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CN112621385B - Rapid identification method for geometric errors of linear axis based on 8 displacement line measurements - Google Patents

Rapid identification method for geometric errors of linear axis based on 8 displacement line measurements Download PDF

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CN112621385B
CN112621385B CN202011453330.8A CN202011453330A CN112621385B CN 112621385 B CN112621385 B CN 112621385B CN 202011453330 A CN202011453330 A CN 202011453330A CN 112621385 B CN112621385 B CN 112621385B
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error
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straightness
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CN112621385A (en
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郭俊康
李勰
南凯刚
刘志刚
洪军
贾康
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Xian Jiaotong University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
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Abstract

The invention discloses a method for quickly identifying geometric errors of a linear axis based on measurement of 8 displacement lines, which comprises the steps of measuring positioning errors along the direction of 3 axes and measuring positioning errors along the direction of a diagonal line of 5 planes. Step-by-step diagonal surface measurement of 6 measurement paths with different starting sequences is respectively carried out in three coordinate planes, and the straightness error of a linear axis can be solved. And substituting the straightness errors into the motion error model of each linear axis to obtain pitching and yawing errors. Step-by-step diagonal measurements of 2 measurement paths in two coordinate planes can be solved for roll errors. Through carrying out the step-by-step surface diagonal measurement of different initial sequences in 5 planes, combine along the positioning error of 3 axis directions, discern other geometric errors of straight line axle, both considered the influence of corner error to surface diagonal error, only need measure the positioning error along each light path simultaneously, reduced the operation degree of difficulty, improved measurement of efficiency.

Description

Rapid identification method for geometric errors of linear axis based on 8 displacement line measurements
Technical Field
The invention belongs to the technical field of numerical control machine tool machining, and particularly relates to a method for quickly identifying geometric errors of a linear shaft based on measurement of 8 displacement lines.
Background
At present, the detection of the geometric error of a linear axis comprises direct measurement and indirect measurement, a direct measurement method adopts a multi-purpose laser interferometer to measure the single geometric error of the linear axis, the laser interferometer needs to be adjusted for multiple times, the required time is too long, and the efficiency is low. Indirect measurement methods, such as a 9-line method and a 12-line method, have certain disadvantages, the 9-line method measures positioning errors or straightness errors on a plurality of straight lines by using a dual-frequency laser interferometry system, solves other errors of a straight line axis by combining an identification algorithm, is high in cost and difficult to operate, and the 12-line method is complex in model solving and has lower solving precision than the 9-line method. The step body diagonal method only needs to measure the displacement change on 4 body diagonals when each linear axis moves step by step, so the measurement efficiency is improved, but the method ignores the influence of corner errors and has certain principle errors.
Disclosure of Invention
The invention aims to provide a method for quickly identifying geometric errors of a linear shaft based on measurement of 8 displacement lines, which is used for identifying the geometric errors of the linear shaft by respectively measuring 3 displacement errors along the axial direction and 5 displacement errors along a face diagonal line, so that the measurement efficiency of the geometric errors is improved.
The invention is realized by adopting the following technical scheme:
a method for quickly identifying geometric errors of a linear shaft based on measurement of 8 displacement lines comprises the following steps:
step 1: measurement of positioning error
Taking the original point O of the measuring space of the linear axis as a starting point, and enabling the main axis to respectively take a single-step distance DX、DYAnd DZMoving along X, Y and Z axis, measuring positioning error of X, Y, Z axis
Figure BDA0002832328670000021
Step 2: straightness error identification
In an XOY plane, a step-by-step moving mode is adopted, so that the main axis moves to the vertex of the facing angular line along the X axis and then along the Y axis, then the main axis moves to the vertex of the facing angular line along the Y axis and then along the X axis, and the displacement change of the process in the facing angular line direction is obtained through a laser range finder; similar to the measurement mode of the XOY plane, a step-by-step movement mode of firstly carrying out an X axis and then carrying out a Z axis and then carrying out an X axis is carried out in the XOZ plane, and the displacement change of the diagonal direction of the plane is measured; step-by-step moving modes of firstly Y axis and then Z axis and firstly Z axis and then Y axis are executed in the YOZ plane, and the displacement change of the process in the direction facing the diagonal line is measured;
respectively establishing X, Y, Z axis geometric error models through homogeneous coordinate transformation; the linearity error of the X axis in the Y direction is obtained by comparing the displacement error of the X and Y directions moving along the X, Y axis with the displacement error of the facing angle linear displacement direction and combining the positioning error of the X, Y axis
Figure BDA0002832328670000022
And the straight line error of Y axis in X direction
Figure BDA0002832328670000023
Similar comparison is carried out to obtain the straightness error
Figure BDA0002832328670000024
And step 3: identification of corner errors
Substituting the straightness errors of the X axis and the Y axis in the XOY plane solved in the step 2 into an error model of XOY plane motion, substituting the straightness errors of the X axis and the Z axis in the XOZ plane into an error model of XOZ plane motion, and substituting the straightness errors of the Y axis and the Z axis in the YOZ plane into an error model of YOZ plane motion to respectively obtain the rotation angle errors of the X axis and the Y axis around the Z axis
Figure BDA0002832328670000025
And
Figure BDA0002832328670000026
angular errors of X-axis and Z-axis about Y-axis
Figure BDA0002832328670000027
And
Figure BDA0002832328670000028
error in rotation angle of Y-axis and Z-axis around X-axis
Figure BDA0002832328670000029
And
Figure BDA00028323286700000210
at XO1The Y plane executes the step-by-step moving mode of the X axis and the Y axis in the YO2The Z plane executes a moving mode of firstly Y axis and then Z axis, and displacement change in the direction of the facing diagonal is measured; by comparing the spindle ratios at XOY and XO1Moving geometric error generated in X and Y directions in Y plane, and displacement variation in diagonal direction of the combined surface to obtain rolling angle error of X axis and Y axis
Figure BDA00028323286700000211
And
Figure BDA00028323286700000212
by comparing principal axes at YOZ and YO2Moving the geometric error generated in the Y and Z directions in the Z plane, and obtaining the roll error of the Z axis by the displacement change of the joint surface in the diagonal direction
Figure BDA00028323286700000213
The invention is further improved in that in step 2, the straightness error
Figure BDA00028323286700000214
And
Figure BDA00028323286700000215
the identification of (2) is as follows:
in the XOY plane, taking O as a starting point, respectively moving to the vertex C of a face diagonal line of a measurement space in the XOY plane step by step in two modes of firstly moving along an X axis and then along a Y axis and firstly moving along the Y axis and then along the X axis, and carrying out homogeneous coordinate transformation on an error matrix of the X axis under the condition of neglecting a verticality error to obtain a kth movement D along the X axisXi(k)Positioning error of
Figure BDA0002832328670000031
And straightness error
Figure BDA0002832328670000032
Geometric error with X axis relationship:
Figure BDA0002832328670000033
wherein i is 1,2,. 8,
Figure BDA0002832328670000034
to move D along the X-axisXi(k)The subsequent machine tool coordinates;
similarly, the kth movement D along the Y axisYi(k)Straightness error in the X direction
Figure BDA0002832328670000035
And positioning error
Figure BDA0002832328670000036
The relationship between the geometric error with the Y-axis is:
Figure BDA0002832328670000037
wherein,
Figure BDA0002832328670000038
to move D along the Y axisYi(k)The subsequent machine tool coordinates;
by comparing the errors of the k-th movement of the main shaft along the X axis in the X and Y directions in the two movement modes, it is found that the main shaft moves along the X axis D in the XOY planeX1(k)And DX2(k)In the coordinates of the machine tool after the machining,
Figure BDA0002832328670000039
and is
Figure BDA00028323286700000310
Thus, as can be seen from equations (1) and (2), D is moved along the X-axisX(k)、DX1(k)And DX2(k)Equal straightness error in the Y direction, and D movement along the Y axisY(k)、DY1(k)And DY2(k)The straightness errors in the X direction are equal, i.e.:
Figure BDA00028323286700000311
by analogy, moving D along the X-axisX(k)、DX1(k)And DX2(k)The positioning error of (2) has the following relationship:
Figure BDA00028323286700000312
moving D along Y-axisY(k)、DY1(k)And DY2(k)The positioning error of (2) has the following relationship:
Figure BDA0002832328670000041
from formulas (4) and (5):
Figure BDA0002832328670000042
the relation between the diagonal displacement error and the positioning error and the straightness error of the joint surface, namely the joint type (3) and (6), is solved to obtain the main shaft movement DX1(k)、DY1(k)、DX2(k)And DY2(k)The positioning error and straightness error in the XOY plane are known, and the movement D along the X axis is knownX(k)And moving D along the Y axisY(k)Straightness error of
Figure BDA0002832328670000043
And
Figure BDA0002832328670000044
the invention is further improved in that in step 2, the straightness error
Figure BDA0002832328670000045
And
Figure BDA0002832328670000046
the identification of (2) is as follows:
in an XOZ plane, taking O as a starting point, respectively moving to a vertex F of a face diagonal line of a measurement space in the XOZ plane step by step according to two modes of moving along an X axis and then along a Z axis and then along the X axis, and carrying out homogeneous coordinate transformation on an error matrix of the Z axis under the condition of neglecting a verticality error to obtain a kth movement D along the Z axisZi(k)Positioning error of (i ═ 1, 2.. 8)
Figure BDA0002832328670000047
And straightnessError of the measurement
Figure BDA0002832328670000048
The relationship between the geometric error with the Z axis is:
Figure BDA0002832328670000049
wherein,
Figure BDA00028323286700000410
to move D along the Z axisZi(k)The subsequent machine tool coordinates;
by comparing the errors of the k-th movement of the main shaft along the X axis in the X and Z directions in the two movement modes, it is found that the main shaft moves along the X axis D in the XOZ planeX3(k)And DX4(k)In the latter coordinates, the position of the lens,
Figure BDA00028323286700000411
and is
Figure BDA00028323286700000412
Then, as can be seen from the equations (2) and (7), D is moved along the X-axisX(k)、DX3(k)And DX4(k)Equal straightness error in the Z direction, and D movement along the Z axisZ(k)、DZ3(k)And DZ4(k)The straightness errors in the X direction are equal, i.e.:
Figure BDA0002832328670000051
by analogy, moving D along the X-axisX(k)、DX3(k)And DX4(k)The positioning error of (2) has the following relationship:
Figure BDA0002832328670000052
moving D along Z-axisZ(k)、DZ3(k)And DZ4(k)The positioning error of (2) has the following relationship:
Figure BDA0002832328670000053
from formulas (9) and (10):
Figure BDA0002832328670000054
the relation between the diagonal displacement error and the positioning error and the straightness error on the joint surface, namely the joint type (8) and (11), solves the main shaft movement DX3(k)、DZ3(k)、DX4(k)And DZ4(k)The positioning error and the straightness error in the XOZ plane are known, and the movement D along the X axis is knownX(k)And moving D along the Z-axisZ(k)Straightness error of
Figure BDA0002832328670000055
And
Figure BDA0002832328670000056
the invention is further improved in that in step 2, the straightness error
Figure BDA0002832328670000057
And
Figure BDA0002832328670000058
the identification of (2) is as follows:
in the YOZ plane, taking O as a starting point, and respectively moving to the vertex H of the facing angle line of a measurement space in the YOZ plane step by step in two modes of moving along the Y axis and then along the Z axis and then along the Y axis;
by comparing the errors of the k-th movement of the main shaft along the Y axis in the Y and Z directions in the two movement modes, it is found that the movement D along the Y axis is in the YOZ planeY5(k)And DY6(k)In the latter coordinates, the position of the lens,
Figure BDA0002832328670000059
and is
Figure BDA00028323286700000510
Then, as can be seen from equations (1) and (7), D is moved along the Y-axisY(k)、DY5(k)And DY6(k)Equal straightness error in the Z direction, and D movement along the Z axisZ(k)、DZ5(k)And DZ6(k)The straightness errors in the Y direction are equal, i.e.:
Figure BDA00028323286700000511
similarly, moving D along the Y axisY(k)、DY5(k)And DY6(k)The positioning error of (2) has the following relationship:
Figure BDA0002832328670000061
moving D along Z-axisZ(k)、DZ5(k)And DZ6(k)The positioning error of (2) has the following relationship:
Figure BDA0002832328670000062
from formulas (13) and (14):
Figure BDA0002832328670000063
the relation between the diagonal displacement error and the positioning error and the straightness error on the joint surface, namely the joint type (12) and (15), solves the main shaft movement DY5(k)、DZ5(k)、DY6(k)And DZ6(k)The positioning error and the straightness error in the YOZ plane are known, and the movement D along the Y axis is knownY(k)And moving D along the Z-axisZ(k)Straightness error of
Figure BDA0002832328670000064
And
Figure BDA0002832328670000065
after the linearity error is solved, the pitch and yaw errors of the three linear axes are obtained from the expressions (4), (5), (9), (10), (13) and (14) in sequence.
The invention is further improved in that in step 3, the roll angle error of the X axis
Figure BDA0002832328670000066
And roll angle error of Y-axis
Figure BDA0002832328670000067
The identification of (2) is as follows:
at XO1In the Y plane, with O1As a starting point, the main shaft is moved along the X axisXThen move D along the Y axisYUntil the vertex G of the diagonal line of the measurement space is reached; recording movement along X-axis DX7(k)Front and rear distance values
Figure BDA0002832328670000068
And
Figure BDA0002832328670000069
moving D along Y-axisY7(k)Front and rear distance values
Figure BDA00028323286700000610
And
Figure BDA00028323286700000611
because of the fact that
Figure BDA00028323286700000612
Therefore, the following equations (1) and (2):
Figure BDA00028323286700000613
in a similar way, the method comprises the following steps:
Figure BDA0002832328670000071
the relation between the displacement error on the diagonal of the joint surface and the positioning error and the straightness error of the linear axis is solved by combining the vertical type (16) and the formula (17) to obtain the rolling angle error of the X axis
Figure BDA0002832328670000072
And roll angle error of Y-axis
Figure BDA0002832328670000073
The invention is further improved in that in step 3, the roll angle error of the Z axis
Figure BDA0002832328670000074
The identification of (2) is as follows:
in YO2In the Z plane, with O2As a starting point, the main shaft is moved along the Y axisYThen move D along the Z axisZUntil the vertex G of the diagonal line of the measurement space is reached; recording movement D along the Y-axisY8(k)Front and rear distance values
Figure BDA0002832328670000075
And
Figure BDA0002832328670000076
moving D along Z-axisZ8(k)Front and rear distance values
Figure BDA0002832328670000077
And
Figure BDA0002832328670000078
because of the fact that
Figure BDA0002832328670000079
Therefore, the following equations (2) and (7):
Figure BDA00028323286700000710
by the equation (18), the relation between the displacement error on the diagonal line of the joint surface and the positioning error and the straightness error of the linear axis is solved to obtain the rolling angle error of the Z axis
Figure BDA00028323286700000711
The invention has at least the following beneficial technical effects:
(1) the invention provides a method for quickly identifying geometric errors of a linear shaft based on 8 displacement line measurements, which can identify all geometric errors of the linear shaft by measuring displacement changes in 8 directions only and improves the measurement efficiency. Compared with the 9-line method, the method only needs to measure the positioning error of each linear direction, reduces the error items required to be measured for identification, reduces the dimming difficulty and improves the measurement efficiency.
(2) Compared with the 12-line method, the 15-line method and the like, the method only needs to solve a simple linear equation set, so that the model is simple to solve.
(3) The invention combines the positioning error, measures the diagonal line by the step-by-step surface with different initial moving sequences in different coordinate planes, considers the influence of the corner error on the diagonal line error, and eliminates the principle error of the step-by-step body diagonal line measurement.
Drawings
FIG. 1 is a schematic diagram of the distribution of 8 shift lines according to the present invention.
FIG. 2 is a measurement path for straightness error identification according to the present invention.
FIG. 3 shows a measurement path for roll angle error identification according to the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention provides a method for rapidly identifying geometric errors of a linear shaft based on 8 displacement line measurement, which measures displacement errors along the directions of 3 axes and 5 surfaces diagonal lines shown in figure 1, and the relation between the joint surface diagonal line displacement error and the positioning error and the straightness error of the linear shaft, identifies the straightness error and the corner error, and comprises the following steps:
step 1: measurement of positioning error
Measurement space L according to a linear axisX×LY×LZDetermining the single-step moving distance D of each linear shaftX、DYAnd DZSo that it satisfies:
Figure BDA0002832328670000081
mounting the reflector on the main shaft, adjusting the laser range finder to make the laser beam perpendicular to the reflector, and making the machine tool use DXFor intervals moving along the X-axis to point B, the movement D along the X-axis is measuredX(k)Positioning error of
Figure BDA0002832328670000082
Similarly, the measurement is shifted along the Y-axis by DY(k)Positioning error of
Figure BDA0002832328670000083
And moving D along the Z-axisZ(k)Positioning error of
Figure BDA0002832328670000084
Step 2: straightness error identification
(1) Error of straightness
Figure BDA0002832328670000085
And
Figure BDA0002832328670000086
is identified by
As shown in FIG. 2, in the XOY plane, with O as the starting point, the X-axis and Y-axis movements are respectively moved to the vertex C of the facing angle line of the measurement space in the XOY plane step by step in two ways of moving along the X-axis and then the Y-axis (path 1) and moving along the Y-axis and then the X-axis (path 2), and under the condition of neglecting the verticality error, the error matrix of the X-axis is subjected to homogeneous coordinate transformation, so that the kth movement D along the X-axis can be obtainedXi(k)Positioning error of (i ═ 1, 2.. 8)
Figure BDA0002832328670000087
And straightness error
Figure BDA0002832328670000088
The relationship between the geometric error with the X-axis is:
Figure BDA0002832328670000091
wherein,
Figure BDA0002832328670000092
to move D along the X-axisXi(k)The latter machine coordinates.
Similarly, the kth movement D along the Y axisYi(k)Straightness error in the X direction
Figure BDA0002832328670000093
And positioning error
Figure BDA0002832328670000094
The relationship between the geometric error with the Y-axis is:
Figure BDA0002832328670000095
wherein,
Figure BDA0002832328670000096
to move D along the Y axisYi(k)The latter machine coordinates.
By comparing the errors in the X and Y directions for the k-th movement of the spindle along the X axis in Path 1 and Path 2, it can be seen that due to the movement D along the X axis in the XOY planeX1(k)And DX2(k)In the latter coordinates, the position of the lens,
Figure BDA0002832328670000097
and is
Figure BDA0002832328670000098
Then, as can be seen from the equations (2) and (3), D is moved along the X-axisX(k)、DX1(k)And DX2(k)Equal straightness error in the Y direction, and D movement along the Y axisY(k)、DY1(k)And DY2(k)The straightness errors in the X direction are equal, i.e.:
Figure BDA0002832328670000099
by analogy, moving D along the X-axisX(k)、DX1(k)And DX2(k)The positioning error of (2) has the following relationship:
Figure BDA00028323286700000910
moving D along Y-axisY(k)、DY1(k)And DY2(k)The positioning error of (2) has the following relationship:
Figure BDA00028323286700000911
from formulas (6) and (7):
Figure BDA0002832328670000101
and displacement errors generated in the diagonal direction inside the XOY plane by moving along the X-axis and the Y-axis
Figure BDA0002832328670000102
The positioning error and the straightness error with respect to the linear axis have the following relationship:
Figure BDA0002832328670000103
wherein,
Figure BDA0002832328670000104
and
Figure BDA0002832328670000105
and
Figure BDA0002832328670000106
and
Figure BDA0002832328670000107
to move D along the X-axisXi(k)And moving D along the Y axisYi(k)Front and rear distance values, RXYIs the face diagonal length of the single step movement.
Simultaneous (4), (7) and (8) can solve the spindle movement DX1(k)、DY1(k)、DX2(k)And DY2(k)The positioning error and straightness error in the XOY plane are known, and the movement D along the X axis is knownX(k)And moving D along the Y axisY(k)Straightness error of
Figure BDA0002832328670000108
And
Figure BDA0002832328670000109
(2) error of straightness
Figure BDA00028323286700001010
And
Figure BDA00028323286700001011
is identified by
As shown in FIG. 2, in the XOZ plane, with O as the starting point, the X-axis and Z-axis movement (path 3) and the X-axis and X-axis movement (path 4) are respectively moved to the vertex F of the facing angle line of the measurement space in the XOZ plane step by step, and the error matrix of the Z axis is subjected to the homogeneous coordinate transformation under the condition of neglecting the verticality error, so that the kth movement D along the Z axis can be obtainedZi(k)Positioning error of
Figure BDA00028323286700001012
And straightness error
Figure BDA00028323286700001013
The relationship between the geometric error with the Z axis is:
Figure BDA00028323286700001014
wherein i is 1,2,. 8,
Figure BDA00028323286700001015
to move D along the Z axisZi(k)The latter machine coordinates.
By comparing the errors in the X and Z directions for the kth movement of the spindle along the X axis in path 3 and path 4, it can be seen that the X axis movement D is due to the movement in the XOZ planeX3(k)And DX4(k)In the latter coordinates, the position of the lens,
Figure BDA0002832328670000111
and is
Figure BDA0002832328670000112
Then, as can be seen from the equations (2) and (9), D is moved along the X-axisX(k)、DX3(k)And DX4(k)Equal straightness error in the Z direction, and D movement along the Z axisZ(k)、DZ3(k)And DZ4(k)The straightness errors in the X direction are equal, i.e.:
Figure BDA0002832328670000113
by analogy, moving D along the X-axisX(k)、DX3(k)And DX4(k)The positioning error of (2) has the following relationship:
Figure BDA0002832328670000114
moving D along Z-axisZ(k)、DZ3(k)And DZ4(k)The positioning error of (2) has the following relationship:
Figure BDA0002832328670000115
from formulas (11) and (12):
Figure BDA0002832328670000116
and displacement errors in the direction of the facing diagonal in the XOZ plane along the X-axis and Z-movement
Figure BDA0002832328670000117
The positioning error and the straightness error with respect to the linear axis have the following relationship:
Figure BDA0002832328670000118
wherein,
Figure BDA0002832328670000119
and
Figure BDA00028323286700001110
and
Figure BDA00028323286700001111
and
Figure BDA00028323286700001112
to move D along the X-axisXi(k)And moving D along the Z-axisZi(k)Distance values measured before and after FSI.
The joint type (10), (13) and (14) can solve the spindle movement DX3(k)、DZ3(k)、DX4(k)And DZ4(k)The positioning error and the straightness error in the XOZ plane are known, and the movement D along the X axis is knownX(k)And moving D along the Z-axisZ(k)Straightness error of
Figure BDA0002832328670000121
And
Figure BDA0002832328670000122
(3) error of straightness
Figure BDA0002832328670000123
And
Figure BDA0002832328670000124
is identified by
As shown in fig. 2, in the YOZ plane, the measurement space is moved stepwise to the vertex H of the subtended angle line of the measurement space in the YOZ plane, starting from O, in two ways, i.e., first along the Y axis and then along the Z axis (path 5) and first along the Z axis and then along the Y axis (path 6).
By comparing the errors in the Y and Z directions for the kth movement of the spindle along the Y axis in path 5 and path 6, it can be seen that the movement D along the Y axis is due to the movement in the YOZ planeY5(k)And DY6(k)In the latter coordinates, the position of the lens,
Figure BDA0002832328670000125
and is
Figure BDA0002832328670000126
Then, as can be seen from equations (3) and (9), D is moved along the Y-axisY(k)、DY5(k)And DY6(k)Equal straightness error in the Z direction, and D movement along the Z axisZ(k)、DZ5(k)And DZ6(k)The straightness errors in the Y direction are equal, i.e.:
Figure BDA0002832328670000127
similarly, moving D along the Y axisY(k)、DY5(k)And DY6(k)The positioning error of (2) has the following relationship:
Figure BDA0002832328670000128
moving D along Z-axisZ(k)、DZ5(k)And DZ6(k)The positioning error of (2) has the following relationship:
Figure BDA0002832328670000129
from formulas (14) and (15):
Figure BDA00028323286700001210
and displacement errors in the direction of the facing diagonal in the YOZ plane along the Y-axis and Z-movement
Figure BDA00028323286700001211
The positioning error and the straightness error with respect to the linear axis have the following relationship:
Figure BDA0002832328670000131
wherein,
Figure BDA0002832328670000132
and
Figure BDA0002832328670000133
and
Figure BDA0002832328670000134
and
Figure BDA0002832328670000135
to move D along the X-axisXi(k)And moving D along the Z-axisZi(k)The distance values before and after.
The joint type (15), (18) and (19) can solve the spindle movement DY5(k)、DZ5(k)、DY6(k)And DZ6(k)The positioning error and the straightness error in the YOZ plane are known, and the movement D along the Y axis is knownY(k)And moving D along the Z-axisZ(k)Straightness error of
Figure BDA0002832328670000136
And
Figure BDA0002832328670000137
and step 3: identification of corner errors
(1) Identification of pitch and yaw errors
The straightness error obtained in the step 3(1) is used
Figure BDA0002832328670000138
And
Figure BDA0002832328670000139
the rotation angle error can be obtained by substituting the formula (5) and the formula (6) respectively
Figure BDA00028323286700001310
And
Figure BDA00028323286700001311
the straightness error obtained in the step 3 and the step 2
Figure BDA00028323286700001312
And
Figure BDA00028323286700001313
can be obtained by substituting the respective expressions (11) and (12)
Figure BDA00028323286700001314
And
Figure BDA00028323286700001315
the straightness error obtained in the step 3 and 3
Figure BDA00028323286700001316
And
Figure BDA00028323286700001317
can be obtained by substituting the formula (16) and the formula (17) respectively
Figure BDA00028323286700001318
And
Figure BDA00028323286700001319
(2) error of roll angle
Figure BDA00028323286700001320
And
Figure BDA00028323286700001321
is identified by
As shown in fig. 3, at XO1In the Y plane, with O1As a starting point, the main shaft is moved along the X axisXThen move D along the Y axisYUntil the vertex G of the diagonal line of the measurement space is reached; recording movement along X-axis DX7(k)Front and rear distance values
Figure BDA00028323286700001322
And
Figure BDA00028323286700001323
moving D along Y-axisY7(k)Front and rear distance values
Figure BDA00028323286700001324
And
Figure BDA00028323286700001325
because of the fact that
Figure BDA00028323286700001326
Therefore, according to formula (2) and formula (3):
Figure BDA00028323286700001327
Figure BDA00028323286700001328
the same principle is as follows:
Figure BDA0002832328670000141
Figure BDA0002832328670000142
from the formula (20)
Figure BDA0002832328670000143
Is solved by substituting formula (8)
Figure BDA0002832328670000144
Can be substituted by formula (21)
Figure BDA0002832328670000145
From the formula (23)
Figure BDA0002832328670000146
Is solved by substituting formula (8)
Figure BDA0002832328670000147
Can be substituted by formula (22)
Figure BDA0002832328670000148
(3) Error of roll angle
Figure BDA0002832328670000149
Is identified by
As shown in FIG. 3, in YO2In the Z plane, with O2As a starting point, the main shaft is moved along the Y axisYThen move D along the Z axisZUntil the vertex G of the diagonal line of the measurement space is reached; recording movement D along the Y-axisY8(k)Front and rear distance values
Figure BDA00028323286700001410
And
Figure BDA00028323286700001411
moving D along Z-axisZ8(k)Front and rear distance values
Figure BDA00028323286700001412
And
Figure BDA00028323286700001413
because of the fact that
Figure BDA00028323286700001414
Therefore, according to formula (3) and formula (9):
Figure BDA00028323286700001415
Figure BDA00028323286700001416
from formula (25)
Figure BDA00028323286700001417
Can be substituted by formula (19)
Figure BDA00028323286700001418
Substitution formula (24) can be solved
Figure BDA00028323286700001419

Claims (1)

1. A method for rapidly identifying geometric errors of a linear axis based on measurement of 8 displacement lines is characterized by comprising the following steps:
step 1: measurement of positioning error
Taking the original point O of the measuring space of the linear axis as a starting point, and enabling the main axis to respectively take a single-step distance DX、DYAnd DZMoving along X, Y and Z axis, measuring positioning error of X, Y, Z axis
Figure FDA0003472107210000011
Step 2: straightness error identification
In an XOY plane, a step-by-step moving mode is adopted, so that the main axis moves to the vertex of the facing angular line along the X axis and then along the Y axis, then the main axis moves to the vertex of the facing angular line along the Y axis and then along the X axis, and the displacement change of the process in the facing angular line direction is obtained through a laser range finder; similar to the measurement mode of the XOY plane, a step-by-step movement mode of firstly carrying out an X axis and then carrying out a Z axis and then carrying out an X axis is carried out in the XOZ plane, and the displacement change of the diagonal direction of the plane is measured; step-by-step moving modes of firstly Y axis and then Z axis and firstly Z axis and then Y axis are executed in the YOZ plane, and the displacement change of the process in the direction facing the diagonal line is measured;
respectively establishing X, Y, Z axis geometric error models through homogeneous coordinate transformation; the linearity error of the X axis in the Y direction is obtained by comparing the displacement error of the X and Y directions moving along the X, Y axis with the displacement error of the facing angle linear displacement direction and combining the positioning error of the X, Y axis
Figure FDA0003472107210000012
And the straight line error of Y axis in X direction
Figure FDA0003472107210000013
Similar comparison is carried out to obtain the straightness error
Figure FDA0003472107210000014
Error of straightness
Figure FDA0003472107210000015
And
Figure FDA0003472107210000016
the identification of (2) is as follows:
in the XOY plane, taking O as a starting point, respectively moving along the X axis and then along the Y axis and moving along the Y axis and then along the X axisMoving to the vertex C of the diagonal line of the measurement space in the XOY plane step by step, and performing homogeneous coordinate transformation on the error matrix of the X axis under the condition of neglecting the verticality error to obtain the kth movement D along the X axisXi(k)Positioning error of
Figure FDA0003472107210000017
And straightness error
Figure FDA0003472107210000018
Geometric error with X axis relationship:
Figure FDA0003472107210000019
wherein i is 1,2,. 8,
Figure FDA0003472107210000021
to move D along the X-axisXi(k)The subsequent machine tool coordinates;
similarly, the kth movement D along the Y axisYi(k)Straightness error in the X direction
Figure FDA0003472107210000022
And positioning error
Figure FDA0003472107210000023
The relationship between the geometric error with the Y-axis is:
Figure FDA0003472107210000024
wherein,
Figure FDA0003472107210000025
to move D along the Y axisYi(k)The subsequent machine tool coordinates;
by comparing the k-th movement of the spindle along the X-axis in the X and Y directionsError, found due to movement of D along the X-axis in the XOY planeX1(k)And DX2(k)In the coordinates of the machine tool after the machining,
Figure FDA0003472107210000026
and is
Figure FDA0003472107210000027
Thus, as can be seen from equations (1) and (2), D is moved along the X-axisX(k)、DX1(k)And DX2(k)Equal straightness error in the Y direction, and D movement along the Y axisY(k)、DY1(k)And DY2(k)The straightness errors in the X direction are equal, i.e.:
Figure FDA0003472107210000028
by analogy, moving D along the X-axisX(k)、DX1(k)And DX2(k)The positioning error of (2) has the following relationship:
Figure FDA0003472107210000029
moving D along Y-axisY(k)、DY1(k)And DY2(k)The positioning error of (2) has the following relationship:
Figure FDA00034721072100000210
from formulas (4) and (5):
Figure FDA00034721072100000211
the relation between the diagonal displacement error and the positioning error and the straightness error of the joint surface, namely the joint type (3) and (6), is solved to obtain the main shaft movement DX1(k)、DY1(k)、DX2(k)And DY2(k)The positioning error and straightness error in the XOY plane are known, and the movement D along the X axis is knownX(k)And moving D along the Y axisY(k)Straightness error of
Figure FDA0003472107210000031
And
Figure FDA0003472107210000032
error of straightness
Figure FDA0003472107210000033
And
Figure FDA0003472107210000034
the identification of (2) is as follows:
in an XOZ plane, taking O as a starting point, respectively moving to a vertex F of a face diagonal line of a measurement space in the XOZ plane step by step according to two modes of moving along an X axis and then along a Z axis and then along the X axis, and carrying out homogeneous coordinate transformation on an error matrix of the Z axis under the condition of neglecting a verticality error to obtain a kth movement D along the Z axisZi(k)Positioning error of (i ═ 1, 2.. 8)
Figure FDA0003472107210000035
And straightness error
Figure FDA0003472107210000036
The relationship between the geometric error with the Z axis is:
Figure FDA0003472107210000037
wherein,
Figure FDA0003472107210000038
to move D along the Z axisZi(k)The subsequent machine tool coordinates;
by comparing the two kinds of moving partsWhere the k-th movement of the spindle along the X-axis has an error in the X and Z directions, it was found that due to the movement D along the X-axis in the XOZ planeX3(k)And DX4(k)In the latter coordinates, the position of the lens,
Figure FDA0003472107210000039
and is
Figure FDA00034721072100000310
Then, as can be seen from the equations (2) and (7), D is moved along the X-axisX(k)、DX3(k)And DX4(k)Equal straightness error in the Z direction, and D movement along the Z axisZ(k)、DZ3(k)And DZ4(k)The straightness errors in the X direction are equal, i.e.:
Figure FDA00034721072100000311
by analogy, moving D along the X-axisX(k)、DX3(k)And DX4(k)The positioning error of (2) has the following relationship:
Figure FDA00034721072100000312
moving D along Z-axisZ(k)、DZ3(k)And DZ4(k)The positioning error of (2) has the following relationship:
Figure FDA00034721072100000313
from formulas (9) and (10):
Figure FDA0003472107210000041
the relation between the diagonal displacement error and the positioning error and the straightness error on the joint surface, namely the joint type (8) and (11), solves the main shaft movement DX3(k)、DZ3(k)、DX4(k)And DZ4(k)The positioning error and the straightness error in the XOZ plane are known, and the movement D along the X axis is knownX(k)And moving D along the Z-axisZ(k)Straightness error of
Figure FDA0003472107210000042
And
Figure FDA0003472107210000043
error of straightness
Figure FDA0003472107210000044
And
Figure FDA0003472107210000045
the identification of (2) is as follows:
in the YOZ plane, taking O as a starting point, and respectively moving to the vertex H of the facing angle line of a measurement space in the YOZ plane step by step in two modes of moving along the Y axis and then along the Z axis and then along the Y axis;
by comparing the errors of the k-th movement of the main shaft along the Y axis in the Y and Z directions in the two movement modes, it is found that the movement D along the Y axis is in the YOZ planeY5(k)And DY6(k)In the latter coordinates, the position of the lens,
Figure FDA0003472107210000046
and is
Figure FDA0003472107210000047
Then, as can be seen from equations (1) and (7), D is moved along the Y-axisY(k)、DY5(k)And DY6(k)Equal straightness error in the Z direction, and D movement along the Z axisZ(k)、DZ5(k)And DZ6(k)The straightness errors in the Y direction are equal, i.e.:
Figure FDA0003472107210000048
similarly, moving D along the Y axisY(k)、DY5(k)And DY6(k)The positioning error of (2) has the following relationship:
Figure FDA0003472107210000049
moving D along Z-axisZ(k)、DZ5(k)And DZ6(k)The positioning error of (2) has the following relationship:
Figure FDA00034721072100000410
from formulas (13) and (14):
Figure FDA0003472107210000051
the relation between the diagonal displacement error and the positioning error and the straightness error on the joint surface, namely the joint type (12) and (15), solves the main shaft movement DY5(k)、DZ5(k)、DY6(k)And DZ6(k)The positioning error and the straightness error in the YOZ plane are known, and the movement D along the Y axis is knownY(k)And moving D along the Z-axisZ(k)Straightness error of
Figure FDA0003472107210000052
And
Figure FDA0003472107210000053
after the straightness errors are solved, obtaining the pitching and yawing errors of the three linear axes from the expressions (4), (5), (9), (10), (13) and (14) in sequence;
and step 3: identification of corner errors
Substituting the straightness errors of the X axis and the Y axis in the XOY plane solved in the step 2 into an error model of the XOY plane motion, and substituting the straightness errors of the X axis and the Z axis in the XOZ plane into the XOZ plane motionSubstituting the error model, the straightness errors of the Y axis and the Z axis on the YOZ plane into the error model of the motion of the YOZ plane to respectively obtain the rotation angle errors of the X axis and the Y axis around the Z axis
Figure FDA0003472107210000054
And
Figure FDA0003472107210000055
angular errors of X-axis and Z-axis about Y-axis
Figure FDA0003472107210000056
And
Figure FDA0003472107210000057
error in rotation angle of Y-axis and Z-axis around X-axis
Figure FDA0003472107210000058
And
Figure FDA0003472107210000059
at XO1The Y plane executes the step-by-step moving mode of the X axis and the Y axis in the YO2The Z plane executes a moving mode of firstly Y axis and then Z axis, and displacement change in the direction of the facing diagonal is measured; by comparing the spindle ratios at XOY and XO1Moving geometric error generated in X and Y directions in Y plane, and displacement variation in diagonal direction of the combined surface to obtain rolling angle error of X axis and Y axis
Figure FDA00034721072100000510
And
Figure FDA00034721072100000511
by comparing principal axes at YOZ and YO2Moving the geometric error generated in the Y and Z directions in the Z plane, and obtaining the roll angle error of the Z axis by the displacement change of the joint surface in the diagonal direction
Figure FDA00034721072100000512
Roll angle error of X-axis
Figure FDA00034721072100000513
And roll angle error of Y-axis
Figure FDA00034721072100000514
The identification of (2) is as follows:
at XO1In the Y plane, with O1As a starting point, the main shaft is moved along the X axisXThen move D along the Y axisYUntil the vertex G of the diagonal line of the measurement space is reached; recording movement along X-axis DX7(k)Front and rear distance values
Figure FDA00034721072100000515
And
Figure FDA00034721072100000516
moving D along Y-axisY7(k)Front and rear distance values
Figure FDA00034721072100000517
And
Figure FDA00034721072100000518
because of the fact that
Figure FDA0003472107210000061
Therefore, the following equations (1) and (2):
Figure FDA0003472107210000062
in a similar way, the method comprises the following steps:
Figure FDA0003472107210000063
the relation between the displacement error on the diagonal of the joint surface and the positioning error and the straightness error of the linear axis is solved by combining the vertical type (16) and the formula (17) to obtain the rolling angle error of the X axis
Figure FDA0003472107210000064
And roll angle error of Y-axis
Figure FDA0003472107210000065
Roll angle error of Z axis
Figure FDA0003472107210000066
The identification of (2) is as follows:
in YO2In the Z plane, with O2As a starting point, the main shaft is moved along the Y axisYThen move D along the Z axisZUntil the vertex G of the diagonal line of the measurement space is reached; recording movement D along the Y-axisY8(k)Front and rear distance values
Figure FDA0003472107210000067
And
Figure FDA0003472107210000068
moving D along Z-axisZ8(k)Front and rear distance values
Figure FDA0003472107210000069
And
Figure FDA00034721072100000610
because of the fact that
Figure FDA00034721072100000611
Therefore, the following equations (2) and (7):
Figure FDA00034721072100000612
by the equation (18), the relation between the displacement error on the diagonal line of the joint surface and the positioning error and the straightness error of the linear axis is solved to obtain the rolling angle error of the Z axis
Figure FDA00034721072100000613
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