CN109375580A - A kind of geometric error recognition methods of the five-axis machine tool yaw based on double ball bars - Google Patents
A kind of geometric error recognition methods of the five-axis machine tool yaw based on double ball bars Download PDFInfo
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- 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
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract
The invention discloses a kind of geometric error recognition methods of five-axis machine tool yaw based on double ball bars, firstly, the moving condition based on five-axis machine tool tilt head, proposes three kinds of X-direction, Y-direction and Z-direction measurement patterns respectively；Secondly, establishing the relative displacement equation of two DBB balls under three kinds of measurement patterns respectively on the basis of homogeneous transform matrix (HTM) and theoretical multi-body system (MBS)；Finally, the geometric error parameter of identification tilt head completely.The present invention has recognized the error term of yaw whole, solves existing coupling phenomenon between parameter, and identification precision is high, has versatility, the error identification for five-axis machine tool yaw provides reference.
Description
Technical field
The present invention relates to a kind of geometric error recognition methods of five-axis machine tool yaw based on double ball bars.The present invention is applicable in
In numerically-controlled machine tool, belong to precision processing technology and field of industrial automation control.
Background technique
With the precision machined fast development of complex parts, workpiece geometries are increasingly complicated, precision machined to meet
It is required that five-axle number control machine tool has been more and more widely used.Five-axle number control machine tool has higher material removing rate, relative to
The advantages that positioning of workpiece and capacity of orientation and lower production cost.However, relative to three axis numerically controlled machine, due to machine
The increase of bed yaw, results in more geometric error sources, so that existing five-axle number control machine tool cannot provide and three number of axle
The identical machining accuracy of lathe is controlled, to hinder the precision machined exploitation of five axis and actual implementation.
In the past few decades, double ball bars have been demonstrated the calibration that can be competent at rotary axis of machine tool, and many is ground
Study carefully personnel and developed some effective methods to measure and identify the geometric error of five-axle number control machine tool, but is directed to five axis
The geometric error recognition methods of numerically-controlled machine tool yaw is seldom.And existing discrimination method can only recognize the geometry unrelated with position
Error.Therefore, exploitation is very necessary suitable for the geometric error recognition methods of five-axle number control machine tool yaw.
Summary of the invention
For five-axle number control machine tool yaw geometric error identification the problem of, the present invention provides a kind of based on double balls
The geometric error discrimination method of bar instrument and the five-axle number control machine tool yaw of many-body theory, The present invention reduces lathe geometric error ginsengs
Several coupled relations, it is theoretical using double ball bars and Duo Ti, establish respectively yaw in the Y direction, X-direction, Z-direction measurement pattern
Under the equation of motion, to realize the identification of yaw geometric error parameter.
A kind of geometric error recognition methods of the five-axis machine tool yaw based on double ball bars, method includes the following steps:
(1) it is based on many-body theory, establishes adjacent two-particle systems relation equation
Fig. 1 is the situation between two adjacent motion bodies, { rj}={ rx ry rz 1}TIndicate P point in BjBody is sat
The location matrix in system is marked, wherein rx, ry, rzRespectively P point is in BjSpace coordinate in body coordinate system is sat in three Descartes
Mark system adds 1, forms a four-vector, then by many-body theory it is found that P point is in BiLocation matrix in body coordinate system indicates
Are as follows:
WhereinRespectively indicate BiBody and BjRelative position transformation matrix between body, phase
To position error transformation matrix, relative motion transformation matrix, relative motion error transformation matrix.
(2) the geometric error parameter identification method of lathe yaw
Five-axle number control machine tool yaw shares 8 geometric error parameters, wherein related with location point have 6, it is δ respectivelyx
(B), δy(B), δz(B), εx(B), εy(B), εz(B), unrelated with location point to have 2, εxB, εBz。
As shown in Fig. 2, being expressed as ball 1 by what the knife rest on yaw stepped up, it is expressed as ball 2 on workbench, is passed through
The change in location of two balls is detected to realize the measurement of yaw.In the measurement process of double ball bars, yaw is connected by multi-axial Simultaneous
Bar is mobile, and the central point with driving spindle around ball 1 rotates, and position needs to remain unchanged.Fig. 3-Fig. 5 respectively illustrates the side Y
To three kinds of measurement patterns of X-direction and Z-direction.For the ease of research, the coordinate system of the central point of ball 2 is expressed as O-XYZ,
And the coordinate system of the centre of gyration of yaw is expressed as O '-X ' Y ' Z '.That is, O-XYZ is remain stationary, O '-X ' Y ' Z ' and and yaw
It moves together.Fig. 6-Fig. 8 shows the location diagram of three kinds of measurement patterns.Due to the presence of the geometric error of yaw, ball 1
Central point is respectively offset from ideal position, and ideal position is expressed as A, C and D, physical location, is expressed as A ', C ' and
D′.In addition, the coordinate of A, C and D respectively indicate in O '-X ' Y ' Z ' are as follows:
{A}O′=[0 0-L 1]T (2)
{C}O′=[0 0-L 1]T (3)
{D}O′=[0 0-L 1]T (4)
Wherein, L indicates the cutter length between the centre of gyration of yaw and the center of ball 1.
(3) measurement pattern of Y-direction
Such as Fig. 3 and Fig. 6, according to formula (1) it is found that D ' positions in coordinate system O-XYZ are as follows:
Wherein, BjIndicate the rotation angle of the yaw when main shaft is moved to position j from initial position.Use dyIndicate that Y-direction is surveyed
The original length of club in amount mode.By simplification (5) and ignore higher order term, in coordinate system O-XYZ, between point D ' and O
Distance indicates are as follows:
On the j of position, LD′OIt is available for the physical length of club:
Wherein, Δ dyIt indicates in measurement pattern in the Y direction, length variable quantity of the club from initial position to position j.It is logical
It crosses and simplifies (7) and ignore higher order term, obtain:
L(εBz cos Bj-εxB sin Bj+εx(Bj))+δy(Bj)=Δ dy (8)
It is assumed that Qj=εBz cos Bj-εxB sin Bj+εx(Bj), then:
LQj+δy(Bj)=Δ dy (9)
For different L values, obtain:
According to (10) it is found that δy(Bj) and QjIt respectively indicates are as follows:
Work as Bj=0 °, yaw is in initial position, εx(Bj)=0, therefore:
εBz=Q0 (13)
Work as BjAt=90 ° or 270 °:
Due to εx(Bj) have periodically, so:
εx(Bj)=Qj-εBz cos Bj+εxB sin Bj (17)
(4) measurement pattern of X-direction
Such as Fig. 4 and Fig. 7, known according to formula (1), A ' positions in coordinate system O-XYZ are as follows:
Use dxIndicate the original length of club in X-direction measurement pattern.By simplified style (18) and ignore higher order term, is sitting
In mark system O-XYZ, point the distance between A ' and O are indicated are as follows:
On the j of position, LA′OFor the physical length of club, obtain:
Wherein, Δ dxIndicate length variable quantity of the club from initial position to position j in the measurement pattern of X-direction.Letter
Change (20) and ignore higher order term, obtains:
-L cos Bjεy(Bj)+cos Bjδx(Bj)+sin Bjδz(Bj)=Δ dx (21)
It enables, Pj=cos Bjδx(Bj)+sin Bjδz(Bj), then,
-L cos Bjεy(Bj)+Pj=Δ dx (22)
For different L values, obtain:
Then:
(5) measurement pattern of Z-direction
Such as Fig. 5 and Fig. 8, according to formula (1) it is found that C ' positions in coordinate system O-XYZ are as follows:
Use dzIndicate the original length of club in Z-direction measurement pattern.By simplified style (26) and ignore higher order term, is sitting
In mark system O-XYZ, point the distance between C ' and O are indicated are as follows:
On the j of position, LC′OFor the physical length of club, obtain:
Wherein, Δ dzIndicate length variable quantity of the club from initial position to position j in the measurement pattern of Z-direction.Letter
Change (28) and ignore higher order term, obtains:
L sin Bjεy(Bj)+cos Bjδz(Bj)-sin Bjδx(Bj)=Δ dz (29)
If it is assumed that Rj=cos Bjδz(Bj)-sin Bjδx(Bj) (30)
Then, Rj=Δ dz-L sin Bjεy(Bj) (31)
In conjunction with (25) (30), δz(Bj)=cos BjRj+sin BjPj (32)
δx(Bj)=cos BjPj-sin BjRj (33)
So far, eight error parameters relevant to yaw all pick out.
Compared with prior art, the invention has the following advantages that
The present invention is based on many-body theory, establish under tri- measurement patterns of X, Y, Z with geometric error the equation of motion and
The equation of motion ideally establishes double ball bar both ends using the working principle of double ball bars under the same coordinate system
Actual range solve the coupling phenomenon between error parameter to pick out all geometric error parameters of lathe yaw,
And accuracy is high.
Detailed description of the invention
Fig. 1 is two adjacent body movement relation schematic diagrames.
Fig. 2 is double ball bar measurement figures.
Fig. 3 is yaw in Y measurement direction movement schematic diagram.
Fig. 4 is yaw in X measurement direction movement schematic diagram.
Fig. 5 is yaw in Z measurement direction movement schematic diagram.
Fig. 6 is the yaw movement position schematic diagram under tri- kinds of measurement patterns of X respectively.
Fig. 7 is the yaw movement position schematic diagram under tri- kinds of measurement patterns of Y respectively.
Fig. 8 is the yaw movement position schematic diagram under tri- kinds of measurement patterns of Z respectively.
Specific embodiment
The method of the invention specifically includes the following steps:
Step 1, it is based on many-body theory, establishes adjacent two-particle systems relation equation
Step 2, by analyzing the geometric error parameter of lathe yaw, according to the working principle of double ball bars, respectively in machine
Under tri- kinds of measurement patterns of X, Y, Z of bed, the geometric error parameter of yaw is recognized.By establishing reference coordinate in workbench
System and kinetic coordinate system, respectively obtain the position coordinates of A, C, D point.
Step 3, according to above-mentioned analysis, under measurement pattern in the Y direction, geometric error parameter is identified, passes through foundation
The relationship of the position equation of actual point D ' and mathematical point D and the variable quantity of Y-direction bar length, identifies ε in O-XYZxBAnd εx(Bj)。
Step 4, it is analyzed according to step 2, under the measurement pattern of X-direction, geometric error parameter is identified, passes through foundation
The position equation and X of actual point A ' and mathematical point A identify ε to the relationship of the long variable quantity of bar in O-XYZyBAnd Pj。εy
(Bj)
Step 5, according to above-mentioned analysis, under measurement pattern in the Y direction, geometric error parameter is identified, passes through foundation
The relationship of the position equation of actual point C ' and mathematical point C and the variable quantity of Y-direction bar length, identifies δ in O-XYZz(Bj) and δx
(Bj)。
A kind of geometric error recognition methods of the five-axis machine tool yaw based on double ball bars, method includes the following steps:
(1) it is based on many-body theory, establishes adjacent two-particle systems relation equation
Fig. 1 is the situation between two adjacent motion bodies, { rj}={ rx ry rz 1}TIndicate P point in BjBody is sat
The location matrix in system is marked, wherein rx, ry, rzRespectively P point is in BjSpace coordinate in body coordinate system is sat in three Descartes
Mark system adds 1, forms a four-vector, then by many-body theory it is found that P point is in BiLocation matrix in body coordinate system indicates
Are as follows:
WhereinRespectively indicate BiBody and BjRelative position transformation matrix between body, phase
To position error transformation matrix, relative motion transformation matrix, relative motion error transformation matrix.
(2) the geometric error parameter identification method of lathe yaw
Five-axle number control machine tool yaw shares 8 geometric error parameters, wherein related with location point have 6, it is δ respectivelyx
(B), δy(B), δz(B), εx(B), εy(B), εz(B), unrelated with location point to have 2, εxB, εBz。
As shown in Fig. 2, being expressed as ball 1 by what the knife rest on yaw stepped up, it is expressed as ball 2 on workbench, is passed through
The change in location of two balls is detected to realize the measurement of yaw.In the measurement process of double ball bars, yaw is connected by multi-axial Simultaneous
Bar is mobile, and the central point with driving spindle around ball 1 rotates, and position needs to remain unchanged.Fig. 3-Fig. 5 respectively illustrates the side Y
To three kinds of measurement patterns of X-direction and Z-direction.For the ease of research, the coordinate system of the central point of ball 2 is expressed as 0-XYZ,
And the coordinate system of the centre of gyration of yaw is expressed as O '-X ' Y ' Z '.That is, 0-XYZ is remain stationary, O '-X ' Y ' Z ' and and yaw
It moves together.Fig. 6-Fig. 8 shows the location diagram of three kinds of measurement patterns.Due to the presence of the geometric error of yaw, ball 1
Central point is respectively offset from ideal position, and ideal position is expressed as A, C and D, physical location, is expressed as A ', C ' and
D′.In addition, the coordinate of A, C and D respectively indicate in O '-X ' Y ' Z ' are as follows:
{A}O′=[0 0-L 1]T (2)
{C}O′=[0 0-L 1]T (3)
{D}O′=[0 0-L 1]T (4)
Wherein, L indicates the cutter length between the centre of gyration of yaw and the center of ball 1.
(3) measurement pattern of Y-direction
Such as Fig. 3 and Fig. 6, according to formula (1) it is found that D ' positions in coordinate system O-XYZ are as follows:
Wherein, BjIndicate the rotation angle of the yaw when main shaft is moved to position j from initial position.Use dyIndicate that Y-direction is surveyed
The original length of club in amount mode.By simplification (5) and ignore higher order term, in coordinate system O-XYZ, between point D ' and O
Distance indicates are as follows:
On the j of position, LD′OIt is available for the physical length of club:
Wherein, Δ dyIt indicates in measurement pattern in the Y direction, length variable quantity of the club from initial position to position j.It is logical
It crosses and simplifies (7) and ignore higher order term, obtain:
L(εBzcos Bj-εxBsin Bj+εx(Bj))+δy(Bj)=Δ dy (8)
It is assumed that Qj=εBzcos Bj-εxBsin Bj+εx(Bj), then:
LQj+δy(Bj)=Δ dy (9)
For different L values, obtain:
According to (10) it is found that δy(Bj) and QjIt respectively indicates are as follows:
Work as Bj=0 °, yaw is in initial position, εx(Bj)=0, therefore:
εBz=Q0 (13)
Work as BjAt=90 ° or 270 °:
Due to εx(Bj) have periodically, so:
εx(Bj)=Qj-εBzcos Bj+εxBsin Bj (17)
(4) measurement pattern of X-direction
Such as Fig. 4 and Fig. 7, known according to formula (1), A ' positions in coordinate system O-XYZ are as follows:
Use dxIndicate the original length of club in X-direction measurement pattern.By simplified style (18) and ignore higher order term, is sitting
In mark system O-XYZ, point the distance between A ' and O are indicated are as follows:
On the j of position, LA′OFor the physical length of club, obtain:
Wherein, Δ dxIndicate length variable quantity of the club from initial position to position j in the measurement pattern of X-direction.Letter
Change (20) and ignore higher order term, obtains:
-L cos Bjεy(Bj)+cos Bjδx(Bj)+sin Bjδz(Bj)=Δ dx (21)
It enables, Pj=cos Bjδx(Bj)+sin Bjδz(Bj), then,
-L cos Bjεy(Bj)+Pj=Δ dx (22)
For different L values, obtain:
Then:
(5) measurement pattern of Z-direction
Such as Fig. 5 and Fig. 8, according to formula (1) it is found that C ' positions in coordinate system O-XYZ are as follows:
Use dzIndicate the original length of club in Z-direction measurement pattern.By simplified style (26) and ignore higher order term, is sitting
In mark system O-XYZ, point the distance between C ' and O are indicated are as follows:
On the j of position, LC′OFor the physical length of club, obtain:
Wherein, Δ dzIndicate length variable quantity of the club from initial position to position j in the measurement pattern of Z-direction.Letter
Change (28) and ignore higher order term, obtains:
L sin Bjεy(Bj)+cos Bjδz(Bj)-sin Bjδx(Bj)=Δ dz (29)
If it is assumed that Rj=cos Bjδz(Bj)-sin Bjδx(Bj) (30)
Then, Rj=Δ dz-L sin Bjεy(Bj) (31)
In conjunction with (25) (30), δz(Bj)=cos BjRj+sin BjPj (32)
δx(Bj)=cos BjPj-sin BjRj (33)
So far, eight error parameters relevant to yaw all pick out.
Claims (2)
1. a kind of geometric error recognition methods of the five-axis machine tool yaw based on double ball bars, which is characterized in that this method includes
Following steps:
Step 1, it is based on many-body theory, establishes adjacent two-particle systems relation equation；
Step 2, by analyzing the geometric error parameter of lathe yaw, according to the working principle of double ball bars, respectively in lathe
X, under tri- kinds of measurement patterns of Y, Z, the geometric error parameter of yaw is recognized；By workbench establish reference frame and
Kinetic coordinate system respectively obtains the position coordinates of A, C, D point；
Step 3, according to above-mentioned analysis, under measurement pattern in the Y direction, geometric error parameter is identified, by establishing in O-
The relationship of the position equation of actual point D ' and mathematical point D and the variable quantity of Y-direction bar length, identifies ε in XYZxBAnd εx(Bj)；
Step 4, it analyzes according to step 2, under the measurement pattern of X-direction, geometric error parameter is identified, by establishing in O-
The position equation and X of actual point A ' and mathematical point A identify ε to the relationship of the long variable quantity of bar in XYZyBAnd Pj；εy(Bj)
Step 5, according to above-mentioned analysis, under measurement pattern in the Y direction, geometric error parameter is identified, by establishing in O-
The relationship of the position equation of actual point C ' and mathematical point C and the variable quantity of Y-direction bar length, identifies δ in XYZz(Bj) and δx(Bj)。
2. a kind of geometric error recognition methods of five-axis machine tool yaw based on double ball bars according to claim 1,
It is characterized in that:
(1) it is based on many-body theory, establishes adjacent two-particle systems relation equation；
In situation between two adjacent motion bodies, { rj}={ rx ry rz 1}TIndicate P point in BjIn body coordinate system
Location matrix, wherein rx,ry,rzRespectively P point is in BjSpace coordinate in body coordinate system adds again in three cartesian coordinate systems
Upper 1, a four-vector is formed, then by many-body theory it is found that P point is in BiLocation matrix in body coordinate system is expressed as:
WhereinRespectively indicate BiBody and BjRelative position transformation matrix between body, opposite position
Set error transformation matrix, relative motion transformation matrix, relative motion error transformation matrix；
(2) the geometric error parameter identification method of lathe yaw；
Five-axle number control machine tool yaw shares 8 geometric error parameters, wherein related with location point have 6, it is δ respectivelyx(B), δy
(B), δz(B), εx(B), εy(B), εz(B), unrelated with location point to have 2, εxB, εBz；
It is expressed as ball 1 by what the knife rest on yaw stepped up, is expressed as ball 2 on workbench, by the position for detecting two balls
Variation is set to realize the measurement of yaw；In the measurement process of double ball bars, yaw is mobile by multi-axial Simultaneous connecting rod, to drive master
Axis is rotated around the central point of ball 1, and position needs to remain unchanged；The coordinate system of the central point of ball 2 is expressed as O-XYZ, and
The coordinate system of the centre of gyration of yaw is expressed as O '-X ' Y ' Z '；That is, O-XYZ is remain stationary, O '-X ' Y ' Z ' and with yaw one
Play movement；Due to the presence of the geometric error of yaw, the central point of ball 1 is respectively offset from ideal position, and ideal position is distinguished table
It is shown as A, C and D, physical location is expressed as A', C' and D'；In addition, the coordinate of A, C and D distinguish table in O '-X ' Y ' Z '
It is shown as:
{A}O′=[0 0-L 1]T (2)
{C}O′=[0 0-L 1]T (3)
{D}O′=[0 0-L 1]T (4)
Wherein, L indicates the cutter length between the centre of gyration of yaw and the center of ball 1；
(3) measurement pattern of Y-direction；
According to formula (1) it is found that D ' positions in coordinate system O-XYZ are as follows:
Wherein, BjIndicate the rotation angle of the yaw when main shaft is moved to position j from initial position；Use dyIndicate that Y-direction measures mould
The original length of club in formula；By simplification (5) and ignore higher order term, in coordinate system O-XYZ, point the distance between D ' and O
It indicates are as follows:
On the j of position, LD′OFor the physical length of club, obtain:
Wherein, Δ dyIt indicates in measurement pattern in the Y direction, length variable quantity of the club from initial position to position j；Pass through letter
Change (7) and ignore higher order term, obtains:
L(εBzcosBj-εxBsinBj+εx(Bj))+δy(Bj)=Δ dy (8)
It is assumed that Qj=εBzcosBj-εxBsinBj+εx(Bj), then:
LQj+δy(Bj)=Δ dy (9)
For different L values, obtain:
Known according to (10), δy(Bj) and QjIt respectively indicates are as follows:
Work as Bj=0 °, yaw is in initial position, εx(Bj)=0, therefore:
εBz=Q0 (13)
Work as BjAt=90 ° or 270 °:
Due to εx(Bj) have periodically, so:
εx(Bj)=Qj-εBzcosBj+εxBsinBj (17)
(4) measurement pattern of X-direction；
Known according to formula (1), A ' positions in coordinate system O-XYZ are as follows:
Use dxIndicate the original length of club in X-direction measurement pattern；By simplified style (18) and ignore higher order term, in coordinate system
In O-XYZ, point the distance between A ' and O are indicated are as follows:
On the j of position, LA′OFor the physical length of club, obtain:
Wherein, Δ dxIndicate length variable quantity of the club from initial position to position j in the measurement pattern of X-direction；Simplify
(20) and ignore higher order term, obtain:
-LcosBjεy(Bj)+cosBjδx(Bj)+sinBjδz(Bj)=Δ dx (21)
It enables, Pj=cosBjδx(Bj)+sinBjδz(Bj), then,
-LcosBjεy(Bj)+Pj=Δ dx (22)
For different L values, obtain:
Then:
(5) measurement pattern of Z-direction；
Known according to formula (1), C ' positions in coordinate system O-XYZ are as follows:
Use dzIndicate the original length of club in Z-direction measurement pattern；By simplified style (26) and ignore higher order term, in coordinate system
In O-XYZ, point the distance between C ' and O are indicated are as follows:
On the j of position, LC′OFor the physical length of club, obtain:
Wherein, Δ dzIndicate length variable quantity of the club from initial position to position j in the measurement pattern of Z-direction；Simplify
(28) and ignore higher order term, obtain:
LsinBjεy(Bj)+cosBjδz(Bj)-sinBjδx(Bj)=Δ dz (29)
If it is assumed that Rj=cosBjδz(Bj)-sinBjδx(Bj) (30)
Then, Rj=Δ dz-LsinBjεy(Bj) (31)
In conjunction with (25) (30), δz(Bj)=cosBjRj+sinBjPj (32)
δx(Bj)=cosBjPj-sinBjRj (33)
So far, eight error parameters relevant to yaw all pick out.
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| CN110794765A (en) * | 2019-11-20 | 2020-02-14 | 重庆大学 | Machine tool geometric error coupling decoupling measurement method |
| CN110794765B (en) * | 2019-11-20 | 2021-02-26 | 重庆大学 | Machine tool geometric error coupling decoupling measurement method |
| CN111487923A (en) * | 2020-03-25 | 2020-08-04 | 成都飞机工业（集团）有限责任公司 | Swing position error detection and identification method for CA double-swing five-axis numerical control machine tool |
| CN111487923B (en) * | 2020-03-25 | 2021-03-30 | 成都飞机工业（集团）有限责任公司 | Swing position error detection and identification method for CA double-swing five-axis numerical control machine tool |
| CN112192317A (en) * | 2020-09-30 | 2021-01-08 | 杭州电子科技大学 | Method for measuring machine tool spindle space three-dimensional error by using double-ball bar instrument |
| CN112518422A (en) * | 2020-11-19 | 2021-03-19 | 西安交通大学 | Five-axis AC swing head gantry machine tool geometric error modeling and separating method |
| CN112518422B (en) * | 2020-11-19 | 2021-12-28 | 西安交通大学 | Five-axis AC swing head gantry machine tool geometric error modeling and separating method |
| CN112558547A (en) * | 2021-02-19 | 2021-03-26 | 成都飞机工业（集团）有限责任公司 | Quick optimization method for geometric error compensation data of translational shaft of five-axis numerical control machine tool |
| CN112558547B (en) * | 2021-02-19 | 2021-06-08 | 成都飞机工业（集团）有限责任公司 | Quick optimization method for geometric error compensation data of translational shaft of five-axis numerical control machine tool |
| CN113967855A (en) * | 2021-11-03 | 2022-01-25 | 天津工业大学 | Identification method for measuring PDGEs of three-axis numerical control machine tool based on ball arm instrument |
| CN113967855B (en) * | 2021-11-03 | 2023-05-26 | 天津工业大学 | Identification method for measuring PDGEs of triaxial numerical control machine tool based on ball arm instrument |
| CN113977352A (en) * | 2021-11-27 | 2022-01-28 | 北京工业大学 | Method for identifying C-axis error parameters of double-swing-head gantry machine tool |
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