CN107728577B - Instantaneous cutting output planing method based on thin-wall curved-surface machining deformation - Google Patents
Instantaneous cutting output planing method based on thin-wall curved-surface machining deformation Download PDFInfo
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- 238000005520 cutting process Methods 0.000 title claims abstract description 140
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Abstract
The present invention is based on the instantaneous cutting output planing methods of thin-wall curved-surface machining deformation to belong to complex curved surface parts high-quality and high-efficiency Milling Process technical field, is related to a kind of instantaneous cutting output planing method based on detail rigidity for thin-wall curved-surface part machining deformation homogenization.This method is primarily based on surface geometry feature, calculate instantaneous cutting output in machining locus, secondly time-varying rigidity curve is processed using numerical methods of solving thin-wall curved-surface, then the corresponding relationship of instantaneous cutting output Yu workpiece time-varying rigidity and machining deformation is determined, finally to homogenize thin-wall curved-surface machining deformation as the instantaneous cutting output of goal programming, lay the foundation for effectively compensating of thin-wall curved-surface machining deformation.This method has comprehensively considered the influence of surface geometry feature and machined parameters to machining deformation, realize that instantaneous cutting output is planned again by the planning to feed speed, so that work pieces process deformation homogenization, provides prerequisite for the processing of thin-wall complicated curved surface part high-quality and high-efficiency.
Description
Technical field
The invention belongs to complex curved surface parts high-quality and high-efficiency Milling Process technologies, and in particular to one kind is added based on thin-wall curved-surface
The instantaneous cutting output planing method of work deformation.
Background technique
Complex thin-wall curved surface part is widely used in fields such as aerospace, energy source and powers.Complex thin-wall curved surface is made now
Type technology is more mature, but the processing of its high-quality and high-efficiency is still the hot spot and difficult point of industrial circle research.Thin-wall curved-surface part has
The features such as material removal amount is big, workpiece stiffness is low, processing technology is poor is also easy to produce machining deformation under cutting force effect, influences
Thin-wall curved-surface part processing quality, and machining deformation compensation be realize thin-wall curved-surface part high-quality and high-efficiency processing effective way it
One.In thin-wall curved-surface process, instantaneous cutting output is with processing constantly variation, while workpiece stiffness constantly becomes with Working position
Change, causes thin-wall curved-surface machining deformation complicated, non-homogeneous under coupling, machining deformation is compensated and proposes great challenge.By
This, based on rigidity time-varying in thin-wall curved-surface process, instantaneous cutting output of making rational planning for, so that thin-wall curved-surface machining deformation is uniform
Change, and then realize the effective compensation of thin-wall curved-surface machining deformation, is of great significance to the processing of thin-wall curved-surface high-quality and high-efficiency.
A kind of " the aerial blade processing method based on error compensation " of Cao Yan et al. patent announcement CN104096889A,
Aerial blade deformation is controlled by cutting surface finite element analysis and cutter path compensation, reduces the machining deformation of aerial blade
Amount.This method mainly applies finite element software, and calculating process is relatively complicated, is not easy to promote, and has certain limitation.Chen etc.
Document " Deformation prediction and error compensation in multilayer milling
processes for thin-walled parts.International Journal of Machine Tools&
Manufacture, 2009,49,859-864. " reduce machining deformation using multiple compensation method, establish prediction thin-walled parts
The dynamic model of mostly each cutting lay machining deformation compensates current cutting lay based on preceding layer machining deformation error.As a result
Although effectively reducing machining deformation, repeatedly processing compensation seriously affects processing efficiency.
Summary of the invention
The present invention is directed to overcome prior art defect, a kind of instantaneous cutting gauge based on thin-wall curved-surface machining deformation is invented
The method of drawing, for influence of the variation to machining deformation of cutting output instantaneous in thin-wall curved-surface process, with instantaneous cutting output and
The incidence relation processed between instantaneous corresponding workpiece stiffness is fundamental plan principle, comprehensively considers surface geometry feature and processing
Influence of the technological parameter to machining deformation proposes a kind of instantaneous cutting output planing method for homogenizing thin-wall curved-surface machining deformation,
Reduce machining deformation variation, realizes the processing of thin-wall complicated curved surface part high-quality and high-efficiency.
The technical scheme is that a kind of instantaneous cutting output planing method based on thin-wall curved-surface machining deformation, feature
It is, this method has comprehensively considered the influence of surface geometry feature and machined parameters to machining deformation, by feed speed
Planning realizes that instantaneous cutting output is planned again；It is primarily based on surface geometry feature, calculates instantaneous cutting output in machining locus, next is adopted
Time-varying rigidity curve is processed with numerical methods of solving thin-wall curved-surface, then determines that instantaneous cutting output and workpiece time-varying rigidity become to processing
The corresponding relationship of shape is processed finally to homogenize thin-wall curved-surface machining deformation as the instantaneous cutting output of goal programming for thin-wall curved-surface
An effectively compensating is deformed to lay the foundation；Specific step is as follows for method:
1) the instantaneous cutting output of thin-wall curved-surface calculates
To establish the instantaneous cutting output computation model of thin-wall curved-surface, coordinate system is initially set up；
Local coordinate system X is established by origin of cutter-contact point Cc-Yc-Zc, XcAxis direction is direction of feed, ZcAxis direction is cutter
Perpendicular to X in feed motion planecAxis is simultaneously directed toward curved surface outside direction, YcAxis direction follows the right-hand rule；With tool base center O
Tool coordinate system X is established for origint-Yt-Zt, XtAxis is directed toward cutter-contact point direction, Z by cutter heart pointtAxis is along cutter axis orientation, YtAxis direction
Follow the right-hand rule；Workpiece coordinate system X is established as origin using one jiao of workpiece bottom planew-Yw-Zw, make workpiece coordinate system and lathe
Coordinate system is overlapped；Based on original cutter location file, the instantaneous cutting output computation model of thin-wall curved-surface is established；
Contact is closed between instantaneous cutting output variation and workpiece local geometric features, cutter and workpiece in thin-wall curved-surface process
System etc. is directly related, and instantaneous cutting output solving model is established under local dynamic station coordinate system；
By the knife rail curvilinear equation F (x to be processed under workpiece coordinate systemw,yw,zw)=0 is indicated in local coordinate system Xc-Yc-
ZcUnder, from workpiece coordinate system Xw-Yw-ZwTransform to local coordinate system Xc-Yc-Zc, convert front and rear coordinate relationship are as follows:
Wherein Rot (z, α) is around ZwThe spin matrix rotated clockwise, rotation angle α XwAxis and XcAxis is in plane Xw-YwOn
The angle of projection:
Rot(y,γx) it is around YwThe spin matrix that axis rotates clockwise, rotation angle γxFor YwAxis and YcAngle between axis:
Trans(xcw,ycw,zcw) it is workpiece coordinate system Xw-Yw-ZwOrigin is to local coordinate system Xc-Yc-ZcThe translation of origin
Matrix, (xcw,ycw,zcw) motion vector between workpiece coordinate system origin and local coordinate system origin:
It is G (x by equation of the transformed knife rail curve to be processed under local coordinate systemc,yc,zc)=0；Next
The model of unit cutting output is established, cutting output is indicated with the area of cut；In actual processing, for each knife rail curve, knife
Has feed motion in Xw-ZwIn plane；It enablesWithFor adjacent two cutter-contact point, base
In Differential Principle, CiCi+1Process can be equivalent to tapered plane processing；CiAnd Ci+1Corresponding local coordinate system is respectively Xci-
Yci-ZciAnd Xci+1-Yci+1-Zci+1；PiAnd QiRespectively CiAnd Ci+1Along ZciSubpoint of the axis on knife rail curve to be processed, Pi+1
For Ci+1Along Zci+1Subpoint of the axis on knife rail curve to be processed, MiAnd Mi+1Respectively CiAnd Ci+1Point at cutter side edge with it is to be added
The intersection point of work knife rail curve, NiAnd Ni+1Respectively MiAnd Mi+1Along ZcSubpoint of the axis on machined knife rail curve；Knife to be processed
Z can be expressed as under local coordinate system in rail curve feed motion plane1,i=g1,i(xc), it is calculated as the area of cut
Upper border line is integrated, machined knife rail curve is the track of cutter-contact point, can be with table under the local coordinate system in feed motion plane
It is shown as z1,i=g1,i(xc), it is calculated as the area of cut and integrates following boundary line, then from CiTo Ci+1Unit between cutter location
Cutting output SiAre as follows:
Wherein, Si,1Indicate quadrangle CiCi+1QiPiArea, Si,2Indicate triangle CiPiMiArea, Si,3Indicate three sides
Shape Ci+1Pi+1Mi+1Area, Si,4Indicate triangle QiCi+1Pi+1Area；η is Zci+1Axis and excessively Ci+1Point ZciThe parallel lines of axis
Between angle；In local coordinate system Xc-Yc-ZcIn, point N coordinate is Ni(d0·tanλi, 0,0), λiAfter (i=1,2,3 ...) is
With angle, d0For cutting-in；Unit cutting output S can be obtained by arranging above formulaiAre as follows:
The instantaneous cutting output of thin-wall curved-surface is by unit cutting output and the expression of unit cutting time ratio, cutting time t0=li/
Fv, li=| Ci+1-Ci| it is cutter moving distance, FvFor feed speed, then the instantaneous cutting output of thin-wall curved-surface indicates are as follows:
2) solution of thin-wall curved-surface workpiece stiffness curve
The geometrical characteristic of thin-wall curved-surface complexity causes thin-wall curved-surface different location rigidity different, and thin-wall curved-surface workpiece stiffness is bent
It is the key that the instantaneous cutting output planning based on thin-wall curved-surface machining deformation that line, which solves,；It is processed in complex thin-wall curved surface tack knife
In, the variation of material removal amount caused by the variation of Tool in Cutting profile, and then the stiffness variation of thin-wall curved-surface workpiece is influenced, because
This is considered in the foundation of workpiece stiffness analysis model；Cutting profile is effectively characterized in view of Tool in Cutting width, because
This solves cutting width to preferably establish workpiece stiffness analysis model first；
Radius is the square end mill face cutter of R from local coordinate system Xc-Yc-ZcTo tool coordinate system Xt-Yt-ZtChange
Change relationship are as follows:
Wherein, Trans (R, 0,0) is translation matrix, and (R, 0,0) indicates that the origin of tool coordinate system and local coordinate system are former
Displacement between point:
Q (λ, ω) is spin matrix, indicates cutter rotating around YcAxis and ZcAxis rotation, wherein λ is YcAxis and YtThe folder of axis
Angle, angle ω are ZcAxis and ZtThe angle of axis:
Formula (9), (10) are substituted into formula (8), are arranged:
The equation in coordinates of tool base profile in tool coordinate system are as follows:
Joint type (11) and formula (12) obtain tool base profile in local coordinate system Yc-ZcThe projection equation of plane are as follows:
To guarantee processing efficiency, when angle of heel ω=0, tool base cuts profile equation are as follows:
Principal direction rectangular coordinate system x-y-z is established at point of contact C, using main direction of normal as z-axis, is with minimum principal direction
X-axis, using maximum principal direction as y-axis；Under principal direction coordinate system, curved surface can be approximatively with two in the region of point of contact vicinity
Equation of n th order n indicates are as follows:
Wherein, kminFor minimum principal curvatures, kmaxFor maximum principal curvatures；The angle of direction of feed and minimum principal direction is enabled to beThen principal direction coordinate system and local coordinate system relationship are as follows:
Then the neighbouring part knife rail curve of cutter-contact point C is in local coordinate system Xc-Yc-ZcIn equation are as follows:
Enable xc,i=0, obtain the curvilinear equation perpendicular to normal section on machining direction are as follows:
The equation of cutting depth offset line of the knife rail curve in line-spacing direction method section can be approximately:
Wherein, zi' for cutting depth offset line z to coordinate, joint type (14), (19), solving corresponding different knife positions has
The intersection point M of effect cutting profile and cutting depth offset line1,i(xc1,i,yc1,i) and M2,i(xc2,i,yc2,i), obtain cutting width are as follows:
Di=| yc1,i-yc2,i| (20)
Cutting width expression are as follows:
Wherein, kiFor knife rail curve perpendicular to the normal curvature of machining direction at cutter-contact point, and
The segmentation of machining area unit is carried out to complex thin-wall Machining of Curved Surface track according to cutting bandwidth D and cutter location, every
Apply Arbitrary Loads in regime of elastic deformation on a processing unit, solves each machining area unit by finite element numerical method and become
Shape amount, according to the generalized definition of rigidity, rigidity k=F/ δ, wherein δ is workpiece deflection, solves complex thin-wall curved surface part and adds
With the stiffness curve of change in location on work track；
3) instantaneous cutting output planning
According to generalized Hooke law, workpiece elastic deformation amount's Δ δiWith instantaneous cutting output Sτ,iWith workpiece stiffness any position ki
The proportional relationship of ratio, then have:
Wherein CnFor workpiece deformation coefficient of discharge, to make workpiece deformation uniformly, the ratio of instantaneous cutting output and rigidity after planning
Value should be constant Ck0:
Instantaneously the ratio of cutting output and stiffness curve is continually changing, uses CkiIndicate that instantaneous cutting output is cut with corresponding workpiece
The proportionality coefficient for cutting rigidity at position, arranges:
Introduce CpiCorrection factor, Cpi=Ck0/Cki, by formula (23), (24), to make work pieces process deformation uniformly, after planning
The ratio of instantaneous cutting output and rigidity is definite value, is obtained:
Feed speed after being planned:
F′v=Cpi·Fv (26)
Instantaneous cutting output after then planning are as follows:
It is definite value as planning principles using instantaneous cutting output and the ratio of rigidity at corresponding thin-wall curved-surface workpiece cutting position,
Realize that instantaneous cutting output is planned again by the planning to feed speed, so that work pieces process deformation homogenization, is thin-wall complicated song
Workpiece high-quality and high-efficiency processing in face provides prerequisite.
Remarkable result and benefit of the invention is for workpiece stiffness in thin-wall curved-surface process and instantaneous cutting output
Change the influence to processing quality, consider the factor for influencing instantaneous cutting output, instantaneous cutting output is realized by planning feed speed
Plan again.It is comprehensive using instantaneous cutting output relationship proportional to instantaneous corresponding workpiece stiffness is processed as main track planning principles
Conjunction considers the influence of surface geometry feature and machined parameters to machining deformation, and this method effectively realizes homogenization machining deformation,
Guarantee workpiece processing quality and efficiency.
Detailed description of the invention
The overall flow figure of Fig. 1 --- method.
Fig. 2 --- leaf model figure.Wherein, curve 1 indicates bite rail curve.
Fig. 3 --- instantaneous cutting output calculated value and instantaneous cutting output planning value.Wherein, curve 1 is the calculating of instantaneous cutting output
Value, curve 2 are instantaneous cutting output planning value, and X-axis indicates that cutting unit number, Y-axis indicate instantaneous cutting output, unit mm2。
Fig. 4 --- the graph of relation between thin-wall curved-surface workpiece stiffness and cutting unit.Wherein, X-axis indicates that cutting is single
Member number, Y-axis indicate workpiece stiffness value, unit N/m.
Fig. 5 --- thin-wall curved-surface workpiece deflection before instantaneous cutting output is planned.Wherein, X-axis indicates measurement point serial number, Y-axis
Indicate thin-wall curved-surface workpiece deflection, unit mm.
Fig. 6 --- thin-wall curved-surface workpiece deflection after instantaneous cutting output planning.Wherein, X-axis indicates measurement point serial number, Y-axis
Indicate thin-wall curved-surface workpiece deflection, unit mm.
Specific embodiment
Combination technology scheme and the attached drawing specific embodiment that the present invention will be described in detail.
During thin-wall curved-surface part five-axis milling, machining deformation seriously affects the processing quality of workpiece and has not
It can avoid property, while the continuous variation of instantaneous cutting output and the continuous change of workpiece stiffness bring difficulty to processing compensation work,
Can high-quality and high-efficiency completion processing compensation work and part machining accuracy and processing efficiency it is closely related.Accordingly, for such as
The completion machining deformation of what high-quality and high-efficiency compensates problem, has devised and a kind of is with the machining deformation for homogenizing thin-wall curved-surface part
The instantaneous cutting output planing method of target, the overall flow of this method is referring to attached drawing 1.
By taking typical aluminium alloy engine blade as an example, initial cutter location data and MATLAB software meter are obtained by UG software
It calculates and emulates, implementation process that the present invention will be described in detail.
Firstly, modeling to blade, attached drawing 2 show leaf model.For being cut on blade shown in curve 1 in attached drawing 2
Sharpener rail gives working process parameter for speed of mainshaft 3000r/min, cutting-in 0.5mm, feed speed 120mm/min, before cutter
Inclination angle is 10 °, and using four sword flat-end cutters, tool radius 2mm obtains initial cutter location coordinate by post-processing, according to formula
(1)-(7) it iterates to calculate, obtains instantaneous cutting output, curve 1 show instantaneous cutting output calculated value in attached drawing 3.
Then, it is iterated to calculate according to formula (8)-(21), obtains cutting width.Blade cutting tool track is wide according to cutting
Degree and cutter location carry out cutting unit segmentation, establish finite element model.Solid187 unit high-order 3 is selected to tie up 10 node entities knots
Structure unit, using free mesh method, division unit number is 34003.Apply the loading analysis of 15N on cutting unit
Workpiece deflection, according to the generalized definition rigidity k=F/ δ of rigidity, wherein δ is workpiece deflection, and fitting solves workpiece stiffness
Relation curve between cutting unit:
K=-0.6940n4+56.6446n3-1647.4177n2+17679.2622n+16529.0626
Wherein, n is that cutting unit is numbered, n=1,2,3 ... 30, the relation curve between workpiece stiffness and cutting unit is such as
Shown in attached drawing 4.
Finally, establishing the corresponding relationship of machining deformation and instantaneous cutting output and workpiece stiffness ratio, calculated according to formula (24)
C in the processing program of initial plan under Constant feeding ratekiValue, in order to guarantee processing efficiency, planning front and back process time is answered
Unanimously, it may be assumed that
Wherein, tiTo plan that the change feed speed after instantaneous cutting output processes corresponding each unit process time, choose
CkiMean value as planning feed speed standard, can meet planning front and back process time it is consistent, obtainThen C is iterated to calculatepiValue, feed speed after being planned according to formula (25) and (26) with
The instantaneous cutting output planned again, instantaneous cutting output planning value is as shown in curve 2 in attached drawing 3.
For the validity for verifying the method, it is real to carry out the original processing program comparison for planning that resulting processing program and UG are generated
It tests.Using the elastic deformation amount of workpiece in current vortex sensor real-time monitoring process, as deliberated index.
Attached drawing 5 show the elastic deformation amount of workpieces processing before instantaneous cutting output is planned, attached drawing 6 show instantaneous cutting output
Plan the elastic deformation amount of post-processing workpiece.Calculate the deflection variance yields that the experiment of planning front and back measures:
The experimental results showed that the flexible deformation of workpiece homogenizes after instantaneous cutting output planning under identical process time,
As shown in attached drawing 5 and attached drawing 6, S=0.0193 before instantaneous cutting output is planned, S=0.0025 after instantaneous cutting output planning, it is known that become
Shape amount homogenization degree increases 86%.Using it is of the invention with instantaneous cutting output with process instantaneous corresponding workpiece stiffness at than
Example relationship is the planing method of main track planning principles, can effectively uniform thin-wall curved-surface work pieces process deformation.
Machining deformation influences processing quality during the present invention is directed to tack knife five-shaft numerical control milling thin-wall curved-surface part
Problem, has invented a kind of instantaneous cutting output planing method based on thin-wall curved-surface machining deformation, and this method establishes one kind with wink
When cutting output with process the instantaneous cutting output planing method that the instantaneous corresponding proportional relationship of workpiece stiffness is fundamental plan principle, have
Effect realizes homogenization machining deformation, realizes the compensation of high-quality and high-efficiency machining deformation.
Claims (1)
1. a kind of instantaneous cutting output planing method based on thin-wall curved-surface machining deformation, which is characterized in that this method comprehensively considers
The influence of surface geometry feature and machined parameters to machining deformation realizes instantaneous cutting output again by the planning to feed speed
Planning；It is primarily based on surface geometry feature, instantaneous cutting output in machining locus is calculated, secondly uses numerical methods of solving thin-wall curved-surface
Process time-varying rigidity curve, then determine instantaneous cutting output and workpiece time-varying rigidity to machining deformation corresponding relationship, finally with
Homogenization thin-wall curved-surface machining deformation is the instantaneous cutting output of goal programming, is established for effectively compensating of thin-wall curved-surface machining deformation
Basis；Specific step is as follows for method:
1) the instantaneous cutting output of thin-wall curved-surface calculates
To establish the instantaneous cutting output computation model of thin-wall curved-surface, coordinate system is initially set up；
Local coordinate system X is established by origin of cutter-contact point Cc-Yc-Zc, XcAxis direction is direction of feed, ZcAxis direction is tool feeding
Perpendicular to X in plane of movementcAxis is simultaneously directed toward curved surface outside direction, YcAxis direction follows the right-hand rule；It is original with tool base center O
Point establishes tool coordinate system Xt-Yt-Zt, XtAxis is directed toward cutter-contact point direction, Z by cutter heart pointtAxis is along cutter axis orientation, YtAxis direction follows
The right-hand rule；Workpiece coordinate system X is established as origin using one jiao of workpiece bottom planew-Yw-Zw, make workpiece coordinate system and machine coordinates
System is overlapped；Based on original cutter location file, the instantaneous cutting output computation model of thin-wall curved-surface is established；
Contact relationship is straight between instantaneous cutting output variation and workpiece local geometric features, cutter and workpiece in thin-wall curved-surface process
Correlation is connect, instantaneous cutting output solving model is established under local dynamic station coordinate system；
By the knife rail curvilinear equation F (x to be processed under workpiece coordinate systemw,yw,zw)=0 is indicated in local coordinate system Xc-Yc-ZcUnder,
From workpiece coordinate system Xw-Yw-ZwTransform to local coordinate system Xc-Yc-Zc, convert front and rear coordinate relationship are as follows:
Wherein Rot (z, α) is around ZwThe spin matrix rotated clockwise, rotation angle α XwAxis and XcAxis is in plane Xw-YwUpper projection
Angle:
Rot(y,γx) it is around YwThe spin matrix that axis rotates clockwise, rotation angle γxFor YwAxis and YcAngle between axis:
Trans(xcw,ycw,zcw) it is workpiece coordinate system Xw-Yw-ZwOrigin is to local coordinate system Xc-Yc-ZcThe translation matrix of origin,
(xcw,ycw,zcw) motion vector between workpiece coordinate system origin and local coordinate system origin:
It is G (x by equation of the transformed knife rail curve to be processed under local coordinate systemc,yc,zc)=0；Next it establishes
The model of unit cutting output, cutting output are indicated with the area of cut；In actual processing, for each knife rail curve, cutter into
To movement in Xw-ZwIn plane；It enablesWithFor adjacent two cutter-contact point, it is based on micro-
Divide principle, CiCi+1Process be equivalent to tapered plane processing；CiAnd Ci+1Corresponding local coordinate system is respectively Xci-Yci-Zci
And Xci+1-Yci+1-Zci+1；PiAnd QiRespectively CiAnd Ci+1Along ZciSubpoint of the axis on knife rail curve to be processed, Pi+1For Ci+1Edge
Zci+1Subpoint of the axis on knife rail curve to be processed, MiAnd Mi+1Respectively CiAnd Ci+1Cutter side edge and knife rail to be processed at point
The intersection point of curve, NiAnd Ni+1Respectively MiAnd Mi+1Along ZcSubpoint of the axis on machined knife rail curve；Knife rail curve to be processed
Z is expressed as under local coordinate system in feed motion plane1,i=g1,i(xc), integral coboundary is calculated as the area of cut
Line, machined knife rail curve are the track of cutter-contact point, are expressed as z under the local coordinate system in feed motion plane1,i=g1,i
(xc), it is calculated as the area of cut and integrates following boundary line, then from CiTo Ci+1Unit cutting output S between cutter locationiAre as follows:
Wherein, Si,1Indicate quadrangle CiCi+1QiPiArea, Si,2Indicate triangle CiPiMiArea, Si,3Indicate triangle
Ci+1Pi+1Mi+1Area, Si,4Indicate triangle QiCi+1Pi+1Area；η is Zci+1Axis and excessively Ci+1Point ZciBetween the parallel lines of axis
Angle；In local coordinate system Xc-Yc-ZcIn, point N coordinate is Ni(d0·tanλi, 0,0), λi(i=1,2,3 ...) it is heel
Angle, d0For cutting-in；It arranges above formula and obtains unit cutting output SiAre as follows:
The instantaneous cutting output of thin-wall curved-surface is by unit cutting output and the expression of unit cutting time ratio, cutting time t0=li/Fv, li=
|Ci+1-Ci| it is cutter moving distance, FvFor feed speed, then the instantaneous cutting output of thin-wall curved-surface indicates are as follows:
2) solution of thin-wall curved-surface workpiece stiffness curve
The geometrical characteristic of thin-wall curved-surface complexity causes thin-wall curved-surface different location rigidity different, and thin-wall curved-surface workpiece stiffness curve is asked
Solution is the key that the instantaneous cutting output planning based on thin-wall curved-surface machining deformation；In the processing of complex thin-wall curved surface tack knife, knife
The variation of material removal amount caused by the variation of tool cutting profile, and then the stiffness variation of thin-wall curved-surface workpiece is influenced, therefore will
It considers in the foundation of workpiece stiffness analysis model；Cutting profile is effectively characterized in view of Tool in Cutting width, therefore is
Preferably workpiece stiffness analysis model is established, first solution cutting width；
Radius is the square end mill face cutter of R from local coordinate system Xc-Yc-ZcTo tool coordinate system Xt-Yt-ZtTransformation close
System are as follows:
Wherein, Trans (R, 0,0) be translation matrix, (R, 0,0) indicate tool coordinate system origin and local coordinate system origin it
Between displacement:
Q (λ, ω) is spin matrix, indicates cutter rotating around YcAxis and ZcAxis rotation, wherein λ is YcAxis and YtThe angle of axis, angle
ω is ZcAxis and ZtThe angle of axis:
Formula (9), (10) are substituted into formula (8), are arranged:
The equation in coordinates of tool base profile in tool coordinate system are as follows:
Joint type (11) and formula (12) obtain tool base profile in local coordinate system Yc-ZcThe projection equation of plane are as follows:
To guarantee processing efficiency, when angle of heel ω=0, tool base cuts profile equation are as follows:
Principal direction rectangular coordinate system x-y-z is established at point of contact C, using main direction of normal as z-axis, using minimum principal direction as x-axis,
Using maximum principal direction as y-axis；Under principal direction coordinate system, curved surface is indicated in the region of point of contact vicinity with quadratic equation are as follows:
Wherein, kminFor minimum principal curvatures, kmaxFor maximum principal curvatures；The angle of direction of feed and minimum principal direction is enabled to beThen
Principal direction coordinate system and local coordinate system relationship are as follows:
Then the neighbouring part knife rail curve of cutter-contact point C is in local coordinate system Xc-Yc-ZcIn equation are as follows:
Enable xc,i=0, obtain the curvilinear equation perpendicular to normal section on machining direction are as follows:
The equation of cutting depth offset line of the knife rail curve in line-spacing direction method section are as follows:
Wherein, zi' for cutting depth offset line z to coordinate, joint type (14), (19) solve corresponding different knife positions and effectively cut
The intersection point M of profile and cutting depth offset line1,i(xc1,i,yc1,i) and M2,i(xc2,i,yc2,i), obtain cutting width are as follows:
Di=| yc1,i-yc2,i| (20)
Cutting width expression are as follows:
Wherein, kiFor knife rail curve perpendicular to the normal curvature of machining direction at cutter-contact point, and
The segmentation of machining area unit is carried out to complex thin-wall Machining of Curved Surface track according to cutting bandwidth D and cutter location, is added each
Apply Arbitrary Loads in regime of elastic deformation in work order member, solves each machining area element deformation by finite element numerical method
Amount, according to the generalized definition of rigidity, rigidity k=F/ δ, wherein δ is workpiece deflection, solves the processing of complex thin-wall curved surface part
With the stiffness curve of change in location on track；
3) instantaneous cutting output planning
According to generalized Hooke law, workpiece elastic deformation amount's Δ δiWith instantaneous cutting output Sτ,iWith workpiece stiffness any position kiRatio
It is worth proportional relationship, then has:
Wherein CnFor workpiece deformation coefficient of discharge, to make workpiece deformation uniformly, the ratio of instantaneous cutting output and rigidity after planning be should be
Constant Ck0:
Instantaneously the ratio of cutting output and stiffness curve is continually changing, uses CkiIndicate that instantaneous cutting output cuts position with corresponding workpiece
The proportionality coefficient for setting place's rigidity, arranges:
Introduce CpiCorrection factor, Cpi=Ck0/Cki, instantaneous after planning to make work pieces process deformation uniformly by formula (23), (24)
The ratio of cutting output and rigidity is definite value, is obtained:
Feed speed after being planned:
F′v=Cpi·Fv (26)
Instantaneous cutting output after then planning are as follows:
It is definite value as planning principles using instantaneous cutting output with the ratio of rigidity at corresponding thin-wall curved-surface workpiece cutting position, passes through
Instantaneous cutting output is planned again to be realized to the planning of feed speed, so that work pieces process deformation homogenization.
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| CN115167276B (en) * | 2022-06-22 | 2023-05-23 | 武汉益模科技股份有限公司 | Cutter life prediction method based on cutter path running track |
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