CN106965032A

CN106965032A - Thin-wall part milling parameter suppressing method

Info

Publication number: CN106965032A
Application number: CN201710171598.4A
Authority: CN
Inventors: 万敏; 党学斌; 张卫红; 杨昀; 马颖超
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2017-03-22
Filing date: 2017-03-22
Publication date: 2017-07-21
Anticipated expiration: 2037-03-22
Also published as: CN106965032B

Abstract

The invention discloses a chatter suppressing method for milling thin-walled parts, which is used to solve the technical problem that the existing milling stability prediction method is poor in practicability. The technical solution is to locally modify the dynamic parameters of thin-walled parts through additional mass, establish an efficient processing method to improve the stability region of milling, and provide a reliable parameter selection range for high-speed milling of thin-walled parts; the final use of optimization Algorithm selection can realize chatter-free and high-efficiency machining parameters, and realize high-speed chatter-free milling of thin-walled parts. The present invention establishes an efficient processing method to improve the stable region of milling by partially modifying the dynamic parameters of the thin-walled parts, and better solves the problem of poor rigidity at both ends of the starting and ending positions of the workpiece and the small range of the stable region , which seriously restricts the selection of processing parameters in the milling process; it provides a reliable parameter selection range for high-speed milling of thin-walled parts, realizes high-speed chatter-free milling of thin-walled parts, and has good practicability.

Description

Method for inhibiting milling vibration of thin-wall part

Technical Field

The invention belongs to the field of thin-wall part manufacturing, and particularly relates to a milling chatter suppression method for a thin-wall part.

Background

Document 1 "Song Q, Liu Z, Wan Y, et al application of Sherman-Morrison-Woodbury for a glass in an alternating dynamic of a peripheral milling for a thin-walled component [ J ]. International Journal of Mechanical Sciences,2015,96-97: 79-90" discloses a milling stability prediction method using the Sherman-Morrison-Woodbury formula to take into account the effect of material removal on the kinetic parameters of thin-walled parts during milling. The method comprises the steps of dispersing a milling process, obtaining a variation rule of a kinetic parameter of a dispersed thin-wall part along with material removal in the milling process through a Sherman-Morrison-Woodbury formula so as to obtain a corresponding kinetic parameter, then obtaining a relation between the axial rotation speed and the axial cutting depth in each dispersing process by utilizing a stability solving equation, and finally obtaining a prediction three-dimensional graph of influence of material removal on stability in the milling process.

Document 2 "Yang Y, Zhang WH, Ma YC, et al, character prediction for using a thin-walled workpiece with a curved surface [ J ]. International journal of Machine Tools and manufacturing, 2016,109: 36-48" discloses a milling stability prediction method that considers the variation of the dynamic parameters of the workpiece at different tool milling positions and axial heights at the same time. The method comprises the steps of firstly dispersing a cutter and a workpiece along the axial direction to obtain a kinetic equation of each dispersed part. And then dispersing the milling process to obtain a kinetic equation of each milling process. And finally, solving the kinetic equation to obtain a milling stability prediction method considering the milling position and the axial height kinetic parameter change.

The above documents all consider the influence of material removal on the dynamic parameters of the workpiece in the milling process, and predict the stable regions at different tool positions; however, the problems of poor workpiece rigidity and low milling stability region at the initial position and the final position of the milling process are not effectively solved, so that the selectable range of parameters of the milling process is small, and the processing efficiency cannot be improved.

Disclosure of Invention

The invention provides a thin-wall part milling chatter suppression method, aiming at overcoming the defect that the existing milling stability prediction method is poor in practicability. The method establishes an efficient processing technique method to improve the stable domain of milling processing through local modification of the dynamic parameters of the thin-wall part by additional mass, and provides a reliable parameter selection range for high-speed milling processing of the thin-wall part; finally, the optimization algorithm is used for selecting machining parameters capable of achieving flutter-free and high efficiency, and high-speed flutter-free milling machining of the thin-wall part is achieved. According to the invention, an efficient processing method is established to improve the stable region of milling by locally modifying the dynamic parameters of the thin-wall part, so that the problems that the rigidity of two ends of the starting position and the ending position of a workpiece is poor, the stable region range is small, and the selection of the processing parameters in the milling process is seriously restricted are solved; the method provides a reliable parameter selection range for the high-speed milling of the thin-wall part, and realizes the high-speed non-flutter milling of the thin-wall part.

The technical scheme adopted by the invention for solving the technical problems is as follows: a thin-wall part milling chatter suppression method is characterized by comprising the following steps:

firstly, establishing a milling dynamic model which is in multipoint contact and considers the deformation of a cutter and a workpiece; the motion equation of the milling system is as follows:

wherein,_t(t) is a vector representing the modal displacement of the tool;_wp(t) is a vector representing modal displacement of the workpiece; zeta_tDiagonal matrix, ζ, representing the damping ratio of the tool_wpA diagonal matrix representing a damping ratio of the workpiece; omega_tA diagonal matrix representing the natural frequency of the tool; omega_wpA diagonal matrix representing the natural frequency of the workpiece; u shape_tRepresenting the modal shape, U, of the tool after mass normalization_wpRepresenting the modal shape of the workpiece after mass normalization; q represents the number of nodes for differentiating the tool from the workpiece in the axial direction; f (t) represents a matrix of milling forces at each contact point;

step two, after the selected milling cutter is installed on a main shaft of a machine tool, measuring the feeding direction of the cutter and modal parameters vertical to the feeding direction by adopting a multi-point tapping test method and a linear interpolation method; zeta_m,t,x，ζ_m,t,yRepresents the damping ratio of the mth order; omega_m,t,x，ω_m,t,yA system natural frequency representing the mth order; u shape_m,t,x，U_m,t,yIs a matrix of dimension q × 1, representing the mode shape of the mth order of the system mass normalization;

step three, establishing a finite element model of the thin-wall workpiece; in the process of establishing the model, a set of removed materials, final workpieces and additional mass is respectively established; giving the model corresponding material properties andadding constraints and loads which are consistent with actual processing to the workpiece, then carrying out finite element analysis to obtain the natural frequency of the whole workpiece, extracting the mass matrix and the rigidity matrix of each unit, finally assembling to obtain a whole workpiece model and the mass matrix and the rigidity matrix of the additional mass, and further obtaining the natural frequency omega of each order of the whole workpiece model_wpSum mode vibration type U_wp；

Step four, assuming that the damping ratio is unchanged, extracting the damping characteristic of the workpiece by using a hammering mode experiment; determining a damping ratio matrix zeta of a workpiece by measuring the frequency response function of the workpiece at different points and fitting it_wp；

Step five, using the modal parameters obtained by the test in the step two and the natural frequency omega of each order of the whole workpiece model obtained in the step three and the step four_wpNormal mode vibration type U_wpAnd damping ratio matrix ζ of workpiece_wpSubstituting the obtained result into the step I, respectively solving the state equations of the tool at the milling initial position and the milling final position by using a semi-discrete method to obtain the axial cutting depth a_pAnd a stability lobe graph of the milling initial position and the milling final position with the main shaft rotating speed n as a variable;

step six, the maximum material removal rate MRR is an objective function, and the MRR is a_p×a_e×n×N×f；a_pIndicating axial cutting depth, a_eThe radial cutting depth is represented, N represents the rotating speed of a main shaft, N represents the number of cutter teeth, and f represents the feed amount of each tooth; radial cutting depth a during milling_eThe number N of cutter teeth and the feed amount f of each tooth are determined in advance; by axial cutting-in of a_pAnd a main shaft rotating speed n variable, setting population size, random seed generation probability, mutation probability, cross probability and genetic algebra parameters by respectively taking the stability lobe graphs of the milling initial position and the milling end position obtained in the step five as constraints, and respectively obtaining optimized axial cutting depths a of the milling initial position and the milling end position by utilizing a genetic algorithm_pAnd a spindle speed n; selecting a corresponding to the initial position and the end position_pThe smallest of which is the selected processing parameter;

step seven, modifyingThe material density rho and the Young modulus E in the material attribute change the mass matrix and the rigidity matrix of the additional mass, the material density rho and the Young modulus E in the material attribute are modified by using a Taguchi method orthogonal test to change the mass matrix and the rigidity matrix of the additional mass, and then the dynamic parameters of the modified workpiece are obtained through assembly; substituting the new kinetic parameters into the fifth step to obtain a stability lobe graph corresponding to the orthogonal test; through the sixth step, the MRR corresponding to the Taguchi method orthogonal experiment and the axial cutting depth a corresponding to the MRR are obtained_pAnd a spindle speed n; finally, analyzing the data obtained by the Taguchi test, and selecting the optimal additional mass combination which can maximize the MRR and the corresponding axial cutting depth a_pAnd a spindle speed n.

The invention has the beneficial effects that: the method establishes an efficient processing technique method to improve the stable domain of milling processing through local modification of the dynamic parameters of the thin-wall part by additional mass, and provides a reliable parameter selection range for high-speed milling processing of the thin-wall part; finally, the optimization algorithm is used for selecting machining parameters capable of achieving flutter-free and high efficiency, and high-speed flutter-free milling machining of the thin-wall part is achieved. According to the invention, an efficient processing method is established to improve the stable region of milling by locally modifying the dynamic parameters of the thin-wall part, so that the problems that the rigidity of two ends of the starting position and the ending position of a workpiece is poor, the stable region range is small, and the selection of the processing parameters in the milling process is seriously restricted are solved; the method provides a reliable parameter selection range for the high-speed milling of the thin-wall part, and realizes the high-speed non-flutter milling of the thin-wall part.

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

Drawings

FIG. 1 is a schematic diagram of a thin-wall part milling dynamic model considering deformation of a cutter and a workpiece in the method, wherein the cutter and the workpiece are respectively differentiated into q micro elements along the axial direction;

FIG. 2 is a schematic diagram of a multi-tap test tool frequency response function, PX1, PX2, PX3, PX4 being four measurement points in the tool feed direction, PY1, PY2, PY3, PY4 being four measurement points perpendicular to the tool feed direction;

FIG. 3 is a sheet and additive mass model validated in an embodiment of the method of the invention;

FIG. 4 is a graph of stability lobes for initial and final milling positions in an embodiment of the method of the present invention.

Detailed Description

The following examples refer to fig. 1-4.

Example 1 sheet size 115mm × 36mm × 3.5.5 mm, material 7075 aluminum alloy, modulus of elasticity 71GPa, density 2810kg/m³The Poisson's ratio is 0.33; the cutter is a hard alloy milling cutter with the number of cutting edges of 2, the diameter of 15.875mm and the helix angle of 30 degrees, and the extension length of the cutter is 78 mm.

Firstly, respectively differentiating a cutter and a workpiece into 40 infinitesimals along the axial direction by utilizing a thin-wall part milling dynamic model of the deformation of the cutter and the workpiece, namely q is 41; respectively establishing a milling kinetic equation at each infinitesimal position, and solving a dynamic milling force:

secondly, after the cutter is installed on a main shaft of the machine tool, measuring the feeding direction of the cutter and modal parameters vertical to the feeding direction by adopting a multi-point knocking test method and a linear interpolation method; zeta_m,t,x，ζ_m,t,yRepresents the damping ratio of the mth order; omega_m,t,x，ω_m,t,yA system natural frequency representing the mth order; u shape_m,t,x，U_m,t,yIs a matrix of q × 1 dimension, representing the m-th order modal vibration of system quality normalizationMolding; in a modal knock experiment, because of the influence of the size of an accelerometer, 4 points are selected and are measured by the accelerometer to obtain a modal vibration mode, and modal displacements at the other infinitesimal points are obtained by a linear interpolation method; four measuring points PX1, PX2, PX3, PX4 in the tool feed direction are located at distances of 5, 23, 50, 72mm from the tool tip point, respectively, and four measuring points PY1, PY2, PY3, PY4 perpendicular to the tool feed direction are located at distances of 0, 29, 43, 72mm from the tool tip point, respectively; selecting the first three modes (m is 1,2 and 3) which are most easily deformed, and providing modal analysis and identification modal parameters below; from U'_m,t,x，U'_m,t,y(m-th order modal shape of tool system quality normalization obtained by four-point test) is subjected to linear interpolation to obtain U_m,t,x，U_m,t,yFinally obtain U_t；

U_t＝[U_1,t…U_1,m,t]

Establishing a finite element model of the thin-wall workpiece, respectively establishing a set of removed materials (the size is 115 × 36 × 0.5.5 mm), a final workpiece (the size is 115 × 36 × 3mm) and three pieces of additional mass (the size is 18 × 18 × 3mm) in the process of establishing the model, giving corresponding material attributes to the model, adding constraints and loads which are consistent with actual processing to the workpiece, performing finite element analysis to obtain the inherent frequency of the whole workpiece, extracting the mass matrix and the rigidity matrix of each unit, finally assembling to obtain the mass matrix and the rigidity matrix of the whole workpiece model and the additional mass, and further obtaining the inherent frequency omega of each order of the whole workpiece model_wpSum mode vibration type U_wp；

Fourthly, assuming that the damping ratio is unchanged, extracting the damping characteristic of the workpiece by using a hammering mode experiment; determining a damping ratio matrix zeta of a workpiece by measuring the frequency response function of the workpiece at different points and fitting it_wp；

Fifthly, using the modal parameters obtained by the test in the second step and the natural frequency omega of each order of the whole workpiece model obtained in the third and fourth steps_wpNormal mode vibration type U_wpAnd damping ratio matrix ζ of workpiece_wpSubstituting the obtained result into the step I, respectively solving the state equations of the tool at the milling initial position and the milling final position by using a semi-discrete method to obtain the axial cutting depth a_p(mm) stability lobe plot of milling initial position (solid line 1) and end position (dashed line 2) with spindle speed n (rpm) as variables;

sixthly, taking the maximum material removal rate MRR as an objective function, wherein MRR is a_p×a_e×n×N×f，a_pIndicating axial cutting depth, a_eThe radial cutting depth is represented, N represents the rotating speed of a main shaft, N represents the number of cutter teeth, and f represents the feed amount of each tooth; during the milling processMedium radial cutting depth a_eThe cutter tooth number N is 2, and the feed amount f of each tooth is 0.1 mm/revolution/tooth; these parameters have been determined in advance; by axial cutting-in of a_pAnd a variable of the rotation speed n of the main shaft, respectively taking the stability lobe graphs of the milling initial position and the milling final position obtained in the step five as constraints, and setting the range of the axial cutting depth to be 7000 a or more according to actual processing parameters_pLess than or equal to 12000; setting the population size to be 20, the random seed generation probability to be 0.12221, the mutation probability to be 0.7, the cross probability to be 0.8 and the genetic algebra parameter to be 30, and respectively obtaining the optimized axial cutting depths a of the initial milling position and the final milling position by utilizing a genetic algorithm_pAnd a spindle speed n; selecting a corresponding to the initial position and the end position_pThe smallest of which is the selected processing parameter;

starting position: a is_p1.852 n 12000 end position: a is_p＝1.675 n＝12000

The parameters finally selected are as follows: a is_p＝1.675 n＝12000 MRR＝2010

Seventhly, adding mass blocks with different masses on the thin plate to locally modify the mass matrix and the rigidity matrix of the workpiece; according to the material parameters of several common materials given in the table I, the method L of the Taguo method is utilized₁₆(4⁴) Modifying the material density rho and the Young modulus E in the material attribute through an orthogonal test to change the mass matrix and the rigidity matrix of three additional masses, and then assembling to obtain the dynamic parameters of the modified workpiece; substituting the new kinetic parameters into the fifth step to obtain a stability lobe graph corresponding to the orthogonal test; through the sixth step, the product is obtained according to the 'Tiankou method' L₁₆(4⁴) Table three data corresponding to the orthogonal experiment; finally, three mass matrixes and stiffness matrixes of the additional mass under different material attributes, corresponding MRRs and corresponding axial cutting depths a are obtained_pAnd a spindle speed n; k₁,K₂,K₃,K₄Shows the influence of various factors on the indexes of the horizontal test, and obtains the optimal additional mass block pasting mode according to the influence, namely 343 the combination, namely the material 45 for the mass block 1 at the starting position^#Steel, middle massCopper for the mass 2 and 45 for the terminating mass 3^#Steel; the processing parameters obtained were: axial cutting depth a_p3.247 and the main shaft speed n 12000, the material removal rate MRR 3896.4; compared with the processing parameters and the material removal rate obtained by not sticking the mass block, the material removal efficiency is improved by 93.8 percent; the method is proved to achieve good expected effect and have good practicability.

Table one: material parameters of several common materials

Table two: use of Tiankou L₁₆(4⁴) Data from orthogonal experiments

Example 2 sheet size 100mm × 40mm × 4.5.5 mm, material aluminum alloy 7075, elastic modulus 71GPa, density 2810kg/m³The Poisson's ratio is 0.33; the cutter is a hard alloy milling cutter with the number of cutting edges of 2, the diameter of 15.875mm and the helix angle of 30 degrees, and the extension length of the cutter is 78 mm.

Firstly, respectively differentiating a cutter and a workpiece into 30 infinitesimals along the axial direction by using a thin-wall part milling dynamic model of the deformation of the cutter and the workpiece, namely q is 31; respectively establishing a milling kinetic equation at each infinitesimal position, and solving a dynamic milling force:

secondly, after the tool is arranged on a main shaft of the machine tool, the feeding direction of the tool is measured and the feeding direction of the tool is perpendicular to the feeding direction of the tool by adopting a multipoint knocking test method and a linear interpolation methodModal parameters of the feed direction; zeta_m,t,x，ζ_m,t,yRepresents the damping ratio of the mth order; omega_m,t,x，ω_m,t,yA system natural frequency representing the mth order; u shape_m,t,x，U_m,t,yThe matrix is q × 1 dimension matrix, representing the m-th order modal shape of system mass normalization, in a modal knock experiment, selecting 4 points to obtain the modal shape by accelerometer measurement, and obtaining modal displacement at the rest infinitesimal points by a linear interpolation method, wherein four measurement points PX1, PX2, PX3 and PX4 in the cutter feeding direction are respectively located at the positions 5, 23, 50 and 72mm away from the cutter point, four measurement points PY1, PY2, PY3 and PY4 perpendicular to the cutter feeding direction are respectively located at the positions 0, 29, 43 and 72mm away from the cutter point, the most deformable first three orders (m is 1,2 and 3) are selected, modal analysis and identification modal parameters are given below, and U's modal shape is used'_m,t,x，U'_m,t,y(m-th order modal shape of tool system quality normalization obtained by four-point test) is subjected to linear interpolation to obtain U_m,t,x，U_m,t,yFinally obtain U_t；

U_t＝[U_1,t…U_1,m,t]

Establishing a finite element model of the thin-wall workpiece, respectively establishing a set of three pieces of additional mass (the size is 20 × 20 × 4mm) of the removed material (100mm × 40mm × 0.5.5 mm) and the final workpiece (100mm × 40mm × 4mm 354 mm) in the process of establishing the model, giving corresponding material attributes to the model, adding constraints and loads which are consistent with actual processing to the workpiece, performing finite element analysis to obtain the inherent frequency of the whole workpiece, extracting the mass matrix and the rigidity matrix of each unit, and finally assembling to obtain the mass matrix and the rigidity matrix of the whole workpiece model and the additional mass, thereby obtaining the inherent frequency omega of each order of the whole workpiece model_wpSum mode vibration type U_wp；

sixthly, taking the maximum material removal rate MRR as an objective function, wherein MRR is a_p×a_e×n×N×f；a_pIndicating axial cutting depth, a_eThe radial cutting depth is represented, N represents the rotating speed of a main shaft, N represents the number of cutter teeth, and f represents the feed amount of each tooth; radial cutting depth a during milling_eThe cutter tooth number N is 2, and the feed amount f of each tooth is 0.1 mm/revolution/tooth; these parameters have been determined beforehand, with axial cutting depth a_pAnd a variable of the rotation speed n of the main shaft, respectively taking the stability lobe graphs of the milling initial position and the milling final position obtained in the step five as constraints, and setting the range of the axial cutting depth to be 7000 a or more according to actual processing parameters_pLess than or equal to 12000; setting the population size to be 20, the random seed generation probability to be 0.12221, the mutation probability to be 0.7, the cross probability to be 0.8 and the genetic algebra parameter to be 30, and respectively obtaining the optimized axial cutting depths a of the initial milling position and the final milling position by utilizing a genetic algorithm_pAnd a spindle speed n; selecting a corresponding to the initial position and the end position_pThe smallest of which is the selected processing parameter;

starting position: a is_p2.833 n-11200 end position: a is_p＝2.763 n＝11400

The parameters finally selected are as follows: a is_p＝2.763 n＝11400 MRR＝3149.82

Seventhly, adding mass blocks with different masses on the thin plate to locally modify the mass matrix and the rigidity matrix of the workpiece; according to the material parameters of several common materials given in the table I, the method L of the Taguo method is utilized₁₆(4⁴) Modifying the material density rho and the Young modulus E in the material attribute through an orthogonal test to change the mass matrix and the rigidity matrix of three additional masses, and then assembling to obtain the dynamic parameters of the modified workpiece; substituting the new kinetic parameters into the fifth step to obtain a stability lobe graph corresponding to the orthogonal test; through the sixth step, the product is obtained according to the 'Tiankou method' L₁₆(4⁴) Table three data corresponding to the orthogonal experiment; finally, a mass matrix and a rigidity matrix of the three additional masses under different material properties, corresponding MRRs and corresponding axial directions thereof are obtainedCutting depth a_pAnd a spindle speed n; k₁,K₂,K₃,K₄The influence of various factors on the indexes of the horizontal test is shown, and the optimal additional mass block pasting mode can be obtained by 423 combination, namely the mass block 1 at the starting position is made of copper, the mass block 2 at the middle position is made of aluminum alloy, and the mass block 3 at the ending position is made of 45^#Steel; the processing parameters obtained were: axial cutting depth a_p5.098 and the main shaft speed n is 10950, the material removal rate MRR is 5582.31; compared with the processing parameters and the material removal rate obtained by not sticking the mass block, the material removal efficiency is improved by 77.2 percent; the method is proved to achieve good expected effect and have good practicability.

Table three: use of Tiankou L₁₆(4⁴) Data from orthogonal experiments

Claims

1. A thin-walled part milling chatter suppression method is characterized in that comprising the following steps:

Step 1. Establish a milling dynamics model that considers the deformation of the tool and workpiece while multi-point contact is established; the equation of motion of the milling system is:

\{\begin{matrix} {\overset{\cdot\cdot \cdot\cdot}{Γ Γ}}_{t t} ((t t)) \\ {\overset{\cdot\cdot \cdot\cdot}{Γ Γ}}_{w w p p} ((t t)) \end{matrix}\} + + [\begin{matrix} 22 {ζ ζ}_{t t} {ω ω}_{n no,, t t} & 00 \\ 00 & 22 {ζ ζ}_{w w p p} {ω ω}_{n no,, w w p p} \end{matrix}] \{\begin{matrix} {\overset{\cdot \cdot}{Γ Γ}}_{t t} ((t t)) \\ {\overset{\cdot &Center Dot;}{Γ Γ}}_{w w p p} ((t t)) \end{matrix}\} + + [\begin{matrix} {ω ω}^{22}_{n no,, t t} & 00 \\ 00 & {ω ω}^{22}_{n no,, w w p p} \end{matrix}] + + \{\begin{matrix} {Γ Γ}_{t t} ((t t)) \\ {Γ Γ}_{w w p p} ((t t)) \end{matrix}\} = = [\begin{matrix} {U u}_{t t}^{T T} \\ {U u}_{w w p p}^{T T} \end{matrix}] F f ((t t))

Among them, Γ _t (t) is a vector representing the modal displacement of the tool; Γ _wp (t) is a vector representing the modal displacement of the workpiece; ζ _t represents the diagonal matrix of the tool damping ratio, and ζ _wp represents the damping ratio of the workpiece Diagonal matrix; ω _t represents the diagonal matrix of the natural frequency of the tool; ω _wp represents the diagonal matrix of the natural frequency of the workpiece; U _t represents the mode shape of the tool after mass normalization, and U _wp represents the workpiece after mass normalization modal shape; q represents the number of nodes used to differentiate the tool and workpiece along the axial direction; F(t) represents the matrix formed by the milling force at each contact point;

Step 2. After the selected milling cutter is installed on the machine tool spindle, the multi-point percussion test method and linear interpolation method are used to measure the feed direction of the cutter and the modal parameters perpendicular to the feed direction; ζ _m,t,x , ζ _m,t,y represents the damping ratio of the mth order; ω _m,t,x , ω _m,t,y represent the system natural frequency of the mth order; U _m,t,x , U _m,t,y are A q×1-dimensional matrix, representing the mode shape of the mth order normalized by the system mass;

Step 3. Establish the finite element model of the thin-walled workpiece; in the process of establishing the model, respectively establish the collection of removed material, final workpiece, and additional mass; assign corresponding material properties to the model and add constraints that match the actual processing to the workpiece The finite element analysis is carried out after loading and the natural frequency of the overall workpiece is obtained, and the mass matrix and stiffness matrix of each unit are extracted. Finally, the mass matrix and stiffness matrix of the overall workpiece model and additional mass are obtained by assembling, and then the order of the overall workpiece model is obtained. Natural frequency ω _wp and mode shape U _wp ;

Step 4, assuming that the damping ratio is constant, the damping characteristics of the workpiece are extracted by hammering method modal experiments; the damping ratio matrix ζ _wp of the workpiece is determined by fitting the frequency response functions of different points of the workpiece;

Step 5. Use the modal parameters obtained from the test in step 2 and the natural frequencies ω _wp of each order of the overall workpiece model obtained in steps 3 and 4, the mode shapes U _wp and the damping ratio matrix ζ _wp of the workpiece, and substitute them into step 1. Using the semi-discrete method to solve the state equations of the cutter at the milling initial position and the final position respectively, the stability lobe diagrams of the milling initial position and the final position with the axial depth of cut a _p and the spindle speed n as variables are obtained;

Step 6. Take the maximum material removal rate MRR as the objective function, MRR=a _p ×a _e ×n×N×f; a _p represents the axial depth of cut, a _e represents the radial depth of cut, n represents the spindle speed, and N represents The number of tool teeth, f represents the feed per tooth; in the milling process, the radial depth of cut a _e , the number of tool teeth N, and the feed per tooth f have been determined in advance; the axial depth of cut a _p and the spindle speed n are variables , taking the stability lobe diagrams of the milling initial position and end position obtained in step 5 as constraints, set the population size, random seed generation probability, mutation probability, crossover probability and genetic algebraic parameters, and use the genetic algorithm to obtain optimized Milling initial position and end position axial depth of cut a _p and spindle speed n; select the minimum of a _p corresponding to the initial position and end position as the selected processing parameters;

Step 7. Modify the material density ρ and Young's modulus E in the material properties to change the mass matrix and stiffness matrix of the additional mass, and use the Taguchi method to modify the material density ρ and Young's modulus E in the material properties to change the additional mass mass matrix and stiffness matrix, and then assembled to obtain the dynamic parameters of the modified workpiece; put the new dynamic parameters into step 5, and obtain the stability lobe diagram corresponding to the orthogonal test; through step 6, obtain the corresponding The MRR corresponding to the Taguchi method orthogonal experiment and the corresponding axial depth of cut a _p and the spindle speed n; finally, by analyzing the data obtained from the Taguchi test, the optimal additional mass combination that can maximize the MRR and its Corresponding axial depth of cut a _p and spindle speed n.