A self-calibration method for an angle encoder

Abstract

The application discloses a self-calibration method for an angle encoder and belongs to the technical field of precision measurement. The method mainly comprises the following steps: optimizing arrangement positions of a plurality of reading heads, and constructing three groups of reading head combinations; rotating the angle encoder and collecting angle data of the three groups of reading heads to obtain three groups of measurement data; establishing error compensation functions of the three groups of reading heads through the three groups of measurement data; and finally, completing cross compensation of error harmonic components through Fourier analysis on the three groups of error compensation functions, so that the self-calibration of the angle encoder is realized. While using fewer reading heads, the application can effectively improve the calibration order of harmonic errors, and realizes high-precision in-situ calibration of the angle encoder at a lower cost.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of precision measurement, and particularly relates to a self-calibration method for an angle encoder. BACKGROUND

[0002] As a key device in the field of precision angle measurement, the angle encoder plays an important role in high-precision positioning systems such as industrial automation, robot control, aerospace, etc. The angle encoder usually includes a grating code disc and a reading head, and realizes high-precision angle measurement by converting mechanical rotation into quantifiable electrical signals. It has the advantages of high resolution, fast response, and easy debugging. With the deepening development of modern industry and intelligent manufacturing, various instruments and equipment have put forward higher requirements for the angle measurement accuracy of angle encoders. In actual work, the error of the angle encoder mainly comes from the installation error and the code disc line error, among which the installation error includes installation eccentricity, installation tilt and code disc local deformation, etc. In order to improve the measurement accuracy of the angle encoder, the encoder usually needs to be calibrated.

[0003] The traditional calibration method is to provide a higher precision angle reference, such as a reference encoder, a regular polyhedral prism, etc. The angle encoder to be measured is coaxially installed with the angle reference, and the error of the angle encoder to be measured is determined by measuring the difference between the two. However, this method usually needs complex coaxial connection links, which is easy to introduce new coaxial installation error, and the actual operation is complicated and the real-time performance is poor. In order to reduce the cost and avoid introducing additional angle measurement reference, at the same time to realize the in-situ fast calibration of the angle encoder on its installation shaft, in recent years, the self-calibration method of the angle encoder has also been widely studied. The method usually uses various algorithms to better perform error curve fitting, compensation model establishment, parameter identification, etc. based on the harmonic error distribution law. Compared with the traditional method, the self-calibration method does not need additional angle measurement device and has lower cost, which provides a new research direction and technical breakthrough for the innovation of angle encoder calibration method.

[0004] Through the search of the existing technical documents, it is found that the US patent with the patent number US7143518B2 adopts the method of uniformly distributing N reading heads at equal angles around the grating code disc, which can calibrate all the remaining harmonic components except N and its multiples in the angle error. However, in order to obtain higher calibration accuracy, the number of reading heads required is also increased, resulting in a significant increase in cost. And due to the size limitation of the grating code disc and the reading head, this method has the problem of limited number of reading head installations, so it is difficult to greatly improve the calibration accuracy under limited cost. Some other documents also give some self-calibration schemes for angle encoders, but all have the shortcomings of using too many reading heads and not optimizing the layout of the reading heads. SUMMARY

[0005] The present application aims to solve the above problems of the prior art. A self-calibration method for an angle encoder is proposed. The technical solution adopted by the present application is as follows:

[0006] A self-calibration method for an angle encoder, comprising the following steps:

[0007] According to the actual sizes of the grating code disc and the reading head, the arrangement positions of the plurality of reading heads are determined, and three groups of reading head combinations are constructed;

[0008] The angle encoder is rotated k times, k≥1, and the angle data of the three groups of reading heads are collected simultaneously, and three groups of measurement data are obtained corresponding to the measurement combinations of the three groups of reading heads, and when the three groups of measurement data have all collected the complete k times of angle data, the next step is performed;

[0009] According to the three groups of measurement data obtained, error compensation functions corresponding to the three groups of reading heads are established;

[0010] Cross compensation of error harmonic components is completed by Fourier analysis of the three groups of error compensation functions, so that the self-calibration of the angle encoder is realized.

[0011] Further, the arrangement positions of the plurality of reading heads are determined, and the three groups of reading head combinations are constructed by the following method: the reading heads are installed around the grating code disc at three different angular intervals, and one reading head is selected from each of the three groups of reading heads as a common reading head.

[0012] Further, the arrangement positions of the plurality of reading heads are determined, and the three groups of reading head combinations are constructed, which specifically comprises the following steps:

[0013] The first group of reading heads HA1 and HA2 are installed around the grating code disc at equal angular intervals, i.e. the reading heads HA1 and HA2 are arranged in pairs relative to the rotation axis on the grating code disc;

[0014] The second group of reading heads HB1, HB2 and HB3 are installed around the grating code disc at equal angular intervals, i.e. the reading heads HB1, HB2 and HB3 are arranged at an angular interval of 120° between each other relative to the rotation axis on the grating code disc;

[0015] The third group of reading heads HC1 and HC2 are installed around the grating code disc at an angular interval of 72°;

[0016] HA1, HB1 and HC1 are selected as common reading heads, i.e. five reading heads are used to construct three groups of reading head combinations.

[0017] Further, the specific steps of obtaining the three groups of measurement data include:

[0018] When the measurement data collected by the angle encoder is less than one revolution, the angle encoder is continuously rotated to complete the collection;

[0019] If the angle encoder collects k (k > 1) turns of measurement data, since the angle encoder repeats the previous angle every turn, three sets of measurement data should be averaged respectively to reduce the influence of random errors. If 1 turn of data is collected, no mean value processing is required.

[0020] Further, the error compensation functions of the three sets of reading heads are respectively: the first set of reading heads HA1 and HA2 are uniformly arranged at the same angle interval, and the second set of reading heads HB1, HB2 and HB3 are uniformly arranged at the same angle interval, so the error compensation function μ HA corresponding to the first set of reading heads is established according to the following formula HB ;

[0021] Error compensation function:

[0022]

[0023] where θ represents the true rotation angle, H i (θ) represents the angle reading of the i-th reading head, represents the average value of the angle readings of the N reading heads, k is a positive integer, M is the highest order of error harmonics, C j is the amplitude of the j-th order error harmonic, and Φ j is the initial phase angle of the j-th order error harmonic.

[0024] The error compensation function μ HC of the third set of reading heads HC1 and HC2 is established as follows:

[0025] Since the angle interval is 72°, the difference δ i (θ) between the i+1-th and i-th reading heads of the two adjacent reading heads in the five reading heads uniformly arranged at an angle interval of 72° is:

[0026]

[0027] represents the angle error of the i-th reading head at the measurement point, and further recursively obtained:

[0028]

[0029] where δ1 represents the reading difference between the 2nd reading head and the 1st reading head, and the reading value of the i-th reading head can be recursively obtained according to δ1, as follows:

[0030]

[0031] H1(θ) represents the angle measurement value of the first reading head at the place, the angle measurement value of the equivalent 5-reading head arrangement is derived from the third group of reading heads HC1 and HC2 according to the above formula, and then the error compensation function μ corresponding to the third group of reading heads is established HC .

[0032] Further, the cross compensation of the error harmonic components is completed by Fourier analysis on the three groups of error compensation functions, and specifically includes the following steps:

[0033] the error compensation function μ of the first group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the even orders; similarly, the error compensation function μ of the second group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the 3rd order and the multiple of 3; and similarly, the error compensation function μ of the third group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the 5th order and the multiple of 5. HA the error compensation function μ of the first group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the even orders; similarly, the error compensation function μ of the second group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the 3rd order and the multiple of 3; and similarly, the error compensation function μ of the third group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the 5th order and the multiple of 5. HB the error compensation function μ of the first group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the even orders; similarly, the error compensation function μ of the second group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the 3rd order and the multiple of 3; and similarly, the error compensation function μ of the third group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the 5th order and the multiple of 5. HC the error compensation function μ of the first group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the even orders; similarly, the error compensation function μ of the second group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the 3rd order and the multiple of 3; and similarly, the error compensation function μ of the third group of reading heads is subjected to Fourier analysis to compensate for the error harmonics except the 5th order and the multiple of 5.

[0034] The error harmonics except the 30th order and the multiple of 30 are also compensated for through cross compensation.

[0035] The application further provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to realize the steps of the self-calibration method for an angle encoder.

[0036] Advantages and beneficial effects of the application are as follows:

[0037] The self-calibration method for an angle encoder provided by the application realizes high-precision in-situ calibration of the angle encoder by using multiple groups of reading heads to optimize the arrangement, and higher-order harmonic errors in the measurement errors of the angle encoder can be calibrated by the method. According to the multiple groups of encoder angle data collected in the measurement process, the application establishes corresponding error compensation functions, cross-compensates the high-order harmonic errors through Fourier analysis, and realizes self-calibration of the angle encoder without the help of external high-precision autocollimator or laser interferometer angle reference. The number of reading heads used is less, and the cost is lower.

[0038] By optimizing the arrangement positions of the 5 reading heads on the grating code disc, the application constructs a measurement combination arrangement of three groups of reading heads, establishes error compensation functions corresponding to the arrangement, and can realize calibration by using the 5 reading heads to obtain all the remaining harmonic components in the angle errors except the 30th order and the multiple of 30. Thus, while using fewer reading heads, the application can effectively improve the calibration order of the harmonic errors, and realize high-precision in-situ calibration of the angle encoder at a lower cost. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 is a general flow chart of the method of the present application;

[0040] Figure 2 is a schematic diagram of a multi-group read head layout scheme for an angle encoder of the present application;

[0041] Figure 3 is a graph of error compensation curves obtained for a first group of read head combinations;

[0042] Figure 4 is a graph of frequency components of error compensation curves obtained for a first group of read head combinations;

[0043] Figure 5 is a graph of error compensation curves obtained for a second group of read head combinations;

[0044] Figure 6 is a graph of frequency components of error compensation curves obtained for a second group of read head combinations;

[0045] Figure 7 is a graph of error compensation curves obtained for a third group of read head combinations;

[0046] Figure 8 is a graph of frequency components of error compensation curves obtained for a third group of read head combinations;

[0047] Figure 9 is a graph of error compensation curves obtained after cross compensation;

[0048] Figure 10 is a graph of frequency components of error compensation curves obtained after cross compensation. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the present application will be described clearly and in detail below with reference to the drawings in the embodiments of the present application. The described embodiments are only some of the embodiments of the present application.

[0050] As shown in Figure 1 , a self-calibration method for an angle encoder specifically comprises the following steps:

[0051] Step 1: according to the actual sizes of a grating code disc and read heads, the arrangement positions of a plurality of read heads are determined, and three groups of read head combinations as shown in the attached Figure 2 are constructed:

[0052] 1) a first group of read heads HA1 and HA2 are installed at equal angular intervals around the grating code disc, i.e. the read heads HA1 and HA2 are arranged in a diametric direction relative to the rotation axis on the grating code disc;

[0053] 2) The second group of reading heads HB1, HB2 and HB3 are installed at equal angular intervals around the grating disc, i.e. the angular interval between each pair of reading heads HB1, HB2 and HB3 is 120° relative to the rotation axis on the grating disc;

[0054] 3) The third group of reading heads HC1 and HC2 are installed at an angular interval of 72° around the grating disc;

[0055] 4) HA1, HB1 and HC1 are selected as the common reading head, i.e. five reading heads are used to construct three groups of reading head combinations.

[0056] Step 2: Rotate the angle encoder k (k≥1) turns, and collect the angle data of the three groups of reading heads to obtain three groups of measurement data corresponding to the measurement combinations of the three groups of reading heads: when the three groups of measurement data have collected complete k turns of angle data, then proceed to step 3.

[0057] 1) When the measurement data collected by the angle encoder is less than one turn, continue to rotate the angle encoder to complete the collection:

[0058] 2) If the angle encoder collects k (k>1) turns of measurement data, since the angle encoder will repeat the previous angle every turn, the three groups of measurement data should be averaged respectively to reduce the influence of random errors, and if 1 turn of data is collected, no average processing is required.

[0059] Step 3: Establish the error compensation function corresponding to the three groups of reading heads according to the three groups of measurement data obtained:

[0060] 1) When N reading heads are uniformly arranged at the same angular interval on the grating disc, the angle reading H i (θ) of the i-th reading head can be obtained as shown in formula (1):

[0061]

[0062] where θ represents the true rotation angle, and ε i represents the angle error of the reading head at the measurement point. Since the error of the angle encoder is a periodic function with a basic period of 2π displacement of the disc, the angle error can be represented as a combination of error harmonic waves of various orders, as shown in formula (2):

[0063]

[0064] where M is the highest order of the error harmonic, C j is the amplitude of the j-th order error harmonic, and Φ j is the initial phase angle of the j-th order error harmonic. Therefore, the average value of the angle readings of the N reading heads arranged uniformly is as shown in formula (3):

[0065]

[0066] By substituting equation (2) into equation (3) and applying the trigonometric function relationship, equation (4) is obtained after rearrangement:

[0067]

[0068] where k is the order of the error harmonic. C kN is the amplitude of the kth N-order harmonic, and Φ kN is the phase angle of the kth N-order harmonic. It can be seen from equation (4) that the average value of the angle reading of the N evenly arranged reading heads is contains only error harmonics of the Nth order and integer multiples of the Nth order, and no longer contains error harmonics other than the kNth order. Further, by eliminating the angle θ through the relative difference of the readings of the two reading heads, a relationship containing only the measurement angle error is obtained, and an error compensation function is established as shown in equation (5):

[0069]

[0070] where k is a positive integer. Therefore, the error compensation function μ i (θ) corresponding to the i th evenly arranged reading head contains only error harmonics other than the kNth order, and can compensate for error harmonics other than the Nth order and integer multiples of the Nth order, effectively improving the measurement accuracy.

[0071] 2) Corresponding to the first group of reading heads HA1 and HA2, since the first group of reading heads HA1 and HA2 are evenly arranged at the same angle interval, according to equation (5), the error compensation function μ HA corresponding to the first group of reading heads can be established as shown in the attached Figure 3 figure; similarly, corresponding to the second group of reading heads HB1, HB2 and HB3, since the second group of reading heads HB1, HB2 and HB3 are evenly arranged at the same angle interval, according to equation (5), the error compensation function μ HB corresponding to the second group of reading heads can be established as shown in the attached Figure 5 figure;

[0072] 3) Corresponding to the third group of reading heads HC1 and HC2, since the angle interval is 72°, it can be regarded as two adjacent reading heads in five reading heads evenly arranged at an angle interval of 72°, according to equation (1), the reading difference of adjacent reading heads can be obtained, and the difference δ i (θ) between the i+1th and i th reading heads is as shown in equation (6):

[0073]

[0074] According to formula (6), formula (7) can be further derived recursively:

[0075]

[0076] wherein δ1 represents the reading difference between the 2nd reading head and the 1st reading head. Therefore, the reading value of the ith reading head can be derived recursively according to δ1, as shown in formula (8):

[0077]

[0078] wherein H1(θ) represents the angle measurement value of the 1st reading head at this position. Therefore, according to formula (8), the angle measurement value of the equivalent 5-reading head arrangement can be derived from the 3rd group of reading heads HC1 and HC2, and then the error compensation function μ HC is established for the 3rd group of reading heads. Figure 7

[0079] Step 4: Cross-compensation of error harmonics is completed by performing Fourier analysis on the three groups of error compensation functions:

[0080] 1) Fourier analysis is performed on the error compensation function μ HA of the 1st group of reading heads, as shown in the following figure: Figure 4 Since the reading heads HA1 and HA2 are uniformly arranged at the same angle interval, the error compensation function μ HA only contains error harmonics other than 2k order, and the error harmonics other than even order can be compensated; similarly, Fourier analysis is performed on the error compensation function μ HB of the 2nd group of reading heads, as shown in the following figure: Figure 6 Since the reading heads HB1, HB2 and HB3 are uniformly arranged at the same angle interval, the error compensation function μ HB only contains error harmonics other than 3k order, and the error harmonics other than 3 order and multiples of 3 order can be compensated; similarly, Fourier analysis is performed on the error compensation function μ HC of the 3rd group of reading heads, as shown in the following figure: Figure 8 Since the reading heads HC1 and HC2 are derived from the equivalent 5-reading head arrangement, the error compensation function μ HC only contains error harmonics other than 5k order, and the error harmonics other than 5 order and multiples of 5 order can be compensated.

[0081] 2) Since HA1, HB1 and HC1 are selected as the common reading heads in step A4, i.e., HA1, HB1 and HC1 share one reading head, the three groups of error compensation functions μ HA , μ HB and μ HC ​The read heads are compensated. Since the least common multiple of 2, 3 and 5 is 30, the error harmonics other than 30 and multiples of 30 can be compensated by cross compensation, as shown in Figs. 8, 9 and 10, so as to realize self-calibration of the angle encoder. Figure 9 and Figs. 9 and 10. Figure 10

[0082] In summary, the present application provides a self-calibration method for an angle encoder, which optimizes the layout of multiple groups of read heads, reduces the number of read heads used, and increases the calibration order of harmonic errors, so as to realize high-precision in-situ calibration of the angle encoder at a lower cost. The scheme of the present application establishes corresponding error compensation functions according to the multiple groups of encoder angle data collected in the measurement process, and cross compensates high-order harmonic errors through Fourier analysis, so as to realize self-calibration of the angle encoder without the aid of external high-precision autocollimator or laser interferometer angle reference, and the number of read heads used is less, so as to greatly reduce the installation and debugging difficulty and use cost, and has good practical value.

[0083] It should be further understood that the terms "comprise", "comprising", or any other variant thereof are intended to cover non-exclusive inclusions, so that processes, methods, articles or devices that comprise a list of elements do not only include those elements, but also include other elements not expressly listed, or inherent to such processes, methods, articles or devices. Without more limitations, the element defined by the phrase "comprising a" does not exclude the presence of additional identical elements in the process, method, article or device that includes the element.

[0084] The above examples are understood to be only for illustrating the present application and not for limiting the protection scope of the present application. After reading the content of the present application, the skilled person can make various changes or modifications to the present application, and these equivalent changes and modifications also fall within the scope defined by the claims of the present application.​

Claims

1. A self-calibration method for an angle encoder, characterized in that, Includes the following steps: Based on the actual dimensions of the grating code disk and the reading head, determine the arrangement positions of multiple reading heads and construct three sets of reading head combinations; specifically, the following steps are included: The first set of reading heads HA1 and HA2 are installed around the grating code disk at equal angular intervals, that is, the reading heads HA1 and HA2 are arranged diametrically opposite to the rotation axis on the grating code disk. A second set of reading heads HB1, HB2 and HB3 are installed around the grating code disk at equal angular intervals, that is, the angular interval between each pair of reading heads HB1, HB2 and HB3 on the grating code disk relative to the rotation axis is 120°. A third set of read heads HC1 and HC2 are installed around the grating code disk at an angle of 72°. HA1, HB1, and HC1 are selected as common reading heads, that is, three sets of reading head combinations are constructed using 5 reading heads; The angle encoder rotates k revolutions, k≥1, and simultaneously collects angle data from three sets of reading heads. The measurement combination of the three sets of reading heads yields three sets of measurement data. Once all three sets of measurement data have been collected and the angle data for k revolutions has been obtained, the next step is performed. Based on the three sets of measurement data obtained, error compensation functions are established for the three sets of reading heads. The error compensation functions for the three sets of reading heads are as follows: the first set of reading heads HA1 and HA2 are evenly arranged with the same angular interval, and the second set of reading heads HB1, HB2, and HB3 are evenly arranged with the same angular interval. Therefore, the error compensation function for the first set of reading heads is established according to the following formula. The error compensation function corresponding to the second set of reading heads ; Error compensation function: Where θ represents the actual rotation angle. This represents the angle reading of the i-th reading head. This represents the average angle readings of N reading heads, where k is a positive integer and M is the highest order of the error harmonics. Let j be the amplitude of the j-th order error harmonic. Let be the initial phase angle of the j-th order error harmonic; Error compensation function for the third set of reading heads The construction process is as follows: For the third set of reading heads HC1 and HC2, since the angular interval is 72°, they can be considered as two adjacent reading heads among the five reading heads evenly arranged at 72° angular intervals, and the difference between the (i+1)th and the ith reading head. for: This represents the angular error of the i-th reading head at the measurement point, and can be recursively derived as follows: in, This represents the difference between the readings of the second and first reading heads. The reading value of the i-th reading head is based on... The result is obtained recursively, as shown below: In the formula This represents the angle measurement value of the first reading head at that location. Based on the above formula, the equivalent angle measurement value of a 5-reading-head arrangement is derived from the third group of reading heads HC1 and HC2. Subsequently, an error compensation function corresponding to the third group of reading heads is established. ; By performing Fourier analysis on the three sets of error compensation functions to complete the cross-compensation of error harmonic components, self-calibration of the angle encoder can be achieved; specifically, the following steps are included: Error compensation function for the first set of reading heads Fourier analysis was performed to compensate for error harmonics other than even-order harmonics; similarly, the error compensation function for the second set of reading heads was also applied. Fourier analysis was performed to compensate for error harmonics other than the 3rd order and multiples of 3; similarly, the error compensation function for the third set of reading heads was also performed. Fourier analysis was performed to compensate for error harmonics other than the 5th order and multiples of 5. It also compensates for error harmonics other than the 30th order and multiples of 30 through cross compensation.

2. The self-calibration method for an angle encoder according to claim 1, characterized in that: The specific steps for obtaining the three sets of measurement data include: When the angle encoder collects less than one revolution of measurement data, continue rotating the angle encoder to complete the data collection. If the angle encoder collects k (k>1) revolutions of measurement data, since the angle encoder repeats the previous angle with each revolution, the three sets of measurement data should be averaged separately to reduce the impact of random errors. If only 1 revolution of data is collected, averaging is not required.

3. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the self-calibration method for an angle encoder as described in claim 1 or 2.

Images