CN113770814B - Method for identifying geometric error of translational axis of numerical control machine tool based on vector direction measurement - Google Patents

Method for identifying geometric error of translational axis of numerical control machine tool based on vector direction measurement Download PDF

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CN113770814B
CN113770814B CN202110987050.3A CN202110987050A CN113770814B CN 113770814 B CN113770814 B CN 113770814B CN 202110987050 A CN202110987050 A CN 202110987050A CN 113770814 B CN113770814 B CN 113770814B
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CN113770814A (en
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王金栋
唐雷雨
郭浩然
赖洋
谢宇鸿
闫府
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Southwest Jiaotong University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
    • B23Q17/00—Arrangements for observing, indicating or measuring on machine tools
    • B23Q17/24—Arrangements for observing, indicating or measuring on machine tools using optics or electromagnetic waves
    • B23Q17/2428—Arrangements for observing, indicating or measuring on machine tools using optics or electromagnetic waves for measuring existing positions of tools or workpieces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The invention discloses a method for identifying geometric errors of a translational shaft of a numerical control machine tool based on a vector direction measuring principle, wherein different measuring points are arranged on a moving part of the machine tool, the measuring points are sequentially connected to form a space vector, the characteristic that the direction change of the formed space vector in the moving process of the machine tool is only related to the angular displacement error of the machine tool shaft and is not related to the linear displacement error is utilized, and the characteristic that a laser tracker adopts a multi-station time-sharing measuring principle to measure the direction change of the formed vector of the measuring points in the moving process of the translational shaft of the machine tool, so that the angular displacement error and the linear displacement error of the translational shaft of the machine tool are sequentially identified. A mathematical model for measuring the geometric errors of the translational axis of the numerical control machine tool based on the space vector direction measurement principle is established, and a laser tracker base station position self-calibration algorithm, a measuring point determination algorithm and a machine tool translational axis single error separation algorithm based on precise numerical control turntable measurement are deduced in sequence. The method has the advantages of high precision, high efficiency, low cost and simple algorithm.

Description

Method for identifying geometric error of translational axis of numerical control machine tool based on vector direction measurement
Technical Field
The invention belongs to the technical field of laser precision measurement, and particularly relates to a method for identifying geometric errors of a translational shaft of a numerical control machine tool based on vector direction measurement.
Background
With the continuous development of modern manufacturing technology, the demand for high-precision numerical control machine tools is increasing. The precision is an important performance index of the numerical control machine tool and directly influences the processing quality of a workpiece. How to economically improve the machining precision of the machine tool is a key problem, and scholars at home and abroad carry out extensive and intensive research in this respect. Compared with a machine tool error hardware compensation technology, error measurement and compensation are used as a soft technology for improving the machine tool precision, the method has the advantages of wide applicability, low cost and the like, and is widely applied to the field of machine tool precision compensation. In the process of processing a workpiece by a machine tool, a plurality of error factors exist, such as geometric errors, thermal deformation errors, cutting force errors, clamping errors and the like, and the final processing precision of the workpiece is influenced by the errors. Among the error factors, the geometric error is a main error factor, and meanwhile, the geometric error is relatively stable, has repeatability in a long working time of a machine tool and is easy to measure and compensate. The measurement and compensation of the geometric error of the machine tool are one of the effective ways for improving the machining precision of the machine tool at present.
At present, there are many methods for measuring the geometric error of the translational axis of a machine tool, and the methods mainly comprise the following steps: a physical reference method, a cue-meter measuring method, an orthogonal grating measuring method, a laser interferometry method, and the like. In recent years, a laser tracker is applied to error detection of machine tools and three-dimensional measuring machines as a new type of three-dimensional measuring instrument. Laser trackers typically employ a spherical coordinate measurement method, and for this mode of measurement, angular measurement errors are a major source of coordinate measurement errors. The laser tracker angle error is assumed to be 1 radian per second, resulting in an error of about 5 μm per meter. At present, the requirement on the detection precision of a machine tool is higher and higher, and the existing measuring method based on the spherical coordinates is difficult to meet the detection requirement on the precision of the machine tool. In order to improve the measurement precision and consider the measurement cost, a multi-station time-sharing measurement method is adopted. The method adopts the GPS measurement principle, only relates to distance measurement in the measurement process, and effectively avoids the influence of angle measurement error on the measurement result. However, this method also has certain disadvantages: 1) during measurement, a machine tool is required to feed in a 3D space, and the measurement track is complex. When the motion trail of the machine tool is a 2D plane and a 1D straight line, the machine tool error cannot be identified; 2) in the base station calibration process, the calibration precision of the base station can be influenced by the self error of the machine tool, so that the measurement precision of the method is further improved to a certain extent. How to simplify the measurement process and the error identification algorithm and overcome the defect that the base station calibration precision is influenced by the error of the machine tool, which has positive effect on 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 method for identifying the geometric error of a translational shaft of a numerical control machine tool based on vector direction measurement, which can quickly and accurately identify the geometric error of the numerical control machine tool.
In order to solve the technical problems, the technical scheme of the invention is as follows: the method for identifying the geometric error of the translational axis of the numerical control machine tool based on vector direction measurement comprises the following steps:
s1, mounting the precision numerical control turntable near the main shaft of the machine tool, and translating along with the main shaft or the workbench; the cat eye is arranged on the precise numerical control rotary table and can rotate along with the precise numerical control rotary table;
s2, installing the laser tracker near the front of the machine tool in a time-sharing manner, and defining the position of the laser tracker as the position of a base station;
s3, controlling the precise numerical control rotary table to rotate by a certain angle theta every time, recording the distance measurement data of the current laser tracker, constructing a least square model based on the ohm distance of the measurement point by using the distance data of the measurement point obtained by the measurement of the laser tracker, and determining the homogeneous transformation matrix between the instrument coordinate system of the laser tracker and the coordinate system of the precise numerical control rotary table, thereby determining the initial position coordinates of each base station of the laser tracker on the rotary table;
s4, controlling the machine tool translation component to feed along the axis of the machine tool according to a preset path, measuring once when the machine tool moves for a certain distance, sequentially rotating the precision rotary table arranged on the main shaft of the machine tool for 120 degrees, wherein the measuring points are respectively named as A, B, C, and the laser tracker sequentially measures at the positions of four base stations;
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 minimum two-component principle to determine the space coordinate of the measuring point;
s6, using the space coordinates of a series of measuring points when the translational part moves along the axis obtained in the step S5, and 3 vectors formed by A, B, C three points in pairs
Figure BDA0003231060850000021
The direction of the vector will change in the motion process of the machine tool, the change of the direction of the vector is only related to the angular displacement error in the motion of the machine tool, and a series of vector establishment is formed according to a homogeneous transformation matrix and measuring points caused by the angular displacement errorSolving an equation set, namely identifying each angular displacement error;
s7, using the space coordinates of a series of measuring points when the translational component moves along the axis obtained in the step S5 and the angular displacement errors of each item obtained in the step S6, determining a series of new points by taking the midpoint of A, B as T, the midpoint of B, C as R and the midpoint of C, A as S, respectively establishing motion error equations for T, R, S to form a redundancy equation set, substituting the solution of the angular displacement errors of each item, and then identifying the linear displacement errors of each item, thereby completing the identification of the geometric errors of the numerical control machine tool.
Further, in step S2, at least four base station positions are selected, and any three of the base station positions are not collinear.
Further, the step S3 further includes the following steps:
s31, determining an initial value of the distance from the centre of the cat eye to the rotation center of the rotary table;
s32, determining the initial value of the position of the base station where the laser tracker is located;
and S33, calibrating the base station.
Further, in step S3, when the precision numerical control turntable rotates by a certain angle θ, the rotating part is controlled to stop moving, the measurement result of the laser tracker at the current position is recorded, then the laser tracker is moved to the next base station position, and the above measurement process is repeated until the measurement is completed at all base station positions.
Further, in step S4, 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 step S4, when the translation component moves to each measurement point position, controlling the translation component to stop moving; when the rotating part of the precise numerical control rotary table moves to a measuring position, the rotary table is controlled to stop moving.
Further, in step S1, the precision numerical control rotary table is installed at a suitable position near the spindle of the turn-milling machining center, and translates along the axial direction of the numerical control machine along with the machine tool table, so as to control the translational component of the numerical control machine to feed along the axial direction of the machine tool along a preset path, and in the motion region, the laser tracker tracks and measures the motion of the translational component in real time.
Further, when the numerical control machine tool translation component feeds along the axis direction of the machine tool, three measuring points are measured respectively when the numerical control machine tool translation component moves for a certain distance.
The invention has the beneficial effects that: according to the method for identifying the geometric errors of the translational shaft of the numerical control machine tool based on the vector direction measurement, the laser tracker tracks and measures the points with the same translational component of the multi-shaft machine tool at least four base station positions on the rotary table of the multi-shaft machine tool in sequence, and the space coordinates of a series of measuring points on the precise numerical control rotary table are respectively determined by using the distance data of the measuring points obtained by measurement. Through the obtained space coordinates of a series of measuring points, every two measuring points obtained from the same position of a translation part of the machine tool form space vectors, and the angular displacement error is identified firstly only related to the angular displacement error by utilizing the change of the directions of the vectors; and respectively fitting out a vector in the direction of the plane axis of the machine tool, and introducing the angular displacement error to identify the linear displacement error, thereby realizing complete identification of the geometric error of the numerical control machine tool. The method solves the problem that the geometric error of the numerical control machine tool is measured by using the laser tracker at present. Meanwhile, the method is based on the GPS principle, only the distance quantity 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 on-site overall measuring precision of the laser tracker is greatly improved. The advantages of rapid measurement of the laser tracker and high precision of the precise numerical control rotary table are utilized to realize high-efficiency high-precision measurement of the geometric error of the numerical control machine. The method has the advantages of rapidness, high precision, simple error identification and the like, and can be used for rapidly and accurately identifying the geometric error of the numerical control machine tool. And a foundation is laid for further improving the integral processing precision of the numerical control machine tool.
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FIG. 1 is a schematic diagram of the position of a base station, a precision numerically controlled turntable and a cat eye relative to a numerically controlled machine tool in the present invention;
FIG. 2 is a schematic diagram of a method for identifying angular displacement errors of a numerically controlled machine tool according to the present invention;
FIG. 3 is a schematic view of a turret coordinate system of the present invention;
FIG. 4 is a schematic diagram of a variation of the coordinate system of the present invention;
FIG. 5 is a diagram of a base station calibration coordinate system according to 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 5, the method for identifying geometric errors of a translational axis of a numerical control machine based on vector direction measurement provided by the invention comprises the following steps:
s1, mounting the precision numerical control turntable near the main shaft of the machine tool, and translating along with the main shaft or the workbench; the cat eye is installed on the accurate numerical control revolving stage to can follow accurate numerical control revolving stage and rotate together.
In the step, the precise numerical control rotary table is arranged at a proper position near a main shaft of a turn-milling machining center, and translates along the axial direction of the numerical control machine along with a machine tool workbench to control the translation component of the numerical control machine to feed along the axial direction of the machine tool along a preset path, and in a motion area, a laser tracker tracks and measures the motion of the translation component in real time.
And S2, installing the laser tracker near the front of the machine tool in a time-sharing mode, namely, at different positions, and defining the position of the laser tracker as the position of the base station.
In this step, at least four base station positions are selected, and any three are not collinear.
S3, controlling the precise numerical control rotary table to rotate by a certain angle theta every time, recording the distance measurement data of the current laser tracker, constructing a least square model based on the ohm distance of the measurement point by using the distance data of the measurement point obtained by the measurement of the laser tracker, and determining the homogeneous transformation matrix between the instrument coordinate system of the laser tracker and the coordinate system of the precise numerical control rotary table, thereby determining the initial position coordinates of each base station of the laser tracker on the rotary table.
In the step, when the precise numerical control rotary table rotates by a certain angle theta, the rotating part is controlled to stop moving, the measurement result of the laser tracker at the current position is recorded, then the laser tracker is moved to the next base station position, and the measurement process is repeated until the measurement is completed at all the base station positions.
In the base station calibration process, a nonlinear redundancy equation set for base station calibration can be established by using a large amount of measured data. When solving the system of nonlinear redundancy equations, it should be linearized first and converted into a linear redundancy equation to solve. The main approach of the present linearization is to perform taylor expansion at a certain point position of the function and omit the terms after the first-order partial derivative, which involves selecting which position to perform taylor expansion, i.e. determining the initial value of the taylor expansion position. Whether the initial value position is selected accurately or not directly influences the calculation precision and efficiency. When the selected initial value is far from the true value, it may cause the iterative computation to be non-convergent, and thus a solution result cannot be obtained, so how to determine the initial value of the base station location is a key problem. And constructing a laser tracker instrument coordinate system based on the measured point ohm distance and a four-axis machine tool self machine tool coordinate system transformation least square model by utilizing a large number of measured point space coordinates obtained by measuring by the laser tracker, thereby determining the initial position of each base station of the laser tracker on the rotary table.
Step S3 specifically includes the following steps:
and S31, determining the initial distance value from the centre of the cat eye to the rotation centre of the rotary table.
During measurement, the coordinates of a series of measurement points on the turntable measured by the laser tracker in the instrument coordinate system are A'i(x′i,y′i,z′i) As shown in FIG. 5, the series of measurement points are K, G, J, I, M … …, A'iDenotes these points, x'i、y′i、z′iThe space plane equation of the measuring points in the instrument coordinate system is fitted through a space plane, and the space plane equation where the measuring points are located is assumed to be z ' ═ Ax ' + By ' + C, and A, B, C are respectively constant. During calibration, the rotary table rotates a certain angle for one time to measure, and N measuring points are shared. According to the least squares fitting principle, the objective function is:
Figure BDA0003231060850000051
according to the extreme principle, if F (a, B, C) is to be minimized, then:
Figure BDA0003231060850000052
wherein
Figure BDA0003231060850000053
The partial derivatives are calculated according to the extreme value principle,
Figure BDA0003231060850000054
for the sign of the partial derivative, the coordinates of each point are measured as known quantities, A, B, C as unknown quantities, F is a function of A, B, C,
bringing formula 1 into formula 2, which is obtained from formula 2:
Figure BDA0003231060850000055
the equation of the spatial plane where the measuring point is located can be determined by the formula (3).
Adjacent 3M points on the rotary tablei(x′i,y′i,z′i)，Mi+1(x′i+1,y′i+1,z′i+1)，Mi+2(x′i+2，y′i+2，z′i+2) Refers to three adjacent measuring points Mi、Mi+1、MiThe spatial coordinate of +2, for example, the center of a spatial circle determined by K, G, J in fig. 5, that is, the coordinate of the rotation center of the turntable in the measurement coordinate system of the laser tracker instrument is O '(u, v, w), and it is easy to know that the center O' is in the plane determined by equation (3), the following equation set can be established:
Figure BDA0003231060850000056
the position coordinate O' (u, v, w) of the rotation center of the rotary table under the measurement coordinate system of the laser tracker instrument can be determined by solving the formula (4), and the rotation radius corresponding to a series of measurement points on the rotary table is as follows: r0The radius is the radius of the cat eye from the rotating center of the turntable, and the cat eye is fixed on the turntable.
Figure BDA0003231060850000057
The initial distance from the center of the cat eye to the rotation center of the rotary table can be determined through the formula (5). The coordinates of the midpoint in step S31 are all in the instrument coordinate system.
And S32, determining the initial value of the position of the base station where the laser tracker is located.
The spatial coordinates of the measurement point given by the laser tracker are the coordinates in the instrument coordinate system and this coordinate system is noted as the old coordinate system X ' Y ' Z '. In order to determine the initial value of the position of the base station, the coordinates of the measuring point in the instrument coordinate system need to be converted into the turntable coordinate system, and the turntable coordinate system needs to be recorded as a new coordinate system O1X1Y1Z1As shown in fig. 3. The change of the coordinate system is shown in fig. 4.
The instrument coordinate system and the turntable coordinate system can be coincided through the rotation and translation transformation of the coordinate system. Assuming that the instrument coordinate system moves by Δ X along the X axis, moves by Δ Y along the Y axis, moves by Δ Z along the Z axis, rotates by an angle α around the X axis, rotates by an angle β around the Y axis, and rotates by γ around the Z axis, the instrument coordinate system can be overlapped with the turntable coordinate system, and the corresponding homogeneous transformation matrix T at this time is the same as equation 27. Assuming that the coordinate of each measurement point in the instrument coordinate system is A'i(x′i,y′i，z′i) The theoretical reference coordinate of each measurement point in the turntable coordinate is A as in step S31i(xi，yi,zi) This is a switch from the instrument coordinate system to the spatial coordinates in the turret coordinate system, where xi＝Rcosθi，yi＝Rsinθi，z i0. Let U 'be [ x'i y′i z′i 1]T，U＝[xi yi zi 1]TAnd constructing a least square model based on the Eugenia distance of the measuring points:
Figure BDA0003231060850000061
in equation (6), 6 unknown parameters (Δ x, Δ y, Δ z, α, β, γ) are involved, and these six parameters are the unknown quantities of the spatial left transformation, which refer to the displacement quantities in the x, y, z directions and the rotation quantities around the x, y, z axes, respectively. The unknown parameters can be determined by solving through a nonlinear least square algorithm, so that a homogeneous transformation matrix corresponding to the instrument coordinate system transformed to the turntable coordinate system is determined, and the initial position of the laser tracker in the turntable coordinate system can be easily determined.
And S33, calibrating the base station.
During measurement, the cat eye is arranged on the precise rotary table, and the distance between the center of the cat eye and the rotary center of the rotary table is R.
And controlling the turntable to stop moving when the turntable rotates by a certain angle theta, and recording the distance measurement data of the current laser tracker. The distance between the center of the cat eye and the rotation center of the rotary table is R, and the rotary table can measure every theta angle so as to obtain a series of measuring points such as G, H and I. By the rotation center O of a precision turntable1As origin of coordinates, with O1The straight line in which G is located is Y1Axial, upward direction being Y1In the positive direction of the axis to pass through O1Point perpendicular to O1Straight line of G is X1Axis, backward direction being X1The positive direction of the axis. Determining Z according to the right-handed screw rule1Axes, thereby establishing a base station calibration coordinate system on the turntable, as shown in fig. 5, where xyz is the machine coordinate system.
The position coordinate of the laser tracker under the coordinate system of the turntable is assumed to be P1(xp1,yp1,zp1) The space coordinate of the laser tracker under the coordinate system of the rotary table, the subscript 1 of P1 indicates the position of the first base station, and the distance measurement reading of the laser tracker is l when the rotary table rotates by theta angles in turn1iFor the measurement points, the following system of equations can be established: l1iSubscript 1 indicates the base station position 1, i corresponds to the different measurement points, and indicates the distance reading of the laser tracker when the ith point was measured at base station position 1
Figure BDA0003231060850000062
Equation (7) is a nonlinear system of redundant equations that can be solved according to the least squares principle.
The residual is recorded as: f. ofiFor residual, i refers to the ith measurement point, θiIs the angle value of the turn corresponding to the ith measuring point
Figure BDA0003231060850000071
Get x0，y0，z0,R0Is xp1，yp1,zp1The approximation of R, namely:
xp1＝x0+Δx，yp1＝y0+Δy，zp1＝z0+Δz，R＝R0+ΔR (9)
the formula (8) is represented by (x) according to Taylor series0，y0，z0,R0) The expansion is obtained by omitting the terms after the first partial derivative in order to eliminate the nonlinear term
Figure BDA0003231060850000072
Order to
Figure BDA0003231060850000073
The formula 8, 9 and 11 are changed into 10 after finishing, so that the product can be obtained:
Figure BDA0003231060850000074
order:
Figure BDA0003231060850000075
then:
Figure BDA0003231060850000076
equation (14) is a system of linear redundancy equations with an objective function of:
Figure BDA0003231060850000077
by the extreme principle, to minimize H, we must have:
Figure BDA0003231060850000078
at the same time, the user can select the required time,
Figure BDA0003231060850000079
it can be seen that the extreme value obtained by each equation in equation (16) is the minimum value, and satisfies the least square condition, and Δ x, Δ y, and Δ z can be obtained by solving equation (16) as shown in equation (18).
Figure BDA0003231060850000081
When Δ x, Δ y, Δ z, and Δ R are obtained, the position of the first base station where the laser tracker is located and the distance from the center of the cat eye to the rotation center of the turntable can be determined according to equations (19) and (20).
Figure BDA0003231060850000082
R＝R0+ΔR (20)
Through the process, the first base station position P of the laser tracker under the turntable coordinate system can be calibrated1Repeating the above process to calibrate other base stations P where the laser tracker is located2、P3、P4The position coordinates of (a).
S4, controlling the machine tool translation component to feed along the axis of the machine tool according to a preset path, measuring once when the machine tool moves for a certain distance, sequentially rotating the precision rotary table arranged on the main shaft of the machine tool for 120 degrees, wherein the measuring points are respectively named as A, B, C, and the laser tracker sequentially measures at the positions of four base stations.
In the step, at least four different cat eye positions are measured at each base station position to obtain data redundancy, so that the reliability and the measurement accuracy of the measurement system are improved. When the translational component moves to each measuring point position, controlling the translational component to stop moving; when the rotating part of the precise numerical control rotary table moves to a measuring position, the rotary table is controlled to stop moving. The certain distance is 50 mm.
The laser tracker is located at a first base station position P1To move the target scope cat eye to A, B, C and measure A, B, C in turn to base station P1The precise numerical control rotary table is controlled to stop rotating and the machine tool stops axial movement during measurement, then the supporting plate is controlled to move to the next position along the x axis, and the measurement process is repeated until the position P of the first base station is reached1The measurement of the machine tool movement is completed. Then the laser tracker is respectively moved to P2、P3、P4At the position and repeated at the base station P1And (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 squares principle to determine the space coordinate of the measuring point.
The base station positions obtained by the assumed calibration are respectively P1(xp1,yp1,zp1)、P2(xp2,yp2,zp2)、P3(xp3,yp3,zp3)、P4(xp4,yp4,zp4) Measuring point M during movement of machine tooliDistances to the base stations are l'1iSubscript 1 indicates the base station position 1, i corresponds to the different measurement points, and indicates the distance reading, l ', of the laser tracker at the point of measurement of the ith at base station position 1'2i,l′3i,l′4i. According to the GPS measurement principle, M in the measurement process is measuredi(xmi,ymi,zmi) The following equation can be established:
Figure BDA0003231060850000091
the actual coordinate M of the measuring point in the movement process of the machine tool can be determined by adopting a solution method similar to the equation set (7)i(xmi,ymi,zmi)。
S6, using the space coordinates of a series of measuring points when the translational part moves along the axis obtained in the step S5, and 3 vectors formed by A, B, C three points in pairs
Figure BDA0003231060850000092
The direction of the vector will change in the movement process of the machine tool, 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 establishing equation sets are formed according to the homogeneous transformation matrix and the measuring points caused by the angular displacement error, and the angular displacement errors can be identified by solving the equation sets. Where the letter A, B, C is the coordinate, angle, or straightness error of the point.
At the initial position, assume measurement point A (x)a0,ya0,za0)，B(xb0,yb0,zb0)，C(xc0,yc0,zc0) At this time, the corresponding direction vectors are:
Figure BDA0003231060850000093
when the pallet moves a distance L along the x-axis from the initial position, points A, B, C move to the A ', B ', C ' positions in sequence.
In the motion process, the theoretical homogeneous transformation matrix is as follows:
Figure BDA0003231060850000094
during the movement of the supporting plate, the angle error epsilonx(x)、εy(x) And εz(x) The resulting homogeneous transformation matrices are:
Figure BDA0003231060850000095
positioning error deltax(x) Straightness error deltay(x)、δz(x) The resulting homogeneous transformation matrix is:
Figure BDA0003231060850000101
the overall error transformation matrix is:
P＝T1T2T3T4T5T6 (26)
after the P finishing, the method can be simplified as follows:
Figure BDA0003231060850000102
when the pallet moves a distance L along the x-axis, the total homogeneous transformation matrix is:
Figure BDA0003231060850000103
suppose A' (x)a1,ya1,za1)，B′(xb1,yb1,zb1)，C′(xc1,yc1,zc1) Then the following relationship should exist between the point a' and the point a:
Figure BDA0003231060850000104
by equation (29), we can calculate the spatial coordinates of the measurement point a'. Similarly, the spatial coordinates of the measurement points B ', C' can be calculated sequentially.
After finishing, the product can be obtained
Figure BDA0003231060850000105
The spatial coordinates of B 'and C' can be calculated sequentially in the same way.
At this time
Figure BDA0003231060850000106
Figure BDA0003231060850000111
Then vector during pallet motion
Figure BDA0003231060850000112
Deviation of direction of
Figure BDA0003231060850000113
The vector can be found by the formula (32) during the movement of the supporting plate
Figure BDA0003231060850000114
The change of direction being only related to the angular displacement error epsilonx(x)，εy(x)，εz(x) Related to the linear displacement error deltax(x)，δy(x)，δz(x) Is irrelevant.
In fig. 2, it is assumed that at the initial position
Figure BDA0003231060850000115
Figure BDA0003231060850000116
When the moving part of the machine tool moves along the x axis L, new vectors are obtained in sequence
Figure BDA0003231060850000117
Figure BDA0003231060850000118
For vectors
Figure BDA0003231060850000119
And vector
Figure BDA00032310608500001110
The following relation should exist
Figure BDA00032310608500001111
After finishing, the method can be obtained:
Figure BDA00032310608500001112
in the same way, vectors can be established
Figure BDA00032310608500001113
And
Figure BDA00032310608500001114
and a vector
Figure BDA00032310608500001115
And vector
Figure BDA00032310608500001116
The mutual relation between the two can be obtained by arranging the following components into a matrix form:
Figure BDA0003231060850000121
the direction value of each vector in equation (35) can be calculated from the coordinates of the measurement point measured by the laser tracker. And solving the equation set by adopting a least square method, so that each angular motion error can be identified. The method increases the redundant data quantity, thereby improving the identification precision of each error.
S7, determining a series of new points by taking the midpoint of A, B as T, the midpoint of B, C as R and the midpoint of C, A as S according to the space coordinates of a series of measuring points when the translational part moves along the axis obtained in the step S5 and the angular displacement errors of each item obtained in the step S6, respectively establishing a motion error equation for T, R, S to form a redundancy equation set, and substituting the redundancy equation set into the solution of each angular displacement error to identify each linear displacement error, thereby completing the identification of the geometric errors of the numerical control machine tool.
At the initial position, the point coordinate in the measurement points A, B is assumed to be T (x)t,yt,zt). When the moving part of the machine moves a distance L along the x-axis, the point T moves to T' (x)t′,yt′,zt') position, the corresponding motion error is then:
Δxt＝x′t-xt，Δyt＝y′t-yt，Δzt＝z′t-zt (36)
Δ x hereint，ΔytAnd Δ ztThe method consists of two parts, wherein one part is displacement errors T on an x axis, a y axis and a z axis caused by angular motion errors of a point T in the motion processx1，ty1，tz1Another part is the linear displacement error during motion, e.g. deltax(x)，δy(x)，δz(x) In that respect From the previous identification of the angular movement error epsilon during movementx(x)，εy(x)，εz(x) The displacement errors T in the x, y and z axes caused by the angular motion errors when the point T moves to T' can be calculatedx1，ty1，tz1. The following set of equations may then be established:
Figure BDA0003231060850000122
in the same way, motion error equations of points R and C in B and C, and points S in A and motion to R 'and S' can be established, a redundant equation set is formed by the motion error equations and the equation (37), and displacement errors of all the lines can be identified by solving.
In the error identification process, the laser tracker can identify corresponding geometric errors only by measuring the movement of the machine tool along a single axis, and the movement track of the machine tool does not need to be in a 3D space, so that the measurement track is simplified.
During measurement, the precise numerical control rotary table is arranged at a proper position near a main shaft of the turning and milling machining center and translates along the axial direction of the numerical control machine along with the machine tool workbench. Controlling the translational part of the numerical control machine tool to feed along the axis direction of the machine tool along a preset path, wherein the motion area is 450mm multiplied by 550mm multiplied by 350mm, and the laser tracker tracks and measures the motion of the translational part in real time.
When the numerical control machine tool translation component feeds along the axis direction of the machine tool, three measuring points are measured respectively when the numerical control machine tool translation component moves for a certain distance.
When the translation component is fed along the x-axis direction, one measuring point is arranged every 50mm of movement, and the total number of the measuring points is 30. When the translation component moves to the position of each measuring point, the machine tool stops moving, the precision rotary table arranged on the main shaft of the machine tool rotates for 120 degrees in sequence, each position controls the precision 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.
As shown in fig. 2, after the laser tracker completes the measurement of each measurement point at the first base station, the laser tracker moves to the next base station and repeats the above measurement process until the measurement of the measurement point is completed at all the base station positions. 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 X axis of the numerical control machine tool can be identified.
The invention realizes the rapid and accurate calibration of the geometric error of the translational shaft of the machine tool, different measuring points are arranged on the moving part of the machine tool and are sequentially connected to form a space vector, the characteristic that the change of the direction of the space vector formed in the moving process of the machine tool is only related to the angular displacement error of the machine tool shaft and is not related to the linear displacement error is utilized, and the measuring point in the moving process of the translational shaft of the machine tool forms the measurement of the change of the direction of the vector formed by the measuring points by using a laser tracker and adopting a multi-station time-sharing measuring principle, thereby sequentially identifying the angular displacement error and the linear displacement error of the translational shaft of the machine tool. A mathematical model for measuring the geometric errors of the translational axis of the numerical control machine tool based on the space vector direction measurement principle is established, and a laser tracker base station position self-calibration algorithm, a measuring point determination algorithm and a machine tool translational axis single error separation algorithm based on precise numerical control turntable measurement are deduced in sequence. The method simplifies the measuring track of the translational axis of the machine tool, reduces the complexity of error identification, and overcomes the defect that the base station calibration precision is influenced by the error of the machine tool. The method has the advantages of high precision, high efficiency, low cost and simple algorithm.
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 (8)

1. The method for identifying the geometric error of the translational axis of the numerical control machine tool based on vector direction measurement is characterized by comprising the following steps of:
s1, mounting the precision numerical control turntable near the main shaft of the machine tool, and translating along with the main shaft or the workbench; the cat eye is arranged on the precise numerical control rotary table and can rotate along with the precise numerical control rotary table;
s2, installing the laser tracker near the front of the machine tool in a time-sharing manner, and defining the position of the laser tracker as the position of a base station;
s3, controlling the precise numerical control rotary table to rotate by a certain angle theta every time, recording the distance measurement data of the current laser tracker, constructing a least square model based on the ohm distance of the measurement point by using the distance data of the measurement point obtained by the measurement of the laser tracker, and determining the homogeneous transformation matrix between the instrument coordinate system of the laser tracker and the coordinate system of the precise numerical control rotary table, thereby determining the initial position coordinates of each base station of the laser tracker on the rotary table;
s4, controlling a machine tool translation component to feed along the axis of the machine tool according to a preset path, measuring once when the machine tool moves for a certain distance, sequentially rotating a precision turntable arranged on a main shaft of the machine tool for 120 degrees, wherein measuring points are respectively named as A, B, C, and a laser tracker sequentially measures at four base station positions;
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;
s6, using the space coordinates of a series of measuring points when the translational part moves along the axis obtained in the step S5, and 3 vectors formed by A, B, C three points in pairs
Figure FDA0003231060840000011
The direction of the vector will be changed in the movement process of the machine tool, 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 angular displacement errors can be identified by solving the equation sets;
s7, determining a series of new points by taking the midpoint of A, B as T, the midpoint of B, C as R and the midpoint of C, A as S according to the space coordinates of a series of measuring points when the translational part moves along the axis obtained in the step S5 and the angular displacement errors of each item obtained in the step S6, respectively establishing a motion error equation for T, R, S to form a redundancy equation set, and substituting the redundancy equation set into the solution of each angular displacement error to identify each linear displacement error, thereby completing the identification of the geometric errors of the numerical control machine tool.
2. The method of claim 1, wherein in step S2, at least four base station positions are selected, and any three base station positions are not collinear.
3. The method for identifying the geometric error of the translational axis of the numerical control machine tool based on the vector direction measurement according to claim 1, wherein the step S3 further comprises the steps of:
s31, determining an initial value of the distance from the centre of the cat eye to the rotation center of the rotary table;
s32, determining an initial value of the position of the base station where the laser tracker is located;
and S33, calibrating the base station.
4. The method for identifying geometric errors of a translational axis of a numerically controlled machine tool based on vector direction measurement as claimed in claim 1, wherein in step S3, when the precision numerically controlled turntable rotates by a certain angle θ, the rotating part is controlled to stop moving, the measurement result of the laser tracker at the current position is recorded, then the laser tracker is moved to the next base station position, and the above measurement process is repeated until the measurement is completed at all the base station positions.
5. The method for identifying geometric errors of a translational axis of a numerical control machine tool based on vector direction measurement according to claim 1, wherein in the step S4, at least four different cat eye positions are measured at each base station position to obtain data redundancy, thereby improving reliability and measurement accuracy of the measurement system.
6. The method for identifying geometric errors of translational axes of numerical control machine tools according to claim 1, wherein in step S4, when the translational member moves to each measurement point, the translational member is controlled to stop moving; when the rotating part of the precise numerical control rotary table moves to a measuring position, the rotary table is controlled to stop moving.
7. The method for identifying the geometric errors of the translational axis of the numerical control machine tool based on the vector direction measurement according to claim 1, wherein in the step S1, the precise numerical control rotary table is installed at a proper position near the spindle of the turning and milling center and translates along the axial direction of the numerical control machine tool along with the machine tool workbench, the translational part of the numerical control machine tool is controlled to feed along the axial direction of the machine tool along a preset path, and in a motion area, the laser tracker tracks and measures the motion of the translational part in real time.
8. The method for identifying the geometric errors of the translational shaft of the numerical control machine tool based on the vector direction measurement of the claim 7 is characterized in that when the translational part of the numerical control machine tool is fed along the axis direction of the machine tool, three measurement points are respectively measured every certain distance of movement.
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