CN113601269B - Novel method for quickly separating geometric errors of rotating shaft of multi-shaft numerical control machine tool - Google Patents
Novel method for quickly separating geometric errors of rotating shaft of multi-shaft numerical control machine tool Download PDFInfo
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Abstract
The invention discloses a new method for quickly separating geometric errors of a rotating shaft of a multi-shaft numerical control machine tool, which is used for measuring vector direction change formed by a series of adjacent measuring points in the moving process of a rotary table, establishing a mutual mapping relation between the vector direction change and the geometric errors of the rotating shaft and realizing the preparation separation of 6 geometric errors of the rotating shaft. The method utilizes the characteristic that the change of the direction of a space vector formed in the movement process of the machine tool is only related to the angular displacement error of a machine tool shaft and is unrelated to the linear displacement error, utilizes the laser tracker to measure the change of the direction of the vector formed by measuring points in the movement process of a machine tool translation shaft by adopting multi-station time-sharing measurement, and sequentially separates the angular displacement error and the linear displacement error of the machine tool rotation shaft. A mathematical model for measuring the geometric errors of the multi-axis machine tool rotating shaft based on the space vector direction deviation measurement is established, and a laser tracker base station position self-calibration algorithm, a measuring point determination algorithm and a machine tool rotating shaft single error separation algorithm based on the precise numerical control turntable measurement are deduced in sequence.
Description
Technical Field
The invention belongs to the technical field of laser precision measurement, and particularly relates to a novel method for quickly separating geometric errors of a rotating shaft of a multi-shaft numerical control machine tool.
Background
Along with the improvement of machining precision and complexity of workpieces, the proportion of multi-axis numerical control machine tools in the manufacturing industry is increasing day by day. A multi-axis machine tool is characterized in that a rotating part is additionally arranged on a traditional three-axis machine tool, so that efficient machining of complex parts is realized. The precision is the main performance index of the numerical control machine tool, and how to further improve the overall machining precision of the multi-axis machine tool becomes a research hotspot problem. In multi-axis machining, geometric errors of the rotating shaft have a large influence on the overall machining precision. The measurement and compensation of the error of the rotating shaft are effective ways for improving the overall processing precision of the multi-shaft machine tool. How to quickly and accurately obtain various geometric errors of a machine tool rotating shaft is a key problem, and the precision compensation effect is directly influenced.
At present, a plurality of methods are used for measuring errors of a translational axis of a machine tool, and the measuring method is mature. The error measurement method of the rotating shaft is relatively few, and is also a difficult problem of machine tool precision detection. The following are mainly available: the autocollimator and the polygon can only evaluate the positioning error of the rotating shaft, but cannot measure other errors; when the ball arm instrument is used for measuring the rotating shaft error, 5 errors except for the positioning error can be separated, and the measuring process and the error separation model are complex; when the R-test measurement is adopted, the displacement in 3 directions can be detected simultaneously, and the measurement efficiency is high. But the requirements on the precision of the measuring device are high.
The laser tracking measurement has the advantages of rapidness, dynamic property, portability and the like, and is widely applied to the large-size measurement fields of aerospace, ships, automobiles and the like. At present, the laser tracker is also applied to the field of machine tool precision detection.
How to utilize the advantages of the laser tracker to provide a geometric error separation method of a multi-axis machine tool rotating shaft, which has high precision, high efficiency and simple error separation algorithm, and has important significance for further improving the overall machining precision of the multi-axis machine tool.
Disclosure of Invention
The invention aims to solve the problems and provides a novel method for quickly separating the geometric errors of the rotating shaft of the multi-shaft numerical control machine tool, which can quickly and accurately separate the geometric errors of the rotating shaft of the numerical control machine tool.
In order to solve the technical problems, the technical scheme of the invention is as follows: a novel method for quickly separating geometric errors of a rotating shaft of a multi-shaft numerical control machine tool comprises the following steps:
s1, mounting a precision numerical control rotary table on a multi-axis machine tool rotating component and rotating along with the multi-axis machine tool rotating component; the cat eye is arranged on the precise numerical control rotary table and can rotate along with the precise numerical control rotary table;
s2, respectively installing the laser trackers near the direct front of the machine tool, and defining the positions of the laser trackers as the positions of the base stations;
s3, controlling the precise numerical control rotary table to record the distance measurement data of the current laser tracker every time the precise numerical control rotary table rotates by a certain angle theta, establishing a large-scale nonlinear redundancy equation set by using the distance data of the measurement points measured by the laser tracker, and solving by using a genetic algorithm to determine the initial position coordinates of each base station of the laser tracker on the rotary table;
s4, controlling a rotating part of the machine tool to rotate around an axis according to a preset path, measuring once when the machine tool rotates for a certain angle, sequentially rotating a precision numerical control turntable arranged on a main shaft of the machine tool for 120 degrees, wherein measuring points are named as A, B, C respectively, and measuring by a laser tracker at four base station positions in sequence;
s5, establishing a nonlinear redundancy equation set by using distance data between the measuring points and each base station, which is measured by the laser tracker, and solving according to the least square principle to determine the space coordinates of the measuring points;
s6, utilizing the space coordinates of a series of measuring points obtained in the step S5 when the rotating component rotates around the axis, and forming 3 vectors in pairs through A, B, C three points
The direction of the vector will be changed in the rotating process of the machine tool rotary table, the change of the direction of the vector is only related to the angular displacement error in the movement of the machine tool, a series of vector establishment equation sets are formed according to a homogeneous transformation matrix and measuring points caused by the angular displacement error, and the solution is carried out, so that each angular displacement error can be separated;
and S7, respectively establishing motion error equations for A, B, C when the machine tool rotary table rotates by different angles by using the space coordinates of a series of measuring points when the rotary part rotates around the axis obtained in the step S5 and the angular displacement errors obtained in the step S6 to form a redundancy equation set, and substituting the redundant equations for solving the angular displacement errors to separate the linear displacement errors, so that the complete separation of the geometric errors of the translation axis of the numerical control machine tool is completed.
Further, in step S2, at least four base station positions are selected, and any three base station positions are not collinear.
Further, in the step S3, when the precision numerical control turntable rotates by a certain angle θ, the rotating component is controlled to stop moving, and a measurement result of the laser tracker at the current position is recorded, wherein the laser tracker comprises a Leica laser tracker with an angle measurement function, a Faro laser tracker, an Api laser tracker and an Etalon laser tracker without an angle measurement function; the laser tracker is then moved to the next base station location and the measurement process is repeated until the measurements are completed at all base station locations.
Further, when the laser tracker is a Leica or Faro laser tracker, the base station P is concerned 1 (x p1 ,y p1 ,z p1 ) Calibration may establish the following system of equations:
wherein R represents the distance from the center of the cat eye to the rotation center of the turntable, and theta i Representing the angle of rotation of the turntable, /) 1i Distance measurement data of the laser tracker at each measurement point position.
Further, when the laser tracker is an Etalon laser tracker, the base station P is concerned 1 (x p1 ,y p1 ,z p1 ) Calibration may establish the following system of equations:
wherein L is 1 Represents the distance, Δ l, from the initial measurement point to the center of the cat's eye 1i The relative distance variation measured by the laser tracker at each measuring point position.
Further, in the step S3, at least four different cat eye positions are measured at each base station position to obtain data redundancy, thereby improving the reliability and the measurement accuracy of the measurement system.
Further, in the step S4, when the machine tool rotating part rotates to each measuring point position, the machine tool rotating part is controlled to stop moving; and when the rotating part of the precise numerical control rotary table moves to the measuring position, controlling the precise numerical control rotary table to stop moving.
Further, the method comprises the following steps: in step S5, the base station positions obtained by calibration are assumed to be P 1 (x p1 ,y p1 ,z p1 )、P 2 (x p2 ,y p2 ,z p2 )、P 3 (x p3 ,y p3 ,z p3 )、P 4 (x p4 ,y p4 ,z p4 ) Measuring point M during movement of machine tool i Distances to the base stations are l' 1i ，l′ 2i ,l′ 3i ,l′ 4i According to the GPS measurement principle, for M in the measurement process i (x mi ，y mi ，z mi ) The following equation can be established:
solving by the principle of similar least square, the actual coordinate M of the measuring point in the movement process of the machine tool can be determined i (x mi ，y mi ，z mi )。
The invention has the beneficial effects that: according to the novel method for quickly separating the geometric errors of the rotating shaft of the multi-shaft numerical control machine tool, the laser tracker tracks and measures the same points of the rotating part of the multi-shaft machine tool at least four base station positions on the rotating platform of the multi-shaft machine tool in sequence, and the space coordinates of a series of measuring points on the precise numerical control rotating platform are respectively determined by using the measured distance data of the measuring points. Through the obtained space coordinates of a series of measuring points, firstly, every two measuring points obtained from the same position of a rotating part of the machine tool form space vectors, and angular displacement errors are separated out firstly only related to the angular displacement errors by utilizing the change of the directions of the vectors; and then, various angular displacement errors when the rotary table rotates through different angles are separated and brought into the established motion error equation of each measuring point, and linear displacement errors are solved, so that the complete separation of the geometric errors of the translational shaft of the numerical control machine tool is realized. The method solves the difficult problem of measuring the geometric error of the rotating shaft of the numerical control machine tool at present. Meanwhile, the method is based on the GPS principle, only the distance is measured in the measuring process, and the influence of the angle measurement error of the laser tracker on the overall measuring precision is effectively avoided, so that the overall measuring precision on site is greatly ensured; the advantages of rapid measurement of the laser tracker and high precision, rapidness, dynamic and portability of the precise numerical control turntable are utilized to realize the high-efficiency and high-precision measurement of the geometric error of the rotating shaft of the numerical control machine. The method has the advantages of rapidness, high precision, simple error separation and the like, and can be used for rapidly and accurately separating the geometric errors of the rotating shaft of the numerical control machine tool. The method has important significance for further improving the integral machining precision of the numerical control machine tool.
Drawings
FIG. 1 is a schematic diagram of the base station position, precision numerically controlled turntable and cat eye position relative to a numerically controlled machine tool of the present invention;
FIG. 2 is a schematic view illustrating a method for separating an error of angular displacement of a rotating shaft of a numerically controlled machine tool according to the present invention;
FIG. 3 is a schematic diagram of a base station calibration model based on precision turntable rotation measurement according to the present invention;
FIG. 4 is a schematic diagram of the genetic algorithm of the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific embodiments:
as shown in fig. 1 to 4, the new method for rapidly separating geometric errors of a rotating shaft of a multi-axis numerical control machine tool provided by the invention comprises the following steps:
s1, mounting a precision numerical control rotary table on a multi-axis machine tool rotating component and rotating along with the multi-axis machine tool rotating component; the cat eye is installed on the accurate numerical control revolving stage to can follow accurate numerical control revolving stage and rotate together.
And S2, respectively installing the laser trackers near the direct front of the machine tool, and defining the positions of the laser trackers as the positions of the base stations. In step S2, at least four base station positions are selected, and any three base station positions are not collinear.
And S3, controlling the precise numerical control rotary table to record the distance measurement data of the current laser tracker every time the precise numerical control rotary table rotates by a certain angle theta, establishing a large-scale nonlinear redundancy equation set by using the distance data of the measurement points measured by the laser tracker, and solving by using a genetic algorithm so as to determine the initial position coordinates of each base station of the laser tracker on the rotary table.
And S3, when the precise numerical control rotary table rotates by a certain angle theta, controlling the rotating part to stop moving, and recording the measurement result of the laser tracker at the current position.
In order to realize accurate calibration of the position of the base station and avoid the influence of the self error of a machine tool on the calibration precision of the base station, a precise numerical control rotary table is introduced. Constructing a base station calibration model based on precision turntable rotation measurement, wherein M 1 、M 2 …M n Is a series of measuring points on the turntable, and P is a base station position point.
The laser tracker comprises a Leica, faro and Api laser tracker with an angle measuring function and an Etalon laser tracker without the angle measuring function; the laser tracker is then moved to the next base station location and the measurement process is repeated until the measurements are completed at all base station locations.
When the laser trackers are Leica or Faro laser trackers, the laser trackers can measure the absolute distance from the target point to the center of the rotating mirror. In relation to base station P 1 (x p1 ,y p1 ,z p1 ) Calibration may establish the following system of equations:
wherein R represents the distance from the center of the cat eye to the rotation center of the turntable, theta i Representing the angle of rotation of the turntable, l 1i Ranging data for the laser tracker at each measurement point location.
When the laser tracker is an Etalon laser tracker, the base station P is concerned 1 (x p1 ,y p1 ,z p1 ) Calibration may establish the following system of equations:
wherein L is 1 Represents the distance, Δ l, from the initial measurement point to the center of the cat's eye 1i The relative distance variation measured by the laser tracker at each measuring point position.
Solving large nonlinear redundancy equation sets of the formulas (1) and (2) by adopting a hybrid genetic algorithm. The genetic algorithm has better global search capability but poorer local search capability, and the simplex method is integrated into the genetic algorithm, so that the poorer local search capability of the genetic algorithm is effectively overcome, and the solving precision is further improved.
Positioning a laser tracker at a first base station position P 1 The first base station position P of the laser tracker under the coordinate system of the rotary table can be calibrated through the process 1 Repeating the above process to mark other base stations P where the laser tracker is located 2 、P 3 、P 4 The position coordinates of (a).
In this embodiment, at least four different cat-eye positions are measured at each base station position in step S3 to obtain data redundancy, thereby improving the reliability and measurement accuracy of the measurement system.
And S4, controlling a rotating part of the machine tool to rotate around an axis according to a preset path, measuring once when the machine tool rotates for a certain angle, sequentially rotating a precision numerical control turntable arranged on a main shaft of the machine tool for 120 degrees, respectively naming measuring points as A, B, C, and successively measuring at four base station positions by a laser tracker.
In step S4 of the present embodiment, when the machine tool rotating member rotates to each measuring point position, the machine tool rotating member is controlled to stop moving; and when the rotating part of the precise numerical control rotary table moves to the measuring position, controlling the precise numerical control rotary table to stop moving.
In particular, the laser tracker is located at a first base station position P 1 At this point, the target scope cat eye is moved to A, B, C and A, B, C is measured in turn to base station P 1 The distance of the precise numerical control rotary table and the machine tool rotary table are controlled to stop rotating during measurementThen the machine turret is rotated to the next position and the measurement process is repeated until the first station position P is reached 1 The measurement of the machine tool movement is completed. Then the laser tracker is respectively moved to P 2 、P 3 、P 4 At the position and repeated at the base station P 1 And (4) measuring at the positions until the laser tracker finishes measuring the movement of the machine tool at all the positions of the base station.
And S5, establishing a nonlinear redundancy equation set by using the distance data between the measuring point and each base station measured by the laser tracker, and solving according to the least square principle to determine the space coordinate of the measuring point.
In step S5, the base station positions obtained by calibration are assumed to be P 1 (x p1 ,y p1 ,z p1 )、P 2 (x p2 ,y p2 ,z p2 )、P 3 (x p3 ,y p3 ,z p3 )、P 4 (x p4 ,y p4 ,z p4 ) Measuring point M during movement of machine tool i Distances to each base station are respectively l 1 ' i ，l' 2i ，l' 3i ，l' 4i According to the GPS measurement principle, M in the measurement process i (x mi ，y mi ，z mi ) The following equation can be established:
solving by the principle of similar least square, the actual coordinate M of the measuring point in the movement process of the machine tool can be determined i (x mi ，y mi ，z mi )。
S6, using the space coordinates of a series of measuring points obtained in the step S5 when the rotating component rotates around the axis, and forming 3 vectors by two three points A, B, C
The direction of the vector will change during the rotation of the machine tool rotary table, and the change of the direction of the vector only corresponds to the movement of the machine toolThe angular displacement errors in the method are related, a series of vectors are formed according to a homogeneous transformation matrix and measuring points caused by the angular displacement errors to establish an equation set, and the equation set is solved, so that each angular displacement error can be separated.
At the initial position, assume measurement point A (x) a0 ,y a0 ,z a0 )，B(x b0 ,y b0 ,z b0 )，C(x c0 ,y c0 ,z c0 ) When the rotary table rotates at different angles, the theoretical coordinate of a series of measuring points is A i (x ai ,y ai ,z ai )、B i (x bi ,y bi ,z bi )、C i (x ci ,y ci ,z ci ). Due to the existence of errors, the actual coordinate of each measuring point is A' i (x' ai ,y' ai ,z' ai )、B i '(x' bi ,y' bi ,z' bi )、C′ i (x' ci ,y' ci ,z' ci )。
When the turntable rotates around the z axis by an angle theta, the theoretical homogeneous transformation matrix is as follows:
in the rotation process, the error transformation matrix is as follows:
for initial measurement point A 0 (x a0 ,y a0 ,z a0 ) When the turntable rotates by theta i At angle, a series of measurement points A 'are obtained' i The actual coordinates are as follows:
similarly, for initial measurement point B 0 (x b0 ,y b0 ,z b0 )、C 0 (x c0 ,y c0 ,z c0 ) When the turntable rotates by theta i Angle time, a series of measurement points B' i 、C′ i The actual coordinates are obtained. The theoretical measurement point A is then measured during the rotation of the turntable i ，B i ，C i Form a vector
The directions of (A) and (B) are respectively as follows:
actual measurement Point A' i ，B′ i ，C′ i Form a vector
The directions of (A) and (B) are respectively as follows:
during the movement
The directional deviation of (2) is:
from the equations (13), (14), (15), it can be seen that during the rotation, the vector
Direction deviation and angular displacement error delta x (θ)、δ y (θ)、δ z (theta) related to linear displacement error epsilon x (θ)、ε y (θ)、ε z (θ) is irrelevant.
At the initial position, the vector formed by adjacent measurement points is:
in the rotating process of the rotary table, the vector formed by the actual adjacent measuring points is as follows:
transforming matrices, vectors, according to turntable motion
And with
The following relationship should exist:
after finishing, the method can be obtained:
similarly, vectors may be established
And with
And
can then obtain the correlation between
By solving the above formula, three-term angular displacement errors epsilon in the rotating process of the turntable can be separated x (θ)、ε y (θ)、ε z (theta). The method increases the redundant data quantity, thereby improving the separation precision of various errors.
And S7, respectively establishing motion error equations for A, B, C when the machine tool rotary table rotates by different angles by using the space coordinates of a series of measuring points when the rotary part rotates around the axis obtained in the step S5 and the angular displacement errors obtained in the step S6 to form a redundancy equation set, and substituting the redundant equations for solving the angular displacement errors to separate the linear displacement errors, so that the complete separation of the geometric errors of the translation axis of the numerical control machine tool is completed.
At measurement point A i Assume that the positional deviation in the x direction caused by the angular displacement error is t axi And the positional deviation caused in the y direction is t ayi And a positional deviation in the z direction is t azi Then the following system of equations can be established:
the same principle can be established at the measurement point B i 、C i The following equation set can be finally obtained by using the kinematic error equation:
by solving the equation, the three-term linear displacement error delta in the rotation process of the rotary table x (θ)、δ y (θ)、δ z (theta) can be separated. In the process, the angular displacement error and the linear displacement error of the rotating shaft are separated, decoupled and separated, so that the complexity of an error separation model is reduced, and the single errors are easily and accurately separated.
During measurement, the precise numerical control rotary table is arranged at a proper position of the multi-axis machine tool rotary table and rotates along with the machine tool rotary table around the z-axis direction. And controlling the machine tool rotary table to rotate around the z axis, and respectively tracking and measuring the movement of the machine tool rotary table at four different base station positions by the laser tracker.
When the machine tool rotary table rotates around the z axis, one measuring point is arranged every time the machine tool rotary table rotates 10 degrees, and the total number of the measuring points is 108. When the translational component moves to each measuring point position, the machine tool stops moving, the precise numerical control rotary table arranged on the main shaft of the machine tool rotates by 120 degrees in sequence, each position is controlled to stop for 5 seconds, and the distance measuring data of the laser tracker of the cat eye at different positions on the rotary table are recorded.
And when the laser tracker finishes measuring the positions of all measuring points at the position of the first base station, moving the laser tracker to the position of the next base station and repeating the measuring process until the measuring points are measured at all the positions of the base stations. In order to reduce the influence of random errors on the measurement result in the measurement process, the measurement point is measured for three times at each base station position, the total measurement time is about 3 hours, and the measurement efficiency is high. By utilizing the measurement algorithm and the machine tool single-term error separation algorithm deduced above, each single-term geometric error of the numerical control machine tool rotating around the z axis can be separated.
The invention realizes the preparation and separation of the 6 geometric errors of the rotating shaft by measuring the vector direction change formed by a series of adjacent measuring points in the moving process of the rotating platform and establishing the mutual mapping relation between the vector direction change and the geometric errors of the rotating shaft. The method utilizes the characteristic that the change of the direction of a space vector formed in the movement process of the machine tool is only related to the angular displacement error of a machine tool shaft but not related to the linear displacement error, and utilizes the laser tracker to measure the change of the direction of the vector formed by measuring points in the movement process of a machine tool translation shaft by adopting a multi-station time-sharing measuring principle, thereby sequentially separating the angular displacement error and the linear displacement error of the machine tool rotation shaft. A mathematical model for measuring the geometric errors of the multi-axis machine tool rotating shaft based on the space vector direction deviation measurement is established, and a laser tracker base station position self-calibration algorithm, a measuring point determination algorithm and a machine tool rotating shaft single error separation algorithm based on the precise numerical control turntable measurement are deduced in sequence. The method realizes the rapid separation of the geometric errors of the rotating shaft, reduces the complexity of error separation, and overcomes the defect that the base station calibration precision is influenced by the self errors of the machine tool. The method has the advantages of high precision, high efficiency and the like, and has a certain application prospect in the separation of geometric errors of the rotating shaft of the multi-shaft machine tool.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (3)
1. A new method for quickly separating geometric errors of a rotating shaft of a multi-shaft numerical control machine is characterized by comprising the following steps:
s1, mounting a precision numerical control rotary table on a multi-axis machine tool rotating component and rotating along with the multi-axis machine tool rotating component; the cat eye is arranged on the precise numerical control rotary table and can rotate along with the precise numerical control rotary table;
s2, respectively installing the laser trackers near the direct front of the machine tool, and defining the positions of the laser trackers as the positions of the base stations;
s3, controlling the precise numerical control rotary table to record the distance measurement data of the current laser tracker every time the precise numerical control rotary table rotates by a certain angle theta, establishing a large-scale nonlinear redundancy equation set by using the distance data of the measurement points measured by the laser tracker, and solving by using a genetic algorithm to determine the initial position coordinates of each base station of the laser tracker on the rotary table;
s4, controlling a rotating part of the machine tool to rotate around an axis according to a preset path, measuring once when the machine tool rotates for a certain angle, sequentially rotating a precision numerical control turntable arranged on a main shaft of the machine tool for 120 degrees, wherein measuring points are named as A, B, C respectively, and measuring by a laser tracker at four base station positions in sequence;
s5, establishing a nonlinear redundancy equation set by using distance data of the measuring points and each base station measured by the laser tracker, and solving according to the least square principle to determine the space coordinates of the measuring points;
in step S5, the base station positions obtained by calibration are assumed to be P 1 (x p1 ,y p1 ,z p1 )、P 2 (x p2 ,y p2 ,z p2 )、P 3 (x p3 ,y p3 ,z p3 )、P 4 (x p4 ,y p4 ,z p4 ) Measuring point M during movement of machine tool i Distances to the base stations are l' 1i ，l' 2i ,l' 3i ,l' 4i According to the GPS measurement principle, M in the measurement process i (x mi ，y mi ，z mi ) The following equation can be established:
solving by the principle of similar least square, the actual coordinate M of the measuring point in the movement process of the machine tool can be determined i (x mi ，y mi ，z mi )；
S6, using the space coordinates of a series of measuring points obtained in the step S5 when the rotating component rotates around the axis, and forming 3 vectors by two three points A, B, C
The direction of the vector will be changed in the rotating process of the machine tool rotary table, the change of the direction of the vector is only related to the angular displacement error in the movement of the machine tool, a series of vector establishment equation sets are formed according to a homogeneous transformation matrix and measuring points caused by the angular displacement error, and the solution is carried out, so that each angular displacement error can be identified;
at the initial position, assume measurement point A (x) a0 ,y a0 ,z a0 )，B(x b0 ,y b0 ,z b0 )，C(x c0 ,y c0 ,z c0 ) When the rotary table rotates at different angles, the theoretical coordinate of a series of measuring points is A i (x ai ,y ai ,z ai )、B i (x bi ,y bi ,z bi )、C i (x ci ,y ci ,z ci ) (ii) a Due to the existence of errors, the actual coordinate of each measuring point is A' i (x' ai ,y' ai ,z' ai )、B i '(x' bi ,y' bi ,z' bi )、C' i (x' ci ,y' ci ,z' ci )；
When the turntable rotates around the z axis by an angle theta, the theoretical homogeneous transformation matrix is as follows:
in the rotating process, an error transformation matrix is as follows:
for initial measurement point A 0 (x a0 ,y a0 ,z a0 ) When the turntable rotates by theta i At an angle, a series of measurement points A are obtained i ' actual coordinates are as follows:
similarly, for initial measurement point B 0 (x b0 ,y b0 ,z b0 )、C 0 (x c0 ,y c0 ,z c0 ) When the turntable rotates by theta i Angle time, a series of measurement points B' i 、C' i The actual coordinates can be obtained; the theoretical measurement point A is then measured during the rotation of the turntable i ，B i ，C i Form a vector
The directions of (A) and (B) are respectively as follows:
actual measurement Point A' i ，B′ i ，C′ i Form a vector
The directions of (A) are respectively:
during the movement
The directional deviation of (2) is:
from the equations (13), (14), (15), it can be seen that during the rotation, the vector
Direction deviation and angular displacement error delta x (θ)、δ y (θ)、δ z (theta) related to the linear displacement error epsilon x (θ)、ε y (θ)、ε z (θ) is irrelevant;
at the initial position, the vector formed by adjacent measurement points is:
in the rotating process of the rotary table, the vector formed by the actual adjacent measuring points is as follows:
transforming the matrix, vector, according to the turntable motion
And
the following relationship should exist:
after finishing, the method can be obtained:
similarly, vectors may be established
And with
And
then the correlation between them can be obtained
By solving the above equation, it can be separated outThree-term angular displacement error epsilon in rotary process of rotary table x (θ)、ε y (θ)、ε z (θ); the method increases the redundant data quantity, thereby improving the separation precision of various errors;
s7, respectively establishing motion error equations for A, B, C when the machine tool rotary table rotates by different angles by using the space coordinates of a series of measuring points when the rotating part rotates around the axis obtained in the step S5 and the angular displacement errors obtained in the step S6 to form a redundancy equation set, and substituting the redundant equations for solving the angular displacement errors to identify the linear displacement errors so as to complete the identification of the geometric errors of the translation shaft of the numerical control machine;
in the step S2, at least four base station positions are selected, and any three base station positions are not collinear;
in the step S3, when the precise numerical control rotary table rotates by a certain angle theta, the rotating part is controlled to stop moving, and the measurement result of the laser tracker at the current position is recorded, wherein the laser tracker comprises a Leica laser tracker with an angle measuring function, a Faro laser tracker and an Api laser tracker without the angle measuring function; then moving the laser tracker to the next base station position, and repeating the measuring process until the measurement is completed at all the base station positions;
when the laser tracker is a Leica or Faro laser tracker, the base station P is related to 1 (x p1 ,y p1 ,z p1 ) Calibration may establish the following system of equations:
wherein R represents the distance from the center of the cat eye to the rotation center of the turntable, and theta i Representing the angle of rotation of the turntable, l 1i Ranging data of the laser tracker at each measuring point position;
when the laser tracker is an Etalon laser tracker, the base station P is related to 1 (x p1 ,y p1 ,z p1 ) Calibration may establish the following system of equations:
wherein L is 1 Represents the distance, Δ l, from the initial measurement point to the center of the cat's eye 1i Relative distance measured by laser tracker at each measuring point position
(ii) an amount of separation variation;
when the machine tool rotary table rotates around the z axis, one measuring point is arranged every time the machine tool rotary table rotates 10 degrees, and the total number of the measuring points is 108; when the translation component moves to the position of each measuring point, the machine tool stops moving, a precise numerical control rotary table arranged on a main shaft of the machine tool rotates for 120 degrees in sequence, each position controls the precise numerical control rotary table to stop for 5 seconds, and distance measuring data of the laser tracker of the cat eye at different positions on the rotary table are recorded;
when the laser tracker finishes measuring the position of each measuring point at the position of a first base station, moving the laser tracker to the position of the next base station and repeating the measuring process until the measuring of the measuring points is finished at the positions of all the base stations; in order to reduce the influence of random errors on the measurement result in the measurement process, three times of measurement are carried out on the measurement point at each base station position, the total measurement time is about 3 hours, and the measurement efficiency is high; by utilizing the measurement algorithm and the machine tool single-term error separation algorithm deduced above, each single-term geometric error of the numerical control machine tool rotating around the z axis can be separated.
2. The new method for rapidly separating geometric errors of a rotating shaft of a multi-axis numerical control machine tool according to claim 1, wherein at least four different cat eye positions are measured at each base station position in the step S3 to obtain data redundancy and improve reliability and measurement accuracy of a measurement system.
3. The new method for rapidly separating geometric errors of a rotating shaft of a multi-axis numerical control machine according to claim 1, wherein in the step S4, when the rotating part of the machine tool rotates to each measuring point position, the rotating part of the machine tool is controlled to stop moving; and when the rotating part of the precise numerical control rotary table moves to the measuring position, controlling the precise numerical control rotary table to stop moving.
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