CN106141814B - The detection of Digit Control Machine Tool translation shaft geometric error and discrimination method based on LaserTRACER - Google Patents
The detection of Digit Control Machine Tool translation shaft geometric error and discrimination method based on LaserTRACER Download PDFInfo
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Abstract
A kind of detection of Digit Control Machine Tool translation shaft geometric error and discrimination method based on LaserTRACER.It includes forming the measuring system being made up of Digit Control Machine Tool and LaserTRACER, and obtains lathe end position and attitude error using the measuring system measurement；The mapping model established between 21 geometric errors of Digit Control Machine Tool and above-mentioned lathe end position and attitude error；The mapping model established between lathe end position and attitude error and 21 geometric error system of polynomials number vectors；Establish the identification equation group of above-mentioned system of polynomials number vector；Identification analysis is carried out to system of polynomials number vector p identification equation group；The steps such as simulation optimization are carried out to the measurement track in working space using Matlab.The present invention can reach preferable identification effect on the premise of little data amount is measured, and the manufacturing capability appraising and error compensation for Digit Control Machine Tool provide data support.
Description
Technical field
The invention belongs to Geometric Error for Computerized Numerical Control Milling Machine accurate measurement and identification technique field, it is based on more particularly to one kind
LaserTRACER Digit Control Machine Tool translation shaft geometric error detection and discrimination method.
Background technology
Error compensation is to improve a kind of effective means of Digit Control Machine Tool geometric accuracy, and the mistake of three translation shafts of Digit Control Machine Tool
Difference detection and identification are an error compensation parts the most basic.The NC Machine Error detection method being most widely used at present
There are two classes：One kind is the individual error direct method of measurement based on laser interferometer, though the method measurement result is accurate, need through
Testing abundant engineers and technicians, repeatedly precisely the position of debugging interferometer microscope group measures every error, automaticity respectively
It is low, take longer.Another kind of is Indirect Error identification method, is " 9 collimation method " and " ball bar method " wherein most widely used, both of which
Can Fast Identification go out whole geometric errors of lathe.But " 9 collimation method " have ignored vertical in measurement and positioning error and straightness error
The influence of Abbe error caused by straight degree error；" ball bar method " although realizing multi-shaft interlocked measurement, measurement range only limits
Semi circular surface using ballbar length as radius, the whole working space of lathe can not be represented completely.
German Etalon AG in 2014 develop a kind of entitled LaserTRACER-NG (hereinafter referred to as LaserTRACER)
Measuring instrument.The measuring instrument mainly includes laser head, target and ECU, and ECU is connected with laser head；Survey
Laser head automatic tracing target in amount, ECU record target to the actual range of laser head automatically.But not yet find at present
LaserTRACER is described into error identification side of the Digit Control Machine Tool translation shaft geometric error with the change of position coordinates for multinomial
The application in face.
The content of the invention
In order to solve the above problems, it is an object of the invention to provide a kind of Digit Control Machine Tool based on LaserTRACER to put down
Moving axis geometric error detects and discrimination method.
In order to achieve the above object, the Digit Control Machine Tool translation shaft geometric error detection based on LaserTRACER and identification side
Method includes the following steps carried out in order：
1) measuring system being made up of Digit Control Machine Tool and LaserTRACER is formed, and is obtained using the measuring system measurement
Lathe end position and attitude error；
2) mapping model established between 21 geometric errors of Digit Control Machine Tool and above-mentioned lathe end position and attitude error；
3) mapping model established between lathe end position and attitude error and 21 geometric error system of polynomials number vectors；
4) the identification equation group of above-mentioned system of polynomials number vector is established；
5) identification analysis is carried out to above-mentioned system of polynomials number vector p identification equation group；
6) simulation optimization is carried out to the measurement track in working space using Matlab.
In measuring system described in step 1), Digit Control Machine Tool mainly includes lathe bed, column, X guide rails, Y guide rail, Y and slided
Platform, Z guide rails, Z slide units and main shaft；The upper surface of its medial bed is workbench, and X guide rails are arranged on the X-direction of lathe bed two sides,
The lower end inside of door shape column forms prismatic pair with X guide rails along X-direction；Y guide rail is arranged on the Y-axis side on end floor beam on column
To Y slide units form prismatic pair with Y guide rail along Y direction；Z guide rails are arranged on the Z-direction of Y slide units, Z slide units and Z guide rails along Z
Direction of principal axis forms prismatic pair；Main shaft is arranged on the lower surface of Z slide units；LaserTRACER mainly includes laser head, target and automatically controlled
Unit；Target is arranged on the lower surface of main shaft；Laser head is placed sequentially in the surface of workbench on four positions of square shape,
And it is connected with ECU, so as to form the measuring system of Digit Control Machine Tool and LaserTRACER.
In step 2), described establishes between 21 geometric errors of Digit Control Machine Tool and above-mentioned lathe end position and attitude error
The method of mapping model is：Digit Control Machine Tool is regarded as to the multi-body system being in series by multiple rigid bodies first；Secondly more bodies are used
Topological relation on theoretical description Digit Control Machine Tool between each moving component；Reuse homogeneous coordinate transformation matrix multiple represent with
Pose transformational relation between the connected reference frame of Digit Control Machine Tool adjacent component；21 geometry of Digit Control Machine Tool are finally set up to miss
Mapping model between difference and lathe end position and attitude error.
In step 3), described establishes between lathe end position and attitude error and 21 geometric error system of polynomials number vectors
The method of mapping model be：The related geometric error in position in 21 geometric errors is described using multinomial model first,
Position independence geometric error, the i.e. error of perpendicularity are not dealt with as a constant, obtain 21 geometric errors and 21 geometry
Mapping relations between error polynomial coefficient vector；Secondly 21 geometric errors of Digit Control Machine Tool and lathe end in step 2) are combined
The mapping model between position and attitude error is held, is established between lathe end position and attitude error and 21 geometric error system of polynomials number vectors
Mapping model.
In step 4), the method for the described identification equation group for establishing above-mentioned system of polynomials number vector is：First in number
Control and m measurement point is selected in the working space of lathe, obtain containing 3 for each measurement point using the mapping model in step 3)
The equation group of error identification equation；Secondly, it is combined into a bag using the obtained m equation group containing 3 error identification equations
Equation group containing 3m error identification equation, that is, obtain the identification equation group of above-mentioned system of polynomials number vector.
In step 5), the identification equation group to above-mentioned system of polynomials number vector p carries out identification analysis
Method is：First, in the case of target does not bias, horizontally and vertically biases three kinds, error of observation mapping matrix
In column vector, it is determined that wherein linearly related and potentially relevant column vector；Secondly, will be linearly related in error map matrix
Column vector and corresponding system of polynomials number vector p in system of polynomials number vector remove, and potential linearly related column vector is led to
Cross measurement parameter and set and make it that its is separate；Finally, the system of polynomials number vector p of Line independent does not have by solving simultaneous target
There is the identification equation group under biasing, horizontally and vertically bias conditions to obtain.
In step 6), the method that simulation optimization is carried out to the measurement track in working space using Matlab
For：One group of 21 geometric error is initially given first；Secondly utilize machine tool error model in step 2) that measurement point is calculated
Ideal position error；Again on above-mentioned ideal position error basis one Gaussian noise of linear superposition simulating actual measurement
As a result random error；The relative error of actual error value and initial error is calculated finally by least square method, is repeated several times
Above procedure, make it that identification relative error is sufficiently small until finding one group of measurement track, so far, complete using Matlab to work
Measurement track in space 10 carries out the process of simulation optimization.
Compared with existing discrimination method, the Digit Control Machine Tool translation shaft provided by the invention first based on LaserTRACER
It is 4 diverse locations that laser head is placed on to numerically controlled machine that geometric error, which is detected with discrimination method, respectively to installation
The position of target on main shaft of numerical control machine tool is demarcated, and with the polygon positioning principle similar to " GPS location ", can be realized
The Fast Calibration of machine tool error, accurate measurement, and Digit Control Machine Tool measurement range is expanded into the whole working space of Digit Control Machine Tool.Separately
Outside, preferable identification effect can be reached on the premise of little data amount is measured.Secondly identification result is used into polynomial module
Type matching position correlation geometric error is with the change of machine tool position, can be obtained using the error model and identification established 21
The error amount at any point in geometric error backwards calculation Digit Control Machine Tool processing space, be Digit Control Machine Tool manufacturing capability appraising with
And error compensation provides data and supported.
Brief description of the drawings
Fig. 1 is the Digit Control Machine Tool translation shaft geometric error detection provided by the invention based on LaserTRACER and identification side
Method flow chart；
Fig. 2 is the measuring system structural representation that the inventive method uses.
Fig. 3 is the position of structure of numerically controlled machine-tool sketch and coordinate system；
Fig. 4 is measurement track emulation flow chart；
Embodiment
With reference to the accompanying drawings and examples, the present invention is described in further detail.
As shown in figure 1, the Digit Control Machine Tool translation shaft geometric error provided by the invention based on LaserTRACER is detected with distinguishing
Knowledge method includes the following steps carried out in order：
1) measuring system being made up of Digit Control Machine Tool and LaserTRACER is formed, and is obtained using the measuring system measurement
Lathe end position and attitude error；
As shown in Fig. 2 in described measuring system, Digit Control Machine Tool, which mainly includes lathe bed 1, column 3, X guide rails 4, Y, leads
Rail, Y slide units 5, Z guide rails, Z slide units 6 and main shaft 7；The upper surface of its medial bed 1 is workbench 2, and X guide rails 4 are arranged on 1 liang of lathe bed
X-axis (front and rear) direction of side, the lower end inside of door shape column 3 form prismatic pair with X guide rails 4 along X-direction；Not shown in figure
Y guide rail be arranged on Y-axis (left and right) direction on column 3 on end floor beam, Y slide units 5 form prismatic pair with Y guide rail along Y direction；
Z guide rails not shown in figure are arranged on Z axis (upper and lower) direction of Y slide units 5, and Z slide units 6 and Z guide rails are formed along Z-direction to be moved
It is secondary；Main shaft 7 is arranged on the lower surface of Z slide units 6；LaserTRACER mainly includes the electricity not shown in laser head 9, target 8 and figure
Control unit；Target 8 is arranged on the lower surface of main shaft 7；The surface that laser head 9 is placed sequentially in workbench 2 is in four of square shape
On position, and it is connected with ECU；What target 8 can be surrounded with main shaft 7 in the maximum magnitude that X, Y, Z axis direction is moved
Space is referred to as working space 10；In measurement process, four automatic tracing clampings of laser head 9 the lower surface of main shaft 7 target 8,
When main shaft 7 is moved to a certain position in working space 10, ECU records target 8 to the reality between corresponding laser head 9 automatically
Border distance, and using the position as a measurement point, then subtract target 8 to the ideal position between corresponding laser head 9, that is, obtain
Cutting tool for CNC machine and workpiece relative pose error (hereinafter referred to as lathe end position and attitude error).LaserTRACER needs to measure
Several points position just can be with the geometric error of accurate calibration Digit Control Machine Tool in lathe working space 10, and these measurement point positions are successively
Connect and compose the error measure track of Digit Control Machine Tool.
2) mapping model established between 21 geometric errors of Digit Control Machine Tool and above-mentioned lathe end position and attitude error；
The geometric error of Digit Control Machine Tool, according to whether it is related to today's numerical control machine tool motion position, position correlation can be divided into
Geometric error (PDGEs) and position independence geometric error (PIGEs).As shown in figure 3, during the present invention is processed with a precision horizontal
Exemplified by the heart, the discrimination method of the present invention is illustrated, above-mentioned machining center is in the case where only considering translation shaft geometric error
Share 21 geometric errors：9 site errors related to three axis coordinate positions and 9 angular errors, and position are only
3 error of perpendicularitys between three vertical axis, 18 PDGEs, 3 PIGEs altogether, as shown in table 1.
21 geometric errors of the Digit Control Machine Tool of table 1
δ in tablex、δy、δzSite error is represented, footmark represents the direction of error；εx、εy、εzRepresent angular errors, footmark table
Show the direction of angular errors rotation axis, the x, y, z in bracket represents the movement position coordinate of X, Y, Z axis；Such as δi(j), its
Middle i, j=x, y, z are represented when reference axis j movement positions coordinate is j, along the site error in reference axis i directions, εi(j), wherein
I, j=x, y, z are represented when reference axis j movement positions coordinate is j, around the angular errors of reference axis i rotations；εxy、εyz、εxzPoint
The error of perpendicularity between other denotation coordination axle X and Y, Y and Z, X and Z.
Digit Control Machine Tool is a kind of multi-body system being in series by multiple rigid bodies, and usable many-body theory describes Digit Control Machine Tool
Topological relation between upper each moving component, represent to be connected with Digit Control Machine Tool adjacent component with homogeneous coordinate transformation matrix multiple and join
Examine the pose transformational relation between coordinate system, so as to set up 21 geometric errors of Digit Control Machine Tool and lathe end position and attitude error it
Between mapping model (hereinafter referred to as machine tool error model)：
Wherein,It is vectorial for lathe end position and attitude error,For the vector being made up of 21 geometric errors of Digit Control Machine Tool, Ar
For the mapping matrix between lathe end position and attitude error and 21 geometric errors.
In order to write conveniently, formula (1) is split into following form：
The related geometric error vector in position is in formula (2)：
The geometric error vector of position independence is：
A in formula (2)rx、Ary、ArzThe error map matrix of every error respectively related to x, y, z axle, ArsFor with hanging down
The related error map matrix of straight degree error；For related to x, y, z shaft position geometric error vector,It is vertical
Straight degree error vector, it is constant.
3) mapping model established between lathe end position and attitude error and 21 geometric error system of polynomials number vectors；
By the related geometric error vector in above-mentioned positionDescribed with multinomial model；Position independence geometry misses
Difference, the i.e. error of perpendicularity are a constant, therefore are not dealt with.
LaserTRACER metering system is measured for relative error, thus the reference for defining the workbench 2 of Digit Control Machine Tool is sat
It is zero to mark items position correlation geometric error numerical value at the origin of coordinates of system, i.e., polynomial constant item is zero.
Site error (including position error and straightness error) is：
Angular errors (including the angle of pitch, deflection angle, rolling angle error) are：
δ in formula (5), (6)ij,kRepresent site error δi(j) k-th of multinomial coefficient in multinomial model；εij,kRepresent
Angular errors εi(j) k-th of multinomial coefficient in multinomial model；K is the k power items in n-order polynomial.
In formula (5), (6)：
In formulaSite error δ is respectively describedi(j), angular errors εi(j) coefficient vector,For corresponding coordinate position matrix；J is X-axis or the present co-ordinate position of Y-axis or Z axis.When the position of target 8 is sat
When marking known to (x, y, z), coordinate position matrixFor known quantity.
Formula (5), (6) are substituted into the geometric error vector related to X-axis positionIn have：
It can similarly obtain：
With
Formula (8) substitution formula (2) can be obtained to the pass between the corresponding system of polynomials number vector of 21 geometric errors
System：
Formula (9) is substituted into formula (1) to obtain between lathe end position and attitude error and 21 geometric error system of polynomials number vectors
Relation：
In formula (10),For position and attitude error vector in lathe end at certain point in working space 10, p is that 21 geometry miss
Poor system of polynomials number vector (hereinafter referred to as system of polynomials number vector).
4) the identification equation group of above-mentioned system of polynomials number vector is established；
In above-mentioned formula (10), lathe end pose at certain point is obtained in working space 10 using LaserTRACER measurements
Error vectorIn contain 3 error components, can form the equation group containing 3 error identification equations, and multinomial coefficient
18n+3 unknowm coefficient is shared in vectorial p, equation group can not solve, and increase the points measured in working space 10 so that equation
Quantity be more than or equal to unknowm coefficient quantity can solve.Assuming that measure m measurement point altogether in working space 10, for
Ith measurement point, (i=1,2 ..., m),In view of there is m measurement point, then system of polynomials number vector p identification
Equation group is：
In formula (11), n is to describe the related polynomial exponent number of geometric error in position；M is use
The measurement point sum that LaserTRACER is measured in working space 10；For the lathe end pose measured in ith measurement point
Error vector；P is system of polynomials number vector, including the 18n item multinomial coefficient vector sums position of position correlation geometric error is only
3 vertical perpendicularity system of polynomials number vectors；MiFor error map matrix corresponding to i-th of space networks lattice point, accurate machine is included
Bed structure parameter, machine tool motion positional information.
In theory, as 3m >=18n+3, i.e., equation number is more than or equal to unknown number number, can pick out system of polynomials
Number vector p.
5) identification analysis is carried out to above-mentioned system of polynomials number vector p identification equation group；
By above-mentioned error map matrix MiSplit into following form：
Mi=[Mxi Myi Mzi Msi] (12)
M in formulaxi、Myi、Mzi、MsiThe respectively error related to three reference axis x, y, z of Digit Control Machine Tool and the error of perpendicularity
Mapping matrix, the cognizable core conditions of system of polynomials number vector p are error map matrix MiIn column vector it is mutually independent；
(1) error of observation mapping matrix Mxi、Myi、Mzi、Msi, when the position of target 8 does not bias, i.e., the coordinate of target 8 to
Amount(Represent the geometric center O of target 8 being arranged on main shaft 7TPosition in main shaft coordinate system T-xyz
Put vector), error map matrix MiIn have five pairs of column vectors, i.e. angular errors εy(x)、εx(y)、εy(y)、εz(y) missed with position
Poor δy(x)、δx(y)、δy(y)、δzAnd site error δ (y)y(y) first order and error of perpendicularity ε inxyLinear phase respectively
Close, the multinomial coefficient in the system of polynomials number vector p corresponding with them can not recognize.
(2) angular errors εz(y) error map matrix M corresponding toyMiddle column vector has three kinds of situations：
A. it is null vector when target 8 does not bias, it is related to all column vectors in error map matrix.
B. when target 8 biases in x directions, and site error δy(y) error map matrix column vector correlation corresponding to.
C. when target 8 biases in y directions, and site error δx(y) error map matrix column vector correlation corresponding to.
(3) in addition to 5 pairs of column vectors above-mentioned, also 3 pairs of column vectors are it is important to note that they are respectively：
Error map matrix Mxi、Myi、MziIn first three columns, i.e. the 1st column position error deltax(x)、δxAnd δ (y)x(z) may be linearly related,
2nd column position error deltay(x)、δyAnd δ (y)y(z) may be linearly related, the 3rd column position error deltaz(x)、δzAnd δ (y)z(z) may
It is linearly related.In order that above-mentioned 3 pairs of column vectors are separate, the starting for deploying measurement in the working space 10 of Digit Control Machine Tool is made
Three coordinate values of point are not mutually equal, i.e. x ≠ y ≠ z.
Error map matrix MiMiddle linearly related column vector so that above-mentioned linearly related system of polynomials number vector p without
Method recognizes, therefore should remove this 5 pairs of system of polynomials number vectors in system of polynomials number vector p and error map square corresponding thereto
Battle array MiIn corresponding column vector, the 14n+3 item system of polynomials number vectors p of Line independent can now be picked out come.And to residue
The linearly related system of polynomials number vector p of 4n items, after the horizontal and vertical biasing of target 8, duplicate measurements and above-mentioned phase
The end position and attitude error of m same measurement point, obtained system of polynomials number vector p identification equation group and above-mentioned target 8 are not had
There is the identification equation group simultaneous that system of polynomials number vector p is obtained during biasing, it is i.e. distinguishable to solve the identification equation group after above-mentioned simultaneous
Know.
6) simulation optimization is carried out to the measurement track in working space using Matlab；
By above-mentioned processing, contain 14n+3 item multinomial coefficients altogether in system of polynomials number vector p, as long as thus measuring
3m >=14n+3 measurement point position is uniformly chosen on track so that error map matrix M full ranks, you can pick out multinomial coefficient
All multinomial coefficients in vectorial p.And in order that error identification precision it is higher, then need in working space 10 m measure
The locus distribution of point, namely measurement track carry out simulation optimization using Matlab so that measurement track meets following 3 simultaneously
Individual condition：
(1) measurement track traversal all controllable degrees of freedom of Digit Control Machine Tool that m measurement point selected by is formed by connecting, and
It is even to be distributed in the whole working space 10 of Digit Control Machine Tool.
(2) when using LaserTRACER measurement lathe terminal position position and attitude errors, measurement trajectory that main shaft 7 is passed by
It is few enough, to reduce the time of measuring of error.
(3) cause step 4), 5) in the obtained error identification precision of system of polynomials number vector p identification equation group be less than
2 microns.
Simulation optimization is carried out to measurement track using Matlab, simulation flow is referring to Fig. 4.It is initial given one group 21 first
Geometric error, the ideal position error of measurement point is calculated using machine tool error model, in above-mentioned ideal position error basis
Upper one Gaussian noise of linear superposition is then calculated real to simulate the random error of actual measured results by least square method
The relative error of border error amount and initial error.
1st step：Two angle steel joints of the measurement space of measurement track composition in working space 10 are set in lathe coordinate system
In coordinate value, measurement trajectory assembled scheme, the installation site coordinate vector of target 8, miss for matching position correlation geometry
Difference polynomial exponent number n and every measurement trajectory on equally distributed measurement point number m；
2nd step：Initial given one group of system of polynomials number vector is used to emulate (to be designated as)；
3rd step：Using the error model namely formula (10) of Digit Control Machine Tool, it is calculated in measurement trajectory corresponding to measuring point
Initial lathe end position and attitude error vector
4th step：The position and attitude error vector in initial lathe endUpper superposition average is zero, and standard deviation is σ normal distribution Ns
The agitation error of (0, σ), with analogue measurement noise and other uncertain factors, obtain actual lathe end position and attitude error vector
5th step：Calculation error mapping matrix M conditional number and order, actual multinomial is calculated using least square method
CoefficientWith relative error ε；
6th step：Evaluation measurement track, when error map matrix M full ranks and conditional number is smaller, and relative error is sufficiently small
When, measurement track emulation optimization terminates.
Above procedure is repeated several times, make it that identification relative error is sufficiently small until finding one group of optimization measurement track.Extremely
This, the Digit Control Machine Tool translation shaft geometric error detection based on LaserTRACER finishes with identification algorithm introduction, can use this calculation
Method measures and recognizes to obtain 21 geometric errors, and the manufacturing capability appraising and error compensation for Digit Control Machine Tool provide data branch
Hold.
Although the preferred embodiments of the present invention are described above in conjunction with accompanying drawing, the invention is not limited in upper
The embodiment stated, above-mentioned embodiment is only schematical, be not it is restricted, this area it is common
Technical staff in the case of present inventive concept and scope of the claimed protection is not departed from, may be used also under the enlightenment of the present invention
By make it is many in the form of, these are belonged within protection scope of the present invention.
Claims (6)
1. a kind of detection of Digit Control Machine Tool translation shaft geometric error and discrimination method based on LaserTRACER, it is included in order
The following steps of progress：
1) measuring system being made up of Digit Control Machine Tool and LaserTRACER is formed, and lathe is obtained using the measuring system measurement
End position and attitude error；
2) mapping model established between 21 geometric errors of Digit Control Machine Tool and above-mentioned lathe end position and attitude error；
3) mapping model established between lathe end position and attitude error and 21 geometric error system of polynomials number vectors；
4) the identification equation group of above-mentioned system of polynomials number vector is established；
5) identification analysis is carried out to above-mentioned system of polynomials number vector p identification equation group；
6) simulation optimization is carried out to the measurement track in working space using Matlab；
It is characterized in that：In measuring system described in step 1), Digit Control Machine Tool, which mainly includes lathe bed (1), column (3), X, leads
Rail (4), Y guide rail, Y slide units (5), Z guide rails, Z slide units (6) and main shaft (7)；The upper surface of its medial bed (1) is workbench (2), X
Guide rail (4) is arranged on the X-direction of lathe bed (1) two sides, and the lower end inside of door shape column (3) and X guide rails (4) are along X-direction
Form prismatic pair；Y guide rail is arranged on the Y direction on end floor beam, Y slide units (5) on column (3) and formed with Y guide rail along Y direction
Prismatic pair；Z guide rails are arranged on the Z-direction of Y slide units (5), and Z slide units (6) form prismatic pair with Z guide rails along Z-direction；Main shaft
(7) it is arranged on the lower surface of Z slide units (6)；LaserTRACER mainly includes laser head (9), target (8) and ECU；Target
(8) it is arranged on the lower surface of main shaft (7)；The surface that laser head (9) is placed sequentially in workbench (2) is in four positions of square shape
On, and be connected with ECU, so as to form the measuring system of Digit Control Machine Tool and LaserTRACER.
2. the detection of Digit Control Machine Tool translation shaft geometric error and identification side according to claim 1 based on LaserTRACER
Method, it is characterised in that：In step 2), described establishes 21 geometric errors of Digit Control Machine Tool and above-mentioned lathe end position and attitude error
Between the method for mapping model be：Digit Control Machine Tool is regarded as to the multi-body system being in series by multiple rigid bodies first；Next makes
The topological relation on Digit Control Machine Tool between each moving component is described with many-body theory；Reuse homogeneous coordinate transformation matrix multiple
Represent the pose transformational relation between the connected reference frame of Digit Control Machine Tool adjacent component；Finally set up Digit Control Machine Tool 21
Mapping model between geometric error and lathe end position and attitude error.
3. the detection of Digit Control Machine Tool translation shaft geometric error and identification side according to claim 1 based on LaserTRACER
Method, it is characterised in that：In step 3), it is described establish lathe end position and attitude error and 21 geometric error multinomial coefficients to
The method of mapping model between amount is：The related geometric error in position in 21 geometric errors is used into multinomial model first
Description, position independence geometric error, the i.e. error of perpendicularity are not dealt with as a constant, obtain 21 geometric errors and 21
Mapping relations between geometric error system of polynomials number vector；Secondly 21 geometric errors of Digit Control Machine Tool and machine in step 2) are combined
Mapping model between the position and attitude error of bed end, establishes lathe end position and attitude error and 21 geometric error system of polynomials number vectors
Between mapping model.
4. the detection of Digit Control Machine Tool translation shaft geometric error and identification side according to claim 1 based on LaserTRACER
Method, it is characterised in that：In step 4), the method for the described identification equation group for establishing above-mentioned system of polynomials number vector is：It is first
M measurement point is first selected in the working space (10) of Digit Control Machine Tool, using the mapping model in step 3) for each measurement
Point obtains the equation group containing 3 error identification equations；Secondly, the obtained m equation group group containing 3 error identification equations is utilized
One equation group for including 3m error identification equation of synthesis, that is, obtain the identification equation group of above-mentioned system of polynomials number vector.
5. the detection of Digit Control Machine Tool translation shaft geometric error and identification side according to claim 1 based on LaserTRACER
Method, it is characterised in that：In step 5), the identification equation group to above-mentioned system of polynomials number vector p carries out identifiability
The method of analysis is：First, in the case of target (8) is without biasing, horizontally and vertically biasing three kinds, the error of observation
Column vector in mapping matrix, it is determined that wherein linearly related and potentially relevant column vector；Secondly, by error map matrix
System of polynomials number vector removes in the column vector of linear correlation and correspondingly system of polynomials number vector p, and potential linearly related
Column vector sets its separate by measurement parameter；Finally, the system of polynomials number vector p of Line independent is joined by solving
Vertical target (8) without bias, the identification equation group horizontally and vertically under bias conditions obtains.
6. the detection of Digit Control Machine Tool translation shaft geometric error and identification side according to claim 1 based on LaserTRACER
Method, it is characterised in that：It is described that simulation optimization is carried out to the measurement track in working space using Matlab in step 6)
Method is：One group of 21 geometric error is initially given first；Secondly utilize machine tool error model in step 2) that measurement is calculated
The ideal position error of point；Again on above-mentioned ideal position error basis one Gaussian noise of linear superposition simulating reality
The random error of measurement result；The relative error of actual error value and initial error is calculated finally by least square method, repeatedly
Above procedure is repeated, make it that identification relative error is sufficiently small until finding one group of measurement track, so far, completes to use Matlab pairs
Measurement track in working space (10) carries out the process of simulation optimization.
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| CN112008492B (en) * | 2020-07-29 | 2022-04-08 | 成都飞机工业（集团）有限责任公司 | Method for identifying perpendicularity error of translational shaft of gantry numerical control machine tool |
| CN112229321B (en) * | 2020-08-31 | 2022-03-08 | 北京工业大学 | Method for solving 21-item geometric errors of three-coordinate measuring machine based on LASSO algorithm |
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| CN112276674B (en) * | 2020-10-13 | 2021-05-11 | 上海交通大学 | Precision measurement method and system for geometric motion error of rotating shaft of multi-axis numerical control machine tool |
| CN112526927B (en) | 2021-02-18 | 2021-06-08 | 成都飞机工业（集团）有限责任公司 | Quick optimization compensation method for space positioning error of rotating 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 |
| CN113770814B (en) * | 2021-08-26 | 2022-05-31 | 西南交通大学 | Method for identifying geometric error of translational axis of numerical control machine tool based on vector direction measurement |
| CN113770809B (en) * | 2021-09-16 | 2024-03-15 | 成都飞机工业（集团）有限责任公司 | Device and method for detecting space positioning precision of numerical control machine tool |
| CN113910001B (en) * | 2021-11-22 | 2024-03-26 | 广西成电智能制造产业技术有限责任公司 | Numerical control machine tool space error identification method |
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| CN102062575B (en) * | 2010-11-10 | 2012-07-04 | 西安交通大学 | Method for detecting geometric accuracy of numerically-controlled machine tool based on multi-channel laser time-sharing measurement |
| CN102200429B (en) * | 2011-04-06 | 2012-07-04 | 西安交通大学 | Precision detection method for numerical control machine based on laser-tracking combined measurement |
| CN103389038B (en) * | 2013-07-16 | 2016-01-13 | 西安交通大学 | Laser tracker set the goal multistation measure numerically-controlled machine geometric accuracy detection method |
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