CN106500631B - Circular gratings eccentric error parameter identification and compensation method - Google Patents
Circular gratings eccentric error parameter identification and compensation method Download PDFInfo
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
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Abstract
The present invention provides a kind of Circular gratings eccentric error parameter identification and compensation methodes, and described method includes following steps：1) equipment for using disk light beam encoder installs an auxiliary reading head B by the position of installation reading head A, and the position of auxiliary reading head B can arbitrarily install；2) Circular gratings installation axle is rotated, the value of observed reading head A records the value of reading head A and B every 5 °, until rotating a circle is obtained 72 groups of data.Using 72 groups of obtained data, 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 reading head A and B, α are angle of two reading heads relative to rotation center O, and a, w, α is the obliquely intersected of Circular gratings；The obliquely intersected a, w, α of Circular gratings are solved using L-M algorithm；3) when using Circular gratings measurement angle, obliquely intersected will be obtained and bring formula into：θA=θ 'A- l- β completes to compensate the eccentric error of reading head A；Wherein l=arcsin (a*sin (w)), β=arcsin (a*sin (- w- θA′))。
Description
Technical field
The present invention relates to a kind of angle measurement methods, and in particular to a kind of Circular gratings eccentric error parameter identification and compensation side
Method.
Background technique
Disk light beam encoder is widely used in high precision turntable, articulated type coordinate is surveyed as accurate angle measurement tool
The fields such as amount machine, robot, radar.Pass through 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 installation heeling error, setting-up eccentricity error, the axial runout and run-out error for installing bearing.Circle light
Grid installation generallys use precision bearing to reduce the error of bearing bounce.The eccentric error of installation is 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.
The some documents delivered successively in recent years propose the side of different Circular gratings obliquely intersected identification and error compensation
Method：《The error compensation and parameter identification of Circular gratings angular transducer》(using the method for Fourier transformation to the inclined of Circular gratings
Heart error is studied, and is solved with particle swarm algorithm to obliquely intersected；《Joint rotation angle based on RBF neural misses
Difference compensation》Based on radial basis function (Radial basis function, RBF) neural network algorithm to the errors of Circular gratings into
It has gone and has studied and compensate.《Benchmark Circular gratings eccentricity detecting and angle error compensation》Two-way reading head signal synthesis to Circular gratings
Lissajous figures detect the eccentric direction and eccentricity of grating, and by error correction, measurement accuracy improves 5 times；《Improve circle
The reading head of grating angle measuring system precision designs》Propose the data processing method that the uniformly distributed reading head of one kind four is added with digital quantity
To improve the precision at Circular gratings measurement angle；《Influence and Research on error compensation technology of the setting-up eccentricity to Circular gratings angle measurement accuracy》It adopts
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》Benefit
The measurement that high-density round grating displacement information carries out eccentricity is extracted with the principle of the diffraction interference of light, resolution ratio 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 is compensated；《Improve the double-reading head turret design of angle measurement accuracy》Subtracted by the way of the installation of double-reading head
The influence of small eccentricity error.
It will increase hardware cost with the method that more reading heads are installed；With a reading head by regular polygonal prism body and photoelectricity from
The method of collimator calibration, experimental provision are built more troublesome, and are limited by regular polygonal prism body, data amount check when calibration
It is less, it will affect calibration result.
Summary of the invention
To solve the above-mentioned problems, the purpose of the present invention is to provide a kind of Circular gratings eccentric error parameter identification and compensation
Method, described method includes following steps：1) equipment for using disk light beam encoder, by the position of installation reading head A, installation
The position of one auxiliary reading head B, auxiliary reading head B can arbitrarily install；2) Circular gratings installation axle is rotated, observed reading head A's
Value, the value of reading head A and B is recorded every 5 °, until rotating a circle is obtained 72 groups of data.Using 72 groups of obtained data,
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 that the reading of Circular gratings reading head A and B, α are angle of two reading heads relative to rotation center O, a, w, α is the inclined of Circular gratings
Heart parameter；The obliquely intersected a, w, α of Circular gratings are solved using L-M algorithm；3) it when using Circular gratings measurement angle, will obtain partially
Heart parameter brings formula into：θA=θ 'A- l- β completes to compensate the eccentric error of reading head A；Wherein l=arcsin (a*sin
(w)), β=arcsin (a*sin (-- W- θA′))。
Preferably, the angle of the reading head A and reading head B is 30 °, 45 °, 90 °, 100 °, 150 ° or 180 °.
It should be appreciated that aforementioned description substantially and subsequent detailed description are exemplary illustration and explanation, it should not
As the limitation to the claimed content of the present invention.
Detailed description of the invention
With reference to the attached drawing of accompanying, the more purposes of the present invention, function and advantage are by the as follows of embodiment through the invention
Description is illustrated, wherein：
Fig. 1 shows the Circular gratings bias schematic diagram of double-reading head installation：Wherein the angle of reading head A is less than in Fig. 1 (a)
The angle of reading head A is greater than reading head B in reading head B, Fig. 1 (b).
Specific embodiment
By reference to 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 exemplary embodiment as disclosed below；Can by different form come
It is realized.The essence of specification is only to aid in those skilled in the relevant arts' Integrated Understanding detail of the invention.
Hereinafter, the embodiment of the present invention will be described with reference to the drawings.In the accompanying drawings, identical appended drawing reference represents identical
Or similar component or same or like step.
The present invention provides a kind of Circular gratings eccentric error parameter identification and compensation method, the method is based on double readings
Head Circular gratings obliquely intersected self-calibration method, this method when carrying out obliquely intersected identification, can only with two reading heads into
Row data acquire and complete the identification of obliquely intersected according to the collected data, and do not have to by other high precision measuring instruments.?
After completing parameter identification, the compensation of eccentric error can be carried out to the angle value of Circular gratings using obtained parameter.
Technical solution used by this invention is：
An auxiliary reading head B is installed by the position for installing former reading head A using the equipment of disk light beam encoder.It is auxiliary
Helping the position of reading head can arbitrarily install, and can install with former reading head diameter, can not also diameter.Such as：Assist reading head B
Angle with former reading head A can be 30 °, 45 °, 90 °, 100 °, 150 ° or 180 °.
It is described in detail with reference to the accompanying drawing：
Fig. 1 is the Circular gratings bias schematic diagram of double-reading head installation.Wherein the angle of reading head A is less than reading in Fig. 1 (a)
The angle of reading head A is greater than reading head B in head B, Fig. 1 (b).
A and B is the installation site of two reading heads in Fig. 1 (a), and Z is the zero degree scribe line position of Circular gratings, and O is practical rotation
Turn center, O ' is theoretical rotation center, and eccentricity of the e between OO ', α is folder of two reading heads relative to rotation center O
Angle, R are the radius of the inswept annulus of reading head.The direction of rotation of Circular gratings is counterclockwise in figure.∠ AO'Z and ∠ BO'Z (are greater than
180 ° of angle) it is theoretical corner value, that is, the reading of Circular gratings reading head, it is denoted as θ respectivelyA' and θB′；∠ AOZ and ∠ BOZ
(angle greater than 180 °) is actual rotational angle value, is denoted as θ respectivelyAAnd θB.In order to derive conveniently, l=∠ OZO ', β=∠ are remembered respectively
OAO ', γ=∠ OBO '.Define eccentricity a=e/R.
In Δ OZO ', it can be obtained by sine：
L=arcsin (a*sin (w)) (1)
In Δ OAO ', it can be obtained by sine：
β=arcsin (a*sin (- W- θA′)) (2)
In Δ OBO ', it can be obtained by sine：
γ=arcsin (a*sin (w+ θB′)) (3)
OZ and O ' B intersection, is obtained by vertical angles are equal：L+ ∠ ZO'B=γ+∠ ZOB, i.e.,：
θB=θB+γ-l (4)
It the interior angle of Δ OZO' and Δ OAO ' and adds up to 360 ° and can obtain：
θA=θ 'A-l-β (5)
It can be obtained by geometrical relationship：
θB-θA=α (6)
Formula (1), (2), (3), (4), (5) are brought into formula (6), abbreviation can obtain：
θ′B-θ′A=α+arcsin (a*sin (w+ θ 'A))-arcsin(a*sin(w+θB′))(7)
When the angle of reading head A is greater than the angle of reading head B, as shown in Fig. 1 (b), the angle of two reading heads at this time
The relationship of value and the opinion of obliquely intersected is as follows：
θ′B-θ′A=α -2 π+arcsin (a*sin (w+ θ 'A))-arcsin(a*sin(w+θB′)) (8)
It only include the reading of two reading heads and the parameter of Circular gratings setting-up eccentricity in formula (7) and formula (8).Wherein two
The reading θ of a reading headA' and θB' can directly be obtained by upper computer software.Joint is rotated a circle, can be obtained multiple groups
θA' and θB', the obliquely intersected of Circular gratings installation can be fitted using nonlinear least square method according to formula (7) and (8), from
And realize the self-calibration of Circular gratings obliquely intersected.Research has selected the L-M algorithm in nonlinear least square method to be joined
Several solutions.The key of L-M algorithm is to be treated to estimate parameter and do linear approximation in its field with pattern function, has neglected second order
Above derivative term, so that it is converted into Linear least squares minimization problem, fast convergence rate.
Specific steps：
Circular gratings installation axle is rotated, the value of observed reading head A records the value of reading head A and B every 5 °, until rotation
72 groups of data are obtained within one week.It, can be in the hope of using L-M algorithm according to self-calibration formula (7) and (8) using 72 groups of obtained data
Solve the obliquely intersected a, w, α of Circular gratings.
Later when using Circular gratings measurement angle, obliquely intersected will be obtained and bring formula (5) into complete to reading head A's
Eccentric error compensation.
Compared with the prior art, the beneficial effects of the present invention are embodied in：
1) self-calibration that obliquely intersected is realized using two reading heads is not had to by external high precision measuring instrument, experiment
Device is built simply, easy to operate.
2) when obliquely intersected recognizes, auxiliary reading head is installed, after the completion of parameter identification, can will assist reading head
It removes, the high-cost problem of more reading heads is not present.
In conjunction with the explanation and practice of the invention disclosed here, the other embodiment of the present invention is for those skilled in the art
It all will be readily apparent and understand.Illustrate and embodiment is regarded only as being exemplary, true scope of the invention and purport are equal
It is defined in the claims.
Claims (2)
1. a kind of Circular gratings eccentric error parameter identification and compensation method, described method includes following steps：
1) equipment for using disk light beam encoder installs an auxiliary reading head B by the position of installation reading head A, and auxiliary is read
The position of several B can arbitrarily install；
2) Circular gratings installation axle is rotated, the value of observed reading head A records the value of reading head A and B every 5 °, until rotation one
72 groups of data are obtained week, using 72 groups of obtained data, 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 reading head A and B, α are folder of two reading heads relative to rotation center O
Angle, a, w, α are the obliquely intersected of Circular gratings；
It is treated using L-M algorithm and estimates parameter and do linear approximation in its field, solve the obliquely intersected a, w, α of Circular gratings；
3) when using Circular gratings measurement angle, obliquely intersected will be obtained and bring formula into：
θA=θ 'A- λ-β completes to compensate the eccentric error of reading head A；
Wherein λ=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 reading head A and reading head
The angle of B is 30 °, 45 °, 90 °, 100 °, 150 ° or 180 °.
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| CN107747931B (en) * | 2017-08-21 | 2019-11-22 | 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 |
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| CN112902877B (en) * | 2021-01-15 | 2024-03-22 | 河南科技大学 | Non-radial mounting double-reading-head circular grating angle measurement error correction method |
| CN113280762B (en) * | 2021-06-29 | 2022-10-11 | 杭州精稳科技有限责任公司 | Circular grating electronic coaxial debugging method |
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