CN110794766A - Quick identification method for measuring perpendicularity error of numerical control machine tool based on ball arm instrument - Google Patents

Quick identification method for measuring perpendicularity error of numerical control machine tool based on ball arm instrument Download PDF

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CN110794766A
CN110794766A CN201911163063.8A CN201911163063A CN110794766A CN 110794766 A CN110794766 A CN 110794766A CN 201911163063 A CN201911163063 A CN 201911163063A CN 110794766 A CN110794766 A CN 110794766A
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detection
machine tool
numerical control
control machine
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蒋晓耕
柴旭
贾经纬
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Tianjin Polytechnic University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/401—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for measuring, e.g. calibration and initialisation, measuring workpiece for machining purposes
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/31—From computer integrated manufacturing till monitoring
    • G05B2219/31304—Identification of workpiece and data for control, inspection, safety, calibration

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Abstract

The invention discloses a quick identification method for measuring perpendicularity error of a numerical control machine based on a ball rod instrument, and belongs to the field of precision detection of numerical control machines. Aiming at the problems of difficult installation of experimental devices, complex detection procedures, long detection time and the like in the traditional verticality error detection method, the invention designs a ball rod instrument spherical motion track to measure the verticality error by adopting a machine tool three-axis linkage mode. The invention uses exponential product formula to explain the geometric characteristics of the error distribution of the numerical control machine. Meanwhile, the method optimizes the detection path, shortens the detection time and improves the detection efficiency.

Description

Quick identification method for measuring perpendicularity error of numerical control machine tool based on ball arm instrument
Technical Field
The invention relates to the field of precision detection of numerical control machines, in particular to a method for quickly identifying verticality errors of a numerical control machine based on ball arm instrument measurement.
Technical Field
With the development of society, the proportion of numerical control machine tools in the manufacturing field is getting larger and larger, which puts higher requirements on the precision of the numerical control machine tools. At present, there are many instruments for detecting the manufacturing accuracy of the numerical control machine tool, such as a ball bar instrument, an R-test instrument, a laser interferometer and the like. Among them, the cue instrument is regarded as an ideal tool for precision detection due to the advantages of low cost, short detection time, simple operation and the like.
The existing method for detecting the precision of the machine tool by using the ball arm instrument has the problems of complicated operation process, long detection time and the like, so that the method which is simple to operate, short in detection time and simple in instrument installation is provided.
Disclosure of Invention
The invention aims to provide a method for quickly identifying the perpendicularity error of a numerical control machine tool based on a ball rod instrument, which utilizes the ball rod instrument to identify the perpendicularity error of three pairwise orthogonal linear axes in the numerical control machine tool. The invention has the advantages of only one-time installation and positioning, simple detection procedure and the like, shortens the detection time to a great extent, and improves the detection efficiency.
A quick identification method for measuring perpendicularity error of a numerical control machine tool based on a ball rod instrument comprises the following steps:
step 1, determining the installation position of a ball arm instrument according to the structure of a five-axis numerical control machine tool, and performing precision detection along a preset path in a three-axis linkage mode.
And 2, establishing an exponential product formula related to the perpendicularity error of the five-axis numerical control machine tool according to the topological structure of the five-axis numerical control machine tool, and performing error decoupling to obtain the perpendicularity error.
Determining the installation position of the ball arm instrument according to the five-axis numerical control machine tool structure in the step 1, and performing precision detection along a preset path in a three-axis linkage mode, wherein the method comprises the following steps:
step 1.1, firstly, a clamp base is arranged on a workbench, and a magnetic base is arranged on the clamp base. The workpiece tool cup center is then determined as the origin of the workpiece coordinate system using the machine tool probe. And finally, moving the main shaft tool cup to a position 100mm in the X-axis negative direction, and mounting one end of a ball bar instrument with the bar length of 100mm on the workpiece tool cup and mounting the other end of the ball bar instrument on the main shaft tool cup.
And step 1.2, as the acquisition speed of the ball rod instrument is constant, the detection points of the ball rod instrument need to be uniformly distributed. Firstly, the radius is set as
Figure BSA0000195650120000011
The circumference of the circle is divided into 1000 parts on average, 500 points of the corresponding circular arc in the negative direction range of the x axis in the coordinate system are firstly taken, and the obtained 500 point coordinate expression is as follows:
Figure BSA0000195650120000012
then, 500 points of the corresponding arc in the positive direction range of the x axis in the coordinate system are taken, and the obtained 500 point coordinate expressions are as follows:
Figure BSA0000195650120000013
step 1.3, respectively using corresponding rotation transformation matrixes to transform 1000 two-dimensional coordinates into 1000 three-dimensional coordinates according to 2 groups of detection points obtained by calculation, wherein the rotation transformation matrixes are as follows:
Figure BSA0000195650120000021
Figure BSA0000195650120000022
and step 1.4, generating a detection path by using a G code according to 1000 detection points obtained by coordinate transformation.
And step 1.5, detecting the ball arm instrument along the generated detection path at the running speed of 300 mm/min. In the detection process, a three-axis linkage mode is adopted for detection, when the ball arm instrument moves to the position of the 1000 th point, the ball arm instrument moves reversely along the original path, and data acquisition of 2000 detection points is completed.
Further, in step 2, according to the topological structure of the five-axis numerical control machine tool, an exponential product formula related to the perpendicularity error of the machine tool is established, and error decoupling is performed, wherein the method comprises the following steps:
step 2.1, establishing a simple model of the machine tool by taking the X axis of the five-axis numerical control machine tool as a reference, and establishing an exponential product formula according to the topological structure of the machine tool Y → X → R → Z:
Figure BSA0000195650120000023
Figure BSA0000195650120000024
Figure BSA0000195650120000025
Figure BSA0000195650120000026
Figure BSA0000195650120000029
T0＝[0 0 0 1]T；
substituting the above items into formula (3), the relationship between the theoretical detection point coordinates and the actual detection point coordinates with respect to the perpendicularity error can be obtained as follows:
Xen＝Xin+Yin*sinθxy+Zin*sinθxz(4)
Yen＝Yin-Zin*sinθyz(5)
Zen＝-Zin(6)
step 2.2, constructing the relationship between the length of the ball arm apparatus and the actual detection point, as follows:
M＝Xen 2+Yen 2+Zen 2(7)
substituting the formula (4-6) into the formula (7) to obtain a relationship between the length of the ball arm apparatus and the verticality error, which is shown as follows:
M＝Yin 2*sinθxy 2+Zin 2*sinθxz 2+Zin 2*sinθyz 2+Xin 2+Yin 2+Zin 2+2*Xin*Yin*sinθxy+2*Xin*Zin*sinθxz-2*Yin*Zin*sinθyz+2*Yin*Zin*sinθxy*sinθxz(8)
and 2.3, substituting 2000 detection point data obtained by measurement of the ball arm instrument into a formula (8) to form 2000 equations, generating 2000 pseudo-inverse matrixes, and solving three perpendicularity errors by using a pseudo-inverse function method.
The invention uses exponential product formula to build the mathematical model of the verticality error of the numerical control machine, and can solve the verticality error of the numerical control machine by using the ball rod instrument to detect data. The invention has the advantages of simple detection program and the like by installing the detection device at one time, shortens the detection time to a great extent, improves the detection efficiency and provides a new method for quickly detecting the perpendicularity error of the numerical control machine.
Drawings
FIG. 1 is a schematic structural diagram of a cradle type five-axis numerical control machine tool.
FIG. 2 is a schematic view of a ball bar instrument installation diagram and a machine coordinate system in an embodiment of the method of the invention.
FIG. 3 is a schematic diagram of a two-dimensional equipartition circle in an embodiment of the method of the present invention.
FIG. 4 is a schematic diagram of transformation from a two-dimensional coordinate system to a three-dimensional coordinate system in an embodiment of the method of the present invention.
FIG. 5 is a simulation diagram of a MATLAB detection path in an embodiment of the method of the present invention.
FIG. 6 is a schematic diagram of a three-dimensional detection path in an embodiment of the method of the present invention.
FIG. 7 is a graph of forward test data for a cue stick apparatus in an example of the method of the present invention.
FIG. 8 is a diagram of data from a cue stick reverse test conducted according to an embodiment of the method of the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
Fig. 1 is a schematic structural diagram of a cradle-type five-axis numerical control machine tool, which is taken as an example to illustrate the method of the invention.
Determining the installation position of the ball arm instrument according to the five-axis numerical control machine tool structure in the step 1, and performing precision detection along a preset path in a three-axis linkage mode, wherein the method comprises the following steps:
step 1.1, firstly, a clamp base is arranged on a workbench, and a magnetic base is arranged on the clamp base. The workpiece tool cup center is then determined with the machine tool probe as the origin of the workpiece coordinate system. Finally, the main shaft tool cup is moved to a position 100mm in the negative direction of the X axis, one end of a ball bar instrument with a bar length of 100mm is installed on the workpiece tool cup, and the other end is installed on the main shaft tool cup, as shown in FIG. 2.
And step 1.2, as the acquisition speed of the ball rod instrument is constant, the detection points of the ball rod instrument need to be uniformly distributed. Firstly, the radius is set as
Figure BSA0000195650120000041
The circumference of the circle is divided into 1000 parts on average, 500 points of the corresponding circular arc in the negative direction range of the x axis in the coordinate system are taken, and as shown in fig. 3, the coordinate expression of the obtained 500 points is as follows:
Figure BSA0000195650120000042
then, 500 points of the corresponding arc in the positive direction range of the x axis in the coordinate system are taken, and the obtained 500 point coordinate expressions are as follows:
and step 1.3, respectively using corresponding rotation transformation matrixes to transform 1000 two-dimensional coordinates into 1000 three-dimensional coordinates according to 2 groups of detection points obtained by calculation. Fig. 4 is a schematic diagram of transformation from a two-dimensional coordinate system to a three-dimensional coordinate system, where (a) is a schematic diagram of coordinate transformation of a first set of 500 coordinates, and (b) is a schematic diagram of coordinate transformation of a second set of 500 coordinates, and the corresponding rotation transformation matrices are as follows:
Figure BSA0000195650120000044
Figure BSA0000195650120000045
step 1.4, generating a detection path by using a G code according to 1000 detection points obtained by coordinate transformation, wherein a simulation diagram of the detection path in MATLAB is shown in FIG. 5, and a three-dimensional detection path simulation diagram is shown in FIG. 6.
And step 1.5, detecting the ball arm instrument along the generated detection path at the running speed of 300 mm/min. In the detection process, a three-axis linkage mode is adopted for detection, when the ball arm instrument moves to the 1000 th point, the ball arm instrument moves reversely along the original path, and data acquisition of 2000 detection points is completed. The diagram of the results of the forward detection errors of the cue plotter is shown in fig. 7, and the diagram of the results of the reverse detection errors of the cue plotter is shown in fig. 8.
Further, in step 2, according to the topological structure of the five-axis numerical control machine tool, an exponential product formula related to the perpendicularity error of the machine tool is established, and error decoupling is performed, wherein the method comprises the following steps:
step 2.1, establishing a simple model of the machine tool by taking the X axis of the five-axis numerical control machine tool as a reference, and establishing an exponential product formula according to the topological structure of the machine tool Y → X → R → Z:
Figure BSA0000195650120000046
Figure BSA0000195650120000051
Figure BSA0000195650120000052
Figure BSA0000195650120000054
Figure BSA0000195650120000055
T0＝[0 0 0 1]T；
substituting the above items into formula (3) can obtain the relationship between the coordinates of the theoretical detection point and the coordinates of the actual detection point with respect to the perpendicularity error.
Xen＝Xin+Yin*sinθxy+Zin*sinθxz(4)
Yen＝Yin-Zin*sinθyz(5)
Zen＝-Zin(6)
Step 2.2, constructing the relationship between the length of the ball arm apparatus and the actual detection point, as follows:
M＝Xen 2+Yen 2+Zen 2(7)
substituting the formula (4-6) into the formula (7) to obtain a relationship between the length of the ball arm apparatus and the verticality error, which is shown as follows:
M＝Yin 2*sinθxy 2+Zin 2*sinθxz 2+Zin 2*sinθyz 2+Xin 2+Yin 2+Zin 2+2*Xin*Yin*sinθxy+2*Xin*Zin*sinθxz-2*Yin*Zin*sinθyz+2*Yin*Zin*sinθxy*sinθxz(8)
and 2.3, substituting 2000 detection point data obtained by measurement of the ball arm instrument into a formula (8) to form 2000 equations, generating 2000 pseudo-inverse matrixes, and solving three perpendicularity errors by using a pseudo-inverse function method, wherein the three perpendicularity errors are as follows:
sinθxy＝-0.00011 θxy＝-0.00630°
sinθxz＝0.00061 θxz＝0.03495°
sinθyz＝-0.00017 θyz＝-0.00974°
the invention finally obtains 3 perpendicularity errors of the machine tool linear axis. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention, as any modifications, equivalent substitutions, improvements and the like, which are within the spirit and principle of the invention, are intended to be covered by the scope of the invention.

Claims (3)

1. A quick identification method for measuring perpendicularity error of a numerical control machine tool based on a ball rod instrument is characterized by comprising the following steps:
step 1, determining the installation position of a ball arm instrument according to the structure of a five-axis numerical control machine tool, and performing precision detection along a preset path in a three-axis linkage mode;
and 2, establishing an exponential product formula related to the perpendicularity error of the five-axis numerical control machine tool according to the topological structure of the five-axis numerical control machine tool, and performing error decoupling to obtain the perpendicularity error.
2. The method for rapidly identifying the perpendicularity error of the numerical control machine tool based on the ball rod instrument as claimed in claim 1, wherein in the step 1, the installation position of the ball rod instrument is determined according to the structure of the five-axis numerical control machine tool, and the precision detection is performed along a preset path in a three-axis linkage mode, and the method comprises the following steps of:
step 1.1, firstly, a clamp base is arranged on a workbench, and a magnetic base is arranged on the clamp base. The workpiece tool cup center is then determined as the origin of the workpiece coordinate system using the machine tool probe. Finally, moving the main shaft tool cup to a position 100mm in the X-axis negative direction, and mounting one end of a ball bar instrument with the bar length of 100mm on the workpiece tool cup and mounting the other end of the ball bar instrument on the main shaft tool cup;
and step 1.2, as the acquisition speed of the ball rod instrument is constant, the detection points of the ball rod instrument need to be uniformly distributed. Firstly, the radius is set as
Figure FSA0000195650110000011
The circumference of the circle is divided into 1000 parts on average, 500 points of the corresponding circular arc in the negative direction range of the x axis in the coordinate system are firstly taken, and the obtained 500 point coordinate expression is as follows:
then, 500 points of the corresponding arc in the positive direction range of the x axis in the coordinate system are taken, and the obtained 500 point coordinate expressions are as follows:
Figure FSA0000195650110000013
step 1.3, respectively using corresponding rotation transformation matrixes to transform 1000 two-dimensional coordinates into 1000 three-dimensional coordinates according to 2 groups of detection points obtained by calculation, wherein the rotation transformation matrixes are as follows:
Figure FSA0000195650110000014
step 1.4, generating a detection path by using a G code according to 1000 detection points obtained by coordinate transformation;
and step 1.5, detecting the ball arm instrument along the generated detection path at the running speed of 300 mm/min. In the detection process, a three-axis linkage mode is adopted for detection, when the ball arm instrument moves to the position of the 1000 th point, the ball arm instrument moves reversely along the original path, and data acquisition of 2000 detection points is completed.
3. The method for rapidly identifying the perpendicularity error of the numerical control machine tool based on the ball rod instrument as claimed in claim 1, wherein in the step 2, an exponential product formula related to the perpendicularity error of the five-axis numerical control machine tool is established according to a topological structure of the five-axis numerical control machine tool, and error decoupling is performed to obtain the perpendicularity error, and the method comprises the following steps of:
step 2.1, establishing a simple model of the machine tool by taking the X axis of the five-axis numerical control machine tool as a reference, and establishing an exponential product formula according to the topological structure of the machine tool Y → X → R → Z:
Figure FSA0000195650110000021
Figure FSA0000195650110000022
Figure FSA0000195650110000023
Figure FSA0000195650110000024
Figure FSA0000195650110000025
Figure FSA0000195650110000027
T0＝[0 0 0 1]T；
substituting the above items into formula (2), the relationship between the theoretical detection point coordinates and the actual detection point coordinates with respect to the perpendicularity error can be obtained as follows:
Xen＝Xin+Yin*sinθxy+Zin*sinθxz(4)
Yen＝Yin-Zin*sinθyz(5)
Zen＝-Zin(6)
step 2.2, constructing the relationship between the length of the ball arm apparatus and the actual detection point, as follows:
M＝Xen 2+Yen 2+Zen 2(7)
substituting the formula (4-6) into the formula (7) to obtain a relationship between the length of the ball arm apparatus and the verticality error, which is shown as follows:
M＝Yin 2*sinθxy 2+Zin 2*sinθxz 2+Zin 2*sinθyz 2+Xin 2+Yin 2+Zin 2+2*Xin*Yin*sinθxy+2*Xin*Zin*sinθxz-2*Yin*Zin*sinθyz+2*Yin*Zin*sinθxy*sinθxz(8)
and 2.3, substituting 2000 detection point data obtained by measurement of the ball arm instrument into a formula (8) to form 2000 equations, generating 2000 pseudo-inverse matrixes, and solving three perpendicularity errors by using a pseudo-inverse function method.
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CN117470105A (en) * 2023-12-26 2024-01-30 天津大学 Perpendicularity error identification method based on club instrument and multi-beam laser interferometer

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CN113967855A (en) * 2021-11-03 2022-01-25 天津工业大学 Identification method for measuring PDGEs of three-axis numerical control machine tool based on ball arm instrument
CN117470105A (en) * 2023-12-26 2024-01-30 天津大学 Perpendicularity error identification method based on club instrument and multi-beam laser interferometer
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Application publication date: 20200214