A double-encoder mutual calibration method based on shearing principle

Abstract

The application relates to the technical field of angle measurement, and discloses a double-encoder mutual calibration method based on a shearing principle, two encoders are coaxially and rigidly connected, one reference reading head and two movable reading heads are installed on the encoder 1, one reference reading head is installed on the encoder 2, two sets of shearing difference functions of the positioning error of one of the encoders are constructed by reading the double-encoder measurement values and performing difference operation, the error function is obtained by shearing reconstruction and weighted fusion on the function; the error function of the other encoder is obtained by substituting the error function into the double-encoder difference value, and the mutual calibration between the double encoders is realized; the application solves the limitations of the traditional encoder calibration steps being complicated and the experimental requirements being high.

Description

Technical Field

[0001] This invention relates to the field of angle measurement technology, and specifically to a dual encoder mutual calibration method based on the shearing principle. Background Technology

[0002] In industrial production, angle encoders have always been a key research focus in precision positioning systems. Compared to other angle measuring instruments, angle encoders offer significant advantages such as a large measurement range, high resolution, and high measurement accuracy. However, the encoder's own systematic errors directly affect the accuracy of the measurement results. Therefore, encoder calibration has become one of the key issues in the field of angle metrology. Currently, commonly used encoder calibration schemes rely on external reference instruments, such as high-precision equipment like multifaceted prisms, multi-tooth indexing stages, and autocollimators, but these have limitations due to stringent experimental requirements and high costs. Therefore, designing a method for real-time encoder calibration that does not require external reference standards is of great significance.

[0003] In 1993, the National Metrology Institute of Japan (NMIJ) proposed the Equal Division Averaged method (EDA) for research on self-calibration methods for angle encoders and developed a high-precision self-calibration system that compares two coaxially mounted encoders to calibrate two encoders with unknown indexing errors (doi:10.2493 / jjspe.67.1091).

[0004] In 2010, Lu XD et al. proposed an improved Time-Measurement Dynamic Reversal (TDR) method for self-calibration of angle encoders. This method is based on spindle dynamics, deriving the actual spatial interval by measuring the time interval between encoder signals, comparing it to the nominal grid pitch to obtain the encoder error, and relying on four equally spaced reading heads combined with Fourier analysis to remove rotational vibration interference. However, this method requires a large amount of data for simulation and has high requirements for environmental stability (doi:10.1016 / j.cirp.2010.03.127).

[0005] In 2016, Ishii Nobuyuki's research team at Keio University in Japan proposed the Virtual Equal Division Average (VEDA) method. This method represents a breakthrough from EDA, calibrating high-order errors without requiring a large number of sensors. It effectively compensates for error terms up to the 30th order using only 2-6 reading heads. Under standard equipment verification, the high-order error amplitude was approximately 0.01″, which decreased to 0.006″ after VEDA calibration. When actually installed on a CNC lathe spindle, the positioning accuracy improved from ±2.25″ to ±1.29″, validating the method's applicability in industrial environments (doi:10.2493 / jjspe.84.717).

[0006] Currently, traditional angle encoder calibration requires comparison with an external benchmark, relies on high-precision angle measuring instruments, and suffers from problems such as discrete measurement positions, time consumption, and stringent installation and environmental requirements, resulting in high encoder calibration costs. In the field of high-precision encoder self-calibration, current research focuses on EDA and its derivative methods, which achieve full-circumference high-precision encoder self-calibration by installing multiple reading heads in equal proportions. However, this method suffers from problems such as a large number of reading heads and complex debugging. The application of shear-based calibration in the angle field is limited to encoder-autocollimator mutual calibration at small angle scales and has not yet been extended to full-circumference measurement, indicating potential for further exploration. Summary of the Invention

[0007] To address the problems in the technical background, this invention aims to provide a mutual calibration method based on the self-signal cutting of dual encoders, overcoming the limitations of traditional encoder calibration steps being cumbersome and having high experimental requirements.

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

[0009] Step 1) Rigidly connect the two encoders coaxially;

[0010] Step 2) Install one reference reading head and two movable reading heads on encoder 1, and denote the angles between them and the reference reading head as β1 and β2. Install only one reference reading head on encoder 2.

[0011] Step 3) Control the shaft to rotate until the encoder 1 reference reading head detects a zero position signal, and use this position as the starting position;

[0012] Step 4) Control the shaft to rotate one revolution and collect the measurement value from the encoder 1 reference reading head. 2 movable reading head measurement values , and encoder 2 reference reading head measurement value ;

[0013] Step 5) Perform a difference operation between the measured values ​​of encoder 2 and the measured values ​​of each reading head of encoder 1 to obtain 3 sets of error difference functions. , , ;

[0014] Step 6) , respectively with The difference is calculated to eliminate the positioning error of encoder 2. Construct two sets of encoder positioning errors. shear difference function , The corresponding shear amounts are β1 and β2;

[0015] Step 7) Based on the inverse operation properties of the shearing difference function, the shearing transfer function is used to... , Perform inverse kinematics to obtain the Fourier coefficient sequences of the two sets of shear difference functions. , ;

[0016] Step 8) The two sets of Fourier coefficients are processed using weighted fusion, and the positioning error of encoder 1 is obtained through inverse operation. ;

[0017] Step 9) Substitute the three sets of difference functions from step 5 into the mean value to obtain the positioning error of encoder 2. This enables mutual calibration between encoder 1 and encoder 2.

[0018] Furthermore, in step 4):

[0019] Based on encoder measurements :

[0020] ;

[0021] in, This represents the actual rotation angle of the encoder. For the encoder in The positioning error at the location is:

[0022] Encoder 1 reference reading head: ;

[0023] Encoder 1 shear angle Reading head: ;

[0024] Encoder 1 shear angle Reading head: ;

[0025] Encoder 2 reference reading head: .

[0026] Furthermore, in step 5): the true rotation angle is eliminated by differentially analyzing the measurements from the two encoders. The error difference function is obtained as follows: .

[0027] Furthermore, in step 6):

[0028] Will , respectively with Difference operation to eliminate encoder 2 positioning error Construct the shearing difference function of encoder 1 , : .

[0029] Furthermore, in step 7):

[0030] By shearing the transfer function Obtaining Fourier coefficients : .

[0031] Furthermore, in step 8)

[0032] The two sets of Fourier coefficients were weighted and fused to obtain Based on this, a shearing and reconstruction process is performed to obtain the positioning error of encoder 1. : .

[0033] Furthermore, Substituting this into step 5), the random error is reduced through mean estimation to obtain the positioning error of encoder 2. : .

[0034] The beneficial effects of this invention are:

[0035] This invention provides a method for mutual calibration of coaxial encoder measurements using a shearing method; furthermore, this invention does not have strict requirements on encoder accuracy, and can more conveniently and quickly complete the error calibration of two encoders simultaneously.

[0036] This invention effectively reduces harmonic leakage generated by the equal division averaging method in encoder calibration by selecting two sets of coprime shear numbers for shear reconstruction, and reduces random errors generated during encoder 2 calibration by mean estimation. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the installation of a dual encoder mutual calibration system. Detailed Implementation

[0038] The present invention will be further described below with reference to the accompanying drawings.

[0039] like Figure 1 As shown, a dual encoder mutual calibration method based on the shearing principle includes the following steps:

[0040] a. Rigidly connect the two encoders coaxially;

[0041] b. Install one reference reading head and two movable reading heads on encoder 1, and denot the angles between them and the reference reading head as β1 and β2. Install only one reference reading head on encoder 2.

[0042] c. Control the rotating shaft to rotate until the encoder 1 reference reading head detects a zero position signal, and use this position as the starting position;

[0043] d. Control the shaft to rotate one revolution and collect the measurement value from the encoder 1 reference reading head. 2 movable reading head measurement values , and encoder 2 reference reading head measurement value ;

[0044] e. Perform a difference operation between the measured values ​​of encoder 2 and the measured values ​​of each reading head of encoder 1 to obtain 3 sets of error difference functions. , , ;

[0045] f. will , respectively with The difference is calculated to eliminate the positioning error of encoder 2. Construct two sets of encoder positioning errors. shear difference function , The corresponding shear amounts are β1 and β2;

[0046] g. To , By selecting an appropriate inverse operation method, two sets of estimation results for the positioning error of encoder 1 are obtained. , ;

[0047] h. Weighted fusion is used to process the two sets of estimation results to obtain the positioning error of encoder 1. ;

[0048] i. will Substitute into the three sets of difference functions , , The positioning error of encoder 2 is obtained by averaging the results. This enables mutual calibration between encoder 1 and encoder 2.

[0049] Encoder measurements include angular position information and error information, and can be defined using the following formula: :

[0050] (1);

[0051] In the formula, This represents the actual rotation angle of the encoder. For the encoder in The positioning error at the location, and due to the periodic characteristics of the encoder, Let be a periodic function with a period of 2π, satisfying .

[0052] For readheads at different positions of the same angle encoder, the difference in output angle is caused only by the phase shift error introduced by the installation position. The measured value is defined as... :

[0053] (2);

[0054] In the formula, This refers to the angle between the reading head and the reference reading head within the same encoder. Encoder positioning error is a key indicator for evaluating encoder accuracy. To reconstruct the periodic error function, a shear differential measurement method is introduced, defining the shear differential function. :

[0055] (3);

[0056] In the formula, It is the original periodic function. It is the phase shift function of the shear quantity s. Through the analysis of... By selecting a suitable inverse operation method, the original function can be reconstructed in reverse. .

[0057] The dual encoder mutual calibration system uses a coaxial rigid connection to ensure the true rotation angle of the two encoders. Completely identical, system installation diagram as follows Figure 1 As shown.

[0058] Encoder 1 is equipped with three reading heads, including one reference reading head and two moving reading heads. The measured values ​​are as follows:

[0059] Reference reading head: (4);

[0060] Shear angle Reading head: (5);

[0061] Shear angle Reading head: (6);

[0062] In the formula, Shear angle, This represents the positioning error of encoder 1.

[0063] Encoder 2 has only one reference reading head installed, and the measured value is: ;

[0064] In the formula, This represents the positioning error of encoder 2.

[0065] The true rotation angle is eliminated by differentially analyzing the measurements from the two encoders. The error difference function is obtained as shown in the following formula: ;

[0066] Subtract Equations 9 and 10 from Equation 8 to eliminate the encoder 2 positioning error. Construct the shearing difference function of encoder 1 , The corresponding shear amount is :

[0067] (11);

[0068] (12);

[0069] By analyzing the shear difference function , By reconstructing the data, the error function of encoder 1 can be obtained. The following section describes how to reconstruct the error using the Fourier method.

[0070] right Perform a Fourier expansion: ;

[0071] In the formula, Error function The Fourier coefficients, where k is the harmonic order.

[0072] Substituting Equation 13 into Equations 11 and 12, we obtain the Fourier expansion of the shear function: ;

[0073] in, Shear difference function Fourier coefficients, defining the shear transfer function ;

[0074] Solving equations 14 and 15 inversely yields two sets of Fourier coefficients: ;

[0075] Two sets of estimation results were obtained using the inverse Fourier operation. The specific expression is as follows: ;

[0076] when When it is not possible to reconstruct the Fourier coefficients of the current order, ,lead to Harmonic leakage exists. Therefore, two coprime shear numbers are selected, and two sets of Fourier coefficients are calculated separately. These coefficients are then weighted and fused to ensure the integrity of the error reconstruction. Since the two sets of data are of similar quality, equal-weight fusion is used.

[0077] ;

[0078] In the formula, w n (k) is the weighting coefficient.

[0079] Fourier coefficients after fusion Performing an inverse discrete Fourier transform yields the positioning error of encoder 1: ;

[0080] Will Substituting this into Equation 8-10, the random error is reduced through mean estimation, thus obtaining the positioning error of encoder 2. : ;

[0081] By reading the measurements from the dual encoders and performing differential calculations, two sets of shearing differential functions for the positioning error of one of the encoders are constructed. By cutting and reconstructing the function and then performing weighted fusion, its error function is obtained. By substituting it into the difference between the two encoders, the error function of the other encoder can be obtained. This enables mutual calibration between the two encoders.

[0082] It is worth noting that the scheme uses Fourier transform as an example for error reconstruction, but this method is not limited to Fourier transform. 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-mentioned case of using Fourier transform for reconstruction.

[0083] 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.

[0084] 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.

[0085] 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 mutual calibration of dual encoders based on the shearing principle, characterized in that, Includes the following steps: Step 1) Rigidly connect the two encoders coaxially; Step 2) Install one reference reading head and two movable reading heads on encoder 1. The angles between the movable reading head and the reference reading head are denoted as β1 and β2, respectively. Install one reference reading head on encoder 2. Step 3) Control the shaft to rotate until the encoder 1 reference reading head detects a zero position signal, and use this position as the starting position; Step 4) Control the shaft to rotate one revolution and collect the measurement value from the encoder 1 reference reading head. 2 movable reading head measurement values , and encoder 2 reference reading head measurement value ; Step 5) Perform a difference operation between the measured values ​​of encoder 2 and the measured values ​​of each reading head of encoder 1 to obtain 3 sets of error difference functions. , , ; Step 6) , respectively with The difference is calculated to eliminate the positioning error of encoder 2. Construct two sets of encoder positioning errors. shear difference function , The corresponding shear amounts are β1 and β2; Step 7) Based on the inverse operation properties of the shearing difference function, the transfer function is sheared... , Perform inverse kinematics to obtain the Fourier coefficient sequences of the two sets of shear difference functions. ; Step 8) The two sets of Fourier coefficient sequences are processed by weighted fusion and then cut and reconstructed to obtain the positioning error of encoder 1. ; Step 9) Substitute the three sets of difference functions from step 5) into the mean value to obtain the positioning error of encoder 2. This enables mutual calibration between encoder 1 and encoder 2.

2. The method for mutual calibration of dual encoders based on the shearing principle according to claim 1, characterized in that, In step 4): Based on encoder measurements : ； in, This represents the actual rotation angle of the encoder. For the encoder in The positioning error at the location is: Encoder 1 reference reading head: ; Encoder 1 shear angle Reading head: ; Encoder 1 shear angle Reading head: ; Encoder 2 reference reading head: .

3. The method for mutual calibration of dual encoders based on the shearing principle according to claim 1, characterized in that, In step 5): the true rotation angle is eliminated by differentially analyzing the measurements from the two encoders. The error difference function is obtained as follows: ； ； 。 4. The method for mutual calibration of dual encoders based on the shearing principle according to claim 1, characterized in that, In step 6): Will , respectively with Difference operation to eliminate encoder 2 positioning error Construct the shearing difference function of encoder 1 : ； 。 5. The method for mutual calibration of dual encoders based on the shearing principle according to claim 1, characterized in that, In step 7): By shearing the transfer function Obtaining Fourier coefficients : ； 。 6. The method for mutual calibration of dual encoders based on the shearing principle according to claim 1, characterized in that, In step 8) The two sets of Fourier coefficients were weighted and fused to obtain Based on this, a shearing and reconstruction process is performed to obtain the positioning error of encoder 1. : ； 。 7. The method for mutual calibration of dual encoders based on the shearing principle according to claim 3, characterized in that, Will Substituting this into step 5), the random error is reduced through mean estimation to obtain the positioning error of encoder 2. : 。

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