CN107335848B - Three-dimensional milling residual stress prediction technique - Google Patents
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- B—PERFORMING OPERATIONS; TRANSPORTING
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Abstract
The invention discloses a kind of three-dimensional milling residual stress prediction technique, the technical issues of the practicability is poor for solving existing milling residual stress prediction technique.Technical solution is that milling process is divided into several small three-dimensional inclined cutting infinitesimals first, and then these infinitesimals are analyzed.The angular relationship of cutting force and cutting speed is calculated again, the shear flow stress of shear surface is then calculated based on J-C constitutive model, to release the normal stress on shear surface.Then the behavior of cutting of point of a knife plough is analyzed, obtains plough shear force and plough cuts the length in region.The stress contact process of inclined cutting is modeled again, using stress tensor three-dimensional coordinate transformation method will shear and plough cut caused by stress distribution be overlapped, obtain the stress-strain course of inside workpiece in milling process.Constitutive behavior of the workpiece in three-dimensional elastic-plastic CYCLIC LOADING is finally predicted with the plastoelastic method of increment, obtains the residual stress of milling workpiece surface, and practicability is good.
Description
Technical field
The present invention relates to a kind of milling residual stress prediction technique, in particular to a kind of three-dimensional milling residual stress prediction side
Method.
Background technique
When predicting cutting residual stress, common method has theoretical modeling and two kinds of finite element simulation.It is existing
The theoretical modeling method of prediction machining residual stress is all based on two-dimensional theoretical model, there is very strong limitation, cannot
It is effectively used for three-dimensional Milling Processes.And when using finite element simulation prediction residue stress, due to the three-dimensional of milling
Structure too complex generally requires to simplify model, and the result obtained in this way is just necessarily deviated.
" S.Agrawal, S.S.Joshi, Analytical modelling of the residual stresses of document 1
in orthogonal machining of AISI4340steel,Journal of Manufacturing Processes
15 (1) (2013) 167-179. " a kind of residual stress prediction model suitable for two-dimentional orthogonal cutting process, the model are disclosed
It is primarily based on the integral that contact mechanics establish inside workpiece contact stress, is then built using plastoelasticity method
The residual stress prediction model of vertical orthogonal cutting process, this method may be only available for two-dimentional right angle turning situation, it is impossible to be used in
Increasingly complex three-dimensional milling process.
" Nejah, Tounsi, Tahany, EI-Wardany, Finite element analysis of chip of document 2
formation and residual stresses induced by sequential cutting in side milling
with microns to submicron uncut chip thickness and finite cutting edge
Radius, Advances in Manufacturing 3 (4) (2015) 309-322. " discloses a kind of suitable for prediction milling
The finite element modeling method of process residues stress, this method assume milling cutter's helix angle be 0 °, then to a section of milling cutter into
Row finite element analysis, and then establish the residual stress calculation model for considering that chip formation and tool arc influence.But this method
The case where being actually still a kind of two-dimensional method, not considering when helical angle is not 0 °, does not account for milling three-dimensional yet
Structure.
The typical feature of document above is: in workpiece cutting residual stress modeling, not accounting for increasingly complex milling feelings
Condition, or the method model of milling has ignored the milling cutter three-dimensional structure as caused by helical angle the considerations of establish.
Summary of the invention
In order to overcome the shortcomings of existing milling residual stress prediction technique, the practicability is poor, and the present invention provides a kind of three-dimensional milling
Residual stress prediction technique.Milling process is divided into several small three-dimensional inclined cutting infinitesimals first by this method, then
These infinitesimals are analyzed according to three-dimensional inclined cutting theory.The angular relationship of cutting force and cutting speed is calculated again, then
The shear flow stress of shear surface is calculated based on J-C constitutive model, to release the normal stress on shear surface.Then with cunning
Lineation opinion is moved to analyze the behavior of cutting of point of a knife plough, plough shear force is obtained and plough cuts the length in region.Inclined cutting is answered again
Power contact process is modeled, using stress tensor three-dimensional coordinate transformation method will shear and plough cut caused by stress distribution into
Row superposition, obtains the stress-strain course of inside workpiece in milling process.Finally workpiece is predicted with the plastoelastic method of increment
Constitutive behavior in three-dimensional elastic-plastic CYCLIC LOADING, obtains the residual stress of milling workpiece surface, and practicability is good.
The technical solution adopted by the present invention to solve the technical problems: a kind of three-dimensional milling residual stress prediction technique,
Feature be the following steps are included:
Step 1: milling process is divided into several three-dimensional inclined cutting infinitesimals.
Step 2: being calculated using the following equation in three-dimensional Oblique Cutting Process, the angular relationship of cutting force and cutting speed:
sinθi=sin βa sinηflow
tan(θn+αn)=tan βa cosηflow
In formula, β is milling cutter's helix angle, αnIt is tool orthogonal rake, βaIt is angle of friction, ηflowIt is chip flow angle, θiAnd θnIt is fixed
Adopted cutting force deflection, φiAnd φnIt is shear velocity deflection.
Step 3: calculating the shear flow stress on shear surface using following formula:
In formula, τsIt is shear flow stress, ε is plastic strain,It is plastic strain rate, ε0It is with reference to strain rate, T is to cut
Section temperature, T0It is room temperature, TmIt is material melting point, A, B, C, m and n are the J-C constitutive parameters of material.
Step 4: calculating Cutting Force Coefficient using following formula:
In formula, KtcIt is the Cutting Force Coefficient in cutting speed direction, KfcIt is perpendicular to the cutting force in workpiece machining surface direction
Coefficient.
Step 5: calculating cutting force using following formula:
Ft=Ktcdaptc+Ktedap
Ff=Kfcdaptc+Kfedap
In formula, dapIt is the axial width of inclined cutting infinitesimal, tcIt is the thickness of cutting of inclined cutting infinitesimal, KteAnd KfeIt is
Plough shear force coefficient.FtIt is the cutting force in cutting speed direction, FfIt is perpendicular to the cutting force in workpiece machining surface direction.
Step 6: the normal direction cutting force F being calculated using the following equation on shear surfacen:
Fn=Ftcosβsinφn+Ffcosφn
In formula, FnIt is the normal direction cutting force on shear surface.
Step 7: being calculated using the following equation the normal stress on shear surface
In formula, psIt is the normal stress on shear plane.
Step 8: being calculated using the following equation the length of shear surface:
In formula,It is the length of shear surface.
Step 9: the stress distribution that tool arc plough cuts region is considered uniformly, to be calculated using the following equation:
In formula, peIt is the normal stress that plough cuts region, qeIt is the tangential stress that plough cuts region, PthrustIt is normal direction plough shear force,
PcutIt is tangential plough shear force,It is the length that plough cuts region, μ is coefficient of friction.
Step 10: calculating separately shearing using following formula and stress distribution caused by plough is cut.
In formula, σxxIt is stress along the x-axis direction, σzzIt is stress along the z-axis direction, τxzIt is the shear stress in the direction xz, a
It is the half of the length of contact area, coordinate value x and z indicate the position of calculation point of stress, and p (s) and q (s) are positive and tangential
Stress value.For share zone, based on step 3 and step 7 as a result, by p (s)=ps, q (s)=qs,In substitution
Formula；Region is cut for plough, based on step 8 as a result, by p (s)=pe, q (s)=qe,Substitute into above formula.
Step 11: will be sheared using following formula and stress distribution is overlapped caused by plough is cut.
[σ1']=Q1 T[σ1]Q1
[σ2']=Q2 T[σ2]Q2
[σ3]=[σ1']+[σ2']
In formula, [σ1] indicate value of the stress distribution under the coordinate system of shear zone caused by shearing, [σ2] indicate plough cut caused by
Value of the stress distribution under the area Li Qie coordinate system, [σ1'] indicate value of the stress distribution under workpiece coordinate system caused by shearing,
[σ2'] indicate plough cut caused by value of the stress distribution under workpiece coordinate system, [σ3] indicate actual stress point under workpiece coordinate system
Implantation.Q1And Q2It is the three-dimensional coordinate transformation matrix of stress tensor.
Step 12: the stress distribution value under inclined cutting unit is transformed into milling coordinate system using following formula.
In formula, φwIt is that milling cutter immerses angle, [σ] is the stress distribution value under milling coordinate system.
Step 13: calculating the stress increment in a tiny time dt using following formula:
[d σ]=[σ (t+dt)]-[σ (t)]
In formula, [d σ] is the stress increment in a tiny time, what [σ (t)] expression was obtained based on step 12 result
The relationship of milling process stress distribution and time.
Step 14: judging whether workpiece enters mecystasis at some moment using following formula:
In formula, J2It is the second invariant of deviatoric tensor of stress, F is yield surface, τsyIt is the shear yield strength of material, SijIt indicates
Deviatoric stress, αijIndicate back stress.
Step 15: using the stress increment under following formula computational plasticity state:
In formula, E is elasticity modulus of materials, and v is Poisson's ratio, d σijIt is the stress increment obtained based on step 13 result,WithIt is the stress increment under mecystasis, d εxxWith d εyyIt is plastic strain increment, nijIt is on plastic strain rate direction
Unit normal vector.
Step 16: judging the boundary condition of stress relaxation using following formula:
In formula,It is the residual stress before relaxation,It is overstrain, f1,2,...,6(z) indicate one has with coordinate value z
The non-zero amount closed.
Step 17: indicating every step relaxed length using following formula:
In formula, M is loose total step number, Δ σijIndicate every step stress relaxation number, Δ εijIndicate every step strain relaxation amount.
Step 18: calculating the stress increment of elastic release process using following formula:
Δσxy=2G Δ εxy
In formula, G indicates elastic properties of materials modulus of shearing.
Step 19: with the stress increment of following formula computational plasticity release process:
Step 20: after calculating relaxation step with following formula, obtained final residual stress:
In formula,WithIt is the final residual stress in the direction workpiece coordinate system x and the direction y respectively.
The beneficial effects of the present invention are: milling process is divided into several small three-dimensional inclined cuttings first by this method
Then infinitesimal is analyzed these infinitesimals according to three-dimensional inclined cutting theory.The angle of cutting force and cutting speed is calculated again
Relationship then calculates the shear flow stress of shear surface based on J-C constitutive model, so that the normal direction released on shear surface is answered
Power.Then the behavior of cutting of point of a knife plough is analyzed with Slip Line Theory, obtains plough shear force and plough cuts the length in region.Again to oblique
The stress contact process of angle cutting is modeled, and will be sheared using the method for stress tensor three-dimensional coordinate transformation and caused by plough cuts
Stress distribution is overlapped, and obtains the stress-strain course of inside workpiece in milling process.Finally use the plastoelastic method of increment
It predicts constitutive behavior of the workpiece in three-dimensional elastic-plastic CYCLIC LOADING, obtains the residual stress of milling workpiece surface, it is real
It is good with property.
It elaborates with reference to the accompanying drawings and detailed description to the present invention.
Detailed description of the invention
Fig. 1 is the contact stress variation schematic diagram in three-dimensional milling residual stress prediction technique embodiment of the invention.
Fig. 2 is the residual stress prediction result in three-dimensional milling residual stress prediction technique embodiment of the invention.
Fig. 3 is three-dimensional milling process geometric representation in three-dimensional milling residual stress prediction technique of the invention.
Specific embodiment
Referring to Fig.1-3.Specific step is as follows for three-dimensional milling residual stress prediction technique of the invention:
Step 1: milling process is divided into several small three-dimensional inclined cutting infinitesimals.
Step 2: angular relationship of the measurement for determining the cutting force from three-dimensional Oblique Cutting Process and cutting speed
Milling cutter's helix angle β is 20 °, tool orthogonal rake αnIt is 5 °, angle of friction βaIt is 17 °.It substitutes them in following formula and calculates cutting force deflection θi
And θn, shear velocity deflection φiAnd φnAnd chip flow angle ηflow。
sinθi=sin βa sinηflow
tan(θn+αn)=tan βa cosηflow
Step 3: calculating the shear flow stress on shear surface using following formula:
Reference literature " J.C.Su, S.Y.Liang, Residual stress modeling in machining
Database disclosed in processes, Georgia Institute of Technology. " determines material melting point Tm, plasticity answers
Become ε, plastic strain rate ε, with reference to strain rate ε0And material J-C constitutive parameter A, B, C, m and n.
Step 4: calculating Cutting Force Coefficient using following formula:
In formula, KtcIt is the Cutting Force Coefficient in cutting speed direction, KfcIt is perpendicular to the cutting force in workpiece machining surface direction
Coefficient.
Step 5: calculating cutting force using following formula:
Ft=Ktcdaptc+Ktedap
Ff=Kfcdaptc+Kfedap
In formula, dapIt is the axial width for the inclined cutting infinitesimal that value is 0.01mm, tcIt is the cutting of inclined cutting infinitesimal
Thickness, KteAnd KfeIt is plough shear force coefficient.FtIt is the cutting force in cutting speed direction, FfIt is perpendicular to workpiece machining surface direction
Cutting force.
Step 6: the normal direction cutting force being calculated using the following equation on shear surface:
Fn=Ftcosβsinφn+Ff cosφn
In formula, FnIt is the normal direction cutting force on shear surface.
Step 7: being calculated using the following equation the normal stress on shear surface:
In formula, psIt is the normal stress on shear plane.
Step 8: being calculated using the following equation the length of shear surface:
In formula,It is the length of shear surface.
Step 9: being calculated using the following equation the stress distribution that tool arc plough cuts region:
In formula, PthrustIt is normal direction plough shear force, PcutIt is tangential plough shear force, obtained plough cuts the normal stress p in regioneFor
1324.6MPa, plough cut the tangential stress q in regioneFor 2317.4MPa, plough cuts the length in regionFor 0.087mm, coefficient of friction
μ is 0.3.
Step 10: calculating separately shearing using following formula and stress distribution caused by plough is cut.
In formula, σxxIt is stress along the x-axis direction, σzzIt is stress along the z-axis direction, τxzIt is the shear stress in the direction xz, just
To with tangential stress value.For share zone, based on step 3 and step 8 as a result, by p (s)=ps, q (s)=qs,Substitute into above formula；Region is cut for plough, it is based on step 9 as a result, by p (s)=pe, q (s)=qe,Generation
Enter above formula.
Step 11: will be sheared using following formula and stress distribution is overlapped caused by plough is cut:
[σ1']=Q1 T[σ1]Q1
[σ2']=Q2 T[σ2]Q2
[σ3]=[σ1']+[σ2']
In formula, [σ1] indicate value of the stress distribution under the coordinate system of shear zone caused by shearing, [σ2] indicate plough cut caused by
Value of the stress distribution under the area Li Qie coordinate system, [σ1'] indicate value of the stress distribution under workpiece coordinate system caused by shearing,
[σ2'] indicate plough cut caused by value of the stress distribution under workpiece coordinate system, [σ3] indicate actual stress point under workpiece coordinate system
Implantation.Q1And Q2It is the three-dimensional coordinate transformation matrix of stress tensor.
Step 12: the stress distribution value under inclined cutting unit is transformed into milling coordinate system using following formula.
In formula, φwIt is that milling cutter immerses angle, [σ] is the stress distribution value under milling coordinate system.
Step 13: calculating the stress increment in a tiny time dt using following formula:
[d σ]=[σ (t+dt)]-[σ (t)]
In formula, [d σ] is the stress increment in a tiny time, what [σ (t)] expression was obtained based on step 12 result
The relationship of milling process stress distribution and time.
Step 14: referring to stress variation schematic diagram in the milling process indicated in Fig. 3.Judge workpiece at certain using following formula
Whether one moment enters mecystasis:
In formula, J2It is the second invariant of deviatoric tensor of stress, the shear yield strength τ of materialsyIt is yield surface for 497MPa, F,
SijIndicate deviatoric stress, αijIndicate back stress.
Step 15: using the stress increment under following formula computational plasticity state:
In formula, elasticity modulus of materials E is 114GPa, and Poisson's ratio v is 0.33, d σijIt is to be obtained based on step 13 result
Stress increment,WithIt is the stress increment under mecystasis, d εxxWith d εyyIt is plastic strain increment, nijIt is that plasticity is answered
Unit normal vector on variability direction.
Step 16: judging the boundary condition of stress relaxation using following formula:
In formulaIt is the residual stress before relaxation,It is overstrain, f1,2,...,6(z) expression one is related with coordinate value z
A non-zero amount.
Step 17: indicating every step relaxed length using following formula:
In formula, the value of relaxation total step number M takes 1000, Δ σijIndicate every step stress relaxation number, Δ εijIndicate that every step should fluff
Relaxation amount.
Step 18: calculating the stress increment of elastic release process using following formula:
Δσxy=2G Δ εxy
In formula, elastic properties of materials shear modulus G is 42.8GPa.
Step 19: using the stress increment of following formula computational plasticity release process:
Step 20: after calculating relaxation step with following formula, obtained final residual stress:
In formula,WithIt is the final residual stress in the direction workpiece coordinate system x and the direction y respectively, by its value and reality
Surveyed value is tested to compare.
From the prediction result of Fig. 2 residual stress can be seen that the present embodiment predict milling residual stress and actual measurement it is residual
Residue stress coincide preferably, illustrates that the residual stress prediction technique has reliability.
Claims (1)
1. a kind of three-dimensional milling residual stress prediction technique, it is characterised in that the following steps are included:
Step 1: milling process is divided into several three-dimensional inclined cutting infinitesimals；
Step 2: being calculated using the following equation in three-dimensional Oblique Cutting Process, the angular relationship of cutting force and cutting speed:
sinθi=sin βasinηflow
tan(θn+αn)=tan βacosηflow
In formula, β is milling cutter's helix angle, αnIt is tool orthogonal rake, βaIt is angle of friction, ηflowIt is chip flow angle, θiAnd θnIt is that definition is cut
Cut power deflection, φiAnd φnIt is shear velocity deflection；
Step 3: calculating the shear flow stress on shear surface using following formula:
In formula, τsIt is shear flow stress, ε is plastic strain,It is plastic strain rate, ε0It is with reference to strain rate, T is shear surface temperature
Degree, T0It is room temperature, TmIt is material melting point, A, B, C, m and n are the J-C constitutive parameters of material；
Step 4: calculating Cutting Force Coefficient using following formula:
In formula, KtcIt is the Cutting Force Coefficient in cutting speed direction, KfcIt is perpendicular to the Cutting Force Coefficient in workpiece machining surface direction；
Step 5: calculating cutting force using following formula:
Ft=Ktcdaptc+Ktedap
Ff=Kfcdaptc+Kfedap
In formula, dapIt is the axial width of inclined cutting infinitesimal, tcIt is the thickness of cutting of inclined cutting infinitesimal, KteAnd KfeIt is that plough is cut
Force coefficient；FtIt is the cutting force in cutting speed direction, FfIt is perpendicular to the cutting force in workpiece machining surface direction；
Step 6: the normal direction cutting force F being calculated using the following equation on shear surfacen:
Fn=Ftcosβsinφn+Ffcosφn
In formula, FnIt is the normal direction cutting force on shear surface；
Step 7: being calculated using the following equation the normal stress on shear surface
In formula, psIt is the normal stress on shear plane；
Step 8: being calculated using the following equation the length of shear surface:
In formula,It is the length of shear surface；
Step 9: the stress distribution that tool arc plough cuts region is considered uniformly, to be calculated using the following equation:
In formula, peIt is the normal stress that plough cuts region, qeIt is the tangential stress that plough cuts region, PthrustIt is normal direction plough shear force, PcutIt is
Tangential plough shear force,It is the length that plough cuts region, μ is coefficient of friction；
Step 10: calculating separately shearing using following formula and stress distribution caused by plough is cut；
In formula, σxxIt is stress along the x-axis direction, σzzIt is stress along the z-axis direction, τxzIt is the shear stress in the direction xz, a is to connect
The half of the length in region is touched, coordinate value x and z indicate the position of calculation point of stress, and p (s) and q (s) are positive and tangential stresses
Value；For share zone, based on step 3 and step 7 as a result, by p (s)=ps, q (s)=qs,Substitute into above formula；It is right
Region is cut in plough, based on step 8 as a result, by p (s)=pe, q (s)=qe,Substitute into above formula；
Step 11: will be sheared using following formula and stress distribution is overlapped caused by plough is cut；
[σ1']=Q1 T[σ1]Q1
[σ2']=Q2 T[σ2]Q2
[σ3]=[σ1']+[σ2']
In formula, [σ1] indicate value of the stress distribution under the coordinate system of shear zone caused by shearing, [σ2] indicate plough cut caused by stress
The value being distributed under the area Li Qie coordinate system, [σ1'] indicate value of the stress distribution under workpiece coordinate system caused by shearing, [σ2'] table
Show value of the stress distribution caused by plough is cut under workpiece coordinate system, [σ3] indicate actual stress distribution value under workpiece coordinate system；Q1
And Q2It is the three-dimensional coordinate transformation matrix of stress tensor；
Step 12: the stress distribution value under inclined cutting unit is transformed into milling coordinate system using following formula；
In formula, φwIt is that milling cutter immerses angle, [σ] is the stress distribution value under milling coordinate system；
Step 13: calculating the stress increment in a tiny time dt using following formula:
[d σ]=[σ (t+dt)]-[σ (t)]
In formula, [d σ] is the stress increment in a tiny time, and [σ (t)] indicates the milling obtained based on step 12 result
The relationship of process stress distribution and time；
Step 14: judging whether workpiece enters mecystasis at some moment using following formula:
In formula, J2It is the second invariant of deviatoric tensor of stress, F is yield surface, τsyIt is the shear yield strength of material, SijExpression is answered partially
Power, αijIndicate back stress；
Step 15: using the stress increment under following formula computational plasticity state:
In formula, E is elasticity modulus of materials, and v is Poisson's ratio, d σijIt is the stress increment obtained based on step 13 result,WithIt is the stress increment under mecystasis, d εxxWith d εyyIt is plastic strain increment, nijIt is the unit on plastic strain rate direction
Normal vector；
Step 16: judging the boundary condition of stress relaxation using following formula:
In formula,It is the residual stress before relaxation,It is overstrain, f1,2,...,6(z) expression one is related with coordinate value z
One non-zero amount；
Step 17: indicating every step relaxed length using following formula:
In formula, M is loose total step number, Δ σijIndicate every step stress relaxation number, Δ εijIndicate every step strain relaxation amount；
Step 18: calculating the stress increment of elastic release process using following formula:
Δσxy=2G Δ εxy
In formula, G indicates elastic properties of materials modulus of shearing；
Step 19: with the stress increment of following formula computational plasticity release process:
Step 20: after calculating relaxation step with following formula, obtained final residual stress:
In formula,WithIt is the final residual stress in the direction workpiece coordinate system x and the direction y respectively.
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| CN111651867B (en) * | 2020-05-15 | 2022-03-08 | 西北工业大学 | Method for determining ultimate shear stress of chip formation in cutting machining |
| CN112180065A (en) * | 2020-09-09 | 2021-01-05 | 中国科学院沈阳自动化研究所 | J-C constitutive model building method of metal material |
| CN113400092B (en) * | 2021-07-01 | 2022-07-19 | 西北工业大学 | Metal cutting force prediction method considering material accumulation |
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