Thin-walled part milling deformation prediction method considering residual stress influence

Abstract

The invention discloses a thin-walled part milling deformation prediction method considering residual stress influence. The method comprises the following steps: (1) establishing an initial residual stress distribution model; (2) constructing a machining residual stress prediction model; (3) establishing an initial residual stress and machining residual stress coupling stress model; and (4) constructing a thin-wall part machining deformation prediction model under the action of the coupling stress. The method is used for accurately calculating the milling deformation of the thin-wall part, and the deformation of the thin-wall part is inhibited by controlling and optimizing the milling process parameters of each milling layer.

Description

Technical Field

[0001] The present invention relates to a method for predicting the milling deformation of thin-walled parts taking into account the influence of residual stress, belonging to the technical field of precision manufacturing of complex thin-walled parts for aerospace, and is mainly used for predicting the machining deformation caused by residual stress during the milling process of complex thin-walled parts. Background Art

[0002] With the rapid development of aviation, aerospace and other industries, thin-walled parts such as aircraft skins, wings, and aircraft engine blades / disks are widely used. Such complex thin-walled parts are mostly made of aluminum alloy materials with the advantages of high specific strength, low density, and good machinability. In addition, during the machining of such aluminum alloy thin-walled parts, due to the violent interaction between the tool and the workpiece, a large amount of cutting force and cutting heat are generated in the material removal process, which will cause a large amount of residual stress to be generated. With the accumulation and redistribution of residual stress, the thin-walled parts will undergo significant machining deformation, which will eventually seriously affect the machining accuracy and quality of the thin-walled parts. Therefore, in order to improve the machining accuracy and quality of thin-walled parts, accurately predicting the milling deformation of thin-walled parts has important engineering application value.

[0003] At present, the analysis of deformation of thin-walled parts caused by residual stress accumulation and redistribution is mainly divided into finite element method, experimental method and analytical method. When predicting the deformation of parts caused by residual stress, the accuracy of finite element method is often restricted by mesh quality and boundary conditions, and it cannot reflect the actual machining situation of thin-walled parts. Although the experimental method can directly reflect the actual machining situation, it has the risk of damaging thin-walled parts. Theoretical analytical method can better predict the deformation of thin-walled parts caused by residual stress. Theoretical analytical method has a wide range of applications in the field of deformation analysis of thin-walled parts, but many studies consider the influence of initial residual stress and machining residual stress on the deformation of thin-walled parts separately, such as [Gao H, Zhang Y, Wu Q, Song J. An analytical model for predicting the machining deformation of a plate blank considers biaxial initial residual stresses. Int J Adv Manuf Technol 2017;93:1473-1486.] The method, in order to study the quantitative relationship between the deformation of thin-walled parts and the initial residual stress, proposes a machining deformation analytical prediction model considering biaxial residual stress. This method does not consider the influence of milling residual stress on the deformation of thin-walled parts, and does not consider the influence of removing each layer of material on the thin-walled parts, which makes the deformation prediction model of thin-walled parts caused by residual stress accumulation and redistribution inaccurate; therefore, the application of this method to the thin-walled part machining deformation prediction model needs further improvement; based on this, the present invention is proposed. Summary of the invention

[0004] In order to solve the problem that the existing methods separately consider the influence of initial residual stress and processing residual stress on the deformation prediction accuracy of thin-walled parts, the present invention proposes a method for predicting the machining deformation of thin-walled parts caused by comprehensive consideration of initial residual stress and processing residual stress - a method for predicting the milling deformation of thin-walled parts considering the influence of residual stress.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solution: a method for predicting milling deformation of thin-walled parts considering the influence of residual stress: comprising the following steps:

[0006] ① Establish the initial residual stress distribution model;

[0007] ②Construct a machining residual stress prediction model;

[0008] ③Establish a coupling stress model of initial residual stress and processing residual stress;

[0009] ④Construct a deformation prediction model for thin-walled parts processing under coupled stress.

[0010] The step flow chart of the present invention is as follows Figure 1 As shown,

[0011] Step ① The specific process is:

[0012] In order to accurately analyze the deformation behavior of thin-walled parts (thin plate substitution, the same below) after milling, the blank is layered along the Z direction into the to-be-processed layer and the processed layer; the to-be-processed layer is marked as S, and the thickness is defined as h, which is removed during the milling process, and the processed layer is regarded as W, which is retained and forms the final shape of the thin-walled part, as shown in Figure 2 As shown; the present invention mainly analyzes the change of the interaction force between the to-be-processed layer S and the processed layer W at each milling stage to reveal the machining deformation mechanism of thin-walled parts;

[0013] In order to further study the deformation behavior of thin-walled parts during milling, the machined layer S is regarded as a whole and the force and moment caused by the initial residual stress are analyzed; the machined layer S is subjected to a force F caused by the initial residual stress in the X direction. SX and moment M SX Similarly, in the Y direction, the layer S to be processed is also subjected to a force F caused by the initial residual stress. SY and moment M SY ,like Figure 3 (a) As shown; in order to obtain the stress state of each milling layer, the layer to be processed S is divided into m layers, and the thickness of each layer is t = h / m, as shown in Figure 3 (b)

[0014] In order to better analyze the force F generated by the initial residual stress in the layer to be processed S S and moment M S , take the i-th layer as an example for analysis, such as Figure 4 As shown, the initial residual stress generates forces F in the X and Y directions. i , expressed as:

[0015]

[0016] In the formula, F x,i and F y,i represents the initial residual stress in layer i X i and Y i The force generated in the direction, σ x,i and σ y,i represents the i-th layer X i and Y i The initial average residual stress in the direction;

[0017] Next, the initial average residual stress σ x,i and σ y,i It is expressed as:

[0018]

[0019] The layer to be processed S is divided into m layers, each of which is subjected to the force F generated by the initial residual stress. i Therefore, in order to accurately describe the total force F generated by the initial residual stress on the layer S to be processed S , the forces on each layer need to be accumulated, and the total force F S It is expressed as:

[0020]

[0021] In addition, the moment M caused by the initial residual stress of the i-th layer S to be processed is i , expressed as:

[0022]

[0023] Where M x,i is the i-th layer X i Moment in the direction, M y,i represents the i-th layer Y i The moment in the direction, ψ x,i and ψ y,i It is expressed as:

[0024]

[0025] In order to accurately describe the total moment M of the layer S to be processed S , the torque of each layer in the to-be-processed layer needs to be accumulated, assuming that Ф(z) and ζ(z)(0≤z≤q) are σ x,i and σ y,i The original function of M S It is expressed as:

[0026]

[0027] where f Sx and f Sy It is expressed as:

[0028]

[0029] For the blank thin-walled parts, the stress is in a balanced state. Therefore, the force F on the to-be-processed layer S and the processed layer W is W and moment M W satisfy:

[0030]

[0031] According to formula (8), the force F on the processing layer W is W and moment MW The force F on the layer to be processed S S and moment M S express:

[0032]

[0033] Next, the force F caused by the initial residual stress release in the machined layer W is analyzed. W and moment M W By analyzing the force F on the layer S to be processed, S and moment M S Convert.

[0034] The specific process of step ② is:

[0035] Based on cutting theory, the mechanical stress generated during milling mainly comes from the shear stress in the first shear zone. and the compressive stress in the third shear zone During the milling process, in the contact area between the tool and the thin-walled part, the shear force acting on the thin-walled part is defined as F si , the normal force is F ni , tangential force is F i , the distance between the differential unit and the tool tip is s i ,like Figure 5 As shown; in order to analyze the cutting force on the differential unit, the differential unit length dsi is selected for analysis;

[0036] During the milling process, the milling force F is represented by the cutting force component on the i-th tooth:

[0037]

[0038] In the formula, and Indicates that the i-th tooth is at X F , Y F and Z F The cutting force component in the direction; N is the number of tool teeth;

[0039] Next, the shear stress The relationship between it and the milling force F is expressed as:

[0040]

[0041] In the formula, and They represent shear angle, friction angle, rake angle, cutting width and cutting depth respectively;

[0042] Extrusion stress The relationship between it and the cutting force F is expressed as:

[0043]

[0044] In order to obtain the relationship between mechanical stress and cutting parameters, combined with reference [Lazoglu I, Ulutan D, Alaca BE, Engin S, Kaftanoglu B. An enhanced analytical model for residual stress prediction in machining. CIRP Annals 2008; 57: 81-84.] and formula (10), formula (11) and formula (12), the mechanical stress is expressed as:

[0045]

[0046] in

[0047]

[0048] During machining, intense friction and shear interaction occurs between the tool and the thin-walled part, which will cause the temperature T in the first deformation zone to sh and the third deformation zone temperature T ru Rapidly rising, such as Figure 6 As shown, and in this area, the shear temperature rise T sh and friction temperature rise T ru It constitutes the total temperature rise T in the area;

[0049] Then, the shear temperature rise T in the total temperature rise T of the region is sh , expressed as:

[0050]

[0051] In the formula, Q sh represents the shear heat source intensity, λw represents the thermal conductivity of the thin-walled part material, and ψ in formula (15) tsh1 It is expressed as:

[0052]

[0053] Where V is the cutting speed, K0 is the zero-order modified Bessel function;

[0054] Shear heat source strength Q sh It is expressed as:

[0055]

[0056] To determine the shear temperature rise T sh The relationship between the cutting parameters and the cutting parameters is obtained by combining equations (15), (16) and (17):

[0057]

[0058] in

[0059]

[0060] In short, the friction temperature rise T in the total temperature rise T in the cutting area is ru It is expressed as:

[0061]

[0062] Where k is the heat transfer coefficient, VB is the wear width of the tool flank, and Q ru represents the friction heat intensity and is expressed as:

[0063]

[0064] Similarly, to determine the friction temperature rise T ru The relationship between the cutting parameters and the cutting parameters is shown in formula (18) and formula (21):

[0065]

[0066] in

[0067]

[0068] In summary, the shear heat T sh and friction heat T ru The total temperature rise T of the composition is expressed as:

[0069] T=T sh (x,z)+T ru (x,z) (76)

[0070] Combining equations (13), (15), (18) and (22), the machining residual stress generated during milling is obtained by superposition of thermal stress and mechanical stress, which can be expressed as:

[0071]

[0072] In the formula, represents the total elastic stress, Table Y F Elastic stress in the direction, ΔT represents the difference between cutting temperature and ambient temperature;

[0073] After the milling of thin-walled parts is completed, as the tool moves away from the thin-walled parts, the mechanical load and thermal load on the machined surface of the thin-walled parts will be unloaded, and the residual stress after unloading is called the machining residual stress; when the mechanical load and thermal load are unloaded, the machining residual stress and strain should meet the following conditions:

[0074]

[0075] In the formula, and After the mechanical load and thermal load of the thin-walled parts are unloaded, the F , Y F , Z F Residual stress redistributed in the direction; and After the mechanical load and thermal load of the thin-walled parts are unloaded, the F , Y F and Z F Strain caused by direction; and is a function that changes with the coordinate Z;

[0076] However, after the processing of thin-walled parts is completed, the residual stress distributed along the Z direction of the thin-walled parts is not zero. F Direction and Y F The strain in the direction is also not zero; therefore, in order to meet the boundary conditions after mechanical and thermal loads are unloaded, these non-zero quantities need to go through a relaxation process to reach the boundary conditions; assuming that the relaxation process requires N′ times in total, and each relaxation increment is expressed as:

[0077]

[0078] Next, during the stress relaxation process, two relaxation states will occur, one is elastic relaxation only, and the other is elastic-plastic relaxation; therefore, if only elastic relaxation occurs, the stress relaxation increment is expressed as:

[0079]

[0080] However, if elastic-plastic relaxation occurs, the stress relaxation increment is expressed as:

[0081]

[0082] Where C and D are represented by:

[0083]

[0084] The specific process of step ③ is:

[0085] During the milling process, there are not only initial residual stresses inside thin-walled parts, but also machining residual stresses caused by the coupling of cutting force and cutting heat. Therefore, when studying the machining deformation of thin-walled parts, it is necessary to comprehensively consider the initial residual stress and machining residual stress. During the milling process, the stress state of thin-walled parts changes due to the gradual removal of initial residual stress and the generation of machining residual stress. As the remaining initial residual stress and machining residual stress accumulate, redistribute and release, the thin-walled parts are deformed. The deformation diagram is shown in the figure. Figure 7 As shown, in Figure 7 In the figure, the distance between the stress layer and the neutral layer of the current milling surface is expressed as:

[0086]

[0087] In the formula, σ xy,ui and σ xy,di is the residual stress caused by milling on the upper and lower surfaces of the i-th layer, δ ui and δ di Indicates the distance from the neutral layer to the upper and lower surface layers of thin-walled parts;

[0088] Depend on Figure 7 (b) Know that δ ui and δ di The relationship between them is expressed as:

[0089] δ ui (x,y,z)+δ di (x,y,z)=δ rei (x,y,z) (84)

[0090] After the i-th milling, the machining residual stress σ on the lower surface of the thin-walled part xy,di It is expressed as:

[0091]

[0092] In addition, the distance δ from the neutral layer to the lower surface of the thin-walled part di It is expressed as:

[0093] δ di (x,y,z)=δ rei (x,y,z)-δ ui (x,y,z) (86)

[0094] Combining equations (33) and (34), the distance δ from the neutral layer of a thin-walled part to its upper surface is ui It is expressed as:

[0095]

[0096] Combining equations (31), (33) to (35), we know that the machining residual stress σ on the jth layer (j>1) of the thin-walled part after milling is mixy,i,j It is expressed as:

[0097]

[0098] In summary, during the milling process, when the i-th layer of material of a thin-walled part is milled, considering the release of the initial residual stress and the generation of the machining residual stress, the thin-walled part will have a coupled residual stress generated by the initial residual stress and the machining residual stress, which can be expressed as:

[0099]

[0100] In the formula, σ rexy,mii,j It represents the coupled residual stress of the jth layer after the i-th milling of the thin-walled part;

[0101] Coupled residual stress σ rexy,mii,j and the equivalent initial residual stress σ eq,i+j+2 The relationship between them is expressed as:

[0102]

[0103] Next, in order to obtain the deformation of the thin-walled part caused by the coupled residual stress, the force F on the i-th layer of the thin-walled part is calculated according to formula (38): ei and moment M ei , expressed as:

[0104]

[0105] In the formula, F ex,i and F ey,i is the force caused by the coupled residual stress in the X and Y directions after milling the i-th layer, M ex,i and M ey,i is the moment generated by the coupling stress in the X and Y directions.

[0106] The specific process of step ④ is:

[0107] In the milling of thin-walled parts, as the material is removed, the initial residual stress inside the thin-walled parts is removed and released, and the residual stress generated and released during milling causes the original stress balance state of the thin-walled parts to be broken. At this time, the thin-walled parts will reach a new stress balance state through deformations such as bending and torsion. At this time, the deformation of the thin-walled parts is expressed as:

[0108]

[0109] Where 1 / R x and 1 / R yThey represent the curvature of the thin plate in the X and Y directions, μ represents the Poisson's ratio of the thin-walled part material, and D p is the bending stiffness, expressed as:

[0110]

[0111] In the formula, I P represents the section moment of inertia of the thin plate, and

[0112]

[0113] Next, when calculating the deformation of thin-walled parts, the deformation curvature of thin-walled parts is expressed by the second-order partial derivative of the deflection deformation:

[0114]

[0115] Then, integrating equation (44) in the range from 0 to the milling thickness, the deflection deformation is expressed as:

[0116]

[0117] Combining equations (41) and (45), the deflection deformation of thin-walled parts can be expressed as:

[0118]

[0119] In order to more clearly analyze the deformation of the thin-walled workpiece when milling each layer, combining equations (40) and (46), the machining deformation of the i-th layer after milling of the thin-walled part is expressed as:

[0120]

[0121] Among them, A i , B i It is expressed as:

[0122]

[0123] Then, after the milling is completed, the layer to be machined S is completely machined, and a total force caused by the release of coupled residual stress is introduced through equation (39):

[0124]

[0125] Similarly, the layer S to be processed is completely processed, and the torque generated by the coupled residual stress is expressed as:

[0126]

[0127] Therefore, after the material of the machining layer is removed, the deformation of the thin-walled part caused by the coupling of the initial residual stress of the thin-walled part and the milling residual stress is expressed as:

[0128]

[0129] in

[0130]

[0131] In summary, through the above calculations, a thin-walled parts milling deformation prediction method considering the influence of residual stress is proposed, which is used to accurately calculate the milling deformation of thin-walled parts and suppress the deformation of thin-walled parts by controlling and optimizing the milling process parameters of each milling layer;

[0132] By adopting the above technical solution, the present invention has the following beneficial effects:

[0133] (1) In the model, the initial residual stress of thin-walled parts and the coupling effect of their processing residual stress are comprehensively considered, which can more truly reflect the milling processing state and more effectively predict the deformation of thin-walled parts than the models proposed in relevant references;

[0134] (2) The present invention establishes a method for predicting the milling deformation of thin-walled parts taking into account the influence of residual stress, accurately predicts the milling deformation of each layer of the thin-walled parts and its total deformation, and suppresses the deformation of the thin-walled parts by controlling and optimizing the milling process parameters of each milling layer. BRIEF DESCRIPTION OF THE DRAWINGS

[0135] Figure 1 is a flow chart of the steps of the present invention;

[0136] Figure 2 Remove material and stress conditions of thin-walled parts for the present invention;

[0137] Figure 3 Schematic diagram of a sublayer of the layer S to be processed according to the present invention;

[0138] Figure 4 is the force analysis diagram of the i-th layer of the present invention;

[0139] Figure 5 It is a schematic diagram of mechanical stress of the present invention;

[0140] Figure 6 It is a schematic diagram of thermal stress of the present invention;

[0141] Figure 7 Schematic diagram of residual stress distribution during the milling process of the i-th layer of the present invention;

[0142] Figure 8 It is a comparison chart of theoretical calculation and experimental results of the present invention. DETAILED DESCRIPTION

[0143] The feasibility and effectiveness of the proposed method are illustrated below by taking aluminum alloy thin-walled parts as an example. Figure 1As shown, a method for predicting milling deformation of thin-walled parts considering the influence of residual stress of the present invention comprises the following steps:

[0144] ①Establish initial residual stress distribution model

[0145] In order to better analyze the initial residual stress state inside the thin-walled parts, any differential unit inside the thin-walled parts is selected to analyze the shear stress inside the micro-prototype, which is expressed as:

[0146]

[0147] In the formula, τ xy,i is the shear stress of the ith microelement x on y, τ yx,i is the shear stress of y on x in the ith microelement; τ yz,i is the shear stress of the ith microelement y on z, τ zy,i is the shear stress of z on y in the ith microelement; τ xz,i is the shear stress of the ith microelement x on z, τ zx,i is the shear stress of z on x in the ith microelement;

[0148] When a thin-walled part is subjected to force in a plane, assuming that the external force does not change along the thickness direction of the plate, the stress at any point in the plate is independent of the coordinate Z and only related to the coordinates X and Y, expressed as:

[0149] τ xz,i (x,y,z)=τ yz,i (x,y,z)=0 (2)

[0150] When a thin-walled part is not subjected to external forces, its internal initial residual stress is in a state of equilibrium; in this state of equilibrium, the stresses of various parts in the thin-walled part offset each other, satisfying the force equilibrium condition (∑F x =0,∑F y =0), and at the same time, the moment equilibrium condition is satisfied, that is, the resultant moment of the thin-walled part in all directions is also zero (∑M c =0), expressed as:

[0151]

[0152] In order to further study the deformation behavior of thin-walled parts during milling, the machined layer S is regarded as a whole and the force and moment caused by the initial residual stress are analyzed; the machined layer S is subjected to a force F caused by the initial residual stress in the X direction. SX and moment M SX Similarly, in the Y direction, the layer S to be processed is also subjected to a force F caused by the initial residual stress. SY and moment M SY ,like Figure 3(a) As shown; in order to obtain the stress state of different milling layers, the layer to be processed S is divided into m layers, and the thickness of each layer is t = h / m, as shown in Figure 3 (b)

[0153] In order to better analyze the force F generated by the initial residual stress in the layer to be processed S i and moment M i , take the i-th layer as an example for analysis, such as Figure 4 As shown, the residual stress generates force F in the X and Y directions i , expressed as:

[0154]

[0155] In the formula, F x,i and F y,i represents the initial residual stress in layer i X i and Y i The force generated in the direction, σ x,i and σ y,i represents the i-th layer X i and Y i The initial average residual stress in the direction;

[0156] Next, the initial average residual stress σ x,i and σ y,i It is expressed as:

[0157]

[0158] The layer to be processed S is divided into m layers, and each layer is subjected to the force generated by the initial residual stress. Therefore, in order to accurately describe the total force on the layer to be processed S, the force on each layer needs to be accumulated to obtain the force F caused by the initial residual stress on the layer to be processed S. S , expressed as:

[0159]

[0160] In addition, the moment M caused by the initial residual stress of the i-th layer S to be processed is i , expressed as:

[0161]

[0162] Where M x,i is the i-th layer X i Moment in the direction, M y,i represents the i-th layer Y i The moment in the direction, ψ x,i and ψ y,i It is expressed as:

[0163]

[0164] In order to accurately describe the total moment M of the layer S to be processed S , the torque of each layer in the to-be-processed layer needs to be accumulated, assuming that Ф(z) and ζ(z)(0≤z≤q) are σ x,i and σ y,i The original function of M S It is expressed as:

[0165]

[0166] where f Sx and f Sy It is expressed as:

[0167]

[0168] For the blank thin-walled parts, the stress is in a balanced state. Therefore, the force F on the to-be-processed layer S and the processed layer W is W and moment M W satisfy:

[0169]

[0170] According to formula (11), the force F on the processing layer W is W and moment M W The force F on the layer to be processed S S and moment M S express:

[0171]

[0172] Next, the force F caused by the release of residual stress in thin-walled parts is analyzed. W and moment M W By analyzing the force F on the layer S to be processed, S and moment M S Convert.

[0173] ②Construct a machining residual stress prediction model

[0174] Based on cutting theory, the mechanical stress generated during milling mainly comes from the shear stress in the first shear zone. and the compressive stress in the third shear zone During the milling process, in the contact area between the tool and the thin-walled part, the shear force acting on the thin-walled part is defined as F si , the normal force is F ni , tangential force is F i , the distance between the differential unit and the tool tip is s i ,like Figure 5As shown; in order to analyze the cutting force on the differential unit, the differential unit length dsi is selected for analysis;

[0175] During the milling process, the milling force F is represented by the cutting force component on the i-th tooth:

[0176]

[0177] In the formula, and Indicates that the i-th tooth is at X F , Y F and Z F The cutting force component in the direction; N is the number of tool teeth;

[0178] Next, the shear stress The relationship between it and the milling force F is expressed as:

[0179]

[0180] In the formula, and They represent shear angle, friction angle, rake angle, cutting width and cutting depth respectively;

[0181] Similarly, the compressive stress The relationship between it and the cutting force F is expressed as:

[0182]

[0183] In order to obtain the relationship between mechanical stress and cutting parameters, combined with reference [Lazoglu I, Ulutan D, Alaca BE, Engin S, Kaftanoglu B. An enhanced analytical model for residual stress prediction in machining. CIRP Annals 2008; 57: 81-84.] and equations (13) and (15), the mechanical stress is expressed as:

[0184]

[0185] in

[0186]

[0187] During machining, intense friction and shear interaction occurs between the tool and the thin-walled part, which will cause the temperature T in the first deformation zone to sh and the third deformation zone temperature T ru Rapidly rising, such as Figure 6 As shown, and in this area, the shear temperature rise Tsh and friction temperature rise T ru It constitutes the total temperature rise T in the area;

[0188] Then, the shear temperature rise T in the total temperature rise T of the region is sh , expressed as:

[0189]

[0190] In the formula, Q sh represents the shear heat source intensity, λw represents the thermal conductivity of the thin-walled part material, and ψ in formula (18) tsh1 It is expressed as:

[0191]

[0192] Where V is the cutting speed, K0 is the zero-order modified Bessel function;

[0193] Shear heat source strength Q sh It is expressed as:

[0194]

[0195] To determine the shear temperature rise T sh The relationship between the cutting parameters and the cutting parameters is obtained by combining equations (18), (19) and (20):

[0196]

[0197] in

[0198]

[0199] In short, the friction temperature rise T in the total temperature rise T in the cutting area is ru It is expressed as:

[0200]

[0201] Where k is the heat transfer coefficient, VB is the wear width of the tool flank, and Q ru represents the friction heat intensity and is expressed as:

[0202]

[0203] Similarly, to determine the friction temperature rise T ru The relationship between θ and cutting parameters is shown in equations (21) to (24):

[0204]

[0205] in

[0206]

[0207] In summary, the shear heat T sh and friction heat T ru The total temperature rise T of the composition is expressed as:

[0208] T=T sh (x,z)+T ru (x,z) (27)

[0209] Combining equations (16), (18), (21) and (25), the machining residual stress generated during milling is obtained by superposition of thermal stress and mechanical stress, which can be expressed as:

[0210]

[0211] In the formula, represents the total elastic stress, Represents Y F Elastic stress in the direction, ΔT represents the difference between cutting temperature and ambient temperature;

[0212] After the milling of thin-walled parts is completed, as the tool moves away from the thin-walled parts, the mechanical load and thermal load on the machined surface of the thin-walled parts will be unloaded, and the residual stress after unloading is called the machining residual stress; when the mechanical load and thermal load are unloaded, the machining residual stress and strain should meet the following conditions:

[0213]

[0214] In the formula, and After the mechanical load and thermal load of the thin-walled parts are unloaded, the F , Y F , Z F Residual stress redistributed in the direction; and After the mechanical load and thermal load of the thin-walled parts are unloaded, the F , Y F and Z F Strain caused by direction; and is a function that changes with the coordinate Z;

[0215] However, after the processing of thin-walled parts is completed, the residual stress distributed along the Z direction of the thin-walled parts is not zero. F Direction and Y F The strain in the direction is also not zero; therefore, in order to meet the boundary conditions after mechanical and thermal loads are unloaded, these non-zero quantities need to go through a relaxation process to reach the boundary conditions; assuming that the relaxation process requires N′ times in total, and each relaxation increment is expressed as:

[0216]

[0217] Next, during the stress relaxation process, two relaxation states will occur, one is elastic relaxation only, and the other is elastic-plastic relaxation; therefore, if only elastic relaxation occurs, the stress relaxation increment is expressed as:

[0218]

[0219] However, if elastic-plastic relaxation occurs, the stress relaxation increment is expressed as:

[0220]

[0221] Where C and D are represented by:

[0222]

[0223] ③Establish the coupling stress model of initial residual stress and processing residual stress

[0224] During the milling process, there are not only initial residual stresses inside thin-walled parts, but also machining residual stresses caused by the coupling of cutting force and cutting heat. Therefore, when studying the machining deformation of thin-walled parts, it is necessary to comprehensively consider the initial residual stress and machining residual stress. During the milling process, the stress state of thin-walled parts changes due to the gradual removal of initial residual stress and the generation of machining residual stress. As the remaining initial residual stress and machining residual stress accumulate, redistribute and release, the thin-walled parts are deformed. The deformation diagram is shown in the figure. Figure 7 As shown, in Figure 7 In the figure, the distance between the stress layer and the neutral layer of the current milling surface is expressed as:

[0225]

[0226] In the formula, σ xy,ui and σ xy,di is the residual stress caused by milling on the upper and lower surfaces of the i-th layer, δ ui and δ di Indicates the distance from the neutral layer to the upper and lower surface layers of thin-walled parts;

[0227] Depend on Figure 7 (b) Know that δ ui and δ di The relationship between them is expressed as:

[0228] δ ui (x,y,z)+δ di (x,y,z)=δ rei (x,y,z) (35)

[0229] According to the triangle similarity theory, after the i-th milling, the machining residual stress σ on the lower surface of the thin-walled part isxy,di It is expressed as:

[0230]

[0231] In addition, the distance δ from the neutral layer to the lower surface of the thin-walled part di It is expressed as:

[0232] δ di (x,y,z)=δ rei (x,y,z)-δ ui (x,y,z) (37)

[0233] Combining equations (36) and (37), the distance δ from the neutral layer of a thin-walled part to its upper surface is ui It is expressed as:

[0234]

[0235] Combining equations (34), (36) to (38), we know that the machining residual stress σ on the jth layer (j>1) of the thin-walled part after milling is mixy,i,j It is expressed as:

[0236]

[0237] In summary, during the milling process, when the i-th layer of material of a thin-walled part is milled, considering the release of the initial residual stress and the generation of the machining residual stress, the thin-walled part will have a coupled residual stress generated by the initial residual stress and the machining residual stress, which can be expressed as:

[0238]

[0239] In the formula, σ rexy,mii,j It represents the coupled residual stress of the jth layer after the i-th milling of the thin-walled part;

[0240] Coupled residual stress σ rexy,mii,j and the equivalent initial residual stress σ eq,i+j+2 The relationship between them is expressed as:

[0241]

[0242] Next, in order to obtain the deformation of the thin-walled part caused by the coupled residual stress, the force F on the i-th layer of the thin-walled part is calculated according to formula (41): ei and moment M ei , expressed as:

[0243]

[0244] In the formula, F ex,i and F ey,iis the force caused by the coupled residual stress in the X and Y directions after milling the i-th layer, M ex,i and M ey,i is the moment generated by the coupling stress in the X and Y directions.

[0245] ④Construct a deformation prediction model for thin-walled parts processing under coupled stress

[0246] In the milling of thin-walled parts, as the material is removed, the initial residual stress inside the thin-walled parts is removed and released, and the residual stress generated and released during milling causes the original stress balance state of the thin-walled parts to be broken. At this time, the thin-walled parts will reach a new stress balance state through deformations such as bending and torsion. At this time, the deformation of the thin-walled parts is expressed as:

[0247]

[0248] Where 1 / R x and 1 / R y They represent the curvature of the thin plate in the X and Y directions, μ represents the Poisson's ratio of the thin-walled part material, and D p is the bending stiffness, expressed as:

[0249]

[0250] In the formula, I P represents the section moment of inertia of the thin plate, and

[0251]

[0252] Next, when calculating the deformation of thin-walled parts, the deformation curvature of thin-walled parts is expressed by the second-order partial derivative of the deflection deformation:

[0253]

[0254] Then, integrating equation (47) in the range from 0 to the milling thickness, the deflection deformation is expressed as:

[0255]

[0256] Combining equations (44) and (48), the deflection deformation of thin-walled parts can be expressed as:

[0257]

[0258] In order to more clearly analyze the deformation of the thin-walled workpiece when milling each layer, combined with equations (43) and (49), the machining deformation of the i-th layer after milling of the thin-walled part is expressed as:

[0259]

[0260] Among them, A i , Bi It is expressed as:

[0261]

[0262] Then, after the milling is completed, the layer to be machined S is completely machined, and a total force caused by the release of coupled residual stress is introduced through equation (42):

[0263]

[0264] Similarly, the layer S to be processed is completely processed, and the torque generated by the coupled residual stress is expressed as:

[0265]

[0266] Therefore, after the material of the machining layer is removed, the deformation of the thin-walled part caused by the coupling of the initial residual stress of the thin-walled part and the milling residual stress is expressed as:

[0267]

[0268] in

[0269]

[0270] In summary, through the above calculations, a thin-walled part milling deformation prediction method considering the influence of residual stress is proposed, which is used to accurately calculate the milling deformation of thin-walled parts and suppress the deformation of thin-walled parts by controlling and optimizing the milling process parameters of each milling layer.

[0271] The present invention uses an aluminum alloy thin-walled part to verify its feasibility; the experiment verifies the feasibility and practicability of the present invention; the following uses a specific example to illustrate the effect of the present invention.

[0272] The aluminum alloy thin-walled parts used in the test are 330mm long, 40mm wide and 4mm thick. The physical parameters of the aluminum alloy thin-walled parts are shown in the following table. During processing, a three-axis milling center (VMC-850E, Chinese) was used to mill the thin-walled parts, and the spindle speed was 2500rev / min. The tool used was a tungsten steel milling cutter with 4 teeth, a helix angle of 30° and a tool diameter of 12m. After processing, a three-coordinate measuring instrument (Global Status 9128, USA) was used to measure the deformation of the thin-walled parts. The comparison between the deformation measurement results and the theoretical calculation results is shown in the figure below. Figure 8 As shown; Figure 8 The maximum error between the deformation measurement results and the theoretical calculation results is 13%, indicating that the deformation prediction is relatively accurate.

[0273] Physical and mechanical properties of aluminum alloy:

[0274]

[0275] This embodiment does not impose any formal limitation on the shape, material, structure, etc. of the present invention. Any simple modification, equivalent change and modification made to the above embodiment based on the technical essence of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for predicting milling deformation of thin-walled parts considering the influence of residual stress, characterized by: The following steps are included: ① Establish the initial residual stress distribution model; ②Construct a machining residual stress prediction model; ③Establish a coupling stress model of initial residual stress and processing residual stress; ④Construct a deformation prediction model for thin-walled parts processing under coupled stress.

2. A method for predicting milling deformation of thin-walled parts considering the influence of residual stress according to claim 1, characterized in that: The initial residual stress distribution model is established, and the calculation formula is as follows: In the formula, F x,i and F y,i represents the initial residual stress in layer i X i and Y i The force generated in the direction, σ x,i and σ y,i represents the i-th layer X i and Y i The initial average residual stress in the direction; Initial average residual stress σ x,i and σ y,i It is expressed as: The forces on each layer are accumulated to obtain the total force F generated by the initial residual stress on the layer S to be processed. S , total force F S It is expressed as: The moment M caused by the initial residual stress of the i-th layer S to be processed i , expressed as: Where M x,i is the i-th layer X i Moment in the direction, M y,i represents the i-th layer Y i The moment in the direction, ψ x,i and ψ y,i It is expressed as: The torque of each layer in the to-be-processed layer is accumulated to obtain the total torque M of the to-be-processed layer S. S , assuming that Ф(z) and ζ(z)(0≤z≤q) are σ x,i and σ y,i The original function of M S It is expressed as: where f Sx and f Sy It is expressed as: The force F on the layer to be processed S and the processed layer W W and moment M W satisfy: According to formula (8), the force F on the processed layer W is W and moment M W The force F on the layer to be processed S S and moment M S express: Analysis of the force F caused by the initial residual stress release in the machined layer W W and moment M W By analyzing the force F on the layer S to be processed, S and moment M S Convert.

3. The method for predicting milling deformation of thin-walled parts considering the influence of residual stress according to claim 1, characterized in that: The calculation formula of the machining residual stress prediction model is as follows: Where, F represents the milling force; and Indicates that the i-th tooth is at X F , Y F and Z F The cutting force component in the direction; N is the number of tool teeth; Shear stress The relationship between it and the milling force F is expressed as: In the formula, and They represent shear angle, friction angle, rake angle, cutting width and cutting depth respectively; Extrusion stress The relationship between it and the cutting force F is expressed as: Substituting equations (10) and (11) into equation (12), we can obtain the relationship between mechanical stress and cutting parameters. The mechanical stress is expressed as: in Severe friction and shear interaction occurs between the tool and the thin-walled part, which will cause the temperature T sh and the third deformation zone temperature T ru Rapidly increases, and in this area, the shear temperature rise T sh and friction temperature rise T ru It constitutes the total temperature rise T in the area; The total temperature rise T in this area is the shear temperature rise T sh , expressed as: In the formula, Q sh represents the shear heat source intensity, λw represents the thermal conductivity of the thin-walled part material, and ψ in formula (15) tsh1 It is expressed as: Where V is the cutting speed, K0 is the zero-order modified Bessel function; Shear heat source strength Q sh It is expressed as: Substituting equations (15) and (16) into equation (17), the shear temperature rise T sh The relationship with cutting parameters is expressed as: in Friction temperature rise T in the total temperature rise T in the cutting area ru It is expressed as: Where k is the heat transfer coefficient, VB is the wear width of the tool flank, and Q ru represents the friction heat intensity, expressed as: Substituting equation (21) into equation (18), the friction temperature rise T ru The relationship with cutting parameters is expressed as: in By shear heat T sh and friction heat T ru The total temperature rise T of the composition is expressed as: T=Tsh(x,z)+Tru(x,z) (24) Substituting equations (15), (18) and (22) into equation (13), the machining residual stress is expressed as: In the formula, represents the total elastic stress, Represents Y F Elastic stress in the direction, ΔT represents the difference between cutting temperature and ambient temperature; After the milling of thin-walled parts is completed, the mechanical load and thermal load on the machined surface of the thin-walled parts will be unloaded, and the residual stress after unloading is the machining residual stress; when the mechanical load and thermal load are unloaded, the machining residual stress and strain meet the following requirements: In the formula, and After the mechanical load and thermal load of the thin-walled parts are unloaded, the F , Y F , Z F Residual stress redistributed in the direction; and After the mechanical load and thermal load of the thin-walled parts are unloaded, the F , Y F and Z F Strain caused by direction; and is a function that changes with the coordinate Z; After the processing of thin-walled parts is completed, in order to meet the boundary conditions after the mechanical load and thermal load are unloaded, these non-zero quantities need to go through a relaxation process to reach the boundary conditions; assuming that the relaxation process requires N′ times in total, and each relaxation increment is expressed as: During the stress relaxation process, two relaxation states will occur, one is elastic relaxation and the other is elastoplastic relaxation; when elastic relaxation occurs, the stress relaxation increment is expressed as: When elastic-plastic relaxation occurs, the stress relaxation increment is expressed as: Where C and D are represented by:

4. A method for predicting milling deformation of thin-walled parts considering the influence of residual stress according to claim 3, characterized in that: The coupling stress model of initial residual stress and processing residual stress is established, and the calculation formula is as follows: In the formula, σ xy,ui and σ xy,di is the residual stress caused by milling on the upper and lower surfaces of the i-th layer, δ ui and δ di Indicates the distance from the neutral layer to the upper and lower surface layers of thin-walled parts; δ ui and δ di The relationship between them is expressed as: δui(x,y,z)+δdi(x,y,z)=δrei(x,y,z) (32) After the i-th milling, the machining residual stress σ on the lower surface of the thin-walled part xy,di It is expressed as: The distance δ from the neutral layer to the lower surface of a thin-walled part di It is expressed as: δdi(x,y,z)=δrei(x,y,z)-δui(x,y,z) (34) Substituting equation (33) into equation (34), the distance δ from the neutral layer of the thin-walled part to its upper surface is ui It is expressed as: Substituting equations (33) to (35) into equation (31), the machining residual stress σ mixy,i,j It is expressed as: During the milling process, thin-walled parts will have coupled residual stress generated by the initial residual stress and the processing residual stress, which can be expressed as: In the formula, σ rexy,mii,j It represents the coupled residual stress of the jth layer after the i-th milling of the thin-walled part; Coupled residual stress σ rexy,mii,j and the equivalent initial residual stress σ eq,i+j+2 The relationship between them is expressed as: According to formula (38), calculate the force F on the i-th layer of the thin-walled part ei and moment M ei , expressed as: In the formula, F ex,i and F ey,i is the force caused by the coupled residual stress in the X and Y directions after milling the i-th layer, M ex,i and M ey,i is the moment generated by the coupling stress in the X and Y directions.

5. The method for predicting milling deformation of thin-walled parts considering the influence of residual stress according to claim 4, characterized in that: The thin-walled parts machining deformation prediction model under the action of coupled stress is constructed, and the calculation formula is as follows: Where 1 / R x and 1 / R y They represent the curvature of the thin plate in the X and Y directions, μ represents the Poisson's ratio of the thin-walled part material, and D p is the bending stiffness, expressed as: In the formula, I P represents the section moment of inertia of the thin plate, expressed as: When calculating the deformation of thin-walled parts, the deformation curvature of thin-walled parts is expressed by the second-order partial derivative of the deflection deformation: Integrating equation (44) in the range from 0 to milling thickness, the deflection deformation is expressed as: Substituting equation (44) into (45), the deflection deformation of thin-walled parts can be expressed as: Substituting equation (40) into equation (46), the machining deformation of the i-th layer after milling of thin-walled parts is expressed as: Among them, A i , B i It is expressed as: Through equation (39), a total force F caused by the release of coupled residual stress is introduced: eS : The torque generated by the coupled residual stress is expressed as: The total milling deformation of thin-walled parts caused by the coupling of initial residual stress and milling residual stress is expressed as: in The above calculation is used to accurately calculate the milling deformation of thin-walled parts, and the deformation of thin-walled parts can be suppressed by controlling and optimizing the milling process parameters of each milling layer.

Images