180 m / min, feed speed of 0.01-0.09 mm / z, tilt angle of 35-75°, and milling depth of 0.1 mm-0.3 mm;

[0095] The rectangular block does not undergo elastic deformation during the milling process, and its milling depth is 0.2 mm;

[0096] The prediction model coefficients corresponding to the five groups of milling process parameters are predicted by the RBF neural network, and the prediction output result is the prediction model coefficients corresponding to the five groups of milling process parameters;

[0097] The prediction model coefficients corresponding to the five sets of milling process parameters obtained by the method of step 3 of the present invention are called the prediction values ​​of the prediction model coefficients, and the fitting accuracy R is obtained at the same time. 2 The predicted value of

[0098] A comparative experiment was conducted on the same five groups of milling process parameters. The comparative experiment was an experiment of multi-axis milling and residual stress measurement. The prediction model coefficients and fitting accuracy corresponding to the five groups of milling process parameters were also obtained. They are called the comparison value of the prediction model coefficient and the fitting accuracy R 2 The comparison value of .

[0099] The above values ​​of the prediction model coefficients and fitting accuracy are calculated according to Direction and The directions are divided into two groups and are listed in Tables 2 and 3, respectively.

[0100] Table 2 Prediction model coefficients and fitting accuracy corresponding to different milling process parameters in different directions

[0101]

[0102] Table 3 Prediction model coefficients and fitting accuracy corresponding to different milling process parameters in different directions

[0103]

[0104] As shown in Table 2, the fitting accuracy R 2 The comparison value is The range of change in direction is 0.882~0.989, and the average value is 0.929;

[0105] Fitting accuracy R 2 The predicted value is The range of change in direction is 0.858~0.927, with an average value of 0.893;

[0106] It can be seen that the average value of 0.929 is very close to the average value of 0.893.

[0107] As shown in Table 3, the fitting accuracy R 2 The comparison value is The range of change in direction is 0.887~0.951, with an average value of 0.919;

[0108] Fitting accuracy R 2 The predicted value is The range of change in direction is 0.842~0.914, with an average value of 0.889;

[0109] It can be seen that the average value of 0.919 is very close to the average value of 0.889.

[0110] When the fitting accuracy R 2 The average value of the predicted value is very close to the fitting accuracy R 2 The average value of the comparison value and the fitting accuracy R 2 When the average value of the predicted values ​​is greater than 0.8, it can be shown that the gradient distribution prediction model established by the present invention can accurately predict the residual stress distribution state under the actual processing state.

[0111] Step 4. According to the method of step 3, the prediction model coefficients of different tool positions of the titanium alloy thin-walled structure whose material is Ti-6Al-4V in step 2 are predicted one by one. The milling depth of the titanium alloy thin-walled structure is the actual milling depth of each tool position listed in Table 1 in step 2.

[0112] The prediction model coefficients of each tool position obtained are calculated according to Direction and The directions are divided into two groups and are listed in Tables 4 and 5, respectively.

[0113] Table 4 Prediction model coefficients of each knife position in the direction

[0114]

[0115] Table 5 Prediction model coefficients of each knife position in the direction

[0116]

[0117] Through the method of multiple linear regression, according to the prediction model coefficients in Table 4 and Table 5, the relationship between the prediction model coefficient of each tool position and the position of each tool position is constructed to obtain the prediction model coefficient with the tool position at Direction and The three-dimensional model coefficient in the direction, that is , , and Each three-dimensional model coefficient is substituted into the gradient distribution prediction model, thereby obtaining the three-dimensional distribution model of the milling residual stress of the thin-walled structure considering elastic deformation of the present invention.

[0118] The Ti-6Al-4V titanium alloy thin-walled structure of this embodiment is processed according to the three-dimensional distribution model. Six test points are selected on the titanium alloy thin-walled structure after processing to test the surface residual stress, and the experimental value of the surface residual stress is obtained. The surface residual stress of the same six points is calculated using the three-dimensional distribution model of the present invention, which is called the predicted value of the surface residual stress. The experimental value of the surface residual stress and the predicted value of the surface residual stress are calculated according to Direction and The directions are divided into two groups and are listed in Table 6. The error value of the surface residual stress is calculated according to error value = (predicted value - experimental value) / experimental value, and the error value is also listed in Table 6.

[0119] Table 6 Experimental values ​​of surface residual stress at each test point and predicted values ​​of surface residual stress

[0120]

[0121] From Table 6, we can see that The maximum error value of the directional surface residual stress is 11.2%, the minimum error value is 3.7%, and the average error value is 6.78%. The maximum error value of the residual stress on the surface of the axial direction is 12.7%, the minimum error value is 6.9%, and the average error value is 9.83%. Direction and The average error values ​​of the surface residual stress in the direction are all less than 10%, which is much smaller than the average error value of 20~30% of the existing surface residual stress prediction model, which shows that the three-dimensional distribution calculation method of residual stress in milling of thin-walled structures considering elastic deformation proposed in the present invention can improve the prediction accuracy of residual stress in titanium alloy thin-walled structures when elastic deformation occurs during processing.

[0122] The titanium alloy thin-walled structure has different stiffness at different processing positions, which makes the residual stress induced by milling unevenly distributed. The existing residual stress prediction model cannot accurately predict this uneven distribution phenomenon. The present invention establishes an iterative relationship between milling force and elastic deformation, realizes the iterative solution of the milling depth of the titanium alloy thin-walled structure, and thus obtains the actual milling depth of different tool positions. This iterative relationship solves the problem of deviation between the actual process parameters and the nominal process parameters caused by the weak rigidity of the complex thin-walled structure of titanium alloy, and provides a basis for the accurate prediction of the residual stress of the complex thin-walled structure.

[0123] Although existing research has recognized the high sensitivity of thin-walled structure dimensions to residual stress, the research on residual stress distribution is still limited to the dimensions of surface residual stress and depth. The present invention combines the iterative relationship between milling force and elastic deformation with a one-dimensional gradient distribution prediction model of titanium alloy residual stress, obtains the residual stress gradient distribution at different tool positions of titanium alloy thin-walled structures, realizes the three-dimensional distribution prediction of milling residual stress of titanium alloy thin-walled structures, and obtains a three-dimensional distribution calculation method for milling residual stress of thin-walled structures considering elastic deformation.

Claims

1. A three-dimensional calculation method for residual stress distribution in thin-walled structure milling considering elastic deformation, characterized in that: Includes the following: Step 1: Use a ball-end milling cutter to multi-axis mill a titanium alloy thin-wall structure, construct a mechanical model of a ball-end milling cutter multi-axis milling, calculate the three-dimensional milling force, and convert the three-dimensional milling force from the tool coordinate system to the workpiece coordinate system; Step 2: Calculate the elastic deformation of each tool position of the titanium alloy thin-walled structure according to the mechanical model of multi-axis milling of the ball-end milling cutter, and iteratively solve the milling depth to obtain the actual milling depth of the titanium alloy thin-walled structure at different tool positions on the tool path line; Step 3, using the hyperbolic tangent function to construct a gradient distribution prediction model for residual stress of titanium alloy during multi-axis milling; inputting sample data of residual stress of titanium alloy into the gradient distribution prediction model, and obtaining the optimal value of the prediction model coefficient of the gradient distribution prediction model through firefly algorithm fitting; using RBF neural network to establish the correlation between milling process parameters and the optimal value of the prediction model coefficient; the output result obtained by RBF neural network prediction is the prediction model coefficient corresponding to any set of milling process parameters in the design parameter domain; The design parameter domain includes four milling process parameters: milling speed, feed speed, tilt angle and milling depth. The milling depth is the actual milling depth obtained in step 2. Step 4, repeating the method of step 3 to obtain the prediction model coefficient of each tool position of the titanium alloy thin-walled structure; By using a multivariate linear regression method, the relationship between the prediction model coefficient of each of the tool positions and the positions of each of the tool positions is constructed to obtain the relationship between the prediction model coefficient and the tool position. Direction and The three-dimensional model coefficients in the direction are substituted into the gradient distribution prediction model to obtain a three-dimensional distribution model of residual stress of thin-walled structure milling considering elastic deformation; in, Direction is the tool feed direction, The direction is perpendicular to the tool feed direction of the machining surface.

2. The method for calculating the three-dimensional distribution of residual stress in thin-walled structure milling considering elastic deformation according to claim 1, characterized in that: The specific method of step 2 includes the following contents: Firstly, according to the mechanical model of multi-axis milling of ball-end milling cutter, the three-dimensional average milling force is calculated; Secondly, the three-dimensional average milling force is substituted into the Abaqus finite element model for deformation simulation, and the elastic deformation of the corresponding tool position is calculated; Then, based on the elastic deformation, the milling depth of the titanium alloy thin-walled structure after each iteration is calculated, and the milling depth value in the ball-end milling cutter multi-axis milling mechanical model is updated, and the iterative calculation is repeated in this way; when the difference between the milling depths calculated twice is within the set range, the iteration is exited; the output of the last iteration is the actual milling depth of the titanium alloy thin-walled structure at the tool position.

3. The method for calculating the three-dimensional distribution of residual stress in thin-walled structure milling considering elastic deformation according to claim 2, characterized in that: The step 3 is specifically as follows: First, the gradient distribution prediction model is constructed, sample data of residual stress of titanium alloy is substituted into the gradient distribution prediction model as training samples, and the prediction model coefficients are initialized; Secondly, the firefly algorithm is initialized and the coefficients of the prediction model are fitted and calculated to obtain the fitting accuracy; When the fitting accuracy is ≤0.8, the prediction model coefficients are updated and the fitting calculation is performed again; When the fitting accuracy is greater than 0.8, the prediction model coefficient at this time is the optimal value of the prediction model coefficient; Then, the RBF neural network is used to establish a correlation between the milling process parameters and the optimal values ​​of the prediction model coefficients, any set of milling process parameters in the design parameter domain is used as the input of the RBF neural network, and the RBF neural network is initialized; The optimal value of the prediction model coefficient is used as the target parameter; wherein the milling depth is the actual milling depth of the corresponding tool position point obtained according to the elastic deformation amount; Calculating and judging the prediction error of the RBF neural network; When the prediction error is ≥ 0.1, recalculate the prediction model coefficients and perform error evaluation again; When the prediction error is less than 0.1, the prediction model coefficients of any group of the milling process parameters input into the RBF neural network can be obtained.

4. The method for calculating the three-dimensional distribution of residual stress in thin-walled structure milling considering elastic deformation according to claim 1, characterized in that: The gradient distribution prediction model in step 3 is: ， In the formula, for Milling residual stress in the direction of is the corresponding depth value of the milling residual stress influence layer of the titanium alloy thin-walled structure, and are all prediction model coefficients of the gradient distribution prediction model, and is a constant.

5. The method for calculating the three-dimensional distribution of residual stress in thin-walled structure milling considering elastic deformation according to claim 4, characterized in that: The three-dimensional distribution model established in step 4 is: ； in, and Both The three-dimensional model coefficients of the three-dimensional distribution model in the direction, and Both The three-dimensional model coefficients of the three-dimensional distribution model in the direction, and is a constant, represents the corresponding depth value of the milling residual stress influence layer of the titanium alloy thin-walled structure, for Milling residual stress in the direction.

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