CN110375694B - Self-calibration method for circular grating angle measurement error based on portable articulated coordinate measuring machine - Google Patents
Self-calibration method for circular grating angle measurement error based on portable articulated coordinate measuring machine Download PDFInfo
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Abstract
The invention discloses a self-calibration method for circular grating angle measurement error based on a portable articulated coordinate measuring machine, which comprises the following steps: establishing a reading head HjMeasuring an angle function model; setting the angle intervals of the three reading heads of the circular grating angle measuring device to obtain the angle measurement values of the circular gratings of the three reading heads; for three reading heads H1、H2、H3Respectively performing curve fitting on the difference function of the two reading heads, and respectively establishing angle measurement difference values H of the two reading heads2‑H1、H3‑H1、H3‑H2As a function of angular position; sampling the fitted difference curve at equal angle intervals, performing discrete Fourier transform on sampling points, and substituting the discrete Fourier transform into a relational expression of the sampling points and a transfer function to obtain a Fourier series coefficient function F (n); performing inverse discrete Fourier transform to determine a compensation function model (theta) of the circular grating angle measurement error; and verifying the compensation effect of the circular grating angle measurement error self-calibration model by using a calibration method combining a polygon with an autocollimator. And the error compensation of the multiple order harmonic is completed by using few reading heads, so that the reliability of the product is improved.
Description
Technical Field
The invention belongs to the field of articulated coordinate measuring machines, and particularly relates to a self-calibration method based on a circular grating angle measurement error of a portable articulated coordinate measuring machine.
Background
The portable joint type coordinate measuring machine is a portable non-orthogonal measuring device made by simulating human body arms, is widely used in the industries of mould manufacture, machining and manufacture, and has the advantages of small volume, light weight, convenient carrying, flexible measurement, large measurement space, strong environmental adaptability and the like. The portable articulated coordinate measuring machine is generally composed of a base, a rotary joint, a measuring arm and a measuring head which are connected in series, and the structure has an error amplification effect. Therefore, it is very important to perform precision calibration for the angle encoder installed at the rotary joint.
The circular grating angle encoder is a complete circle angle measuring device, and in the angle measuring process of the portable joint type coordinate measuring machine, the angle measuring precision is inevitably influenced by the angle measuring error of the encoder. Encoder angular errors typically involve many error components such as raster ruling errors, installation eccentricity errors, and shafting motion errors. In practical applications, the influence of the above angle measurement error of the encoder should be reduced or even eliminated. At present, a common mode for correcting the error of the encoder is mutual calibration, the mutual calibration method is a common angle error calibration method based on an error separation technology, an auxiliary measuring device such as a polygon or other higher-precision auxiliary angle encoder is needed to be compared with the measured data of the angle encoder to be calibrated, and the error of the mutual calibration method meets the circle closing condition determined by a linear equation. However, the mutual calibration method is very time-consuming as the amount of data increases and is susceptible to changes in the measurement environment.
In order to solve the above problems, a self-calibration method is proposed. Scholars at home and abroad conduct relevant research on self calibration of an angle encoder, and the method is widely applied to various high-precision measurement tasks at present. The self-calibration method applies inversion, redundancy and error separation techniques, is faster and more efficient than the cross-calibration method, and does not require the use of external reference standards. Internationally recognized methods mainly include the eda (equal Division acquired) method, the Ernst method, and the pfd (prime Factor Division) method, and the TDR (Time-measure Dynamic reverse) method. These self-calibration methods may enable self-calibration of a single sensor for use in certain specific, ideal operating environments.
Disclosure of Invention
The invention aims to solve the problem and provides a self-calibration method for circular grating angle measurement errors based on a portable articulated coordinate measuring machine.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the self-calibration method based on the circular grating angle measurement error of the portable articulated coordinate measuring machine is characterized by comprising the following steps of: 1) establishing a reading head HjMeasuring an angle function model;
2) setting the angle interval among three reading heads installed in the circular grating angle measuring device to obtain the circular grating angle measurement values of the three reading heads;
3) for three reading heads H1、H2、H3Respectively performing curve fitting on the difference function of the two reading heads, and respectively establishing angle measurement difference values H of the two reading heads2-H1、H3-H1、H3-H2As a function of angular position;
4) sampling the fitted difference curve at equal angle intervals, performing discrete Fourier transform on sampling points, and substituting the sampling points into a relational expression of the sampling points and the transfer function W (n) to obtain a Fourier series coefficient function F (n); performing inverse discrete Fourier transform on the coefficient function F (n) to determine a compensation function model (theta) of the circular grating angle measurement error;
5) and verifying the compensation effect of the circular grating angle measurement error self-calibration model by using a calibration method combining a polygon with an autocollimator.
Preferably, 1) the read head H is establishedjThe angle measurement function model comprises the steps of arranging M reading heads uniformly distributed on the surface of the circular grating according to an EDA model, and establishing a reading head HjAngle measurement function model:
Hj(θ)＝θ+(θ+αj)，
reading head HjRelative to the reference reading head H1Has a positioning angle value of alphajThe rotation angle is theta, the error value of the encoder angle is theta, and any two reading heads HjAnd HiThe difference of the angle measurement data can be obtained as follows:
ji(θ)＝Hj(θ)-Hi(θ)＝(θ+αj)-(θ+αi)，
the encoder angle error value (θ) is obtained by discrete fourier transform:
where f (n) is the coefficient of the fourier series (θ):
θk＝2πk/N，
where N is the number of equally spaced angles taken in the discrete fourier transform.
Preferably, 2) the angular interval between the reading heads is that three reading heads are arranged in the circular grating angle measuring device, and the first reading head H1And a second reading head H2At an angular interval of 81 °, a first reading head H1And a third read head H3Is 252 deg..
Preferably, 2) the round grating angle measurement value of the reading head comprises the steps of collecting angle measurement data of a round grating angle measurement device of a base shafting of the portable articulated coordinate measuring machine, enabling the angle measurement system at the joint of the base shafting to rotate around an axis at a constant speed for a circle by a handheld articulated arm, collecting reading head data once at intervals of 3-10 degrees, collecting 120-36 circles of data by each reading head, and multiplying the selected data collection angle interval by the total quantity of the collected data of each reading head to meet the requirement that the data collection angle interval is greater than or equal to 360 degrees.
Preferably, 3) the curve fitting step is to perform curve fitting on the difference values of the three reading heads respectively, and fit a curve function:
wherein: a is0Is a constant term ofiAnd biIs a coefficient, theta is a sampling angle value,
the angle measurement data theta of the reference reading head and the difference f (theta) thereof) Substituting into the fitted curve function model, and solving model coefficient a by using least square method0、aiAnd bi。
Preferably, 4) sampling the fitted curve at equal intervals, and performing discrete Fourier transform on the sampled values according to the model in the step 1 to respectively obtain E21(n)、E31(n)、E32(n)：
E21(n)＝DFT21(θ)；E31(n)＝DFT31(θ)；E32(n)＝DFT32(θ)，
The coefficient relation in the Fourier series is obtained as F (n):
wherein, Pji(n) is a weight coefficient:
at Eji(n) determining the encoder error compensation function (theta) by performing an Inverse Discrete Fourier Transform (IDFT) on f (n) under the known premise.
Preferably, 5) comparing the measurement result with the error correction value calculated by using the polygon and the autocollimator for the same axis system, thereby verifying the compensation effect of (theta).
Compared with the prior art, the invention has the beneficial effects that:
compared with the prior compensation method, the method has the following advantages: the influence of different actual operating environments on the angle measurement precision of the circular grating is considered, and the angle measurement error can be compensated on line; the compensation of more order harmonic errors can be completed by using a small number of reading heads; the multi-reading-head circular grating angle measurement error compensation model can be applied to a rotary joint, so that the angle measurement precision of the rotary joint is improved, the online measurement precision of the portable joint type coordinate measuring machine is further improved, and the product reliability is improved.
The invention relates to a method for a portable articulated coordinate measuring machine angle encoder based on a multi-reading head harmonic analysis method, which obtains the relationship between the layout of the reading heads and correctable error components by analyzing the characteristics of a transfer function so as to achieve the aim of completing higher-precision measurement by using fewer reading heads. And carrying out simulation and experiment to verify the optimization result and establish a calibration method of the angle encoder at the joint of the portable joint type coordinate measuring machine.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention.
Fig. 1 is a schematic view of the angular distribution of the reading head of the circular grating based on the self-calibration method for the angular measurement error of the circular grating of the portable articulated coordinate measuring machine of the present invention.
Fig. 2 is a diagram showing the effect of curve fitting of the difference between the angle measurement data of the second reading head and the angle measurement data of the first reading head in the self-calibration method based on the angle measurement error of the circular grating of the portable articulated coordinate measuring machine according to the present invention.
FIG. 3 is a diagram showing the effect of curve fitting of the difference between the angle measurement data of the third reading head and the first reading head of the self-calibration method based on the angle measurement error of the circular grating of the portable articulated coordinate measuring machine according to the present invention.
FIG. 4 is a diagram showing the effect of curve fitting of the difference between the angle measurement data of the third readhead and the angle measurement data of the second readhead based on the self-calibration method for the angle measurement error of the circular grating of the portable articulated coordinate measuring machine of the present invention.
FIG. 5 is a schematic diagram of a comparative experimental apparatus of the self-calibration method for circular grating angle measurement error based on the portable articulated coordinate measuring machine of the present invention.
Fig. 6 is a diagram of experimental compensation effect of the measurement of the base axis of the articulated arm.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.
The embodiment of the self-calibration method based on the circular grating angle measurement error of the portable articulated coordinate measuring machine is to establish a circular grating angle measurement error compensation model of a multi-reading head, and the self-calibration method comprises the following stepsThe method comprises the following steps: 1) establishing a reading head HjMeasuring an angle function model;
according to EDA model, M uniformly distributed reading heads are arranged on the surface of the circular grating, and the reading heads HjRelative to the reference reading head H1Has a positioning angle value of alphajEstablishing a reading head HjAngle measurement function model:
Hj(θ)＝θ+(θ+αj)，
Hj(theta) is affected by the encoder angle error value (theta), which is usually phase shifted due to the position of the readheads, for any two readheads H in order to eliminate the unknown rotation angle thetajAnd HiThe difference of the angle measurement data can be obtained as follows:
ji(θ)＝Hj(θ)-Hi(θ)＝(θ+αj)-(θ+αi)，
to obtain the encoder error value (θ), it is available by Discrete Fourier Transform (DFT):
where f (n) is the coefficient of the fourier series (θ):
θk＝2πk/N，
where N is the number of equally spaced angles taken in the DFT, at Eji(n) given, the encoder error compensation model can be determined by Inverse Discrete Fourier Transform (IDFT):
(θ)＝IDFT(F(n))。
2) setting the angle interval among three reading heads installed in the circular grating angle measuring device to obtain the circular grating angle measurement values of the three reading heads;
in order to achieve the purpose of correcting more error harmonic components by using fewer reading heads, three reading heads are arranged in the circular grating angle measuring device, and the first reading head H1And a second reading head H2At an angular interval of 81 °, a first reading head H1And a third read head H3Is 252 deg..
According to the error correction principle, the transfer function is recorded as:
it follows that if the reading head mounting position angle interval is equal to 2 pi k/M, where k is 1,2jiWhen (n) | is 0, a harmonic suppression phenomenon occurs. Based on the analysis of the transfer function characteristics, it can be known that the proper angle interval is a key factor influencing harmonic errors;
definition fn(α2,α3) To judge that the angle intervals of the three reading heads are respectively alpha2,α3Whether the nth order harmonic error can be corrected:
then all the harmonic components of the first nth order that cannot be detected can be expressed as:
in the case of a three-reading head goniometric system, as shown in FIG. 1, the angle is measured by f (α)2,α3)-α2,α3The functional relation is used for deducing the angle interval of the optimization schemes of the three reading heads to be 81 degrees and 252 degrees;
taking the process of collecting the angle measurement data of the portable articulated coordinate measuring machine base shafting circular grating angle measuring device as an example, the handheld articulated arm enables the angle measuring system at the joint of the base shafting to rotate around the axis at a constant speed for a circle, reading head data are collected once every 3-10 degrees, each reading head collects 120-36 circles of data, and the selected data collection angle interval is multiplied by the total quantity of the collected data of each reading head to meet the condition that the data is more than or equal to 360 degrees.
TABLE 1 round grating reading head angle measurement data and difference (base shafting)
3) For three reading heads H1、H2、H3Respectively performing curve fitting on the difference function of the two reading heads, and respectively establishing angle measurement difference values H of the two reading heads2-H1、H3-H1、H3-H2As a function of angular position; the fitting effect as shown in fig. 2, 3, 4;
due to the non-uniformity of data acquisition, the Fourier transform can not be directly carried out, and the difference data H needs to be processed2-H1、H3-H1、H3-H2Curve fitting was performed separately. The fitted curve function is as follows:
wherein: a is0Is a constant term ofiAnd biIs a coefficient, θ is a sampling angle value.
Substituting the reference reading head angle measurement data theta and the reading head angle measurement data difference f (theta) into the function model of the fitting curve, and solving the model coefficient a by using a least square method0、aiAnd biAnd part of the data is shown in table 2.
TABLE 2 difference fitting function model coefficients (parts) of reading head angle measurement data
4) Sampling the fitted difference curve at equal angle intervals, and performing discrete Fourier transform on sampling points according to the model in the step 1 to respectively obtain E21(n)、E31(n)、E32(n)：
E21(n)＝DFT21(θ)；E31(n)＝DFT31(θ)；E32(n)＝DFT32(θ)，
A coefficient function F (n) of Fourier series is obtained by substituting the relation between the coefficient function F (n) and the transfer function W (n):
wherein, Pji(n) is a weight coefficient:
according to the principle described in 1, at EjiAnd (n) under the known premise, performing Inverse Discrete Fourier Transform (IDFT) on the coefficient function F (n) to determine a circular grating angle measurement error compensation function model (theta).
5) And (3) comparing the measurement result with the error correction value obtained by using the polygon and the autocollimator for the same axis system, and verifying the compensation effect of the (theta).
As shown in fig. 5, the comparative experiment apparatus includes a photoelectric autocollimator 1, a polygon 2, a shaft 3, and an oven 4, and as shown in fig. 6, in order to verify the compensation effect of the new circular grating angle measurement error self-calibration model, for the same axis, the measurement result is compared with the error correction value obtained by measurement and calculation using the polygon 2 and the photoelectric autocollimator 1, so as to verify the compensation effect of (θ).
The embodiments described above are only a part of the embodiments of the present invention, and not all of them. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Claims (6)
1. The self-calibration method based on the circular grating angle measurement error of the portable articulated coordinate measuring machine is characterized by comprising the following steps of: 1) establishing a reading head HjMeasuring an angle function model;
2) setting the angle interval between three reading heads installed in the circular grating angle measuring device to obtain the circular grating angle measurement values of the three reading heads;
3) for three reading heads H1、H2、H3Respectively performing curve fitting on the difference function of the two reading heads, and respectively establishing angle measurement difference values H of the two reading heads2-H1、H3-H1、H3-H2As a function of angular position;
4) sampling the fitted curves at equal intervals, and performing discrete Fourier transform on the sampling values according to the model in the step 1 to respectively obtain E21(n)、E31(n)、E32(n)：
E21(n)＝DFT21(θ)；E31(n)＝DFT31(θ)；E32(n)＝DFT32(θ)，
The coefficient relation in the Fourier series is obtained as F (n):
wherein, Pji(n) is a weight coefficient:
at Eji(n) inverse discrete Fourier transform (ID) is performed on F (n) under the known premiseFT) determining an encoder error compensation function (theta);
5) and verifying the compensation effect of the circular grating angle measurement error self-calibration model by using a calibration method combining a polygon with an autocollimator.
2. The self-calibration method for angular error measurement based on portable articulated coordinate measuring machine circular grating of claim 1, wherein 1) the reading head H is establishedjThe angle measurement function model comprises the steps of arranging M reading heads uniformly distributed on the surface of the circular grating according to an EDA model, and establishing a reading head HjAngle measurement function model:
Hj(θ)＝θ+(θ+αj)，
reading head HjRelative to the reference reading head H1Has a positioning angle value of alphajThe rotation angle is theta, the error value of the encoder angle is theta, and any two reading heads HjAnd HiThe difference of the angle measurement data can be obtained as follows:
ji(θ)＝Hj(θ)-Hi(θ)＝(θ+αj)-(θ+αi)，
the encoder angle error value (θ) is obtained by discrete fourier transform:
where f (n) is the coefficient of the fourier series (θ):
θk＝2πk/N，
where N is the number of equally spaced angles taken in the discrete fourier transform.
3. The self-calibration method for angular error measurement based on portable articulated coordinate measuring machine circular grating of claim 1, characterized by 2) the self-calibration between the reading headsThe angle interval step comprises mounting three reading heads in the circular grating angle measuring device, wherein the first reading head H1And a second reading head H2At an angular interval of 81 °, a first reading head H1And a third read head H3Is 252 deg..
4. The self-calibration method for the angle measurement error of the circular grating based on the portable articulated coordinate measuring machine according to claim 1, wherein 2) the step of measuring the angle of the circular grating of the reading head comprises the steps of collecting the angle measurement data of the circular grating angle measurement device of the base shafting of the portable articulated coordinate measuring machine, enabling the handheld articulated arm to enable the angle measurement system at the joint of the base shafting to rotate around the axis at a stable and uniform speed, collecting the data of the reading head once every 3-10 degrees, collecting 120-36 circles of data for each reading head, and multiplying the selected angle interval of the data by the total quantity of the collected data of each reading head to satisfy more than or equal to 360 degrees.
5. The self-calibration method for angular measurement error based on portable articulated coordinate measuring machine circular grating of claim 1, wherein 3) the curve fitting step is to respectively perform curve fitting to the difference values of the three reading heads, fitting a curve function:
wherein: a is0Is a constant term ofiAnd biIs a coefficient, theta is a sampling angle value,
substituting the reference reading head angle measurement data theta and the difference f (theta) thereof into the fitting curve function model, and solving the model coefficient a by using a least square method0、aiAnd bi。
6. The self-calibration method for angular measurement error of circular grating based portable articulated coordinate measuring machine according to claim 1, wherein 5) the compensation effect of (θ) is verified by comparing the measurement result with the error correction value calculated by using the polygon and the autocollimator for the same axis.
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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 |
| CN115355813B (en) * | 2022-10-21 | 2023-03-24 | 北京科技大学 | High-precision three-axis nonmagnetic test turntable system |
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