CN110375694A - Method for self-calibrating based on portable articulated coordinate machine Circular gratings angle error - Google Patents
Method for self-calibrating based on portable articulated coordinate machine Circular gratings angle error Download PDFInfo
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
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- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
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Abstract
The present invention discloses the method for self-calibrating based on portable articulated coordinate machine Circular gratings angle error, includes the following steps: to establish reading head HjAngle measurement function model；The angle interval of three reading heads of Circular gratings angle-measuring equipment is set, the Circular gratings angle measurement of three reading heads is obtained；To three reading head H1、H2、H3In the difference functions of two reading heads carry out curve fitting respectively, establish two reading head angle measurement difference H respectively2‑H1、H3‑H1、H3‑H2With the functional relation of angle position；Difference curve after fitting carries out equiangularly spaced sampling, and sampled point is carried out discrete Fourier transform, and the relational expression for bringing itself and transmission function into acquires the coefficient function F (n) of Fourier space；Carry out the penalty function model ε (θ) that inverse discrete Fourier transform determines Circular gratings angle error；Using the scaling method of polygon combination autocollimator, the compensation effect of Circular gratings angle error self calibration model is verified.Multistage subharmonic error compensation is completed with few reading head, improves product reliability.
Description
Technical field
The invention belongs to articulated coordinate machine fields, more particularly to are based on portable articulated coordinate machine Circular gratings
The method for self-calibrating of angle error.
Background technique
Portable articulated coordinate machine is portable nonopiate measuring device made of a kind of simulation human arm, extensively
For mold manufacture, machining and manufacturing industry, have it is small in size, it is light-weight, it is easy to carry, measurement flexibly, measurement space it is big,
The advantages that environmental suitability is strong.For portable articulated coordinate machine usually by pedestal, rotary joint measures arm and gauge head series connection group
At this structure has error amplification.Therefore, precision calibration is carried out for being mounted on the angular encoder at rotary joint
It is extremely important.
Circular gratings angular encoder is a kind of full circle week angle-measuring equipment, in the angle measurement of portable articulated coordinate machine
In the process, angle measurement accuracy is inevitably influenced by encoder angle error.Encoder angle error is usually directed to many
Error component, such as grating ruling error, setting-up eccentricity error and spindle motion error etc..In practical applications, should weaken
Even being eliminated the above angle error of encoder influences.Correcting common mode for encoder errors at present is mutually calibration, mutual school
Quasi- method is a kind of common angular error calibration method based on error separating technology, needs aided measurement device, such as multi-panel
Rib body or other higher precisions assist angular encoder, are compared with angular encoder measurement data to be calibrated, error
Meet the circle closure condition determined by linear equation.However, mutual calibration method can be very time-consuming with the increase of data volume, and
Changing bring vulnerable to measurement environment influences.
To solve the above-mentioned problems, method for self-calibrating is proposed.Domestic and foreign scholars carry out the self calibration of angular encoder
Correlative study, is widely used to various high-acruracy survey tasks at present.Method for self-calibrating application inverting, redundancy and error point
From technology, faster than mutual calibration method, more effectively, and do not need using external reference standard.Internationally recognized method is main
Including EDA (Equal Division Averaged) method, Ernst method and the side PFD (Prime Factor Division)
Method and TDR (Time-measurement Dynamic Reversal) method.These method for self-calibrating may be implemented to use Mr. Yu
The self calibration of single sensor in a little specific, ideal working environments.
Summary of the invention
The purpose of the present invention is to solve this problems, provide a kind of based on portable articulated coordinate machine Circular gratings
The method for self-calibrating of angle error, by the data measured online, error of fitting function curve analyzes its transfer function characteristics
The relationship between reading head layout and recoverable error component is obtained, corrects more multiple error harmonic wave point with less reading head to reach
The purpose Circular gratings angle error modification method of amount.
For achieving the above object, the technical scheme is that
Based on the method for self-calibrating of portable articulated coordinate machine Circular gratings angle error, that is, establish the circle of more reading heads
Grating angle error compensation model, which comprises the steps of: 1) establish reading head HjAngle measurement function model；
2) angle interval between three reading heads installed in Circular gratings angle-measuring equipment is set, the circle of three reading heads is obtained
Grating angle measured value；
3) to three reading head H1、H2、H3In the difference functions of two reading heads carry out curve fitting respectively, build respectively
Found two reading head angle measurement difference H2-H1、H3-H1、H3-H2Functional relation between angle position；
4) equiangularly spaced sampling is carried out to the difference curve after fitting, discrete Fourier transform is carried out to sampled point, and
The relational expression for bringing itself and transmission function W (n) into acquires the coefficient function F (n) of Fourier space；To coefficient function F (n) carry out from
Scattered inverse Fourier transform determines the penalty function model ε (θ) of Circular gratings angle error；
5) scaling method for utilizing polygon combination autocollimator, verifies the benefit of Circular gratings angle error self calibration model
Repay effect.
Preferably, the reading head H 1) is establishedjAngle measurement function model step is, according to EDA model, on Circular gratings surface
Equipped with M uniformly distributed reading head, reading head H is establishedjAngle measurement function model:
Hj(θ)=θ+ε (θ+αj),
Reading head HjRelative to datum readings head H1Orientation angle angle value be αj, rotation angle is θ, encoder angle error
Value is ε (θ), any two reading heads HjAnd HiAngle measurement data difference can obtain:
δji(θ)=Hj(θ)-Hi(θ)=ε (θ+αj)-ε(θ+αi),
Encoder angle error value ε (θ) can be obtained by discrete Fourier transform:
Wherein, F (n) is the coefficient of Fourier space ε (θ):
θk=2 π k/N,
Wherein, quantity of the N by taking angle at equal intervals in discrete Fourier transform.
Preferably, 2) the angle intervening step between the reading head is that three readings are installed in Circular gratings angle-measuring equipment
Head, the first reading head H1With the second reading head H2Angle between be divided into 81 °, the first reading head H1With third reading head H3Angle
Between be divided into 252 °.
Preferably, 2) the Circular gratings angle measurement step of the reading head is to acquire portable articulated coordinate machine
The angle measurement data of pedestal shafting Circular gratings angle-measuring equipment, hand-held joint arm keep the angle measuring system of pedestal shafting joint steady
It at the uniform velocity rotates about the axis one week, at interval of 3 ° -10 ° acquisition single reading head data, each one circle data of reading head acquisition are
120 to 36, selected data acquisition angles interval and each reading head acquisition data count amount is corresponding be multiplied should meet greater than etc.
In 360 °.
Preferably, 3) curve fitting step is to carry out curve fitting respectively to three reading head differences, matched curve
Function:
Wherein: a0For constant term, aiAnd biFor coefficient, θ is sampling angle value,
Datum readings head angle measurement data θ and its difference f (θ) is substituted into above-mentioned matched curve function model, minimum is utilized
Square law solving model coefficient a0、aiAnd bi。
Preferably, equal interval sampling 4) is carried out to the curve after fitting, sampled value model according to step 1 is carried out
Discrete Fourier transform respectively obtains E21(n)、E31(n)、E32(n):
E21(n)=DFT δ21(θ)；E31(n)=DFT δ31(θ)；E32(n)=DFT δ32(θ),
The Relationship of Coefficients formula for bringing Fourier space into finds out F (n):
Wherein, Pji(n) it is weight coefficient:
In Eji(n) under the premise of known, inverse discrete Fourier transform (IDFT) is carried out to F (n) and determines that encoder errors are mended
Repay function of ε (θ).
Preferably, 5) for same shafting, by measurement result and the mistake being calculated using polygon and autocollimator
Poor correction value is compared, and is verified with this to the compensation effect of ε (θ).
Compared with prior art, the beneficial effects of the present invention are:
The present invention has the following advantages compared to previous compensation method: considering that actual operating condition difference surveys Circular gratings
The influence of angular accuracy can online compensate angle error；More order harmonics can be completed with the reading head of negligible amounts
The compensation of error；More reading head Circular gratings angle error compensation models can be applied to rotary joint, improve rotary joint angle measurement essence
Degree, and then the on-line measurement precision of portable articulated coordinate machine is improved, improve product reliability.
The present invention is based on the method for the portable articulated coordinate machine angular encoder of more reading head harmonic analysis methods,
The relationship between reading head layout and recoverable error component is obtained, by analysis transfer function characteristics to reach with less
Reading head completes the purpose of higher precision measurement.It is simulated and is tested to verify optimum results, establish portable articulated type coordinate
The calibration method of measuring machine joint angular encoder.
Detailed description of the invention
The drawings herein are incorporated into the specification and forms part of this specification, and shows and meets implementation of the invention
Example, and be used to explain the principle of the present invention together with specification.
Fig. 1 is that the present invention is based on the Circular gratings of the method for self-calibrating of portable articulated coordinate machine Circular gratings angle error
Reading head angular distribution schematic diagram.
Fig. 2 is that the present invention is based on the method for self-calibrating second of portable articulated coordinate machine Circular gratings angle error readings
Head and the first reading head angle measurement data difference curve matching effect picture.
Fig. 3 is that the present invention is based on the method for self-calibrating third of portable articulated coordinate machine Circular gratings angle error readings
Head and the first reading head angle measurement data difference curve matching effect picture.
Fig. 4 is that the present invention is based on the method for self-calibrating third of portable articulated coordinate machine Circular gratings angle error readings
Head and the second reading head angle measurement data difference curve matching effect picture.
Fig. 5 is that the present invention is based on the comparison of the method for self-calibrating of portable articulated coordinate machine Circular gratings angle error realities
Experiment device schematic diagram.
Fig. 6 is the experiment compensation effect figure of joint arm standard shaft measurement.
Specific embodiment
Below in conjunction with attached drawing, technical scheme in the embodiment of the invention is clearly and completely described.
Method for self-calibrating of the embodiment based on portable articulated coordinate machine Circular gratings angle error establishes more readings
The Circular gratings angle error compensation model of head, includes the following steps: 1) to establish reading head HjAngle measurement function model；
According to EDA model, M uniformly distributed reading head, reading head H are equipped on Circular gratings surfacejRelative to datum readings head H1
Orientation angle angle value be αj, establish reading head HjAngle measurement function model:
Hj(θ)=θ+ε (θ+αj),
Hj(θ) is influenced by encoder angle error value ε (θ), and encoder errors would generally be due to the position of reading head
And phase shift is generated, in order to eliminate unknown rotation angle, θ, to any two reading heads HjAnd HiAngle measurement data difference can obtain:
δji(θ)=Hj(θ)-Hi(θ)=ε (θ+αj)-ε(θ+αi),
In order to obtain encoder errors value ε (θ), can be obtained by discrete Fourier transform (DFT):
Wherein, F (n) is the coefficient of Fourier space ε (θ):
θk=2 π k/N,
Wherein, quantity of the N by taking angle at equal intervals in DFT, in Eji(n) under the premise of known, direct computation of DFT can be passed through
Leaf inverse transformation (IDFT) determines encoder errors compensation model:
ε (θ)=IDFT (F (n)).
2) angle interval between three reading heads installed in Circular gratings angle-measuring equipment is set, the circle of three reading heads is obtained
Grating angle measured value；
In order to achieve the purpose that correct more multiple error harmonic component with less reading head, three are installed in Circular gratings angle-measuring equipment
A reading head, the first reading head H1With the second reading head H2Angle between be divided into 81 °, the first reading head H1With third reading head H3
Angle between be divided into 252 °.
According to error correction principle, transmission function is remembered are as follows:
Thus, if reading head installation site angle interval is equal to 2 π k/M, wherein k=1,2 ..., M-1, | Wji(n)|
=0, it may appear that harmonics restraint phenomenon.Based on the analysis to transfer function characteristics, it is known that angle interval appropriate is to influence harmonic wave
The key factor of error；
Define fn(α2,α3) judge that at three reading head angle intervals be respectively α2,α3In the case where, n order harmonics error
Whether can be corrected:
Then all harmonic components that cannot be detected of preceding N rank may be expressed as:
As shown in Figure 1, in the angle measuring system of three reading heads, by f (α2,α3)-α2,α3Functional relation pushes away to obtain three
81 ° and 252 ° are divided between reading head prioritization scheme angle；
To acquire the processing of the angle measurement data of portable articulated coordinate machine pedestal shafting Circular gratings angle-measuring equipment
For, hand-held joint arm rotates about the axis the angle measuring system of pedestal shafting joint steadily at the uniform velocity one week, at interval of 3 ° -10 °
Single reading head data are acquired, one circle data of each reading head acquisition are 120 to 36, selected data acquisition angles interval and every
A corresponding be multiplied of reading head acquisition data count amount should meet more than or equal to 360 °.
1 Circular gratings reading head angle measurement data of table and difference (pedestal shafting)
3) to three reading head H1、H2、H3In the difference functions of two reading heads carry out curve fitting respectively, build respectively
Found two reading head angle measurement difference H2-H1、H3-H1、H3-H2Functional relation between angle position；As shown in Figure 2, Figure 3, Figure 4
Fitting effect；
Due to the heterogeneity of data acquisition, Fourier transformation can not be directly carried out, is needed to difference data H2-H1、H3-
H1、H3-H2It carries out curve fitting respectively.Matched curve function is as follows:
Wherein: a0For constant term, aiAnd biFor coefficient, θ is sampling angle value.
Datum readings head angle measurement data θ and reading head angle measurement data difference f (θ) is substituted into the Function Modules of above-mentioned matched curve
In type, least square method solving model coefficient a is utilized0、aiAnd bi, partial data is as shown in table 2.
2 reading head angle measurement data difference fitting function model coefficient (part) of table
4) equiangularly spaced sampling is carried out to the difference curve after fitting, by sampled point model according to step 1 into
Row discrete Fourier transform respectively obtains E21(n)、E31(n)、E32(n):
E21(n)=DFT δ21(θ)；E31(n)=DFT δ31(θ)；E32(n)=DFT δ32(θ),
The relational expression for bringing itself and transmission function W (n) into finds out the coefficient function F (n) of Fourier space:
Wherein, Pji(n) it is weight coefficient:
The principle according to 1, in Eji(n) under the premise of known, discrete fourier inversion is carried out to coefficient function F (n)
It changes (IDFT) and determines Circular gratings angle error penalty function model ε (θ).
5) for same shafting, by measurement result and the error correction values being calculated using polygon and autocollimator
It is compared, compensation effect of ε (θ) is verified with this.
As shown in figure 5, comparative experiments device, including photoelectric auto-collimator 1, polygon 2, axis body 3, insulating box 4, such as scheme
Shown in 6, it will be surveyed to verify the compensation effect that novel Circular gratings angle error self calibration model has been established for same shafting
Amount result is compared with using polygon 2 with the error correction values that 1 survey calculation of photoelectric auto-collimator obtains, with this to ε
The compensation effect of (θ) is verified.
Embodiments described above is only a part of the embodiment of the present invention, instead of all the embodiments.Based on this
Embodiment in invention, every other reality obtained by those of ordinary skill in the art without making creative efforts
Example is applied, shall fall within the protection scope of the present invention.
Claims (7)
1. the method for self-calibrating based on portable articulated coordinate machine Circular gratings angle error, which is characterized in that including as follows
Step: 1) reading head H is establishedjAngle measurement function model；
2) the angle interval installed between three reading heads in Circular gratings angle-measuring equipment is set, the Circular gratings of three reading heads are obtained
Angle measurement；
3) to three reading head H1、H2、H3In the difference functions of two reading heads carry out curve fitting respectively, establish two respectively
A reading head angle measurement difference H2-H1、H3-H1、H3-H2Functional relation between angle position；
4) equiangularly spaced sampling is carried out to the difference curve after fitting, discrete Fourier transform is carried out to sampled point, and bring into
The relational expression of itself and transmission function W (n) acquire the coefficient function F (n) of Fourier space；Discrete Fu is carried out to coefficient function F (n)
In leaf inverse transformation determine the penalty function model ε (θ) of Circular gratings angle error；
5) scaling method of polygon combination autocollimator, the compensation effect of verifying Circular gratings angle error self calibration model are utilized
Fruit.
2. the method for self-calibrating according to claim 1 based on portable articulated coordinate machine Circular gratings angle error,
It is characterized in that, 1) establish the reading head HjAngle measurement function model step is, according to EDA model, to be equipped on Circular gratings surface equal
M reading head of cloth, establishes reading head HjAngle measurement function model:
Hj(θ)=θ+ε (θ+αj),
Reading head HjRelative to datum readings head H1Orientation angle angle value be αj, rotation angle is θ, and encoder angle error value is ε
(θ), any two reading heads HjAnd HiAngle measurement data difference can obtain:
δji(θ)=Hj(θ)-Hi(θ)=ε (θ+αj)-ε(θ+αi),
Encoder angle error value ε (θ) can be obtained by discrete Fourier transform:
Wherein, F (n) is the coefficient of Fourier space ε (θ):
θk=2 π k/N,
Wherein, quantity of the N by taking angle at equal intervals in discrete Fourier transform.
3. the method for self-calibrating according to claim 1 based on portable articulated coordinate machine Circular gratings angle error,
It is characterized in that, 2) the angle intervening step between the reading head is that three reading heads are installed in Circular gratings angle-measuring equipment, first
Reading head H1With the second reading head H2Angle between be divided into 81 °, the first reading head H1With third reading head H3Angle between be divided into
252°。
4. the method for self-calibrating according to claim 1 based on portable articulated coordinate machine Circular gratings angle error,
It is characterized in that, 2) the Circular gratings angle measurement step of the reading head is to acquire portable articulated coordinate machine pedestal axis
Be the angle measurement data of Circular gratings angle-measuring equipment, hand-held joint arm make the angle measuring system of pedestal shafting joint steadily at the uniform velocity around
Axis rotates a circle, and at interval of 3 ° -10 ° acquisition single reading head data, each one circle data of reading head acquisition are 120 to 36
A, the multiplication corresponding with each reading head acquisition data count amount of selected data acquisition angles interval should meet more than or equal to 360 °.
5. the method for self-calibrating according to claim 1 based on portable articulated coordinate machine Circular gratings angle error,
It is characterized in that, 3) curve fitting step is to carry out curve fitting respectively to three reading head differences, matched curve function:
Wherein: a0For constant term, aiAnd biFor coefficient, θ is sampling angle value,
Datum readings head angle measurement data θ and its difference f (θ) is substituted into above-mentioned matched curve function model, least square is utilized
Method solving model coefficient a0、aiAnd bi。
6. the method for self-calibrating according to claim 1 based on portable articulated coordinate machine Circular gratings angle error,
It is characterized in that, 4) equal interval sampling is carried out to the curve after fitting, sampled value model according to step 1 is subjected to discrete Fu
In leaf transformation respectively obtain E21(n)、E31(n)、E32(n):
E21(n)=DFT δ21(θ)；E31(n)=DFT δ31(θ)；E32(n)=DFT δ32(θ),
The Relationship of Coefficients formula for bringing Fourier space into finds out F (n):
Wherein, Pji(n) it is weight coefficient:
In Eji(n) under the premise of known, inverse discrete Fourier transform is carried out to F (n) and determines encoder errors penalty function ε (θ).
7. the method for self-calibrating according to claim 1 based on portable articulated coordinate machine Circular gratings angle error,
It is characterized in that, 5) for same shafting, by measurement result and the error correction being calculated using polygon and autocollimator
Value is compared, and is verified with this to the compensation effect of ε (θ).
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| CN111520456A (en) * | 2020-04-29 | 2020-08-11 | 浙江大学昆山创新中心 | Intelligent speed reducer |
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| CN111520456A (en) * | 2020-04-29 | 2020-08-11 | 浙江大学昆山创新中心 | Intelligent speed reducer |
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| CN114417532B (en) * | 2022-01-21 | 2024-04-16 | 西安交通大学 | Method and system for optimizing assembly inclination error of circular grating encoder |
| CN115355813A (en) * | 2022-10-21 | 2022-11-18 | 北京科技大学 | High-precision three-axis nonmagnetic test turntable system |
| CN116608816A (en) * | 2023-07-18 | 2023-08-18 | 东营市工业产品检验与计量检定中心 | Calibration method and device for calibrating device of small-angle measuring instrument |
| CN116608816B (en) * | 2023-07-18 | 2023-09-26 | 东营市工业产品检验与计量检定中心 | Calibration method and device for calibrating device of small-angle measuring instrument |
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