Self-calibration method for angle encoder

Abstract

The invention 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 the arrangement positions of a plurality of reading heads, and constructing three groups of reading head combinations; rotating an angle encoder and acquiring angle data of the three groups of reading heads to obtain three groups of measurement data; establishing error compensation functions corresponding to the three groups of reading heads through the three groups of measurement data; and finally, performing Fourier analysis on the three groups of error compensation functions to complete cross compensation of error harmonic components, and realizing self-calibration of the angle encoder. While fewer reading heads are used, the calibration order of the harmonic error can be effectively improved, and high-precision in-situ calibration of the angle encoder is realized with lower cost.

Description

Technical Field

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

[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, and aerospace. The angle encoder usually includes a grating code disk and a reading head, and realizes high-precision angle measurement by converting the mechanical rotation amount into a quantifiable electrical signal, with the advantages of high resolution, fast response, and convenient debugging. With the deep development of modern industry and intelligent manufacturing, higher requirements are put forward for the angle measurement accuracy of various instruments and equipment. During the actual working process, the errors of the angle encoder mainly come from installation errors and code disk scribing errors, among which the installation errors include installation eccentricity, installation tilt, and local deformation of the code disk, etc. In order to improve the measurement accuracy of the angle encoder, it is usually necessary to calibrate the encoder.

[0003] The traditional calibration method is to provide a higher-precision angle reference, such as a reference encoder, a regular polygon prism, etc., coaxially install the angle encoder to be measured with the angle reference, and determine the error of the encoder to be measured by measuring the difference between the two. However, this method usually requires a complex coaxial connection link, which is easy to introduce new coaxial installation errors, and the actual operation is cumbersome and the real-time performance is poor. In order to reduce costs, avoid introducing additional angle measurement references, and at the same time realize the in-situ rapid calibration of the angle encoder on its installation axis, in recent years, the self-calibration method for the angle encoder has also been widely studied. The methods adopted usually rely on the harmonic error distribution law and use various algorithms to better perform error curve fitting, compensation model establishment, parameter identification, etc. Compared with the traditional method, the self-calibration method does not require an additional angle measurement device and has a lower cost, providing a new research direction and technical breakthrough for the innovation of the angle encoder calibration method.

[0004] After retrieving the existing technical literature, it is found that the US patent with the patent number US7143518B2 adopts the method of evenly distributing N reading heads around the grating code disk at equal angular intervals, and can calibrate and obtain all the remaining harmonic components in the angle error except for the Nth and multiples of N. However, in order to obtain higher calibration accuracy, the number of reading heads required also needs to increase, resulting in a significant increase in cost. And due to the limitations of the size of the grating code disk and the reading head, there is a problem of limited number of reading heads installed in this method. Therefore, it is difficult to greatly improve the calibration accuracy at a limited cost. There are also other literatures that give several self-calibration schemes for the angle encoder, but they all have the disadvantages of using a large number of reading heads and unoptimized reading head layouts. Summary of the Invention

[0005] The present invention aims to solve the problems of the above prior art and proposes a self - calibration method for an angle encoder. The technical solution adopted by the present invention 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 disk and the reading head, determine the arrangement positions of a plurality of reading heads, and construct three groups of reading head combinations;

[0008] Rotate the angle encoder k circles, where k≥1, and simultaneously collect the angle data of the three groups of reading heads, and obtain three groups of measurement data corresponding to the measurement combinations of the three groups of reading heads. When the angle data of a complete k - circle has been collected for all three groups of measurement data, proceed to the next step;

[0009] Establish error compensation functions corresponding to the three groups of reading heads according to the obtained three groups of measurement data;

[0010] Complete the cross - compensation of the error harmonic components by performing Fourier analysis on the three groups of error compensation functions, and thus the self - calibration of the angle encoder can be realized.

[0011] Further, the determination of the arrangement positions of a plurality of reading heads and the construction of three groups of reading head combinations are achieved by the following method: Install the reading heads around the grating code disk at three different angular intervals, and select one from each of the three groups of reading heads as a common reading head.

[0012] Further, the determination of the arrangement positions of a plurality of reading heads and the construction of three groups of reading head combinations specifically include the following steps:

[0013] Install the first group of reading heads HA1 and HA2 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;

[0014] Install the second group of reading heads HB1, HB2, and HB3 around the grating code disk at equal angular intervals, that is, the angular intervals between the reading heads HB1, HB2, and HB3 relative to the rotation axis on the grating code disk are all 120°;

[0015] Install the third group of reading heads HC1 and HC2 around the grating code disk at an angular interval of 72°;

[0016] Select HA1, HB1, and HC1 as the common reading heads, that is, use 5 reading heads to construct three groups of reading head combinations.

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

[0018] When the measurement data collected by the angle encoder is less than one circle, continue to rotate the angle encoder to complete the collection;

[0019] If the angle encoder collects k (k>1) circles of measurement data, since the angle encoder will repeat the previous angle every time it rotates one circle, the three groups of measurement data should be averaged separately to reduce the influence of random errors. If 1 circle of data is collected, no averaging process is required.

[0020] Furthermore, the error compensation functions of the three groups of reading heads are as follows: The first group of reading heads HA1 and HA2 are evenly arranged at the same angular interval, and the second group of reading heads HB1, HB2, and HB3 are evenly arranged at the same angular interval. Therefore, the error compensation function μ corresponding to the first group of reading heads is established according to the following formula HA , and the error compensation function μ corresponding to the second group of reading heads HB ;

[0021] Error compensation function:

[0022]

[0023] where θ represents the true rotation angle, H i (θ) represents the angular reading of the i-th reading head, represents the average value of the angular readings of N reading heads, k is a positive integer, 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;

[0024] The error compensation function μ of the third group of reading heads HC is constructed as follows:

[0025] For the corresponding third group of reading heads HC1 and HC2, since the angular interval is 72°, they can be regarded as two adjacent reading heads among 5 reading heads evenly arranged at an angular interval of 72°. The difference δ i (θ) between the (i + 1)-th and the i-th reading heads is:

[0026]

[0027] represents the angular error of the i-th reading head at the measurement point, and then by recursion, we get:

[0028]

[0029] where δ1 represents the reading difference between the 2nd and the 1st reading heads, and the reading value of the i-th reading head can be obtained by recursion based on δ1 as follows:

[0030]

[0031] Wherein, H1(θ) represents the angle measurement value of the first reading head at that position. According to the above formula, the angle measurement value of the equivalent 5-reading-head arrangement is derived from the third group of reading heads HC1 and HC2, 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 performing Fourier analysis on the three groups of error compensation functions, which specifically includes the following steps:

[0033] Perform Fourier analysis on the error compensation function μ of the first group of reading heads HA and compensate for the error harmonics except for the even orders; similarly, perform Fourier analysis on the error compensation function μ of the second group of reading heads HB and compensate for the error harmonics except for the 3rd order and multiples of the 3rd order; similarly, perform Fourier analysis on the error compensation function μ of the third group of reading heads HC and compensate for the error harmonics except for the 5th order and multiples of the 5th order;

[0034] Also compensate for the error harmonics except for the 30th order and multiples of the 30th order through cross compensation.

[0035] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned self-calibration method for an angle encoder are realized.

[0036] The advantages and beneficial effects of the present invention are as follows:

[0037] The self-calibration method for an angle encoder proposed by the present invention realizes high-precision in-situ calibration of the angle encoder by optimizing the layout of multiple groups of reading heads. Through this method, the harmonic errors of higher orders in the measurement error of the angle encoder can be calibrated. The present invention establishes corresponding error compensation functions based on multiple groups of encoder angle data collected during the measurement process, and cross-compensates the high-order harmonic errors through Fourier analysis. Without relying on external high-precision autocollimators or laser interferometers and other angle references, the self-calibration of the angle encoder can be realized. The number of reading heads used is small and the cost is low.

[0038] Through the optimized arrangement positions of 5 reading heads on the grating code disk, the present invention constructs a measurement combination layout of three groups of reading heads; an error compensation function is established corresponding to this layout, and all the remaining harmonic components in the angle error except for the 30th order and multiples of the 30th order can be calibrated with 5 reading heads. Thus, while using fewer reading heads, the present invention can effectively improve the calibration order of harmonic errors and realize high-precision in-situ calibration of the angle encoder at a lower cost. Description of the Drawings

[0039] Figure 1 is the overall flow chart of the method of the present invention;

[0040] Figure 2 is a schematic diagram of the layout scheme of multiple reading heads of the angle encoder of the present invention;

[0041] Figure 3 is the error compensation curve graph obtained by the first group of reading head combinations;

[0042] Figure 4 is the frequency component graph of the error compensation curve obtained by the first group of reading head combinations;

[0043] Figure 5 is the error compensation curve graph obtained by the second group of reading head combinations;

[0044] Figure 6 is the frequency component graph of the error compensation curve obtained by the second group of reading head combinations;

[0045] Figure 7 is the error compensation curve graph obtained by the third group of reading head combinations;

[0046] Figure 8 is the frequency component graph of the error compensation curve obtained by the third group of reading head combinations;

[0047] Figure 9 is the error compensation curve graph obtained after cross compensation;

[0048] Figure 10 is the frequency component graph of the error compensation curve obtained after cross compensation. Detailed implementation manners

[0049] Next, the technical solutions in the embodiments of the present invention will be clearly and detailedly described in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only a part of the embodiments of the present invention.

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

[0051] Step 1: According to the actual sizes of the grating code disk and the reading heads, determine the arrangement positions of multiple reading heads, and construct three groups of reading head combinations as shown in the appended Figure 2 figure:

[0052] 1) Install the first group of reading heads HA1 and HA2 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;

[0053] 2) Install the second group of reading heads HB1, HB2, and HB3 around the grating code disk at equal angular intervals, that is, the angular intervals between the reading heads HB1, HB2, and HB3 relative to the rotation axis on the grating code disk are all 120°;

[0054] 3) Install the third group of reading heads HC1 and HC2 around the grating code disk at an angular interval of 72°;

[0055] 4) Select HA1, HB1, and HC1 as the common reading heads, that is, use 5 reading heads to construct three groups of reading head combinations.

[0056] Step 2: Rotate the angle encoder k (k≥1) turns, and at the same time collect the angular 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 angular data of the complete k turns have been collected for all three groups of measurement 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 repeats the previous angle every time it turns one circle, the three groups of measurement data should be averaged respectively to reduce the influence of random errors. If 1 turn of data is collected, no averaging process is required.

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

[0060] 1) When N reading heads are evenly arranged on the grating code disk at the same angular interval, the angular reading H i (θ) of the i-th reading head is shown in Formula (1):

[0061]

[0062] where θ represents the true rotation angle, and ε i represents the angular error of this reading head at the measurement point. Since the error of the angle encoder is a periodic function with a basic period of 2π of the code disk displacement, the angular error can be expressed as the synthesis of error harmonics of each order, as shown in Formula (2):

[0063]

[0064] where M is the highest order of the error harmonics, and 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 angular readings of N evenly arranged reading heads is shown in Formula (3):

[0065]

[0066] By substituting Equation (2) into Equation (3) and applying trigonometric relations, Equation (4) is obtained after rearrangement:

[0067]

[0068] where k is the order of the error harmonic. C kN is the amplitude of the kN-th harmonic, and Φ kN is the phase angle of the kN-th harmonic. It can be seen from Equation (4) that the average value of the angular readings of N uniformly arranged reading heads only contains error harmonics of the N-th order and integer multiples of N-th order, and no longer contains error harmonics other than the kN-th order. Furthermore, by eliminating the angle θ through the relative difference between the readings of 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 reading head of the uniform arrangement only contains error harmonics other than the kN-th order, and can compensate for error harmonics other than the N-th order and integer multiples of N-th order, effectively improving the measurement accuracy.

[0071] 2) For the first group of reading heads HA1 and HA2, since the first group of reading heads HA1 and HA2 are uniformly arranged at the same angular interval, an error compensation function μ HA corresponding to the first group of reading heads can be established according to Equation (5), as shown in Appendix Figure 3 ; similarly, for the second group of reading heads HB1, HB2, and HB3, since the second group of reading heads HB1, HB2, and HB3 are uniformly arranged at the same angular interval, an error compensation function μ HB corresponding to the second group of reading heads can be established according to Equation (5), as shown in Appendix Figure 5 ;

[0072] 3) For the third group of reading heads HC1 and HC2, since the angular interval is 72°, they can be regarded as two adjacent reading heads among 5 reading heads uniformly arranged at an angular interval of 72°. According to Equation (1), the reading difference between adjacent reading heads can be obtained, and the difference δ i (θ) between the (i + 1)-th and the i-th reading heads is as shown in Equation (6):

[0073]

[0074] According to Equation (6), Equation (7) can be further derived by recursion:

[0075]

[0076] Among them, δ1 represents the reading difference between the second reading head and the first reading head. Therefore, the reading value of the i-th reading head can be derived by recursion based on δ1, as shown in Equation (8):

[0077]

[0078] In the formula, H1(θ) represents the angle measurement value of the first reading head at that position. Therefore, according to Equation (8), the angle measurement value of the equivalent 5-reading head arrangement can be derived from the third group of reading heads HC1 and HC2, and then the error compensation function μ corresponding to the third group of reading heads can be established HC , as shown in the appendix Figure 7 .

[0079] Step 4: Complete the cross-compensation of the error harmonic components by performing Fourier analysis on the three groups of error compensation functions:

[0080] 1) Perform Fourier analysis on the error compensation function μ HA of the first group of reading heads, as shown in the appendix Figure 4 . Since the reading heads HA1 and HA2 are evenly arranged at the same angular interval, the error compensation function μ HA only contains error harmonics other than the 2k-th order, and the error harmonics other than the even-order can be compensated; similarly, perform Fourier analysis on the error compensation function μ HB of the second group of reading heads, as shown in the appendix Figure 6 . Since the reading heads HB1, HB2, and HB3 are evenly arranged at the same angular interval, the error compensation function μ HB only contains error harmonics other than the 3k-th order, and the error harmonics other than the 3rd order and multiples of 3 can be compensated; similarly, perform Fourier analysis on the error compensation function μ HC of the third group of reading heads, as shown in the appendix Figure 8 . Since the equivalent 5-reading head is evenly arranged by deriving the reading heads HC1 and HC2, the error compensation function μ HC only contains error harmonics other than the 5k-th order, and the error harmonics other than the 5th order and multiples of 5 can be compensated.

[0081] 2) Since HA1, HB1, and HC1 are selected as the common reading heads in step A4, that is, HA1, HB1, and HC1 share one reading head, so the three groups of error compensation functions μ HA , μ HB and μ HCIt has a compensation effect on the reading head. Also, since the least common multiple of 2, 3, and 5 is 30, cross compensation can be used to compensate for error harmonics other than the 30th order and multiples of the 30th order, as shown in Figure 9 and Figure 10 shown, thereby realizing the self-calibration of the angle encoder.

[0082] In summary, the present invention proposes a self-calibration method for an angle encoder. By optimizing the layout of multiple reading heads, the number of reading heads used is reduced, and at the same time, the calibration order of harmonic errors is increased, enabling high-precision in-situ calibration of the angle encoder at a lower cost. The solution of the present invention is based on multiple groups of encoder angle data collected during the measurement process, establishes a corresponding error compensation function, and compensates for high-order harmonic errors through Fourier analysis cross compensation. It can achieve self-calibration of the angle encoder without relying on external high-precision autocollimators or laser interferometers and other angle references, and uses fewer reading heads. Therefore, it can greatly reduce the installation and debugging difficulty and usage cost, and has good practical value.

[0083] It should also be noted that the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, commodity or device. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, method, commodity or device including the said element.

[0084] The above embodiments should be understood as being only for the purpose of illustrating the present invention and not for limiting the protection scope of the present invention. After reading the content recorded in the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A self - calibration method for an angle encoder, characterized in that, It includes the following steps: According to the actual sizes of the grating code disk and the reading heads, determine the arrangement positions of multiple reading heads, and construct three groups of reading head combinations; The angle encoder rotates k circles, where k≥1. At the same time, collect the angle data of the three groups of reading heads, and obtain three groups of measurement data corresponding to the measurement combinations of the three groups of reading heads. When the angle data of the complete k circles have been collected for all three groups of measurement data, proceed to the next step; Establish error compensation functions corresponding to the three groups of reading heads based on the obtained three groups of measurement data; Complete the cross-compensation of the error harmonic components by performing Fourier analysis on the three groups of error compensation functions, and the self-calibration of the angle encoder can be achieved.

2. The self - calibration method for an angle encoder according to claim 1, wherein: The determination of the arrangement positions of multiple reading heads and the construction of three groups of reading head combinations are achieved through the following method: Install reading heads around the grating code disk at three different angular intervals, and select one from each of the three groups of reading heads as a common reading head.

3. The self-calibration method for an angle encoder according to claim 1 or 2, characterized in that: The determination of the arrangement positions of multiple reading heads and the construction of three groups of reading head combinations specifically include the following steps: Install the first group of reading heads HA1 and HA2 around the grating code disk at equal angular intervals, that is, the reading heads HA1 and HA2 are diametrically arranged relative to the rotation axis on the grating code disk; Install the second group of reading heads HB1, HB2, and HB3 around the grating code disk at equal angular intervals, that is, the angular intervals between the reading heads HB1, HB2, and HB3 relative to the rotation axis on the grating code disk are all 120°; Install the third group of reading heads HC1 and HC2 around the grating code disk at an angular interval of 72°; Select HA1, HB1, and HC1 as the common reading heads, that is, use 5 reading heads to construct three groups of reading head combinations.

4. The self-calibration method for an angle encoder according to claim 1, wherein: The specific steps for obtaining the three groups of measurement data include: When the measurement data collected by the angle encoder is less than one circle, continue to rotate the angle encoder to complete the collection; If the angle encoder collects k (k>1) circles of measurement data, since the angle encoder repeats the previous angle every time it rotates one circle, the three groups of measurement data should be averaged respectively to reduce the influence of random errors. If 1 circle of data is collected, no averaging process is required.

5. The self - calibration method for an angle encoder according to claim 1, wherein: The error compensation functions of the three groups of reading heads are as follows: The first group of reading heads HA1 and HA2 are evenly arranged at the same angular interval, and the second group of reading heads HB1, HB2, and HB3 are evenly arranged at the same angular interval. Therefore, the error compensation function μ corresponding to the first group of reading heads is established according to the following formula HA , and the error compensation function μ corresponding to the second group of reading heads HB ; Error compensation function: where θ represents the true rotation angle, H i (θ) represents the angular reading of the i-th reading head, represents the average value of the angular readings of N reading heads, k is a positive integer, M is the highest order of the error harmonics, C j is the amplitude of the j-th order error harmonic, Φ j is the initial phase angle of the j-th order error harmonic; Error compensation function μ of the third group of reading heads HC The construction process is as follows: For the third group of reading heads HC1 and HC2, since the angular interval is 72°, they can be regarded as two adjacent reading heads among five reading heads evenly arranged at an angular interval of 72°. The difference δ i (θ) between the (i + 1)-th and the i-th reading heads is as follows: ε[] represents the angular error of the i-th reading head at the measurement point, and then it can be recursively obtained: Among them, δ1 represents the reading difference between the second reading head and the first reading head, and the reading value of the i-th reading head can be recursively obtained based on δ1, as follows: Where H1(θ) represents the angular measurement value of the first reading head at that position. According to the above formula, the angular measurement values of the equivalent 5-reading head arrangement are derived from the third group of reading heads HC1 and HC2, and then the error compensation function μ corresponding to the third group of reading heads is established. HC 。 6. The self-calibration method for an angle encoder according to claim 1, characterized in that: The completion of the cross-compensation of the error harmonic components by performing Fourier analysis on the three groups of error compensation functions specifically includes the following steps: The error compensation function μ for the first set of read heads HA is subjected to Fourier analysis to compensate for error harmonics other than even orders; similarly, the error compensation function μ for the second set of read heads HB is subjected to Fourier analysis to compensate for error harmonics other than the 3rd order and multiples of the 3rd order; similarly, the error compensation function μ for the third set of read heads HC is subjected to Fourier analysis to compensate for error harmonics other than the 5th order and multiples of the 5th order; Cross-compensation is also performed to compensate for error harmonics other than the 30th order and multiples of the 30th order.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the self-calibration method for an angle encoder described in any one of claims 1 to 6.

Images