CN115781416A - Method for quickly measuring and compensating geometric errors of machine tool - Google Patents

Method for quickly measuring and compensating geometric errors of machine tool Download PDF

Info

Publication number
CN115781416A
CN115781416A CN202211349075.1A CN202211349075A CN115781416A CN 115781416 A CN115781416 A CN 115781416A CN 202211349075 A CN202211349075 A CN 202211349075A CN 115781416 A CN115781416 A CN 115781416A
Authority
CN
China
Prior art keywords
error
axis
along
sample point
movement
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202211349075.1A
Other languages
Chinese (zh)
Inventor
刘宏伟
张文
付敏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hubei University of Arts and Science
Original Assignee
Hubei University of Arts and Science
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Hubei University of Arts and Science filed Critical Hubei University of Arts and Science
Priority to CN202211349075.1A priority Critical patent/CN115781416A/en
Publication of CN115781416A publication Critical patent/CN115781416A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • 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
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

The invention discloses a method for quickly measuring and compensating geometric errors of a machine tool, which comprises the following steps: step 1, respectively fixing cross standard gauges with holes uniformly on a plane of a workbench, and fixing an angular displacement sensor on a main shaft; sampling along the cross mark, and measuring the angle error, the position error and the perpendicularity error of each sample point; step 2, combining a movement error and a corner error generated by the operation of the machine tool and a verticality error between all the axes, and fitting and solving by using a least square method to establish a comprehensive mathematical model of the errors; and 3, writing the logical relation of the error compensation into an error compensation module, embedding the compensation module into a numerical control system, and enabling the position of the tool to approach to an expected position by compensating the position of the tool relative to the workpiece. The measuring system mainly comprises the angular displacement sensor and the cross-shaped standard gauge, is simple and efficient, does not need a laser interferometer, greatly reduces the threshold of equipment, can improve the measuring efficiency, and can provide important basis for error compensation.

Description

Method for quickly measuring and compensating geometric errors of machine tool
Technical Field
The invention discloses a method for quickly measuring and compensating geometric errors of a machine tool, and belongs to the field of research on precision control of the machine tool.
Background
The geometric error of the machine tool influences the machining precision of the machine tool, and along with the increase of the service time of the machine tool, the fit clearance between each part is increased, and the geometric precision of the machine tool is reduced. The hardware method is adopted to maintain the precision of the machine tool, and the cost for prolonging the service life of the machine tool is very high. The improvement of the machining accuracy of the machine tool by the error compensation technique is a simple and economical method. Measurement and modeling are prerequisites for compensating geometric errors of the machine tool, and it is difficult to develop a geometric error identification system with high detection efficiency, convenient installation and operation and high measurement precision.
Disclosure of Invention
Aiming at the technical problem, the invention provides an indirect measuring method, wherein a measuring system mainly comprises an angular displacement sensor and a cross-shaped standard gauge, and compared with the measuring process of a laser interferometer, the method has higher measuring efficiency. And establishing a comprehensive error model of the three-axis machine tool according to the machine tool error transmission chain, wherein the research result provides an important basis for error compensation.
The technical scheme provided by the invention is as follows:
a method for quickly measuring and compensating geometric errors of a machine tool comprises the following steps:
step 1, respectively fixing cross standard gauges with holes uniformly on an XOY plane of a workbench, and fixing an angular displacement sensor on a main shaft; setting a workbench to move along the X, Y axis direction, moving to the central axis position of the cross gauge hole each time for pausing, moving the main shaft downwards to the central hole depth H/2 for sampling, sampling at the next hole position after sampling is finished, and measuring the angle error, the position error and the perpendicularity error of each sample point; similarly, three error values are measured by respectively fixing the cross standard gauge on an XOZ plane and a YOZ plane of the workbench;
step 2, combining a movement error and a corner error generated by the operation of the machine tool and a verticality error between all the axes, and fitting and solving by using a least square method to establish a comprehensive mathematical model of the errors;
and 3, writing the logical relation of the error compensation into an error compensation module, embedding the compensation module into a numerical control system, and enabling the position of the tool to approach to an expected position by compensating the position of the tool relative to the workpiece.
Furthermore, the cross standard gauge is formed by intersecting two mutually perpendicular shafts, and spaced hole sites are uniformly formed on the two shafts.
Furthermore, the cross standard gauge is uniformly provided with 21 holes, the hole diameter is R, the depth is H, and the radius of the angular displacement sensor is R/2.
Further, the angle measurement precision of the sensor is 0.001 degrees, and the positioning precision is 0.001mm. When the sensor moves down to H/2 in one of the holes, the position error and the angle error of the point can be sensed.
Further, in the step 1, when the cross standard gauge is fixed on the XOY plane, the main shaft moves along an axis of the cross standard gauge parallel to the X axis, and then moves along an axis of the cross standard gauge parallel to the Y axis;
when the angular displacement sensor measures the ith hole while moving along the X axis, the angular error of the sample point is
Figure BDA0003918252110000021
And
Figure BDA0003918252110000022
wherein the content of the first and second substances,
Figure BDA0003918252110000023
indicating that movement of the table along the X-axis produces a calculated angular error about the X-axis,
Figure BDA0003918252110000024
indicating that the worktable moves along the X axis to generate an angle error calculation value around the Y axis; corner mark x xoy In X Representing the X-axis case (around or moving), xoy denotes the xoy plane, and similar expressions below are consistent;
the angular error of each sample point with respect to the ideal position can be expressed as:
Figure BDA0003918252110000025
Figure BDA0003918252110000026
Figure BDA0003918252110000027
and
Figure BDA0003918252110000028
means that the angle value, x, of the worktable at the ith sample point is measured i Representing the situation where the cross gauge moves the ith sample point along the X-axis,
Figure BDA0003918252110000029
and
Figure BDA00039182521100000210
representing the angle value of each sample point of the workbench at an ideal position;
the position error of the sample point is
Figure BDA00039182521100000211
And
Figure BDA00039182521100000212
wherein the content of the first and second substances,
Figure BDA00039182521100000213
indicating that the movement of the table along the X-axis produces a calculated positioning error in the X-axis direction,
Figure BDA00039182521100000214
the straightness error calculation value in the y direction generated by the movement of the workbench along the X axis is represented; the deviation of each sample point from the ideal position is expressed as:
Figure BDA00039182521100000215
Figure BDA00039182521100000216
Figure BDA00039182521100000217
and
Figure BDA00039182521100000218
the coordinate value of the measured workbench at the ith sample point is represented;
Figure BDA00039182521100000219
indicating the movement distance of the worktable along the X axis, the ith sample point is calibrated in the X direction,
Figure BDA00039182521100000220
the movement distance of the ith sample point is calibrated in the Y direction for the movement of the workbench along the X axis;
when the angular displacement sensor measures the ith hole while moving along the Y axis, the angular error of the sample point is
Figure BDA00039182521100000221
And
Figure BDA0003918252110000031
wherein the content of the first and second substances,
Figure BDA0003918252110000032
the representation indicates that movement of the table along the Y-axis produces calculated angular errors about the X-axis,
Figure BDA0003918252110000033
indicating that the worktable moves along the Y axis to generate an angle error calculation value around the Y axis; the angular error of each sample point with respect to the ideal position can be expressed as:
Figure BDA0003918252110000034
Figure BDA0003918252110000035
Figure BDA0003918252110000036
and
Figure BDA0003918252110000037
indicating that the angle value of the workbench at the ith sample point is measured;
Figure BDA0003918252110000038
and
Figure BDA0003918252110000039
representing the angle value of each sample point of the workbench at an ideal position;
the position error of the sample point is
Figure BDA00039182521100000310
And
Figure BDA00039182521100000311
wherein the content of the first and second substances,
Figure BDA00039182521100000312
a calculated positioning error value in the X-axis direction is generated for the movement of the table along the Y-axis,
Figure BDA00039182521100000313
generating a straightness error calculation in the Y direction for the table movement along the Y axis; the deviation of each sample point from the ideal position is expressed as:
Figure BDA00039182521100000314
Figure BDA00039182521100000315
Figure BDA00039182521100000316
and
Figure BDA00039182521100000317
indicating the measured coordinate value of the stage at the ith sample point,
Figure BDA00039182521100000318
indicating the movement distance of the worktable along the Y axis, the ith sample point is calibrated in the Y direction,
Figure BDA00039182521100000319
the movement distance of the ith sample point is calibrated in the Y direction for the movement of the workbench along the Y axis;
in the same way, the following parameters were calculated:
the cross standard gauge is fixed on a YOZ plane, and the worktable moves along the Y axis to obtain
Figure BDA00039182521100000320
Figure BDA00039182521100000321
And
Figure BDA00039182521100000322
the working table moves along the Z axis to obtain
Figure BDA00039182521100000323
And
Figure BDA00039182521100000324
the cross standard gauge is fixed on the XOZ plane, and the worktable moves along the X axis to obtain
Figure BDA00039182521100000325
And
Figure BDA00039182521100000326
the working table moves along the Z axis to obtain
Figure BDA00039182521100000327
And
Figure BDA00039182521100000328
by measuring the movement of the table along the X-axis, information of 3 rotation angle errors and 3 movement errors is collected. Standard cross gauges are arranged on different planes, and the corresponding orientation of the angular displacement sensor is adjusted to measure various angle errors, position errors and perpendicularity errors generated on XOY, XOZ and YOZ planes.
Further, the step 2 comprises the following substeps:
solving the movement error and the rotation angle error data obtained in the step 1 by using least square fitting;
the angular error produced by the movement of the stage along the X-axis can be expressed as:
Figure BDA0003918252110000041
in the formula of xxi (i =1,2, …, n) represents the coefficients of a fitting polynomial where xxn first X represents stage movement along the X-axis, xn represents the nth sample point in the X-direction, X n Wherein x is an unknown number;
ignoring errors above third order, equation (5) can be expressed as:
θ x (x)＝λ xx1 ·x+λ xx2 ·x 2 +λ xx3 ·x 3 (6)
in the same way, the method for preparing the composite material,
θ y (x)＝λ yx1 ·x+λ yx2 ·x 2 +λ yx3 ·x 3 (7)
θ z (x)＝λ zx1 ·x+λ zx2 ·x 2 +λ zx3 ·x 3 (8)
the angular error produced by the movement of the stage along the Y-axis can be expressed as:
Figure BDA0003918252110000042
the angular error produced by the headstock moving along the Z axis can be expressed as:
Figure BDA0003918252110000043
respectively calculating a movement error and a verticality error in the same way;
and establishing a comprehensive mathematical model of errors by combining the moving errors and the corner errors generated by the operation of the machine tool and the perpendicularity errors among the axes, wherein the comprehensive mathematical model comprises the following steps:
Figure BDA0003918252110000051
in the formula, delta x (x) Representing the positioning error, delta, produced by movement of the table along the X-axis y (y) and δ z (Z) a positioning error generated by the movement of the table along the Y-axis and the movement of the headstock along the Z-axis; delta y (x) And delta z (x) Representing the straightness error generated by the movement of the worktable along the X axis; delta x (y) and δ z (Y) represents a straightness error caused by movement of the table along the Y-axis; delta y (z) and delta x (Z) represents a straightness error generated by the movement of the headstock along the Z-axis; gamma ray xy 、γ xz And gamma yz Indicating the error in perpendicularity between the three axes.
Further, in step 3, the method for compensating the position of the tool relative to the workpiece is as follows:
when the desired position is P i The error generated by predicting the expected position according to the error model is e (P) i ) The error-compensated position P can be calculated b So that the error compensates for the position P b The data is sent to a compensation module and converted into a numerical control code to realize error compensation;
P b ＝P i -e(P i ) (12)
P i representing an ideal tool position; p b Error compensation bits calculated by error compensation modelPlacing; e (P) i ) Indicating the error generated at the desired location;
however, when the machine tool is moved to P according to the demand of the compensation command b After the position is reached, the actual position and the ideal position of the tool tip point relative to the machining point still have deviation, and the compensated deviation can be expressed as
P f ＝P b -e(P b ) (13)
P f Representing the actual position of the compensated tool tip point; e (P) b ) Indicating the compensated error.
The invention has the following beneficial effects:
according to the invention, the acquisition of error data of different planes can be realized through the cross standard gauge and the angular displacement sensor, the method is simple and efficient, a laser interferometer is not required, the threshold of equipment is greatly reduced, and the measurement efficiency can be improved; and then establishing a comprehensive error model of the three-axis machine tool according to the machine tool error transmission chain, and solving the geometric error of the machine tool by using an iterative algorithm. The method predicts the positioning error of the machine tool so that the relative position of the tool nose and the workpiece machining point is on the expected position, and the research result provides important basis for error compensation.
Drawings
FIG. 1 is a block diagram of a measurement system; wherein, the 1-cross standard gauge and the 2-angular displacement sensor are arranged on the frame;
FIG. 2 Standard gauge measurements;
figure 3 machine geometry error compensation.
Detailed Description
The present invention will be described in further detail below in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a method for establishing a motion error model of a machine tool machining test piece, which mainly comprises the following steps in the actual application process:
a method for quickly measuring and compensating geometric errors of a machine tool comprises the following steps:
step 1, respectively fixing cross standard gauges with holes uniformly on an XOY plane of a workbench, and fixing an angular displacement sensor on a main shaft; setting a workbench to move along the X, Y axis direction, stopping for 8s when moving to the central axis position of the cross gauge hole each time, moving the main shaft downwards to the position with the central hole depth H/2 for sampling, sampling at the next hole position after sampling is finished, and measuring the angle error, the position error and the perpendicularity error of each sample point; similarly, three error values are measured by respectively fixing the cross standard gauge on XOZ and YOZ planes of the workbench, and the workbench runs along two axes of the cross standard gauge in sequence;
the cross standard gauge is formed by intersecting two mutually perpendicular shafts, and spaced hole sites are uniformly formed on the two shafts; 21 holes are uniformly formed in the cross standard gauge, the aperture is R, the depth is H, and the radius of the angular displacement sensor is R/2;
the angle measurement precision of the sensor is 0.001 degrees, and the positioning precision is 0.001mm. When the sensor moves down to H/2 in one of the holes, the position error and the angle error of the point can be sensed;
(1) the cross standard gauge is fixed on an XOY plane, and the main shaft firstly moves along an axis of the cross standard gauge parallel to the X axis and then moves along an axis of the cross standard gauge parallel to the Y axis;
when the angular displacement sensor measures the ith hole while moving along the X axis, the angular error of the sample point is
Figure BDA0003918252110000061
And
Figure BDA0003918252110000062
wherein the content of the first and second substances,
Figure BDA0003918252110000063
indicating that movement of the table along the X-axis produces a calculated angular error about the X-axis,
Figure BDA0003918252110000064
indicating that the worktable moves along the X axis to generate an angle error calculation value around the Y axis; corner mark x xoy Representing the X-axis case (around or moving), xoy denotes the xoy plane, and similar expressions below are consistent;
the angular error of each sample point with respect to the ideal position can be expressed as:
Figure BDA0003918252110000065
Figure BDA0003918252110000071
Figure BDA0003918252110000072
and
Figure BDA0003918252110000073
means that the angle value, x, of the worktable at the ith sample point is measured i Representing the situation where the cross gauge moves the ith sample point along the X-axis,
Figure BDA0003918252110000074
and
Figure BDA0003918252110000075
representing the angle value of each sample point of the workbench at an ideal position;
the position error of the sample point is
Figure BDA0003918252110000076
And
Figure BDA0003918252110000077
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003918252110000078
indicating that the movement of the table along the X-axis produces a calculated positioning error in the X-axis direction,
Figure BDA0003918252110000079
the straightness error calculation value in the y direction generated by the movement of the workbench along the X axis is represented; the deviation of each sample point from the ideal position is expressed as:
Figure BDA00039182521100000710
Figure BDA00039182521100000711
Figure BDA00039182521100000712
and
Figure BDA00039182521100000713
the coordinate value of the measured workbench at the ith sample point is represented;
Figure BDA00039182521100000714
indicating the movement distance of the worktable along the X axis, the ith sample point is calibrated in the X direction,
Figure BDA00039182521100000715
the movement distance of the ith sample point is calibrated in the Y direction for the movement of the workbench along the X axis;
when the angular displacement sensor measures the ith hole while moving along the Y axis, the angular error of the sample point is
Figure BDA00039182521100000716
And
Figure BDA00039182521100000717
wherein the content of the first and second substances,
Figure BDA00039182521100000718
the representation indicates that the movement of the table along the Y-axis produces an angular error about the X-axisThe calculated value is calculated by calculating the value of,
Figure BDA00039182521100000719
indicating that the worktable moves along the Y axis to generate an angle error calculation value around the Y axis; the angular error of each sample point with respect to the ideal position can be expressed as:
Figure BDA00039182521100000720
Figure BDA00039182521100000721
Figure BDA00039182521100000722
and
Figure BDA00039182521100000723
indicating that the angle value of the workbench at the ith sample point is measured;
Figure BDA00039182521100000724
and
Figure BDA00039182521100000725
representing the angle value of each sample point of the workbench at an ideal position;
the position error of the sample point is
Figure BDA00039182521100000726
And
Figure BDA00039182521100000727
wherein the content of the first and second substances,
Figure BDA00039182521100000728
a calculated positioning error value in the X-axis direction is generated for the movement of the table along the Y-axis,
Figure BDA00039182521100000729
generating a straightness error calculation in the Y direction for the table movement along the Y axis; the deviation of each sample point from the ideal position is expressed as:
Figure BDA0003918252110000081
Figure BDA0003918252110000082
Figure BDA0003918252110000083
and
Figure BDA0003918252110000084
indicating the measured coordinate value of the stage at the ith sample point,
Figure BDA0003918252110000085
indicating the movement distance of the stage along the Y-axis, the i-th sample point is calibrated in the Y-direction,
Figure BDA0003918252110000086
the movement distance of the ith sample point is calibrated in the Y direction for the stage to move along the Y axis.
(2) The cross standard gauge is fixed on a YOZ plane, and the main shaft firstly moves along an axis of the cross standard gauge parallel to a Y axis and then moves along an axis of the cross standard gauge parallel to a Z axis;
the worktable moves along the Y axis, and when the angular displacement sensor measures the ith hole, the angular error of the sample point is
Figure BDA0003918252110000087
And
Figure BDA0003918252110000088
wherein the content of the first and second substances,
Figure BDA0003918252110000089
a calculated angular error about the Z axis is generated for movement of the table along the Y axis,
Figure BDA00039182521100000810
generating a calculated angular error about the Y-axis for movement of the table along the Y-axis; the angular error of each sample point with respect to the ideal position can be expressed as:
Figure BDA00039182521100000811
Figure BDA00039182521100000812
Figure BDA00039182521100000813
and
Figure BDA00039182521100000814
indicating that the angle value of the workbench at the ith sample point is measured,
Figure BDA00039182521100000815
and
Figure BDA00039182521100000816
representing the angle value of each sample point of the workbench at an ideal position;
the position error of the sample point is
Figure BDA00039182521100000817
And
Figure BDA00039182521100000818
wherein the content of the first and second substances,
Figure BDA00039182521100000819
a calculated positioning error in the Z-axis direction is generated for movement of the table along the Y-axis,
Figure BDA00039182521100000820
generating a calculated positioning error value in the Y-axis direction for the movement of the table along the Y-axis; the deviation of each sample point from the ideal position is expressed as:
Figure BDA00039182521100000821
Figure BDA00039182521100000822
Figure BDA00039182521100000823
and
Figure BDA00039182521100000824
indicating the measured coordinate value of the stage at the ith sample point,
Figure BDA00039182521100000825
the movement distance of the ith sample point marked in the Y direction for the movement of the worktable along the Y axis,
Figure BDA00039182521100000826
the movement distance of the ith sample point in the Z direction is calibrated for the stage movement along the Y axis.
The working platform moves along the Z axis, and when the angular displacement sensor measures the ith hole, the angular error of the sample point is
Figure BDA0003918252110000091
And
Figure BDA0003918252110000092
wherein the content of the first and second substances,
Figure BDA0003918252110000093
a calculated angular error about the Z-axis is generated for movement of the table along the Z-axis,
Figure BDA0003918252110000094
generating a calculated angular error about the Y axis for the table to move along the Z axis; the angular error of each sample point with respect to the ideal position can be expressed as:
Figure BDA0003918252110000095
Figure BDA0003918252110000096
Figure BDA0003918252110000097
and
Figure BDA0003918252110000098
the angle value of the workbench at the ith sample point is measured;
Figure BDA0003918252110000099
and
Figure BDA00039182521100000910
representing the angle value of each sample point of the workbench at an ideal position;
the position error of the sample point is
Figure BDA00039182521100000911
And
Figure BDA00039182521100000912
the deviation of each sample point from the ideal position is expressed as:
Figure BDA00039182521100000913
Figure BDA00039182521100000914
Figure BDA00039182521100000915
and
Figure BDA00039182521100000916
indicating the measured coordinate value of the stage at the ith sample point,
Figure BDA00039182521100000917
and
Figure BDA00039182521100000918
coordinate values representing each sample point of the stage at the desired position.
(3) The cross standard gauge is fixed on the XOZ plane, and the main shaft firstly moves along the axis of the cross standard gauge parallel to the X axis and then moves along the axis of the cross standard gauge parallel to the Z axis;
the worktable moves along the X axis, and when the angular displacement sensor measures the ith hole, the angular error of the sample point is
Figure BDA00039182521100000919
And
Figure BDA00039182521100000920
wherein the content of the first and second substances,
Figure BDA00039182521100000921
a calculated angular error about the Z axis is generated for movement of the table along the X axis,
Figure BDA00039182521100000922
generating a calculated angular error about the X-axis for movement of the table along the X-axis; the angular error of each sample point with respect to the ideal position can be expressed as:
Figure BDA00039182521100000923
Figure BDA0003918252110000101
Figure BDA0003918252110000102
and
Figure BDA0003918252110000103
indicating that the angle value of the workbench at the ith sample point is measured;
Figure BDA0003918252110000104
and
Figure BDA0003918252110000105
representing the angle value of each sample point of the workbench at the ideal position;
the position error of the sample point is
Figure BDA0003918252110000106
And
Figure BDA0003918252110000107
wherein the content of the first and second substances,
Figure BDA0003918252110000108
a calculated positioning error in the Z-axis direction is generated for the stage movement along the X-axis,
Figure BDA0003918252110000109
generating a calculated positioning error value in the X-axis direction for the movement of the table along the X-axis; the deviation of each sample point from the ideal position is expressed as:
Figure BDA00039182521100001010
Figure BDA00039182521100001011
Figure BDA00039182521100001012
and
Figure BDA00039182521100001013
indicating the measured coordinate value of the stage at the ith sample point,
Figure BDA00039182521100001014
the movement distance of the ith sample point marked in the X direction for the movement of the worktable along the X axis,
Figure BDA00039182521100001015
the movement distance of the ith sample point is calibrated in the Z direction for the movement of the workbench along the X axis;
the working platform moves along the Z axis, and when the angular displacement sensor measures the ith hole, the angular error of the sample point is
Figure BDA00039182521100001016
And
Figure BDA00039182521100001017
wherein the content of the first and second substances,
Figure BDA00039182521100001018
a calculated angular error about the Z-axis is generated for movement of the table along the Z-axis,
Figure BDA00039182521100001019
generating a calculated angular error about the X axis for movement of the table along the Z axis; the angular error of each sample point with respect to the ideal position can be expressed as:
Figure BDA00039182521100001020
Figure BDA00039182521100001021
Figure BDA00039182521100001022
and
Figure BDA00039182521100001023
indicating that the angle value of the workbench at the ith sample point is measured;
Figure BDA00039182521100001024
and
Figure BDA00039182521100001025
representing the angle value of each sample point of the workbench at an ideal position;
the position error of the sample point is
Figure BDA00039182521100001026
And
Figure BDA00039182521100001027
the deviation of each sample point from the ideal position is expressed as:
Figure BDA00039182521100001028
Figure BDA00039182521100001029
Figure BDA0003918252110000111
and
Figure BDA0003918252110000112
indicating the measured coordinate value of the stage at the ith sample point,
Figure BDA0003918252110000113
for movement of the table along the Z axis, sample iThe moving distance marked by the point in the X direction,
Figure BDA0003918252110000114
the movement distance of the ith sample point in the Z direction is calibrated for the movement of the stage along the Z axis.
Standard cross gauges are arranged on different planes, and the corresponding orientation of the angular displacement sensor is adjusted to measure various angle errors, position errors and perpendicularity errors generated on XOY, XOZ and YOZ planes.
Step 2, combining a movement error and a corner error generated by the operation of the machine tool and a verticality error between all the axes, and fitting and solving by using a least square method to establish a comprehensive mathematical model of the errors;
the method comprises the following specific steps:
solving the movement error and the rotation angle error data obtained in the step 1 by using least square fitting;
the angular error produced by the movement of the stage along the X-axis can be expressed as:
Figure BDA0003918252110000115
in the formula of xxi (i =1,2, …, n) represents the coefficients of a fitting polynomial where xxn first X represents stage movement along the X-axis, xn represents the nth sample point in the X-direction, X n Wherein x is an unknown number;
ignoring errors above third order, equation (5) can be expressed as:
θ x (x)＝λ xx1 ·x+λ xx2 ·x 2 +λ xx3 ·x 3 (6)
in the same way, the method has the advantages of,
θ y (x)＝λ yx1 ·x+λ yx2 ·x 2 +λ yx3 ·x 3 (7)
θ z (x)＝λ zx1 ·x+λ zx2 ·x 2 +λ zx3 ·x 3 (8)
the angular error produced by the movement of the stage along the Y-axis can be expressed as:
Figure BDA0003918252110000116
the angular error produced by the headstock moving along the Z axis can be expressed as:
Figure BDA0003918252110000121
and calculating the moving error and the verticality error respectively in the same way.
And establishing a comprehensive mathematical model of errors by combining the moving errors and the corner errors generated by the operation of the machine tool and the perpendicularity errors among the axes, wherein the comprehensive mathematical model comprises the following steps:
Figure BDA0003918252110000122
in the formula, delta x (x) Representing the positioning error, delta, produced by movement of the table along the X-axis y (y) and δ z (Z) a positioning error generated by the movement of the table along the Y-axis and the movement of the headstock along the Z-axis; delta y (x) And delta z (x) Representing the straightness error generated by the movement of the worktable along the X axis; delta x (y) and δ z (Y) represents a straightness error caused by the movement of the table along the Y axis; delta. For the preparation of a coating y (z) and delta x (Z) represents a straightness error generated by the movement of the headstock along the Z-axis; gamma ray xy 、γ xz And gamma yz Indicating the perpendicularity error between the three axes.
Step 3, writing the logical relation of the error compensation into an error compensation module, wherein the compensation module is embedded into a numerical control system, and the position of the tool is close to the expected position by compensating the position of the tool relative to the workpiece;
the method of compensating the position of the tool relative to the workpiece is as follows:
when the desired position is P i The error resulting from predicting the desired position from the error model is e (P) i ) The position of the error compensation can be calculatedP b So that the error compensates for the position P b The data is sent to a compensation module and converted into a numerical control code to realize error compensation;
P b ＝P i -e(P i ) (12)
P i representing an ideal tool position; p b Representing the error compensation position calculated by the error compensation model; e (P) i ) Indicating the error generated at the desired location;
however, when the machine tool is moved to P according to the demand of the compensation command b After the position is reached, the actual position and the ideal position of the tool tip point relative to the machining point still have deviation, and the compensated deviation can be expressed as
P f ＝P b -e(P b ) (13)
P f Representing the actual position of the compensated tool tip point; e (P) b ) Indicating the compensated error. The solution to the machine tool geometric error uses an iterative algorithm that predicts the machine tool positioning error so that the relative position of the tool tip and the workpiece machining point is at the desired position.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any modification, equivalent replacement, and improvement made by those skilled in the art within the technical scope of the present invention should be included in the scope of the present invention.

Claims (5)

1. A method for rapidly measuring and compensating geometric errors of a machine tool is characterized by comprising the following steps:
step 1, respectively fixing cross standard gauges with uniform holes on an XOY plane of a workbench, and fixing an angular displacement sensor on a main shaft; setting a workbench to move along the X, Y axis direction, moving to the central axis position of the cross gauge hole each time for pausing, moving the main shaft downwards to the central hole depth H/2 for sampling, sampling at the next hole position after sampling is finished, and measuring the angle error, the position error and the perpendicularity error of each sample point; similarly, three error values are measured by respectively fixing the cross standard gauge on XOZ and YOZ planes of the workbench;
step 2, combining a movement error and a corner error generated by the operation of the machine tool and a perpendicularity error among all axes, and applying a least square method to fit and solve to establish a comprehensive mathematical model of the errors;
and 3, writing the logical relation of the error compensation into an error compensation module, embedding the compensation module into a numerical control system, and enabling the position of the tool to approach to an expected position by compensating the position of the tool relative to the workpiece.
2. The rapid measurement and compensation method of claim 1, wherein the cross gauge is formed by intersecting two perpendicular axes, and spaced holes are uniformly formed on the two axes.
3. The method for rapid measurement and compensation according to claim 1, wherein in step 1, when the cross gauge is fixed on the XOY plane, the spindle moves along an axis parallel to the X axis of the cross gauge and then moves along an axis parallel to the Y axis of the cross gauge;
when the angular displacement sensor measures the ith hole while moving along the X axis, the angular error of the sample point is
Figure FDA0003918252100000011
And
Figure FDA0003918252100000012
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003918252100000013
indicating that movement of the table along the X-axis produces a calculated angular error about the X-axis,
Figure FDA0003918252100000014
indicating that the worktable moves along the X axis to generate an angle error calculation value around the Y axis;
the angular error of each sample point with respect to the ideal position can be expressed as:
Figure FDA0003918252100000015
Figure FDA0003918252100000016
Figure FDA0003918252100000017
and
Figure FDA0003918252100000018
means that the angle value, x, of the worktable at the ith sample point is measured i Representing the situation where the cross gauge moves the ith sample point along the X-axis,
Figure FDA0003918252100000019
and
Figure FDA00039182521000000110
representing the angle value of each sample point of the workbench at an ideal position;
the position error of the sample point is
Figure FDA00039182521000000111
And
Figure FDA00039182521000000112
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00039182521000000113
indicating that the table is moving along the X-axis to produce a calculated positioning error in the X-axis direction,
Figure FDA0003918252100000021
the straightness error calculation value in the y direction generated by the movement of the workbench along the X axis is represented; each sample point being relative to an ideal positionThe deviation of (d) is expressed as:
Figure FDA0003918252100000022
Figure FDA0003918252100000023
Figure FDA0003918252100000024
and
Figure FDA0003918252100000025
the coordinate value of the measured workbench at the ith sample point is represented;
Figure FDA0003918252100000026
indicating the movement distance of the worktable along the X axis, the ith sample point is calibrated in the X direction,
Figure FDA0003918252100000027
the movement distance of the ith sample point is calibrated in the Y direction for the movement of the workbench along the X axis;
when the angular displacement sensor measures the ith hole while moving along the Y axis, the angular error of the sample point is
Figure FDA0003918252100000028
And
Figure FDA0003918252100000029
wherein the content of the first and second substances,
Figure FDA00039182521000000210
indicating that movement of the table along the Y-axis produces a calculated angular error about the X-axis,
Figure FDA00039182521000000211
indicating that the worktable moves along the Y axis to generate an angle error calculation value around the Y axis; the angular error of each sample point with respect to the ideal position can be expressed as:
Figure FDA00039182521000000212
Figure FDA00039182521000000213
Figure FDA00039182521000000214
and
Figure FDA00039182521000000215
indicating that the angle value of the workbench at the ith sample point is measured;
Figure FDA00039182521000000216
and
Figure FDA00039182521000000217
representing the angle value of each sample point of the workbench at an ideal position;
the position error of the sample point is
Figure FDA00039182521000000218
And
Figure FDA00039182521000000219
wherein the content of the first and second substances,
Figure FDA00039182521000000220
a calculated positioning error value in the X-axis direction is generated for the movement of the table along the Y-axis,
Figure FDA00039182521000000221
generating a straightness error calculation in the Y direction for the table moving along the Y axis; the deviation of each sample point from the ideal position is expressed as:
Figure FDA00039182521000000222
Figure FDA00039182521000000223
Figure FDA00039182521000000224
and
Figure FDA00039182521000000225
indicating the measured coordinate value of the stage at the ith sample point,
Figure FDA00039182521000000226
indicating the movement distance of the worktable along the Y axis, the ith sample point is calibrated in the Y direction,
Figure FDA00039182521000000227
the movement distance of the ith sample point is calibrated in the Y direction for the movement of the workbench along the Y axis;
in the same way, the following parameters were calculated:
the cross standard gauge is fixed on a YOZ plane, and the worktable moves along the Y axis to obtain
Figure FDA0003918252100000031
Figure FDA0003918252100000032
And
Figure FDA0003918252100000033
the working table moves along the Z axis to obtain
Figure FDA0003918252100000034
And
Figure FDA0003918252100000035
the cross standard gauge is fixed on the XOZ plane, and the worktable moves along the X axis to obtain
Figure FDA0003918252100000036
And
Figure FDA0003918252100000037
the working table moves along the Z axis to obtain
Figure FDA0003918252100000038
And
Figure FDA0003918252100000039
4. the fast measurement and compensation method of claim 1, wherein the step 2 comprises the sub-steps of:
solving the movement error and the rotation angle error data obtained in the step 1 by using least square fitting;
the angular error produced by the movement of the stage along the X-axis can be expressed as:
Figure FDA00039182521000000310
in the formula of xxi (i =1,2, …, n) represents the coefficients of a fitting polynomial where xxn first X represents stage movement along the X-axis, xn represents the nth sample point in the X-direction, X n Wherein x is an unknown number;
ignoring errors above third order, equation (5) can be expressed as:
θ x (x)＝λ xx1 ·x+λ xx2 ·x 2 +λ xx3 ·x 3 (6)
in the same way, the method for preparing the composite material,
θ y (x)＝λ yx1 ·x+λ yx2 ·x 2 +λ yx3 ·x 3 (7)
θ z (x)＝λ zx1 ·x+λ zx2 ·x 2 +λ zx3 ·x 3 (8)
the angular error produced by the movement of the stage along the Y-axis can be expressed as:
Figure FDA00039182521000000311
the angular error produced by the headstock moving along the Z axis can be expressed as:
Figure FDA0003918252100000041
respectively calculating a movement error and a verticality error in the same way;
and establishing a comprehensive mathematical model of errors by combining the moving errors and the corner errors generated by the operation of the machine tool and the perpendicularity errors among the axes, wherein the comprehensive mathematical model comprises the following steps:
Figure FDA0003918252100000042
in the formula, delta x (x) Representing positioning errors, delta, caused by movement of the table along the X-axis y (y) and δ z (Z) a positioning error generated by the movement of the table along the Y-axis and the movement of the headstock along the Z-axis; delta. For the preparation of a coating y (x) And delta z (x) Representing the straightness error generated by the movement of the worktable along the X axis; delta x (y) and δ z (Y) represents a straightness error caused by the movement of the table along the Y axis; delta y (z) and delta x (Z) represents a straightness error generated by the movement of the headstock along the Z-axis; gamma ray xy 、γ xz And gamma yz Indicating the error in perpendicularity between the three axes.
5. The rapid measurement and compensation method according to claim 1, wherein the method for compensating the position of the tool relative to the workpiece in step 3 is as follows:
when the desired position is P i The error resulting from predicting the desired position from the error model is e (P) i ) The error-compensated position P can be calculated b So that the error compensates for the position P b The data is sent to a compensation module and converted into a numerical control code to realize error compensation;
P b ＝P i -e(P i ) (12)
P i representing an ideal tool position; p b Representing the error compensation position calculated by the error compensation model; e (P) i ) Indicating the error generated at the desired location;
however, when the machine tool is moved to P according to the demand of the compensation command b After the position, the actual position and the ideal position of the tool tip point relative to the machining point are still deviated, and the compensated deviation can be expressed as
P f ＝P b -e(P b ) (13)
P f Representing the actual position of the compensated tool tip point; e (P) b ) Indicating the compensated error.
CN202211349075.1A 2022-10-31 2022-10-31 Method for quickly measuring and compensating geometric errors of machine tool Pending CN115781416A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202211349075.1A CN115781416A (en) 2022-10-31 2022-10-31 Method for quickly measuring and compensating geometric errors of machine tool

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202211349075.1A CN115781416A (en) 2022-10-31 2022-10-31 Method for quickly measuring and compensating geometric errors of machine tool

Publications (1)

Publication Number Publication Date
CN115781416A true CN115781416A (en) 2023-03-14

Family

ID=85434617

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202211349075.1A Pending CN115781416A (en) 2022-10-31 2022-10-31 Method for quickly measuring and compensating geometric errors of machine tool

Country Status (1)

Country Link
CN (1) CN115781416A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117020754A (en) * 2023-10-08 2023-11-10 成都飞机工业（集团）有限责任公司 Tool and method for detecting geometric precision of numerical control machining center of flexible production line

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117020754A (en) * 2023-10-08 2023-11-10 成都飞机工业（集团）有限责任公司 Tool and method for detecting geometric precision of numerical control machining center of flexible production line
CN117020754B (en) * 2023-10-08 2024-02-23 成都飞机工业（集团）有限责任公司 Tool and method for detecting geometric precision of numerical control machining center of flexible production line

Similar Documents

Publication Publication Date Title
CN112008492B (en) Method for identifying perpendicularity error of translational shaft of gantry numerical control machine tool
Jha et al. Analysis of geometric errors associated with five-axis machining centre in improving the quality of cam profile
CN112518422A (en) Five-axis AC swing head gantry machine tool geometric error modeling and separating method
Lee et al. A comprehensive method for calibration of volumetric positioning accuracy of CNC-machines
CN107315391B (en) A kind of pretravel error compensating method of numerically-controlled machine tool on-line checking
CN109732402B (en) Laser interferometer based multi-line machine tool space geometric error measurement identification method
Fu et al. Product-of-exponential formulas for precision enhancement of five-axis machine tools via geometric error modeling and compensation
CN107806825B (en) Three faces, five line lathe space geometry error measure discrimination method based on plane grating
CN113074663A (en) Light beam vector deviation planning compensation method for spectrum confocal on-line measurement
Wu et al. A method for tracing key geometric errors of vertical machining center based on global sensitivity analysis
CN115781416A (en) Method for quickly measuring and compensating geometric errors of machine tool
CN108332688A (en) A kind of ball line slideway auxiliary raceway straightness On-line Measuring Method
Yao et al. Modeling of kinematics errors and alignment method of a swing arm ultra-precision diamond turning machine
CN111580459A (en) Five-axis machining center assembly error analysis control method
Huang et al. Identification of integrated geometric errors of rotary axis and setup position errors for 5-axis machine tools based on machining test
CN113359609B (en) Key geometric error optimization proportioning compensation method for five-axis numerical control machine tool
CN109739180A (en) Based on the determination method of the work of numerical control machine plane Instantaneous center of SolidWorks, ADAMS
CN107900781B (en) Calibration device and calibration method for contact type online detection system of lathe
CN104914787A (en) Method of estimating precision of machine tool body diagonals
CN114782513B (en) Point laser sensor mounting pose calibration method based on plane
CN116810483A (en) Five-axis machine tool rotating shaft geometric error identification method based on machining test
CN112355712B (en) Trigger type on-machine measurement precision calibration method and system
Xu et al. Error modeling and accuracy optimization of rotating ultrasonic vibration assisted EDM machine tool
Xu et al. Geometric error compensation of spherical surface grinding system
Nikam Coordinate Measuring Machine (CMM)

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination