A multi-reading head angular displacement sensor self-calibration layout method and application

Abstract

The present application belongs to the technical field of self-calibration layout method, and discloses a kind of multi-reading head angular displacement sensor self-calibration layout method, comprising: using S reading head to carry out self-calibration;The position of reading head is calculated, and reference reading head is determined, and the indication of reference reading head is used to carry out full circumference N point uniform sampling, and S reading head obtains S group data altogether;The S group data obtained is pairwise difference, and the data measured by the kth reading head is difference with the data of the rth reading head;Then its N point discrete fourier transform is obtained;N point discrete fourier transform of reference reading head system error is obtained by transfer function and variance optimization weight;Full circumference error is obtained by curve fitting, and self-calibration is completed.The present application method has important significance for the self-calibration of high-precision angular displacement sensor, can satisfy relevant application requirements, can realize the self-calibration of ultrahigh-precision angular displacement sensor, and improves the self-calibration precision of ultrahigh-precision angular displacement sensor.

Description

Technical Field

[0001] This invention belongs to the technical field of self-calibration layout methods, and in particular to a self-calibration layout method and application of a multi-reading head angular displacement sensor. Background Technology

[0002] With the continuous development of production and science, angle measurement is increasingly widely used in various fields such as machinery, optics, and aerospace. At the same time, the requirements for the measurement accuracy of angular displacement sensors are also increasing in these fields. A high-precision angular displacement sensor mainly consists of two parts: a circular grating and a reading head. The circular grating is coaxially mounted with the rotating shaft, and the reading head measures the angular displacement by reading the grating line information. In the measurement process, errors are ubiquitous and unavoidable. Accurate angle measurement relies on calibration. Self-calibration does not require external references and utilizes the sensor's own error characteristics and structural features to achieve self-calibration. However, existing self-calibration methods only obtain partial systematic errors, meaning that some residual errors have not yet been calibrated. This is due to the low order of the calibrated residuals, which limits further improvements in the accuracy of self-calibration methods. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide a self-calibration layout method and application for a multi-reading head angular displacement sensor.

[0004] The technical solution adopted by this invention to solve its technical problem is:

[0005] A self-calibration layout method for a multi-reading-head angular displacement sensor, the method utilizing a circular grating and multiple reading heads, specifically includes the following steps:

[0006] (1) Self-calibration is performed using S reading heads. First, a reference reading head is set up. Using the measurement value of the reference reading head, the remaining reading heads are arranged clockwise according to formula (1). With the reference reading head as the reference, the position β of the kth reading head is... k It should be:

[0007]

[0008] Where, β k Let be the angular position of the k-th reading head; k is the position number of the reading head, and the value of k is 1, 2, ..., S; S is the number of reading heads, and S is a factor of 360. When S is odd, a is 1, and when S is even, a is 0.

[0009] (2) Calculate the position of the reading head according to the method in step (1), and determine the reference reading head. Use the reading of the reference reading head to perform uniform sampling at N points around the entire circumference. S sets of data are obtained from S reading heads, denoted as

[0010] (3) Subtract each pair of the obtained S sets of data to get The difference data is calculated by subtracting the data measured by the k-th reading head from the data measured by the r-th reading head, and denoted as . As shown in equation (2); then the discrete Fourier transform of its N points is obtained. As in equation (3);

[0011]

[0012] in, This represents the difference between the data measured by the k-th reading head and the data measured by the r-th reading head. The data is obtained from the kth reading head; The data is obtained from the r-th reading head;

[0013]

[0014] in, for The N-point Discrete Fourier Transform; N is the number of uniform samples; m and n are the indices of the N-point Discrete Fourier Transform.

[0015] (4) The N-point discrete Fourier transform F[δ1](m) of the systematic error of the reference reading head is obtained by using the transfer function and variance optimization weights, as shown in equation (4):

[0016]

[0017] Where F[δ1](m) is the N-point discrete Fourier transform of the systematic error of the reference reading head; S is the number of reading heads; k, r are the reading head serial numbers; for The N-point discrete Fourier transform;

[0018]

[0019] Among them, T kr (m) is the transfer function, m is the index, m, = 0, 1, 2...N-1, and N is the number of sampling points; β k Let β be the angular position of the k-th reading head. r Let r be the angular position of the reading head;

[0020]

[0021] Where, p kr (m) represents the optimal weight. For T kr The conjugate complex number of (m), |T kr (m)| is T krThe modulus of (m);

[0022] (5) According to equation (3), the discrete Fourier transform value F[δ1](m) of the systematic error contained in the data measured by the reference reading head is obtained. The systematic error can be obtained by inverse Fourier transform. The full circumference error is obtained by curve fitting, thus completing the self-calibration.

[0023] Furthermore, the method is implemented using a multi-reading head angular displacement sensor, which includes a circular grating and multiple reading heads, which are spaced apart along the circumferential direction on the outer surface of the circular grating.

[0024] Furthermore, taking a configuration of six reading heads as an example, the included angles of the multiple reading heads are 55°, 112°, 171°, 232°, and 295°, respectively.

[0025] The above method is applied to the high-precision self-calibration of angular displacement sensors.

[0026] The advantages and positive effects of this invention are as follows:

[0027] 1. The method of this invention utilizes the suppression effect of multiple reading heads on random errors and the advantage of optimizing weights to maximize the use of measurement data. The residual order of this method is an integer multiple of 360, and it has the advantages of simple device, high calibration accuracy, and strong anti-interference ability, which can fill the gap in related technologies. This method is of great significance for the self-calibration of high-precision angular displacement sensors, can meet relevant application requirements, can realize the self-calibration of ultra-high precision angular displacement sensors, and improve the self-calibration accuracy of ultra-high precision angular displacement sensors.

[0028] 2. The method of the present invention is to achieve self-calibration of ultra-high precision angular displacement sensors. Based on the transfer function method, a multi-read head layout is designed to accurately calculate the system error.

[0029] 3. The method of this invention has the advantage of strong anti-interference capability due to the simultaneous operation of multiple reading heads; and it features high residual harmonic order due to the optimized layout. The calibration accuracy of this method is determined by parameters such as the measurement accuracy and arrangement accuracy of the reading heads. By optimizing the layout, the self-calibration accuracy of the measuring device can be significantly improved. The proposed device can overcome the limitation of existing self-calibration schemes with excessively low residual order.

[0030] 4. The method of the present invention is also effective for the calibration of disk grating type sensors: The layout method and measurement principle of this invention are not limited to circular gratings, and are also effective for encoders composed of magnetic grating structures and capacitive grating structures with similar shapes.

[0031] 5. The method of this invention adopts the self-calibration principle. Unlike mutual calibration, self-calibration can complete self-calibration without relying on external references. Therefore, the application threshold of self-calibration is low. It also provides new ideas and technical means to break through the current calibration limits.

[0032] 6. The measuring device on which the method of the present invention relies is simple in composition, consisting of only multiple reading heads and a circular grating, and has the advantages of simple device and wide application. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the multi-reading head angular displacement sensor device in this invention;

[0034] Figure 2 This is a schematic diagram of the arrangement of the six reading heads in this invention;

[0035] Figure 3 This is a system error image in this invention;

[0036] Figure 4 This is a systematic error image measured by six reading heads in this invention;

[0037] Figure 5 This is the system error image obtained from the calibration experiment example in this invention;

[0038] Figure 6 This is a residual image diagram in this invention;

[0039] Figure 7 The systematic error image (720-point sampling) measured by the 6 reading heads in this invention;

[0040] Figure 8 The systematic error image (3600 sampling points) measured by the 6 reading heads in this invention;

[0041] Figure 9 Schematic diagrams of layout methods other than those of the present invention;

[0042] Figure 10 System error images (360-point sampling) were measured for layout methods other than those of the present invention. Detailed Implementation

[0043] The present invention will be further described below with reference to the embodiments. The following embodiments are descriptive and not limiting, and should not be used to limit the scope of protection of the present invention.

[0044] The various experimental operations involved in the specific embodiments are all conventional techniques in the field. For parts not specifically annotated in this invention, those skilled in the art can refer to various commonly used reference books, scientific and technological documents or related instructions and manuals before the filing date of this invention to carry out the operations.

[0045] A self-calibration layout method for a multi-reading-head angular displacement sensor, the method utilizing a circular grating and multiple reading heads, specifically includes the following steps:

[0046] (1) Self-calibration is performed using S reading heads. First, a reference reading head is set up. Using the measurement value of the reference reading head, the remaining reading heads are arranged clockwise according to formula (1). With the reference reading head as the reference, the position β of the kth reading head is... k It should be:

[0047]

[0048] Where, β k Let be the angular position of the k-th reading head; k is the position number of the reading head, and the value of k is 1, 2, ..., S; S is the number of reading heads, and S is a factor of 360. When S is odd, a is 1, and when S is even, a is 0.

[0049] (2) Calculate the position of the reading head according to the method in step (1), and determine the reference reading head. Use the reading of the reference reading head to perform uniform sampling at N points around the entire circumference. S sets of data are obtained from S reading heads, denoted as

[0050] (3) Subtract each pair of the obtained S sets of data to get The difference data is calculated by subtracting the data measured by the k-th reading head from the data measured by the r-th reading head, and denoted as . As shown in equation (2); then the discrete Fourier transform of its N points is obtained. As in equation (3);

[0051]

[0052] in, This represents the difference between the data measured by the k-th reading head and the data measured by the r-th reading head. The data is obtained from the kth reading head; The data is obtained from the r-th reading head;

[0053]

[0054] in, for The N-point Discrete Fourier Transform; N is the number of uniform samples; m and n are the indices of the N-point Discrete Fourier Transform.

[0055] (4) The N-point discrete Fourier transform F[δ1](m) of the systematic error of the reference reading head is obtained by using the transfer function and variance optimization weights, as shown in equation (4):

[0056]

[0057] Where F[δ1](m) is the N-point discrete Fourier transform of the systematic error of the reference reading head; S is the number of reading heads; k, r are the reading head serial numbers; for The N-point discrete Fourier transform;

[0058]

[0059] Among them, T kr (m) is the transfer function, m is the index, m, = 0, 1, 2...N-1, and N is the number of sampling points; β k Let β be the angular position of the k-th reading head. r Let r be the angular position of the reading head;

[0060]

[0061] Where, p kr (m) represents the optimal weight. For T kr The conjugate complex number of (m), |T kr (m)| is T kr The modulus of (m);

[0062] (5) According to equation (3), the discrete Fourier transform value F[δ1](m) of the systematic error contained in the data measured by the reference reading head is obtained. The systematic error can be obtained by inverse Fourier transform. The full circumference error is obtained by curve fitting, thus completing the self-calibration.

[0063] Preferably, the method is implemented using a multi-reading head angular displacement sensor, which includes a circular grating and multiple reading heads, which are spaced apart along the circumferential direction on the outer surface of the circular grating.

[0064] Preferably, the plurality of reading heads are arranged in a configuration of six reading heads, with the included angles of the multiple reading heads being 55°, 112°, 171°, 232°, and 295°, respectively.

[0065] The above method is applied to the high-precision self-calibration of angular displacement sensors.

[0066] Specifically, the relevant preparation and testing methods are as follows:

[0067] A self-calibration layout method for a multi-reading-head angular displacement sensor, the method utilizing a circular grating and multiple reading heads, specifically includes the following steps:

[0068] Figure 1This is a schematic diagram of a 6-reading-head measurement system. The arrangement of the 6-reading-head system is detailed below.

[0069] 1. The device involved in this invention employs a multi-reading head angular displacement sensor, such as... Figure 1 As shown, the multi-reading head angular displacement sensor includes a circular grating 2 and multiple reading heads 1, which are spaced apart along the circumferential direction on the outer surface of the circular grating.

[0070] 2. Taking the arrangement of 6 reading heads as an example, the reference reading head is denoted as H1, and the included angles of reading heads H1, H2, H3, H4, H5 and H6 are obtained by formula (1).

[0071]

[0072] Where, β k Let be the angular position of the k-th reading head; k is the position number of the reading head, and the value of k is 1, 2, ..., S; S is the number of reading heads, and S is a factor of 360. When S is odd, a is 1, and when S is even, a is 0.

[0073] That is, S = 6, at which point a = 0. Substituting these values ​​into the formula, we get the following positions: Reading head H1: k = 1, 0°; Reading head H2: k = 2, 55°; Reading head H3: k = 3, 112°; Reading head H4: k = 4, 171°; Reading head H5: k = 5, 232°; Reading head H6: k = 6, 295°. The six reading heads 1 are distributed around the circular grating 2, maintaining a specified included angle. The layout is shown below. Figure 2 .

[0074] The specific implementation process of the device function in this invention is described in detail below.

[0075] First, complete the installation and setup for this method. Referring to the measurement data from reading head 1, complete full-circumferential sampling of the circular grating 2, obtaining measurement data from all six reading heads. The six sets of data were fed into the self-calibration process to calculate the discrete system error.

[0076] By fitting discrete system error data, the system error of the circular grating around the entire circle is obtained, enabling self-calibration of the ultra-high precision angular displacement sensor. The final calibration accuracy is related to parameters such as the resolution of the reading head and the installation accuracy of the reading head.

[0077] Calibration Experiment Example: The outer diameter of the circular grating is 260 mm, the inner diameter is 210 mm, the linear thermal expansion coefficient is 16 μm / mm / K, and the deformation error of the circular grating is 3 μm for second-order deformation and 4 μm for fifth-order deformation. The system's indexing error is 1 μm with a uniform distribution, the eccentricity error is 4 μm, the tilt error is 10″, and the ambient temperature variation is 0.1 K. The full-circumferential system error formed by the coupling of structural parameters and installation errors is as follows: Figure 3 As shown, the size is around 8″, exhibiting obvious low-order characteristics. The maximum error does not exceed 8″. In the final error, the error caused by eccentricity and disk tilt accounts for the majority of the low-order error, with a maximum value of around 6″. The graduation error caused by inaccurate engraving is the main source of high-order error, with a maximum value of around 2″. The maximum value of the final overall error is around 8″.

[0078] The phase relationship can be obtained from the included angle of the reading head, and thus the systematic error image of the reading head can be obtained. For example... Figure 4 The six sets of data are then subtracted pairwise, and the results are used in the self-calibration process to calculate the systematic error obtained through the self-calibration principle. Figure 5 .

[0079] The residual refers to the difference between the calibration error and the actual error. The magnitude of the residual can be used to examine the quality of the calibration results: a larger residual indicates a larger difference between the calibration error and the actual error, meaning the calibration is less accurate; a smaller residual indicates a smaller difference between the calibration error and the actual error, meaning the calibration is more accurate. By comparing the difference between the simulated system error and the calculated system error, the residual of this experiment under this arrangement is as follows: Figure 6 Observing the amplitude range in the above figure, it can be found that the residual obtained by this layout method reaches the level of 10 to the power of -13, which is almost close to 0. It can be regarded as completely solving all the systematic errors contained in the 360-point sampling information.

[0080] To examine the effectiveness of this layout method, the number of sampling points was increased. When 720 sampling points were used, the residual image and amplitude-frequency response curve were as follows: Figure 7 As shown.

[0081] Observing the spectrum image reveals that the residual is the 360th order harmonic, and the amplitude of the residual is around 0.02″.

[0082] When the number of sampling points is increased again to 3600 points, the residual and amplitude-frequency curve results are as follows: Figure 8 As shown.

[0083] Observing the spectrum image reveals that these residuals are harmonics of the 360th, 720th, 1080th, 1440th, and 1800th orders, with amplitudes around 0.05″.

[0084] This indicates that this arrangement will capture all harmonic information from the harmonic information, except for the 360, 720, 1080, and 1440th orders.

[0085] In summary, the self-calibration layout optimization method for multi-reading head angular displacement sensors proposed in this invention can utilize the inherent characteristics of the self-calibration principle to perform high-precision self-calibration of high-precision angular displacement sensors. The device has the advantages of high calibration accuracy and strong anti-interference capability.

[0086] In addition, a comparison was made with similar methods in the prior art, as follows:

[0087] Currently, some scholars have proposed a layout scheme with 3 reading heads, which can be extended to 6 reading heads using the principle of symmetry, arranged as follows: Figure 9 As shown: 0°, 27°, 144°, 180°, 207° and 324° are used.

[0088] The residual harmonic orders of this layout are integer multiples of 40. The residual image and its spectrum image obtained using this layout are as follows: Figure 10 As shown.

[0089] Observing its spectrum, it can be seen that this residual is the 40th, 80th, 120th, and 160th harmonics. The residual amplitude is around 0.5″.

[0090] Compared to the effects of this invention, which also uses 6 reading heads and 360 points of uniform sampling, Figure 6 The layout method proposed in this invention achieves a residual of 10 to the power of -13, which can be considered as completely resolving all the systematic errors contained in the 360-point sampling information. Therefore, the layout method proposed in this invention has better calibration performance and is more superior.

[0091] Although embodiments of the invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations, and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the scope of the invention is not limited to the contents disclosed in the embodiments.

Claims

1. A self-calibration layout method for a multi-reading head angular displacement sensor, characterized in that: The method utilizes a circular grating and multiple reading heads, and specifically includes the following steps: (1) Self-calibration using S reading heads: First, set up a reference reading head. Then, arrange the remaining reading heads clockwise according to formula (1) using the measurement value of the reference reading head. The position of the kth reading head is determined by the reference reading head. It should be: (1) in, This represents the angular position of the k-th reading head; k is the position number of the reading head, and the value of k is... S is the number of reading heads, and S is a factor of 360. When S is odd, a is 1, and when S is even, a is 0. (2) Calculate the position of the reading head according to the method in step (1), and determine the reference reading head. Use the reading of the reference reading head to perform uniform sampling at N points around the entire circumference. S sets of data are obtained from S reading heads, denoted as ; (3) Subtract each pair of the obtained S sets of data to get The difference data is calculated by subtracting the data measured by the k-th reading head from the data measured by the r-th reading head, and denoted as . As shown in equation (2); then the discrete Fourier transform of its N points is obtained. As shown in equation (3); (2)； in, This represents the difference between the data measured by the k-th reading head and the data measured by the r-th reading head. The data is obtained from the kth reading head; The data is obtained from the r-th reading head; (3)； in, for The N-point Discrete Fourier Transform; N is the number of uniform samples; m and n are the indices of the N-point Discrete Fourier Transform. (4) Obtain the N-point Discrete Fourier Transform of the System Error of the Reference Reading Head by using the transfer function and variance optimization weights. As in equation (4): (4)； in, The N-point discrete Fourier transform of the systematic error of the reference reading head; S is the number of reading heads; k and r are the reading head serial numbers; for The N-point discrete Fourier transform; (5) in, Here, m is the transfer function, and m is the ordinal number. N is the number of sampling points; The angle position of the k-th reading head. Let r be the angular position of the reading head; (6) in, To optimize the weights, for The conjugate of complex numbers, for The model; (5) Obtain the discrete Fourier transform value of the systematic error contained in the data measured by the reference reading head according to equation (3). The systematic error can be obtained using the inverse Fourier transform. The full circumference error is obtained through curve fitting, thus completing the self-calibration.

2. The method according to claim 1, characterized in that: The method is implemented using a multi-reading head angular displacement sensor, which includes a circular grating and multiple reading heads, which are spaced apart along the circumferential direction on the outer surface of the circular grating.

3. The method according to claim 2, characterized in that: The multiple reading heads are arranged in a six-head configuration, with the included angles of the multiple reading heads being 55°, 112°, 171°, 232° and 295° respectively.

4. The application of the method as described in any one of claims 1 to 3 in the high-precision self-calibration of angular displacement sensors.

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