CN110045682A - The offline compensation method of five-axis robot cutter distortion error based on least square method - Google Patents
The offline compensation method of five-axis robot cutter distortion error based on least square method Download PDFInfo
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Abstract
A kind of offline compensation method of five-axis robot cutter distortion error based on least square method, this method obtains tool path data file according to machined parameters first, solves the peak value Milling Force at each cutter location along tool coordinate axis direction by five-axis robot peak value Milling Force Model；Secondly, selected part cutter location is transformed into after workpiece coordinate system according to image theory based on Flexural cantilever model calculating cutter distortion come iterative compensation cutter location position and generating tool axis vector at equal intervals；Finally, being fitted to obtain deformation-compensated amount along each workpiece coordinate axis direction and the functional relation of corresponding Milling Force based on least square method, and the compensation coordinate position and generating tool axis vector of remaining cutter location are solved using functional relation, obtain compensated cutter path.Under the premise of not tool changing, which is suitable for the compensation processing of other cutter paths under experiment condition.The present invention helps to reduce the cutter distortion error as caused by Milling Force in process, and compensation efficiency is more efficient compared with prior art.
Description
Technical field
The offline compensation method of five-axis robot cutter distortion error based on least square method that the present invention relates to a kind of, to realization
High-precision and the high efficiency processing of complicated skew surface are of great significance, and the invention belongs to mechanical machining technique necks
Domain.
Background technique
Complex-curved class part is widely used in work due to factors such as its good mechanics, fluid property and designs
The every field of industry manufacture.Such part is often the key components and parts of machine, has precision high, the service life is long, reliability height etc.
Feature, the requirement to processing quality are very high.
Five-shaft numerical control processing is suitable for the processing and manufacturing of complex curved surface parts, but in the actual processing process, cutter is due to cutting
The effect for cutting power can occur bending and deformation, and be the error source that can not ignore to influence the machining accuracy of part.Therefore,
The size of cutter distortion error is predicted by establishing cutter distortion error model, and the cutter path of processing part is added
Offline compensation before work is of great significance to eliminate cutter distortion bring error when processing, is the processing quality of part
Provide guarantee.
" Wei Z C, Wang M J, Tang W C, the et al.Form error compensation in of document 1
ball-end milling of sculptured surface with z-level contouring tool path[J]
.The International Journal of Advanced Manufacturing Technology,2013,67(9-
12): 2853-2861. " discloses a kind of comprehensive deformation error compensating method of ball-end milling processing, mainly by milling
It cuts and compensates mismachining tolerance in such a way that tool deflection is as offset after balance is analyzed in part.However, this method
It is only applicable to the three axis ball-end millings processing in Z-shaped profile cutters path, is not suitable for five-axis milling processing.
" Ma W, He G, Zhu L, the et al.Tool deflection error compensation in of document 2
five-axis ball end milling of sculptured surface[J].International Journal of
Andvanced Manufacturing Technology, 2016,84:1421-1430. " disclose a kind of five-axis milling processing
The method of cutter distortion error compensation is mainly iterated compensation by image theory to modify cutter path, reduces processing
Error.However, this method needs all to carry out an iteration compensation to all cutter locations in every cutter path, when iteration repeatedly
Milling Force is calculated, is carrying out that the plenty of time can be consumed when a large amount of cutter locations compensate offline, is making the reduction of part processing efficiency indirectly,
It is not suitable for the cutter distortion error compensation of large complicated carved part.
Summary of the invention
The present invention is based on the analysis to cutter stress deformation during five-axis robot, provide a kind of based on least square method
Five-axis robot cutter distortion error quickly offline compensation method, it is intended to avoid the prior art to knife positions all in every cutter path
Point is all iterated compensation, and iterative repetition calculates the defect of Milling Force every time, before guaranteeing Dimension Measurement precision
It puts, solves the problems, such as that the offline compensation efficiency of complex parts knife rail is low.
The present invention is achieved through the following technical solutions:
A kind of offline compensation method of five-axis robot cutter distortion error based on least square method, it is characterised in that this method
The following steps are included:
1) tool path data file is obtained according to the threedimensional model of processing part and machined parameters, is determined in workpiece end face
One fixed global workpiece coordinate system OW-XYZ；Mobile local tool coordinate system O is established at cutter lower end surfaceC-XYZ, the seat
Mark system origin OCAt point of a knife point, ZCAxis along generating tool axis vector straight up, YCAxis is by ZCAxis and instantaneous direction of feed vector fork
Multiply determination, XCAxis is then determined according to the right-hand rule；
2) transformational relation of tool coordinate system at workpiece coordinate system and each cutter location is established by matrixing:
Wherein, [xW,yW,zW]TFor the point under workpiece coordinate system；[xC,yC,zC]TFor the point under tool coordinate system；
Respectively tool coordinate system is around workpiece coordinate axis YWAxis and ZWThe spin matrix of axis, TpFor the translation matrix of tool coordinate system；
3) the peak value Milling Force along each tool coordinate axis direction is solved according to five-axis robot peak value Milling Force Model:
By cutter it is axially discrete be L cutting edge infinitesimal, by being acted on along axial integral and to J cutter tooth summation
Respectively along tool coordinate axis X on entire cutterC, YCAnd ZCThe instantaneous peak value Milling Force size in direction:
Wherein,Angle is radially contacted at peak value Milling Force position for upper first of cutting edge infinitesimal of cutter tooth j；dFtjl,
dFrjlAnd dFajlIt is tangential at peak value Milling Force position respectively to act on upper first of cutting edge infinitesimal of cutter tooth j, radial direction and axis
To cutting force infinitesimal；And Fz CRespectively along tool coordinate axis XC, YCAnd ZCThe instantaneous peak value Milling Force size in direction；
It is obtained according to the sum of each infinitesimal torque and the relation of equality of concentrated moment:
Wherein, LcFor cutter overall length, hxAnd hyRespectively tool coordinate axis XCDirection and YCConcentrate Milling Force to admittedly on direction
The arm of force of fixed end, hxjlAnd hyjlRespectively tool coordinate axis XCDirection and YCThe arm of force of each infinitesimal Milling Force to fixing end on direction；
4) the cutter total deformation error under the effect of peak value Milling Force is calculated based on Flexural cantilever model:
In peak value Milling ForceWithIt is calculated separately out under effect along tool coordinate axis XCAnd YCThe cutter distortion in direction
Are as follows:
Wherein, E is the elasticity modulus of cutter material, I1And I2The respectively bending stiffness of knife handle and blade, L1It is long for knife handle
Degree；WithRespectively along tool coordinate axis XCAnd YCThe cutter distortion in direction；
Then the total deformation error of cutter location position is
5) m cutter location, i-th of theoretical cutter location position and cutter shaft are chosen from cutter path equal intervals described in step 1)
Vector respectively indicates are as follows:
Wherein, i=1,2 ..., m；For cutter locationThree components under workpiece coordinate system； For generating tool axis vectorThree components under workpiece coordinate system；
A. iteration count value k=1 and dimensional tolerance ε is initialized, judges whether the total deformation error of i-th of cutter location meets
Following formula:
δ (k) < ε
B. if it is not, by i-th of cutter location along tool coordinate axis XCAnd YCThe cutter distortion in directionWithIt is transformed into work
Part coordinate system obtains the deflection along each workpiece coordinate axisWith theoretical cutter location positionWith generating tool axis vectorOn the basis of, the cutter location position of kth time compensation is obtained according to image theoryAnd generating tool axis vectorUpdate cutter location letter
Breath, and enables k=k+1, step 3) and 4) is repeated, until total deformation error is met the requirements；
If c. meeting the requirements, the cutter location information under current equilibrium state is recorded, i.e., after i-th of cutter location finally compensates
Cutter location positionAnd generating tool axis vector
According to the cutter location position under equilibrium stateObtain the deformation-compensated amount [γ along each workpiece coordinate axis directionix；
γiy；γiz]；
Step a~c is repeated, the cutter location of selection is traversed, respectively obtains m cutter location along the change of each workpiece coordinate axis direction
Shape compensation rate:
6) by step 3) along the peak value Milling Force of each tool coordinate axis directionAnd Fz CAnd workpiece and cutter are sat
The transformational relation of mark system is obtained along workpiece coordinate axis XW, YWAnd ZWThe Milling Force in directionAnd Fz W:
Milling Force of the m cutter location then chosen along each workpiece coordinate axis direction are as follows:
By obtained m cutter location along workpiece coordinate axis XWThe deformation-compensated amount in direction is surpassed with corresponding Milling Force size
Determine equation group:
I.e.
Wherein m is multinomial number, and n is polynomial unknown number number, m > n；
It is fitted to obtain along workpiece coordinate axis X based on least square methodWThe deformation-compensated amount γ in directionxWith corresponding milling
PowerFunctional relation
Wherein,For the multinomial coefficient of fitting function relationship；
7) it solves to obtain along workpiece coordinate axis Y with method identical in step 6)WAnd ZWThe deformation-compensated amount in direction with it is corresponding
The functional relation of Milling ForceWith γ (Fz W), remaining cutter location, which is calculated, using functional relation mends along workpiece coordinate shaft distortion
The amount of repaying γrest, and then obtain the compensated coordinate position of remaining cutter location and generating tool axis vector；
8) all compensated cutter location information are arranged, compensated cutter path and nc program are obtained, i.e., it is complete
It is quickly compensated offline at the cutter distortion error of the cutter path.
Compared with prior art, the present invention having the following advantages that and high-lighting technical effect: the present invention has fully considered five
The influence that cutter distortion processes part in axis process obtains functional relation by fitting and directly sits cutter location along workpiece
The deformation-compensated amount in parameter direction is connected with corresponding Milling Force, is obtained each cutter location by functional relation direct solution and is compensated
Position afterwards avoids and is iterated compensation to cutter locations all in every cutter path, and iterative repetition calculates milling every time
The defect for cutting power realizes the quick offline compensation of cutter distortion error, and under the premise of not tool changing, and obtained function closes
System is suitable for the compensation processing of other cutter paths under experiment condition, and compensation efficiency more efficiently, has compared with prior art
Good application prospect.Meanwhile present invention effect in the cutter distortion error to large complicated carved part compensates offline is outstanding
It is significant.
Detailed description of the invention:
Fig. 1 is that the five-axis robot cutter distortion error based on least square method compensates flow chart offline.
Fig. 2 is skew surface part machining sketch chart.
Fig. 3 (a) and 3 (b) is the position angle schematic diagram of peak value Milling Force in monodentate and multiple tooth situation respectively.
Fig. 4 is Flexural cantilever model schematic diagram.
Fig. 5 is according to cutter distortion come the schematic diagram of mirror compensated cutter location position and generating tool axis vector.
Fig. 6 is along workpiece coordinate axis XWThe function relation figure of Direction distortion compensation rate and corresponding Milling Force.
Fig. 7 is along workpiece coordinate axis YWThe function relation figure of Direction distortion compensation rate and corresponding Milling Force.
Fig. 8 is the location error comparison diagram of cutter location in cutter path after not compensating and compensate.
Appended drawing reference: 1-workpiece；2-cutters；The cutting of 3-monodentates；4-multiple tooth cuttings；5-cutters and work piece contact zone
Domain；6-theoretical tool positions；7-practical tool positions；8-compensation tool positions.
Specific embodiment
Fig. 1 is the offline compensation method flow chart of five-axis robot cutter distortion error based on least square method.The method
Tool path data file is obtained according to the threedimensional model of processing part and machined parameters first, establishes workpiece coordinate system and knife position
Tool coordinate system at point, and obtain the transformational relation of workpiece and tool coordinate system；Secondly, according to five-axis robot peak value Milling Force mould
Type solves the peak value Milling Force size along each tool coordinate axis direction, and obtains corresponding trail force load position according to moment conditions；
Again, m cutter location is chosen in the cutter path equal intervals, is calculated based on Flexural cantilever model and chooses peak value milling at cutter location
The cutter distortion under power effect is cut, is transformed into after workpiece coordinate system according to image theory come iterative compensation cutter location position and knife
Axial vector records equilbrium position and obtains the deformation-compensated amount along each workpiece coordinate axis；Finally, being obtained according to coordinate system transformational relation
To the Milling Force chosen at cutter location along workpiece coordinate axis direction, it is fitted to obtain along workpiece coordinate axis direction based on least square method
Deformation-compensated amount and the functional relation of corresponding Milling Force size, and using function solve the compensation position of remaining cutter location with
Generating tool axis vector completes five-axis robot cutter distortion error to obtain compensated cutter path and nc program
Quickly offline compensation.The present invention has fully considered the influence that cutter distortion processes part during five-axis robot, passes through fitting
It obtains functional relation directly to connect cutter location with corresponding Milling Force along the deformation-compensated amount of workpiece coordinate axis direction, pass through
Functional relation direct solution obtains the compensated position of each cutter location, avoids and carries out to cutter locations all in every cutter path
Iterative compensation, and iterative repetition calculates the defect of Milling Force every time, realizes the quick offline compensation of cutter distortion error, and
And under the premise of not tool changing, obtained functional relation is suitable for the compensation processing of other cutter paths under experiment condition, mends
It is more efficient compared with prior art to repay efficiency, has a good application prospect.Meanwhile the present invention is to large complicated carved part
Cutter distortion error compensate offline in effect it is especially pronounced.
The present invention will be further described with reference to the accompanying drawings and embodiments.
Step 1, tool path data file (total M knife position is obtained according to the threedimensional model of processing part and machined parameters
Point), it is as shown in Figure 2 to establish tool coordinate system at workpiece coordinate system and cutter location；
1) a fixed global workpiece coordinate system O is determined in workpiece end faceW-XYZ, origin OWWith three reference axis XW
Axis, YWAxis and ZWAxis is fixed；
2) mobile local tool coordinate system O is established at milling cutter lower end surfaceC-XYZ, coordinate origin OCPositioned at point of a knife point
Place, ZCAxis along generating tool axis vector straight up, YCAxis is by ZCAxis and the vector multiplication cross of instantaneous direction of feed are determining, XCAxis then basis
The right-hand rule determines；
Step 2, the transformational relation of tool coordinate system and workpiece coordinate system at each cutter location is established；
Pass through the cutter location position under workpiece coordinate systemAnd generating tool axis vector
The tool coordinate system at cutter location is obtained around workpiece coordinate axis YWThe angle turned over is θy, around workpiece coordinate axis ZWThe angle turned over
For θz, then any point may switch to workpiece coordinate system, transition matrix T under tool coordinate system are as follows:
Wherein,Respectively tool coordinate system is around YWAxis and ZWThe spin matrix of axis, TpFor the flat of tool coordinate system
Matrix is moved, is respectively indicated as follows:
At this point, the coordinate transformation relation of workpiece coordinate system and the tool coordinate system at cutter location may be expressed as:
[xW,yW,zW,1]T=T [xC,yC,zC,1]T
Wherein, [xW,yW,zW]TFor the point under workpiece coordinate system；[xC,yC,zC]TFor the point under tool coordinate system；
Step 3, the transformational relation based on workpiece and tool coordinate system solves edge according to five-axis robot peak value Milling Force Model
The peak value Milling Force size of each tool coordinate axis direction, and corresponding trail force load position is obtained according to moment conditions；
1) according to peak value Milling Force Model, the corresponding cutter radial contact angle in maximum Milling Force position at cutter location is obtained:
For tool in cutting sword closer to the place of entrance angle, instantaneous undeformed chip thickness is bigger, by taking monodentate is cut as an example, when
When all axial cutting edges of cutter tooth are just cut, the sum of instantaneous undeformed chip thickness maximum, position at this time is exactly peak value
The position of Milling Force；
As shown in figure 3, being cut when cutter monodentate milling arc length is less than angle between teeth for monodentate, at this time peak value Milling Force position
The bottom contact angle for setting corresponding first cutter tooth isWhen monodentate milling arc length is greater than angle between teeth,
For multiple tooth cutting, the bottom contact angle of corresponding first cutter tooth in peak value Milling Force position is at this time
Wherein, θentryFor entrance angle, apFor axial cutting-in, α is cutter helical angle, and r is tool radius,For angle between teeth；
By cutter axially it is discrete be L cutting infinitesimal, cutter tooth number be J, then upper first of cutting edge infinitesimal of cutter tooth j is at peak
The angle that radially contacts at value Milling Force position is
Wherein,For the bottom contact angle of corresponding first cutter tooth in peak value Milling Force position；Dz is cutting infinitesimal height；
2) by, along axial integral and to the summation of each cutter tooth, being obtained acting on entire milling cutter respectively to cutting force infinitesimal
Along tool coordinate axis XC, YCAnd ZCThe instantaneous peak value Milling Force in direction:
Wherein,Angle is radially contacted at peak value Milling Force position for upper first of cutting edge infinitesimal of cutter tooth j；dFtjl,
dFrjl, dFajlIt is tangential at peak value Milling Force position respectively to act on upper first of cutting edge infinitesimal of cutter tooth j, it is radial and
Axial cutting force infinitesimal；And Fz CRespectively along tool coordinate axis XC, YCAnd ZCThe instantaneous peak value Milling Force in direction is big
It is small；
3) it is obtained according to the sum of each infinitesimal torque and the relation of equality of concentrated moment:
Wherein, LcFor cutter overall length, hxAnd hyRespectively workpiece coordinate axis XCDirection and YCConcentrate Milling Force to admittedly on direction
The arm of force of fixed end, hxjlAnd hyjlRespectively workpiece coordinate axis XCDirection and YCThe arm of force of each infinitesimal Milling Force to fixing end on direction；
Arrange to obtain position hxAnd hyIt is respectively as follows:
Step 4, the cutter total deformation error under the effect of peak value Milling Force is calculated based on Flexural cantilever model；
Cutter is reduced to one end to fix, the two-part cantilever beam that one end overhangs, as shown in Figure 4.Since cutter is axially rigid
Degree is very big, therefore axial Milling Force is deformed caused by cutter and be can be ignored；In peak value Milling ForceWithUnder effect
It calculates separately out along tool coordinate axis XCAnd YCThe cutter distortion in direction are as follows:
Wherein, E is the elasticity modulus of cutter material, I1And I2The respectively bending stiffness of knife handle and blade, L1It is long for knife handle
Degree；WithRespectively along tool coordinate axis XCAnd YCThe cutter distortion in direction；
Then the total deformation error of cutter location position is
Step 5, m cutter location is chosen from cutter path equal intervals described in step 1, obtains choosing cutter location along cutter seat
The deflection in parameter direction solves m according to mirror image iteration compensation method and chooses cutter location along the change of each workpiece coordinate axis direction
Shape compensation rate；
1) cutter location is taken every ten cutter locations from the cutter path, chooses m cutter location, i-th of reason altogether
It is respectively indicated by cutter location position with generating tool axis vector are as follows:
Wherein, i=1,2 ..., m；For cutter locationThree components under workpiece coordinate system； For generating tool axis vectorThree components under workpiece coordinate system；
2) iteration count value k=1 and dimensional tolerance ε is initialized, judges whether i-th of cutter location position total deformation error be full
Foot formula:
δ (k) < ε
A. by i-th of cutter location along tool coordinate axis XCAnd YCThe cutter distortion in directionWithIt is transformed into workpiece seat
Mark system, obtains the deflection along each workpiece coordinate axisWith theoretical cutter location positionWith generating tool axis vectorFor
Benchmark obtains the compensated cutter location position of kth time according to image theoryAnd generating tool axis vectorCutter location information is updated, and
K=k+1 is enabled, step 3 and 4 is repeated, until total deformation error is met the requirements；
As shown in figure 5, i-th of cutter location position and generating tool axis vector are expressed as in theoretical cutter pathWithCutter is acted on by Milling Force and being deformed in process, practical cutter location position
It sets and is with generating tool axis vectorWithError vectorThen
Cutter location position and generating tool axis vector after single compensation can respectively indicate are as follows:
Wherein,
If b. meeting the requirements, the cutter location information under current equilibrium state is recorded, i.e., final compensated cutter location position
It setsAnd generating tool axis vector
According to the cutter location position under equilibrium stateObtain the deformation-compensated amount [γ along each workpiece coordinate axis directionix；
γiy；γiz]；
3) step 2) is repeated, the cutter location of selection is traversed, respectively obtains m cutter location along the change of each workpiece coordinate axis direction
Shape compensation rate:
Step 5, it obtains choosing at cutter location along workpiece coordinate axis direction Milling Force according to coordinate system transformational relation
And Fz W, it is fitted to obtain the function along each deformation-compensated amount of workpiece coordinate axis direction and corresponding Milling Force size based on least square method
RelationshipWith γ (Fz W), along workpiece coordinate axis XWAnd YWThe functional relation in direction is respectively such as Fig. 6 and Fig. 7 institute
Show, and solves the compensated coordinate position of remaining cutter location and generating tool axis vector using function；
1) respectively along workpiece coordinate axis XW, YWAnd ZWThe Milling Force in directionAnd Fz WIt is obtained by following transformational relation:
Milling Force of the m cutter location then chosen along each workpiece coordinate axis direction are as follows:
2) the m cutter location as obtained in step 4 is along workpiece coordinate axis XWThe deformation-compensated amount in direction and corresponding Milling Force
The available over-determined systems of size:
I.e.
Wherein m is multinomial formula number, and n is polynomial unknown number number, m > n；
After being carried out vectorization are as follows:
In general obvious equation group does not solve, so allowing the equation to set up as far as possible to choose most suitable β, introduce
Residual sum of squares (RSS) function S:
WhenWhen, S (β) is minimized, it is denoted as:
Most it is worth by asking function S (β) differential, available:
If matrixNonsingular, then β has unique solution:
It has obtained along workpiece coordinate axis XWThe deformation-compensated amount γ in directionxWith corresponding Milling ForceFunctional relation
It is solved and is obtained along workpiece coordinate axis Y respectively with above-mentioned identical methodW, ZWThe deformation-compensated amount γ in directiony, γzWith
Corresponding Milling ForceFz WFunctional relationWith γ (Fz W)；
3) deformation-compensated amount γ of remaining cutter location along each workpiece coordinate axis direction is calculated using functional relationrest:
And then obtain the compensated coordinate position of remaining cutter location and generating tool axis vector；Under the premise of not tool changing, the function
Relationship is suitable for the compensation processing of other cutter paths under experiment condition.
Step 6, all compensated cutter location information are arranged, compensated cutter path and nc program are obtained,
Five-axis robot cutter distortion error is completed quickly to compensate offline.Emulate obtain do not compensate and compensate after knife in cutter path
The location error comparison in site is as shown in Figure 8.
Claims (2)
1. a kind of offline compensation method of five-axis robot cutter distortion error based on least square method, it is characterised in that this method packet
Include following steps:
1) tool path data file is obtained according to the threedimensional model of processing part and machined parameters, determines one in workpiece end face
Fixed global workpiece coordinate system OW-XYZ；Mobile local tool coordinate system O is established at cutter lower end surfaceC-XYZ, the coordinate system
Origin OCAt point of a knife point, ZCAxis along generating tool axis vector straight up, YCAxis is by ZCAxis and instantaneous direction of feed vector multiplication cross are true
It is fixed, XCAxis is then determined according to the right-hand rule；
2) transformational relation of tool coordinate system at workpiece coordinate system and each cutter location is established by matrixing:
Wherein, [xW,yW,zW]TFor the point under workpiece coordinate system；[xC,yC,zC]TFor the point under tool coordinate system；Respectively
It is tool coordinate system around workpiece coordinate axis YWAxis and ZWThe spin matrix of axis, TpFor the translation matrix of tool coordinate system；
3) the peak value Milling Force along each tool coordinate axis direction is solved according to five-axis robot peak value Milling Force Model:
By cutter it is axially discrete be L cutting edge infinitesimal, by obtaining acting on whole along axial integral and to J cutter tooth summation
Respectively along tool coordinate axis X on a cutterC, YCAnd ZCThe instantaneous peak value Milling Force size in direction:
Wherein,Angle is radially contacted at peak value Milling Force position for upper first of cutting edge infinitesimal of cutter tooth j；dFtjl, dFrjlWith
dFajlIt is tangential at peak value Milling Force position respectively to act on upper first of cutting edge infinitesimal of cutter tooth j, radial and axial cutting
Power infinitesimal；WithRespectively along tool coordinate axis XC, YCAnd ZCThe instantaneous peak value Milling Force size in direction；
It is obtained according to the sum of each infinitesimal torque and the relation of equality of concentrated moment:
Wherein, LcFor cutter overall length, hxAnd hyRespectively tool coordinate axis XCDirection and YCConcentrate Milling Force to fixing end on direction
The arm of force, hxjlAnd hyjlRespectively tool coordinate axis XCDirection and YCThe arm of force of each infinitesimal Milling Force to fixing end on direction；
4) the cutter total deformation error under the effect of peak value Milling Force is calculated based on Flexural cantilever model:
In peak value Milling ForceWithIt is calculated separately out under effect along tool coordinate axis XCAnd YCThe cutter distortion in direction are as follows:
Wherein, E is the elasticity modulus of cutter material, I1And I2The respectively bending stiffness of knife handle and blade, L1For shank length；WithRespectively along tool coordinate axis XCAnd YCThe cutter distortion in direction；
Then the total deformation error of cutter location position is
5) m cutter location, i-th of theoretical cutter location position and generating tool axis vector are chosen from cutter path equal intervals described in step 1)
It respectively indicates are as follows:
Wherein, i=1,2 ..., m；For cutter locationThree components under workpiece coordinate system； For generating tool axis vectorThree components under workpiece coordinate system；
A. iteration count value k=1 and dimensional tolerance ε is initialized, under judging whether the total deformation error of i-th of cutter location meets
Formula:
δ (k) < ε
B. if it is not, by i-th of cutter location along tool coordinate axis XCAnd YCThe cutter distortion in directionWithIt is transformed into workpiece seat
Mark system, obtains the deflection along each workpiece coordinate axisWith theoretical cutter location positionWith generating tool axis vectorFor base
Standard obtains the cutter location position of kth time compensation according to image theoryAnd generating tool axis vectorCutter location information is updated, and enables k
=k+1 repeats step 3) and 4), until total deformation error is met the requirements；
If c. meeting the requirements, the cutter location information under current equilibrium state is recorded, i.e. the final compensated knife of i-th of cutter location
Site locationAnd generating tool axis vector
According to the cutter location position under equilibrium stateObtain the deformation-compensated amount [γ along each workpiece coordinate axis directionix；γiy；
γiz]；
Step a~c is repeated, the cutter location of selection is traversed, the deformation for respectively obtaining m cutter location along each workpiece coordinate axis direction is mended
The amount of repaying:
6) by step 3) along the peak value Milling Force of each tool coordinate axis directionWithAnd workpiece and tool coordinate system
Transformational relation obtain along workpiece coordinate axis XW, YWAnd ZWThe Milling Force in directionAnd Fz W:
Milling Force of the m cutter location then chosen along each workpiece coordinate axis direction are as follows:
By obtained m cutter location along workpiece coordinate axis XWThe deformation-compensated amount in direction obtains overdetermination side with corresponding Milling Force size
Journey group:
I.e.
Wherein m is multinomial number, and n is polynomial unknown number number, m > n；
It is fitted to obtain along workpiece coordinate axis X based on least square methodWThe deformation-compensated amount γ in directionxWith corresponding Milling Force
Functional relation
Wherein,For the multinomial coefficient of fitting function relationship；
7) it solves to obtain along workpiece coordinate axis Y with method identical in step 6)WAnd ZWThe deformation-compensated amount in direction and corresponding milling
The functional relation of powerWithRemaining cutter location is calculated along workpiece coordinate shaft distortion compensation rate using functional relation
γrest, and then obtain the compensated coordinate position of remaining cutter location and generating tool axis vector；
8) all compensated cutter location information are arranged, compensated cutter path and nc program is obtained, that is, completes
The cutter distortion error of the cutter path quickly compensates offline.
2. a kind of five-axis robot cutter distortion error based on least square method described in accordance with the claim 1 side of compensation offline
Method, it is characterised in that: the process tool selects flat-end cutter or rose cutter.
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| CN201910308206.3A Active CN110045682B (en) | 2019-04-17 | 2019-04-17 | Five-axis machining cutter deformation error off-line compensation method based on least square method |
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| CN114995281A (en) * | 2022-05-10 | 2022-09-02 | 清华大学 | Non-developable straight line curved surface optimal tool position planning method and device |
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