Turntable positioning error self-calibration method based on single-read head signal time clipping

Abstract

The application relates to the field of angle measurement and discloses a rotary table positioning error self-calibration method based on single-read head signal time shearing. First, the rotary table is controlled to accelerate to a preset rotating speed, then the driving is cut off to make the rotary table rotate freely under the action of inertia; a first group of whole-circumferential-angle position sequences are collected at equal time intervals; then a fixed time shearing amount is applied, sampling data at a corresponding moment of the time shearing amount is taken as a starting point, and a second group of whole-circumferential-angle position sequences are obtained; a difference function is obtained by subtracting read head reading signals at the same time points in the sequences before and after shearing; the shearing angle displacement amount actually occurring at each sampling moment is removed from the difference function, and a shearing differential function is obtained; finally, the rotary table positioning error in the whole-circumferential-angle range is reconstructed through a reconstruction algorithm. The application replaces multi-read head space phase collection with time domain time shearing, and does not need to additionally add read heads or repeatedly sample by starting and stopping the rotary table multiple times.

Description

Technical Field

[0001] This invention relates to the field of angle measurement, and more specifically to a self-calibration method for turntable positioning error based on time shearing of a single reading head signal. Background Technology

[0002] Turntable calibration typically relies on national angular standard devices for traceability and transfer of measurement values. This method is complex and prone to inconvenience and risks during equipment transportation and on-site installation. In recent years, self-calibration methods based on natural circumferential references have gradually developed into a new traceability scheme. Unlike traditional methods that rely on external instruments for system calibration, self-calibration technology achieves error compensation through the system's own structure, significantly improving calibration efficiency and applicability, and providing a stable and reliable solution for turntable calibration.

[0003] In 1993, the National Institute of Metrology of Japan proposed the Equal Division Averaged method (EDA) and developed a high-precision angle encoder system based on this method (doi:10.2493 / jjspe.67.1091). In 2005, the National Institute of Metrology of Japan further optimized the system structure, proposed the Self-calibrating encoder (Self-calibratable Angle device), and designed a national angle reference device (doi:10.1088 / 1742-6596 / 13 / 1 / 056).

[0004] The EDA method can obtain the calibration error curve composed of harmonic components other than those that are integer multiples of the number of reading heads. To reduce the cost pressure caused by too many reading heads while ensuring calibration accuracy, researchers have made various optimizations to the EDA method by starting with the layout of the reading heads. For example, the SelfA235 system developed by the Japan Metrology Institute has reading heads arranged at 2, 3, and 5 equal division positions on the circumference, which increases the harmonic order that cannot be calibrated to the 30th harmonic, and finally achieves an angle measurement accuracy of ±0.03″ and a resolution of 0.0015″ (doi:10.1088 / 0957-0233 / 25 / 6 / 065002).

[0005] Lu XD et al. proposed a self-calibration model based on the Time-Measurement Dynamic Reversal (TDR) method. This method combines the principle of circumferential closure with the reverse method technique. It calibrates the sensor's engraving error and installation error by measuring the time it takes for the shaft system to rotate through a unit angular displacement, ultimately achieving a sensor accuracy of ±0.04″. To more accurately separate the radial error motion of the spindle and the rotational vibration caused by shaft torque disturbance, an EDA method with four reading heads was combined with the TDR method, reducing the measurement error of the calibrated angle encoder from approximately ±2″ to ±0.02″. However, the TDR method is more suitable for high-speed turntables, requires the acquisition of a large amount of data, and places high demands on system design and shaft stability (doi:10.1016 / j.cirp.2010.03.127).

[0006] The frequency domain shearing algorithm was initially proposed by PTB experts around 2000. Subsequently, PTB angle metrology researchers applied this technique to the calibration of subdivision errors in encoders and autocollimators in 2014 (doi:10.1088 / 0957-0233 / 25 / 10 / 105009). The shearing algorithms used by PTB and other institutions for small-angle calibration are mainly based on Discrete Fourier Transform and natural continuation techniques. Addressing the limitations of these methods in terms of limited measurement range selection and high computational complexity, Jiao Yang proposed a time-domain shearing algorithm based on shearing technology for subdivision error calibration. This method directly reconstructs the error in the angle domain without needing to transform to the frequency domain, providing a more convenient implementation scheme for shearing-based subdivision error calibration.

[0007] The core idea of ​​the aforementioned self-calibration method is to utilize the phase differences in signals generated by multiple reading heads at different spatial installation positions, and to achieve error separation and suppression through signal processing. Currently, the application of the shearing method in the angle domain is still in its early stages, mainly focusing on the calibration of encoder and autocollimator subdivision errors. Research on self-calibration based on time shearing of single reading head signals is insufficient. During turntable rotation, the signals from a single reading head at different times correspond to error information at different spatial positions of the grating disk, thus forming the concept of time shearing. Since the shearing method can effectively extract periodic error components, and turntable positioning errors also possess periodic characteristics, applying the shearing method to turntable positioning error self-calibration is feasible. Summary of the Invention

[0008] Against this backdrop, this invention aims to propose a turntable positioning error self-calibration method based on time shearing of a single reading head. This method extracts the angle error through time shearing operation of a single reading head, and reconstructs the positioning error using Fourier and matrix equation methods. It overcomes the limitation of existing self-calibration methods that generally rely on multi-reading head layouts, reducing cost and installation complexity, and providing a more economical and efficient solution for turntable self-calibration technology.

[0009] The technical solution adopted in this invention is as follows:

[0010] A self-calibration method for turntable positioning error based on single reading head time shearing includes the following steps:

[0011] Step 1) Install a reading head into the turntable angle measurement system;

[0012] Step 2) Accelerate the turntable to the preset speed. Then, the drive enable is cut off, allowing the turntable to rotate freely under inertia;

[0013] Step 3) Record the moment when the reading head detects the zero-position Z-line of the rotary table circular grating as the starting moment. At equal time intervals throughout the entire circumference Collect N sampling points; then... Each sampling time is recorded as , The angular position corresponding to the sampling time is denoted as The sequence of positions of the full circumference angles obtained from the collection is denoted as... ;

[0014] Step 4) For each sampling point, process the angular position data in its neighboring area to obtain the instantaneous angular rate corresponding to each sampling moment of the entire circle. ;

[0015] Step 5) Apply a time shearing factor ,Will Using the sampled data at time 1 as the starting point, the second set of whole circle angle position sequences is obtained. ;at this time The angle between the angular position and the Z-mark of the turntable zero position is denoted as ;

[0016] Step 6) Each sampling point starts with a continuous Summing the angular displacements within each sampling interval yields the actual shear angular displacement at each sampling moment along the entire circumference. ,in ;

[0017] Step 7) Within the entire circumference, cut the sequence before cutting. and cut sequence The difference function is obtained by subtracting. And then and By taking the difference, we can obtain the shear difference function. ;

[0018] Step 8) Based on the shear difference function Select an appropriate reconstruction method to correct the turntable positioning error. The reconstruction.

[0019] Furthermore, in step 3), the output signal of the reading head includes true angular position information and positioning error information.

[0020] The output signal of the reading head before shearing is:

[0021] ;

[0022] Among them, the Each sampling time is recorded as , for The corner position of the turntable is sampled at all times. For the turntable in Positioning error at the location.

[0023] Furthermore, in step 5), the output signal of the reading head, after time clipping, still contains the true angular position information and positioning error information.

[0024] The signal after shearing is:

[0025] ;

[0026] in, For the turntable after shearing The true angular position at any given moment. For the turntable in Positioning error at the location, Time shearing amount The corresponding actual angular displacement.

[0027] Furthermore, in step 6): for Each sampling point starts with a continuous Summing the angular displacements within each sampling interval yields the actual shear angular displacement at each sampling moment along the entire circumference. :

[0028] ;

[0029] Furthermore, in step 7):

[0030] Two sets of data and Subtracting them yields the difference function. :

[0031] ;

[0032] To handle the time shearing amount in the above difference The corresponding actual angular displacement is used to define the turntable positioning error. Shear difference function in the angle domain :

[0033] .

[0034] Furthermore, in step 8), the shear difference function Contains only turntable positioning error The components, using the reconstruction method Refactoring ,Right now:

[0035] .

[0036] The design concept of this invention is as follows: This invention breaks away from the traditional approach of relying on the spatial phase difference of multiple reading heads, and completes the entire calibration using only a single reading head of the turntable itself: First, the turntable is accelerated to a preset speed, and then the drive enable is cut off, allowing the turntable to rotate freely under inertia; a first set of full-circumference angle position sequences is collected at equal time intervals; then a fixed-duration time shear is applied, and the sampling data at the time corresponding to the time shear is used as the starting point to obtain a second set of full-circumference angle position sequences; by subtracting the reading signals of the reading heads at the same time points in the sequences before and after shearing, a difference function is obtained, and then the actual shear angular displacement corresponding to each sampling time is removed from the difference function to obtain a shear difference function; finally, the turntable positioning error within the entire circumference range is reconstructed through a reconstruction algorithm. This invention replaces the spatial phase acquisition of multiple reading heads with time-domain time shearing, eliminating the need for additional reading heads and repeated sampling by starting and stopping the turntable multiple times. The solution is adaptable to various turntable angle measurement systems, offering greater versatility and implementation flexibility.

[0037] The beneficial effects of this invention are as follows: This method utilizes a single reading head signal from a turntable angle measurement system to reconstruct turntable positioning errors. This method does not rely on a complex multi-read head system, enabling more convenient and rapid self-calibration of turntable positioning errors. Implementing error correction based on a single reading head presents conceptual challenges. The reading head measurement signal contains both the true angular position and the positioning error. Traditional self-calibration methods typically rely on the phase differences generated by signals from multiple reading heads installed at different locations. Under single-read head conditions, different measurement sequences must be constructed to separate and suppress errors, placing demands on signal processing. To overcome this difficulty, this invention addresses the requirements for sampling time interval, rotational speed acquisition, precise application of time shearing, and data alignment. This invention also brings significant technical advantages. The hardware cost and system complexity of this method are greatly reduced. It no longer relies on the physical spatial phase difference of the multi-reader signal, but instead obtains information through time clipping, which reduces the cost and installation complexity required for the multi-reader system. All data in the measurement process of this method comes from the same set of continuous rotation processes, without the need to stop or restart repeatedly, avoiding the additional errors introduced by multiple installations and adjustments, and thus achieving higher calibration efficiency. In addition, this method has good versatility for different types of turntable systems, so it is highly flexible. Attached Figure Description

[0038] Figure 1 This is a diagram of the shearing process for turntable positioning error self-calibration based on single reading head signal shearing;

[0039] Figure 2 This is a diagram illustrating the data processing procedure for turntable positioning error self-calibration based on single-reader signal shearing. Detailed Implementation

[0040] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0041] A self-calibration method for turntable positioning error based on single reading head time shearing specifically includes the following steps:

[0042] a. Install a reading head into the turntable angle measurement system;

[0043] b. Accelerate the turntable to the preset speed. Then, the drive enable is cut off, allowing the turntable to rotate freely under inertia; the preset speed... As long as the enable condition is met, it can pass through the entire circumference completely. Angle values ​​within the specified range are acceptable.

[0044] c. Record the moment when the turntable rotates to the point where the reading head detects the zero-position Z-line of the circular grating as the starting moment. At equal time intervals throughout the entire circumference Collect N sampling points sequentially; then... Each sampling time is recorded as , The angular position corresponding to the sampling time is denoted as The first set of angular position sampling sequences obtained by collecting data around the entire circle is denoted as... ;

[0045] d. For each sampling point, the angular position data of its neighboring region are processed to obtain the instantaneous angular velocity corresponding to each sampling moment of the entire circle. ;

[0046] For the first set of angular position sequences Every moment in At each sampling time Centered on a point, a local data window is extracted, encompassing the point and several adjacent sampling points before and after it. Within this local data window, the local slope at the center point is fitted using the least squares method, utilizing the correspondence between the angular positions of each sampling point and time. This slope represents the turntable's position at the center point. instantaneous angular velocity at time t It is worth noting that the above-mentioned slope calculation method can be implemented in a variety of ways known in the art. This invention does not limit the specific method to a single one. All processing methods that use local angular position data to calculate instantaneous velocity fall within the scope of this step.

[0047] e. Apply a time shearing factor ,Will Using the sampled data at time 1 as the starting point, a second set of readhead sampling sequences is obtained. ;at this time The angle between the angular position and the Z-mark of the turntable zero position is denoted as ;

[0048] f. To Each sampling point starts with a continuous Summing the angular displacements within each sampling interval yields the actual shear angular displacement at each sampling moment along the entire circumference. ,in ;

[0049] g. Within the entire circumference, the sequence before cutting... and cut sequence The difference function is obtained by subtracting. And then and By taking the difference, we can obtain the shear difference function. ;

[0050] h. Based on the shear difference function Select an appropriate reconstruction method to correct the turntable positioning error. The reconstruction.

[0051] During operation, a deviation exists between the target angular position and the actual angular position reached by the turntable; this deviation is defined as the turntable's positioning error. For any actual angular position of the turntable... The positioning error of the turntable is defined as:

[0052] (1);

[0053] In the formula, The target angle position of the turntable. This represents the actual angular position of the turntable. For the turntable at the corner position The positioning error at that location forms the basis for error analysis and self-calibration research.

[0054] To isolate the turntable's positioning error, this method employs time shearing, requiring only a single reading head to reconstruct the turntable's positioning error across the entire circumference. During the measurement process, the turntable is first accelerated to a preset speed. The drive is then cut off, allowing the turntable to rotate freely under inertia and ensuring it completes a full rotation. The moment when the reading head detects the zero-position Z-line of the rotary table circular grating is recorded as the starting moment. At equal time intervals throughout the entire circumference Sampling N positioning points in sequence, the first Each sampling time is recorded as , The angular position of the sampling point at time t is denoted as The sequence of positions of the full circumference angles obtained is denoted as Reading head output signal It includes the turntable's true angular position information and positioning error information, namely:

[0055] (2);

[0056] In the formula, For reading the reading head, for The actual angular position of the turntable at the sampling time. For the turntable in Positioning error at the location.

[0057] For each sampling point, the angular position data in its neighboring region are processed to obtain the instantaneous angular velocity corresponding to each sampling moment of the entire circle. Apply a time shearing factor. The number of discrete point moves corresponding to the time shear is ,Right now:

[0058] (3);

[0059] Will Using the sampled data at time 1 as the starting point, the second set of whole circle angle position sequences is obtained. The data cutting process is as follows Figure 1 As shown, at this time The angle between the angular position and the Z-mark of the turntable zero position is denoted as Starting from the initial moment, through the first set of measurement data... The ideal shear displacement is obtained by summing the products of the instantaneous angular velocity within each sampling interval and the sampling interval itself. :

[0060] (4);

[0061] right Each sampling point starts with a continuous Summing the angular displacements within each sampling interval yields the actual shear angular displacement at each sampling moment along the entire circumference. ,in , It can be represented as:

[0062] (5);

[0063] The second set of whole-circumference angle position sequences after time shearing can be represented as:

[0064] (6);

[0065] in, For the turntable after shearing The true angular position at any given moment. For the turntable in Positioning error at the location, This represents the actual shear angular displacement that occurred at each sampling time.

[0066] To avoid introducing additional errors from restarting after a shutdown, all data were derived from the same set of continuous rotation measurements. The sheared reading sequence was constructed by time shearing the original measurement data. For each sampling moment of the reading head sampling sequence before and after shearing on the entire circumference, the same time points in the pre-shear and post-shear sequences were compared. By subtracting the readings from the reading heads at each point, common differences can be eliminated. The true angular position of the turntable at the sampling time The difference function is obtained. :

[0067] (7);

[0068] Processing the above original shear difference function The actual shear angular displacement corresponding to each sampling time. And then and By taking the difference, we obtain the shear difference function. :

[0069] (8);

[0070] Shear difference function Including turntable positioning error The components, therefore, by selecting an appropriate reconstruction method, can be obtained from the shear difference function. The positioning error of the turntable was reconstructed in the middle. .

[0071] The following section will use the Fourier method and the matrix equation solving method as reconstruction methods, and will describe the specific reconstruction process respectively.

[0072] Example 1: Fourier Method

[0073] Based on the circumferential closure of the turntable, the positioning error of the turntable is... Since it is a periodic continuous function, we can consider using the Fourier transform method for reconstruction.

[0074] Will , and Perform a Fourier expansion:

[0075] (9);

[0076] (10);

[0077] (11);

[0078] In the formula, For harmonic orders, Error function The Fourier coefficients corresponding to the order Shear difference function The Fourier coefficients, It is the representation of the shear difference function in the Fourier domain. Time shearing amount The corresponding ideal angular displacement is defined as the first... Shear transfer function corresponding to the order :

[0079] (12);

[0080] Therefore, the Fourier coefficients of the positioning error It can be recovered from the Fourier coefficients of the shear difference function:

[0081] (13);

[0082] Fourier coefficients By performing an inverse discrete Fourier transform, the positioning error of the turntable can be obtained, thus realizing the turntable error. Cutting and reconstructing.

[0083] (14);

[0084] Example 2: Matrix Equation Solving Method

[0085] For the turntable in The positioning error at the location is represented by a vector consisting of the positioning errors corresponding to each sampling point:

[0086] (15);

[0087] Time shear The corresponding number of discrete point moves is The actual shear angular displacement corresponding to each sampling moment of the entire circle is: Shearing amount at each time interval At discrete locations, the shear difference function can establish the following linear relationship:

[0088] (16);

[0089] For ease of calculation, this system of equations can be written in matrix form:

[0090] (17);

[0091] In the formula, It is the positioning error vector to be determined; It is by The observation vector is composed of; This is the coefficient matrix of the shear difference functions, where each row corresponds to a shear difference function, and the elements contain only 0, 1, and -1. Since the number of equations exceeds the number of unknowns, this system of equations is overdetermined and can be solved using the least squares method.

[0092] (18);

[0093] By solving this system of equations, the positioning error of the turntable can be reconstructed. .

[0094] It is worth noting that the scheme uses Fourier method and least squares method as examples for error reconstruction, but the reconstruction method is not limited to Fourier method and least squares method. It is also applicable to other error reconstruction methods based on shear difference. Therefore, the scope of protection of this invention is not limited to the above-mentioned cases of reconstruction using Fourier method and least squares method.

[0095] The symbols used in this invention and their physical meanings are shown in the table below:

[0096] Table 1. Symbols and their physical meanings ;

[0097] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0098] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0099] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A self-calibration method for turntable positioning error based on single reading head time shearing, characterized in that, The angle error is extracted by time shearing operation of a single reading head, and the positioning error is reconstructed. Includes the following steps: Step 1) Install a reading head into the turntable angle measurement system; Step 2) Accelerate the turntable to the preset speed. Then, the drive enable is cut off, allowing the turntable to rotate freely under inertia; Step 3) Record the moment when the reading head detects the zero-position Z-line of the rotary table circular grating as the starting moment. At equal time intervals throughout the entire circumference Collect N sampling points; then... Each sampling time is recorded as , The angular position corresponding to the sampling time is denoted as The sequence of positions of the full circumference angles obtained from the collection is denoted as... ; Step 4) For each sampling point, process the angular position data in its neighboring area to obtain the instantaneous angular rate corresponding to each sampling moment of the entire circle. ; Step 5) Apply a time shearing factor , The number of discrete points moved corresponding to the time shearing amount; Using the sampled data at time 1 as the starting point, a second set of whole circle angle position sequences is obtained. ;at this time The angle between the angular position and the Z-mark of the zero position of the turntable is denoted as ; Step 6) Each sampling point starts with a continuous Summing the angular displacements within each sampling interval yields the actual shear angular displacement at each sampling moment along the entire circumference. ,in ; Step 7) Within the entire circumference, cut the sequence before cutting. and cut sequence The difference function is obtained by subtracting. And then and By taking the difference, we can obtain the shear difference function. ; Step 8) Based on the shear difference function Select the appropriate reconstruction method to correct the turntable positioning error. The reconstruction.

2. The method for self-calibrating turntable positioning error based on single reading head time shearing according to claim 1, characterized in that, In step 3), the output signal of the reading head includes true angular position information and positioning error information. The output signal of the reading head before shearing is: ； Among them, the Each sampling time is recorded as , for The corner position of the turntable is sampled at all times. For the turntable in Positioning error at the location.

3. The method for self-calibrating turntable positioning error based on single reading head time shearing according to claim 1, characterized in that, In step 5), the output signal of the reading head, even after time clipping, still contains true angular position information and positioning error information. The signal after shearing is: ； in, For the turntable after shearing The true angular position at any given moment. For the turntable in Positioning error at the location, Time shearing amount The corresponding actual angular displacement.

4. The method for self-calibrating turntable positioning error based on single reading head time shearing according to claim 1, characterized in that, In step 7): Two sets of data and Subtracting them yields the difference function. : ； To handle the time shearing amount in the above difference The corresponding actual angular displacement is used to define the turntable positioning error. Shear difference function in the angle domain : 。 5. The method for self-calibrating turntable positioning error based on single reading head time shearing according to claim 1, characterized in that, Step 8) shear difference function Contains only turntable positioning error The components, using the reconstruction method Refactoring ,Right now: 。

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