CN106500631A - Circular gratings eccentric error parameter identification and compensation method - Google Patents

Circular gratings eccentric error parameter identification and compensation method Download PDF

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Publication number
CN106500631A
CN106500631A CN201610917541.XA CN201610917541A CN106500631A CN 106500631 A CN106500631 A CN 106500631A CN 201610917541 A CN201610917541 A CN 201610917541A CN 106500631 A CN106500631 A CN 106500631A
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circular gratings
read head
arcsin
sin
angle
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CN106500631B (en
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潘志康
冯超鹏
祝连庆
郭阳宽
董明利
娄小平
刘超
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Beijing Information Science and Technology University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical means
    • G01B11/26Measuring arrangements characterised by the use of optical means for measuring angles or tapers; for testing the alignment of axes

Abstract

The invention provides a kind of Circular gratings eccentric error parameter identification and compensation method, methods described comprises the steps:1) using the equipment of disk light beam encoder, by the position for installing read head A, an auxiliary read head B is installed, aids in the position of read head B arbitrarily can install;2) Circular gratings installation axle is rotated, the value of observed reading head A records the value of read head A and B every 5 °, until rotating a circle is obtained 72 groups of data.Using the 72 groups of data for obtaining, according to following two formula:θ′B‑θ′A=α+arcsin (a*sin (w+ θ 'A))‑arcsin(a*sin(w+θB′));θ′B‑θ′A=α 2 π+arcsin (a*sin (w+ θ 'A))‑arcsin(a*sin(w+θB')) wherein, θA' and θBThe reading of ' expression Circular gratings read head A and B, α are angle of two read heads relative to center of rotation O, and a, w, α are the obliquely intersected of Circular gratings;The obliquely intersected a for going out Circular gratings using L M Algorithm for Solving, w, α;3), when angle is measured using Circular gratings, will obtain obliquely intersected and bring formula into:θA=θ 'AL β, complete the eccentric error to read head A and compensate;Wherein l=arcsin (a*sin (w)), β=arcsin (a*sin (w θA′)).

Description

Circular gratings eccentric error parameter identification and compensation method
Technical field
The present invention relates to a kind of angle measurement method, and in particular to a kind of Circular gratings eccentric error parameter identification and compensation side Method.
Background technology
Disk light beam encoder is widely used in high precision turntable, articulated type coordinate and surveys as accurate angle measurement tool The fields such as amount machine, robot, radar.By the analysis to Circular gratings, it is known that the error source of Circular gratings mainly includes:Circular gratings are carved Line error, Circular gratings are installed heeling error, setting-up eccentricity error, install the axial runout and run-out error of bearing.Circle light Grid install the error for generally reducing bearing bounce using precision bearing.The eccentric error of installation is used as Circular gratings measurement error One of principal element, carries out parameter identification and error compensation to the eccentric error of Circular gratings, will significantly improve the survey of Circular gratings angle The precision of amount.
Some documents that delivered successively in recent years propose the side of different Circular gratings obliquely intersected identifications and error compensation Method:《The error compensation of Circular gratings angular transducer and parameter identification》(method of Fourier transformation is employed to the inclined of Circular gratings Heart error is studied, and obliquely intersected is solved with particle cluster algorithm;《Joint rotation angle based on RBF neural is missed Difference compensation》The error of Circular gratings is entered based on RBF (Radial basis function, RBF) neural network algorithm Go and studied and compensate.《Benchmark Circular gratings eccentricity detecting and angle error compensation》The two-way read head signal of Circular gratings is synthesized Detecting eccentric direction and the eccentric throw of grating, by error correction, certainty of measurement improves 5 times to lissajous figures;《Improve circle The read head design of grating angle measuring system precision》The data processing method that a kind of four uniform read heads are added is proposed with digital quantity To improve the precision of Circular gratings measurement angle;《Impact and Research on error compensation technology of the setting-up eccentricity to Circular gratings angle measurement accuracy》Adopt Reduce the setting-up eccentricity error of Circular gratings with the mode of double-reading head;《Circular gratings diffraction interference of light misalignment measurement method》Profit High-density round grating displacement information is extracted with the principle of the diffraction interference of light carries out the measurement of offset, and resolution can reach 1nm; 《The analysis of Circular gratings angle error and compensation based on Monte Carlo method》The angle measurement of Circular gratings is missed using the method for Monte Carlo Difference is analyzed and compensation;《Improve the double-reading head turret design of angle measurement accuracy》Subtracted by the way of the installation of double-reading head The impact of small eccentricity error.
The method that is installed with many read heads can increase hardware cost;With a read head by regular polygonal prism body and photoelectricity from The method that collimator is demarcated, experimental provision is built cumbersome, and is limited by regular polygonal prism body, data amount check during demarcation Less, calibration result can be affected.
Content of the invention
In order to solve the above problems, it is an object of the invention to provide a kind of Circular gratings eccentric error parameter identification and compensation Method, methods described comprise the steps:1) using the equipment of disk light beam encoder, by the position for installing read head A, install One auxiliary read head B, aids in the position of read head B arbitrarily can install;2) Circular gratings installation axle is rotated, observed reading head A's Value, records the value of read head A and B every 5 °, until rotating a circle is obtained 72 groups of data.Using the 72 groups of data for obtaining, According to following two formula:
θ′B-θ′A=α+arcsin (a*sin (w+ θ 'A))-arcsin(a*sin(w+θB′));
θ′B-θ′A=α -2 π+arcsin (a*sin (w+ θ 'A))-arcsin(a*sin(w+θB')) wherein, θA' and θB' table Show the reading of Circular gratings read head A and B, α is angle of two read heads relative to center of rotation O, and a, w, α are inclined for Circular gratings Heart parameter;The obliquely intersected a for going out Circular gratings using L-M Algorithm for Solving, w, α;3), when measuring angle using Circular gratings, will obtain partially Heart parameter brings formula into:θA=θ 'A- l- β, complete the eccentric error to read head A and compensate;Wherein l=arcsin (a*sin (w)), β=arcsin (a*sin (-- W- θA′)).
Preferably, the angle of the read head A and read head B is 30 °, 45 °, 90 °, 100 °, 150 ° or 180 °.
It should be appreciated that aforementioned description substantially and follow-up description in detail are exemplary illustration and explanation, should not It is used as the restriction to claimed content of the invention.
Description of the drawings
With reference to the accompanying drawing that encloses, the present invention more purpose, function and advantages are by by the as follows of embodiment of the present invention Description is illustrated, wherein:
Fig. 1 shows the Circular gratings bias schematic diagram that double-reading head is installed:In wherein Fig. 1 (a), the angle of read head A is less than Read head B, in Fig. 1 (b), the angle of read head A is more than read head B.
Specific embodiment
By reference to one exemplary embodiment, the purpose of the present invention and function and the side for realizing these purposes and function Method will be illustrated.However, the present invention is not limited to one exemplary embodiment disclosed below;Can by multi-form come Which is realized.The essence of description is only to aid in the detail of the various equivalent modifications Integrated Understanding present invention.
Hereinafter, embodiments of the invention will be described with reference to the drawings.In the accompanying drawings, identical reference represents identical Or similar part, or same or like step.
The invention provides a kind of Circular gratings eccentric error parameter identification and compensation method, methods described is based on double readings The method of the Circular gratings obliquely intersected self-calibration of head, the method only can be entered with two read heads when obliquely intersected identification is carried out Row data acquisition simultaneously completes the identification of obliquely intersected according to the data of collection, and without by other high precision measuring instruments.? After completing parameter identification, eccentric error can be carried out to the angle value of Circular gratings using the parameter for obtaining compensation.
The technical scheme adopted by this invention is:
Using the equipment of disk light beam encoder, by the position for installing former read head A, an auxiliary read head B is installed.Auxiliary Help the position of read head arbitrarily can install, can install with former read head diameter, it is also possible to not diameter.For example:Auxiliary read head B Angle with former read head A can be 30 °, 45 °, 90 °, 100 °, 150 ° or 180 °.
It is described in detail below in conjunction with the accompanying drawings:
Fig. 1 is the Circular gratings bias schematic diagram that double-reading head is installed.In wherein Fig. 1 (a), the angle of read head A is less than reading Head B, in Fig. 1 (b), the angle of read head A is more than read head B.
In Fig. 1 (a), A and B are the installation site of two read heads, and zero degree scribe line positions of the Z for Circular gratings, O are actual rotation Turn center, O ' is theoretical center of rotation, and e is the eccentric throw between OO ', and α is folder of two read heads relative to center of rotation O Angle, radiuses of the R for the inswept annulus of read head.In figure, the direction of rotation of Circular gratings is counterclockwise.∠ AO'Z and ∠ BO'Z (are more than 180 ° of angle) it is theoretical corner value, that is, the reading of Circular gratings read head, it is designated as θ respectivelyA' and θB′;∠ AOZ and ∠ BOZ (angles more than 180 °) are actual rotational angle values, are designated as θ respectivelyAAnd θB.In order to derive conveniently, l=∠ OZO ', β=∠ is remembered respectively OAO ', γ=∠ OBO '.Define eccentricity a=e/R.
In Δ OZO ', can be obtained by sine:
L=arcsin (a*sin (w)) (1)
In Δ OAO ', can be obtained by sine:
β=arcsin (a*sin (- W- θA′)) (2)
In Δ OBO ', can be obtained by sine:
γ=arcsin (a*sin (w+ θB′)) (3)
OZ and O ' B intersect, and are obtained by vertical angles are equal:L+ ∠ ZO'B=γ+∠ ZOB, i.e.,:
θBB+γ-l (4)
The interior angle of Δ OZO' and Δ OAO ' and add up to 360 ° and can obtain:
θA=θ 'A-l-β (5)
Can be obtained by geometrical relationship:
θBA=α (6)
Formula (1), (2), (3), (4), (5) are brought in formula (6), abbreviation can be obtained:
θ′B-θ′A=α+arcsin (a*sin (w+ θ 'A))-arcsin(a*sin(w+θB′))(7)
When the angle of read head A is more than the angle of read head B, such as Fig. 1 (b) is shown, now the angle of two read heads The relation of the opinion of value and obliquely intersected is as follows:
θ′B-θ′A=α -2 π+arcsin (a*sin (w+ θ 'A))-arcsin(a*sin(w+θB′)) (8)
Only include the parameter of the reading and Circular gratings setting-up eccentricity of two read heads in formula (7) and formula (8).Wherein two The reading θ of individual read headA' and θB' directly can be obtained by upper computer software.Joint is rotated a circle, you can obtain multigroup θA' and θB', the obliquely intersected that Circular gratings are installed can be fitted according to formula (7) and (8) using nonlinear least square method, from And achieve the self-calibration of Circular gratings obliquely intersected.Research have selected L-M algorithms in nonlinear least square method to be joined Several solutions.The key of L-M algorithms is to be treated to estimate parameter and make linear approximation in its field with pattern function, has neglected second order Above derivative term, so that be converted into Linear least squares minimization problem, fast convergence rate.
Concrete steps:
Circular gratings installation axle is rotated, the value of observed reading head A records the value of read head A and B every 5 °, until rotation 72 groups of data are obtained within one week.Using the 72 groups of data for obtaining, can be in the hope of using L-M algorithms according to self-calibration formula (7) and (8) Solve the obliquely intersected a of Circular gratings, w, α.
Afterwards when angle being measured using Circular gratings, will obtain obliquely intersected and bring formula (5) into complete to read head A's Eccentric error is compensated.
Compared with the prior art, beneficial effects of the present invention are embodied in:
1) self-calibration of obliquely intersected is realized using two read heads, without by outside high precision measuring instrument, experiment Device is built simply, easy to operate.
2) when obliquely intersected is recognized, auxiliary read head is installed, after the completion of parameter identification, read head can will be aided in Pull down, there are no many read head high costs.
In conjunction with the explanation and practice of the present invention for disclosing here, the other embodiment of the present invention is for those skilled in the art All will be readily apparent and understand.Illustrate and embodiment be to be considered only as exemplary, the present invention true scope and purport equal It is defined in the claims.

Claims (2)

1. a kind of Circular gratings eccentric error parameter identification and compensation method, methods described comprise the steps:
1) using the equipment of disk light beam encoder, by the position for installing read head A, an auxiliary read head B is installed, auxiliary is read Arbitrarily can install the position of several B;
2) Circular gratings installation axle is rotated, the value of observed reading head A records the value of read head A and B every 5 °, until rotation one 72 groups of data are obtained week.Using the 72 groups of data for obtaining, according to following two formula:
θ′B-θ′A=α+arcsin (a*sin (w+ θ 'A))-arcsin(a*sin(w+θB′));
θ′B-θ′A=α -2 π+arcsin (a*sin (w+ θ 'A))-arcsin(a*sin(w+θB′))
Wherein, θA' and θBThe reading of ' expression Circular gratings read head A and B, α is folder of two read heads relative to center of rotation O Angle, the obliquely intersected of a, w, α for Circular gratings;
The obliquely intersected a for going out Circular gratings using L-M Algorithm for Solving, w, α;
3), when angle is measured using Circular gratings, will obtain obliquely intersected and bring formula into:θA=θ 'A- l- β, complete to read head A's Eccentric error is compensated;
Wherein l=arcsin (a*sin (w)), β=arcsin (a*sin (- w- θA′)).
2. Circular gratings eccentric error parameter identification according to claim 1 and compensation method, the read head A and read head The angle of B is 30 °, 45 °, 90 °, 100 °, 150 ° or 180 °.
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CN107747931A (en) * 2017-08-21 2018-03-02 上海微泓自动化设备有限公司 For the self-alignment reading head optimization placement method of angular encoder
CN109211175A (en) * 2018-09-18 2019-01-15 中国科学院长春光学精密机械与物理研究所 Blind area data processing method when a kind of straight line steel band encoder angle measurement
CN109269399A (en) * 2018-10-25 2019-01-25 清华大学 A kind of online error parameter identification and self-compensating system and method
CN109631976A (en) * 2019-01-07 2019-04-16 武汉海达数云技术有限公司 The compensation method of Circular gratings angular error and device
CN109724639A (en) * 2018-12-29 2019-05-07 中国科学院长春光学精密机械与物理研究所 A kind of Circular gratings acquisition modification method and device
CN109974628A (en) * 2019-04-09 2019-07-05 合肥工业大学 A kind of circular raster sensor angle error modification method based on Analysis of error source
CN110186398A (en) * 2019-05-15 2019-08-30 大连理工大学 A kind of rotary table and measurement method with movement warp real-time measurement function
CN111076678A (en) * 2019-12-26 2020-04-28 北京卫星制造厂有限公司 Device and method for measuring radial error of joint axis of mobile robot
CN111457837A (en) * 2020-04-15 2020-07-28 大连理工高邮研究院有限公司 Measuring device for measuring five-degree-of-freedom motion error of rotary table in real time by using circular grating and eddy current sensor and using method
CN113280762A (en) * 2021-06-29 2021-08-20 杭州精稳科技有限责任公司 Circular grating electronic coaxial debugging method

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Publication number Priority date Publication date Assignee Title
CN107747931A (en) * 2017-08-21 2018-03-02 上海微泓自动化设备有限公司 For the self-alignment reading head optimization placement method of angular encoder
CN109211175A (en) * 2018-09-18 2019-01-15 中国科学院长春光学精密机械与物理研究所 Blind area data processing method when a kind of straight line steel band encoder angle measurement
CN109269399B (en) * 2018-10-25 2020-05-19 清华大学 Online error parameter identification and self-compensation system and method
CN109269399A (en) * 2018-10-25 2019-01-25 清华大学 A kind of online error parameter identification and self-compensating system and method
CN109724639A (en) * 2018-12-29 2019-05-07 中国科学院长春光学精密机械与物理研究所 A kind of Circular gratings acquisition modification method and device
CN109631976A (en) * 2019-01-07 2019-04-16 武汉海达数云技术有限公司 The compensation method of Circular gratings angular error and device
CN109974628A (en) * 2019-04-09 2019-07-05 合肥工业大学 A kind of circular raster sensor angle error modification method based on Analysis of error source
CN109974628B (en) * 2019-04-09 2020-09-01 合肥工业大学 Circular grating sensor angle measurement error correction method based on error source analysis
CN110186398A (en) * 2019-05-15 2019-08-30 大连理工大学 A kind of rotary table and measurement method with movement warp real-time measurement function
CN110186398B (en) * 2019-05-15 2020-04-28 大连理工大学 Rotary workbench with motion deviation real-time measurement function and measurement method
CN111076678A (en) * 2019-12-26 2020-04-28 北京卫星制造厂有限公司 Device and method for measuring radial error of joint axis of mobile robot
CN111457837A (en) * 2020-04-15 2020-07-28 大连理工高邮研究院有限公司 Measuring device for measuring five-degree-of-freedom motion error of rotary table in real time by using circular grating and eddy current sensor and using method
CN111457837B (en) * 2020-04-15 2021-11-16 大连理工高邮研究院有限公司 Measuring device for measuring five-degree-of-freedom motion error of rotary table in real time by circular grating and eddy current sensor
CN113280762A (en) * 2021-06-29 2021-08-20 杭州精稳科技有限责任公司 Circular grating electronic coaxial debugging method

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