CN114234877A - Displacement sensor vector calibration method for R-test instrument - Google Patents
Displacement sensor vector calibration method for R-test instrument Download PDFInfo
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- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
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- G—PHYSICS
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
- G01B21/042—Calibration or calibration artifacts
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Abstract
The invention provides a displacement sensor vector calibration method for an R-Test instrument, which comprises the following steps: step S1, preparing instrument calibration, relating to the setting of the displacement sensor origin, the processing coordinate system and the R-Test instrument measurement coordinate system; s2, constructing an axial direction vector of the displacement sensor, and establishing a mathematical model between the displacement sensor and the coordinates of the sphere center of the calibration sphere; s3, solving the axial direction vector of the displacement sensor based on a hyperstatic least square method according to the vector equation set expansion form of the mathematical model; and step S4, calibrating and verifying the instrument, constructing a calibration sphere center coordinate inverse solution model, and completing the verification of the sphere center coordinate by combining the sphere center coordinate conversion models in different installation modes. The invention does not need complicated intelligent algorithm solution, solves the problem of the attitude calibration of the displacement sensor for the R-test instrument, has simple process and quick calculation, improves the detection efficiency and is convenient for implementing automatic measurement.
Description
Technical Field
The invention belongs to the technical field of detection instrument calibration, and particularly relates to a displacement sensor vector calibration method for an R-Test instrument.
Background
The five-axis numerical control machine tool has the capability of processing a complex curved surface, is widely applied to the field of manufacturing high-end equipment such as aviation structural parts, turbine blades, medical instruments and the like, and has increasingly serious problem of reduction of the processing precision of the five-axis machine tool caused by unstable precision control of a machine tool rotating shaft. In contrast, ISO230-1 proposes an R-Test instrument, which is provided with 3 displacement sensors distributed in a three-dimensional space according to different design schemes. Although the distribution mode is slightly different, the method can be used for measuring the space precision of the rotating shaft, compared with instruments such as a ball rod instrument and a laser tracker, the R-Test instrument can simultaneously obtain errors in three directions by one-time measurement, and has the advantages of high precision, high efficiency, simple structure and the like.
At present, according to the structure of the R-Test instrument, the R-Test instrument is divided into a contact type and a non-contact type. Liu Da we et al (Liu Da Wei et al, an R-test ball head and ball center detection device structure optimization design method [ J ]. Mechanics engineering report, 2016) have constructed the mathematical relationship between the detection calibration ball and the ball head displacement sensor, the construction method is based on the design of the contact R-test instrument, but the specific calculation method of the conversion between the displacement sensor and the ball center coordinate is not detailed. Penkang et al (Penkang et al, a non-contact R-test instrument field calibration method research [ J ] manufacturing technology and machine tool, 2019 (10)) researched a non-contact R-test instrument calibration method using an eddy current displacement sensor, and a differential evolution algorithm is used for solving a calibration equation set. Subsequently, Penkang et al (Penkang et al. calibration of a contact R-test measuring instrument and a calculation method of a sphere center coordinate research [ J ]. mechanical science and technology, 2020, 39(9):1385 1389) obtain a calibration equation set of the position of the ball head sensor by constructing a vector equation set aiming at the calibration of the contact R-test instrument, and still solve the calibration equation set by using a differential evolution algorithm. However, no matter a contact type or non-contact type R-Test instrument, the calculation of the differential evolution algorithm is related to the selection of an initial value, the performance of a computer and the like, and is not beneficial to the rapid calculation of the subsequent spherical center coordinates, and for the structural form of the R-Test instrument, the posture of the displacement sensor after being installed is directly reflected by the processing precision of the instrument base, so that the calibration precision of the instrument is influenced, but the calibration method related to the patent does not embody the characteristics. In general, the existing calibration method for the R-test instrument has the problem of low calculation efficiency in the forward calculation and the backward calculation of the spherical center coordinates during calibration.
Disclosure of Invention
Aiming at the problem that the calculation efficiency is low in both the forward calculation and the reverse calculation of the center coordinates of the sphere in the calibration process of the R-Test instrument in the prior art, the invention provides a displacement sensor vector calibration method for the R-Test instrument.
In order to achieve the above purpose, the invention comprises the following concrete contents:
the invention provides a displacement sensor vector calibration method for an R-test instrument, which comprises the following steps:
step S1: calibration preparation, namely installing an R-Test instrument on a machine tool workbench, determining a machining coordinate system and an R-Test instrument measurement coordinate system, and simultaneously recording the displacement value of a displacement sensor;
step S2: constructing a displacement sensor attitude calibration model, setting an axial direction vector of the displacement sensor, and establishing a mathematical model between the displacement sensor and a calibration sphere center coordinate;
step S3: solving a vector equation set of the displacement sensor, and solving the vector in the axial direction of the displacement sensor based on a hyperstatic least square method according to an expansion form of the vector equation set;
step S4: and (4) calibration verification, namely constructing a calibration sphere center coordinate inverse solution model according to the displacement sensor posture calibration model constructed in the step S2, and completing the conversion and verification of the calibration sphere center coordinate by combining different installation modes of the R-Test instrument.
In order to better implement the present invention, further, the specific steps of the calibration preparation performed in step S1 are as follows:
step S1.1: clamping the calibration ball on a machine tool spindle;
step S1.2: installing an R-Test instrument on a machine tool workbench;
step S1.3: after the calibration ball and the R-Test instrument are installed, moving the calibration ball at the main shaft end to be right above the R-Test instrument;
step S1.4: slowly moving the calibration ball in the Z direction to enable the center of the calibration ball to be located at the intersection point of the axes of the three displacement sensors in the R-Test instrument, enabling the displacement values of the three displacement sensors to be consistent, and recording the displacement values of the three displacement sensors at the moment as di(i=1,2,3)；
Step S1.5: determining X, Y, Z coordinates of the current machine tool coordinate system at the end of the numerical control machine tool as machining coordinate system coordinates, and simultaneously reading d in software of an R-Test instrumentiSet as the origin reading d0And the intersection point of the axes of the three displacement sensors is determined as the origin of the measurement coordinate system of the R-Test instrument, so that the directions of the measurement coordinate system of the R-Test instrument, the processing coordinate system and the machine tool coordinate system are consistent in the calibration state.
In order to better implement the present invention, further, the specific steps of constructing the displacement sensor posture calibration model in step S2 are as follows:
step S2.1: and expressing the axial direction vector of the displacement sensor under an R-Test instrument measurement coordinate system as follows:
step S2.2: according to the fact that the center of the calibration sphere is located at the intersection point of the axes of the three displacement sensors in the R-Test instrument in the step S1.1, the center position of the center of the calibration sphere located at the 3 displacement sensors can be obtained, and under a measurement coordinate system of the R-Test instrument, the initial coordinate of the center of the sphere at the top end of the displacement sensor is as follows:
wherein R is the radius of a calibration sphere, and R is the radius of the spherical surface of the displacement sensor probe;
step S2.3: sequentially moving the calibration ball at the main shaft end to different calibration point positions under the machining coordinate system
,
N is the total number of moves, and after each move is completed, the displacement readings of the 3 displacement sensors are
And obtaining the change of the spherical center coordinates of the probe of the displacement sensor along with the calibration process as follows:
wherein the content of the first and second substances,
，dijindicating the displacement of the ith displacement sensor in the jth movement;
step S2.4: in the calibration process, the displacement sensor and the calibration ball are always kept in a contact state, and the following vector equation set is obtained:
any one of the three displacement sensors can be calibrated by the position of the calibration point and the combination of the vector equation set.
In order to better implement the present invention, further, the specific steps of solving the displacement sensor vector equation set in step S3 are as follows:
step S3.1: expanding the vector equation set:
wherein the content of the first and second substances,
and
the meaning is the same as that in step S2.3;
step S3.2: the system of vector equations in step S3.1 is further expanded to:
since the unit vector of the axial direction vector of each displacement sensor satisfies the principle that the sum of squares is 1, the complementary equation according to the principle that the unit vector satisfies the sum of squares is 1 is expressed as:
let L = R + R, and in combination with the expansion equation and the complementary equation of step S3.2, the vector equation set is rewritten into a matrix form as:
wherein:
from the least squares solution of the hyperstatic equation:
the vector V is an axial direction vector of the displacement sensor, namely an attitude vector of the displacement sensor, and comprises all elements of the axial direction vector of the displacement sensor, and the calibration of the three displacement sensors can be completed by repeating the step on each displacement sensor;
step S3.3: in step S2.3 and step S2.4, different positions of the calibration point need to be designed
The calibration purpose is achieved, and the setting mode of the calibration points is as follows: the movable range of the X, Y, Z axis is established as a space grid, and boundary points, the middle points of face diagonal lines and the middle points of body diagonal lines on the grid are taken as calibration points, so that the design requirements on the number of the calibration points and the precision of the calibration points can be met.
In order to better implement the present invention, further, the specific steps of the calibration verification of the R-Test instrument in step S4 are as follows:
step S4.1: according to the inverse solution model of the coordinates of the center of sphere of the calibration sphere constructed in the step S2, the vector equation set is re-derived as follows, and the vector equation set is transformed into the following form:
wherein:
L=R+r；
and (3) operating the matrix to obtain the coordinates of the center of the calibration sphere:
(Vector)
namely the coordinates (x, y, z) of the sphere center of the calibration sphere;
step S4.2: and (4) on the basis of the step (S4.1), carrying out the calibration verification process of the R-Test instrument, and verifying the accuracy of the calibration result.
In order to better implement the invention, further, after the calibration verification of the R-Test instrument is completed, the installation form of the instrument is various.
To better implement the invention, further, when in the instrument mounting positionWhen the calibration is carried out under the condition of unchanging, the state of the instrument is consistent with the calibration state, so that the main shaft end calibration ball is directly driven to move to the set verification point position
The software matched with the instrument can automatically read the value d of the displacement sensor after reaching the verification pointkKnowing the current displacement sensor reading dkThe origin reading d0And the axial vector Vi (i =1,2,3) of the displacement sensor is substituted into the step S4.1, and the verification point vector can be completed
Calculating (1);
if it is
Otherwise, the step S2 and the step S3 are continued, and the number of calibration points is increased, thereby improving the calibration precision.
In order to better implement the invention, further, when the mounting position of the instrument is remounted, the posture of the remounted displacement sensor is changed with the calibration, and the calibration verification of the instrument specifically comprises the following steps:
step 1: firstly, the main shaft end calibration ball is driven to move to the original point position during calibration, and the reading of the displacement sensor and the reading d can be used0The difference between the two coordinate systems is judged, and meanwhile, a machining coordinate system is set at the position of the point, the machining coordinate system is still consistent with a machine tool coordinate system, but the R-Test instrument measurement coordinate system is inconsistent with the machining coordinate system;
step 2: starting from the origin, respectively driving the main shaft calibration ball to move in the X, Y direction of the machining coordinate system1、l2mm; respectively obtaining readings of the displacement sensors
、
；
And step 3: establishing a conversion relation between a measurement coordinate system and a processing coordinate system of the original R-Test instrument by using the following formula:
wherein the content of the first and second substances,
and 4, step 4: then the main shaft end calibration ball is driven to move to the set verification point position
Step S4.1 is substituted to complete the verification point vector
The calculation of (2):
if it is
Otherwise, the step S2 and the step S3 are continued, and the number of calibration points is increased, thereby improving the calibration precision.
To better implement the present invention, further, in the matrix equation established in the step S3.2, when the displacement sensor is a laser displacement sensor, L = R.
In order to better implement the invention, the calibration ball for the R-Test instrument is used with the R-Test instrument and has a diameter of 22 mm.
The invention has the following beneficial effects:
1. the invention provides a displacement sensor vector calibration method for an R-test instrument, which solves the difficult problem of the attitude calibration of a displacement sensor for the R-test instrument, including but not limited to a ball head displacement sensor and a laser displacement sensor, and has the fundamental reason that the displacement of the ball head displacement sensor or the laser displacement sensor shows nonlinear displacement change along with the detection position, and the traditional scheme utilizes an intelligent algorithm to solve.
2. The displacement sensor vector calibration method for the R-test instrument provided by the invention realizes accurate measurement of the micro-displacement change of the calibration ball, and after one-time calibration is finished, the verification method adopting the step S4 still has higher precision in subsequent actual measurement, thereby avoiding repeated calibration, improving the detection efficiency and being particularly convenient for automatic measurement.
Drawings
FIG. 1 is a flow chart of the present invention for calibrating a displacement sensor in an R-test instrument;
FIG. 2 is a model diagram of the displacement sensor of the present invention as a ball head displacement sensor;
FIG. 3 is a model diagram of the displacement sensor of the present invention as a laser displacement sensor;
FIG. 4 is a schematic diagram showing a positional relationship between a ball head displacement sensor and a calibration ball;
FIG. 5 is a schematic diagram showing the positional relationship between the laser displacement sensor and the calibration ball;
the device comprises a base, a calibration ball, a displacement sensor and a control unit, wherein the base comprises a base, a calibration ball and a displacement sensor, and the calibration ball is arranged on the base, and the displacement sensor is arranged on the base, wherein the calibration ball is arranged on the base, and the displacement sensor is arranged on the displacement sensor.
Detailed Description
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it should be understood that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments, and therefore should not be considered as a limitation to the scope of protection. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
In the description of the present invention, it is to be noted that, unless otherwise explicitly specified or limited, the terms "disposed," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Example 1:
the invention provides a vector calibration method of a displacement sensor 2 for an R-test instrument, which comprises the following steps as shown in figure 1:
step S1: calibration preparation, namely installing an R-Test instrument on a machine tool workbench, determining a machining coordinate system and an R-Test instrument measurement coordinate system, and simultaneously recording the displacement value of the displacement sensor 2;
step S2: constructing a posture calibration model of the displacement sensor 2, setting an axial direction vector of the displacement sensor 2, and establishing a mathematical model between the spherical center coordinates of the displacement sensor 2 and the calibration ball 1;
step S3: solving a vector equation set of the displacement sensor 2, and solving the vector of the displacement sensor 2 in the axial direction based on a hyperstatic least square method according to an expansion form of the vector equation set;
step S4: and (4) calibration verification, namely constructing a reverse solution model of the spherical center coordinates of the calibration ball 1 according to the posture calibration model of the displacement sensor 2 constructed in the step S2, and completing the conversion and verification of the spherical center coordinates of the calibration ball 1 by combining different installation modes of the R-Test instrument.
The working principle is as follows: the displacement sensor 2 vector calibration method for the R-test instrument provided by the invention starts from a model mechanism, does not need complicated intelligent algorithm solution, solves the problem of posture calibration of the displacement sensor 2 for the R-test instrument, including but not limited to a ball head displacement sensor and a laser displacement sensor, has the advantages of simple process and quick calculation, improves the detection efficiency and is convenient for implementing automatic measurement.
Example 2:
in this embodiment, on the basis of embodiment 1, as shown in fig. 2 and fig. 4, calibration of the calibration ball 1 is completed by using the ball head displacement sensor 2.
The working principle is as follows: the structural model of the R-Test instrument is shown in FIG. 2, and mainly comprises 3 ball head displacement sensors 2 and a calibration ball 1 which are uniformly distributed. And calibrating the posture of the ball head displacement sensor 2 according to the space geometric relation between the center of the calibration ball 1 and the ball head displacement sensor 2.
The specific implementation steps are as follows:
step S1: calibration preparation, namely installing an R-Test instrument on a machine tool workbench, determining a machining coordinate system and an R-Test instrument measurement coordinate system, and simultaneously recording the displacement value of the ball head displacement sensor 2;
step S2: constructing a posture calibration model of the ball head displacement sensor 2, setting an axial direction vector of the ball head displacement sensor 2, and establishing a mathematical model between the ball head displacement sensor 2 and a spherical center coordinate of the calibration ball 1;
step S3: solving a vector equation set of the ball head displacement sensor 2, and solving the axial direction vector of the ball head displacement sensor 2 based on a hyperstatic least square method according to an expansion form of the vector equation set;
step S4: and (4) calibration verification, namely constructing a calibration ball 1 spherical center coordinate inverse solution model according to the ball head displacement sensor 2 posture calibration model constructed in the step S2, and completing the conversion and verification of the spherical center coordinate of the calibration ball 1 by combining different installation modes of the R-Test instrument.
The step S1 specifically includes the following steps:
step S1.1: clamping the calibration ball 1 on a machine tool spindle;
step S1.2: installing an R-Test instrument on a machine tool workbench;
step S1.3: calibration balls 1 and R-After the Test instrument is installed, the calibration ball 1 at the main shaft end is moved to the position right above the R-Test instrument, as shown in FIG. 2, V1、V2、V3The vector of the axial direction of the 3 ball head displacement sensors 2 is the attitude vector of the sensors. The calibration aims to accurately calculate the attitude vector of the sensor and realize the conversion of the reading of the sensor to the coordinates of the sphere center;
step S1.4: slowly moving the calibration ball 1 in the Z direction to enable the center of the calibration ball 1 to be located at the intersection point of the axes of the three ball head displacement sensors 2 in the R-Test instrument, enabling the displacement values of the three ball head displacement sensors 2 to be consistent, and recording the displacement values of the three ball head displacement sensors 2 as di(i=1,2,3)；
Step S1.5: determining X, Y, Z coordinates of the current machine tool coordinate system at the end of the numerical control machine tool as machining coordinate system coordinates, and simultaneously reading d in software of an R-Test instrumentiSet as the origin reading d0And the intersection point of the axes of the three ball head displacement sensors 2 is determined as the origin of the measurement coordinate system of the R-Test instrument, so that the directions of the measurement coordinate system of the R-Test instrument, the processing coordinate system and the machine tool coordinate system are consistent in the calibration state.
In order to better implement the present invention, further, the specific steps of constructing the ball head displacement sensor 2 attitude calibration model in step S2 include:
step S2.1: the axial direction vector of the ball head displacement sensor 2 is expressed as follows in an R-Test instrument measurement coordinate system:
step S2.2: according to the position of the center of the calibration ball 1 at the intersection point of the axes of the three ball head displacement sensors 2 in the R-Test instrument described in step S1.1, the center of the calibration ball 1 at the center positions of the 3 ball head displacement sensors 2 can be obtained, and in the measurement coordinate system of the R-Test instrument, the initial coordinate of the center of the ball surface at the top end of the ball head displacement sensor 2 at this time is:
wherein R is the radius of a calibration ball 1, and R is the radius of the spherical surface of a probe of a ball head displacement sensor 2;
step S2.3: sequentially moving the main shaft end calibration ball 1 to different calibration point positions under the machining coordinate system
,
N is the total number of movements, and after each movement is completed, the displacement readings of the 3 ball head displacement sensors 2 are as
The change of the spherical center coordinates of the probe spherical surface of the ball head displacement sensor 2 along with the calibration process is obtained as follows:
wherein the content of the first and second substances,
，dijthe displacement of the ith ball head displacement sensor 2 in the jth movement is shown;
step S2.4: in the calibration process, the ball head displacement sensor 2 and the calibration ball 1 are always kept in a contact state, and the following vector equation set is obtained:
through the position of the calibration point and the combination of the vector equation set, any one ball head displacement sensor 2 in the three ball head displacement sensors 2 can be calibrated.
In order to better implement the present invention, further, the specific steps of solving the vector equation set of the ball head displacement sensor 2 in step S3 are as follows:
step S3.1: expanding the vector equation set:
wherein the content of the first and second substances,
and
the meaning is the same as that in step S2.3;
step S3.2: the system of vector equations in step S3.1 is further expanded to:
since the unit vector of the axial direction vector of each ball head displacement sensor 2 satisfies the principle that the sum of squares is 1, the complementary equation according to the principle that the unit vector satisfies the sum of squares is 1 is expressed as:
let L = R + R, and in combination with the expansion equation and the complementary equation of step S3.2, the vector equation set is rewritten into a matrix form as:
wherein:
from the least squares solution of the hyperstatic equation:
the vector V is an axial vector of the ball head displacement sensor 2, namely an attitude vector of the ball head displacement sensor 2, and comprises all elements of the axial vector of the ball head displacement sensor 2, and the calibration of the three ball head displacement sensors 2 can be completed by repeating the step on each ball head displacement sensor 2;
step S3.3: in step S2.3 and step S2.4, different positions of the calibration point need to be designed
The calibration purpose is achieved, and the setting mode of the calibration points is as follows: the movable range of the X, Y, Z axis is established as a space grid, and boundary points, the middle points of face diagonal lines and the middle points of body diagonal lines on the grid are taken as calibration points, so that the design requirements on the number of the calibration points and the precision of the calibration points can be met.
In order to better implement the present invention, further, the specific steps of the calibration verification of the R-Test instrument in step S4 are as follows:
step S4.1: according to the inverse solution model of the sphere center coordinates of the calibration sphere 1 constructed in the step S2, the vector equation set is re-derived as follows, and the vector equation set is transformed into the following form:
because three ball head displacement sensors 2 are needed to determine the coordinates of the center of the calibration ball 1, the vector equation set in the step S4.1 is rewritten into a matrix form:
wherein:
L=R+r；
and (3) performing operation on the matrix to obtain the spherical center coordinates of the calibration sphere 1:
(Vector)
namely the coordinates (x, y, z) of the center of the calibration ball 1;
step S4.2: and (4) on the basis of the step (S4.1), carrying out the calibration verification process of the R-Test instrument, and verifying the accuracy of the calibration result.
In order to better implement the invention, further, after the calibration verification of the R-Test instrument is completed, the installation form of the instrument is various.
In order to better realize the invention, further, when the verification is carried out under the condition that the installation position of the instrument is not changed, the instrument state is consistent with the calibration state, so that the spindle end calibration ball 1 is directly driven to move to the set verification point position
Software matched with the instrument can automatically read the numerical value d of the ball head displacement sensor 2 after reaching the verification pointkKnowing the current reading d of the ball head displacement sensor 2kThe origin reading d 02 axis vector V of ball head displacement sensori(i =1,2,3), substituting into step S4.1 may complete the verification point vector
Calculating (1);
if it is
Otherwise, the step S2 and the step S3 are continued, and the number of calibration points is increased, thereby improving the calibration precision.
In order to better implement the invention, further, when the mounting position of the instrument is remounted, the posture and calibration of the remounted ball head displacement sensor 2 are changed, and the calibration verification of the instrument specifically comprises the following steps:
step 1: firstly, the main shaft end calibration ball 1 is driven to move to the original point position during calibration, and the reading of the ball head displacement sensor 2 and the reading d can be used0The difference between the two coordinate systems is judged, and meanwhile, a machining coordinate system is set at the position of the point, the machining coordinate system is still consistent with a machine tool coordinate system, but the R-Test instrument measurement coordinate system is inconsistent with the machining coordinate system;
step 2: starting from the origin, the spindle calibration balls 1 are respectively driven to move in the X, Y direction of the machining coordinate system1、l2mm; respectively obtain the readings of the ball head displacement sensor 2
、
；
And step 3: establishing a conversion relation between a measurement coordinate system and a processing coordinate system of the original R-Test instrument by using the following formula:
wherein the content of the first and second substances,
，
，
represents a cross product between two vectors;
and 4, step 4: then the main shaft end calibration ball 1 is driven to move to the set verification point position
Step S4.1 is substituted to complete the verification point vector
The calculation of (2):
if it is
Otherwise, the step S2 and the step S3 are continued, and the number of calibration points is increased, thereby improving the calibration precision.
In order to better implement the invention, the calibration ball 1 for the R-Test instrument is used with the R-Test instrument and has a diameter of 22 mm.
Other parts of this embodiment are the same as any of embodiment 1, and thus are not described again.
Example 3:
in this embodiment, on the basis of any one of the above embodiments 1-2, as shown in fig. 3 and 5, the calibration of the calibration ball 1 is completed by using the laser displacement sensor 2.
The working principle is as follows: the structural model of the R-Test instrument is shown in FIG. 2 and mainly comprises 3 laser displacement sensors 2 and a calibration sphere 1 which are uniformly distributed. And calibrating the posture of the laser displacement sensor 2 according to the space geometric relation between the sphere center of the calibration sphere 1 and the laser displacement sensor 2.
The specific implementation steps are as follows:
step S1: calibration preparation, namely installing an R-Test instrument on a machine tool workbench, determining a processing coordinate system and an R-Test instrument measuring coordinate system, and simultaneously recording the displacement value of the laser displacement sensor 2;
step S2: constructing a posture calibration model of the laser displacement sensor 2, setting an axial direction vector of the laser displacement sensor 2, and establishing a mathematical model between the spherical center coordinates of the laser displacement sensor 2 and the calibration ball 1;
step S3: solving a vector equation set of the laser displacement sensor 2, and solving the vector of the displacement sensor 2 in the axial direction based on a hyperstatic least square method according to an expansion form of the vector equation set;
step S4: and (4) calibration verification, namely constructing a calibration ball 1 spherical center coordinate inverse solution model according to the laser displacement sensor 2 posture calibration model constructed in the step S2, and completing the conversion and verification of the calibration ball 1 spherical center coordinate by combining different installation modes of the R-Test instrument.
The step S1 specifically includes the following steps:
step S1.1: clamping the calibration ball 1 on a machine tool spindle;
step S1.2: installing an R-Test instrument on a machine tool workbench;
step S1.3: after the calibration balls 1 and the R-Test instrument are installed, the calibration balls 1 at the main shaft end are moved to be right above the R-Test instrument, as shown in figure 2, V1、V2、V3The vector of the axial direction of the 3 laser displacement sensors 2, namely the attitude vector of the sensors. The calibration aims to accurately calculate the attitude vector of the sensor and realize the conversion of the reading of the sensor to the coordinates of the sphere center;
step S1.4: slowly moving the calibration ball 1 in the Z direction to enable the center of the calibration ball 1 to be located at the intersection point of the axes of the three laser displacement sensors 2 in the R-Test instrument, enabling the displacement values of the three laser displacement sensors 2 to be consistent, and recording the displacement values of the three laser displacement sensors 2 as di(i=1,2,3)；
Step S1.5: determining X, Y, Z coordinates of the current machine tool coordinate system at the end of the numerical control machine tool as machining coordinate system coordinates, and simultaneously reading d in software of an R-Test instrumentiSet as the origin reading d0And the intersection point of the axes of the three laser displacement sensors 2 is determined as the origin of the measuring coordinate system of the R-Test instrument, so that the directions of the measuring coordinate system of the R-Test instrument, the processing coordinate system and the machine tool coordinate system are consistent in the calibration state.
In order to better implement the present invention, the specific steps of constructing the attitude calibration model of the laser displacement sensor 2 in step S2 include:
step S2.1: the axial direction vector of the laser displacement sensor 2 is expressed as follows in an R-Test instrument measurement coordinate system:
step S2.2: according to the position of the center of the calibration ball 1 at the intersection point of the three laser axes in the R-Test instrument described in step S1.1, the center of the calibration ball 1 at the center positions of the 3 laser displacement sensors 2 can be obtained, and in the measurement coordinate system of the R-Test instrument, the initial coordinates of the center of the spherical surface at the top end of the laser displacement sensor 2 at this time are:
wherein R is the radius of a calibration ball 1, and R is the radius of the spherical surface of a probe of a laser displacement sensor 2;
step S2.3: sequentially moving the main shaft end calibration ball 1 to different calibration point positions under the machining coordinate system
,
N is the total number of movements, and after each movement is completed, the displacement readings of the 3 laser displacement sensors 2 are as
The change of the spherical center coordinates of the probe of the laser displacement sensor 2 along with the calibration process is obtained as follows:
wherein the content of the first and second substances,
，dijindicating the displacement of the ith laser displacement sensor 2 in the jth movement;
step S2.4: in the calibration process, the laser displacement sensor 2 and the calibration ball 1 are always kept in a contact state, and the following vector equation set is obtained:
any one displacement sensor 2 in the three laser displacement sensors 2 can be calibrated by the position of the calibration point and the combination of the vector equation set.
In order to better implement the present invention, further, the specific steps of solving the vector equation set of the laser displacement sensor 2 in step S3 are as follows:
step S3.1: expanding the vector equation set:
wherein the content of the first and second substances,
and
the meaning is the same as that in step S2.3;
step S3.2: the system of vector equations in step S3.1 is further expanded to:
since the unit vector of the axial direction vector of each laser displacement sensor 2 satisfies the principle that the sum of squares is 1, the complementary equation according to the principle that the unit vector satisfies the sum of squares is 1 is expressed as:
assuming L = R, the vector equation set is rewritten into a matrix form by combining the expansion equation and the complementary equation of step S3.2:
wherein:
from the least squares solution of the hyperstatic equation:
the vector V is an axial vector of the laser displacement sensor 2, namely an attitude vector of the laser displacement sensor 2, and comprises all elements of the axial vector of the laser displacement sensor 2, and the calibration of the three laser displacement sensors 2 can be completed by repeating the step on each laser displacement sensor 2;
step S3.3: in step S2.3 and step S2.4, different positions of the calibration point need to be designed
The calibration purpose is achieved, and the setting mode of the calibration points is as follows: the movable range of the X, Y, Z axis is established as a space grid, and boundary points, the middle points of face diagonal lines and the middle points of body diagonal lines on the grid are taken as calibration points, so that the design requirements on the number of the calibration points and the precision of the calibration points can be met.
In order to better implement the present invention, further, the specific steps of the calibration verification of the R-Test instrument in step S4 are as follows:
step S4.1: according to the inverse solution model of the sphere center coordinates of the calibration sphere 1 constructed in the step S2, the vector equation set is re-derived as follows, and the vector equation set is transformed into the following form:
because three laser displacement sensors 2 are arranged to determine the coordinates of the center of the calibration sphere 1, the vector equation set in the step S4.1 is rewritten into a matrix form:
wherein:
L=R；
and (3) performing operation on the matrix to obtain the spherical center coordinates of the calibration sphere 1:
(Vector)
namely the coordinates (x, y, z) of the center of the calibration ball 1;
step S4.2: and (4) on the basis of the step (S4.1), carrying out the calibration verification process of the R-Test instrument, and verifying the accuracy of the calibration result.
In order to better implement the invention, further, after the calibration verification of the R-Test instrument is completed, the installation form of the instrument is various.
In order to better realize the invention, further, when the verification is carried out under the condition that the installation position of the instrument is not changed, the instrument state is consistent with the calibration state, so that the spindle end calibration ball 1 is directly driven to move to the set verification point position
The software matched with the instrument can automatically read the value d of the laser displacement sensor 2 after reaching the verification pointkKnowing the current laser displacement sensor 2 reading dkThe origin reading d 02 axis vector V of laser displacement sensori(i =1,2,3), substituting into step S4.1 may complete the verification point vector
Calculating (1);
if it is
Otherwise, the step S2 and the step S3 are continued, and the number of calibration points is increased, thereby improving the calibration precision.
In order to better implement the invention, further, when the mounting position of the instrument is remounted, the posture and calibration of the remounted laser displacement sensor 2 are changed, and the calibration verification of the instrument specifically comprises the following steps:
step 1: firstly, the main shaft end calibration ball 1 is driven to move to the original point position during calibration, and the reading of the laser displacement sensor 2 and the reading d can be used0The difference between the two coordinate systems is judged, and meanwhile, a machining coordinate system is set at the position of the point, the machining coordinate system is still consistent with a machine tool coordinate system, but the R-Test instrument measurement coordinate system is inconsistent with the machining coordinate system;
step 2: starting from the origin, the spindle calibration balls 1 are respectively driven to move in the X, Y direction of the machining coordinate system1、l2mm; respectively obtain the readings of the laser displacement sensor 2
、
；
And step 3: establishing a conversion relation between a measurement coordinate system and a processing coordinate system of the original R-Test instrument by using the following formula:
wherein the content of the first and second substances,
and 4, step 4: then the main shaft end calibration ball 1 is driven to move to the set verification point position
Step S4.1 is substituted into, and the process is finishedPaired verification point vectors
The calculation of (2):
if it is
Otherwise, the step S2 and the step S3 are continued, and the number of calibration points is increased, thereby improving the calibration precision.
In order to better implement the invention, the calibration ball 1 for the R-Test instrument is used with the R-Test instrument and has a diameter of 22 mm.
Other parts of this embodiment are the same as any of embodiments 1-2 described above, and thus are not described again.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and all simple modifications and equivalent variations of the above embodiments according to the technical spirit of the present invention are included in the scope of the present invention.
Claims (9)
1. A displacement sensor vector calibration method for an R-test instrument is characterized by comprising the following steps:
step S1: calibration preparation, namely installing an R-Test instrument and a calibration ball (1) on a machine tool, determining a machining coordinate system and an R-Test instrument measurement coordinate system, moving the calibration ball (1) under the machining coordinate system and the R-Test instrument measurement coordinate system, measuring the displacement of the calibration ball (1) through a displacement sensor (2) on the R-Test instrument, and recording the measured displacement value;
step S2: constructing a posture calibration model of the displacement sensor (2), setting an axial direction vector of the displacement sensor (2), and establishing a mathematical model between the spherical center coordinates of the displacement sensor (2) and the calibration ball (1);
step S3: solving a vector equation set of the displacement sensor (2), and completing the solution of the vector in the axial direction of the displacement sensor (2) based on a hyperstatic least square method according to the expansion form of the vector equation set;
step S4: and (4) calibration verification, namely constructing a sphere center coordinate inverse solution model of the calibration sphere (1) according to the posture calibration model of the displacement sensor (2) constructed in the step S2 to finish the conversion and verification of the sphere center coordinate of the calibration sphere (1).
2. The method for calibrating the vector of the displacement sensor for the R-test instrument as claimed in claim 1, wherein the calibration preparation in step S1 comprises the following specific steps:
step S1.1: clamping a calibration ball (1) on a machine tool spindle;
step S1.2: installing an R-Test instrument on a machine tool workbench;
step S1.3: after the calibration ball (1) and the R-Test instrument are installed, moving the calibration ball (1) at the main shaft end to be right above the R-Test instrument;
step S1.4: slowly moving the calibration ball (1) in the Z direction to enable the center of the calibration ball (1) to be located at the intersection point of the axes of the three displacement sensors (2) in the R-Test instrument, enabling the displacement values of the three displacement sensors (2) to be consistent, and recording the displacement values of the three displacement sensors (2) as di(i=1,2,3)；
Step S1.5: determining X, Y, Z coordinates of the current machine tool coordinate system at the end of the numerical control machine tool as machining coordinate system coordinates, and simultaneously reading d in software of an R-Test instrumentiSet as the origin reading d0And the intersection point of the axes of the three displacement sensors (2) is determined as the origin of the measurement coordinate system of the R-Test instrument, so that the directions of the measurement coordinate system of the R-Test instrument, the processing coordinate system and the machine tool coordinate system are consistent in a calibration state.
3. The method for calibrating the displacement sensor vector for the R-test instrument as claimed in claim 2, wherein the step S2 of constructing the attitude calibration model of the displacement sensor (2) comprises the following specific steps:
step S2.1: and expressing the axial direction vector of the displacement sensor (2) in an R-Test instrument measurement coordinate system as follows:
wherein, ViThe axial direction vector of the displacement sensor (2) in an R-Test instrument measuring coordinate system is shown, T is the transposition of the vector, i represents the ith displacement sensor (2), ui，vi，wiRepresenting axial vectors V of three displacement sensors (2)iMeasuring space coordinates of u, v and w directions in a coordinate system by using an R-Test instrument;
step S2.2: according to the step S1.1, the center of the calibration ball (1) is located at the intersection point of the axes of the three displacement sensors (2) in the R-Test instrument, the center of the calibration ball (1) is located at the center of the three displacement sensors (2), and under the measurement coordinate system of the R-Test instrument, the initial coordinate of the center of the spherical surface at the top end of the displacement sensor (2) is as follows:
wherein, Pi0Is the initial coordinate of the spherical center of the top of the displacement sensor (2), T is the transposition of the vector, i represents the ith displacement sensor (2), ui，vi，wiRepresenting axial vectors V of three displacement sensors (2)iMeasuring space coordinates of u, v and w directions in a coordinate system by using an R-Test instrument, wherein R is the radius of a calibration ball (1), and R is the radius of a probe spherical surface of a displacement sensor (2);
step S2.3: sequentially moving the main shaft end calibration ball (1) to different calibration point positions under a processing coordinate system
,
N is the total number of movements, and after each movement is completed, the displacement readings of 3 displacement sensors (2) are
And the change of the spherical center coordinates of the probe spherical surface of the displacement sensor (2) along with the calibration process is obtained as follows:
wherein, PijThe spherical center coordinate of the probe of the displacement sensor (2) is the displacement changed along with the calibration process, dijIndicating the displacement of the ith displacement sensor (2) in the jth movement,
represents the displacement readings, V, of 3 displacement sensors (2)iThe axial direction vector of the displacement sensor (2) in an R-Test instrument measuring coordinate system is represented by i, i represents the ith displacement sensor (2), and j represents the movement times of the displacement sensor (2);
step S2.4: during the calibration, the displacement sensor (2) and the calibration ball (1) are always kept in contact state, and the following vector equation system is obtained:
wherein, OjTo mark the point position, PijIs the position of the spherical center coordinate of the probe spherical surface of the displacement sensor (2) changing along with the calibration processMoving, wherein R is the radius of a calibration sphere, R is the radius of the probe spherical surface of the displacement sensor (2), i represents the ith displacement sensor (2), and j represents the moving times of the displacement sensor (2);
and through the position of the calibration point and the combination of the vector equation set, any one displacement sensor (2) in the three displacement sensors (2) can be calibrated.
4. The vector calibration method for the displacement sensor of the R-test instrument as claimed in claim 3, wherein the specific steps of the step S3 are as follows:
step S3.1: expanding the vector equation set:
wherein the content of the first and second substances,
represents the displacement readings, x, of 3 displacement sensors (2)j，yj，zjFor indexing the point position OjR is the radius of the calibration sphere, R is the radius of the probe spherical surface of the displacement sensor (2), i represents the ith displacement sensor (2), j represents the moving times of the displacement sensor (2), ui，vi，wiRepresenting axial vectors V of three displacement sensors (2)iMeasuring space coordinates of u, v and w directions in a coordinate system by using an R-Test instrument;
step S3.2: the system of vector equations in step S3.1 is further expanded to:
wherein the content of the first and second substances,
representsDisplacement reading, x, of 3 displacement sensors (2)j，yj，zjFor indexing the point position OjR is the radius of the calibration sphere, R is the radius of the probe spherical surface of the displacement sensor (2), i represents the ith displacement sensor (2), j represents the moving times of the displacement sensor (2), ui，vi，wiRepresenting axial vectors V of three displacement sensors (2)iMeasuring space coordinates of u, v and w directions in a coordinate system by using an R-Test instrument;
since the unit vector of the axial direction vector of each displacement sensor (2) satisfies the principle that the sum of squares is 1, the complementary equation according to the principle that the unit vector satisfies the sum of squares is 1 is:
wherein i represents the i-th displacement sensor (2), ui，vi，wiRepresenting axial vectors V of three displacement sensors (2)iMeasuring space coordinates of u, v and w directions in a coordinate system by using an R-Test instrument;
let L = R + R, and in combination with the expansion equation and the complementary equation of step S3.2, the vector equation set is rewritten into a matrix form as:
wherein:
the vector V is expressed as:
wherein the vector V is an axial direction vector of the displacement sensor (2), namely an attitude vector of the displacement sensor (2), and the vector V comprises all elements of the axial direction vectors of the three displacement sensors (2), namely the vector V can represent the vector V1、V2、V3Repeating the step S3.2 on each displacement sensor (2) in the three displacement sensors (2) to finish the calibration of the three displacement sensors (2), wherein L is the distance between the center of the calibration ball (1) and the center of the ball head contacted by the displacement sensor (2);
step S3.3: in step S2.3 and step S2.4, different positions of the calibration point need to be designed
The calibration is carried out, and the setting mode of the calibration point is as follows: the movable range of the X, Y, Z axis is established as a space grid, and boundary points, the middle points of face diagonal lines and the middle points of body diagonal lines on the grid are taken as calibration points, so that the design requirements on the number of the calibration points and the precision of the calibration points can be met.
5. The vector calibration method for the displacement sensor of the R-test instrument as claimed in claim 3, wherein the specific steps of the step S4 are as follows:
step S4.1: according to the step S2, constructing the sphere center coordinate inverse solution model of the calibration sphere (1), re-deriving the vector equation set as follows, and transforming the vector equation set into the form as follows:
wherein i represents the i-th displacement sensor (2), ui，vi，wiRepresenting axial vectors V of three displacement sensors (2)iMeasuring the space coordinates of u, v and w directions in a coordinate system by an R-Test instrument,
represents the displacement readings, x, of 3 displacement sensors (2)j，yj，zjFor indexing the point position OjR is the radius of the calibration sphere, and R is the radius of the probe spherical surface of the displacement sensor (2);
because three displacement sensors (2) are arranged to determine the sphere center coordinates of the calibration sphere (1), the vector equation set in the step S4.1 is rewritten into a matrix form:
wherein:
wherein L = R + R, i represents the i-th displacement sensor (2), u1，v1，w1Representing the axial vector V of the first displacement sensor (2)1In the R-Test instrument measurement coordinate system, three of u, v and wSpatial coordinates of direction, u2，v2，w2Represents the axial vector V of the second displacement sensor (2)2In the R-Test instrument, the spatial coordinates of u, v and w in three directions, u3，v3，w3Represents the axial direction vector V of the third displacement sensor (2)3Measuring the space coordinates of u, v and w directions in a coordinate system by an R-Test instrument,
representing the displacement reading of the first displacement sensor (2),
representing the displacement reading of the second displacement sensor (2),
represents the displacement reading, x, of a third displacement sensor (2)j，yj，zjFor indexing the point position OjR is the radius of the calibration sphere, and R is the radius of the probe spherical surface of the displacement sensor (2)
The spherical center coordinates of the calibration sphere (1) can be obtained by performing operation on the matrix:
(Vector)
namely the coordinates (x, y, z) of the center of the calibration ball (1);
step S4.2: and (4) on the basis of the step (S4.1), carrying out the calibration verification process of the R-Test instrument, and verifying the accuracy of the calibration result.
6. The method for calibrating the vector of the displacement sensor used for the R-test instrument as recited in claim 5, wherein the step S4.1 comprises the following specific steps:
when verification is carried out under the condition that the installation position of the R-test instrument is not changed, the state of the R-test instrument is consistent with the calibration state, and the main shaft end calibration ball (1) is driven to move to the set verification point position
Software matched with the R-test instrument can automatically read the numerical value d of the displacement sensor (2) after reaching the verification pointkKnowing the current displacement sensor (2) reading dkThe origin reading d0The axial vector V of the displacement sensor (2)i(i =1,2,3), substituting into step S4.1 may complete the verification point vector
Calculating (1);
if it is
Otherwise, the step S2 and the step S3 are continued, and the number of calibration points is increased, thereby improving the calibration precision.
7. The method for calibrating the displacement sensor vector for the R-test instrument as claimed in claim 5, wherein when the mounting position of the R-test instrument is remounted, the posture and calibration of the remounted displacement sensor (2) are changed, and the step S4.1 specifically comprises the following steps:
step S4.1.1: firstly, the main shaft end calibration ball (1) is driven to move to the original point position during calibration, and the reading of the displacement sensor (2) and the reading d can be used0The difference between the two coordinate systems is judged, and meanwhile, the position of the point is set as a machining coordinate system which is still consistent with a machine tool coordinate system, but the R-Test instrument measurement coordinate system is inconsistent with the machining coordinate system;
step S4.1.2: starting from the origin, the main shaft calibration balls (1) are respectively driven to move in the X, Y direction of a processing coordinate system1、l2(ii) a Respectively obtain the readings of the displacement sensors (2)
、
；
Step S4.1.3: establishing a conversion relation between a measurement coordinate system and a processing coordinate system of the original R-Test instrument by using the following formula:
wherein the content of the first and second substances,
wherein the content of the first and second substances,
represents T1、T2Cross-product between two vectors, superscript T representing the transpose of the vector, l1Representing the distance of movement of the calibration ball of the spindle in the X-direction of the machining coordinate system, l2Represents the moving distance of the main shaft calibration ball along the Y direction of the processing coordinate system,
the moving distance of the main shaft calibration ball along the X direction of the processing coordinate system is represented as l1The reading of the time-shift sensor (2),
representing the calibrated ball edge of the main shaftThe moving distance in the Y direction of the work coordinate system is l2Reading of the time displacement sensor (2);
step S4.1.4: then the main shaft end calibration ball (1) is driven to move to the set verification point position
Step S4.1 is substituted to complete the verification point vector
The calculation of (2):
if it is
Otherwise, the step S2 and the step S3 are continued, and the number of calibration points is increased, thereby improving the calibration precision.
8. The method for calibrating the displacement sensor vector for the R-test instrument as recited in claim 4, wherein in the matrix equation established in the step S3.2, when the displacement sensor (2) is a laser displacement sensor, L = R.
9. The method for calibrating the vector of the displacement sensor for the R-Test instrument is characterized in that the calibration ball (1) for the R-Test instrument is matched with the R-Test instrument and has the diameter of 22 mm.
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