CN109032070B - Non-contact R-test measuring instrument calibration method adopting eddy current displacement sensor - Google Patents
Non-contact R-test measuring instrument calibration method adopting eddy current displacement sensor Download PDFInfo
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Abstract
The invention discloses a non-contact R-test measuring instrument calibration method adopting an eddy current displacement sensor, which comprises the steps of calibrating a measuring coordinate system and calibrating a displacement sensor plane surface. Installing a measuring ball on a machine tool main shaft, placing the bottom surface of a measuring instrument on a machine tool workbench, moving the main shaft to enable the center of the measuring ball to be approximately positioned at the intersection point of the axes of three displacement sensors, calibrating the origin of a measuring coordinate system of an R-test measuring instrument, and taking the direction of the machine tool coordinate system as the direction of the measuring coordinate system; and moving the main shaft to enable the ball head to move to different coordinate points, and completing calibration of the sensor sensing plane of the non-contact R-test measuring instrument according to the distance from each coordinate point to the sensor sensing plane. The invention can greatly reduce the influence of the installation error of the non-contact R-test measuring instrument on the measuring precision during the processing and the assembly and on the machine tool, thereby reducing the manufacturing and using cost of the instrument and improving the measuring precision and the measuring efficiency.
Description
Technical Field
The invention relates to the technical field of numerical control machine tool error measurement, in particular to a non-contact type R-test measuring instrument calibration method adopting an eddy current displacement sensor.
Background
Along with the improvement of machining precision, the method is increasingly important for measuring the geometric error of the five-axis numerical control machine tool, and the currently commonly adopted measuring instruments are a ball rod instrument and a laser interferometer aiming at measuring the geometric error of a rotating shaft of the five-axis numerical control machine tool. However, these measuring instruments are not dedicated to error measurement of the rotating shaft, and have disadvantages of low efficiency, difficulty in eliminating mounting errors, and the like. Compared with the defects of the instrument, the R-test measuring instrument has the advantages of simple structure, high measuring efficiency and the like, and can better meet the requirement of measuring the geometric error of the rotating shaft of the five-axis numerical control machine tool. FIDIA, IBS and other companies have already commercialized corresponding products, and have obtained better application in the industry.
The R-test measuring instrument mainly adopts two measuring modes, namely measuring the center coordinates of the center ball by a contact type displacement sensor or a non-contact type displacement sensor. Most of the existing research on R-test measuring instruments focuses on contact type measuring modes, and Liu Da Wei, Li Bright and the like put forward the measuring principle of the R-test instrument adopting a contact type displacement sensor, and the structure of the R-test instrument is optimized and analyzed. The Bringmann B, the Ibaraki S and the like analyze the error identification theory of the rotating shaft of the five-axis numerical control machine tool by using an R-test instrument of a contact type displacement sensor, and verify the effectiveness of the equipment by using corresponding experiments and simulation. Li J proposes an R-test instrument using a non-contact displacement sensor and analyzes the identification algorithm of the device. The contact type R-test measuring instrument has a simple measuring algorithm, the deviation of the installation position of the sensor cannot influence the measuring result, but the reading sensitivity of the sensor is not high due to the problem of a mechanical structure, and meanwhile, the contact abrasion also influences the measuring precision to a certain extent. The non-contact R-test measuring instrument can avoid measuring errors caused by measuring abrasion, can measure under the condition that the main shaft rotates at a high speed, and has better measuring sensitivity and stability. But the influence of the structure processing and assembly of the non-contact measuring instrument on the measuring precision is great, and the difficulty in improving the precision of the instrument is great. Furthermore, due to the limitations of the measurement site, it is difficult to achieve pre-calibrated mounting accuracy when the instrument is mounted on a machine tool. Therefore, there is a need for a field calibration method (including calibration of a measurement coordinate system, calibration of a sensor sensing plane in the measurement coordinate system, and calibration of a center of a sensing plane in the measurement coordinate system), which can reduce the requirements for processing and assembling the structure of the non-contact measuring instrument and field installation on the premise of ensuring the precision of the measuring instrument.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a calibration method for a non-contact R-test measuring instrument, which can greatly reduce the influence of the installation error of the non-contact R-test measuring instrument on the measurement precision during the process assembly and on the machine tool, thereby reducing the manufacturing and using costs of the instrument and improving the measurement efficiency. The technical scheme is as follows:
a calibration method of a non-contact R-test measuring instrument adopting an eddy current displacement sensor comprises the following steps;
step 1: calibrating a measurement coordinate system of the non-contact R-test measuring instrument:
installing a measuring ball on a machine tool main shaft, placing the bottom surface of a measuring instrument on a machine tool workbench, moving the main shaft to enable the center of the measuring ball to be approximately positioned at the intersection point position of the axes of the 3 eddy current displacement sensors, establishing a measuring coordinate system by taking the center of the measuring ball at the moment as an original point, and enabling the directions of coordinate axes to be consistent with the directions of a machine tool coordinate system;
step 2: calibrating the induction plane of the eddy current displacement sensor of the non-contact R-test measuring instrument:
the radius of the sensor end is denoted as RProbeRadius of the measuring ball is RBall with ball-shaped section；
a) When the induced voltage variation generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is negligible, the equation of the induced voltage characteristic curve of the sensor is as follows:
wherein, UiTo induce a voltage, LiFor measuring the distance, k, from the centre of the sphere to the sensing plane of the ith sensori、mi、qiInducing voltage characteristic parameters for the sensor (all constants provided by the sensor manufacturer);
the induction plane equation of the sensor 1 is set as a under the measurement coordinate system1x+b1y+c1z+d1＝0；
Operating the machine tool, moving the spindle to move the ball head to 4 different coordinate points Pj(xj,yj,zj)，j＝1,2,3,4；PjDistance L to the sensing plane of the sensor 11,jAccording to the induced voltage U of the sensor 1 at the moment1,jAnd the above formula is converted, namely:
the induction plane parameter a of the sensor 1 is obtained through the equation set1、b1、c1、d1A value of (d); obtaining plane equation coefficients of the induction planes of the other two sensors under the measurement coordinate system in the same way;
further, when the variation of induced voltage generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is negligible, in the solving process of the equation parameters of the induced plane, the solution of the equation set is converted into an optimization problem by adopting a differential evolution algorithm, and the following nonlinear equation is constructed:
according to the above formula, the objective function is set as:
the closer the value of the objective function is to zero, the more accurate the solution of the above non-linear equation.
b) When the induced voltage change generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is not negligible, the equation of the induced voltage curve of the sensor is as follows:
wherein, UiIs the induced voltage of the ith sensor, LiFor measuring the distance from the centre of the sphere to the sensing plane of the ith sensor, ti、ki、mi、ni、qiInducing voltage characteristic parameters for the sensor (all constants provided by the sensor manufacturer);
the plane equation of the sensor 1 is set as a under the measurement coordinate system1x+b1y+c1z+d1Moving the spindle to 0The ball head moves to 12 different coordinate points P under the measurement coordinate systemj(xj,yj,zj)，j＝1,…,12；
According to the distance equation and the Pythagorean theorem from the point to the plane, the following equation set is obtained by combining the induction voltage characteristic curve equation of the sensor 1:
the system of equations above yields the sensor 1 sensing plane parameter a1、b1、c1、d1And sensing the coordinates (x) of the center of the circle of the plane1-0、y1-0、z1-0) (ii) a In the same way, the induction plane parameters and the circle center coordinates of the induction planes of the other two sensors can be obtained.
Further, when the induced voltage variation generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is not negligible, in the solving process of the equation parameters of the induction plane, the differential evolution algorithm is adopted to convert the solution of the equation set into the optimization problem, and the following nonlinear equation is constructed according to the distance formula from the point to the plane and the characteristic curve equation of the induced voltage of the sensor at the moment:
fj(a1,b1,c1,d1)＝(xj-x1-0)2+(yj-y1-0)2+(zj-z1-0)2-r1-j 2-L1-j 2j＝1,...,12
according to the above formula, the objective function is set as:
the closer the value of the objective function is to zero, the more accurate the solution of the above non-linear equation.
The invention has the beneficial effects that: the invention aims at the non-contact R-test five-axis numerical control machine tool rotating shaft error measuring instrument, and the designed instrument calibration method can greatly reduce the influence of the installation error of the non-contact R-test measuring instrument on the processing assembly and the machine tool on the measuring precision, thereby reducing the manufacturing and using cost of the instrument, improving the measuring efficiency, and simultaneously, calibrating the instrument per se regularly can better ensure the measuring precision of the instrument.
Drawings
FIG. 1 is a structural model diagram of a non-contact R-test measuring instrument using an eddy current displacement sensor.
Fig. 2 is a schematic diagram of the spatial relationship between the eddy current displacement sensor and the measuring ball.
FIG. 3 is a schematic diagram of the calibration of the sensing plane of the eddy current displacement sensor.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
(1) Structural description of the non-contact R-test measuring instrument:
the structural model of the non-contact R-test measuring instrument is shown in figure 1 and mainly comprises 3 non-contact eddy current displacement sensors and a standard measuring ball which are uniformly distributed. And calculating the coordinate of the center point P of the measuring sphere according to the spatial position relation of the shortest distance between the sensing plane of the sensor and the measuring sphere.
AA in FIG. 11、BB1、CC1Is 3 sensor axes (A)1、B1、C1Is the center point of the sensing plane of 3 sensors, A, B, C is the center point of the bottom end of 3 sensors), the radius of the end of the sensor is RProbeThe radius of the measuring ball is RBall with ball-shaped section. The plane where Δ ABC is located is defined as a reference plane, and the elevation angles (included angles between the sensor axis and the reference plane) of the sensors are both alpha. And establishing a measurement coordinate system, wherein the distance between the origin of the measurement coordinate system and the 3 induction planes is basically consistent, and the XY coordinate plane is parallel to the reference plane.
The spatial relationship between the sensor and the measuring sphere is shown in FIG. 2, and the distance from the center of the measuring sphere to the sensing plane of the ith sensor is set to be LiThe distance from the center of the sphere to the central axis of the sensor is riThe corresponding induced voltage is Ui. According to the induction principle and the calibration test of the sensor, the sensing can be obtainedThe induction voltage characteristic curve equation of the inductor is as follows:
in the formula of UiThe induction voltage value measured by the sensor; r isiIs the distance of the center of sphere from the axis of the sensor; t is ti、ki、mi、ni、qiThe characteristic parameters of the induced voltage of the sensor can be obtained through a calibration test of the sensor or a factory certificate.
According to whether the induced voltage variation generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range can be ignored, the calibration of the sensor induction plane can be divided into the following two conditions:
1) when the variation of induced voltage generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is negligible, namely the influence of the induced voltage characteristic parameters t and n of the sensor on the induced voltage U is negligible, the characteristic parameters t and n can not be considered, and the induced voltage characteristic curve equation of the sensor can be simplified into
2) When the change of the induced voltage generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is not negligible, namely the influence of the induced voltage characteristic parameters t and n of the sensor on the induced voltage U cannot be ignored, otherwise, the influence on the accuracy of the measuring result is large, and the induced voltage characteristic curve of the sensor is expressed by the formula (1).
(2) And (3) calibrating a measurement coordinate system of the non-contact R-test measuring instrument:
before the sensor induction plane coefficient is calibrated, a measurement coordinate system needs to be calibrated. As shown in fig. 1, during calibration, a measuring ball is mounted on a machine tool spindle, and the bottom surface of the measuring instrument is placed on a machine tool workbench. After the equipment is powered on, the main shaft is moved to enable the measuring ball to be approximately positioned at the center position of the 3 sensors (the coordinates can be adjusted by observing the induced voltage of the sensors), a measuring coordinate system is established by taking the center of the ball at the moment as an origin, and the directions of coordinate axes are consistent with the directions of a machine tool coordinate system.
(3) Calibrating the induction plane of the displacement sensor of the non-contact R-test measuring instrument:
the calibration method of the sensor sensing plane is also divided into the following two cases according to whether the induced voltage change generated by the radial deviation of the measuring ball from the sensor axis in the measuring range can be ignored.
1) When the variation of induced voltage generated by the measuring ball radially deviating from the axis of the sensor in the measuring range is negligible, the central deviation r of the ball perpendicular to the axis direction of the sensor does not affect the induced voltage value of the sensor, the influence of the induced voltage characteristic parameters t and n of the sensor on the measuring result is negligible, and only 3 sensor induced plane equation coefficients of the measuring instrument need to be calibrated.
Take the sensing plane of the sensor 1 as an example. As shown in FIG. 3, the induction plane equation of the sensor 1 is set as a under the measurement coordinate system1x+b1y+c1z+d10. Operating the machine tool, moving the spindle to move the ball head to 4 different coordinate points Pj(xj,yj,zj)(j＝1,2,3,4)，PjThe distance to the sensing plane of the sensor 1 can be converted according to the sensor sensing voltage and the formula (2), namely:
the parameter a of the induction plane of the sensor 1 can be obtained through the equation set (3)1、b1、c1、d1The value of (c). The plane equation coefficients of the planes of the other two sensors in the measurement coordinate system can be obtained in the same way.
In the process of solving the induction plane equation parameters, the induction voltage value is an approximate value, and the solved plane equation coefficient is also an approximate value. In order to solve the accuracy of the result, the invention adopts a differential evolution algorithm to convert the solution of the equation set (3) into an optimization problem so as to improve the calibration precision as much as possible.
From equation set (3), the following non-linear equations can be constructed:
according to equation (4), the objective function is set to
Obviously, if equation (4) has a solution, the minimum value of the objective function (5) is zero. In the algorithm, the closer the value of the objective function (5) is to zero, the more accurate the solution of the corresponding equation set (4) is.
The parameters of the differential evolution algorithm adopted by the invention are set as shown in table 1(D ═ 4).
2) When the change of the induced voltage generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is not negligible, the change means that the influence of the induced voltage value of the sensor on the center deviation r of the ball body in the direction perpendicular to the axis of the sensor is large, and the influence of the characteristic parameters t and n of the induced voltage of the sensor on the measuring result cannot be ignored. Not only the induction plane equation coefficients of 3 sensors of the measuring instrument need to be calibrated, but also the circle centers P of 3 induction plane circles need to be calibrated1-0、P2-0And P3-0。
The description will be given taking the sensing plane of the sensor 1 as an example, as shown in fig. 3. The plane equation of the sensor 1 is set as a under the measurement coordinate system1x+b1y+c1z+d10. The ball head is moved to 12 different coordinate points P under the measurement coordinate system by the moving main shaftj(xj,yj,zj) (j-1, … 12). According to the distance equation and the Pythagorean theorem from the point to the plane, the following equation set can be obtained by combining the induction voltage characteristic curve equation of the sensor 1:
the sensor 1 can determine the sensor plane parameter a by equation (6)1、b1、c1、d1And sensing the coordinates (x) of the center of the circle of the plane1-0、y1-0、z1-0). In the same way, the induction plane parameters and the circle center coordinates of the induction planes of the other two sensors can be obtained.
In the process of solving the induction plane equation parameters, the induction voltage value is an approximate value, and the solved plane equation coefficient is also an approximate value. In order to solve the accuracy of the result, the invention also adopts a differential evolution algorithm to convert the solution of the equation set (6) into an optimization problem so as to improve the calibration precision as much as possible. From the point-to-plane distance equation and equation (1), the following nonlinear equation can be constructed:
fj(a1,b1,c1,d1)＝(xj-x1-0)2+(yj-y1-0)2+(zj-z1-0)2-r1-j 2-L1-j 2(j＝1,...,12)(7)
the objective function form is identical to equation (5) (where j is 1,2, …, 12). If equation (7) has a solution, the minimum value of the objective function is zero. In the algorithm, the closer the value of the objective function is to zero, the more accurate the solution of the corresponding equation set (7) is.
The parameters of the differential evolution algorithm adopted by the present invention are set as shown in table 1(D ═ 7).
TABLE 1 differential evolution Algorithm parameter settings
(1) Calibration method verification
A16U eddy current displacement sensor (measuring range is 4mm) of kaman company and a standard measuring ball are selected, a measuring instrument is manufactured and assembled, and the length, the width and the height of the instrument (without the measuring ball) are 170mm, 170mm and 120mm respectively.
When the variation of induced voltage generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is negligible, 4 different ball center positions are obtained by moving the main shaft and are used as the calibration points P1、P2、P3、P4(none of the calibration points can be the origin of the measurement coordinate system), the coordinates of the calibration points and the sensorsThe voltage readings of the devices are shown in table 2. From the data in table 2, the coefficients of the plane of induction equation of each sensor can be solved by a differential evolution algorithm as shown in table 3.
TABLE 2 calibration point coordinates and sensor induced voltage readings with negligible induced voltage change
Note: u shape1＝0.512L1-6.251；U2＝0.501L2-6.062；U3＝0.524L3-6.456。
TABLE 3 sensor plane of induction equation coefficients with negligible induced voltage change
When the variation of the induced voltage generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is not negligible, the main shaft is moved to obtain 12 different ball center positions as the calibration points P1、P2、…、P11And P12(neither index point can be the origin of the measurement coordinate system), the coordinates of the index points and the voltage readings of each sensor are shown in table 4. According to the data in table 4, the equation coefficients of the sensing plane of each sensor and the coordinates of the center of the sensing plane can be solved by a differential evolution algorithm as shown in tables 5 and 6.
TABLE 4 calibration point coordinates and induced voltage readings of each sensor when induced voltage changes are not negligible
Note: u shape1＝0.532L1 0.5+0.065r1 0.5+0.168；U2＝0.526L2 0.5+0.072r2 0.5+0.183；U3＝0.531L3 0.5+0.068r3 0.5+0.168。
TABLE 5 sensor plane of induction equation coefficients for non-negligible induced voltage change
TABLE 6 center coordinates (unit: mm) of sensing plane of sensor when the variation of sensing voltage is not negligible
(2) Sphere center coordinate calculation verification
When the induced voltage variation caused by the radial deviation of the measuring ball from the sensor axis in the measuring range is negligible, 3 different ball center positions are taken as verification points, and the voltage reading of each sensor of the 3 verification points is shown in table 7. The ratio of the center of sphere coordinate calculation result of the R-test measuring instrument using the calibration method to the theoretical coordinate value is shown in Table 8. From the comparison of the data in Table 8, it can be found that the difference between the sphere center coordinates measured by this method and the theoretical coordinates is not more than 0.0001 mm.
TABLE 7 verification points for negligible change in induced Voltage readings (units: V) of each sensor
TABLE 8 comparison of the calculated coordinate values of the verification points with the theoretical coordinate values (unit: mm) when the change in induced voltage is negligible
When the induced voltage variation caused by the radial deviation of the measuring ball from the sensor axis in the measuring range is not negligible, 3 different ball center positions are taken as verification points, and the voltage readings of each sensor of the 3 verification points are shown in table 9. The comparison between the result of the center of sphere coordinate calculation of the R-test measuring instrument using the calibration method and the theoretical coordinate value is shown in Table 10. From the comparison of the data in Table 10, it can be seen that the difference between the spherical center coordinates measured by this method and the theoretical coordinates is not more than 0.00039 mm.
TABLE 9 verification points for non-negligible change in induced Voltage readings (units: V) of each sensor
TABLE 10 comparison of the calculated coordinate values of the verification points with the theoretical coordinate values (unit: mm) when the induced voltage change is not negligible
Claims (3)
1. A non-contact R-test measuring instrument calibration method adopting an eddy current displacement sensor is characterized by comprising the following steps:
step 1: calibrating a measurement coordinate system of the non-contact R-test measuring instrument:
installing a measuring ball on a machine tool main shaft, placing the bottom surface of a measuring instrument on a machine tool workbench, moving the main shaft to enable the center of the measuring ball to be approximately positioned at the intersection point position of the axes of the 3 eddy current displacement sensors, establishing a measuring coordinate system by taking the center of the measuring ball at the moment as an original point, and enabling the directions of coordinate axes to be consistent with the directions of a machine tool coordinate system;
step 2: calibrating the induction plane of the eddy current displacement sensor of the non-contact R-test measuring instrument:
a) when the induced voltage variation generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is negligible, the equation of the induced voltage characteristic curve of the sensor is as follows:
wherein, UiTo induce a voltage, LiFor measuring the distance, k, from the centre of the sphere to the sensing plane of the ith sensori、mi、qiThe characteristic parameters of the induced voltage of the sensor are constants;
the induction plane equation of the sensor 1 is set as a under the measurement coordinate system1x+b1y+c1z+d1＝0；
Operating the machine tool, moving the spindle to move the ball head to 4 different coordinate points Pj(xj,yj,zj)，j＝1,2,3,4；PjDistance L to the sensing plane of the sensor 11,jAccording to the induced voltage U of the sensor 1 at the moment1,jAnd the above formula is converted, namely:
the induction plane parameter a of the sensor 1 is obtained through the equation set1、b1、c1、d1A value of (d); obtaining plane equation coefficients of the induction planes of the other two sensors under the measurement coordinate system in the same way;
b) when the induced voltage variation generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is not negligible, the equation of the induced voltage characteristic curve of the sensor is as follows:
wherein, UiIs the induced voltage of the ith sensor, LiFor measuring the distance from the centre of the sphere to the sensing plane of the ith sensor, ti、ki、mi、ni、qiThe characteristic parameters of the induced voltage of the sensor are constants;
the plane equation of the sensor 1 is set as a under the measurement coordinate system1x+b1y+c1z+d1Moving the spindle to move the ball head to the measurement position12 different coordinate points P under the coordinate systemj(xj,yj,zj)，j＝1,…12；
According to the distance equation and the Pythagorean theorem from the point to the plane, the following equation set is obtained by combining the induction voltage characteristic curve equation of the sensor 1:
the parameter a of the sensing plane of the sensor 1 can be determined by the equation system1、b1、c1、d1And sensing the coordinates (x) of the center of the circle of the plane1-0、y1-0、z1-0) In the same way, the sensing plane parameters and the circle center coordinates of the sensing planes of the other two sensors can be obtained.
2. The method for calibrating the non-contact R-test measuring instrument by using the eddy current displacement sensor as claimed in claim 1, wherein when the variation of induced voltage generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is negligible, in the process of solving the equation parameters of the induced plane, the solution of the above equation set is converted into an optimization problem by using a differential evolution algorithm, and the following nonlinear equation is constructed:
according to the above formula, the objective function is set as:
the closer the value of the objective function is to zero, the more accurate the solution of the above non-linear equation.
3. The method for calibrating the non-contact R-test measuring instrument by using the eddy current displacement sensor as claimed in claim 1, wherein when the induced voltage variation generated by the radial deviation of the measuring ball from the axis of the sensor in the measuring range is not negligible, in the process of solving the equation parameters of the induction plane, the solution of the equation set is converted into an optimization problem by using a differential evolution algorithm, and the following nonlinear equation is constructed according to a point-to-plane distance formula and a characteristic curve equation of the induced voltage of the sensor at the moment:
fj(a1,b1,c1,d1)＝(xj-x1-0)2+(yj-y1-0)2+(zj-z1-0)2-r1-j 2-L1-j 2j＝1,...,12
according to the above formula, the objective function is set as:
the closer the value of the objective function is to zero, the more accurate the solution of the above non-linear equation.
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