CN108732995B - The fast acquiring method of milling process workpiece kinetic parameter - Google Patents
The fast acquiring method of milling process workpiece kinetic parameter Download PDFInfo
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- CN108732995B CN108732995B CN201810376359.7A CN201810376359A CN108732995B CN 108732995 B CN108732995 B CN 108732995B CN 201810376359 A CN201810376359 A CN 201810376359A CN 108732995 B CN108732995 B CN 108732995B
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Abstract
For the acquisition and milling parameter stability quick predict for considering that material removal and tool position variation cause the workpiece kinetic parameter of workpiece kinetic parameter variation in thin-wall part milling process；The present invention provides the methods that the method for a kind of reduction of freedom degree and matrix dimensionality reduction obtains the time-varying dynamics parameter of workpiece；This method obtains the quality and stiffness matrix of workpiece using finite element；Reduce the quality of workpiece and the dimension of stiffness matrix by reducing freedom degree and the matrix dimensionality reduction of workpiece；Kinetic parameter of the workpiece at different tool position points is quickly obtained finally by the method that numerical value calculates and carries out stability prediction.
Description
Technical field
It is main suitable the present invention relates to the method for the acquisition of a kind of intrinsic frequency of Milling Processes workpiece and mode formation
With the quick predict of thin-wall part milling whole process chatter stability lobes.
Background technique
" Budak E, Tunc L.T., Alan S., the et al.Prediction of workpiece of document 1
dynamics and its effects on chatter stability in milling[J].CIRP Annals-
Manufacturing Technology, 2012,61:339-342. " disclose a kind of frequency response function using workpiece
The matrix of kinetic parameter carries out the method for inverse matrix to calculate the kinetic parameter of the workpiece in process；Using limited
Member method obtain workpiece mass matrix and stiffness matrix and extract be removed material mass matrix and stiffness matrix simultaneously
It takes in the frequency response function of initial workpiece and calculates the kinetic parameter of workpiece in milling process, it is pre- then to carry out flutter stability
It surveys.
" PetraKersting, DirkBiermann, Modeling workpiece the dynamics using of document 2
sets of decoupled oscillator models,Machining Science and Technology 16(2012)
564-579. " a kind of method using decoupled oscillator models has been disclosed to obtain workpiece difference cutter
The workpiece kinetic parameter of position.Experimental modal method that this method is tapped using multiple spot obtains workpiece in the transmitting of measurement point
Function simultaneously couples the intrinsic frequency and mode for calculate the particular locations of workpiece after material removes with a series of modes
Formation.
Document above has all carried out the acquisition of the workpiece kinetic parameter in milling process with material removal time-varying；But
In the actual operation process, method disclosed in document one is computationally intensive, and elapsed time is more, and computational efficiency is relatively low.Document one
Disclosed method needs to carry out a large amount of mode tap test, process very complicated, and versatility is poor.This all limits milling
Cut the quick predict of milling parameter in process.
Summary of the invention
Technical problems to be solved
In order to avoid the shortcomings of the prior art, the present invention proposes a kind of the quick of milling process workpiece kinetic parameter
Acquisition methods.
Technical solution
A kind of fast acquiring method of milling process workpiece kinetic parameter, by freedom degree reduction and matrix dimensionality reduction come fast
The method that speed obtains the workpiece kinetic parameter of time-varying；It is characterized by the following steps:
Step 1: for the characteristic of thin-wall part milling, establishing while considering the milling of the Multi-contact of cutter and workpiece deformation
Kinetic model；The Milling Force of each infinitesimal is focused on into section at q infinitesimal by cutter and workpiece contact zone differential along axial direction
On point and find out dynamic milling force:
The kinetics equation of milling system are as follows:
MW,0,0,CW,0,0,KW,0,0Respectively indicate quality, the damping, stiffness matrix of initial workpiece；QW(t) indicate workpiece in object
Manage the dynamic displacement under coordinate；Above formula is transformed into Modal Space by physical space to obtain:
Γw,0,0It (t) is the modal displacement matrix for indicating initial workpiece；ζw,0,0Indicate initial workpiece damping ratio matrix；
ωw,0,0Indicate initial workpiece intrinsic frequency matrix；Uw,0,0Indicate the Mode Shape of workpiece；The dynamic of F (t) expression milling system
Milling Force；
Step 2: the damping ratio of workpiece is constant in setting process, and the damping of workpiece is obtained using mode tap test
Than；By measuring the frequency response function of workpiece, identification obtains the damping ratio matrix ζ of workpiecew,0,0；Enable F (t)=0, the public affairs in step 1
Formula can be written as:
Step 3: according to workpiece is small in axial dynamic displacement and the dynamic displacement of fixing end also smaller phenomenon, to work
The mass matrix and stiffness matrix of part carry out freedom degree reduction；The finite element model interstitial content of workpiece is nW, the section of fixing end
Points are nSW；Indicate that remaining node, d indicate the node of reduction with a；Formula after reduction in step 2 can be written as:
After being reduction
Workpiece quality matrix,It is the workpiece stiffness matrix after reduction；It will after reduction
The mass matrix and stiffness matrix of workpiece are by 3nW×3nWDimension becomes (2nW-2nSW)×(2nW-2nSW), this preferably saves square
The calculation amount that the memory space and characteristic value of battle array solve；
Step 4: in process, by whole process along being divided axially into p cutting lay, for each cutting lay,
Entire milling layer is divided into l-1 sections with l cutter location；In milling cutting processing, material category is assigned to removal collection of material
Property 10-6；State equation of the cutter in k-th of cutting lay, b-th of cutter location position are as follows:
Wherein 0 < k≤p, 0 < b≤l；
Step 5: dimensionality reduction being carried out to the state equation in step 4 and solves characteristic value；Using dimensionality reduction formula,
By step 4
In state equation dimensionality reduction after express are as follows:
Characteristic value is carried out to above formula to solve to obtain the intrinsic frequency of the workpiece in k-th of cutting lay, b-th of cutter location position
MatrixWith mode formation matrix
It is a kind of to obtain milling process workpiece kinetic parameter solution the stability lobes diagram using the fast acquiring method
Method, it is characterised in that: milling dynamics equation of the workpiece cutter in k-th of cutting lay, b-th of cutter location position are as follows:
By the step 1 of claim 1~5 obtain in k-th of cutting lay, b-th of cutter location position workpiece it is intrinsic
FrequencyMode formationDamping ratio matrixAbove formula is substituted into, the equation is solved respectively using semi-discrete method, obtains
To with axial cutting-in ap(mm) and speed of mainshaft n (rpm) is the workpiece of variable in k-th of cutting lay, b-th of cutter location position
Milling system the stability lobes diagram；Minimum packet is asked to the stability lobes diagram obtained at all cutter locations of k-th of cutting lay
Winding thread is guaranteed the stable the stability lobes diagram of entire cutting lay process.
Beneficial effect
A kind of fast acquiring method of milling process workpiece kinetic parameter proposed by the present invention, by freedom degree reduction and
Dimensionality reduction greatly reduces the dimension of workpiece quality matrix and stiffness matrix and saves memory space, improves computational efficiency, saves
Calculate the time；And a finite element model only need to be established in whole process, is modeled without repeating；Guaranteeing to calculate reliable feelings
It is the kinetic parameter of quick obtaining workpiece under shape, realizes efficient quick predict whole process flutter stability prediction
Function.
Detailed description of the invention
Fig. 1: the straight sheet model of the plane verified in embodiment
Fig. 2: the curved sheets model verified in embodiment；
Fig. 3: the milling stability flap figure envelope that b-th of cutting lay obtains in milling process.
Specific embodiment
Workpiece kinetic parameter is caused to become for considering that material removal and tool position change in thin-wall part milling process
The acquisition and milling parameter stability quick predict of the workpiece kinetic parameter of change；The present invention provides a kind of freedom degree reduction and
The method that the method for matrix dimensionality reduction obtains the time-varying dynamics parameter of workpiece；This method using finite element obtain workpiece quality and
Stiffness matrix；Reduce the quality of workpiece and the dimension of stiffness matrix by reducing freedom degree and the matrix dimensionality reduction of workpiece；Finally
Kinetic parameter of the workpiece at different tool position points is quickly obtained by the method that numerical value calculates and carries out stability prediction.
Following embodiment referring to Fig.1-3.
Embodiment 1: sheet size be 102mm × 36mm × 4mm, material be aluminium alloy 7075, elasticity modulus 71GPa,
Density is 2810kg/m3, Poisson's ratio 0.33.
One, for the characteristic of thin-wall part milling, establish while considering that the milling of the Multi-contact of cutter and workpiece deformation is dynamic
Mechanical model；The Milling Force of each unit is focused on into section at 35 infinitesimals by cutter and workpiece contact zone differential along axial direction
On point and find out dynamic milling force:
The kinetics equation of milling system are as follows:
MW,0,0,CW,0,0,KW,0,0Indicate the quality of initial workpiece, damping, stiffness matrix；Q (t) indicates that workpiece is sat in physics
Dynamic displacement under mark；Above formula is transformed into Modal Space by physical space to obtain:
Γw,0,0It (t) is the modal displacement matrix for indicating initial workpiece；ζw,0,0Indicate initial workpiece damping ratio matrix；
ωw,0,0Indicate initial workpiece intrinsic frequency matrix；Uw,0,0Indicate the Mode Shape of workpiece；The milling of F (t) expression milling system
Power；
Two, the damping ratio for setting workpiece in process is constant, and the damping ratio of workpiece is obtained using mode tap test；It is logical
The frequency response function of measurement workpiece is crossed, identification obtains the damping ratio matrix ζ of workpiecew,0,0；F (t)=0 is enabled, the formula in step 1 can
To be written as:
Three, according to workpiece is small in axial dynamic displacement and the dynamic displacement of fixing end also smaller phenomenon, to workpiece
Mass matrix and stiffness matrix carry out freedom degree reduction；The finite element model interstitial content of workpiece is nW(nW=13312), Gu
The number of nodes of fixed end is nSW(nSW=3952)；Indicate that remaining node, d indicate the node of reduction with a；After reduction in step 2
Formula can be written as:
After being reduction
Workpiece quality matrix,It is the workpiece stiffness matrix after reduction；It will after reduction
The mass matrix and stiffness matrix of workpiece become 18712 × 18712 from 39936 × 39936 dimensions, and matrix amount of storage reduces 78%；
The calculation amount that this preferably saves the memory space of matrix and characteristic value solves；
Four, in process, by whole process along 6 cutting lays are divided axially into, for each cutting lay, with 15
Entire milling layer is divided into 14 sections by a cutter location；In milling cutting processing, material properties 10 are assigned to removal collection of material-6；State equation of the cutter in kth (0 k≤6 <) a cutting lay, b (0 b≤15 <) a cutter location position are as follows:
Five, dimensionality reduction is carried out to the state equation in step 4 and solves characteristic value；Using dimensionality reduction formula,
It will step
It is expressed after state equation dimensionality reduction in rapid four are as follows:
WithIt is converted into 6 × 6 matrixWithCharacteristic value is carried out to above formula to solve to obtain
The intrinsic frequency matrix of workpiece in k-th of cutting lay, b-th of cutter location positionWith mode formation matrix
Six, milling dynamics equation of the workpiece cutter in k-th of cutting lay, b-th of cutter location position are as follows:
It will be Step 2: three, four, the five obtained intrinsic frequencies of workpiece in k-th of cutting lay, b-th of cutter location positionMode formationDamping ratio matrixStep 6 is substituted into, the equation is solved respectively using semi-discrete method, obtains
With axial cutting-in ap(mm) and speed of mainshaft n (rpm) is the workpiece of variable in k-th of cutting lay, b-th of cutter location position
The stability lobes diagram of milling system；Minimum envelope is asked to the stability lobes diagram obtained at the 3rd all cutter locations of cutting lay
Line is guaranteed the stable the stability lobes diagram of entire cutting lay process；It is 2323 seconds the time required to direct solution；It utilizes
It is 1557 seconds the time required to this method, the time saves 714 seconds, improved efficiency 32.97%.
Embodiment 2: curved sheets are having a size of long 104mm, high 35mm, thick 3.5mm, radius of curvature 297mm；Material is aluminium
Alloy 7075, elasticity modulus 71GPa, density 2810kg/m3, Poisson's ratio 0.33.
One, for the characteristic of thin-wall part milling, establish while considering that the milling of the Multi-contact of cutter and workpiece deformation is dynamic
Mechanical model；The Milling Force of each unit is focused on into section at 34 infinitesimals by cutter and workpiece contact zone differential along axial direction
On point and find out dynamic milling force:
The kinetics equation of milling system are as follows:
MW,0,0,CW,0,0,KW,0,0Indicate the quality of initial workpiece, damping, stiffness matrix；Q (t) indicates that workpiece is sat in physics
Dynamic displacement under mark；Above formula is transformed into Modal Space by physical space to obtain:
Γw,0,0It (t) is the modal displacement matrix for indicating initial workpiece；ζw,0,0Indicate initial workpiece damping ratio matrix；
ωw,0,0Indicate initial workpiece intrinsic frequency matrix；Uw,0,0Indicate the Mode Shape of workpiece；The milling of F (t) expression milling system
Power；
Two, the damping ratio for setting workpiece in process is constant, and the damping ratio of workpiece is obtained using mode tap test；It is logical
The frequency response function of measurement workpiece is crossed, identification obtains the damping ratio matrix ζ of workpiecew,0,0；F (t)=0 is enabled, the formula in step 1 can
To be written as are as follows:
Three, according to workpiece is small in axial dynamic displacement and the dynamic displacement of fixing end also smaller phenomenon, to workpiece
Mass matrix and stiffness matrix carry out freedom degree reduction；The finite element model interstitial content of workpiece is nW(nW=17132), Gu
The number of nodes of fixed end is nSW(nSW=5096)；Indicate that remaining node, d indicate the node of reduction with a；After reduction in step 2
Formula can be written as:
It is after reducing
Workpiece quality matrix,It is the workpiece stiffness matrix after reduction；By work after reduction
The mass matrix and stiffness matrix of part become 24072 × 24072 from 51396 × 51396 dimensions, and matrix amount of storage reduces 78.2%；
The calculation amount that this preferably saves the memory space of matrix and characteristic value solves；
Four, in process, by whole process along 5 cutting lays are divided axially into, for each cutting lay, with 18
Entire milling layer is divided into 17 sections by a cutter location；In milling cutting processing, material properties 10 are assigned to removal collection of material-6；State equation of the cutter in kth (0 k≤5 <) a cutting lay, b (0 b≤18 <) a cutter location position are as follows:
Five, dimensionality reduction is carried out to the state equation in step 4 and solves characteristic value；Using dimensionality reduction formula,
It will step
It is expressed after state equation dimensionality reduction in rapid four are as follows:
WithIt is converted into 5 × 5 matrixWithCharacteristic value is carried out to above formula to solve to obtain
The intrinsic frequency matrix of workpiece in k-th of cutting lay, b-th of cutter location positionWith mode formation matrix
Six, milling dynamics equation of the workpiece cutter in k-th of cutting lay, b-th of cutter location position are as follows:
It will be Step 2: three, four, the five obtained intrinsic frequencies of workpiece in k-th of cutting lay, b-th of cutter location positionMode formationDamping ratio matrixStep 6 is substituted into, the equation is solved respectively using semi-discrete method, obtains
With axial cutting-in ap(mm) and speed of mainshaft n (rpm) is the workpiece of variable in k-th of cutting lay, b-th of cutter location position
The stability lobes diagram of milling system；Minimum envelope is asked to the stability lobes diagram obtained at the 2nd all cutter locations of cutting lay
Line is guaranteed the stable the stability lobes diagram of entire cutting lay process；It is 3290 seconds the time required to direct solution；It utilizes
It is 2146 seconds the time required to this method, the time saves 714 seconds, improved efficiency 34.77%.
Claims (2)
1. a kind of fast acquiring method of milling process workpiece kinetic parameter, by freedom degree reduction and matrix dimensionality reduction come quickly
The method for obtaining the workpiece kinetic parameter of time-varying；It is characterized by the following steps:
Step 1: for the characteristic of thin-wall part milling, establishing while considering the milling power of the Multi-contact of cutter and workpiece deformation
Learn model；Cutter and workpiece contact zone differential are focused on the Milling Force of each infinitesimal on node at q infinitesimal along axial direction
And find out dynamic milling force:
The kinetics equation of milling system are as follows:
MW,0,0,CW,0,0,KW,0,0Respectively indicate quality, the damping, stiffness matrix of initial workpiece；QW(t) indicate that workpiece is sat in physics
Dynamic displacement under mark；Above formula is transformed into Modal Space by physical space to obtain:
Γw,0,0It (t) is the modal displacement matrix for indicating initial workpiece；ζw,0,0Indicate initial workpiece damping ratio matrix；ωw,0,0Table
Show initial workpiece intrinsic frequency matrix；Uw,0,0Indicate the Mode Shape of workpiece；The dynamic milling force of F (t) expression milling system；
Step 2: the damping ratio of workpiece is constant in setting process, and the damping ratio of workpiece is obtained using mode tap test；It is logical
The frequency response function of measurement workpiece is crossed, identification obtains the damping ratio matrix ζ of workpiecew,0,0；F (t)=0 is enabled, the formula in step 1 can be with
It is written as:
Step 3: according to workpiece is small in axial dynamic displacement and the dynamic displacement of fixing end also smaller phenomenon, to workpiece
Mass matrix and stiffness matrix carry out freedom degree reduction；The finite element model interstitial content of workpiece is nW, the number of nodes of fixing end
For nSW；Indicate that remaining node, d indicate the node of reduction with a；Formula after reduction in step 2 can be written as:
It is the workpiece after reduction
Mass matrix, It is the workpiece stiffness matrix after reduction, Maa、Mda、MddIndicate with
Workpiece residue node a and the relevant piecemeal mass matrix of the node d of reduction；Kda、Kdd、KaaIt indicates and workpiece residue node a and contracting
The relevant piecemeal stiffness matrix of the node d subtracted；By the mass matrix of workpiece and stiffness matrix by 3n after reductionW×3nWDimension becomes
(2nW-2nSW)×(2nW-2nSW), the calculation amount that this preferably saves the memory space of matrix and characteristic value solves；
Step 4: in process, by whole process along p cutting lay is divided axially into, for each cutting lay, with l
Entire milling layer is divided into l-1 sections by cutter location；In milling cutting processing, material properties 10 are assigned to removal collection of material-6；
State equation of the cutter in k-th of cutting lay, b-th of cutter location position are as follows:
Wherein 0 < k≤p, 0 <b≤l；
Step 5: dimensionality reduction being carried out to the state equation in step 4 and solves characteristic value；Using dimensionality reduction formula,By step 4
In state equation dimensionality reduction after express are as follows:
Characteristic value is carried out to above formula to solve to obtain the intrinsic frequency matrix of the workpiece in k-th of cutting lay, b-th of cutter location positionWith mode formation matrix
2. a kind of obtain milling process workpiece kinetic parameter solution stability using fast acquiring method described in claim 1
The method of flap figure, it is characterised in that: milling dynamics side of the workpiece cutter in k-th of cutting lay, b-th of cutter location position
Journey are as follows:
The intrinsic frequency of workpiece in k-th of cutting lay, b-th of cutter location position that the step 1 of claim 1~5 are obtainedMode formationDamping ratio matrixSubstitute into above formula, solve the equation respectively using semi-discrete method, obtain with
Axial cutting-in apWith milling system of the workpiece in k-th of cutting lay, b-th of cutter location position that speed of mainshaft n is variable
The stability lobes diagram；Minimum envelope is asked to be guaranteed the stability lobes diagram obtained at all cutter locations of k-th of cutting lay
The stable the stability lobes diagram of entire cutting lay process.
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| CN109840380B (en) * | 2019-02-16 | 2021-03-12 | 北京理工大学 | Stability prediction method considering multi-mode vibration and workpiece processing response |
| CN109968099B (en) * | 2019-03-11 | 2020-10-27 | 西北工业大学 | Thin-wall part milling flutter suppression method based on dynamic support |
| CN110321652B (en) * | 2019-07-11 | 2021-03-02 | 山东大学 | Dynamic modeling method and system for blade cyclone milling process |
| CN113792469B (en) * | 2021-09-22 | 2023-10-24 | 宁波工程学院 | Structural dynamic characteristic analysis method and system based on dimension reduction calculation |
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