Method for calculating three-dimensional distribution of variable-roll-angle four-axis milling residual stress

Abstract

The invention discloses a calculation method for three-dimensional distribution of variable-roll-angle four-axis milling residual stress. The calculation method comprises the following steps: step 1, obtaining a representation model; 2, establishing an optimization model, and solving a model coefficient optimal value of the optimization model; step 3, carrying out normalization processing; 4, establishing a regression prediction model; and 5, substituting the regression prediction model in the step 4 into the characterization model in the step 1, and then replacing the cutter attitude roll angle in the characterization model with the processing curved surface position of the workpiece surface to obtain a residual stress three-dimensional distribution calculation model. Predicting three-dimensional distribution residual stress corresponding to the feeding direction and the width cutting direction through the calculation model; according to the method, the three-dimensional distribution condition of the residual stress at any point of the machining curved surface can be intuitively reflected, and the problem of non-uniformity of residual stress distribution caused by the change of a cutter attitude roll angle is solved, so that the out-of-tolerance deformation of a workpiece is effectively controlled.

Description

Technical Field

[0001] The present invention belongs to the field of residual stress prediction in four-axis precision milling, and in particular relates to a method for calculating the three-dimensional distribution of residual stress in four-axis milling with a variable roll angle. Background Art

[0002] Aeroengines contain numerous complex, U-shaped, thin-walled titanium alloy structures. These U-shaped structures are prone to deformation during four-axis machining due to milling residual stress, and the degree of deformation is correlated with the tool's tilt angle. The complex, double-walled, U-shaped titanium alloy thin-walled structures, coupled with high machining precision requirements, lead to significant residual stress and deformation issues during finishing using tapered ball-end cutters on five-axis machining centers, severely impacting the lifespan and reliability of the aircraft engine.

[0003] The residual stress distribution state of titanium alloy thin-walled structures has an important influence on their deformation. When the residual stress is unevenly distributed or there is a large stress concentration, it will cause local deformation, which will lead to torsion or expansion of the titanium alloy thin-walled structure. During the four-axis machining of titanium alloy thin-walled structures, the tool attitude tilt angle continues to change, resulting in uneven distribution of cutting residual stress on the surface, showing position dependence. The residual stress of four-axis machining is highly sensitive to the tool attitude tilt angle, and the randomness of the tool attitude tilt angle can easily cause randomness in the residual stress distribution. The finishing stage of titanium alloy thin-walled structures is completed by four-axis machining with a tapered ball end mill. During the machining process, the tool attitude tilt angle continues to change, which has a more obvious effect on the residual stress gradient distribution, causing the residual stress to present a complex three-dimensional distribution state on the surface of the thin-walled structure, causing complex bending and torsional deformation of the thin-walled structure.

[0004] At present, the research on machining residual stress basically stays in the depth direction, and the three-dimensional distribution of residual stress on the machined surface of the workpiece due to time-varying working conditions cannot be obtained. Summary of the Invention

[0005] The purpose of the present invention is to provide a calculation method for the three-dimensional distribution of residual stress in four-axis milling with variable roll angle, which can predict the three-dimensional distribution of residual stress of titanium alloy U-shaped thin-walled structures under the constantly changing tool posture roll angle during four-axis milling.

[0006] The present invention adopts the following technical solution: a method for calculating the three-dimensional distribution of residual stress in four-axis milling with variable rake angle, comprising: Step 1: Use the hyperbolic tangent model to obtain the characterization model of the residual stress gradient distribution in four-axis milling of titanium alloy U-shaped structure with a tapered ball end cutter; Step 2: An optimization model is established based on the measured values ​​of the residual stresses on the workpiece surface along the feed direction and the cutting width direction and the characterization model. The optimization model is solved using the Firefly optimization algorithm to obtain the optimal values ​​of the model coefficients of the characterization model in the feed direction and the cutting width direction at various tool posture tilt angles. Step 3: Normalize the optimal values ​​of the model coefficients in the feed direction and cutting width direction under each tool posture tilt angle and each tool posture tilt angle; Step 4: Using the tilt angle of each tool posture as input and the optimal value of the model coefficient corresponding to the feed direction and cutting width direction as output, a regression prediction model is established; Step 5: First, substitute the regression prediction model of step 4 into the characterization model of step 1, and then replace the tool posture tilt angle in the characterization model with the machining surface position of the workpiece surface, and then obtain the calculation model of the three-dimensional distribution of residual stress. The three-dimensional distribution residual stress corresponding to the feed direction and cutting width direction is predicted through the calculation model.

[0007] Furthermore, the characterization model is: , Where: σ(h) is the residual stress after processing, MPa; h is the depth of the position corresponding to the residual stress, μm; ω and k are the unknown coefficients of the characterization model; and are all constants, =100MPa, =100μm.

[0008] Furthermore, the optimization model is: , Where: σ exp is the measured value of residual stress, MPa; σ fit is the calculated value of residual stress of the model under corresponding ω and k, MPa; is the average value of the measured residual stress, MPa; ω i is σ fit The weight coefficient, and ω i =1, R 2 is the fitting accuracy.

[0009] The beneficial effects of the present invention are: The present invention constructs a characterization model of residual stress gradient distribution, and then obtains the optimal value of the model coefficient of the characterization model through an optimization model, and then obtains the relationship between the optimal value of the model coefficient and the tool posture roll angle. Then, the tool posture roll angle in the characterization model is replaced by the position of the machined surface of the workpiece surface, and then a calculation model of the three-dimensional distribution of residual stress is obtained. The present invention can intuitively reflect the three-dimensional distribution of residual stress at any point on the machined surface, solves the problem of uneven residual stress distribution caused by changes in the tool posture inclination angle, and thus effectively controls the out-of-tolerance deformation of the workpiece. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 The surface residual stress distribution curve predicted by the calculation model of the residual stress in the feed direction when the tool posture tilt angle is 45°; Figure 2 The surface residual stress distribution curve predicted by the calculation model of the residual stress in the feed direction when the tool posture tilt angle is 55°; Figure 3 The surface residual stress distribution curve predicted by the calculation model of the residual stress in the cutting width direction when the tool posture side tilt angle is 45°; Figure 4 The surface residual stress distribution curve predicted by the calculation model of the residual stress in the cutting width direction when the tool posture side tilt angle is 55°; Figure 5 This is a schematic diagram of the four-axis machining of the titanium alloy U-shaped thin-walled structure of the present invention. DETAILED DESCRIPTION

[0011] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0012] The present invention discloses a method for calculating the three-dimensional distribution of residual stress in four-axis milling with a variable rake angle, comprising: Step 1: The hyperbolic tangent model is used to obtain the characterization model of the residual stress gradient distribution in four-axis milling of titanium alloy U-shaped structures using a tapered ball-end cutter.

[0013] During the four-axis machining process, the gradient distribution curve of the residual stress of TC4 titanium alloy is similar to the hyperbolic tangent function. Therefore, the hyperbolic tangent model is used to characterize the residual stress gradient distribution of TC4 titanium alloy during four-axis milling with a tapered ball end cutter. The specific characterization model is: , Where: σ(h) is the residual stress after processing, MPa; h is the depth of the position corresponding to the residual stress, μm; ω and k are the unknown coefficients of the characterization model; and are all constants, =100MPa, =100μm.

[0014] Define the fitting accuracy R of the characterization model 2 for: , Where: σexp is the measured value of residual stress, MPa; σ fit is the calculated value of residual stress of the model under corresponding ω and k, MPa; is the average value of the measured residual stress, MPa; ω i is σ fit The weight coefficient, and ω i =1.

[0015] Step 2: An optimization model is established based on the measured values ​​of the residual stress in the feed direction and the cutting width direction of the workpiece surface and the characterization model, and the optimization model is solved using the firefly optimization algorithm to obtain the optimal values ​​of the model coefficients of the characterization model in the feed direction and the cutting width direction under various tool posture inclination angles.

[0016] The Firefly Algorithm (FA) is used to obtain the optimal value of the model coefficient. The optimal value of the model coefficient is regarded as an optimization problem, and the objective function is the fitting accuracy R 2 , R 2 The value is within the range of [0, 1]. Design optimization variables k and ω, the optimization space is k∈[0, 10], ω∈[0, 10], and establish the optimization model:

[0017] Step 3: Normalize the optimal values ​​of the model coefficients in the feed direction and cutting width direction under each tool posture tilt angle and each tool posture tilt angle.

[0018] Step 4: Using the tilt angle of each tool posture as input and the optimal value of the model coefficient corresponding to the feed direction and cutting width direction as output, a regression prediction model is established.

[0019] Step 5: First, substitute the regression prediction model of step 4 into the characterization model of step 1, and then replace the tool posture tilt angle in the characterization model with the machining surface position of the workpiece surface, and then obtain the calculation model of the three-dimensional distribution of residual stress. The three-dimensional distribution residual stress corresponding to the feed direction and cutting width direction is predicted through the calculation model.

[0020] The present invention adopts a hyperbolic tangent model to characterize the residual stress gradient distribution in four-axis milling of titanium alloy with a tapered ball-end cutter, so that the residual stress gradient distribution can be characterized by a function; the firefly optimization algorithm is used to obtain the optimal value of the model coefficient of the characterization model under different tool posture inclination angles, so that the residual stress gradient distribution characterization is more accurate; the optimal value of the model coefficient under each tool posture inclination angle and each tool posture inclination angle are normalized to make them of the same order of magnitude, thereby establishing a more accurate regression prediction model in step 4; and then a calculation model for the three-dimensional distribution of residual stress is established, which can predict the three-dimensional distribution residual stress corresponding to different machining surface positions.

[0021] Example 1: Step 1: A hyperbolic tangent model is used to obtain a characterization model for the residual stress gradient distribution during four-axis milling of a titanium alloy U-shaped structure using a tapered ball-end cutter.

[0022] The representation model is: , Where: σ(h) is the residual stress after processing, MPa; h is the depth of the position corresponding to the residual stress, μm; ω and k are the unknown coefficients of the characterization model; and are all constants, =100MPa, =100μm.

[0023] Step 2: An optimization model is established based on the measured values ​​of the residual stress in the feed direction and the cutting width direction of the workpiece surface and the characterization model, and the optimization model is solved using the firefly optimization algorithm to obtain the optimal values ​​of the model coefficients of the characterization model in the feed direction and the cutting width direction under various tool posture inclination angles.

[0024] First, a four-axis machining experiment of TC4 titanium alloy was carried out, and the measured values ​​of residual stress on the workpiece surface along the feed direction and cutting width direction were obtained. The machining process parameters are shown in Table 1. In Table 1, f is the feed rate, n is the milling speed, a p is the milling depth, a e is the milling width, and θ is the tool attitude tilt angle.

[0025] Table 1 TC4 titanium alloy four-axis machining process parameters

[0026] The residual stress on the surface of the machined workpiece was measured using a Proto LXRD MG2000 residual stress analyzer and a ProtoPolish 600 electrolytic polishing instrument.

[0027] Then, an optimization model is established based on the measured values ​​and characterization models of the residual stresses on the workpiece surface along the feed direction and the cutting width direction, specifically: , Where: σ exp is the measured value of residual stress, MPa; σ fit is the calculated value of residual stress of the model under corresponding ω and k, MPa; is the average value of the measured residual stress, MPa; ω i is σ fit The weight coefficient, and ω i =1; R 2 is the fitting accuracy.

[0028] Finally, the optimal values ​​of the model coefficients k and ω of the characterization model are obtained by the firefly optimization algorithm. Table 2 shows the optimal values ​​of the model coefficients and fitting accuracy of the characterization model for the five groups of experiments, where σ x is the residual stress in the feed direction, σ y is the residual stress in the cutting width direction.

[0029] Table 2 Optimal values ​​of model coefficients for residual stress

[0030] Step 3: Normalize the optimal values ​​of the model coefficients in the feed direction and cutting width direction under each tool posture tilt angle and each tool posture tilt angle.

[0031] The model coefficient k in the feed direction at each tool posture tilt angle x and ω x , Model coefficient k in the cutting width direction under each tool posture tilt angle y and ω y And the tilt angle of each tool posture is normalized.

[0032] Step 4: Take the tilt angle of each tool posture as input and the optimal value of the model coefficient corresponding to the feed direction and cutting width direction as output to establish a regression prediction model, specifically: , Where k x is the optimal value k of the model coefficient in the feed direction; k y is the optimal value k of the model coefficient in the cutting width direction; ω x is the optimal value of the model coefficient in the feed direction; y is the optimal value of the model coefficient ω in the cutting width direction.

[0033] Table 3 Analysis of variance of regression prediction model

[0034] k x As an example, we conduct variance analysis test. From Table 3, we can see that k in the feed direction x The P value of the regression prediction model is less than 0.05, the degree of freedom is 2, and the residual is 2. By consulting the variance analysis table, when the regression equation is at a significant level of α=0.05 and a confidence level of 95%, the F 0.05 =19, calculated statistic F=73.55, F=73.55>F 0.05 (2, 2)=19.

[0035] Therefore, the regression prediction model is significant under α=0.05, and the same method is used to find the optimal value of the model coefficient ωx 、k y and ω y The test shows that the regression prediction model is significant under α=0.05, indicating that the regression prediction model has good prediction accuracy.

[0036] Step 5: First, substitute the regression prediction model of step 4 into the characterization model of step 1, and then replace the tool posture tilt angle in the characterization model with the machining surface position of the workpiece surface, and then obtain the calculation model of the three-dimensional distribution of residual stress. The three-dimensional distribution residual stress corresponding to the feed direction and cutting width direction is predicted through the calculation model.

[0037] Taking the feed direction as an example, the k in the feed direction x and ω x Substitute the regression prediction model into the characterization model in step 1 to obtain the calculation model of residual stress, which is:

[0038] The tool roll angle is affected by the tool position and can be expressed as a function of the position (u, v) of the cutting contact point on the machined surface, that is, θ = f(u, v). The mapping relationship between the residual stress σ and [u, v, h] can be obtained; thus, the calculation model of the three-dimensional distribution of residual stress is:

[0039] Where: u is the feed direction of the tool, and v is the cutting width direction of the tool.

[0040] The U-shaped thin-walled structure is simplified based on the thin-walled structure of an aircraft engine. The tool attitude roll angle also changes from 45° to 85° along the v direction, while the tool attitude roll angle in the u direction does not change. Therefore, the residual stress in the u direction remains basically unchanged; the residual stress in the v direction shows a trend of first decreasing and then increasing in the range of 45° to 85°; the residual stress in the h direction gradually decays along the depth to the stress level in the matrix.

[0041] The processing area of ​​the U-shaped thin-walled structure is as follows Figure 5 As shown in Figure 2, the tool attitude tilt angle θ at the machining surface position (u, v) is:

[0042] After machining the U-shaped thin-walled structure using the machining parameters in Table 1, a test point was selected in the machining area at inclination angles of 45°, 55°, 65°, 75°, and 85°, and the measured surface residual stress value at each test point was measured. Simultaneously, the surface residual stress at each test point was predicted using the calculation model for the three-dimensional residual stress distribution of this embodiment, resulting in predicted residual stress values. Specific data are shown in Table 4.

[0043] Table 4 Measured and predicted values ​​of surface residual stress at each test point

[0044] From Table 4, we can see that in σ x The maximum error of the surface residual stress in the direction is 4.7%, the minimum error is 2.8%, and the average error is 3.92%. y The maximum error of the surface residual stress in the direction is 6.1%, the minimum error is 3.6%, and the average error is 4.84%. x Direction and σ y The average error values ​​of the surface residual stress in all directions are less than 7%, which shows that the calculation model of the three-dimensional distribution of residual stress in this embodiment is feasible.

[0045] A test point is selected in the machining area where the tool posture tilt angle is 45° and 55°, and the measured values ​​of the surface residual stress at these two test points are measured; at the same time, the surface residual stress distribution curves of these two test points are predicted using the calculation model of the three-dimensional distribution of residual stress of this embodiment, and then the fitting accuracy R of the calculation model of the three-dimensional distribution of residual stress of this embodiment is calculated. 2 ,like Figure 1-4 As shown in Table 5. As can be seen from Table 5, the predicted values ​​of the calculation model for the three-dimensional distribution of residual stress in this embodiment are well matched with the measured values, and the prediction accuracy is high; the surface residual stress distribution curve predicted by the calculation model for the three-dimensional distribution of residual stress in this embodiment has a highest accuracy of 93.85%, a lowest accuracy of 91.11%, and an average prediction accuracy of 92.88%.

[0046] Table 5 Fitting accuracy of surface residual stress at each test point

[0047] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the three-dimensional distribution of residual stress in four-axis milling with variable rake angle, characterized in that: include: Step 1: Use the hyperbolic tangent model to obtain the characterization model of the residual stress gradient distribution in four-axis milling of titanium alloy U-shaped structure with a tapered ball end cutter; Step 2: Establish an optimization model based on the measured values ​​of the residual stresses on the workpiece surface along the feed direction and the cutting width direction and the characterization model, and use the Firefly optimization algorithm to solve the optimization model to obtain the optimal values ​​of the model coefficients of the characterization model in the feed direction and the cutting width direction under various tool posture tilt angles; Step 3: normalizing the optimal values ​​of the model coefficients in the feed direction and the cutting width direction under each tool posture tilt angle and each tool posture tilt angle; Step 4: using the tool posture tilt angle as input and the optimal value of the model coefficient corresponding to the feed direction and the cutting width direction as output to establish a regression prediction model; Step 5: First, substitute the regression prediction model of step 4 into the characterization model of step 1, and then replace the tool posture inclination angle in the characterization model with the machining surface position of the workpiece surface, and then obtain the calculation model of the three-dimensional distribution of residual stress. The three-dimensional distribution residual stress corresponding to the feed direction and the cutting width direction is predicted by the calculation model.

2. The method for calculating the three-dimensional distribution of residual stress in variable rake angle four-axis milling according to claim 1, characterized in that: The characterization model is: ， Where: σ(h) is the residual stress after processing, MPa; h is the depth of the position corresponding to the residual stress, μm; ω and k are the unknown coefficients of the characterization model; and are all constants, =100MPa, =100μm.

3. The method for calculating the three-dimensional distribution of residual stress in variable rake angle four-axis milling according to claim 2, characterized in that: The optimization model is: ， Where: σ exp is the measured value of residual stress, MPa; σ fit is the calculated value of residual stress of the model under corresponding ω and k, MPa; is the average value of the measured residual stress, MPa; ω i is σ fit The weight coefficient, and ω i =1, R 2 is the fitting accuracy.

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