CN108415371A - A kind of general five-axle number control machine tool geometric error compensation method - Google Patents

A kind of general five-axle number control machine tool geometric error compensation method Download PDF

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CN108415371A
CN108415371A CN201810092755.7A CN201810092755A CN108415371A CN 108415371 A CN108415371 A CN 108415371A CN 201810092755 A CN201810092755 A CN 201810092755A CN 108415371 A CN108415371 A CN 108415371A
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axis
machine tool
control machine
number control
axle number
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CN108415371B (en
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张卫红
万敏
刘洋
邢婉静
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Northwestern Polytechnical University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/49—Nc machine tool, till multiple
    • G05B2219/49087—Adjust parameter to compensate path deviation

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  • Human Computer Interaction (AREA)
  • Manufacturing & Machinery (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Numerical Control (AREA)

Abstract

The shortcomings that in order to overcome existing five-axle number control machine tool geometric error compensation model that cannot be used in arbitrary structures five-axle number control machine tool, the present invention proposes a kind of general five-axle number control machine tool geometric error compensation method, particular for the non-orthogonal five-axle number control machine tool of rotary shaft.This method individually considers that generating tool axis vector obtains the compensation campaign instruction of rotation axis by solving Paden Kahan subproblems 2 ' first；Then, individually consider cutter location, the compensation campaign that the incremental motion instruction by solving translation shaft obtains translation shaft indirectly instructs.Geometric error compensation method proposed by the present invention can be adapted for the five-axle number control machine tool of arbitrary structures, especially for the non-orthogonal five-axis machine tool of rotary shaft.Meanwhile the present invention provides unified specific analytical expression for the compensation campaign instruction of each kinematic axis.

Description

A kind of general five-axle number control machine tool geometric error compensation method
Technical field
The invention belongs to field of electromechanical technology, and in particular to a kind of general five-axle number control machine tool geometric error compensation method, Particular for the non-orthogonal five-axle number control machine tool of rotary shaft.
Background technology
" S.Ding, X.D.Huang, C.J.Yu, W.Wang, Actual inverse the kinematics for of document 1 position-independent and position-dependent geometric error compensation of five-axis machine tools,International Journal of Machine Tools and Manufacture 111 (2016) 55-62. " discloses one kind by establishing the practical inverse kinematics model of five-axle number control machine tool Method to compensate numerically-controlled machine tool (PIGEs) unrelated to position and (PDGEs) geometric error related with position.This method uses Homogeneous transform matrix (HTM) builds the geometric error model of numerically-controlled machine tool, and utilizes the invertibity and rotational invariance of HTM Acquire the compensation campaign instruction of each kinematic axis.But this method is only applicable to the five-axle number control machine tool of rotating shaft direct cross, Bu Nengyong To be compensated to the geometric error of the nonopiate five-axle number control machine tool of rotary shaft.
" X.D.Zhou, Z.X.Jiang, B.Song, X.Q.Tang, S.Q.Zheng, the A compensation of document 2 method for the geometric errors of five-axis machine tools based on the topology relation between axes,International Journal of Machine Tools and Manufacture 88 (2017) 1993-2007. " discloses a kind of alternative manner of decoupling to compensate five-axle number control machine tool PIGEs and PDGEs.This method acquires rotation axis successively according to topological structure relationship of the machine tool motion axis in machine tool motion chain It is instructed with the compensation campaign of translation shaft.But this method is only applicable to the five-axle number control machine tool of rotating shaft direct cross, cannot be used for rotation The geometric error of the non-orthogonal five-axle number control machine tool of shaft compensates.
The typical feature of document above is：The Geometric Error for Computerized Numerical Control Milling Machine compensation model of foundation does not have versatility, can only Suitable for the five-axle number control machine tool of rotating shaft direct cross, it is not applied for the non-orthogonal five-axle number control machine tool of rotary shaft.In addition, being directed to The geometric error compensation model that specific machine tool structure is established is not directly applicable the five-axle number control machine tool of other structures, and error is mended Repay formula redundant and complicated.
Invention content
Technical problems to be solved
In order to overcome existing five-axle number control machine tool geometric error compensation model that cannot be used in arbitrary structures five shafts numerical controlled machine The shortcomings that bed, the present invention proposes a kind of general five-axle number control machine tool geometric error compensation method, nonopiate particular for rotary shaft Five-axle number control machine tool.
Technical solution
A kind of general five-axle number control machine tool geometric error compensation method, it is characterised in that steps are as follows：
Step 1：The compensation campaign instruction of rotary shaft is obtained by solving Paden-Kahan subproblems 2 '
The compensation campaign instruction of rotary shaft calculates as follows：
Wherein, θpAnd θsFor first rotary shaft counted from workpiece side in the machine tool motion chain that is calculated and second The compensation campaign of rotary shaft instructs, SpAnd SsTo represent the sign function of first rotary shaft and second rotary shaft position；When two A rotation axis is located at S when on workpiece motion s chainp=Ss=-1, the S when two rotation axis are located on tool motion chainp=Ss=1, When a rotation axis is located at another rotation axis is located on tool motion chain on workpiece motion s chain when Sp=-1, Ss=1；Unit to Measure ωpAnd ωsIndicate the positive direction of first rotary shaft and second rotational axis；
u11, c11, c22, u22It calculates as follows：
u1And u2It calculates as follows：
For the five-axle number control machine tool of main shaft rotation
T=Ent
For the five-axle number control machine tool of worktable rotary
For the five-axle number control machine tool of main shaft and worktable rotary
Wherein, EτtIndicate the error transformation matrix of the τ kinematic axis on tool motion chain,It indicates On workpiece motion s chainThe error transformation matrix of a kinematic axis,；For five-axle number control machine tool, m+n=5；WithIndicate that workpiece coordinate system and tool coordinate system are relative to reference to seat when each reference axis amount of exercise of lathe is zero respectively Mark the transformation matrix of system；QwAnd QtDirection vector of the cutter relative to workpiece coordinate system and tool coordinate system is indicated respectively；
c1And c2It calculates as follows：
c1=α ωs+βωsωp+γωp
c2=Tc1=α T ωs+βTωsωp+γTωp
γ is obtained by solving following linear equation in two unknowns group：
Lγ2+ M γ+N=0
Wherein
N=F2+H2-||u1||2
α and β calculates as follows：
α=E γ+F
β=G γ+H
Step 2：Incremental motion instruction by solving translation shaft obtains the compensation campaign instruction of translation shaft indirectly
Introduce the incremental motion instruction δ θ of translation shaftx, δ θyWith δ θz, translation shaft compensation campaign instruction calculate it is as follows：
Wherein,WithFor the compensation campaign instruction for the translation shaft being calculated；θx, θyAnd θzTo pass through ideal inverse The ideal movements for the translation shaft being calculated to kinematics model instruct；Sx, SyAnd SzTo represent X-axis, Y-axis and Z axis position Sign function, works as X-axis, and Y-axis and Z axis are located at S when on workpiece motion s chainx=-1, Sy=-1, SzX-axis, Y-axis and Z axis position are worked as in=- 1 S when on tool motion chainx=1, Sy=1, Sz=1.WithX-axis, Y are indicated respectively The unit vector of axis and Z axis reference axis forward direction；
PwAnd PtThe coordinate for being cutter location in workpiece coordinate system and tool coordinate system；Subscript κ represent machine tool motion chain from from The κ translation shaft that workpiece side counts, κ=1,2,3；EκIndicate the error transformation matrix of the τ kinematic axis on tool motion chain； TκIndicate the translation transformation matrix of the τ kinematic axis on tool motion chain；SκTo represent the sign function of translation shaft position；When flat Moving axis is located at S when on workpiece motion s chainκ=-1, the S when translation shaft is located on tool motion chainκ=1；
Tpw, Tsw, TptAnd TstIndicate influence of the rotary motion to cutter location coordinate in workpiece coordinate system；Their calculating Method is as follows：
For the five-axle number control machine tool of main shaft rotation
Tpw=I4×4
Tsw=I4×4
Tpt=E(n-1)t×Tp
Tst=Ent×Ts
For the five-axle number control machine tool of worktable rotary
Tpw=Emw×Tp
Tsw=E(m-1)w×Ts
Tpt=I4×4
Tst=I4×4
For the five-axle number control machine tool of main shaft and worktable rotary
Tpw=Emw×Tp
Tsw=I4×4
Tpt=I4×4
Tst=E(m-1)t×Ts
Wherein, TpAnd TsIndicate the rotational transformation matrix of first rotary shaft and second rotary shaft.
Advantageous effect
The present invention proposes a general five-axle number control machine tool geometric error compensation method, by solving Paden-Kahan Subproblem 2 ' and the incremental motion instruction for introducing translation shaft, the compensation campaign instruction for five-axle number control machine tool kinematic axis provide unification Specific analytical expression.The present invention can be directly applied for the five shafts numerical controlled machine of arbitrary structures without any other theory deduction Bed, especially for the non-orthogonal five-axle number control machine tool of rotary shaft.
Description of the drawings
Fig. 1 is impeller blade normal error measurement result figure before compensation.
Fig. 2 is impeller blade normal error measurement result figure after compensation.
Specific implementation mode
In conjunction with embodiment, attached drawing, the invention will be further described：
The present invention individually considers that generating tool axis vector obtains the compensation of rotation axis by solving Paden-Kahan subproblems 2 ' first Movement instruction；Then, individually consider cutter location, the incremental motion instruction by solving translation shaft obtains the compensation of translation shaft indirectly Movement instruction.Geometric error compensation method proposed by the present invention can be adapted for the five-axle number control machine tool of arbitrary structures, especially right In the non-orthogonal five-axis machine tool of rotary shaft.Meanwhile the present invention provides unified define for the compensation campaign instruction of each kinematic axis Analytical expression.
The technical solution adopted by the present invention to solve the technical problems is：A kind of general five-axle number control machine tool geometric error benefit Compensation method includes the following steps：
Step 1: the compensation campaign for obtaining rotary shaft by solving Paden-Kahan subproblems 2 ' instructs.
The compensation campaign instruction of rotary shaft calculates as follows：
Wherein, θpAnd θsFor first rotary shaft counted from workpiece side in the machine tool motion chain that is calculated and second The compensation campaign of rotary shaft instructs, SpAnd SsTo represent the sign function of first rotary shaft and second rotary shaft position.When two A rotation axis is located at S when on workpiece motion s chainp=Ss=-1, the S when two rotation axis are located on tool motion chainp=Ss=1, When a rotation axis is located at another rotation axis is located on tool motion chain on workpiece motion s chain when Sp=-1, Ss=1.Unit to Measure ωpAnd ωsIndicate the positive direction of first rotary shaft and second rotational axis.
u11, c11, c22, u22It calculates as follows：
u1And u2It calculates as follows：
For the five-axle number control machine tool of main shaft rotation
T=Ent
For the five-axle number control machine tool of worktable rotary
For the five-axle number control machine tool of main shaft and worktable rotary
Wherein, EτtIndicate the error transformation matrix of the τ kinematic axis on tool motion chain,It indicates On workpiece motion s chainThe error transformation matrix of a kinematic axis,For five-axle number control machine tool, m+n=5.WithIndicate that workpiece coordinate system and tool coordinate system are relative to reference to seat when each reference axis amount of exercise of lathe is zero respectively Mark the transformation matrix of system.QwAnd QtIndicate respectively cutter relative to workpiece coordinate system and
The direction vector of tool coordinate system.
c1And c2It calculates as follows：
c1=α ωs+βωsωp+γωp
c2=Tc1=α T ωs+βTωsωp+γTωp
γ is obtained by solving following linear equation in two unknowns group：
Lγ2+ M γ+N=0
Wherein
N=F2+H2-||u1||2
α and β calculates as follows：
α=E γ+F
β=G γ+H
Step 2: the compensation campaign for obtaining translation shaft indirectly by solving the incremental motion instruction of translation shaft instructs.
Introduce the incremental motion instruction δ θ of translation shaftx, δ θyWith δ θz, translation shaft compensation campaign instruction calculate it is as follows：
Wherein,WithFor the compensation campaign instruction for the translation shaft being calculated.θx, θyAnd θzTo pass through ideal inverse The ideal movements for the translation shaft being calculated to kinematics model instruct.Sx, SyAnd SzTo represent X-axis, the symbol of Y-axis and Z axis position Number function, works as X-axis, Y-axis and Z axis are located at S when on workpiece motion s chainx=-1, Sy=-1, Sz=-1, works as X-axis, and Y-axis and Z axis are located at S when on tool motion chainx=1, Sy=1, Sz=1.WithX-axis, Y-axis are indicated respectively With the unit vector of Z axis reference axis forward direction.
PwAnd PtThe coordinate for being cutter location in workpiece coordinate system and tool coordinate system.Subscript κ represent machine tool motion chain from from The κ translation shaft that workpiece side counts, κ=1,2,3.EκIndicate the error transformation matrix of the τ kinematic axis on tool motion chain. TκIndicate the translation transformation matrix of the τ kinematic axis on tool motion chain.SκTo represent the sign function of translation shaft position.When flat Moving axis is located at S when on workpiece motion s chainκ=-1, the S when translation shaft is located on tool motion chainκ=1.
Tpw, Tsw, TptAnd TstIndicate influence of the rotary motion to cutter location coordinate in workpiece coordinate system.Their calculating Method is as follows：
For the five-axle number control machine tool of main shaft rotation
Tpw=I4×4
Tsw=I4×4
Tpt=E(n-1)t×Tp
Tst=Ent×Ts
For the five-axle number control machine tool of worktable rotary
Tpw=Emw×Tp
Tsw=E(m-1)w×Ts
Tpt=I4×4
Tst=I4×4
For the five-axle number control machine tool of main shaft and worktable rotary
Tpw=Emw×Tp
Tsw=I4×4
Tpt=I4×4
Tst=E(m-1)t×Ts
Wherein, TpAnd TsIndicate the rotational transformation matrix of first rotary shaft and second rotary shaft.
Following embodiment is for illustrating the present invention.Embodiment 1 is for verifying effectiveness of the invention, and embodiment 2 is for testing Demonstrate,prove the versatility of the present invention.
Embodiment 1：
The JR200 worktable rotary formula five-axle number control machine tools of Beijing finishing impression company production are selected to verify the effective of the present invention Property.Workpiece motion s chain is made of Y-axis, B axle and C axis composition, tool motion chain X-axis and Z axis.Kinematic axis is counted from lathe side Sequence is followed successively by C axis, B axle, Y-axis, X-axis and Z axis.
Step 1: the compensation campaign for obtaining rotary shaft by solving Paden-Kahan subproblems 2 ' instructs.
The compensation campaign instruction of rotary shaft calculates as follows：
For the five-axle number control machine tool of the worktable rotary of selection, θpIndicate C axis, θsIndicate B axle, Sp=Ss=-1.
Unit vector ωp=[0,0, -1] and ωs=[0,0, -1].
u11, c11, c22, u22It calculates as follows：
u1And u2It calculates as follows：
For the five-axle number control machine tool of the worktable rotary of selection
Wherein n=2, m=3
c1And c2It calculates as follows：
c1=α ωs+βωsωp+γωp
c2=Tc1=α T ωs+βTωsωp+γTωp
γ is obtained by solving following linear equation in two unknowns group：
Lγ2+ M γ+N=0
Wherein
N=F2+H2-||u1||2
α and β calculates as follows：
α=E γ+F
β=G γ+H
Step 2: the compensation campaign for obtaining translation shaft indirectly by solving the incremental motion instruction of translation shaft instructs.
Incremental motion by introducing translation shaft instructs δ θx, δ θyWith δ θz, translation shaft compensation campaign instruction calculate it is as follows：
For the five-axle number control machine tool S of the worktable rotary of selectionx=Sz=1, Sy=-1. WithTherefore
Wherein S1=-1, S2=S3=-1, Tpw=E2w×Tp, Tsw=E1w×Ts, Tpt=I4×4, Tst=I4×4。
JR200 five-axle number control machine tool Impeller Machining compensation effects are emulated using the present invention, it can by the data in table To find out cutter location and cutter axis orientation error is compensated is greatly reduced.
Cutter spacing point tolerance Cutter axis orientation error
Before compensation 2268.87μrad 348.1μm
After compensation 7.42μrad 1.31μm
Referring to Fig.1, Fig. 2 compensates processing, the normal direction measured using method proposed by the present invention to impeller blade The maximum value of Error Absolute Value is reduced to from 87.7 μm of 28.9 μm of bands of reduction, the absolute value of normal error average value from 71.1 μm 13.0 μm.Therefore it may be concluded that the absolute value of the maximum value and average value for normal error absolute value, uses this hair The geometric error compensation method of bright proposition can improve machining accuracy up to 67.05% and 81.72%, absolutely prove the present invention The validity of the geometric error compensation method of proposition.
Embodiment two：
The non-orthogonal worktable rotary formula five-axle number control machine tool of rotary shaft is selected to verify the versatility of the present invention.Workpiece is transported Dynamic chain is made of Y-axis, B axle and C axis composition, tool motion chain X-axis and Z axis.The sequence of kinematic axis is counted from lathe side successively For C axis, B axle, Y-axis, X-axis and Z axis.
Step 1: the compensation campaign for obtaining rotary shaft by solving Paden-Kahan subproblems 2 ' instructs.
The compensation campaign instruction of rotary shaft calculates as follows：
For the five-axle number control machine tool of the worktable rotary of selection, θpIndicate C axis, θsIndicate B axle, Sp=Ss=-1.Unit Vectorial ωp=[0,0, -1] and
u11, c11, c22, u22It calculates as follows：
u1And u2It calculates as follows：
For the five-axle number control machine tool of the worktable rotary of selection
Wherein n=2, m=3
c1And c2It calculates as follows：
c1=α ωs+βωsωp+γωp
c2=Tc1=α T ωs+βTωsωp+γTωp
γ is obtained by solving following linear equation in two unknowns group：
Lγ2+ M γ+N=0
Wherein
N=F2+H2-||u1||2
α and β calculates as follows：
α=E γ+F
β=G γ+H
Step 2: the compensation campaign for obtaining translation shaft indirectly by solving the incremental motion instruction of translation shaft instructs.
Incremental motion by introducing translation shaft instructs δ θx, δ θyWith δ θz, translation shaft compensation campaign instruction calculate it is as follows：
For the five-axle number control machine tool S of the worktable rotary of selectionx=Sz=1, Sy=-1. WithTherefore
Wherein S1=-1, S2=S3=-1, Tpw=E2w×Tp, Tsw=E1w×Ts, Tpt=I4×4, Tst=I4×4。
The non-orthogonal five-axle number control machine tool Impeller Machining compensation effect of rotary shaft is emulated using the present invention, by table Data can be seen that cutter location and cutter axis orientation error have obtained good compensation, fully demonstrate the present invention versatility.
Cutter spacing point tolerance Cutter axis orientation error
Before compensation 2554.88μrad 365.33μm
After compensation 14.84μrad 2.46μm

Claims (1)

1. a kind of general five-axle number control machine tool geometric error compensation method, it is characterised in that steps are as follows：
Step 1：The compensation campaign instruction of rotary shaft is obtained by solving Paden-Kahan subproblems 2 '
The compensation campaign instruction of rotary shaft calculates as follows：
Wherein, θpAnd θsFor first rotary shaft counted from workpiece side in the machine tool motion chain that is calculated and second rotation The compensation campaign of axis instructs, SpAnd SsTo represent the sign function of first rotary shaft and second rotary shaft position；Turn when two Moving axis is located at S when on workpiece motion s chainp=Ss=-1, the S when two rotation axis are located on tool motion chainp=Ss=1, when one A rotation axis is located at another rotation axis on workpiece motion s chain and is located at S when on tool motion chainp=-1, Ss=1；Unit vector ωp And ωsIndicate the positive direction of first rotary shaft and second rotational axis；
u11, c11, c22, u22It calculates as follows：
u1And u2It calculates as follows：
For the five-axle number control machine tool of main shaft rotation
T=Ent
For the five-axle number control machine tool of worktable rotary
For the five-axle number control machine tool of main shaft and worktable rotary
Wherein, EτtThe error transformation matrix of the τ kinematic axis on expression tool motion chain, τ=1,2 ... n,Indicate workpiece On kinematic chainThe error transformation matrix of a kinematic axis,For five-axle number control machine tool, m+n=5；WithIndicate that workpiece coordinate system and tool coordinate system are relative to reference frame when each reference axis amount of exercise of lathe is zero respectively Transformation matrix；QwAnd QtDirection vector of the cutter relative to workpiece coordinate system and tool coordinate system is indicated respectively；
c1And c2It calculates as follows：
c1=α ωs+βωsωp+γωp
c2=Tc1=α T ωs+βTωsωp+γTωp
γ is obtained by solving following linear equation in two unknowns group：
Lγ2+ M γ+N=0
Wherein
N=F2+H2-||u1||2
α and β calculates as follows：
α=E γ+F
β=G γ+H
Step 2：Incremental motion instruction by solving translation shaft obtains the compensation campaign instruction of translation shaft indirectly
Introduce the incremental motion instruction δ θ of translation shaftx, δ θyWith δ θz, translation shaft compensation campaign instruction calculate it is as follows：
Wherein,WithFor the compensation campaign instruction for the translation shaft being calculated；θx, θyAnd θzTo pass through ideal reverse fortune The dynamic ideal movements instruction for learning the translation shaft that model is calculated；Sx, SyAnd SzTo represent X-axis, the symbol letter of Y-axis and Z axis position Number, works as X-axis, Y-axis and Z axis are located at S when on workpiece motion s chainx=-1, Sy=-1, Sz=-1, works as X-axis, and Y-axis and Z axis are located at cutter S when on kinematic chainx=1, Sy=1, Sz=1.WithX-axis, Y-axis and Z axis are indicated respectively The unit vector of reference axis forward direction；
PwAnd PtThe coordinate for being cutter location in workpiece coordinate system and tool coordinate system；Subscript κ represents machine tool motion chain from from workpiece The κ translation shaft that side counts, κ=1,2,3；EκIndicate the error transformation matrix of the τ kinematic axis on tool motion chain；TκTable Show the translation transformation matrix of the τ kinematic axis on tool motion chain；SκTo represent the sign function of translation shaft position；Work as translation shaft S when on workpiece motion s chainκ=-1, the S when translation shaft is located on tool motion chainκ=1；
Tpw, Tsw, TptAnd TstIndicate influence of the rotary motion to cutter location coordinate in workpiece coordinate system；Their computational methods It is as follows：
For the five-axle number control machine tool of main shaft rotation
Tpw=I4×4
Tsw=I4×4
Tpt=E(n-1)t×Tp
Tst=Ent×Ts
For the five-axle number control machine tool of worktable rotary
Tpw=Emw×Tp
Tsw=E(m-1)w×Ts
Tpt=I4×4
Tst=I4×4
For the five-axle number control machine tool of main shaft and worktable rotary
Tpw=Emw×Tp
Tsw=I4×4
Tpt=I4×4
Tst=E(m-1)t×Ts
Wherein, TpAnd TsIndicate the rotational transformation matrix of first rotary shaft and second rotary shaft.
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Publication number Priority date Publication date Assignee Title
WO2022174657A1 (en) * 2021-02-19 2022-08-25 成都飞机工业（集团）有限责任公司 Fast optimization method for geometric error compensation data of translational axis of five-axis computer numerical control machine tool

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