Method for shearing reconstruction of circumferential positioning error based on double reading head signals of rotary table

Abstract

The present application relates to the technical field of angle measurement, and discloses a circumferential positioning error shearing reconstruction method based on double reading head signals of a rotary table, 1) a reading head is installed into an angle measurement system of the rotary table; 2) the rotary table is controlled to rotate to a zero position Z scale line of a circular grating detected by the reading head; 3) another reading head is installed into the angle measurement system of the rotary table, and the two reading heads are at an included angle β; 4) the rotary table is rotated for one circle, and signals output by the two reading heads are collected; 5) the signals are subtracted to obtain shearing difference of the rotary table error in the angle domain with β as a shearing amount; 6) reconstruction of the rotary table error is completed; the present application uses two reading head signals of the angle measurement system of the rotary table to perform a full-circle error reconstruction method, and more conveniently and quickly completes calibration of the rotary table error.

Description

Technical Field

[0001] This invention relates to the field of angle measurement technology, and specifically to a method for reconstructing the circumferential positioning error of a turntable based on dual reading head signals. Background Technology

[0002] In defense industries and other fields, turntables are widely used to achieve continuous measurement of full-circumference angles. To improve angle measurement accuracy, the turntable needs to be calibrated and error compensation for major error sources needs to be implemented. The calibration and verification of the turntable can be performed by comparison with high-precision external equipment, with traceability of measurement values ​​achieved through step-by-step transmission from various metrology institutes. Because this comparison and calibration transmission chain is long and prone to inconvenience due to equipment transportation, designing a self-calibration method that allows the turntable angle measurement system to achieve rapid real-time calibration without the need for external reference standards is of great significance.

[0003] The Equal Division Averaged (EDA) method, proposed by the National Institute of Metrology of Japan in 1993, is a self-calibration method capable of simultaneously calibrating two encoders with unknown graduation errors (doi:10.2493 / jjspe.67.1091). This method achieves high-precision angle standard supply with an expanded uncertainty of 0.01″ by arranging multiple reading heads in equal circular divisions and obtaining the graduation error curve based on the average signal value.

[0004] The Physics and Technology Institute (PTB) in Germany has proposed the Prime Factor Division (PFD) method. This self-calibration method is based on the prime factor algorithm of discrete Fourier transform. It does not require a large number of read heads and has a shorter process, but the calculation process is extremely cumbersome, and the uncertainty of the calibration results is greater than that of other encoder calibration methods (doi:10.1088 / 0957-0233 / 19 / 1 / 015101).

[0005] Lu XD et al. proposed the Time-Measurement Dynamic Reversal method (TDR). This self-calibration method combines the principle of circumferential closure and calibrates the sensor's engraving error and installation error by measuring the time taken for the shaft system to rotate through a unit spatial angular displacement. After self-calibration, the sensor accuracy is ±0.04″. However, this method needs to be applied to high-speed turntables and requires the acquisition of a large amount of data. It requires targeted system design and also has high requirements for the stability of the shaft system (doi:10.1016 / j.cirp.2010.03.127).

[0006] Currently, most common error calibration methods are related to Fourier methods, while the concept of shear reconstruction is rarely mentioned. Meanwhile, current self-calibration methods require multiple reading heads, primarily installed at circumferentially equidistant points. A turntable full-circle error reconstruction system based on the shear principle is still in its infancy. Summary of the Invention

[0007] To address the problems in the technical background, this invention aims to provide a turntable error shearing reconstruction method based on dual readhead signals, which enables the installation of readheads to be extended from equal divisions to the full circle range, and avoids the use of a large number of readheads, thereby reducing system costs and avoiding the limitations of other self-calibration methods to a certain extent.

[0008] The technical solution adopted in this invention includes the following steps:

[0009] The method for reconstructing circumferential positioning error shearing based on turntable dual readout head signals includes the following steps:

[0010] Step 1) Install a reading head M1 into the turntable angle measurement system;

[0011] Step 2) Control the turntable to rotate until the reading head detects the zero-position Z-line of the circular grating, record position 1, and use position 1 as the starting position;

[0012] Step 3) Install another reading head M2 into the turntable angle measurement system;

[0013] Step 4) Rotate the turntable one revolution and collect the output signal of the reading head M1. The output signal of the reading head M2 ;

[0014] Step 5) Define the shearing map within the entire circular range, i.e., the measurement interval [0, 2π]. Turntable error The shearing process is described as follows:

[0015] ;

[0016] Where s is the shear rate. for Cutting, When the shear rate is s Shear difference;

[0017] Step 6) Obtain the turntable error based on the angle β between reading head M2 and reading head M1. Shear difference with β as the shear quantity in the angular domain ;

[0018] Step 7) Based on Choose an appropriate reconstruction method, such as Fourier transform or matrix equation solving, to complete the turntable error. The reconstruction.

[0019] Furthermore, in step 4), the output signal of the reading head includes angular position information and error information.

[0020] The output signal of the reading head M1 is:

[0021] ;

[0022] The installation interval between reading head M2 and reading head M1 is β. The output signal of reading head M2 is:

[0023] .

[0024] Furthermore, in step 5):

[0025] For interval Undefined ,because For a continuous function with a period of 2π, by considering the interval... of Cut and extract.

[0026] Furthermore, in step 5):

[0027] Will and Subtract to obtain the turntable error. Shear difference with β as the shear quantity in the angular domain :

[0028] Turntable positioning error In the angular domain shear difference :

[0029] .

[0030] Furthermore, in step 7), the shear difference... Including turntable positioning error The components, using the reconstruction method Refactoring ,Right now:

[0031] .

[0032] in accordance with Complete the turntable error The reconstruction.

[0033] The beneficial effects of this invention are: this invention provides a method for reconstructing full-circle errors using two reading head signals inherent in the shear turntable angle measurement system; furthermore, this invention has no strict requirements on the installation position of the reading heads, and can more conveniently and quickly complete turntable error calibration. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the installation of the reading head of the turntable angle measuring system. Detailed Implementation

[0035] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings:

[0036] The method for reconstructing circular positioning error based on dual readout head signals of a turntable comprises the following steps:

[0037] a. Install a reading head into the turntable angle measurement system;

[0038] b. Control the turntable to rotate until the reading head detects the zero-position Z-line of the circular grating, and use this position as the starting position;

[0039] c. Install another reading head into the turntable angle measurement system, forming an angle β with the previously installed reading head;

[0040] d. Rotate the turntable one revolution and collect the signals output from the two reading heads. and , where θ is the angular position of the turntable;

[0041] e. will and Subtract to obtain the turntable error. Shear difference with β as the shear quantity in the angular domain ;

[0042] f. Based on Choose an appropriate reconstruction method, such as Fourier transform or matrix equation solving, to complete the turntable error. The reconstruction.

[0043] like Figure 1 As shown, the reading head output signal contains angular position information and error information, and the reading head measurement value can be defined by the following formula. :

[0044] (1);

[0045] In the formula, The rotation angle of the turntable. For the turntable in Positioning error at the location. For the shear reconstruction problem of the full-circle positioning error of the turntable, its measurement interval can be regarded as [0, 2π], so a shear mapping can be defined within this interval. ,and The shearing process can be described as follows:

[0046] (2);

[0047] Where s is the shear rate. yes The result of a translation transformation with a shift of s. This is called... for Cutting, When the shear rate is s The shear difference; in particular, for intervals Undefined ,because It is a continuous function with a period of 2π, and its value can be obtained by applying the interval... of The data is obtained by shearing, ensuring that the data in the entire shearing interval is continuous.

[0048] Reading head and Installed inside the turntable, with an installation interval of β. For incremental encoders, the reading head measurement only exhibits a phase difference introduced by the installation position, thus the reading head measurement value is:

[0049] (3);

[0050] (4);

[0051] The difference between the two values ​​gives the turntable positioning error. In the angular domain shear difference :

[0052] (5);

[0053] Shear difference Including turntable positioning error The components are thus determined, allowing for the selection of appropriate reconstruction methods. Refactoring ,Right now:

[0054] (6);

[0055] 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.

[0056] Example 1: Fourier Method

[0057] Based on the circumferential closed characteristic of the turntable, , , , Both are continuous functions with a period of 2π, therefore, Fourier transform can be considered for reconstruction. , Expand into Fourier series form:

[0058] (7);

[0059] (8);

[0060] In the formula, This is the representation of the shear difference in the Fourier domain, where k is the harmonic order. These are the Fourier coefficients corresponding to the k-th order. From equations 7 and 8, it is easy to see that the coefficients obtained by Fourier transform in the frequency domain are... , The relationship is as follows:

[0061] (9);

[0062] That is: the shear difference function obtained by measuring signals through two reading heads. The Fourier coefficients between the unknown circular positioning error function and each term only exist The multiple difference allows for the definition of reconstruction. The shear transfer function required for the k-th order component :

[0063] (10);

[0064] therefore The reconstruction process can be represented as:

[0065] (11);

[0066] Shear difference is obtained by reading the measurements from the dual reading heads. Then, the transfer functions of each order corresponding to the reading head installation interval β are calculated. Turntable error can be achieved Cutting and reconstructing.

[0067] Example 2: Matrix Equation Solving Method

[0068] In actual measurement, the turntable rotates one revolution, and the reading head output signal is collected at N discrete points at equal angular intervals. The angular position corresponding to the nth sampling point is denoted as:

[0069] (12);

[0070] 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:

[0071] (13);

[0072] Let shear quantity The corresponding number of discrete point offsets is m, that is:

[0073] (14);

[0074] Based on equation (5), the shear amount at each phase interval At discrete locations, the shear difference can establish the following linear relationship:

[0075] (15);

[0076] For ease of calculation, this system of equations can be written in matrix form:

[0077] (16);

[0078] In the formula, It is the positioning error vector to be determined; It is by The vector formed; This is the coefficient matrix of a system of difference equations, where each row corresponds to a difference equation, 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.

[0079] (17);

[0080] The turntable error can be determined by solving this system of equations using the least squares method. Cutting and reconstructing.

[0081] It is worth noting that the scheme uses Fourier transform and matrix equation solving as examples for error reconstruction, but the reconstruction method is not limited to the above methods. It is also applicable to other error reconstruction methods based on shearing difference. Therefore, the scope of protection of this invention is not limited to the above situations.

[0082] 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.

[0083] 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.

[0084] 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 method for reconstructing circumferential positioning error shearing based on dual readout head signals of a turntable, characterized in that, Includes the following steps: Step 1) Install a reading head M1 into the turntable angle measurement system; Step 2) Control the turntable to rotate until the reading head detects the zero-position Z-line of the circular grating, record position 1, and use position 1 as the starting position; Step 3) Install another reading head M2 into the turntable angle measurement system; Step 4) Rotate the turntable one revolution and collect the output signal of the reading head M1. The output signal of the reading head M2 ; Step 5) Define the shearing map within the entire circular range, i.e., the measurement interval [0, 2π]. Turntable error The shearing process is described as follows: ； Where s is the shear rate. for Cutting, When the shear rate is s Shear difference; Step 6) Obtain the turntable error based on the angle β between reading head M2 and reading head M1. Shear difference with β as the shear quantity in the angular domain ; Step 7) Based on Select the appropriate reconstruction method to complete the turntable error. The reconstruction.

2. The method for reconstructing circumferential positioning error based on dual readout head signals of a turntable according to claim 1, characterized in that, In step 4), the output signal of the reading head includes angular position information and error information. The output signal of the reading head M1 is: ； The installation interval between reading head M2 and reading head M1 is β. The output signal of reading head M2 is: 。 3. The method for reconstructing circumferential positioning error based on dual readout head signals of a turntable according to claim 2, characterized in that, In step 5): For interval Undefined ,because For a continuous function with a period of 2π, by considering the interval... of Cut and extract.

4. The method for reconstructing circumferential positioning error based on dual readout head signals of a turntable according to claim 2, characterized in that, In step 5): Will and Subtract to obtain the turntable error. Shear difference with β as the shear quantity in the angular domain : Turntable positioning error In the angular domain shear difference : 。 5. The method for reconstructing circumferential positioning error based on dual readout head signals of a turntable according to claim 1, characterized in that, The shear difference in step 7) Including turntable positioning error The components, using the reconstruction method Refactoring ,Right now: 。 6. The method for reconstructing circumferential positioning error based on dual readout head signals of a turntable according to claim 5, characterized in that, The reconstruction method selected is either Fourier transform or matrix equation solving.

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