CN109115095B - Structural parameter optimization method of non-contact R-test measuring instrument - Google Patents
Structural parameter optimization method of non-contact R-test measuring instrument Download PDFInfo
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Abstract
The invention discloses a structural parameter optimization method of a non-contact R-test measuring instrument, belonging to the field of rotating shaft error measuring instruments of non-contact R-test five-axis numerical control machines; the method comprises the following steps of 1: establishing a structural model of a non-contact R-test measuring instrument adopting an eddy current displacement sensor, and preprocessing coordinates of the structural model; step 2: constructing a measurement sensitivity equation based on the induced voltage measured in the step 1 and the sensor to obtain a sensor elevation angle corresponding to the maximized sensitivity; and step 3: calculating a measurement constraint equation of each sensor based on the structural model with maximized sensitivity; and 4, step 4: after the number of the measurement points which simultaneously satisfy the measurement constraint equation, namely the measurement space volume, is calculated, the sensor center distance corresponding to the maximum measurement space is obtained, and the structural parameter optimization is completed; the problems that the existing contact type R-test measuring instrument is poor in reading sensitivity and low in measuring precision due to contact wear and mechanical structure are solved, and accurate measurement of the measuring instrument is achieved.
Description
Technical Field
The invention belongs to the field of non-contact R-test five-axis numerical control machine tool rotating shaft error measuring instruments, and particularly relates to a structural parameter optimization method of a non-contact R-test measuring instrument.
Background
With the increase of the service life of the machine tool, the geometric accuracy of each part of the machine tool is reduced due to abrasion, deformation and the like, so that the machining accuracy is reduced. The accurate measurement of the error of the tool point of the machine tool is the key for error compensation to improve the processing precision of the machine tool, the measurement of the geometric error of the rotating shaft of the machine tool has no special precise measurement instrument and standard, the indirect measurement is generally carried out by adopting a laser interferometer, a ball bar instrument and the like, and the problems of low measurement efficiency, installation error influence on the measurement precision and the like exist; compared with the defects of the instruments, the R-test measuring instrument combines the RTCP \ RPCP linkage function of the five-axis numerical control machine tool, can directly measure, identify and obtain the geometric error of the rotating shaft, the motion error, the thermal deformation error and the like, and realizes the simple and convenient measurement of the geometric error of the rotating shaft of the machine tool; 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; in the prior art, research on the R-test measuring instrument is few, and research on the R-test measuring instrument is concentrated on a contact type measuring mode, wherein Liu Da Wei, Li Bright and the like propose 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 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 mechanical structure of the contact type R-test measuring instrument causes low reading sensitivity of the sensor, and the contact brings abrasion, so that the measuring precision is low. The non-contact R-test measuring instrument can avoid measuring errors caused by measuring abrasion, can carry out measurement under the condition of high-speed rotation of the main shaft, and has better measuring sensitivity and stability, but the research on the non-contact R-test measuring instrument in the prior art is less; the main performance index of the non-contact R-test measuring instrument is greatly influenced by the structural parameters of the measuring instrument, so a method is needed to optimize the structural parameters of the non-contact R-test measuring instrument and realize high sensitivity and large measuring space of non-contact R-test measurement.
Disclosure of Invention
The invention aims to: the invention provides a structural parameter optimization method of a non-contact R-test measuring instrument, which solves the problems of poor measuring sensitivity and low measuring precision of the existing contact R-test measuring instrument due to contact wear and mechanical structure.
The technical scheme adopted by the invention is as follows:
a structural parameter optimization method of a non-contact R-test measuring instrument comprises the following steps:
step 1: establishing a structural model of a non-contact R-test measuring instrument adopting an eddy current displacement sensor, and preprocessing coordinates of the structural model;
and step 3: calculating a measurement constraint equation of each eddy current displacement sensor based on the structural model with maximized sensitivity;
and 4, step 4: and after the number of the measurement points which simultaneously satisfy the measurement constraint equation, namely the measurement space volume is calculated, obtaining the sensor center distance lambda corresponding to the maximum measurement space volume, and finishing the structural parameter optimization.
Preferably, the step 1 comprises the steps of:
step 1.1: establishing a structural model comprising three non-contact eddy current displacement sensors which are uniformly distributed and a measuring ball;
step 1.2, defining a plane delta ABC where the central points of the bottom ends of the three sensors are located as a reference plane, wherein included angles between the axes of the sensors and the reference plane are sensor elevation α;
step 1.3: and establishing a measurement coordinate system XYZ, wherein the Z axis of the coordinate system is superposed with the central axis of the measuring instrument, and the XOY coordinate plane of the coordinate system is parallel to the reference plane.
Preferably, the step 2 comprises the steps of:
step 2.1: combining the preprocessed structure model, and constructing a first equation of a measuring characteristic curve of the sensor according to the induction principle of the eddy current sensor and the calibration test of the sensor, wherein the first equation is as follows:
wherein k, t, m, n and q are characteristic parameters measured by the sensor and measuring range of the sensor LiFor measuring the distance from the centre of the sphere to the sensing end face of the ith sensor, riFrom the center of the sphere to the central axis of the ith sensorDistance of line, rmaxMaximum r allowed for the sensor to be able to measure effectivelyi，UiInduced voltage, R, measured for the ith sensorBall with ball-shaped sectionTo measure the spherical radius;
step 2.2, assuming that the measurement characteristic parameters of all the sensors are consistent, the origin of the measurement coordinate system is defined as the intersection point of the central axes of the sensors, namely the elevation angles of the sensors are α, and the distance r from the center of sphere to the central axis of the sensorsiWhen 0, the following sensor measurement characteristic curve equation two is obtained:
step 2.3, calculating the distance L between the center of the sphere and the end face of the sensori：
Wherein, (x, y, z) is a sphere center coordinate, ai、bi、ci、diSensing end surface equation coefficients for each sensor;
step 2.4: LiSubstituting the measured characteristic curve equation II of the sensor into the measured characteristic curve equation II of the sensor to calculate the variation delta U of the induced voltage, wherein the calculation formula is as follows:
step 2.5: the variation delta U of the induced voltage is mathematically transformed to obtain the following formula:
step 2.6: due to ai、bi、ci、diFor each sensor, the end equation coefficients are sensed, and diThe value of (a) does not affect the relationship between Δ U and Δ x, Δ y, and Δ z, and thus a can be expressed by any unit normal vector of the sensor end surfacei、bi、ciA value of
Obtaining a group of unit normal vectors of the induction end surface according to the elevation angle of the sensor of the measuring instrument, and calculating a measuring sensitivity equation of the measuring instrument, wherein the equation is based on an XOZ surface:
wherein, the delta P is a micro-change matrix of the coordinate of the sphere center of the measuring sphere
The matrix J about the elevation angle α of the sensor represents the mapping relation between the micro-change matrix Δ P of the center coordinates of the measuring ball and the change quantity Δ U of the induction voltage measured by the sensor.
And 2.7, defining the reciprocal of a condition number of a matrix J related to the elevation angle α of the sensor as a measurement sensitivity evaluation index Prec, drawing a relation curve of the measurement instrument sensitivity evaluation index Prec and the elevation angle a of the sensor according to a measurement sensitivity equation, and obtaining the sensor elevation angle α with the maximized sensitivity according to the curve.
Preferably, the step 3 comprises the steps of:
step 3.1: deducing the maximum r allowed by the sensor to be able to effectively measure based on the sensitivity-maximized structural model (based on the XOZ plane)iNamely rmaxThe equation:
wherein M (x, y, z) is any point of the outer cylindrical surface of the sensor, V is the normal vector of the sensing end surface of the sensor, and P isi-0For each sensor sensing the end surface center point, rmaxThe maximum r allowed for each sensor to be able to effectively measurei；
Step 3.2: based on r corresponding to sensor 3maxAnd M point to sensor induction end face distance obtaining sensor3, measurement constraint equation:
wherein R isProbeIs the radius of the sensor tip, RBall with ball-shaped sectionThe radius of a measuring ball is taken as the measuring range of the sensor, and lambda is the distance between the centers of the sensors, namely the distance between the central axis of the measuring instrument and the center of a circle of the sensing end surface of the sensor;
step 3.3: based on r corresponding to sensor 2maxAnd obtaining a measurement constraint equation of the sensor 2 according to the distance between the M point and the sensor sensing end face:
step 3.4: based on r corresponding to sensor 1maxAnd obtaining a measurement constraint equation of the sensor 1 according to the distance between the M point and the sensor sensing end face:
preferably, the step 4 comprises the steps of:
step 4.1: calculating the measurement space volume by using a Monte Carlo search method, namely the number of measurement points meeting the requirements of 3 measurement constraint equations under the current lambda;
step 4.2: calculating the measurement space S under different lambdas based on the step 4.1jWherein j is 1, …, m; m is the number of the taken lambada;
step 4.3: and drawing an S-lambda relation curve to obtain the sensor center distance lambda corresponding to the maximum measurement volume, so that the maximum measurement sensitivity and the maximum measurement space are realized, and the structural parameter optimization is completed.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. according to the invention, by establishing a non-contact R-test structural model and optimizing the elevation angle α of the structural parameter sensor and the center distance lambda of the sensor, the maximization of the measurement sensitivity and the measurement space of the measuring instrument is realized, the problems of poor measurement sensitivity and low measurement precision caused by contact wear and mechanical structure of the existing contact R-test measuring instrument are solved, and the effect of improving the measurement precision of the measuring instrument is achieved;
2. the sensitivity of the R-test measuring instrument is the minimum movement of the sphere center capable of generating effective induced voltage signals, is related to the elevation α of the sensor, and constructs an induced voltage U according to a characteristic curve equation of the induced voltage measurement of the sensor and a point-to-plane distance formulaiModeling the function relation of the measured spherical center coordinates (x, y, z) to establish the variation delta U of the induced voltageiAnd measuring the coordinate trace change matrix delta P (delta x, delta y, delta z) of the sphere centerTReplacing the plane coefficient a of the sensing end face of the sensor in the delta U-delta P matrix equation with a set of unit normal vector matrixes J about the elevation angle α of the sensori、bi、ciAnd diAccording to a matrix analysis theory, taking the reciprocal of the condition number of a matrix J as a measurement sensitivity evaluation index Prec, determining the corresponding relation between the Prec and α, obtaining a sensor elevation angle α which enables the measurement sensitivity evaluation index Prec to be maximum, and realizing the maximization of the measurement sensitivity of a measuring instrument;
3. the maximum measurement space of the non-contact R-test measuring instrument is the maximum range of the movement of the sphere center of the measuring sphere in the measuring process and is related to the distance lambda between the centers of the sensors; on the basis of ensuring the maximum measurement sensitivity of the measuring instrument, a measurement constraint equation of each eddy current displacement sensor about the center distance lambda of the sensor is established, a Monte Carlo search interval is defined, points meeting the measurement constraint equation in the search interval are searched by using a Monte Carlo search method, the number of points under different sensor center distances lambda is the measurement space S corresponding to the sensor center distance lambda, the sensor center distance lambda which enables the measurement space S to be the maximum is obtained, and the measurement space maximization of the measuring instrument is realized.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of a non-contact R-test measuring instrument according to the present invention;
FIG. 3 is a schematic representation of the spatial relationship of the sensor-measuring sphere of the present invention;
FIG. 4 is a graph of the sensitivity evaluation index Prec of the present invention versus the sensor elevation angle α;
FIG. 5 is a schematic view of the range of movement of the center of sphere of the present invention;
FIG. 6 is a schematic diagram of the geometric position of the sensor and the measuring ball of the present invention;
FIG. 7 is a flow chart of the measurement space S calculation of the present invention;
fig. 8 is a graph of the measurement space S of the present invention versus the sensor center-to-center spacing λ.
Reference numerals: 1-measuring ball, 2-sensor i, 3-sensor i induction end face, 4-measuring ball center movement range, 5-sensor A, 6-sensor B, 7-sensor C, A-sensor A bottom center point, B-sensor B bottom center point, C-sensor C bottom center point, A-sensor C bottom center point1Sensor A sensing end face center point, B1Sensor B sensing end face center point, C1Sensor C senses the end face centre point.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
It is noted that relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The technical problem is as follows: the problems of poor measurement sensitivity and low measurement precision of the existing contact type R-test measuring instrument due to contact wear and mechanical structure are solved;
the technical means is as follows:
a structural parameter optimization method of a non-contact R-test measuring instrument comprises the following steps:
step 1: establishing a structural model of a non-contact R-test measuring instrument adopting an eddy current displacement sensor, and preprocessing coordinates of the structural model;
and step 3: calculating a measurement constraint equation of each eddy current displacement sensor based on the structural model with maximized sensitivity;
and 4, step 4: and after the number of the measurement points which simultaneously satisfy the measurement constraint equation, namely the measurement space volume is calculated, obtaining the sensor center distance lambda corresponding to the maximum measurement space volume, and finishing the structural parameter optimization.
The step 1 comprises the following steps:
step 1.1: establishing a structural model comprising three non-contact eddy current displacement sensors which are uniformly distributed and a measuring ball; the three non-contact eddy current displacement sensors are respectively a sensor A, a sensor B and a sensor C;
step 1.2, defining a plane delta ABC where the central points of the bottom ends of the three sensors are located as a reference plane, wherein included angles between the axes of the sensors and the reference plane are sensor elevation α;
step 1.3: and establishing a measurement coordinate system XYZ, wherein the Z axis of the coordinate system is superposed with the central axis of the measuring instrument, and the XOY coordinate plane of the coordinate system is parallel to the reference plane.
The step 2 comprises the following steps:
step 2.1: combining the preprocessed structure model, and constructing a first equation of a measuring characteristic curve of the sensor according to the induction principle of the eddy current sensor and the calibration test of the sensor, wherein the first equation is as follows:
wherein k, t, m, n and q are characteristic parameters measured by the sensor and measuring range of the sensor LiFor measuring the distance from the centre of the sphere to the sensing end face of the ith sensor, riIs the distance from the center of sphere to the central axis of the ith sensor, rmaxMaximum r allowed for the sensor to be able to measure effectivelyi，UiInduced voltage, R, measured for the ith sensorBall with ball-shaped sectionTo measure the spherical radius;
step 2.2, defining the measurement characteristic parameters of all the sensors to be consistent, defining the origin of a measurement coordinate system as the intersection point of the central axes of the sensors, namely the elevation angles of the sensors to be α, and defining the distance r from the center of sphere to the central axes of the sensorsiWhen 0, the following sensor measurement characteristic curve equation two is obtained:
step 2.3, calculating the distance L between the center of the measuring ball and the end face of the sensori：
Wherein, (x, y, z) is a sphere center coordinate, ai、bi、ci、diSensing end surface equation coefficients for each sensor;
step 2.4: LiSubstituting the measured characteristic curve equation II of the sensor into the measured characteristic curve equation II of the sensor to calculate the variation delta U of the induced voltage, wherein the calculation formula is as follows:
step 2.5: the variation delta U of the induced voltage is mathematically transformed to obtain the following formula:
step 2.6: due to ai、bi、ci、diFor each sensor, the end equation coefficients are sensed, and diThe value of (a) does not affect the relationship between Δ U and Δ x, Δ y, and Δ z, and thus a can be expressed by any unit normal vector of the sensor end surfacei、bi、ciA value of
Obtaining a group of unit normal vectors of the induction end surface according to the elevation angle of the sensor of the measuring instrument, and calculating a measuring sensitivity equation of the measuring instrument, wherein the equation is based on an XOZ surface:
wherein, the delta P is a micro-change matrix of the coordinate of the sphere center of the measuring sphere
The matrix J about the elevation angle α of the sensor represents the mapping relation between the micro-change matrix Δ P of the center coordinates of the measuring ball and the change quantity Δ U of the induction voltage measured by the sensor.
And 2.7, defining the reciprocal of a condition number of a matrix J related to the elevation angle α of the sensor as a measurement sensitivity evaluation index Prec, drawing a relation curve of the measurement instrument sensitivity evaluation index Prec and the elevation angle a of the sensor according to a measurement sensitivity equation, and obtaining the sensor elevation angle α with the maximized sensitivity according to the curve.
The step 3 comprises the following steps:
step 3.1: deducing the maximum r allowed by the sensor to be able to effectively measure based on the sensitivity-maximized structural model (based on the XOZ plane)iNamely rmaxThe equation:
wherein M (x, y, z) is any point of the outer cylindrical surface of the sensor, V is the normal vector of the sensing end surface of the sensor, and P isi-0For each sensor sensing the end surface center point, rmaxThe maximum r allowed for each sensor to be able to effectively measurei；
Step 3.2: based on r corresponding to sensor 3maxAnd obtaining a measurement constraint equation of the sensor 3 according to the distance from the M point to the sensor sensing end face:
wherein R isProbeIs the radius of the sensor tip, RBall with ball-shaped sectionThe radius of a measuring ball is taken as the measuring range of the sensor, and lambda is the distance between the centers of the sensors, namely the distance between the central axis of the measuring instrument and the center of a circle of the sensing end surface of the sensor;
step 3.3: based on r corresponding to sensor 2maxAnd obtaining a measurement constraint equation of the sensor 2 according to the distance between the M point and the sensor sensing end face:
step 3.4: based on r corresponding to sensor 1maxAnd obtaining a measurement constraint equation of the sensor 1 according to the distance between the M point and the sensor sensing end face:
the step 4 comprises the following steps:
step 4.1: calculating the measurement space volume by using a Monte Carlo search method, namely the number of measurement points meeting the requirements of 3 measurement constraint equations under the current lambda;
step 4.2: calculating the measurement space S under different lambdas based on the step 4.1jWherein j is 1, …, m; m is the number of the taken lambada;
step 4.3: and drawing an S-lambda relation curve to obtain the sensor center distance lambda corresponding to the maximum measurement volume, so that the maximum measurement sensitivity and the maximum measurement space are realized, and the structural parameter optimization is completed.
The technical effects that the maximization of the measurement sensitivity and the measurement space of the measuring instrument is realized by establishing a non-contact R-test structural model and optimizing the elevation angle α of a structural parameter sensor and the center distance lambda of the sensor, the problems of poor measurement sensitivity and low measurement precision of the existing contact R-test measuring instrument due to contact wear and mechanical structure are solved, and the effect of improving the measurement precision of the measuring instrument is achieved;
the features and properties of the present invention are described in further detail below with reference to examples.
Example 1
As shown in fig. 2, 3, 5 and 6, a structural model comprising three non-contact eddy current displacement sensors and a measuring ball 1 which are uniformly distributed is established; three non-contact eddy current displacement sensors are respectively a sensorA sensor A5, a sensor B6 and a sensor C7, as shown in FIG. 4, the measurement sensitivity index Prec of the non-contact R-test measuring instrument changes along with the change of the elevation angle α of the sensor, the measurement sensitivity index Prec is monotonically increased and then monotonically decreased, the measurement sensitivity index Prec is determined to be maximum when α is 33.69 degrees, and the relation between the measurement space S of the non-contact R-test measuring instrument and the center distance lambda of the sensor (R) is determined on the basis of ensuring the measurement sensitivity (α is 33.69 degrees)max＝4mm，RProbe＝7mm，RBall with ball-shaped section15mm, 4mm) as shown in fig. 8, it was determined that when λ is 14mm, the measurement space S is maximum, about 33mm3。
The calculation flow of the measurement space volume S is as follows, and the flow chart is shown in fig. 7:
(1) defining a search interval: x [ x ]min,xmax]，y[ymin,ymax]，z[zmin,zmax](xmin、xmax、ymin、ymax、zmin、zmaxThe value of (a) should be ensured to cover all the point intervals meeting the requirements);
(2) dividing the search interval into n measurement point sets with unit length as step length, and defining the measurement point as Pi(i＝1,…,n)；
(3) Set α ═ 33.69 °, in [ RProbe，RBall with ball-shaped section+]In the range of lambda0Take λ (λ) in order for step size0＝1mm)；
(4) Will measure the point PiTogether with a parameter rmax、RProbe、RBall with ball-shaped sectionα are substituted into the measurement constraint equations of the sensors 1, 2 and 3, and if the constraint equations (9), (10) and (11) are simultaneously satisfied, P is indicatediWithin the effective sphere center motion range;
(5) the measurement space S is equal to the number of measurement points meeting the requirements of 3 measurement constraint equations under the current lambda;
(6) repeating the steps (3) to (5) to obtain measurement spaces S under different lambadaj(j is 1, …, m; m is the number of lambda taken).
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (3)
1. A structural parameter optimization method of a non-contact R-test measuring instrument is characterized by comprising the following steps: the method comprises the following steps:
step 1: establishing a structural model of a non-contact R-test measuring instrument adopting an eddy current displacement sensor, and preprocessing coordinates of the structural model;
step 2, constructing a measurement sensitivity equation according to the preprocessed structure model and the induced voltage measured by the eddy current displacement sensor to obtain a sensor elevation α corresponding to the maximized sensitivity;
and step 3: calculating a measurement constraint equation of each eddy current displacement sensor based on the structural model with maximized sensitivity;
and 4, step 4: after the number of the measurement points which simultaneously satisfy the measurement constraint equation, namely the measurement space volume is calculated, the sensor center distance lambda corresponding to the maximum measurement space volume is obtained, and the structural parameter optimization is completed;
the step 1 comprises the following steps:
step 1.1: establishing a structural model comprising three non-contact eddy current displacement sensors which are uniformly distributed and a measuring ball;
step 1.2, defining a plane delta ABC where the central points of the bottom ends of the three sensors are located as a reference plane, wherein included angles between the axes of the sensors and the reference plane are sensor elevation α;
step 1.3: establishing a measurement coordinate system XYZ, wherein the Z axis of the coordinate system is superposed with the central axis of the measuring instrument, and the XOY coordinate plane of the coordinate system is parallel to the reference plane;
the step 2 comprises the following steps:
step 2.1: combining the preprocessed structure model, and constructing a first equation of a measuring characteristic curve of the sensor according to the induction principle of the eddy current sensor and the calibration test of the sensor, wherein the first equation is as follows:
wherein k, t, m, n and q are characteristic parameters measured by the sensor and measuring range of the sensor LiFor measuring the distance from the centre of the sphere to the sensing end face of the ith sensor, riIs the distance from the center of sphere to the central axis of the ith sensor, rmaxMaximum r allowed for the sensor to be able to measure effectivelyi，UiInduced voltage, R, measured for the ith sensorBall with ball-shaped sectionTo measure the spherical radius;
step 2.2, the measurement characteristic parameters of all the sensors are consistent, the origin of the measurement coordinate system is defined as the intersection point of the central axes of the sensors, namely the elevation angles of the sensors are α, and the distance r from the center of sphere to the central axis of the sensorsiWhen 0, the following sensor measurement characteristic curve equation two is obtained:
Ui＝kLi m+q(i＝1,2,3)
step 2.3, calculating the distance L between the center of the sphere and the end face of the sensori：
Wherein, (x, y, z) is a sphere center coordinate, ai、bi、ci、diSensing end surface equation coefficients for each sensor;
step 2.4: LiSubstituting the measured characteristic curve equation II of the sensor into the measured characteristic curve equation II of the sensor to calculate the variation delta U of the induced voltage, wherein the calculation formula is as follows:
step 2.5: the variation delta U of the induced voltage is mathematically transformed to obtain the following formula:
step 2.6: due to ai、bi、ci、diSensing end surface equation coefficients for each sensorAnd d isiThe value of (a) does not affect the relationship between Δ U and Δ x, Δ y, and Δ z, and thus a can be expressed by any unit normal vector of the sensor end surfacei、bi、ciA value of
Obtaining a group of unit normal vectors of the induction end surface according to the elevation angle of the sensor of the measuring instrument, and calculating a measuring sensitivity equation of the measuring instrument, wherein the equation is based on an XOZ surface:
wherein, the delta P is a micro-variation matrix (Vx, Vy, Vz) for measuring the spherical center coordinate of the sphereTThe delta U is the induced voltage variation measured by the sensor, and a matrix J related to the elevation angle α of the sensor represents the mapping relation between a measurement ball center coordinate micro-variation matrix delta P and the induced voltage variation delta U measured by the sensor;
and 2.7, defining the reciprocal of a condition number of a matrix J related to the elevation angle α of the sensor as a measurement sensitivity evaluation index Prec, drawing a relation curve of the measurement instrument sensitivity evaluation index Prec and the elevation angle a of the sensor according to a measurement sensitivity equation, and obtaining the sensor elevation angle α with the maximized sensitivity according to the curve.
2. The method for optimizing the structural parameters of the non-contact R-test measuring instrument as claimed in claim 1, wherein the method comprises the following steps: the step 3 comprises the following steps:
step 3.1: deducing the maximum r allowed by the sensor to be able to effectively measure based on the sensitivity-maximized structural model (based on the XOZ plane)iNamely rmaxThe equation:
wherein M (x, y, z) is any point of the outer cylindrical surface of the sensor, V is the normal vector of the sensing end surface of the sensor, and P isi-0For each sensingThe center point of the induction end face rmaxThe maximum r allowed for each sensor to be able to effectively measurei；
Step 3.2: based on r corresponding to sensor 3maxAnd obtaining a measurement constraint equation of the sensor 3 according to the distance from the M point to the sensor sensing end face:
wherein R isProbeIs the radius of the sensor tip, RBall with ball-shaped sectionThe radius of a measuring ball is taken as the measuring range of the sensor, and lambda is the distance between the centers of the sensors, namely the distance between the central axis of the measuring instrument and the center of a circle of the sensing end surface of the sensor;
step 3.3: based on r corresponding to sensor 2maxAnd obtaining a measurement constraint equation of the sensor 2 according to the distance between the M point and the sensor sensing end face:
step 3.4: based on r corresponding to sensor 1maxAnd obtaining a measurement constraint equation of the sensor 1 according to the distance between the M point and the sensor sensing end face:
3. the method for optimizing the structural parameters of the non-contact R-test measuring instrument according to the claim 1 or 2, wherein the method comprises the following steps: the step 4 comprises the following steps:
step 4.1: calculating the measurement space volume by using a Monte Carlo search method, namely the number of measurement points meeting the requirements of 3 measurement constraint equations under the current lambda;
step 4.2: calculating the measurement space S under different lambdas based on the step 4.1jWherein j is 1, …, m; m is the number of the taken lambada;
step 4.3: and drawing an S-lambda relation curve to obtain a sensor center distance lambda corresponding to the maximum measurement space, so that the maximum measurement sensitivity and the maximum measurement space are realized, and the structural parameter optimization is completed.
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| CN111580460B (en) * | 2020-06-05 | 2023-05-16 | 沈机（上海）智能系统研发设计有限公司 | Error detection system, error detection and compensation method for five-axis machine tool |
| CN111854658B (en) * | 2020-07-22 | 2021-04-20 | 四川大学 | R-test precision ball head detection device and calibration method thereof |
| CN112013766A (en) * | 2020-08-31 | 2020-12-01 | 华中科技大学 | Non-contact R-test structural parameter redundancy-free calibration method |
| CN113031514B (en) * | 2021-03-18 | 2022-03-18 | 西南交通大学 | R-test calibration uncertainty evaluation method based on metrology |
| 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 |
| 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 |
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