CN109032069B - Non-contact R-test measuring instrument sphere center coordinate calculation method adopting eddy current displacement sensor - Google Patents

Non-contact R-test measuring instrument sphere center coordinate calculation method adopting eddy current displacement sensor Download PDF

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CN109032069B
CN109032069B CN201810793830.2A CN201810793830A CN109032069B CN 109032069 B CN109032069 B CN 109032069B CN 201810793830 A CN201810793830 A CN 201810793830A CN 109032069 B CN109032069 B CN 109032069B
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丁国富
江磊
朱绍维
彭炳康
丁国华
张剑
邹益胜
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Chengdu Tianyou Chuangruan Technology Co ltd
Chengdu Aircraft Industrial Group Co Ltd
Southwest Jiaotong University
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Chengdu Aircraft Industrial Group Co Ltd
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    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/401—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for measuring, e.g. calibration and initialisation, measuring workpiece for machining purposes
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses a method for calculating the center coordinates of a non-contact R-test measuring instrument by adopting an eddy current displacement sensor, which is used for calibrating a measuring coordinate system of the non-contact R-test measuring instrument according to the design and measuring characteristics of the non-contact R-test measuring instrument; and solving a coordinate result of the accurate sphere center point in the measurement coordinate system by using a differential evolution algorithm according to an induced voltage characteristic curve equation of the eddy current displacement sensor and an induced plane equation of the sensor. The invention can realize the accurate measurement of the three-dimensional displacement error of the cutter point of the five-axis numerical control machine tool, and has better measurement precision, range and stability.

Description

Non-contact R-test measuring instrument sphere center coordinate calculation method adopting eddy current displacement sensor
Technical Field
The invention relates to the technical field of numerical control machine tool error measurement, in particular to a method for calculating a sphere center coordinate of a non-contact R-test measuring instrument by adopting an eddy current displacement sensor.
Background
Along with the improvement of the machining precision, the method is increasingly important for measuring the geometric error of the five-axis numerical control machine tool, the accurate measurement of the error of the tool point of the machine tool is the key for performing error compensation on the rotating shaft of the five-axis numerical control machine tool so as to improve the machining precision, a special precision measuring instrument and a standard for measuring the geometric error of the rotating shaft of the machine tool are not available, and the currently generally adopted measuring instruments are a ball bar instrument and a laser interferometer. 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 instrument has a simple measurement algorithm, the deviation of the installation position of the sensor cannot influence the measurement result, but the reading sensitivity of the sensor is not high due to the problem of a mechanical structure, and meanwhile, the measurement precision is also influenced to a certain extent by contact abrasion. The non-contact R-test instrument can avoid measurement errors caused by measurement abrasion, can perform measurement under the condition of high-speed rotation of the main shaft, has better measurement sensitivity and stability, but has a complex and incomplete sphere center coordinate measurement algorithm.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a method for calculating a spherical center coordinate of a non-contact R-test measuring instrument, which can accurately measure a three-dimensional run-out error of a tool bit point of a spindle of a machine tool, avoid a measurement error caused by contact wear, perform measurement under a high-speed rotation condition of the spindle, and have a better measurement range and stability. The technical scheme is as follows:
a method for calculating the sphere center coordinate of a non-contact R-test measuring instrument by adopting an eddy current displacement sensor comprises the following steps:
step 1: establishing a measurement coordinate system:
mounting a measuring ball on a machine tool main shaft, placing the bottom surface of a measuring instrument on a machine tool workbench, and moving the main shaft to enable the measuring ball to be approximately positioned at the central position of 3 eddy current displacement sensors; establishing a measurement coordinate system, wherein the distance between the origin of the measurement coordinate system and the sensing plane of the 3 sensors is basically consistent, and the XY coordinate plane is parallel to the reference plane;
step 2: calculating the measurement spherical center coordinate 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 induced voltage characteristic curve equation of the sensor is as follows:
Figure BDA0001735492340000021
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 coefficients of the characteristic curve equation of the induced voltage of the sensor are constants;
the equation for setting the sensing planes of 3 sensors under the measurement coordinate system is as follows:
aix+biy+ciz+di＝0 i＝1,2,3 (2)
according to the distance formula from the point to the plane, the following equation system is constructed by combining the equation (1):
Figure BDA0001735492340000022
obtaining the coordinate of the center point P in the measuring coordinate system through the equation set;
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 characteristic curve of the sensor is as follows:
Figure BDA0001735492340000023
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 coefficients of the characteristic curve equation of the induced voltage of the sensor are constants; r isiThe distance from the center of the sphere to the central axis of the sensor;
the center coordinate of the sensing plane of the ith sensor in the measuring coordinate system is known as (x)i-0，yi-0，zi-0) According to the point to
And (3) constructing the following equation set by combining the distance formula of the plane and the pythagorean theorem and the equations (4) and (2):
Figure BDA0001735492340000024
the coordinates of the center point P in the measurement coordinate system are determined by the system of equations.
Further, in the process of solving the coordinates of the center point P in the measurement coordinate system by the equation (4), in order to ensure the accuracy of the solution result, the following nonlinear equation set is established according to the equation (4), and the solution of the equation set is the center coordinates:
Figure BDA0001735492340000025
the objective function is set as:
Figure BDA0001735492340000031
the closer the value of the objective function is to zero, the more accurate the solution of the above-mentioned system of nonlinear equations.
Furthermore, in the process of solving the coordinates of the center point P in the measurement coordinate system by the equation (5), in order to ensure the accuracy of the solution result, the following non-linear equation set is constructed according to the equation (5), and the solution of the equation set is the center coordinates:
fi(x,y,z)＝(x-xi-0)2+(y-yi-0)2+(z-zi-0)2-ri 2-Li 2＝0 i＝1,2,3 (9)
the objective function is set as:
Figure BDA0001735492340000032
the closer the value of the objective function is to zero, the more accurate the solution of the above-mentioned system of nonlinear equations.
The invention has the beneficial effects that: aiming at the non-contact type R-test five-axis numerical control machine tool rotating shaft error measuring instrument, the designed sphere center coordinate calculation method can finish the accurate measurement of the three-dimensional displacement error of the tool position point of the machine tool spindle, avoid the measurement error generated by contact abrasion, simultaneously can carry out the measurement under the condition of high-speed rotation of the spindle, and has better measurement accuracy, range and stability.
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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.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
The structure of the non-contact R-test measuring instrument adopting the eddy current displacement sensor is described as follows:
the structural model of the non-contact R-test measuring instrument adopting the eddy current displacement sensor is shown in figure 1 and mainly comprises 3 eddy current displacement sensors which are uniformly distributed and a standard measuring ball. 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 eddy current displacement sensor axes (A)1、B1、C1Is the center point of the induction plane of 3 sensors, A, B, C is the center point of the bottom end of 3 sensors), the radius of the end part 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 sensors and the measuring ball is shown in FIG. 2, and the distance from the center of the measuring ball to the sensing plane of the ith sensor is set as 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 experiment of the eddy current displacement sensor, the induction voltage formula of the sensor is as follows:
Figure BDA0001735492340000041
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; k is a radical ofi、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 calculation of the coordinates of the center of the measuring ball can be divided into the following two cases:
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 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 be not considered, and the induced voltage characteristic curve equation of the sensor can be simplified as follows:
Figure BDA0001735492340000042
the simplified solution method for the spherical center coordinates designed in this embodiment is as follows:
in the measurement coordinate system, the equation of the induction planes of the 3 sensors is set as
aix+biy+ciz+di＝0 (i＝1,2,3) (3)
According to the distance formula from the point to the plane, the following equation set can be constructed by combining the following equations:
Figure BDA0001735492340000043
and (4) obtaining the coordinates of the center point P in the measurement coordinate system.
2) 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 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 represented by formula (1).
The method for accurately solving the spherical center coordinates designed in the embodiment is as follows:
in the measurement coordinate system, the center coordinate of the sensing plane of the known ith sensor is (x)i-0,yi-0,zi-0). According to the distance formula from the point to the plane and the Pythagorean theorem, the following equation set can be constructed by combining the formula (1) and the formula (3):
Figure BDA0001735492340000044
and (5) obtaining the coordinates of the center point P in the measurement coordinate system.
And (3) carrying out numerical solution by a differential evolution algorithm:
because the induced voltage values in the equation sets (4) and (5) are approximate values, the conventional equation set solving method may not obtain a more accurate settlement result, or the settlement result may have multiple solutions. In order to ensure the accuracy of the solution result, the invention converts the solution of the equation set into an optimal value solution problem. Compared with the traditional optimization algorithm, the differential evolution algorithm has the characteristics of less calculation time and high robustness while ensuring the calculation precision, so the differential evolution algorithm is adopted to solve the optimal value.
While the differential evolution algorithm is used for solving, the algorithm solving of the sphere center coordinates is also divided into the following two cases:
1) simplified solution of sphere center coordinates
From equation set (4), the following non-linear equation set can be constructed, and the solution of the equation set is the sphere center coordinates.
Figure BDA0001735492340000051
Setting the objective function as
Figure BDA0001735492340000052
It is clear that if the system of equations (6) has a solution, the minimum value of the objective function (7) is zero. In the algorithm, the closer the value of the objective function (7) is to zero, the more accurate the solution of the corresponding equation set (6) is.
The parameters of the differential evolution algorithm adopted by the invention are set as shown in table 1.
2) Exact solution of sphere center coordinates
From equation set (5), the following non-linear equation set can be constructed, and the solution of the equation set is the sphere center coordinates.
fi(x,y,z)＝(x-xi-0)2+(y-yi-0)2+(z-zi-0)2-ri 2-Li 2＝0 (i＝1,2,3) (8)
Setting the objective function as
Figure BDA0001735492340000053
It is clear that if the system of equations (8) has a solution, the minimum value of the objective function (9) is zero. In the algorithm, the closer the value of the objective function (9) is to zero, the more accurate the solution of the corresponding equation set (8) is.
The parameters of the differential evolution algorithm adopted by the invention are set as shown in table 1.
TABLE 1 differential evolution Algorithm parameter settings
Figure BDA0001735492340000054
Figure BDA0001735492340000061
The invention selects a 16U eddy current displacement sensor (measuring range is 4mm) of kaman company and a standard measuring ball to manufacture an R-test measuring instrument, and the length, width and height of the instrument (without the measuring ball) are 170mm, 170mm and 120mm respectively.
(1) Known calibration data
When the variation of the induced voltage generated by the measuring ball deviating from the axis of the sensor in the radial direction in the measuring range is negligible, the coefficients of the calibrated induction plane equation of each sensor are shown in table 2.
TABLE 2 sensor plane of induction equation coefficients
Figure BDA0001735492340000062
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 calibrated induced plane equation coefficients and the plane center coordinates of the sensors are shown in tables 3 and 4.
TABLE 3 sensor plane of induction equation coefficients for non-negligible induced voltage change
Figure BDA0001735492340000063
TABLE 4 center coordinates (unit: mm) of sensing plane of sensor when the variation of sensing voltage is not negligible
Figure BDA0001735492340000064
(2) Sphere center coordinate calculation verification
When the induced voltage variation generated by the radial deviation of the measuring ball from the sensor axis in the measuring range is negligible, 3 different sphere center positions are taken as verification points, and the induced voltage of each sensor of the 3 verification points is shown in table 5. The theoretical coordinates of the 3 validation points in the measured coordinate system are shown on the right hand side of table 6. 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 6. From the comparison of the data in Table 6, 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 5 Induction Voltage (Unit: V) of each sensor at verification point when the variation in induction voltage is negligible
Figure BDA0001735492340000071
TABLE 6 comparison of the calculated coordinate values of the verification points with the theoretical coordinate values (unit: mm) when the induced voltage change is negligible
Figure BDA0001735492340000072
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, 3 different ball center positions are taken as verification points, and the induced voltage of each sensor of the 3 verification points is shown in table 7. The theoretical coordinates of the 3 validation points in the measured coordinate system are shown on the right side of table 8. 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 seen that the difference between the spherical center coordinates measured by this method and the theoretical coordinates was not more than 0.00039 mm.
TABLE 7 Induction Voltage (Unit: V) of each sensor at verification point when the variation in induction voltage is not negligible
Figure BDA0001735492340000073
TABLE 8 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
Figure BDA0001735492340000074

Claims (3)

1. A method for calculating the sphere center coordinate of a non-contact R-test measuring instrument by adopting an eddy current displacement sensor is characterized by comprising the following steps:
step 1: establishing a measurement coordinate system:
mounting a measuring ball on a machine tool main shaft, placing the bottom surface of a measuring instrument on a machine tool workbench, and moving the main shaft to enable the measuring ball to be approximately positioned at the central position of 3 eddy current displacement sensors; establishing a measurement coordinate system, wherein the distance between the origin of the measurement coordinate system and the sensing plane of the 3 sensors is basically consistent, and the XY coordinate plane is parallel to the reference plane;
step 2: calculating the measurement spherical center coordinate 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 induced voltage characteristic curve equation of the sensor is as follows:
Figure FDA0002595631800000011
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 coefficients of the characteristic curve equation of the induced voltage of the sensor are constants;
the equation for setting the sensing planes of 3 sensors under the measurement coordinate system is as follows:
aix+biy+ciz+di＝0 i＝1,2,3 (2)
according to the distance formula from the point to the plane, the following equation system is constructed by combining the equation (1):
Figure FDA0002595631800000012
obtaining the coordinate of the center point P in the measuring coordinate system through the equation set;
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 characteristic curve of the sensor is as follows:
Figure FDA0002595631800000013
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 coefficients of the characteristic curve equation of the induced voltage of the sensor are constants; r isiThe distance from the center of the sphere to the central axis of the sensor;
the center coordinate of the sensing plane of the ith sensor in the measuring coordinate system is known as (x)i-0，yi-0，zi-0) According to the distance formula from the point to the plane and the Pythagorean theorem, the following equation set is constructed by combining the formula (4) and the formula (2):
Figure FDA0002595631800000021
the coordinates of the center point P in the measurement coordinate system are determined by the system of equations.
2. The method for calculating the coordinates of the center of sphere of the non-contact R-test measuring instrument using the eddy current displacement sensor according to claim 1, wherein in the process of solving the coordinates of the center point P in the measuring coordinate system by the equation (4), in order to ensure the accuracy of the solution result, the following non-linear equation set is established according to the equation (4), and the solution of the equation set is the coordinates of the center of sphere:
Figure FDA0002595631800000022
the objective function is set as:
Figure FDA0002595631800000023
the closer the value of the objective function is to zero, the more accurate the solution of the above-mentioned system of nonlinear equations.
3. The method for calculating the coordinates of the center of sphere of the non-contact R-test measuring instrument using the eddy current displacement sensor according to claim 1, wherein in the process of solving the coordinates of the center point P in the measurement coordinate system by the equation (5), in order to ensure the accuracy of the solution result, the following non-linear equation set is constructed according to the equation (5), and the solution of the equation set is the coordinates of the center of sphere:
fi(x,y,z)＝(x-xi-0)2+(y-yi-0)2+(z-zi-0)2-ri 2-Li 2＝0 i＝1,2,3 (9)
the objective function is set as:
Figure FDA0002595631800000024
the closer the value of the objective function is to zero, the more accurate the solution of the above-mentioned system of nonlinear equations.
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