CN105538038B - Lathe translation shaft geometric error discrimination method - Google Patents
Lathe translation shaft geometric error discrimination method Download PDFInfo
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Abstract
The invention discloses a kind of lathe translation shaft geometric error discrimination method, methods described includes：Determine to be respectively provided with multiple nodes in 13 linkage trajectories and every linkage trajectory in the working space that lathe translation shaft movement travel is formed, operation lathe makes main shaft move along a plurality of linkage trajectory respectively and records preferable stroke and traveled distance at node；Carry out translation shaft geometrical error modeling and the geometric error of lathe translation shaft is calculated according to the preferable stroke and traveled distance at each node.According to the lathe translation shaft geometric error discrimination method of the present invention, it is only necessary to be used cooperatively with common laser interferometer, testing cost is low, and the detection process used time is few, and identification precision is high, can provide Main Basiss for the diagnosis and compensation of Digit Control Machine Tool translation shaft geometric accuracy.
Description
Technical field
The present invention relates to mechanical device design field and lathe detection field, more particularly, to a kind of lathe translation shaft geometry
Error identification method.
Background technology
With developing rapidly for China's Aero-Space and auto manufacturing, multi-shaft linkage numerical control machine is widely used in various
The processing of complex parts.When multi-axis NC Machine Tools are applied to complex parts processing, mainly have two in terms of its geometric accuracy guarantee
Individual hot issue：(1) it is to meet the requirement on machining accuracy of complex partses, it is necessary to ensure that use multi-axis NC Machine Tools with enough
Enough initial geometric accuracies.(2) after multi-axis NC Machine Tools are applied to the processing of part, over time, the essence of lathe
Degree has declined.For that purpose it is necessary to error-detecting and compensation periodically are carried out to lathe, to ensure that machine finish maintains more
Stable level.
The initial precision of lathe is either evaluated, or periodically machine tool accuracy is detected and compensated, geometric error inspection
Survey is all most important, and its key problem is error-detecting instrument and corresponding discrimination method.The acquisition methods of lathe geometric error
Including：Direct measurement and indirectly two kinds of approach of identification.In direct measuring method, typically using laser interferometer detection translation shaft
Position error, translation shaft angular error is detected with electrolevel, detected with laser interferometer and a variety of prism arrangements straight
Dimension error and the error of perpendicularity.API companies of the U.S. also have developed can one-time detection go out the 6D laser of 6 errors of translation shaft and do
Interferometer.Although directly being detected by the progress translation shaft geometric error that is applied in combination of a variety of detection devices, translation shaft can be obtained
Every geometric error, but electrolevel can not detect rotation error of the translation shaft around vertical direction, laser under normal circumstances
, it is necessary to the pose of optical instrument repeatedly precisely be adjusted, to work when interferometer and prism arrangement detection of straight lines degree and the error of perpendicularity
Cheng Shi engineering experience dependence is very big, and adjusts process and take.Although 6D laser interferometer can realize single, debugging detection is multinomial
Geometric error, but usually require to adjust 6 road laser simultaneously during using 6D laser interferometer, regulation difficulty is very big, general operating mode
Lathe be difficult to the 6 road laser in big impulse stroke while meet testing requirements, and the cost of this kind of instrument is very high.
Relative to direct measurement, the geometry that the method recognized indirectly can obtain translation shaft based on a certain detecting instrument misses
Difference, cost is relatively low, but identification precision depends on used discrimination method.At present, for the mistake of multi-axis NC Machine Tools translation shaft
Difference detection and identification, are exactly laser interferometer using most instruments.Based on laser interferometer, scholar both domestic and external proposes very
More error identification methods, such as 22 collimation methods, 14 collimation methods, 12 collimation methods, 9 collimation methods etc..22 collimation methods need complicated traversal or changed
In generation, calculates, and it is larger to implement comparatively laborious and difficulty；" the vacation that is straightness error and being zero " of translation shaft during 14 collimation methods have
If condition causes this method to lack certain versatility.The detection of translation shaft position error have ignored accordingly in 12 collimation methods and 9 collimation methods
The influence of angular error, needs laser interferometer and prism repeatedly to combine installation when being detected in addition using 9 collimation methods, consumption is compared in regulation
When.
The content of the invention
It is contemplated that at least solves one of technical problem present in prior art.Therefore, the invention reside in propose one
Kind of lathe translation shaft geometric error discrimination method, methods described have that testing cost is low, and the detection process used time is few and identification precision
The advantages of high.
According to the lathe translation shaft geometric error discrimination method of the present invention, methods described includes：Moved in lathe translation shaft
Determine to be respectively provided with multiple nodes in 13 linkage trajectories and every linkage trajectory in the working space that stroke is formed, run
Lathe makes main shaft be moved respectively along 13 linkage trajectories and records preferable stroke and traveled distance at node；Put down
Moving axis geometrical error modeling and the geometric error that lathe translation shaft is calculated according to the preferable stroke and traveled distance at each node.
According to the lathe translation shaft geometric error discrimination method of the present invention, by detecting Digit Control Machine Tool translation shaft linkage track
The positioning precision of line, realize the high-precision identification algorithm for obtaining translation shaft geometric error.
In some embodiments of the invention, methods described also includes：Speculum is arranged on lathe master by magnet base
In axial end, laser interferometer and interference mirror are installed, adjust laser optical path and by numerical control unit control machine edge of bed linkage track
Spool motion, in motion process during every node, machine tool motion unit stops the scheduled time and waits laser interferometer collection
Data.
In some embodiments of the invention, the top in the cuboid working space formed with lathe translation shaft movement travel
Point A is origin and be respectively that X-axis, Y-axis and Z axis establish coordinate system by summit A three sides, respectively along X-axis, Y-axis and Z axis by institute
State working space n deciles and form node in point of intersection, the working space discrete processes are formed into (n+1)3Individual node.
In some embodiments of the invention, every linkage trajectory includes n+1 node, the linkage track
Line includes：On the working space altogether summit A three surfaces on paralleled by X axis three sides form three X-axis trajectory L1,
L2、L3；On the working space altogether summit A three surfaces on parallel Y-axis three sides form three Y-axis trajectory L4,
L5、L6；On the working space altogether summit A three surfaces on parallel Z axis three sides form three Z axis trajectory L7,
L8、L9；It is located at X, the Y-axis linkage rail that the diagonal on X-Y plane is formed on the working space on summit A three surfaces altogether
Trace L10；It is located at X, the Z-axis linkage that the diagonal on X-Z plane is formed on the working space on summit A three surfaces altogether
Trajectory L11；Y, the Z axis of the diagonal composition on summit A three surfaces on Y-Z plane join altogether on the working space
Dynamic rail trace L12；The X, Y, Z axis linkage trajectory L13 formed on the working space by summit A diagonal.
In some embodiments of the invention, i-th of node since first node A in the linkage trajectory
Preferable stroke and traveled distance are as follows：
The preferable stroke difference Lx of the 3 X-axis trajectories parallel with X single axial movements directioniAnd actually detected stroke difference
For L1i、L2i、L3i,
The preferable stroke difference Ly of the 3 Y-axis trajectories parallel with Y single axial movements directioniAnd actually detected stroke difference
For L4i、L5i、L6i,
The preferable stroke difference Lz of the 3 Z axis trajectories parallel with Z single axial movements directioniAnd actually detected stroke difference
For L7i、L8i、L9i,
The preferable stroke moved along X, Y linkage trajectory distinguishes LxyiAnd actually detected stroke is respectively L10i,
The preferable stroke moved along X, Z linkage trajectory distinguishes LxziAnd actually detected stroke is respectively L11i,
The preferable stroke moved along Y, Z linkage trajectory distinguishes LyziAnd actually detected stroke is respectively L12i,
The preferable stroke moved along X, Y, Z linkage trajectory distinguishes LxyziAnd actually detected stroke is respectively L13i,
Wherein i is the integer from 1 to n+1.
In some embodiments of the invention, carrying out the method for translation shaft geometrical error modeling includes：
Connecting firmly space coordinates for bed piece and translation shaft moving cell is respectively：{O0-X0Y0Z0, { Ox-XxYxZx,
{Oy-XyYyZyAnd { Oz-XzYzZz, setting all coordinate systems has identical posture, and the origin of all coordinate systems is located at X, Y,
The point of intersection of Z axis axis of movement, when being set for linkage track position error detection, mirror mirror center is relative to three seats
The distance of parameter origin is L, three linearity error sources and three angular errors of the setting X-axis moving cell relative to bed piece
Source is respectively：Xx, Yx,Zx, αx, βx,γx；Y-axis is respectively relative to the three linearity error sources and three angular error sources of X-axis：
Xy, Yy,Zy, αy, βy,γy；Z axis is respectively relative to the three linearity error sources and three angular error sources of Y-axis：Xz, Yz,Zz,
αz, βz,γz.Wherein, X, Y, Z, α, beta, gamma represent the direction of linearity error and angular error, the geometric error of speculum respectively
In some embodiments of the invention, the discrimination method bag of translation shaft Run-out error, top pendulum error and position error
Include：
The preferable control instruction value for defining 3 straightways corresponding with X single axial movements direction is Lxi, it is corresponding actual
Detected value is L1i, L2i, L3i.The distance between movement locus L1 and L2 are that the distance between D12, movement locus L1 and L3 is
D13, Run-out error of the X-axis moving cell in each discrete nodes of X-axis movement travel and top pendulum error are respectively：
The preferable control instruction value for defining 3 straightways corresponding with Y single axial movements direction is Lyi, it is corresponding actual
Detected value is L4i, L5i, L6i.The distance between movement locus L4 and L5 are that the distance between D45, movement locus L4 and L6 is
D46.According to geometric knowledge, Run-out error of the Y-axis moving cell in each discrete nodes of Y-axis movement travel can be recognized and top pendulum misses
Difference is as follows：
The preferable control instruction value for defining 3 straightways corresponding with Z single axial movements direction is Lzi, it is corresponding actual
Detected value is L7i, L8i, L9i.The distance between movement locus L7 and L8 are that the distance between D78, movement locus L7 and L9 is
D79.According to geometric knowledge, Run-out error of the Z axis moving cell in each discrete nodes of Z axis movement travel can be recognized and top pendulum misses
Difference is as follows：
When X, Y, Z axis single axial movement, geometric error only related to moving cell has an impact to movement locus, no
The geometric error for participating in the kinematic axis of movement locus can be considered zero, and the detection of X, Y, Z single axial movement shares three trajectories, for lifting
The identification precision of position error, the detection and identification result of three trajectories of X, Y, Z axis can be averaging processing.Try to achieve X, Y, Z
The position error difference of axle is as follows：
Further, the discrimination method of translation shaft roll error includes：
The hypothesized angle difference of the trajectory that links and single axial movement trajectory is as follows：
X, the hypothesized angle of Y-axis linkage trajectory and X-axis trajectory is：
X, the hypothesized angle of Y-axis linkage trajectory and Y-axis trajectory is：
X, the hypothesized angle of Z-axis linkage trajectory and X-axis trajectory is：
X, the hypothesized angle of Z-axis linkage trajectory and Z axis trajectory is：
Y, the hypothesized angle of Z-axis linkage trajectory and Y-axis trajectory is：
Y, the hypothesized angle of Z-axis linkage trajectory and Z axis trajectory is：
Link track L13 and the hypothesized angle of X, Y, Z axis
X, Y, Z axis linkage trajectory and X-axis trajectory angle be：
X, Y, Z axis linkage trajectory and Y-axis trajectory angle be：
X, Y, Z axis linkage trajectory and Z axis trajectory angle be：
Consider influence of the angular error to position error, link track L10, L11, the L12 actual folder with X, Y, Z axis respectively
Angle is：
X, the angle of Y-axis linkage trajectory and X-axis trajectory is：
X, the angle of Y-axis linkage trajectory and Y-axis trajectory is：
X, the actual angle of Z-axis linkage trajectory and X-axis trajectory is：
X, the actual angle of Z-axis linkage trajectory and Z axis trajectory is：
Y, the actual angle of Z-axis linkage trajectory and Y-axis trajectory is：
Y, the actual angle of Z-axis linkage trajectory and Z axis trajectory is：
Link track L13 and the angle of X, Y, Z axis
X, Y, Z axis linkage trajectory and X-axis trajectory actual angle be：
X, Y, Z axis linkage trajectory and Y-axis trajectory angle be：
X, Y, Z axis linkage trajectory and Z axis trajectory actual angle be：
Wherein Dx, Dy, Dz distinguish
During to do linkage detection, the amount of movement of X, Y, Z axis single.
According to the angle of multi-shaft interlocked trajectory and single axial movement trajectory, the detection error for the trajectory that links can be projected
To each kinematic axis, translation shaft roll errorI=1,2,
3...n。
Further, the discrimination method of translation shaft straightness error includes：
X-axis translation unit is fitted along the linear residual error of Y-direction, fitting a straight line is as follows：
WhereinFor linear residual error function of the X-axis translation unit along Y-direction,For Monomial coefficient,To be normal
Several, its expression is as follows
X-axis translation unit is fitted along the linear residual error of Z-direction, fitting a straight line is as follows：
WhereinFor linear residual error function of the X-axis translation unit along Z-direction,For Monomial coefficient,To be normal
Several, its expression is as follows：
The linear residual error of Y-axis translation unit in X direction is fitted, fitting a straight line is as follows：
WhereinFor the linear residual error function of Y-axis translation unit in X direction,For Monomial coefficient,For constant
, its expression is as follows：
Y-axis translation unit is fitted along the linear residual error of Z-direction, fitting a straight line is as follows：
WhereinFor linear residual error function of the X-axis translation unit along Z-direction,For Monomial coefficient,For constant
, its expression is as follows：
The linear residual error of Z axis translation unit in X direction is fitted, fitting a straight line is as follows：
WhereinFor the linear residual error function of Z axis translation unit in X direction,For Monomial coefficient,For constant
, its expression is as follows：
Z axis translation unit is fitted along the linear residual error of Y-direction, fitting a straight line is as follows：
WhereinFor linear residual error function of the Z axis translation unit along Y-direction,For Monomial coefficient,For constant
, its expression is as follows：
The straightness error of each translation shaft is that the linearity error vertical with each translation shaft direction of motion is its corresponding most
The deviation of good fitting a straight line.Therefore, the straightness error of three translation shaftsWithSolution it is public
Formula is as follows：
Further, the discrimination method of the translation between centers error of perpendicularity includes：X, the trajectory of Y, Z single axial movement is most
Space vector corresponding to good fitting a straight line is respectively：
According to the direction vector of single axial movement track best-fitting straight line, the perpendicularity between X, Y, Z translation shaft can be solved
Error is as follows：
The additional aspect and advantage of the present invention will be set forth in part in the description, and will partly become from the following description
Obtain substantially, or recognized by the practice of the present invention.
Brief description of the drawings
Fig. 1 is the schematic diagram of lathe according to embodiments of the present invention；
Fig. 2 is the schematic diagram of the space sliding-model control of lathe translation shaft shown in Fig. 1；
Fig. 3 is the schematic diagram for carrying out the detection of X-axis single shaft trajectory error；
Fig. 4 is the schematic diagram for carrying out the detection of Y-axis single shaft trajectory error；
Fig. 5 is the schematic diagram for carrying out the detection of Z axis single shaft trajectory error；
Fig. 6 is the schematic diagram of two-axle interlocking trajectory error detection；
Fig. 7 is the schematic diagram for carrying out the detection of X, Y, Z three-shaft linkage trajectory error；
Fig. 8 is the schematic diagram of 13 detection trajectory distributions.
Embodiment
Embodiments of the invention are described below in detail, the example of the embodiment is shown in the drawings, wherein from beginning to end
Same or similar label represents same or similar element or the element with same or like function.Below with reference to attached
The embodiment of figure description is exemplary, it is intended to for explaining the present invention, and is not considered as limiting the invention.
Following disclosure provides many different embodiments or example is used for realizing the different structure of the present invention.For letter
Change disclosure of the invention, hereinafter the part and setting of specific examples are described.Certainly, they are only example, and
Purpose does not lie in the limitation present invention.In addition, the present invention can in different examples repeat reference numerals and/or letter.It is this heavy
It is the relation between itself not indicating discussed various embodiments and/or setting for purposes of simplicity and clarity again.This
Outside, the invention provides various specific techniques and material examples, but those of ordinary skill in the art can be appreciated that
The applicable property of other techniques and/or the use of other materials.
Lathe translation shaft geometric error discrimination method according to embodiments of the present invention is described below with reference to Fig. 1-Fig. 8.
Lathe translation shaft geometric error discrimination method according to embodiments of the present invention, including：Translation shaft linkage trajectory error
Inspection policies, translation shaft geometric error identification algorithm and translation shaft linearity and three portions of between centers error of perpendicularity approximating method
Point.
1st, translation shaft linkage trajectory error inspection policies.As shown in Fig. 2 the work that lathe translation shaft movement travel is formed
Space is a cuboid, to lift identification precision, can carry out sliding-model control to the rectangular parallelepiped space.By the length and width of cuboid
N deciles are respectively divided into height, then whole working space will be divided into n3Individual small cuboid, (n is distributed with whole space
+1)3Individual node.A kind of line geometry error identification method of lathe translation shaft 13 based on laser interferometer that this patent is proposed,
It focuses on the positioning precision for 13 linkage trajectories that detection is distributed in lathe working space.13 linkage trajectories point
It is not：
(1) as shown in figure 3, detects schematic diagram for 3 straight line localization errors corresponding with X single axial movements direction.It is first
First speculum is arranged on machine tool chief axis end face by magnet base, it is A points to mark the mount point.Then laser interferometer is installed
And interference mirror, adjust laser optical path and moved by numerical control unit control machine edge of bed X-axis.Every X-axis fortune in motion process
When moving the node after stroke discretization, machine tool motion unit stops waiting laser interferometer gathered data in several seconds, now lathe
Numerical control unit ideal movements parameter is Lxi, record the actually detected length L1 of laser interferometeri, detection process opens from i=1
Begin, terminate to i=n+1.Using A points as reference point, mount point D is obtained to lathe Y-axis positive direction offset distance D12.By speculum
The D points being installed on machine tool chief axis end face, then laser interferometer and interference mirror are installed, adjust laser optical path and pass through numerical control list
First control machine edge of bed X-axis motion.In motion process during node after every X-axis movement travel discretization, machine tool motion list
Member stops waiting laser interferometer gathered data in several seconds, and now numerical control of machine tools unit ideal movements parameter is Lxi, record sharp
The actually detected length L2 of optical interferometeri, detection process terminates since i=1 to i=n+1.Using A points as reference origin, to Z
Axle negative direction offset distance D13 obtains mount point E points.E points speculum being installed on machine tool chief axis end face, adjust laser light
Simultaneously moved by numerical control unit control machine edge of bed X-axis on road.Node in motion process after every X-axis movement travel discretization
When, machine tool motion unit stops waiting laser interferometer gathered data in several seconds, now numerical control of machine tools unit ideal movements parameter
For Lxi, record the actually detected length L3 of laser interferometeri, detection process terminates since i=1 to i=n+1.
(2) as shown in figure 4, the detects schematic diagram of 3 straight line localization errors corresponding with Y single axial movements direction.First
By A point of the speculum by magnet base on machine tool chief axis end face.Then laser interferometer and interference mirror are installed, regulation swashs
Light light path is simultaneously moved by numerical control unit control machine edge of bed Y-axis.In motion process after the discretization of every Y motion stroke
During node, machine tool motion unit stops waiting laser interferometer gathered data in several seconds, now numerical control of machine tools unit ideal movements
Parameter is Lyi, record the actually detected length L4 of laser interferometeri, detection process terminates since i=1 to i=n+1.With
A points are reference point, and mount point B is obtained to lathe X-axis positive direction offset distance D45.Speculum is installed on machine tool chief axis end face
On B points, then laser interferometer and interference mirror are installed, regulation laser optical path simultaneously passes through numerical control unit control machine edge of bed Y-axis and transported
It is dynamic.In motion process during node after every Y motion stroke discretization, machine tool motion unit stops waiting laser in several seconds
Interferometer gathered data, now numerical control of machine tools unit ideal movements parameter is Lyi, record the actually detected length of laser interferometer
Spend L5i, detection process terminates since i=1 to i=n+1.Using A points as reference origin, obtained to Z negative direction offset distances D46
To mount point E points.E points speculum being installed on machine tool chief axis end face, adjust laser optical path and controlled by numerical control unit
Lathe moves along Y-axis.In motion process during node after every Y motion stroke discretization, machine tool motion unit stops several
Second wait laser interferometer gathered data, now numerical control of machine tools unit ideal movements parameter is Lyi, record laser interferometer
Actually detected length L6i, detection process terminates since i=1 to i=n+1.
(3) it is illustrated in figure 5, the detects schematic diagram of 3 straight line localization errors corresponding with Z single axial movements direction.It is first
The A points first speculum being arranged on by magnet base on machine tool chief axis end face.Then laser interferometer and interference mirror, regulation are installed
Laser optical path is simultaneously moved by numerical control unit control machine edge of bed Z axis.In motion process after the discretization of every Z movement travel
Node when, machine tool motion unit stops waiting laser interferometer gathered data in several seconds, now the preferable fortune of numerical control of machine tools unit
Dynamic parameter is Lzi, record the actually detected length L7 of laser interferometeri, detection process terminates since i=1 to i=n+1.
Using A points as reference point, mount point B is obtained to lathe X-axis positive direction offset distance D78.Speculum is installed on machine tool chief axis end
B points on face, then laser interferometer and interference mirror are installed, adjust laser optical path and pass through numerical control unit control machine edge of bed Z axis
Motion.In motion process during node after every Z movement travel discretizations, machine tool motion unit, which stops waiting for several seconds, to swash
Optical interferometer gathered data, now numerical control of machine tools unit ideal movements parameter is Lzi, record the actually detected of laser interferometer
Length L8i, detection process terminates since i=1 to i=n+1.Using A points as reference origin, to Y-axis positive direction offset distance
D79 obtains mount point D points.D points speculum being installed on machine tool chief axis end face, adjust laser optical path and pass through numerical control unit
Control machine edge of bed Z axis moves.In motion process during node after every Z movement travel discretizations, machine tool motion unit stops
Only wait laser interferometer gathered data within several seconds, now numerical control of machine tools unit ideal movements parameter is Lzi, record laser and do
The actually detected length L9 of interferometeri, detection process terminates since i=1 to i=n+1.
(4) it is as shown in Figure 6 and Figure 7 the multi-shaft interlocked trajectory accuracy detection schematic diagram of X, Y, Z axis.It is X-Y linkages first
Trajectory positioning precision detects.By A point of the speculum by magnet base on machine tool chief axis end face, then laser is installed done
Interferometer and interference mirror, regulation laser optical path simultaneously control lathe X, Y-axis to move simultaneously by numerical control unit so that speculum is along X-Y
Axle linkage trajectory motion.In motion process during node after the discretization of every X-Y ganged movement strokes, machine tool motion
Unit stops waiting laser interferometer gathered data in several seconds, and now numerical control of machine tools unit ideal movements parameter is Lxyi, record
The actually detected length L10 of lower laser interferometeri, detection process terminates since i=1 to i=n+1.Next to that X-Z links
Trajectory positioning precision detects.A points speculum being installed on machine tool chief axis end face, then laser interferometer and interference are installed
Mirror, regulation laser optical path simultaneously control lathe X, Z axis to move simultaneously by numerical control unit so that speculum is along X-Z axles linkage track
Line moves.In motion process during node after the discretization of every X-Z ganged movement strokes, machine tool motion unit stops several
Second wait laser interferometer gathered data, now numerical control of machine tools unit ideal movements parameter is Lxzi, record laser interference
The actually detected length L11 of instrumenti, detection process terminates since i=1 to i=n+1.Followed by Y-Z linkage trajectory positioning
Accuracy detection.By A point of the speculum by magnet base on machine tool chief axis end face.Then laser interferometer and interference are installed
Mirror, regulation laser optical path simultaneously control lathe Y, Z axis to move simultaneously by numerical control unit so that speculum is along Y-Z axles linkage track
Line moves.In motion process during node after the discretization of every Y-Z ganged movement strokes, machine tool motion unit stops several
Second wait laser interferometer gathered data, now numerical control of machine tools unit ideal movements parameter is Lyzi, record laser interference
The actually detected length L12 of instrumenti, detection process terminates since i=1 to i=n+1.It is finally X-Y-Z three-shaft linkages track
Line positioning precision detects.By A point of the speculum by magnet base on machine tool chief axis end face.Then laser interferometer is installed
And interference mirror, regulation laser optical path simultaneously control lathe X, Y, Z axis to move simultaneously by numerical control unit so that speculum is along X-Y-Z
Axle linkage trajectory motion.In motion process during node after the discretization of every X-Y-Z ganged movement strokes, lathe fortune
Moving cell stops waiting laser interferometer gathered data in several seconds, and now numerical control of machine tools unit ideal movements parameter is Lxyzi, note
The actually detected length L13 of the lower laser interferometer of recordi, detection process terminates since i=1 to i=n+1.
2nd, the distribution schematic diagram of 13 collimation method geometric error identification algorithms detection track is illustrated in figure 8, X, Y, Z translation shaft are several
What error identification, specifically includes the identification of respective three linearity errors of three translation shafts and three angular errors.
(1) it is the identification of development Digit Control Machine Tool translation shaft geometric error, it is necessary first to carry out translation shaft geometrical error modeling.
The topological structure of general lathe is extra bed lathe bed-X-axis moving cell-Y-axis moving cell-Z axis moving cell.For machine tool
Body and translation shaft moving cell connect firmly space coordinates and are respectively：{O0-X0Y0Z0, { Ox-XxYxZx, { Oy-XyYyZyAnd { Oz-
XzYzZz}.Setting all coordinate systems has identical posture, and the origin of all coordinate systems is located at X, Y, the friendship of Z axis axis of movement
At point.Be set for linking the detection of track position error when, mirror mirror center is relative to three reference axis origins (and Z
Axis coordinate system origin) distance be L.In three dimensions, position orientation relation between any two rigid body can with three linear dimensions and
Three angle parameters are expressed by homogeneous coordinate transformation matrix.Thus, the position and attitude error between the rigid body of arbitrary neighborhood two can
Expressed with the homogeneous coordinate transformation matrix being made up of three linearity error sources and three angular error sources.Set X-axis fortune
Moving cell is respectively relative to the three linearity error sources and three angular error sources of bed piece：Xx, Yx, Zx, αx, βx,γx；Y
Axle is respectively relative to the three linearity error sources and three angular error sources of X-axis：Xy, Yy,Zy, αy, βy, γy；Z axis is relative to Y
The three linearity error sources and three angular error sources of axle are respectively：Xz, Yz, Zz, αz, βz, γz.Wherein, X, Y, Z, α, beta, gamma point
Not Biao Shi linearity error and angular error direction, subscript represents to produce the moving cell of corresponding geometric error.By above-mentioned mistake
Poor source is as follows respectively with the expression of next coordinates matrix：
WhereinError transfer matrixes of the X-axis moving cell relative to bed piece are represented,Represent Y-axis moving cell
Relative to the error transfer matrixes of X-axis moving cell,Represent error propagation of the Z axis moving cell relative to Y-axis moving cell
Matrix.
Under the conditions of error free, the ideal position at mirror mirror center by tri- translation shafts of X, Y, Z amount of exercise and machine
The geometric parameter of bed determines, specific as follows：
Wherein,Respectively lathe X, Y, Z axis
Move transfer matrix, Pinitial=[0,0 ,-L, 1]TFor position of the initial time mirror mirror center in the case where Z axis connects firmly coordinate system
Put.
Under conditions of having error, amount of exercise, the machine of the physical location at mirror mirror center by tri- translation shafts of X, Y, Z
The geometric parameter and error transfer matrixes of bed determine jointly, specific as follows：
So when carrying out linkage track position error detection using laser interferometer, linkage track position error can be with table
Up to for：
Perror=Pactual-Pideal
Each translation shaft error source and initial geometric parameter are substituted into geometric error model, the tool of the geometric error of speculum
Body expression formula is as follows：
(2) identification of translation shaft Run-out error, top pendulum error and position error.It is corresponding to X-axis moving cell first
The identification of Run-out error and top pendulum error.The preferable control instruction value of 3 straightways corresponding with X single axial movements direction is
Lxi, corresponding actually detected value is L1i, L2i, L3i.The distance between movement locus L1 and L2 are D12, movement locus L1 and L3
The distance between be D13.According to geometric knowledge, beat of the X-axis moving cell in each discrete nodes of X-axis movement travel can be recognized
Error and top pendulum error are as follows：
Next to that the identification of the Run-out error and top pendulum error corresponding to Y-axis moving cell.It is corresponding with Y single axial movements direction
The preferable control instruction values of 3 straightways be Lyi, corresponding actually detected value is L4i, L5i, L6i.Movement locus L4 with
The distance between L5 is D45, and the distance between movement locus L4 and L6 are D46.According to geometric knowledge, Y can be recognized
Run-out error of the axle moving cell in each discrete nodes of Y-axis movement travel and top pendulum error are as follows：
Followed by the identification of the Run-out error corresponding to Z axis moving cell and top pendulum error.It is corresponding with Z single axial movements direction
The preferable control instruction values of 3 straightways be Lzi, corresponding actually detected value is L7i, L8i, L9i.Movement locus L7 with
The distance between L8 is D78, and the distance between movement locus L7 and L9 are D79.According to geometric knowledge, it is single that Z axis motion can be recognized
Run-out error and top pendulum error of the member in each discrete nodes of Z axis movement travel are as follows：
When X, Y, Z axis single axial movement, geometric error only related to moving cell has an impact to movement locus, no
The geometric error for participating in the kinematic axis of movement locus can be considered zero.X, Y, Z single axial movement detection shares three trajectories, for lifting
The identification precision of position error, the detection and identification result of three trajectories of X, Y, Z axis can be averaging processing.Try to achieve X, Y, Z
The position error difference of axle is as follows：
(3) identification of the roll error of translation shaft and other linearity errors.According to the detected value of single axial movement trajectory and
The detected value of multi-shaft interlocked trajectory, the angle difference that can recognize linkage trajectory and single axial movement trajectory are as follows：
Visible linkage track L10 as shown in Figure 6, L11, L12 are respectively with the hypothesized angle of X, Y, Z axis：
X, the hypothesized angle of Y-axis linkage trajectory and X-axis trajectory is：
X, the hypothesized angle of Y-axis linkage trajectory and Y-axis trajectory is：
X, the hypothesized angle of Z-axis linkage trajectory and X-axis trajectory is：
X, the hypothesized angle of Z-axis linkage trajectory and Z axis trajectory is：
Y, the hypothesized angle of Z-axis linkage trajectory and Y-axis trajectory is：
Y, the hypothesized angle of Z-axis linkage trajectory and Z axis trajectory is：
Link track L13 and the hypothesized angle of X, Y, Z axis as shown in Figure 7
X, Y, Z axis linkage trajectory and X-axis trajectory angle be：
X, Y, Z axis linkage trajectory and Y-axis trajectory angle be：
X, Y, Z axis linkage trajectory and Z axis trajectory angle be：
Consider influence of the angular error to position error, link track L10, L11, the L12 actual folder with X, Y, Z axis respectively
Angle is：
X, the angle of Y-axis linkage trajectory and X-axis trajectory is：
X, the angle of Y-axis linkage trajectory and Y-axis trajectory is：
X, the actual angle of Z-axis linkage trajectory and X-axis trajectory is：
X, the actual angle of Z-axis linkage trajectory and Z axis trajectory is：
Y, the actual angle of Z-axis linkage trajectory and Y-axis trajectory is：
Y, the actual angle of Z-axis linkage trajectory and Z axis trajectory is：
Link track L13 and the angle of X, Y, Z axis as shown in Figure 7
X, Y, Z axis linkage trajectory and X-axis trajectory actual angle be：
X, Y, Z axis linkage trajectory and Y-axis trajectory angle be：
X, Y, Z axis linkage trajectory and Z axis trajectory actual angle be：
Wherein Dx, Dy, Dz distinguish
During to do linkage detection, the amount of movement of X, Y, Z axis single.
According to the angle of multi-shaft interlocked trajectory and single axial movement trajectory, the detection error for the trajectory that links can be projected
To each kinematic axis, it is as follows that identification equation group is established according to lathe geometric error model：
AX=B
Wherein：
X=[Yxi Zxi Xyi Zyi Xzi Yzi αxi βyi]T
I=1,2,3...n
Due to error term γziIt is identical with cutter direction of rotation, the site error of cutter is not influenceed, therefore this error can not
Identification.Equation group AX=B shares 9 equations and contains 8 unknown numbers, to solve the indeterminate equation group, can use least square
Method solves equation group ATAX=ATB, obtaining error amount of the remainder error on various discrete point is：
X=[Yxi Zxi Xyi Zyi Xzi Yzi αxi βyi]T
3rd, translation shaft straightness error and the identification of the between centers error of perpendicularity.It can be obtained based on above-mentioned discrimination method and be worked in lathe
In space in discrete nodes, every error of X, Y, Z axis is specific as follows：
Xxi, Yxi,Zxi,αxi,βxi,γxi,Xyi, Yyi,Zyi,αyi,βyi,γyi,Xzi, Yzi,Zzi,αzi,βzi
In above-mentioned error elements, perpendicular to the translation shaft direction of motion linearity error by translation shaft angular error and
The joint effect of straightness error.To recognize the straightness error of translation shaft, need to be gone first with the method for angular error integration
Except the influence of the angular error element pair linearity error vertical with the translation shaft direction of motion, you can obtain and hung down with the translation shaft direction of motion
Straight linear residual error, expression are as follows：
δYxi=Yxi-∫γxiDx, δ Zxi=Zxi+∫βxiDx, δ Xyi=Xyi+∫γyidy
δZyi=Zyi-∫αyiDy, δ Xzi=Xzi-∫βziDz, δ Yzi=Yzi+∫αzidz
Be fitted to being utilized respectively least square method perpendicular to the linear residual error of the translation shaft direction of motion, linear residual error away from
From with a distance from best-fitting straight line both for the translation shaft the direction straightness error, it is specific as follows：
(1) X-axis translation unit is fitted along the linear residual error of Y-direction, fitting a straight line is as follows：
WhereinFor linear residual error function of the X-axis translation unit along Y-direction,For Monomial coefficient,To be normal
Several, its expression is as follows
(2) X-axis translation unit is fitted along the linear residual error of Z-direction, fitting a straight line is as follows：
WhereinFor linear residual error function of the X-axis translation unit along Z-direction,For Monomial coefficient,To be normal
Several, its expression is as follows：
(3) the linear residual error of Y-axis translation unit in X direction is fitted, fitting a straight line is as follows：
WhereinFor the linear residual error function of Y-axis translation unit in X direction,For Monomial coefficient,For constant
, its expression is as follows：
(4) Y-axis translation unit is fitted along the linear residual error of Z-direction, fitting a straight line is as follows：
WhereinFor linear residual error function of the X-axis translation unit along Z-direction,For Monomial coefficient,For constant
, its expression is as follows：
(5) the linear residual error of Z axis translation unit in X direction is fitted, fitting a straight line is as follows：
WhereinFor the linear residual error function of Z axis translation unit in X direction,For Monomial coefficient,For constant
, its expression is as follows：
(6) Z axis translation unit is fitted along the linear residual error of Y-direction, fitting a straight line is as follows：
WhereinFor linear residual error function of the Z axis translation unit along Y-direction,For Monomial coefficient,For constant
, its expression is as follows：
The straightness error of each translation shaft is that the linearity error vertical with each translation shaft direction of motion is its corresponding most
The deviation of good fitting a straight line.Therefore, the straightness error of three translation shaftsWithSolution formula
It is as follows：
The translation between centers error of perpendicularity is the angular error between the best-fitting straight line of three translation shaft single axial movement tracks.
The best-fitting straight line of the linear residual error vertical with the translation shaft direction of motion, as single axial movement track best-fitting straight line is two
The projection of individual Different Plane.Therefore, can be solved according to the best-fitting straight line of the linear residual error vertical with the translation shaft direction of motion
Space vector corresponding to single axial movement trajectory best-fitting straight line, it is specific as follows：
Therefore, the space vector corresponding to the trajectory best-fitting straight line of X, Y, Z single axial movement is respectively：
According to the direction vector of single axial movement track best-fitting straight line, the perpendicularity between X, Y, Z translation shaft can be solved
Error is as follows：
According to above discrimination method, you can obtain translation shaft X, Y, Z position error：
Xxi, Yyi, Zzi
Translation shaft X, Y, Z Run-out error, top put error and roll error is as follows：
αxi, βxi, γxi, αyi, βyi, γyi, αzi, βzi, γzi,
Translation shaft X, Y, Z straightness error are as follows：
The error of perpendicularity is between translation shaft X, Y, Z：
Qxy, Qxz, Qyz
Lathe translation shaft geometric error discrimination method according to embodiments of the present invention, the main conventional laser interferometer of basis
Cleaning Principle, linked the positioning precision of track by detecting in lathe working space 13 straightways, by track position error with
Lathe translation shaft geometric error model is combined, and picks out the position error of translation shaft with geometric knowledge, error is put on top and inclined
Put error.Using least square method by solve indeterminate system of linear equations ask for translation shaft roll error and with translation shaft transport
Two vertical linearity errors of dynamic direction.According to influence of the angular error for linearity error, missed using angle integration from linear
The influence of angular error is separated in difference, so as to obtain the linear residual error vertical with the translation shaft direction of motion.Based on least square method
The best base directrix of linear residual error, the bias identification based on linear residual error and optimal criteria axis go out the straight line of each translation shaft
Error is spent, the direction in space vector of optimal criteria axis synthesis translation shaft movement locus is then based on, based on all directions vector
Between angular relationship pick out the error of perpendicularitys of three translation between centers.Only needed according to the discrimination method of the present invention with commonly swashing
Optical interferometer is used cooperatively, and testing cost is low, and the detection process used time is few, and identification precision is high, can be Digit Control Machine Tool translation shaft geometry
The diagnosis and compensation of precision provide Main Basiss.
Lathe translation shaft geometric error discrimination method according to embodiments of the present invention, it can overcome and existing be based on laser interference
The deficiency of the translation shaft geometric error discrimination method of instrument, it is only necessary to the conventional laser interferometer of application and normal mirror and interference
The positioning precision for 13 straightways that microscopy is surveyed in lathe working space, detection method is simple, and instrument regulation is time saving.In addition, root
According to the lathe translation shaft geometric error discrimination method of the embodiment of the present invention, indeterminate linear side is solved by application least square method
Journey asks for each error term, the influence of angular error factor has been separated from linearity error, therefore identification precision is higher.Meanwhile adopt
Detecting instrument cost is relatively low, and detection process is simply time saving, and error identification precision is high, in detecting instrument Software for Design and lathe
Detection field has broad application prospects.
In the description of the invention, it is to be understood that term " " center ", " longitudinal direction ", " transverse direction ", " on ", " under ",
"front", "rear", "left", "right", " vertical ", " level ", " top ", " bottom ", " interior ", " outer ", " axial direction ", " radial direction ", " circumference " etc.
The orientation or position relationship of instruction are based on orientation shown in the drawings or position relationship, are for only for ease of the description present invention and letter
Change description, rather than instruction or imply signified device or element must have specific orientation, with specific azimuth configuration and
Operation, therefore be not considered as limiting the invention.
In addition, term " first ", " second " are only used for describing purpose, and it is not intended that instruction or hint relative importance
Or the implicit quantity for indicating indicated technical characteristic.Thus, define " first ", the feature of " second " can be expressed or
Implicitly include one or more this feature.In the description of the invention, " multiple " are meant that two or more,
Unless otherwise specifically defined.
In the present invention, unless otherwise clearly defined and limited, term " installation ", " connected ", " connection ", " fixation " etc.
Term should be interpreted broadly, for example, it may be fixedly connected or be detachably connected, or integrally；It can be direct phase
Even, it can also be indirectly connected by intermediary, can be that the connection of two element internals or the interaction of two elements are closed
System.For the ordinary skill in the art, above-mentioned term in the present invention specific can be understood as the case may be
Implication.
In the present invention, unless otherwise clearly defined and limited, fisrt feature can be with "above" or "below" second feature
It is that the first and second features directly contact, or the first and second features pass through intermediary mediate contact.Moreover, fisrt feature exists
Second feature " on ", " top " and " above " but fisrt feature are directly over second feature or oblique upper, or be merely representative of
Fisrt feature level height is higher than second feature.Fisrt feature second feature " under ", " lower section " and " below " can be
One feature is immediately below second feature or obliquely downward, or is merely representative of fisrt feature level height and is less than second feature.
In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show
The description of example " or " some examples " etc. means specific features, structure, material or the spy for combining the embodiment or example description
Point is contained at least one embodiment or example of the present invention.In this manual, to the schematic representation of above-mentioned term not
Identical embodiment or example must be directed to.Moreover, specific features, structure, material or the feature of description can be with office
Combined in an appropriate manner in one or more embodiments or example.In addition, in the case of not conflicting, the skill of this area
Art personnel can be tied the different embodiments or example and the feature of different embodiments or example described in this specification
Close and combine.
Although an embodiment of the present invention has been shown and described, it will be understood by those skilled in the art that：Not
In the case of departing from the principle and objective of the present invention a variety of change, modification, replacement and modification can be carried out to these embodiments, this
The scope of invention is limited by claim and its equivalent.
Claims (9)
1. a kind of lathe translation shaft geometric error discrimination method, it is characterised in that methods described includes：
13 linkage trajectories and every linkage trajectory are determined in the working space that lathe translation shaft movement travel is formed
On be respectively provided with multiple nodes, operation lathe makes main shaft be moved respectively along 13 linkage trajectories and records the ideal at node
Stroke and traveled distance；
Carry out translation shaft geometrical error modeling and lathe translation shaft is calculated according to the preferable stroke and traveled distance at each node
Geometric error,
Every linkage trajectory includes n+1 node, and the linkage trajectory includes：
On the working space altogether summit A three surfaces on paralleled by X axis three sides form three X-axis trajectory L1, L2,
L3；
On the working space altogether summit A three surfaces on parallel Y-axis three sides form three Y-axis trajectory L4, L5,
L6；
On the working space altogether summit A three surfaces on parallel Z axis three sides form three Z axis trajectory L7, L8,
L9；
It is located at X, the Y-axis linkage track that the diagonal on X-Y plane is formed on the working space on summit A three surfaces altogether
Line L10；
It is located at X, the Z-axis linkage track that the diagonal on X-Z plane is formed on the working space on summit A three surfaces altogether
Line L11；
It is located at Y, the Z-axis linkage track that the diagonal on Y-Z plane is formed on the working space on summit A three surfaces altogether
Line L12；
The X, Y, Z axis linkage trajectory L13 formed on the working space by summit A diagonal.
2. lathe translation shaft geometric error discrimination method according to claim 1, it is characterised in that methods described is also wrapped
Include：
Speculum is arranged on machine tool chief axis end face by magnet base, laser interferometer and interference mirror are installed, adjust laser light
Simultaneously linked track spool motion, in motion process during every node, machine tool motion by numerical control unit control machine edge of bed on road
Unit stops scheduled time wait laser interferometer gathered data.
3. lathe translation shaft geometric error discrimination method according to claim 2, it is characterised in that transported with lathe translation shaft
Summit A in the cuboid working space that dynamic stroke is formed for origin and is respectively X-axis, Y-axis and Z axis by summit A three sides
Coordinate system is established, node is formed along X-axis, Y-axis and Z axis by the working space n deciles and in point of intersection respectively, by the work
Make spatial spreading processing and form (n+1)3Individual node.
4. lathe translation shaft geometric error discrimination method according to claim 1, it is characterised in that the linkage trajectory
On i-th of node since first node A preferable stroke and traveled distance it is as follows：
The preferable stroke difference Lx of the 3 X-axis trajectories parallel with X single axial movements directioniAnd actually detected stroke is respectively L1i、
L2i、L3i,
The preferable stroke difference Ly of the 3 Y-axis trajectories parallel with Y single axial movements directioniAnd actually detected stroke is respectively L4i、
L5i、L6i,
The preferable stroke difference Lz of the 3 Z axis trajectories parallel with Z single axial movements directioniAnd actually detected stroke is respectively L7i、
L8i、L9i,
The preferable stroke moved along X, Y linkage trajectory distinguishes LxyiAnd actually detected stroke is respectively L10i,
The preferable stroke moved along X, Z linkage trajectory distinguishes LxziAnd actually detected stroke is respectively L11i,
The preferable stroke moved along Y, Z linkage trajectory distinguishes LyziAnd actually detected stroke is respectively L12i,
The preferable stroke moved along X, Y, Z linkage trajectory distinguishes LxyziAnd actually detected stroke is respectively L13i,
Wherein i is the integer from 1 to n+1.
5. lathe translation shaft geometric error discrimination method according to claim 4, it is characterised in that carry out translation shaft geometry
The method of error modeling includes：
Connecting firmly space coordinates for bed piece and translation shaft moving cell is respectively：{O0-X0Y0Z0, { Ox-XxYxZx, { Oy-
XyYyZyAnd { Oz-XzYzZz, setting all coordinate systems has identical posture, and the origin of all coordinate systems is located at X, Y, Z axis
The point of intersection of axis of movement, when being set for linkage track position error detection, mirror mirror center is relative to three coordinates
The distance of axle origin is L, sets three linearity error sources and three angular error sources of the X-axis moving cell relative to bed piece
Respectively：Xx, Yx,Zx, αx, βx,γx；Y-axis is respectively relative to the three linearity error sources and three angular error sources of X-axis：
Xy, Yy,Zy, αy, βy,γy；Z axis is respectively relative to the three linearity error sources and three angular error sources of Y-axis：Xz, Yz,Zz,
αz, βz,γz, wherein, X, Y, Z, α, beta, gamma represent the direction of linearity error and angular error, the geometric error of speculum respectively
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6. the lathe translation shaft geometric error discrimination method according to claim 4 or 5, it is characterised in that translation shaft beat
The discrimination method of error, top pendulum error and position error includes：
The preferable control instruction value for defining 3 straightways corresponding with X single axial movements direction is Lxi, corresponding actually detected value
For L1i, L2i, L3i, the distance between movement locus L1 and L2 are D12, and the distance between movement locus L1 and L3 are D13, X-axis
Run-out error of the moving cell in each discrete nodes of X-axis movement travel and top pendulum error are respectively：
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The preferable control instruction value for defining 3 straightways corresponding with Y single axial movements direction is Lyi, corresponding actually detected value
For L4i, L5i, L6i, the distance between movement locus L4 and L5 are D45, and the distance between movement locus L4 and L6 are D46, according to
Geometric knowledge, can recognize Run-out error of the Y-axis moving cell in each discrete nodes of Y-axis movement travel and top pendulum error is as follows：
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The preferable control instruction value for defining 3 straightways corresponding with Z single axial movements direction is Lzi, corresponding actually detected value
For L7i, L8i, L9i, the distance between movement locus L7 and L8 are D78, and the distance between movement locus L7 and L9 are D79, according to
Geometric knowledge, can recognize Run-out error of the Z axis moving cell in each discrete nodes of Z axis movement travel and top pendulum error is as follows：
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When X, Y, Z axis single axial movement, geometric error only related to moving cell has an impact to movement locus, is not involved in
The geometric error of the kinematic axis of movement locus can be considered zero, and the detection of X, Y, Z single axial movement shares three trajectories, is positioned for lifting
The identification precision of error, the detection and identification result of three trajectories of X, Y, Z axis can be averaging processing, try to achieve X, Y, Z axis
Position error difference is as follows：
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<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>L&alpha;</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>+</mo>
<mfrac>
<mrow>
<mo>(</mo>
<mi>L</mi>
<msub>
<mn>4</mn>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>X</mi>
<msub>
<mn>4</mn>
<mi>i</mi>
</msub>
<mo>)</mo>
<mo>+</mo>
<mo>(</mo>
<mi>L</mi>
<msub>
<mn>5</mn>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>X</mi>
<msub>
<mn>5</mn>
<mi>i</mi>
</msub>
<mo>)</mo>
<mo>+</mo>
<mo>(</mo>
<mi>L</mi>
<msub>
<mn>6</mn>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>X</mi>
<msub>
<mn>6</mn>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</mfrac>
<mo>,</mo>
</mrow>
<mrow>
<msub>
<mi>X</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>(</mo>
<mi>L</mi>
<msub>
<mn>7</mn>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>X</mi>
<msub>
<mn>7</mn>
<mi>i</mi>
</msub>
<mo>)</mo>
<mo>+</mo>
<mo>(</mo>
<mi>L</mi>
<msub>
<mn>8</mn>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>X</mi>
<msub>
<mn>8</mn>
<mi>i</mi>
</msub>
<mo>)</mo>
<mo>+</mo>
<mo>(</mo>
<mi>L</mi>
<msub>
<mn>9</mn>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>X</mi>
<msub>
<mn>9</mn>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>3</mn>
</mfrac>
<mo>.</mo>
</mrow>
7. lathe translation shaft geometric error discrimination method according to claim 6, it is characterised in that
The discrimination method of translation shaft roll error includes：
The hypothesized angle difference of the trajectory that links and single axial movement trajectory is as follows：
X, the hypothesized angle of Y-axis linkage trajectory and X-axis trajectory is：
X, the hypothesized angle of Y-axis linkage trajectory and Y-axis trajectory is：
X, the hypothesized angle of Z-axis linkage trajectory and X-axis trajectory is：
X, the hypothesized angle of Z-axis linkage trajectory and Z axis trajectory is：
Y, the hypothesized angle of Z-axis linkage trajectory and Y-axis trajectory is：
Y, the hypothesized angle of Z-axis linkage trajectory and Z axis trajectory is：
Consider influence of the angular error to position error, link track L10, L11, the L12 actual angle with X, Y, Z axis respectively
For：
X, the angle of Y-axis linkage trajectory and X-axis trajectory is：
X, the angle of Y-axis linkage trajectory and Y-axis trajectory is：
X, the actual angle of Z-axis linkage trajectory and X-axis trajectory is：
X, the actual angle of Z-axis linkage trajectory and Z axis trajectory is：
Y, the actual angle of Z-axis linkage trajectory and Y-axis trajectory is：
Y, the actual angle of Z-axis linkage trajectory and Z axis trajectory is：
Linkage track L13 and X, Y, Z axis angle X, Y, Z axis linkage trajectory and X-axis trajectory actual angle be：
X, Y, Z axis linkage trajectory and Y-axis trajectory angle be：
X, Y, Z axis linkage trajectory and Z axis trajectory actual angle be：
Wherein Dx, Dy, Dz are respectively to do
During linkage detection, the amount of movement of X, Y, Z axis single；
According to the angle of multi-shaft interlocked trajectory and single axial movement trajectory, the detection error for the trajectory that links can be projected to each
Kinematic axis, translation shaft roll error
8. lathe translation shaft geometric error discrimination method according to claim 7, it is characterised in that
The discrimination method of translation shaft straightness error includes：
X-axis translation unit is fitted along the linear residual error of Y-direction, fitting a straight line is as follows：
<mrow>
<msubsup>
<mi>L</mi>
<mi>x</mi>
<mi>y</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>y</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>y</mi>
</msubsup>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
WhereinFor linear residual error function of the X-axis translation unit along Y-direction,For Monomial coefficient,For constant term,
Its expression is as follows
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>y</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mrow>
<msup>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
</mrow>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mrow>
<msup>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
</mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Y</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Y</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>y</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&delta;Y</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Y</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
X-axis translation unit is fitted along the linear residual error of Z-direction, fitting a straight line is as follows：
<mrow>
<msubsup>
<mi>L</mi>
<mi>x</mi>
<mi>z</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>z</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>z</mi>
</msubsup>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
WhereinFor linear residual error function of the X-axis translation unit along Z-direction,For Monomial coefficient,For constant term,
Its expression is as follows：
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>z</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Z</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Z</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>z</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<mi>n</mi>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&delta;Z</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Z</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
The linear residual error of Y-axis translation unit in X direction is fitted, fitting a straight line is as follows：
<mrow>
<msubsup>
<mi>L</mi>
<mi>y</mi>
<mi>x</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>x</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>x</mi>
</msubsup>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
</mrow>
WhereinFor the linear residual error function of Y-axis translation unit in X direction,For Monomial coefficient,For constant term, it has
Body expression formula is as follows：
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>x</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;X</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;X</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>x</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mrow>
<msup>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
</mrow>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<mi>n</mi>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&delta;X</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;X</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
Y-axis translation unit is fitted along the linear residual error of Z-direction, fitting a straight line is as follows：
<mrow>
<msubsup>
<mi>L</mi>
<mi>y</mi>
<mi>z</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>z</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>z</mi>
</msubsup>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
</mrow>
WhereinFor linear residual error function of the X-axis translation unit along Z-direction,For Monomial coefficient,For constant term, it has
Body expression formula is as follows：
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>z</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Z</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Z</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>z</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mrow>
<msup>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
</mrow>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&delta;Z</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Z</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
The linear residual error of Z axis translation unit in X direction is fitted, fitting a straight line is as follows：
<mrow>
<msubsup>
<mi>L</mi>
<mi>z</mi>
<mi>x</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>z</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>x</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>z</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>x</mi>
</msubsup>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
</mrow>
WhereinFor the linear residual error function of Z axis translation unit in X direction,For Monomial coefficient,For constant term, it has
Body expression formula is as follows：
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>z</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>x</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msup>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;X</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;X</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>z</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>x</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mrow>
<msup>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
</mrow>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<mi>n</mi>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&delta;X</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;X</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
Z axis translation unit is fitted along the linear residual error of Y-direction, fitting a straight line is as follows：
<mrow>
<msubsup>
<mi>L</mi>
<mi>z</mi>
<mi>y</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>z</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>y</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>z</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>y</mi>
</msubsup>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
</mrow>
WhereinFor linear residual error function of the Z axis translation unit along Y-direction,For Monomial coefficient,For constant term, it has
Body expression formula is as follows：
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>z</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>y</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mrow>
<msup>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
</mrow>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mrow>
<msup>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
</mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Y</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Y</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
<mrow>
<msubsup>
<mi>C</mi>
<mrow>
<mi>z</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mi>y</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mrow>
<msup>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mn>2</mn>
</msup>
</mrow>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<mi>n</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&delta;Y</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&delta;Y</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
The straightness error of each translation shaft is its corresponding optimal plan of the linearity error vertical with each translation shaft direction of motion
Close the deviation of straight line, therefore, the straightness error of three translation shaftsWithSolution formula such as
Under：
<mrow>
<msubsup>
<mi>S</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
<mi>y</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>Y</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<msubsup>
<mi>L</mi>
<mi>x</mi>
<mi>y</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
<msubsup>
<mi>S</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
<mi>z</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>Z</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<msubsup>
<mi>L</mi>
<mi>x</mi>
<mi>z</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
<msubsup>
<mi>S</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
<mi>x</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>X</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<msubsup>
<mi>L</mi>
<mi>y</mi>
<mi>x</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
<mrow>
<msubsup>
<mi>S</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
<mi>z</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>Z</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<msubsup>
<mi>L</mi>
<mi>y</mi>
<mi>z</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
<msubsup>
<mi>S</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
<mi>x</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>X</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<msubsup>
<mi>L</mi>
<mi>z</mi>
<mi>x</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
<msubsup>
<mi>S</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
<mi>y</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>Y</mi>
<mrow>
<mi>z</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>-</mo>
<msubsup>
<mi>L</mi>
<mi>z</mi>
<mi>y</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
9. lathe translation shaft geometric error discrimination method according to claim 8, it is characterised in that the translation between centers hangs down
The discrimination method of straight degree error includes：
X, the space vector corresponding to the trajectory best-fitting straight line of Y, Z single axial movement is respectively：
<mrow>
<msub>
<mi>V</mi>
<mi>x</mi>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>,</mo>
<msubsup>
<mi>C</mi>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
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| CN106959667A (en) * | 2017-04-11 | 2017-07-18 | 西南交通大学 | A kind of lathe translation shaft error of perpendicularity modeling method |
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| 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 |
| CN113093649A (en) * | 2021-04-02 | 2021-07-09 | 广东海洋大学 | 13-step measurement method for measuring geometric errors of machine tool |
| US11886162B2 (en) | 2022-02-23 | 2024-01-30 | Guangdong Ocean University | Method for identifying pitch error and yaw error of numerically-controlled (NC) machine tool |
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