CN109032069A - A kind of contactless R-test measuring instrument sphere centre coordinate calculation method using eddy current displacement sensor - Google Patents
A kind of contactless R-test measuring instrument sphere centre coordinate calculation method using eddy current displacement sensor Download PDFInfo
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/401—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for measuring, e.g. calibration and initialisation, measuring workpiece for machining purposes
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract
The present invention discloses a kind of contactless R-test measuring instrument sphere centre coordinate calculation method using eddy current displacement sensor, for the design and measuring characteristic of contactless R-test measuring instrument, demarcates contactless R-test measuring instrument measurement coordinate system；According to eddy current displacement sensor induced voltage characteristic curve equation and sensor sensing plane equation, coordinate result of the accurate center point in measurement coordinate system is solved using differential evolution algorithm.The precise measurement of the three direction displacement error of five-axle number control machine tool cutter cutter location may be implemented in the present invention, and measurement accuracy, range and stability are more preferable.
Description
Technical field
The present invention relates to NC Machine Error field of measuring technique, specially a kind of using the non-of eddy current displacement sensor
Contact R-test measuring instrument sphere centre coordinate calculation method.
Background technique
With the raising of machining accuracy, also become more and more important to the geometric error measurement of five-axle number control machine tool, for five number of axle
The rotation axis of lathe is controlled, the accurate error for measuring lathe point of a knife point is the key that carry out error compensation to improve its machining accuracy,
And the measurement there has been no dedicated fine measuring instrument and specification, generallyd use at present is measured the geometric error of lathe rotation axis
Instrument is ball bar and laser interferometer.However, these measuring instruments are not fully dedicated to the error measure of rotation axis, and there is effect
Rate is lower, installation error is difficult to the deficiencies of eliminating.Compared to the deficiency of above-mentioned instrument, R-test measuring instrument is simple with structure, surveys
The advantages that amount efficiency is high can preferably meet the geometric error measurement request of five-axle number control machine tool rotation axis.FIDIA, IBS etc.
Company has corresponding commercially produced product, and has in industry obtained preferable application.
R-test measuring instrument mainly uses two kinds of measurement methods, that is, passes through tangent displacement sensor or contactless displacement
Sensor measurement astrosphere sphere centre coordinate.The existing research about R-test measuring instrument is mostly focused on contact type measurement mode,
Liu great Wei, Li Liangliang etc. propose the measuring principle of the R-test instrument using tangent displacement sensor, and to its structure into
Optimization of having gone is analyzed.The application such as Bringmann B, Ibaraki S is using the R-test instrument of tangent displacement sensor to five
The error identification theory of Shaft and NC Machining Test rotary axis of machine tool is analyzed, and with having for the equipment of corresponding experiment and simulating, verifying
Effect property.Li J proposed one kind using the R-test instrument of non-contact displacement transducer, and to the identification algorithm of the equipment into
Analysis is gone.Contact R-Test apparatus measures algorithm is simpler, and sensor mounting location deviation will not be to measurement result structure
At influence, but since mechanical structure problem causes the reading susceptibility of sensor not high, while contact wear is also to a certain extent
Affect measurement accuracy.The measurement error that contactless R-test instrument can generate to avoid measurement abrasion, and can be in main shaft
It is measured under the conditions of high-speed rotation, sensitivity of measurement and stability are more preferable, but sphere centre coordinate Measurement Algorithm is complicated and not yet complete
It is kind.
Summary of the invention
In view of the above-mentioned problems, the purpose of the present invention is to provide the three-dimensional bounces that one kind can complete machine tool chief axis cutter location
The precise measurement of error, and the measurement error that abrasion generates is avoided contact with, while can carry out under the conditions of main shaft high-speed rotation
Measurement, the sphere centre coordinate calculation method of the better contactless R-test measuring instrument of measurement range and stability.Technical solution is such as
Under:
A kind of contactless R-test measuring instrument sphere centre coordinate calculation method using eddy current displacement sensor, including with
Lower step:
Step 1: establish measurement coordinate system:
Measurement ball is mounted on machine tool chief axis, measuring instrument bottom surface is placed on platen, and mobile main shaft makes to measure
Ball is located substantially at the center of 3 eddy current displacement sensors；Establish measurement coordinate system, the sense of origin and 3 sensors
Answer the distance of plane almost the same, XY coordinate surface is parallel with datum level；
Step 2: calculate the measurement sphere centre coordinate of contactless R-test measuring instrument:
A) when measurement ball is radially offset from the variation of induced voltage caused by sensor axis in measurement range can be ignored,
The induced voltage characteristic curve equation of sensor are as follows:
Wherein, UiFor induced voltage, LiDistance for the measurement centre of sphere to i-th of sensor sensing plane, ki、mi、qiTo pass
Sensor induced voltage characteristic curve equation coefficient, is constant；
The equation of 3 sensor sensing planes is divided into measurement coordinate system are as follows:
aix+biy+ciz+di=0 i=1,2,3 (2)
The range formula that plane is arrived according to point constructs following equations group in conjunction with formula (1):
It asks to obtain coordinate of the center point P in measurement coordinate system by equation group；
B) it can not ignore when measurement ball is radially offset from the variation of induced voltage caused by sensor axis in measurement range
When, sensor sensing voltage response equation are as follows:
Wherein, UiFor the induced voltage of i-th of sensor, LiFor the measurement centre of sphere to i-th sensor sensing plane away from
From ti、ki、mi、ni、qiIt is constant for sensor sensing voltage response equation coefficient；riFor the centre of sphere to center sensor
The distance of axis；
It is known in measurement coordinate system, the induction planes central coordinate of circle of i-th of sensor is (xi-0, yi-0, zi-0), according to
Point arrives
The range formula and Pythagorean theorem of plane construct following equations group in conjunction with formula (4) and formula (2):
It asks to obtain coordinate of the center point P in measurement coordinate system by equation group.
Further, center point P is solved in measuring coordinate system during coordinate, in order to guarantee to solve by formula (4)
As a result accuracy builds following Nonlinear System of Equations according to formula (4), and solution of equations is sphere centre coordinate:
If objective function are as follows:
For the value of objective function closer to zero, the solution of above-mentioned Nonlinear System of Equations is more accurate.
Further, center point P is solved during measuring the coordinate in coordinate system by formula (5), in order to guarantee
The accuracy of solving result constructs following Nonlinear System of Equations according to formula (5), and solution of equations is sphere centre coordinate:
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)
If objective function are as follows:
For the value of objective function closer to zero, the solution of above-mentioned Nonlinear System of Equations is more accurate.
The beneficial effects of the present invention are: the present invention is directed to contactless R-test five-axle number control machine tool rotation axis error measure
Instrument, the sphere centre coordinate calculation method of design can complete the precise measurement of the three direction displacement error of machine tool chief axis cutter location, and
The measurement error that abrasion generates is avoided contact with, while can be measured under the conditions of main shaft high-speed rotation, measurement accuracy, range
It is more preferable with stability.
Detailed description of the invention
Fig. 1 is the contactless R-test measuring instrument structural model figure using eddy current displacement sensor.
Fig. 2 is eddy current displacement sensor-measurement spherical space relation schematic diagram.
Specific embodiment
The present invention is described in further details in the following with reference to the drawings and specific embodiments.
Illustrated using the contactless R-test measuring instrument structure of eddy current displacement sensor:
Using the structural model of the contactless R-test measuring instrument of eddy current displacement sensor as shown in Figure 1, main packet
Include equally distributed 3 eddy current displacement sensors and a canonical measure ball.According to sensor sensing plane and measure ball
Shortest distance spatial relation, the coordinate for measuring ball center point P calculate.
AA in Fig. 11、BB1、CC1For 3 eddy current displacement sensor axis (A1、B1、C1For 3 sensor sensing flat circles
Heart point, A, B, C are the bottom end centre point of 3 sensors), sensor end is that radius is RIt visitsInduction planes circle, measure ball
Radius be RBall.Plane is benchmark face where defining Δ ABC, and the sensor elevation angle (angle of sensor axis and datum level) is
α.Measurement coordinate system is established, origin is almost the same at a distance from 3 induction planes, and XY coordinate surface is parallel with datum level.
The spatial relationship of sensor and measurement ball is as shown in Fig. 2, set the measurement ball centre of sphere to i-th sensor sensing plane
Distance is Li, the distance of the centre of sphere to center sensor axis is ri, corresponding induced voltage is Ui.It is sensed according to current vortex displacement
The principle of induction and calibration experiment of device, it is known that the induced voltage formula of sensor are as follows:
U in formulaiThe inductive voltage value measured for sensor；riDeviate the distance of sensor axis for the centre of sphere；ki、mi、ni、qi
For sensor sensing voltage characteristic parameter, it can be tested by transducer calibration or producer's factory certificate obtains.
It is radially offset from the variation of induced voltage caused by sensor axis in measurement range whether can be with according to measurement ball
Ignore, the calculating of measurement ball sphere centre coordinate can be divided into following two situation:
1) when measurement ball is radially offset from the variation of induced voltage caused by sensor axis in measurement range can be ignored,
Influence of the sensor sensing voltage characteristic parameter t and n to induced voltage U is ignored, and can not consider characterisitic parameter t and n, can
By sensor sensing voltage response equation simplification are as follows:
It is as follows that the sphere centre coordinate of the present embodiment design simplifies method for solving:
In measurement coordinate system, if the equation of 3 sensor sensing planes is
aix+biy+ciz+di=0 (i=1,2,3) (3)
The range formula that plane is arrived according to point, can construct following equations group in conjunction with formula:
By equation group (4), coordinate of the center point P in measurement coordinate system can be obtained.
2) it can not ignore when measurement ball is radially offset from the variation of induced voltage caused by sensor axis in measurement range
When, influence of the sensor sensing voltage characteristic parameter t and n to induced voltage U cannot be ignored, otherwise to the precision shadow of measurement result
Sound is larger, and sensor sensing voltage response is formula (1) at this time.
The sphere centre coordinate method for precisely solving of the present embodiment design is as follows:
In measurement coordinate system, it is known that the induction planes central coordinate of circle of i-th of sensor is (xi-0,yi-0,zi-0).According to
Point arrives the range formula and Pythagorean theorem of plane, can construct following equations group in conjunction with formula (1) and formula (3):
By equation group (5), coordinate of the center point P in measurement coordinate system can be obtained.
Differential evolution algorithm numerical solution:
Since the inductive voltage value in equation group (4) and (5) is approximation, conventional solving equations method may
Multiple solutions may be had by being unable to get accurate checkout result or checkout result.In order to guarantee the accuracy of solving result,
Solving equations are converted optimal value Solve problems by the present invention.Since differential evolution algorithm can be compared to traditional optimization algorithm
Guarantee have the calculating time few while computational accuracy, the high feature of robustness, therefore the present invention is solved using differential evolution algorithm
Optimal value.
While being solved using differential evolution algorithm, the algorithm solution of sphere centre coordinate is also classified into following two situation:
1) simplifying for sphere centre coordinate solves
Following Nonlinear System of Equations can be constructed according to equation group (4), solution of equations is sphere centre coordinate.
If objective function is
Obviously, if equation group (6) has solution, the minimum value of objective function (7) is zero.In the algorithm, objective function (7)
Value is closer to zero, then the solution of corresponding equation group (6) is more accurate.
The differential evolution algorithm parameter setting that the present invention uses is as shown in table 1.
2) the accurate solution of sphere centre coordinate
Following Nonlinear System of Equations can be constructed according to equation group (5), solution of equations is sphere centre coordinate.
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)
If objective function is
Obviously, if equation group (8) has solution, the minimum value of objective function (9) is zero.In the algorithm, objective function (9)
Value is closer to zero, then the solution of corresponding equation group (8) is more accurate.
The differential evolution algorithm parameter setting that the present invention uses is as shown in table 1.
1 differential evolution algorithm parameter setting of table
What the present invention selected is the 16U eddy current displacement sensor (range 4mm) of kaman company, canonical measure ball, system
Make R-test measuring instrument, the length, width and height (without measurement ball) of instrument are respectively 170mm, 170mm, 120mm.
(1) nominal data known to
When measurement ball is radially offset from the variation of induced voltage caused by sensor axis in measurement range can be ignored, mark
The coefficient of fixed each sensor sensing plane equation is as shown in table 2.
2 sensor sensing plane equation coefficient of table
When measurement ball is radially offset from the variation of induced voltage caused by sensor axis in measurement range can not ignore,
Each sensor sensing plane equation coefficient and plane central coordinate of circle of calibration are as shown in Table 3 and Table 4.
Sensor sensing plane equation coefficient when the variation of 3 induced voltage of table be can not ignore
Sensor sensing plane central coordinate of circle (unit: mm) when the variation of 4 induced voltage of table be can not ignore
(2) sphere centre coordinate calculates verifying
When measurement ball is radially offset from the variation of induced voltage caused by sensor axis in measurement range can be ignored, take
For 3 different sphere center positions as check post, each sensor sensing voltage of 3 check posts is as shown in table 5.3 check posts exist
The theoretical coordinate in coordinate system is measured as shown in 6 right side of table.Using the sphere centre coordinate meter of the R-test measuring instrument of this scaling method
The comparison for calculating result and theoretical coordinate value is as shown in table 6.From the data comparison of table 6 it can be found that the ball measured by this method
Difference between heart coordinate and theoretical coordinate is no more than 0.0001mm.
Each sensor sensing voltage (unit: V) of check post when the variation of 5 induced voltage of table is negligible
The coordinates computed value and theoretical coordinate value comparison (unit: mm) of check post when the variation of 6 induced voltage of table is negligible
When measurement ball is radially offset from the variation of induced voltage caused by sensor axis in measurement range can not ignore
When, take 3 different sphere center positions as check post, each sensor sensing voltage of 3 check posts is as shown in table 7.3 verifyings
Point is in the theoretical coordinate in measurement coordinate system as shown in 8 right side of table.It is sat using the centre of sphere of the R-test measuring instrument of this scaling method
The comparison for marking calculated result and theoretical coordinate value is as shown in table 8.From the data comparison of table 8 it can be found that being measured by this method
Sphere centre coordinate and theoretical coordinate between difference no more than 0.00039mm.
Each sensor sensing voltage (unit: V) of check post when the variation of 7 induced voltage of table be can not ignore
The coordinates computed value of check post of 8 induced voltage of table variation when can not ignore and the comparison of theoretical coordinate value (unit:
mm)
Claims (3)
1. a kind of contactless R-test measuring instrument sphere centre coordinate calculation method using eddy current displacement sensor, feature exist
In, comprising the following steps:
Step 1: establish measurement coordinate system:
Measurement ball is mounted on machine tool chief axis, measuring instrument bottom surface is placed on platen, and mobile main shaft keeps measurement ball big
Cause the center for being located at 3 eddy current displacement sensors；Measurement coordinate system is established, the induction of origin and 3 sensors is flat
The distance in face is almost the same, and XY coordinate surface is parallel with datum level；
Step 2: calculate the measurement sphere centre coordinate of contactless R-test measuring instrument:
A) when measurement ball is radially offset from the variation of induced voltage caused by sensor axis in measurement range can be ignored, sensing
The induced voltage characteristic curve equation of device are as follows:
Wherein, UiFor induced voltage, LiDistance for the measurement centre of sphere to i-th of sensor sensing plane, ki、mi、qiFor sensor
Induced voltage characteristic curve equation coefficient, is constant；
The equation of 3 sensor sensing planes is divided into measurement coordinate system are as follows:
aix+biy+ciz+di=0 i=1,2,3 (2)
The range formula that plane is arrived according to point constructs following equations group in conjunction with formula (1):
It asks to obtain coordinate of the center point P in measurement coordinate system by equation group；
B) it when measurement ball is radially offset from the variation of induced voltage caused by sensor axis in measurement range can not ignore, passes
Sensor induced voltage characteristic curve equation are as follows:
Wherein, UiFor the induced voltage of i-th of sensor, LiDistance for the measurement centre of sphere to i-th of sensor sensing plane, ti、
ki、mi、ni、qiIt is constant for sensor sensing voltage response equation coefficient；riFor the centre of sphere to center sensor axis
Distance；
It is known in measurement coordinate system, the induction planes central coordinate of circle of i-th of sensor is (xi-0, yi-0, zi-0), it is arrived according to point
The range formula and Pythagorean theorem of plane construct following equations group in conjunction with formula (4) and formula (2):
It asks to obtain coordinate of the center point P in measurement coordinate system by equation group.
2. the sphere centre coordinate calculation method of contactless R-test measuring instrument according to claim, which is characterized in that logical
It crosses formula (4) and solves center point P in measuring coordinate system during coordinate, in order to guarantee the accuracy of solving result, according to formula
(4) following Nonlinear System of Equations is built, solution of equations is sphere centre coordinate:
If objective function are as follows:
For the value of objective function closer to zero, the solution of above-mentioned Nonlinear System of Equations is more accurate.
3. the scaling method of contactless R-test measuring instrument according to claim, which is characterized in that asked by formula (5)
Center point P is solved during measuring the coordinate in coordinate system, in order to guarantee the accuracy of solving result, is constructed according to formula (5)
Following Nonlinear System of Equations, solution of equations are sphere centre coordinate:
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)
If objective function are as follows:
For the value of objective function closer to zero, the solution of above-mentioned Nonlinear System of Equations is more accurate.
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| CN113532275B (en) * | 2021-07-26 | 2022-05-06 | 西安交通大学 | Non-contact R-test sphere center coordinate calibration method adopting laser displacement sensor |
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| CN114252036B (en) * | 2021-12-15 | 2022-10-25 | 成都飞机工业（集团）有限责任公司 | Contact type R-Test instrument calibration method adopting ball head displacement sensor |
| CN114234877A (en) * | 2022-02-28 | 2022-03-25 | 成都飞机工业（集团）有限责任公司 | Displacement sensor vector calibration method for R-test instrument |
| CN114234877B (en) * | 2022-02-28 | 2022-06-14 | 成都飞机工业（集团）有限责任公司 | Displacement sensor vector calibration method for R-test instrument |
| CN115128857A (en) * | 2022-09-01 | 2022-09-30 | 深圳市共赢晶显技术有限公司 | Method and system for detecting surface defects of liquid crystal display |
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