CN116380147A - Round grating self-calibration method and device based on inertia and single reading head - Google Patents

Round grating self-calibration method and device based on inertia and single reading head Download PDF

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CN116380147A
CN116380147A CN202310346448.8A CN202310346448A CN116380147A CN 116380147 A CN116380147 A CN 116380147A CN 202310346448 A CN202310346448 A CN 202310346448A CN 116380147 A CN116380147 A CN 116380147A
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line
circular grating
time interval
reading head
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王笑一
肖龙远
郑坤磊
赵呈祥
刘明康
姚天阳
孙秀照
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Henan University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D18/00—Testing or calibrating apparatus or arrangements provided for in groups G01D1/00 - G01D15/00
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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 invention provides a circular grating self-calibration method and device based on inertia and a single reading head, which are used for acquiring time intervals of successive occurrence of adjacent graduation lines of a circular grating according to a steady rotating speed brought by a large inertia flywheel, pulse width measurement of an encoder and a circumference sealing principle, establishing a circular grating error compensation model, converting the rotating time of the circular grating into an actual rotating angle of the circular grating, and further obtaining a compensation value of the angle measurement error of the circular grating encoder. The calibration accuracy of the technical scheme provided by the invention does not depend on the standard device, can reach higher calibration accuracy than that of a common standard device, has lower cost compared with the traditional technical scheme, and can be applied to round grating calibration in key extreme occasions such as space satellites, special robots and the like.

Description

Round grating self-calibration method and device based on inertia and single reading head
Technical Field
The invention belongs to the technical field of precision measurement, and particularly relates to a round grating self-calibration method and device based on a reading head.
Background
The circular grating is a commonly used encoder for angle measurement, has the advantages of high resolution, small volume, convenient installation, high response speed and the like, and is widely applied to the fields of aerospace, intelligent robots, high-grade numerical control machine tools, high-precision coordinate measuring machines and the like. Along with the development of science and technology, various instruments and equipment have higher requirements on angle measurement precision, and higher requirements on the angle measurement precision of the circular grating are also provided;
a circular grating system is typically composed of a circular grating and a reading head. The angle measurement error of the circular grating system mainly comes from the line scribing error and the installation error (including eccentricity, inclination, circular grating ring deformation) of the circular grating, and the like. In order to improve the measurement accuracy of the circular grating, calibration of the circular grating is a common effective means.
The round grating calibration method can be classified into a general method (non-self-calibration method) by means of an etalon or other instrument and a self-calibration method. A common round grating calibration method needs to be used for a precise polygon and an auto-collimator, and at the moment, the calibration precision is limited by the manufacturing precision and the calibration precision of the polygon, and the calibration process is complex and has high requirements on environment. Another common round grating calibration method needs to use a measuring instrument with a higher precision level such as a laser interferometer, and is difficult to realize unmanned remote on-machine calibration. Both of the above methods are non-self-calibrating methods.
At present, a circular grating self-calibration method is generally realized based on a multi-reading head, and the common method is as follows: n readheads are evenly distributed around the circular grating, and the average of the n readhead readings is calculated as the final measurement value. The method is simple in principle, and can remove the influence of harmonic components except for the integer multiple frequency of n in an error curve on reading accuracy;
in addition, the research of self-calibration of the circular grating by using a plurality of reading heads in a special arrangement mode of 2*3 or 3×4 is also available, so that the number of the reading heads required for self-calibration can be reduced to a certain extent, but the number of the reading heads used in the method is still more, and generally exceeds 4. Such self-calibration methods also suffer from certain drawbacks: (1) The number of read heads is relatively large, so that the cost is high, and the more read heads are used, the higher the cost of the self-calibration system is;
(2) The accuracy of the goniometer system is affected by the number of readheads, which can lead to a decrease in the goniometer accuracy of the goniometer system.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a circular grating self-calibration method based on inertia and a single reading head and a circular grating self-calibration device based on inertia and a single reading head. The invention can be applied to the calibration of circular gratings in key extreme occasions such as space satellites, special robots and the like, and can also be used for the calibration of displacement sensors such as magnetic gratings, steel gratings and time gratings.
One or more embodiments of the present specification provide a circular grating self-calibration method based on inertia and a single read head, the method comprising the steps of:
step one: the reading head is fixed, the circular grating rotates freely by k×360 degrees, k is larger than or equal to 4, and the time interval between k×m adjacent graduation lines of the circular grating is measured in the period, and is recorded as g 1 ,g 2 ,...,g km The matrix notation is adopted to be marked as G= { G 1 ,g 2 ,...,g km M is the total number of lines in one circle of the circular grating, g 1 G for the time interval of the m-th line and the 1-th line appearing successively 2 For the time interval between the occurrence of the 1 st line and the 2 nd line, and so on, g i The time interval of the i-1 th line and the i th line appearing in sequence is set;
step two: data in G obtained by
Figure SMS_1
Processing to obtain omega 1 ,ω 2 ,...,ω km Denoted as w= { ω 1 ,ω 2 ,...,ω km }, wherein->
Figure SMS_2
θ 0 In rad, ω i Is in rad/s;
step three: dividing the data in the array W into m groups, and marking the m groups as W by adopting a matrix notation 1 ,W 2 ,...,W m Let W 1 ＝{ω 1 ,ω 1+m ,...,ω 1+(z-1)m }，W 2 ＝{ω 2 ,ω 2+m ,...,ω 2+(z-1)m }，…，W m ＝{ω m ,ω 2m ,...,ω zm -wherein z is equal to the integer part of k;
step four: for the obtained m groups of data W 1 ,W 2 ,...,W m Respectively performing least square polynomial fitting to obtain m angular velocity-time curves, denoted as f 1 (t),f 2 (t),...,f m (t) substituting it into
Figure SMS_3
The angular velocity of the circular grating at time t can be obtained>
Figure SMS_4
Wherein->
Figure SMS_5
Step five: sum the data in matrix G with a function
Figure SMS_6
Substituted into->
Figure SMS_7
Obtain c 1 ,c 2 ,...c km Denoted as c= { C 1 ,c 2 ,...c km }, wherein c i In units of degrees;
step six: by means of averaging, i.e.
Figure SMS_8
Processing the data in C to obtain m data, which is marked as C' = { C 1 ',c 2 ',...c m '}；
Step seven: formulating the data in C
Figure SMS_9
Processing and marking the data obtained as +.>
Figure SMS_10
Step eight: taking the mth line as the reference (i.e. the measurement error of the mth line is 0), the measurement error of the jth line is
Figure SMS_11
And obtaining the angle measurement error compensation value of the reading head on the circular grating.
One or more embodiments of the present specification also provide another inertial and single read head based circular grating self-calibration method, comprising the steps of:
step one: the reading head is fixed, the circular grating rotates freely by k×360 degrees, k is larger than or equal to 4, and the time interval between k×m adjacent graduation lines of the circular grating is measured in the period, and is recorded as g 1 ,g 2 ,...,g km The matrix notation is adopted to be marked as G= { G 1 ,g 2 ,...,g km M is the total number of lines in one circle of the circular grating, g 1 G for the time interval of the m-th line and the 1-th line appearing successively 2 For the time interval between the occurrence of the 1 st line and the 2 nd line, and so on, g i The time interval of the i-1 th line and the i th line appearing in sequence is set;
step two: fitting a least square polynomial and a trigonometric function to the data in the matrix G so as to remove some random error components contained in the original data, and optimizing the original data to obtain a 1-time-interval number discrete curve, which is marked as T (x), wherein x represents an xth time interval, and x is more than or equal to 1 and less than or equal to km; taking k x m data from T (x), and recording by matrixThe method is denoted as t= { T 1 ,t 2 ,...,t km }, t is i ＝T(i)；
Step three: data in the array T is pressed
Figure SMS_12
Processing to obtain omega 1 ,ω 2 ,...,ω km Denoted as w= { ω 1 ,ω 2 ,...,ω km }, wherein->
Figure SMS_13
θ 0 In rad, ω i Is in rad/s;
step four: fitting the data in W by using a least square polynomial to obtain 1 angular velocity-time curve, recording as omega (t), and obtaining the angular velocity omega (t) of the circular grating at the moment t, wherein
Figure SMS_14
Step five: substituting the data and function ω (T) in the matrix T
Figure SMS_15
Obtain c 1 ,c 2 ,...c km Denoted as c= { C 1 ,c 2 ,...c km }, wherein c i In units of degrees;
step six: by means of averaging, i.e.
Figure SMS_16
Processing the data in C to obtain m data, which is marked as C' = { C 1 ',c 2 ',...c m ' wherein z is equal to the integer portion of k;
step seven: formulating the data in C
Figure SMS_17
Processing and marking the data obtained as +.>
Figure SMS_18
Step eight: based on the mth line (i.e. conventionThe measurement error of the mth line is 0), then the measurement error of the jth line is
Figure SMS_19
And obtaining the angle measurement error compensation value of the reading head on the circular grating.
One or more embodiments of the present specification also provide yet another inertial and single read head based circular grating self-calibration method, comprising the steps of:
step one: the reading head is fixed, the circular grating rotates freely by k×360 degrees, k is larger than or equal to 4, and the time interval between k×m adjacent graduation lines of the circular grating is measured in the period, and is recorded as g 1 ,g 2 ,...,g km The matrix notation is adopted to be marked as G= { G 1 ,g 2 ,...,g km M is the total number of lines in one circle of the circular grating, g 1 G for the time interval of the m-th line and the 1-th line appearing successively 2 For the time interval between the occurrence of the 1 st line and the 2 nd line, and so on, g i The time interval of the i-1 th line and the i th line appearing in sequence is set;
step two: fitting a least square polynomial and a trigonometric function to the data in the matrix G so as to remove some random error components contained in the original data, and optimizing the original data to obtain a 1-time-interval number discrete curve, which is marked as T (x), wherein x represents an xth time interval, and x is more than or equal to 1 and less than or equal to km; taking k×m data from T (x), and using matrix notation to mark as t= { T 1 ,t 2 ,...,t km }, t is i ＝T(i)；
Step three: data in the array T is pressed
Figure SMS_20
Processing to obtain omega 1 ,ω 2 ,...,ω km Denoted as w= { ω 1 ,ω 2 ,...,ω km }, wherein->
Figure SMS_21
θ 0 In rad, ω i Is in rad/s;
step four: dividing the data in the array W into m groups, and marking the m groups as W by adopting a matrix notation 1 ,W 2 ,...,W m Let W 1 ＝{ω 1 ,ω 1+m ,...,ω 1+(z-1)m }，W 2 ＝{ω 2 ,ω 2+m ,...,ω 2+(z-1)m }，…，W m ＝{ω m ,ω 2m ,...,ω zm -wherein z is equal to the integer part of k;
step five: for the obtained m groups of data W 1 ,W 2 ,...,W m Respectively performing least square polynomial fitting to obtain m angular velocity-time curves, denoted as f 1 (t),f 2 (t),...,f m (t) substituting it into
Figure SMS_22
The angular velocity of the circular grating at time t can be obtained>
Figure SMS_23
Wherein->
Figure SMS_24
Step six: sum data and functions in matrix T
Figure SMS_25
Substituted into->
Figure SMS_26
Obtain c 1 ,c 2 ,...c km Denoted as c= { C 1 ,c 2 ,...c km }, wherein c i In units of degrees;
step seven: by means of averaging, i.e.
Figure SMS_27
Processing the data in C to obtain m data, which is marked as C' = { C 1 ',c 2 ',...c m '}；
Step eight: formulating the data in C
Figure SMS_28
Processing and matrix-forming the obtained dataNotation->
Figure SMS_29
Step nine: taking the mth line as the reference (i.e. the measurement error of the mth line is 0), the measurement error of the jth line is
Figure SMS_30
And obtaining the angle measurement error compensation value of the reading head on the circular grating.
One or more embodiments of the present specification further provide a circular grating self-calibration device based on inertia and a single reading head, the device including a flywheel, a high-precision bearing, a turntable, a circular grating, and a data acquisition module; the flywheel has large rotational inertia to ensure the rotational stability of the turntable; the high-precision bearing is used for reducing errors caused by friction, runout and other factors in the rotation process; the data acquisition module comprises a microcontroller and a sensor signal input interface module, wherein the microcontroller is responsible for acquisition, processing, storage and transmission of grating data and time data, and the sensor signal input interface module is used for receiving original reading data of the circular grating sensor.
The invention has the following beneficial effects:
the calibration precision of the technical scheme provided by the invention does not depend on the standard, and can reach higher calibration precision than that of a common standard; the calibration process is independent of other high-precision angle measuring instruments, and can be used for remote on-machine calibration of unmanned operation. Compared with the traditional technical scheme, the technical scheme provided by the invention has lower cost, and the method can be also applied to round grating calibration in key extreme occasions such as space satellites, special robots and the like.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method of self-calibration of a circular grating based on inertia and a single read head in example 1;
FIG. 2 is a flow chart of a method of self-calibration of a circular grating based on inertia and a single read head in example 2;
FIG. 3 is a flow chart of a method of self-calibrating a circular grating based on inertia and a single read head in example 3;
FIG. 4 is a schematic diagram of a circular grating self-calibration device based on inertia and a single read head;
FIG. 5 is a graph of time data collected by the data collection module;
FIG. 6 is a graph of the self-calibration method of example 1 compensating for angle measurement errors of front and back circular gratings;
FIG. 7 is a graph of the self-calibration method of example 2 compensating for angle measurement errors of front and back circular gratings;
FIG. 8 is a graph of the self-calibration method of example 3 compensating for angle errors of the front and back circular gratings.
Detailed Description
The advantages, features and embodiments of the present invention will be further described with reference to the accompanying drawings. These embodiments are given by way of example only with reference to the accompanying drawings, which are non-limiting illustrations, representations and explanations of the present invention.
In order to solve the problems in the prior art, the invention provides three kinds of circular grating self-calibration methods based on an inertia single-reading head and a circular grating self-calibration device based on the inertia single-reading head. The calibration accuracy of the calibration method in the patent does not depend on the standard, and can reach higher calibration accuracy than that of a common standard; the calibration process is independent of other high-precision angle measuring instruments, and can be used for remote on-machine calibration of unmanned operation; when the harmonic component errors such as installation eccentricity of the circular grating are corrected, the method can be realized by only using one reading head, and the cost of the angle measuring system is effectively reduced. The difference between the method and other disclosed inertial-based circular grating self-calibration methods is that the method adopts a data grouping method (see the first embodiment and the third embodiment) and a time data optimizing method (see the second embodiment and the third embodiment), so that a more accurate self-calibration result can be obtained.
Embodiment one:
as shown in fig. 1, the circular grating self-calibration method 1 based on inertia and a single reading head comprises the following steps:
step one: the reading head is fixed, the circular grating rotates freely by k x 360 degrees (k is more than or equal to 4), and the time interval of k x m adjacent scale marks of the circular grating appearing in sequence is obtained by co-measurement, and is recorded as g 1 ,g 2 ,...,g km The matrix notation is adopted to be marked as G= { G 1 ,g 2 ,...,g km M is the total number of lines in one circle of the circular grating, g 1 G for the time interval of the m-th line and the 1-th line appearing successively 2 For the time interval between the occurrence of the 1 st line and the 2 nd line, and so on, g i The time interval of the i-1 th line and the i th line appearing in sequence is set;
step two: data in G obtained by
Figure SMS_31
Processing to obtain omega 1 ,ω 2 ,...,ω km Denoted as w= { ω 1 ,ω 2 ,...,ω km }, wherein->
Figure SMS_32
θ 0 In rad, ω i Is in rad/s;
step three: dividing the data in the array W into m groups, and marking the m groups as W by adopting a matrix notation 1 ,W 2 ,...,W m Let W 1 ＝{ω 1 ,ω 1+m ,...,ω 1+(z-1)m }，W 2 ＝{ω 2 ,ω 2+m ,...,ω 2+(z-1)m }，…，W m ＝{ω m ,ω 2m ,...,ω zm -wherein z is equal to the integer part of k;
step four: for the obtained m groups of data W 1 ,W 2 ,...,W m Respectively performing least square polynomial fitting to obtain m angular velocity-time curves, denoted as f 1 (t),f 2 (t),...,f m (t) substituting it into
Figure SMS_33
The angular velocity of the circular grating at time t can be obtained>
Figure SMS_34
Wherein->
Figure SMS_35
Step five: sum the data in matrix G with a function
Figure SMS_36
Substituted into->
Figure SMS_37
Obtain c 1 ,c 2 ,...c km Denoted as c= { C 1 ,c 2 ,...c km }, wherein c i In units of degrees;
step six: by means of averaging, i.e.
Figure SMS_38
Processing the data in C to remove part of residual errors to obtain m data, namely C' = { C 1 ',c 2 ',...c m '}；
Step seven: formulating the data in C
Figure SMS_39
Processing to remove DC component in the data, and marking the obtained data as +.>
Figure SMS_40
Step eight: taking the mth line as the reference (i.e. the measurement error of the mth line is 0), the measurement error of the jth line is
Figure SMS_41
And obtaining the angle measurement error compensation value of the reading head on the circular grating.
Preferably, in the first step of the method, the accuracy of the measured time data should reach the picosecond or even the femtosecond level; in the specific implementation, the time interval of each adjacent graduation line appearing in sequence can be calculated by using a method for measuring the appearance time of each graduation line.
Preferably, in the above method, the processing sequence of the second step and the third step may be exchanged, that is, the data in G may be first grouped, and the grouped data may be substituted into the data
Figure SMS_42
Obtaining W 1 ,W 2 ,...,W m ；
Preferably, in the third step of the method, W may be 1 ＝{ω 1 ,ω 1+m ,...,ω 1+zm }，W 2 ＝{ω 2 ,ω 2+m ,...,ω 2+zm }，…，W (k-z)m ＝{ω (k-z)m ,ω (k-z+1)m ,...,ω km },W (k-z)m+1 ＝{ω (k-z)m+1 ,ω (k-z+1)m+1 ,...,ω (k-1)m+1 },…，W m ＝{ω m ,ω 2m ,...,ω zm Then processing the m sets of data as per the steps in method 1;
preferably, in the fifth step of the method, c is not performed i The unit of (2) is converted into the degree, and the degree can be calculated directly by radian;
preferably, in the above method step six, a correction method such as a least squares method may be used instead of the average method, for example, a method of using
Figure SMS_43
Processing the data in the step C;
preferably, in the sixth method step, the data in C may be processed without a method such as a mean value method or a least square method, and directly enter a subsequent processing flow, and it is preferable (but not necessary) that the data in C is processed by a method such as a mean value method or a least square method to correct errors in the data;
preferably, the method can introduce iteration between the seventh step and the eighth step to achieve better compensation effect, and the specific process is that
Figure SMS_44
θ in the data replacement step two 0 I.e. +.>
Figure SMS_45
Obtaining new W, then processing according to the steps three to seven, and repeating the steps for n times (n is more than or equal to 1);
preferably, the number of the reading heads used in the method can be increased from a single reading head to two or more reading heads, so that a better compensation effect on the angle measurement error of the circular grating is achieved;
preferably, the method can also be used for magnetic grid, steel grid, time grid and other angular displacement sensors.
To verify the correctness of the method, experiments were performed, and fig. 5 and 6 are graphs of raw time data acquired at m=1800 and k=10 and graphs of angle errors of the circular gratings before and after the compensation of method 1.
Embodiment two:
as shown in fig. 2, the circular grating self-calibration method 2 based on inertia and a single reading head comprises the following steps:
step one: the reading head is fixed, the circular grating rotates freely by k x 360 degrees (k is more than or equal to 4), and the time interval of k x m adjacent scale marks of the circular grating appearing in sequence is obtained by co-measurement, and is recorded as g 1 ,g 2 ,...,g km The matrix notation is adopted to be marked as G= { G 1 ,g 2 ,...,g km M is the total number of lines in one circle of the circular grating, g 1 G for the time interval of the m-th line and the 1-th line appearing successively 2 For the time interval between the occurrence of the 1 st line and the 2 nd line, and so on, g i The time interval of the i-1 th line and the i th line appearing in sequence is set;
step two: fitting a least square polynomial and a trigonometric function to the data in the matrix G so as to remove some random error components contained in the original data, thereby realizing the optimization of the original data and obtaining1 time-time interval number discrete curve, which is marked as T (x), wherein x represents the x-th time interval, and x is more than or equal to 1 and less than or equal to km; taking k×m data from T (x), and using matrix notation to mark as t= { T 1 ,t 2 ,...,t km }, t is i ＝T(i)；
Step three: data in the array T is pressed
Figure SMS_46
Processing to obtain omega 1 ,ω 2 ,...,ω km Denoted as w= { ω 1 ,ω 2 ,...,ω km }, wherein->
Figure SMS_47
θ 0 In rad, ω i Is in rad/s;
step four: fitting the data in W by using a least square polynomial to obtain 1 angular velocity-time curve, recording as omega (t), and obtaining the angular velocity omega (t) of the circular grating at the moment t, wherein
Figure SMS_48
Step five: substituting the data and function ω (T) in the matrix T
Figure SMS_49
Obtain c 1 ,c 2 ,...c km Denoted as c= { C 1 ,c 2 ,...c km }, wherein c i In units of degrees;
step six: by means of averaging, i.e.
Figure SMS_50
Processing the data in C to remove part of residual errors to obtain m data, namely C' = { C 1 ',c 2 ',...c m ' wherein z is equal to the integer portion of k;
step seven: formulating the data in C
Figure SMS_51
Processing to remove DC component in data, and marking the obtained data according to matrix methodMarked as->
Figure SMS_52
Step eight: taking the mth line as the reference (i.e. the measurement error of the mth line is 0), the measurement error of the jth line is
Figure SMS_53
And obtaining the angle measurement error compensation value of the reading head on the circular grating.
To verify the correctness of method 2, it was tested and fig. 7 is a graph of the angle error of the circular grating before and after the method 2 compensation when m=2000, k=9.
Embodiment III:
as shown in fig. 3, the circular grating self-calibration method 3 based on inertia and a single reading head comprises the following steps:
step one: the reading head is fixed, the circular grating rotates freely by k x 360 degrees (k is more than or equal to 4), and the time interval of k x m adjacent scale marks of the circular grating appearing in sequence is obtained by co-measurement, and is recorded as g 1 ,g 2 ,...,g km The matrix notation is adopted to be marked as G= { G 1 ,g 2 ,...,g km M is the total number of lines in one circle of the circular grating, g 1 G for the time interval of the m-th line and the 1-th line appearing successively 2 For the time interval between the occurrence of the 1 st line and the 2 nd line, and so on, g i The time interval of the i-1 th line and the i th line appearing in sequence is set;
step two: fitting a least square polynomial and a trigonometric function to the data in the matrix G so as to remove some random error components contained in the original data, and optimizing the original data to obtain a 1-time-interval number discrete curve, which is marked as T (x), wherein x represents an xth time interval, and x is more than or equal to 1 and less than or equal to km; taking k×m data from T (x), and using matrix notation to mark as t= { T 1 ,t 2 ,...,t km }, t is i ＝T(i)；
Step three: data in the array T is pressed
Figure SMS_54
Processing to obtain omega 1 ,ω 2 ,...,ω km Denoted as w= { ω 1 ,ω 2 ,...,ω km }, wherein->
Figure SMS_55
θ 0 In rad, ω i Is in rad/s;
step four: dividing the data in the array W into m groups, and marking the m groups as W by adopting a matrix notation 1 ,W 2 ,...,W m Let W 1 ＝{ω 1 ,ω 1+m ,...,ω 1+(z-1)m }，W 2 ＝{ω 2 ,ω 2+m ,...,ω 2+(z-1)m }，…，W m ＝{ω m ,ω 2m ,...,ω zm -wherein z is equal to the integer part of k;
step five: for the obtained m groups of data W 1 ,W 2 ,...,W m Respectively performing least square polynomial fitting to obtain m angular velocity-time curves, denoted as f 1 (t),f 2 (t),...,f m (t) substituting it into
Figure SMS_56
The angular velocity of the circular grating at time t can be obtained>
Figure SMS_57
Wherein->
Figure SMS_58
Step six: sum data and functions in matrix T
Figure SMS_59
Substituted into->
Figure SMS_60
Obtain c 1 ,c 2 ,...c km Denoted as c= { C 1 ,c 2 ,...c km }, wherein c i In units of degrees;
step seven: by means of averaging, i.e.
Figure SMS_61
Processing the data in C to remove part of residual errors to obtain m data, namely C' = { C 1 ',c 2 ',...c m '}；
Step eight: formulating the data in C
Figure SMS_62
Processing to remove DC component in the data, and marking the obtained data as +.>
Figure SMS_63
Step nine: taking the mth line as the reference (i.e. the measurement error of the mth line is 0), the measurement error of the jth line is
Figure SMS_64
And obtaining the angle measurement error compensation value of the reading head on the circular grating.
To verify the correctness of method 3, it was tested and fig. 8 is a graph of the angle error of the circular grating before and after the method 3 compensates when m=2100, k=8.
It should be noted that, when knowing or deducing that the error of the angle measurement system is mainly a harmonic component, better compensation effect can be obtained by using the method 2 and the method 3; when it is unclear what the main component of the goniometric system error is, method 1 is generally used for compensation.
As shown in FIG. 4, a circular grating self-calibration device based on inertia and a single reading head is structurally schematic, and comprises a flywheel, a high-precision bearing, a turntable, a circular grating and a data acquisition module; the flywheel with large rotational inertia is selected to ensure the rotational stability of the rotary platform; the high-precision bearings can be selected from air bearing, magnetic air bearing composite bearing and the like, so that systematic errors caused by radial runout, axial runout and the like of the main shaft in the rotation process of the circular grating are reduced, and friction is reduced; the data acquisition module comprises a microcontroller and a sensor signal input interface module, wherein the microcontroller is responsible for acquisition, processing, storage and transmission of grating data and time data, and the sensor signal input interface module is used for receiving original reading data of the circular grating sensor.
It is necessary to explain that:
1) A high-precision timing module (such as TDC) can be added in the device, so that the precision of measured time data reaches a higher level, which is the simple reasoning of the device, and other people cannot apply for other patents;
2) The sensor mainly refers to a reading head of a circular grating, and in practical implementation, if a photoelectric microscope is used for directly identifying the position of a scribing line, the sensor is a simple reasoning of the device of the invention, and other people should not apply for other patents;
3) The device can be added with an upper computer communication module, the original data acquired by the data acquisition module is uploaded to an upper computer, the original data is processed by the upper computer by using a circular grating angle measurement error compensation model to obtain an angle measurement error compensation value of the reading head on the circular grating, which is simple reasoning of the device, and other people cannot apply other patents.
In practical application, the workflow of the apparatus shown in fig. 4 is: the flywheel is stored with energy, namely the flywheel is rotated, the rotary platform rotates at a stable speed by means of the rotational inertia of the flywheel, at the moment, the reading head is started, the data acquisition module is used for acquiring measurement data, the data are processed in the microcontroller by using the circular grating angle measurement error compensation model, and then the angle measurement error compensation value of the reading head on the circular grating is obtained.
Specifically, for the data acquisition module in fig. 4, the microcontroller can select high-performance microcontrollers such as Arduino, STM32, FPGA and the like to realize the functions of acquisition, processing, storage, transmission and the like of measurement signals. The data acquisition module acquires data in the following manner: because the reading head sends a pulse signal outwards every time the circular grating scale mark passes through the reading head, the time interval between every two pulses is measured and recorded by adopting methods such as an analog method, a digital insertion method, a digital delay method and the like in the microcontroller. The time resolution measured in this way can reach the picosecond level.
In summary, the method of the invention collects the time intervals of the adjacent graduation marks of the circular grating according to the principle of stable rotation speed, pulse width measurement and circumference sealing of the encoder caused by the large inertia flywheel, establishes the circular grating error compensation model, converts the rotation time of the circular grating into the actual rotation angle of the circular grating, and further obtains the compensation value of the angle measurement error of the circular grating encoder.
The above is only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited by this, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (4)

1. A circular grating self-calibration method based on inertia and a single reading head is characterized by comprising the following steps:
step one: the reading head is fixed, the circular grating rotates freely by k×360 degrees, k is larger than or equal to 4, and the time interval between k×m adjacent graduation lines of the circular grating is measured in the period, and is recorded as g 1 ,g 2 ,...,g km The matrix notation is adopted to be marked as G= { G 1 ,g 2 ,...,g km M is the total number of lines in one circle of the circular grating, g 1 G for the time interval of the m-th line and the 1-th line appearing successively 2 For the time interval between the occurrence of the 1 st line and the 2 nd line, and so on, g i The time interval of the i-1 th line and the i th line appearing in sequence is set;
step two: data in G obtained by
Figure FDA0004159925550000011
Processing to obtain omega 1 ,ω 2 ,...,ω km Denoted as w= { ω 1 ,ω 2 ,...,ω km }, wherein->
Figure FDA0004159925550000012
θ 0 In rad, ω i Is in rad/s;
step three: dividing the data in the array W into m groups, and marking the m groups as W by adopting a matrix notation 1 ,W 2 ,...,W m Let W 1 ＝{ω 1 ,ω 1+m ,...,ω 1+(z-1)m }，W 2 ＝{ω 2 ,ω 2+m ,...,ω 2+(z-1)m }，…，W m ＝{ω m ,ω 2m ,...,ω zm -wherein z is equal to the integer part of k;
step four: for the obtained m groups of data W 1 ,W 2 ,...,W m Respectively performing least square polynomial fitting to obtain m angular velocity-time curves, denoted as f 1 (t),f 2 (t),...,f m (t) substituting it into
Figure FDA0004159925550000013
The angular velocity of the circular grating at time t can be obtained>
Figure FDA0004159925550000014
Wherein->
Figure FDA0004159925550000015
Step five: sum the data in matrix G with a function
Figure FDA0004159925550000016
Substituted into->
Figure FDA0004159925550000017
Obtain c 1 ,c 2 ,...c km Denoted as c= { C 1 ,c 2 ,...c km }, wherein c i In units of degrees;
step six: by means of averaging, i.e.
Figure FDA0004159925550000018
For the number in CThe data were processed to obtain m data, denoted C' = { C 1 ',c 2 ',...c m '}；
Step seven: formulating the data in C
Figure FDA0004159925550000019
Processing and marking the obtained data as matrix notation
Figure FDA00041599255500000110
Step eight: taking the mth line as the reference (i.e. the measurement error of the mth line is 0), the measurement error of the jth line is
Figure FDA0004159925550000021
And obtaining the angle measurement error compensation value of the reading head on the circular grating.
2. A circular grating self-calibration method based on inertia and a single reading head is characterized by comprising the following steps:
step one: the reading head is fixed, the circular grating rotates freely by k×360 degrees, k is larger than or equal to 4, and the time interval between k×m adjacent graduation lines of the circular grating is measured in the period, and is recorded as g 1 ,g 2 ,...,g km The matrix notation is adopted to be marked as G= { G 1 ,g 2 ,...,g km M is the total number of lines in one circle of the circular grating, g 1 G for the time interval of the m-th line and the 1-th line appearing successively 2 For the time interval between the occurrence of the 1 st line and the 2 nd line, and so on, g i The time interval of the i-1 th line and the i th line appearing in sequence is set;
step two: fitting a least square polynomial and a trigonometric function to the data in the matrix G so as to remove some random error components contained in the original data, and optimizing the original data to obtain a 1-time-interval number discrete curve, which is marked as T (x), wherein x represents an xth time interval, and x is more than or equal to 1 and less than or equal to km; taking k.m data from T (x), usingThe matrix notation is denoted as t= { T 1 ,t 2 ,...,t km }, t is i ＝T(i)；
Step three: data in the array T is pressed
Figure FDA0004159925550000022
Processing to obtain omega 1 ,ω 2 ,...,ω km Denoted as w= { ω 1 ,ω 2 ,...,ω km }, wherein->
Figure FDA0004159925550000023
θ 0 In rad, ω i Is in rad/s;
step four: fitting the data in W by using a least square polynomial to obtain 1 angular velocity-time curve, recording as omega (t), and obtaining the angular velocity omega (t) of the circular grating at the moment t, wherein
Figure FDA0004159925550000024
Step five: substituting the data and function ω (T) in the matrix T
Figure FDA0004159925550000025
Obtain c 1 ,c 2 ,...c km Denoted as c= { C 1 ,c 2 ,...c km }, wherein c i In units of degrees;
step six: by means of averaging, i.e.
Figure FDA0004159925550000026
Processing the data in C to obtain m data, which is marked as C' = { C 1 ',c 2 ',...c m ' wherein z is equal to the integer portion of k;
step seven: formulating the data in C
Figure FDA0004159925550000027
Processing and marking the obtained data as matrix notation
Figure FDA0004159925550000028
Step eight: taking the mth line as the reference (i.e. the measurement error of the mth line is 0), the measurement error of the jth line is
Figure FDA0004159925550000031
And obtaining the angle measurement error compensation value of the reading head on the circular grating.
3. A circular grating self-calibration method based on inertia and a single reading head is characterized by comprising the following steps:
step one: the reading head is fixed, the circular grating rotates freely by k×360 degrees, k is larger than or equal to 4, and the time interval between k×m adjacent graduation lines of the circular grating is measured in the period, and is recorded as g 1 ,g 2 ,...,g km The matrix notation is adopted to be marked as G= { G 1 ,g 2 ,...,g km M is the total number of lines in one circle of the circular grating, g 1 For the time interval of the occurrence of the m-th line and the 1 st line before and after each other, g 2 For the time interval between the occurrence of the 1 st line and the 2 nd line, and so on, g i The time interval of the i-1 th line and the i th line appearing in sequence is set;
step two: fitting a least square polynomial and a trigonometric function to the data in the matrix G so as to remove some random error components contained in the original data, and optimizing the original data to obtain a 1-time-interval number discrete curve, which is marked as T (x), wherein x represents an xth time interval, and x is more than or equal to 1 and less than or equal to km; taking k×m data from T (x), and using matrix notation to mark as t= { T 1 ,t 2 ,...,t km }, t is i ＝T(i)；
Step three: data in the array T is pressed
Figure FDA0004159925550000032
Processing to obtain omega 1 ,ω 2 ,...,ω km Denoted as w= { ω 1 ,ω 2 ,...,ω km }, wherein->
Figure FDA0004159925550000033
θ 0 In rad, ω i Is in rad/s;
step four: dividing the data in the array W into m groups, and marking the m groups as W by adopting a matrix notation 1 ,W 2 ,...,W m Let W 1 ＝{ω 1 ,ω 1+m ,...,ω 1+(z-1)m }，W 2 ＝{ω 2 ,ω 2+m ,...,ω 2+(z-1)m }，…，W m ＝{ω m ,ω 2m ,...,ω zm -wherein z is equal to the integer part of k;
step five: for the obtained m groups of data W 1 ,W 2 ,...,W m Respectively performing least square polynomial fitting to obtain m angular velocity-time curves, denoted as f 1 (t),f 2 (t),...,f m (t) substituting it into
Figure FDA0004159925550000034
The angular velocity of the circular grating at time t can be obtained>
Figure FDA0004159925550000035
Wherein->
Figure FDA0004159925550000036
Step six: sum data and functions in matrix T
Figure FDA0004159925550000037
Substituted into->
Figure FDA0004159925550000038
Obtain c 1 ,c 2 ,...c km Denoted as c= { C 1 ,c 2 ,...c km }, wherein c i In units of degrees;
step seven:by means of averaging, i.e.
Figure FDA0004159925550000041
Processing the data in C to obtain m data, which is marked as C' = { C 1 ',c 2 ',...c m '}；
Step eight: formulating the data in C
Figure FDA0004159925550000042
Processing and marking the obtained data as matrix notation
Figure FDA0004159925550000043
Step nine: taking the mth line as the reference (i.e. the measurement error of the mth line is 0), the measurement error of the jth line is
Figure FDA0004159925550000044
And obtaining the angle measurement error compensation value of the reading head on the circular grating.
4. The circular grating self-calibration device based on inertia and a single reading head is characterized by comprising a flywheel, a high-precision bearing, a turntable, a circular grating and a data acquisition module; the flywheel has large rotational inertia to ensure the rotational stability of the turntable; the high-precision bearing is used for reducing errors caused by friction, runout and other factors in the rotation process; the data acquisition module comprises a microcontroller and a sensor signal input interface module, wherein the microcontroller is responsible for acquisition, processing, storage and transmission of grating data and time data, and the sensor signal input interface module is used for receiving original reading data of the circular grating sensor.
CN202310346448.8A 2023-04-03 2023-04-03 Round grating self-calibration method and device based on inertia and single reading head Pending CN116380147A (en)

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