Inertial and single reading head based circular grating self-calibration method and device

Abstract

The application provides a circular grating self-calibration method and device based on inertia and a single reading head, according to the stable rotating speed brought by a large-inertia flywheel, the pulse width measurement of an encoder and the principle of a closed circle, the time interval of the appearance of adjacent scale lines of a circular grating is collected, a circular grating error compensation model is established, the rotating time of the circular grating is converted into the actual rotating angle of the circular grating, and then the compensation value of the angle measurement error of the circular grating encoder is obtained. The calibration precision of the technical scheme provided by the application is not dependent on a standard device, and can achieve higher calibration precision than common standard devices. Compared with the traditional technical scheme, the technical scheme provided by the application has lower cost, and the application can also be applied to the calibration of circular gratings in key extreme occasions such as space satellites and special robots.

Description

A method and apparatus for self-calibrating circular gratings based on inertia and a single reading head. Technical Field

[0001] This invention belongs to the field of precision measurement technology, specifically relating to a circular grating self-calibration method and device based on a reading head. Background Technology

[0002] Circular gratings are commonly used encoders for angle measurement, offering advantages such as high resolution, small size, easy installation, and fast response. They are widely used in aerospace, intelligent robotics, high-end CNC machine tools, and high-precision coordinate measuring machines. However, with technological advancements, the requirements for angle measurement accuracy in various instruments and equipment are becoming increasingly stringent, placing even higher demands on the angle measurement accuracy of circular gratings.

[0003] A circular grating system typically consists of a circular grating and a reading head. The angular measurement error of a circular grating system mainly originates from the grating's engraving errors and installation errors (including eccentricity, tilt, and deformation of the grating ring). To improve the measurement accuracy of the circular grating, calibration is a commonly used and effective method.

[0004] Circular grating calibration methods can be divided into two types: general methods using standards or other instruments (non-self-calibration methods) and self-calibration methods. One common circular grating calibration method requires a precision polygon and an autocollimator. In this case, the calibration accuracy is limited by the manufacturing and calibration accuracy of the polygon, and the calibration process is complex and requires strict environmental conditions. Another common circular grating calibration method requires higher-precision measuring instruments such as laser interferometers, making unmanned remote on-machine calibration difficult. Both of these methods belong to the category of non-self-calibration methods.

[0005] Currently, circular grating self-calibration methods are generally based on multiple reading heads. A common approach is to uniformly distribute n reading heads around the circular grating and calculate the average of the readings from these n reading heads as the final measurement value. This method is simple in principle and can remove the influence of harmonic components other than integer multiples of n on the reading accuracy in the error curve.

[0006] In addition, there are studies on circular grating self-calibration using multiple reading heads arranged in special ways such as 2*3 or 3*4, which can reduce the number of reading heads required for self-calibration to a certain extent. However, the number of reading heads used in this type of method is still relatively large, usually more than 4. This type of self-calibration method also has certain shortcomings: (1) The number of reading heads is relatively large, so the cost is high. The more reading heads used, the higher the cost of the self-calibration system.

[0007] (2) The accuracy of the angle measurement system is affected by the number of reading heads. A reduction in the number of reading heads will lead to a decrease in the angle measurement accuracy of the angle measurement system. Summary of the Invention

[0008] To address the problems existing in current technologies, this invention proposes a circular grating self-calibration method and device based on inertia and a single reading head. The principle is based on the stable rotational speed provided by a large-inertia flywheel, the pulse width measurement of the encoder, and the principle of circumferential closure. It collects the time interval between the appearance of adjacent scale lines of the circular grating, establishes a circular grating error compensation model, and converts the rotation time of the circular grating into its actual rotation angle, thereby obtaining the compensation value for the angular measurement error of the circular grating encoder. This invention can be applied to the calibration of circular gratings in critical extreme situations such as aerospace satellites and special robots. It can also be used for the calibration of angular displacement sensors such as magnetic gratings, steel gratings, and time gratings.

[0009] One or more embodiments of this specification provide a circular grating self-calibration method based on inertia and a single readout head, the method comprising the following steps:

[0010] Step 1: With the reading head fixed, the circular grating is freely rotated k*360°, where k≥4. During this period, the time intervals between the appearance of adjacent scale lines of the circular grating are measured for a total of k*m, and denoted as g1, g2, ..., g km Using matrix notation, it is denoted as G = {g1, g2, ..., g...} km}, where m is the total number of lines in one revolution of the circular grating, g1 is the time interval between the appearance of the m-th line and the 1st line, g2 is the time interval between the appearance of the 1st line and the 2nd line, and so on, g i The time interval between the (i-1)th etch line and the i-th etch line appearing sequentially;

[0011] Step 2: Process the data in the obtained G according to... After processing, we obtain ω1,ω2,...,ω km Let W = {ω1, ω2, ..., ω km},in θ0 is in rad, ω i The unit is rad / s;

[0012] Step 3: Divide the data in array W into m groups, and denote them as W1, W2, ..., W using matrix notation. m Let W1 = {ω1, ω 1+m ,...,ω 1+(z-1)m}, W2={ω2,ω 2+m ,...,ω 2+(z-1)m},…,W m ={ω m ,ω 2m ,...,ω zm}, where z equals the integer part of k;

[0013] Step 4: Process the obtained m sets of data W1, W2, ..., W m Least squares polynomial fitting is performed on each curve to obtain m angular velocity-time curves, denoted as f1(t), f2(t), ..., f... m (t), substitute it into The angular velocity of the circular grating at time t can be obtained. in

[0014] Step 5: Combine the data and functions in matrix G Substitution We obtain c1, c2, ... c km Let C = {c1, c2, ..., c} km}, where c i The unit is °;

[0015] Step Six: Use the mean method, i.e. Process the data in C to obtain m data points, denoted as C'={c1',c2',...c m '};

[0016] Step 7: Calculate the data in C' according to the formula. The data is processed and then recorded in matrix notation.

[0017] Step 8: Taking the m-th mark as the reference (i.e., assuming the measurement error of the m-th mark is 0), the measurement error of the j-th mark is... This yields the angle measurement error compensation value of the reading head on the circular grating.

[0018] One or more embodiments of this specification also provide another method for self-calibration of circular gratings based on inertia and a single readout head, the method comprising the following steps:

[0019] Step 1: With the reading head fixed, the circular grating is freely rotated k*360°, where k≥4. During this period, the time intervals between the appearance of adjacent scale lines of the circular grating are measured for a total of k*m, and denoted as g1, g2, ..., g km Using matrix notation, it is denoted as G = {g1, g2, ..., g...} km}, where m is the total number of lines in one revolution of the circular grating, g1 is the time interval between the appearance of the m-th line and the 1st line, g2 is the time interval between the appearance of the 1st line and the 2nd line, and so on, g i The time interval between the (i-1)th etch line and the i-th etch line appearing sequentially;

[0020] Step 2: Perform least-squares polynomial and trigonometric function fitting on the data in matrix G to remove some random error components in the original data, thereby optimizing the original data. This yields a discrete time-time interval curve, denoted as T(x), where x represents the x-th time interval, 1 ≤ x ≤ km. Take k*m data points from T(x) and denote them using matrix notation as T = {t1, t2, ..., t...} km}, where t i =T(i);

[0021] Step 3: Arrange the data in array T according to... After processing, we obtain ω1,ω2,...,ω km Let W = {ω1, ω2, ..., ω km},in θ0 is in rad, ω i The unit is rad / s;

[0022] Step 4: Perform least-squares polynomial fitting on the data in W to obtain an angular velocity-time curve, denoted as ω(t). This yields the angular velocity ω(t) of the circular grating at time t.

[0023] Step 5: Substitute the data from matrix T and the function ω(t) into... We obtain c1, c2, ... c km Let C = {c1, c2, ..., c} km}, where c i The unit is °;

[0024] Step Six: Use the mean method, i.e. Process the data in C to obtain m data points, denoted as C'={c1',c2',...c m '}, where z equals the integer part of k;

[0025] Step 7: Calculate the data in C' according to the formula. The data is processed and then recorded in matrix notation.

[0026] Step 8: Taking the m-th mark as the reference (i.e., assuming the measurement error of the m-th mark is 0), the measurement error of the j-th mark is... This yields the angle measurement error compensation value of the reading head on the circular grating.

[0027] One or more embodiments of this specification also provide yet another method for self-calibrating circular gratings based on inertia and a single readout head, the method comprising the following steps:

[0028] Step 1: With the reading head fixed, the circular grating is freely rotated k*360°, where k≥4. During this period, the time intervals between the appearance of adjacent scale lines of the circular grating are measured for a total of k*m, and denoted as g1, g2, ..., g km Using matrix notation, it is denoted as G = {g1, g2, ..., g...} km}, where m is the total number of lines in one revolution of the circular grating, g1 is the time interval between the appearance of the m-th line and the 1st line, g2 is the time interval between the appearance of the 1st line and the 2nd line, and so on, g i The time interval between the (i-1)th etch line and the i-th etch line appearing sequentially;

[0029] Step 2: Perform least-squares polynomial and trigonometric function fitting on the data in matrix G to remove some random error components in the original data, thereby optimizing the original data. This yields a discrete time-time interval curve, denoted as T(x), where x represents the x-th time interval, 1 ≤ x ≤ km. Take k*m data points from T(x) and denote them using matrix notation as T = {t1, t2, ..., t...} km}, where t i =T(i);

[0030] Step 3: Arrange the data in array T according to... After processing, we obtain ω1,ω2,...,ω km Let W = {ω1, ω2, ..., ω km},in θ0 is in rad, ω i The unit is rad / s;

[0031] Step 4: Divide the data in array W into m groups, and denote them using matrix notation as W1, W2, ..., W m Let W1 = {ω1, ω 1+m ,...,ω 1+(z-1)m}, W2={ω2,ω 2+m ,...,ω 2+(z-1)m},…,W m ={ω m ,ω 2m ,...,ω zm}, where z equals the integer part of k;

[0032] Step 5: Process the obtained m sets of data W1, W2, ..., W m Least squares polynomial fitting is performed on each curve to obtain m angular velocity-time curves, denoted as f1(t), f2(t), ..., f... m (t), substitute it into The angular velocity of the circular grating at time t can be obtained. in

[0033] Step Six: Combine the data and functions in matrix T Substitution We obtain c1, c2, ... c km Let C = {c1, c2, ..., c} km}, where c i The unit is °;

[0034] Step 7: Use the mean method, i.e. Process the data in C to obtain m data points, denoted as C'={c1',c2',...c m '};

[0035] Step 8: Calculate the data in C' according to the formula. The data is processed and then recorded in matrix notation.

[0036] Step Nine: Taking the m-th mark as the reference (i.e., assuming the measurement error of the m-th mark is 0), the measurement error of the j-th mark is... This yields the angle measurement error compensation value of the reading head on the circular grating.

[0037] One or more embodiments of this specification also provide a circular grating self-calibration device based on inertia and a single reading head. This device includes a flywheel, a high-precision bearing, a turntable, a circular grating, and a data acquisition module. The flywheel has a large moment of inertia to ensure the smooth rotation of the turntable. The high-precision bearing is used to reduce errors caused by friction and runout during rotation. The data acquisition module includes a microcontroller and a sensor signal input interface module. The microcontroller is responsible for acquiring, processing, storing, and transmitting grating data and time data, while the sensor signal input interface module receives the raw reading data from the circular grating sensor.

[0038] The beneficial effects of this invention are as follows:

[0039] The calibration accuracy proposed in this invention does not depend on a standard and can achieve higher accuracy than common standards. The calibration process does not rely on other high-precision angle measuring instruments and can be used for unmanned remote on-machine calibration. Compared to traditional solutions, the proposed solution is less expensive and can also be applied to circular grating calibration in critical extreme situations such as aerospace satellites and special robots. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 is a flowchart of the circular grating self-calibration method based on inertia and a single reading head in Example 1;

[0042] Figure 2 is a flowchart of the circular grating self-calibration method based on inertia and a single reading head in Example 2;

[0043] Figure 3 is a flowchart of the circular grating self-calibration method based on inertia and a single reading head in Example 3;

[0044] Figure 4 is a schematic diagram of a circular grating self-calibration device based on inertia and a single reading head;

[0045] Figure 5 is a graph of the time data collected by the data acquisition module;

[0046] Figure 6 is a graph showing the circular grating angle measurement error curves before and after compensation by the self-calibration method in Example 1.

[0047] Figure 7 is a graph showing the circular grating angle measurement error curves before and after compensation by the self-calibration method in Example 2.

[0048] Figure 8 is a graph showing the angular measurement error curves of the circular grating before and after compensation by the self-calibration method in Example 3. Detailed Implementation

[0049] The advantages, features, and specific embodiments of the present invention will be further described below with reference to the accompanying drawings. These embodiments are given by way of example only with reference to the accompanying drawings and are non-limiting illustrations, diagrams, and explanations of the present invention.

[0050] To address the problems existing in the prior art, this invention proposes three inertial-based single-readhead circular grating self-calibration methods and one inertial-based single-readhead circular grating self-calibration device. The principle is based on the principle of circumferential closure and the stable rotational speed brought by a large-inertia flywheel. The time of appearance of each circular grating scale line is collected, and the rotation time of the circular grating is converted into the actual rotation angle of the circular grating, thereby obtaining the compensation value for the angle measurement error of the circular grating encoder. The calibration method in this patent does not depend on a standard instrument, achieving a calibration accuracy higher than that of common standards. The calibration process does not rely on other high-precision angle measuring instruments, and can be used for unmanned remote on-machine calibration. When correcting harmonic component errors such as installation eccentricity of the circular grating, this method can be achieved using only one readhead, effectively reducing the cost of the angle measurement system. The difference between this invention and other disclosed inertial-based circular grating self-calibration methods lies in the use of a data grouping method (see Examples 1 and 3) and a time data optimization method (see Examples 2 and 3), which can obtain more accurate self-calibration results.

[0051] Example 1:

[0052] As shown in Figure 1, the circular grating self-calibration method 1 based on inertia and a single reading head consists of the following steps:

[0053] Step 1: With the reading head fixed in place, the circular grating is freely rotated k*360° (k≥4). During this period, the time intervals between the appearance of adjacent scale lines of the circular grating are measured and recorded as g1, g2, ..., g km Using matrix notation, it is denoted as G = {g1, g2, ..., g...} km}, where m is the total number of lines in one revolution of the circular grating, g1 is the time interval between the appearance of the m-th line and the 1st line, g2 is the time interval between the appearance of the 1st line and the 2nd line, and so on, g i The time interval between the (i-1)th etch line and the i-th etch line appearing sequentially;

[0054] Step 2: Process the data in the obtained G according to... After processing, we obtain ω1,ω2,...,ω km Let W = {ω1, ω2, ..., ω km},in θ0 is in rad, ω i The unit is rad / s;

[0055] Step 3: Divide the data in array W into m groups, and denote them as W1, W2, ..., W using matrix notation. m Let W1 = {ω1, ω 1+m ,...,ω 1+(z-1)m}, W2={ω2,ω2+m ,...,ω 2+(z-1)m},…,W m ={ω m ,ω 2m ,...,ω zm}, where z equals the integer part of k;

[0056] Step 4: Process the obtained m sets of data W1, W2, ..., W m Least squares polynomial fitting is performed on each curve to obtain m angular velocity-time curves, denoted as f1(t), f2(t), ..., f... m (t), substitute it into The angular velocity of the circular grating at time t can be obtained. in

[0057] Step 5: Combine the data and functions in matrix G Substitution We obtain c1, c2, ... c km Let C = {c1, c2, ..., c} km}, where c i The unit is °;

[0058] Step Six: Use the mean method, i.e. The data in C is processed to remove some residual errors, resulting in m data points, denoted as C'={c1',c2',...c m '};

[0059] Step 7: Calculate the data in C' according to the formula. The data is processed to remove the DC component, and the resulting data is denoted in matrix notation.

[0060] Step 8: Taking the m-th mark as the reference (i.e., assuming the measurement error of the m-th mark is 0), the measurement error of the j-th mark is... This yields the angle measurement error compensation value of the reading head on the circular grating.

[0061] Preferably, in step one of the above methods, the accuracy of the measured time data should reach the picosecond or even femtosecond level; in specific implementation, the time interval between the successive appearances of each adjacent scale line can be calculated by measuring the time of appearance of each scale line.

[0062] Preferably, in the above method, the processing order of steps two and three can be reversed; that is, the data in G can be grouped first, and then the grouped data can be substituted into... We obtain W1, W2, ..., W m ;

[0063] Preferably, in step three of the above method, W1 can also be set to {ω1, ω...} 1+m ,...,ω 1+zm}, W2={ω2,ω 2+m ,...,ω 2+zm},…,W (k-z)m ={ω (k-z)m ,ω (k-z+1)m ,...,ω km},W (k-z)m+1 ={ω (k-z)m+1 ,ω (k-z+1)m+1 ,...,ω (k-1)m+1},…,W m ={ω m ,ω 2m ,...,ω zm Then, process the m sets of data according to the steps in Method 1;

[0064] Preferably, in step five of the above method, c is not included. i You can convert the units to degrees, or you can calculate directly using radians;

[0065] Preferably, in step six of the above method, the mean method can be replaced by a correction method such as the least squares method. Process data in C;

[0066] Preferably, in step six of the above method, the data in C can be processed without using the mean method or least squares method, and can directly proceed to the subsequent processing flow. It is preferred (but not necessary) to process the data in C first using the mean method or least squares method to correct the errors in the data.

[0067] Preferably, the above method can introduce iteration between steps seven and eight to achieve better compensation results. The specific process is as follows: Replace θ0 in step two with the data in step two, that is Once a new W is obtained, proceed with steps three through seven, iterating in this manner n times (n≥1).

[0068] Preferably, the number of reading heads used in the above method can be increased from a single reading head to two or more reading heads, so as to achieve a better compensation effect for the angle measurement error of the circular grating;

[0069] Preferably, the above method can also be used for angular displacement sensors such as magnetic gratings, steel gratings, and time gratings.

[0070] To verify the correctness of the method, an experiment was conducted. Figures 5 and 6 show the original time data collected at m=1800 and k=10, and the circular grating angle measurement error curves before and after compensation by method 1.

[0071] Example 2:

[0072] As shown in Figure 2, the circular grating self-calibration method 2 based on inertia and a single reading head consists of the following steps:

[0073] Step 1: With the reading head fixed in place, the circular grating is freely rotated k*360° (k≥4). During this period, the time intervals between the appearance of adjacent scale lines of the circular grating are measured and recorded as g1, g2, ..., g km Using matrix notation, it is denoted as G = {g1, g2, ..., g...} km}, where m is the total number of lines in one revolution of the circular grating, g1 is the time interval between the appearance of the m-th line and the 1st line, g2 is the time interval between the appearance of the 1st line and the 2nd line, and so on, g i The time interval between the (i-1)th etch line and the i-th etch line appearing sequentially;

[0074] Step 2: Perform least-squares polynomial and trigonometric function fitting on the data in matrix G to remove some random error components in the original data, thereby optimizing the original data. This yields a discrete time-time interval curve, denoted as T(x), where x represents the x-th time interval, 1 ≤ x ≤ km. Take k*m data points from T(x) and denote them using matrix notation as T = {t1, t2, ..., t...} km}, where t i =T(i);

[0075] Step 3: Arrange the data in array T according to... After processing, we obtain ω1,ω2,...,ω km Let W = {ω1, ω2, ..., ω km},in θ0 is in rad, ω i The unit is rad / s;

[0076] Step 4: Perform least-squares polynomial fitting on the data in W to obtain an angular velocity-time curve, denoted as ω(t). This yields the angular velocity ω(t) of the circular grating at time t.

[0077] Step 5: Substitute the data from matrix T and the function ω(t) into... We obtain c1, c2, ... c km Let C = {c1, c2, ..., c} km}, where c i The unit is °;

[0078] Step Six: Use the mean method, i.e. The data in C is processed to remove some residual errors, resulting in m data points, denoted as C'={c1',c2',...c m '}, where z equals the integer part of k;

[0079] Step 7: Calculate the data in C' according to the formula. The data is processed to remove the DC component, and the resulting data is denoted in matrix notation.

[0080] Step 8: Taking the m-th mark as the reference (i.e., assuming the measurement error of the m-th mark is 0), the measurement error of the j-th mark is... This yields the angle measurement error compensation value of the reading head on the circular grating.

[0081] To verify the correctness of Method 2, an experiment was conducted. Figure 7 shows the circular grating angle measurement error curves before and after compensation for Method 2 when m=2000 and k=9.

[0082] Example 3:

[0083] As shown in Figure 3, the circular grating self-calibration method 3 based on inertia and a single reading head consists of the following steps:

[0084] Step 1: With the reading head fixed in place, the circular grating is freely rotated k*360° (k≥4). During this period, the time intervals between the appearance of adjacent scale lines of the circular grating are measured and recorded as g1, g2, ..., g km Using matrix notation, it is denoted as G = {g1, g2, ..., g...} km}, where m is the total number of lines in one revolution of the circular grating, g1 is the time interval between the appearance of the m-th line and the 1st line, g2 is the time interval between the appearance of the 1st line and the 2nd line, and so on, g i The time interval between the (i-1)th etch line and the i-th etch line appearing sequentially;

[0085] Step 2: Perform least-squares polynomial and trigonometric function fitting on the data in matrix G to remove some random error components in the original data, thereby optimizing the original data. This yields a discrete time-time interval curve, denoted as T(x), where x represents the x-th time interval, 1 ≤ x ≤ km. Take k*m data points from T(x) and denote them using matrix notation as T = {t1, t2, ..., t...} km}, where t i =T(i);

[0086] Step 3: Arrange the data in array T according to... After processing, we obtain ω1,ω2,...,ω kmLet W = {ω1, ω2, ..., ω km},in θ0 is in rad, ω i The unit is rad / s;

[0087] Step 4: Divide the data in array W into m groups, and denote them using matrix notation as W1, W2, ..., W m Let W1 = {ω1, ω 1+m ,...,ω 1+(z-1)m}, W2={ω2,ω 2+m ,...,ω 2+(z-1)m},…,W m ={ω m ,ω 2m ,...,ω zm}, where z equals the integer part of k;

[0088] Step 5: Process the obtained m sets of data W1, W2, ..., W m Least squares polynomial fitting is performed on each curve to obtain m angular velocity-time curves, denoted as f1(t), f2(t), ..., f... m (t), substitute it into The angular velocity of the circular grating at time t can be obtained. in

[0089] Step Six: Combine the data and functions in matrix T Substitution We obtain c1, c2, ... c km Let C = {c1, c2, ..., c} km}, where c i The unit is °;

[0090] Step 7: Use the mean method, i.e. The data in C is processed to remove some residual errors, resulting in m data points, denoted as C'={c1',c2',...c m '};

[0091] Step 8: Calculate the data in C' according to the formula. The data is processed to remove the DC component, and the resulting data is denoted in matrix notation.

[0092] Step Nine: Taking the m-th mark as the reference (i.e., assuming the measurement error of the m-th mark is 0), the measurement error of the j-th mark is... This yields the angle measurement error compensation value of the reading head on the circular grating.

[0093] To verify the correctness of Method 3, an experiment was conducted. Figure 8 shows the circular grating angle measurement error curves before and after compensation for Method 3 when m = 2100 and k = 8.

[0094] It should be noted that when it is known or inferred that the error of the angle measurement system is mainly composed of harmonic components, methods 2 and 3 can achieve better compensation results; when it is unclear what the main components of the angle measurement system error are, method 1 is generally used for compensation.

[0095] Figure 4 shows a schematic diagram of a circular grating self-calibration device based on inertia and a single reading head. The device includes a flywheel, high-precision bearings, a turntable, a circular grating, and a data acquisition module. The flywheel is selected for its large moment of inertia to ensure the smooth rotation of the rotating platform. The high-precision bearings can be air-bearing, magnetic-bearing, or a magnetic-air-bearing composite bearing to reduce system errors caused by radial and axial runout of the spindle during the rotation of the circular grating, and to reduce friction. The data acquisition module includes a microcontroller and a sensor signal input interface module. The microcontroller is responsible for acquiring, processing, storing, and transmitting grating data and time data, while the sensor signal input interface module receives the raw reading data from the circular grating sensor.

[0096] Note:

[0097] 1) A high-precision timing module (such as TDC) can be added to this device to achieve a higher level of accuracy in the measured time data. This is a simple deduction of the device of this invention, and others should not apply for other patents based on this.

[0098] 2) The above-mentioned sensor mainly refers to the reading head of the circular grating. In actual implementation, it is also feasible to directly identify the position of the engraving line using a photoelectric microscope. These are simple inferences about the device of this invention, and others should not apply for other patents based on this.

[0099] 3) A host computer communication module can be added to this device to upload the raw data collected by the data acquisition module to the host computer. The host computer can then use the circular grating angle measurement error compensation model to process the raw data and obtain the angle measurement error compensation value of the reading head on the circular grating. These are simple inferences about the device of this invention, and others should not apply for other patents based on this.

[0100] In practical applications, the working process of the device shown in Figure 4 is as follows: First, energy is stored in the flywheel, that is, the flywheel is made to rotate. Then, the rotational inertia of the flywheel causes the rotating platform to rotate at a stable speed. At this time, the reading head is started, and the data acquisition module is used to collect the measurement data. The circular grating angle measurement error compensation model is used in the microcontroller to process the data, and then the angle measurement error compensation value of the reading head on the circular grating is obtained.

[0101] Specifically, for the data acquisition module in Figure 4, the microcontroller can be a high-performance microcontroller such as Arduino, STM32, or FPGA to realize the functions of acquiring, processing, storing, and transmitting measurement signals. The data acquisition module acquires data as follows: since the reading head sends out a pulse signal every time the circular grating scale line passes through it, the microcontroller uses analog, digital interpolation, and digital delay methods to measure and record the time interval between every two pulses. This method can achieve a time resolution at the picosecond level.

[0102] In summary, the method of this invention, based on the stable rotational speed brought by the large inertia flywheel, the pulse width measurement of the encoder, and the principle of circumferential closure, collects the time interval between the successive appearances of adjacent scale lines of the circular grating, establishes a circular grating error compensation model, converts the rotation time of the circular grating into the actual rotation angle of the circular grating, and thus obtains the compensation value of the angle measurement error of the circular grating encoder. The method is simple, does not rely on a standard, can achieve a calibration accuracy higher than that of common standards, has low cost, and is beneficial for practical production applications.

[0103] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A self-calibration method for circular gratings based on inertia and a single readout head, characterized in that, The method includes the following steps: Step 1: The reading head is fixed in place, while the circular grating rotates freely. , k≥ 4, during which a total of measurements were obtained The time interval between the successive appearance of adjacent scale lines of a circular grating is denoted as . , denoted using matrix notation as Where m is the total number of lines around the circular grating. The time interval between the appearance of the m-th etch line and the 1st etch line is given. The time interval between the appearance of the first and second engraving lines, and so on. The time interval between the (i-1)th and ith etch lines; Step 2: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] Data in Processing is performed to obtain , recorded as ,in ， The unit is rad. The unit is rad / s; Step 3: Array The data in the dataset is divided into m groups, and is represented using matrix notation. ,make ， ，...， Step 4: Process the obtained m sets of data. By performing least-squares polynomial fitting, m angular velocity-time curves are obtained, denoted as... Substitute it into The angular velocity of the circular grating at time t can be obtained. ,in Step 5: Convert the matrix Data and functions in Substitution ,get , recorded as ,in The unit is °; Step 6: Use the mean method, i.e. Process the data in C to obtain m data points, denoted as m. Step 7: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] The data in the formula The data is processed and then recorded in matrix notation. Step 8: Taking the m-th marking as the reference, the measurement error of the j-th marking is... Thus, the angle measurement error compensation value of the reading head on the circular grating is obtained.

2. A self-calibration method for circular gratings based on inertia and a single reading head, characterized in that, The method includes the following steps: Step 1: The reading head is fixed in place, while the circular grating rotates freely. , k≥ 4, during which a total of measurements were obtained The time interval between the successive appearance of adjacent scale lines of a circular grating is denoted as . , denoted using matrix notation as Where m is the total number of lines around the circular grating. The time interval between the appearance of the m-th etch line and the 1st etch line is given. The time interval between the appearance of the first and second engraving lines, and so on. The time interval between the (i-1)th and ith etch lines; Step 2: Calculate the matrix... The data in the original dataset is fitted using least-squares polynomials and trigonometric functions to remove random error components and optimize the original data. This yields a discrete time-time interval curve, denoted as [missing information]. Where x represents the x-th time interval, ;from Nakadori The data, denoted using matrix notation, are as follows: ,in Step 3: Convert the array Data in Processing is performed to obtain , recorded as ,in ， The unit is rad. The unit is rad / s; Step 4: For The data in the figure were fitted with a least-squares polynomial to obtain a single angular velocity-time curve, denoted as . The angular velocity of the circular grating at time t can be obtained. ,in Step 5: Convert the matrix Data and functions in Substitution ,get , recorded as ,in The unit is °; Step 6: Use the mean method, i.e. Process the data in C to obtain m data points, denoted as m. Where z equals the integer part of k; Step 7: The data in the formula The data is processed and then recorded in matrix notation. Step 8: Taking the m-th marking as the reference, the measurement error of the j-th marking is... Thus, the angle measurement error compensation value of the reading head on the circular grating is obtained.

3. A circular grating self-calibration method based on inertia and a single reading head, characterized in that, The method includes the following steps: Step 1: The reading head is fixed in place, while the circular grating rotates freely. , k≥ 4, during which a total of measurements were obtained The time interval between the successive appearance of adjacent scale lines of a circular grating is denoted as . , denoted using matrix notation as Where m is the total number of lines around the circular grating. Let m be the time interval between the appearance of the m-th etch line and the first etch line. The time interval between the appearance of the first and second engraving lines, and so on. The time interval between the (i-1)th and ith etch lines; Step 2: Calculate the matrix... The data in the original dataset is fitted using least-squares polynomials and trigonometric functions to remove random error components and optimize the original data. This yields a discrete time-time interval curve, denoted as [missing information]. Where x represents the x-th time interval, ;from Nakadori The data, denoted using matrix notation, are as follows: ,in Step 3: Convert the array Data in Processing is performed to obtain , recorded as ,in ， The unit is rad. The unit is rad / s; Step 4: Convert the array The data in the dataset is divided into m groups, and is represented using matrix notation. ,make ， ，...， Step 5: Process the obtained m sets of data. By performing least-squares polynomial fitting, m angular velocity-time curves are obtained, denoted as... Substitute it into The angular velocity of the circular grating at time t can be obtained. ,in Step Six: Convert the matrix Data and functions in Substitution ,get , recorded as ,in The unit is °; Step 7: Use the mean method, i.e. Process the data in C to obtain m data points, denoted as m. Step 8: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full The data in the formula The data is processed and then recorded in matrix notation. Step 9: Taking the m-th engraving line as the reference, the measurement error of the j-th engraving line is... Thus, the angle measurement error compensation value of the reading head on the circular grating is obtained.

4. The apparatus used in the circular grating self-calibration method based on inertia and a single reading head according to any one of claims 1-3, characterized in that, The device includes a flywheel, high-precision bearings, a turntable, a circular grating, and a data acquisition module. The flywheel has a large moment of inertia to ensure the smooth rotation of the turntable. The high-precision bearings are used to reduce errors caused by friction and runout during rotation. The data acquisition module includes a microcontroller and a sensor signal input interface module. The microcontroller is responsible for the acquisition, processing, storage, and transmission of grating data and time data, while the sensor signal input interface module receives the raw reading data from the circular grating sensor.

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