Cylindrical grating ruling error detection method and system

Abstract

The application belongs to the technical field of photoelectric displacement precision measurement, and particularly provides a cylindrical grating ruling error detection method and system; firstly, the positioning error of the cylindrical grating is calibrated through two angles, then the different-axis errors are calculated according to the gray data of the cylindrical grating collected by the point light source and the line array image sensor at different measurement angles, and finally the different-axis errors are eliminated from the positioning error to realize the detection of the ruling error; the application can effectively suppress the interference of the different-axis errors in the ruling error detection process, effectively improve the inherent precision of the cylindrical grating displacement measurement, and is suitable for high-precision industrial, aerospace and other scenes.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of photoelectric displacement precision measurement, and specifically provides a cylindrical grating ruling error detection method and system. BACKGROUND

[0002] The grating angular displacement measurement technology converts the information of the angular position into the corresponding binary code through a high-precision circular grating, so as to realize high-precision angular displacement measurement. The technology exhibits excellent measurement performance due to its high measurement accuracy, wide measurement range, small volume and easy maintenance. The grating angular displacement measurement has been widely applied to photoelectric theodolites, mechanical arms, numerical control machine tools and coordinate vector machines and plays a key role in industrial automation.

[0003] The existing grating displacement measurement technology takes the "Moire fringe" method as the core: the Moire fringe signal is generated through the cooperation of the indicating grating and the calibration grating, the signal is converted into an electrical signal by a photoelectric conversion element, the electrical signal is input into a microprocessor by a digital-to-analog converter, and the angular displacement information of the current position is obtained through "phase discrimination operation". However, the technology has certain limitations: (1) when the "Moire fringe" measurement method is used alone, absolute position information cannot be obtained; (2) when multiple code channels are used to realize absolute position measurement, the time phase sequence of multiple signals needs to be aligned; (3) in order to further improve the measurement performance, the ruling density of the grating needs to be improved; (4) the grating angular displacement measurement is extremely sensitive to code disc stains, and the stains will reduce the measurement accuracy and even cause code errors.

[0004] In comparison, the cylindrical grating has an absolute single code channel engraved on the grating body, so that each angular position corresponds to a unique optical encoding image, without the need for complex multi-code channel cooperation, which indirectly enhances the fault tolerance and robustness of the system while simplifying the installation requirements, and has become a research hotspot in photoelectric precision measurement. The technology exhibits significant advantages in solving the above problems: (1) it is easy to realize miniaturized design, can greatly reduce the volume of the measurement system, and is suitable for application scenarios with limited space; (2) due to its larger cross-sectional thickness, the grating can effectively suppress the tilt error in the longitudinal direction and improve the measurement stability; (3) its unique central hole structure is particularly suitable for large hollow shaft equipment. However, the preparation of the cylindrical grating needs to use a high-repetition-frequency laser ruling instrument to engrave the encoding grating lines on the cylindrical grating body with high precision. A slight shift of the laser ruling line position will cause a ruling error, which will significantly reduce the inherent positioning accuracy of the angular displacement. SUMMARY

[0005] Therefore, the present application aims to provide a cylindrical grating ruling error detection method and system. A spherical wave exposure device composed of a point light source and a linear array image sensor is used to collect the gray scale data of the cylindrical grating at different measurement angles, calculate and extract the amplitude and phase information of different axis errors, and then eliminate the different axis errors from the positioning errors obtained by calibration to realize the detection of the ruling error.

[0006] To achieve the above object, the technical scheme of the present application is as follows:

[0007] A cylindrical grating line error detection method, comprising the following contents:

[0008] Step one, the calibration of the positioning error of the cylindrical grating : , wherein is the measurement angle, that is, the rotation angle of the cylindrical grating read by the reading head, is the rotation angle of its own output by the angle reference connected coaxially with the cylindrical grating;

[0009] Step two, the calculation of the misalignment error of the cylindrical grating, specifically comprising the following contents:

[0010] S1: calculating the shortest transmission distance of the spherical wave with the maximum gray value on the linear array image sensor after the spherical wave emitted by the point light source is reflected by the cylindrical grating , the calculation steps are as follows:

[0011] S11: establishing the expression of the spherical wave transmission distance of the spherical wave emitted by the point light source and reflected by the cylindrical grating to any pixel point on the linear array image sensor :

[0012] ;

[0013] , wherein = 0 represents the center pixel point, represents the distance between the center pixel point and the pixel point with the maximum gray value on the linear array image sensor;

[0014] S12: establishing the expression between the spherical wave transmission distance and the gray value of the corresponding pixel point :

[0015] ;

[0016] , wherein represents the exposure coefficient of the linear array image sensor, represents the pixel physical size constant of the linear array image sensor;

[0017] The gray value is processed as follows to obtain the quadratic function expression about :

[0018] ;

[0019] , wherein​ , the maximum value of the gray value, the constant term, the first-order polynomial coefficient and the second-order polynomial coefficient of the quadratic function expression are respectively , and ;

[0020] S13: According to the gray values of all pixel points on the linear array image sensor, the least square method is used for fitting to obtain the values of the coefficients , and ;

[0021] According to the values of the coefficients , and , the value of is calculated;

[0022] S2: Calculate , wherein represents the distance between the point light source and the pixel point with the maximum gray value on the linear array image sensor, represents the shortest distance from the point light source to the outer cylindrical surface of the cylindrical grating, represents the shortest distance from the pixel point with the maximum gray value on the linear array image sensor to the outer cylindrical surface of the cylindrical grating, represents and both produce a distance change amount;

[0023] S3: Calculate under a plurality of measurement angles , fit with as the reference to obtain , which is the amplitude of the curve, , which is the phase of the curve, , which is the direct current component of the curve;

[0024] S4: Calculate the different axis error of the cylindrical grating with a radius of when the measurement angle is :

[0025] ;

[0026] , wherein is the different axis offset distance, ;

[0027] Step three, by subtracting the positioning error from the different axis error, the ruling error of the cylindrical grating is obtained .

[0028] A cylindrical grating ruling error detection system, comprising:

[0029] cylindrical grating;

[0030] reading head: used for reading the rotation angle of the cylindrical grating, denoted as the measured angle;

[0031] angle reference: the angle reference rotates synchronously with the cylindrical grating under the driving of the motor and outputs its own rotation angle;

[0032] positioning error calibration module: used for calculating the difference between the measured angle and the rotation angle to obtain the positioning error;

[0033] spherical wave exposure detection device: including a point light source and a linear array image sensor, wherein the spherical wave emitted by the point light source is irradiated on the cylindrical grating, and after being reflected by the cylindrical grating, it is received by the linear array image sensor, and the linear array image sensor generates pixel gray value data;

[0034] different axis error calculation module: according to the spherical wave characteristics of the point light source and the gray value of the pixels on the linear array image sensor, the different axis error is calculated;

[0035] ruling error detection module: by eliminating the different axis error from the positioning error, the ruling error detection is realized.

[0036] Preferably, the angle reference is an absolute encoder or an incremental encoder, and the angle reference is coaxially connected with the cylindrical grating and rotates synchronously.

[0037] Preferably, the cylindrical grating is an absolute single code channel grating.

[0038] Preferably, the pixel arrangement of the linear array image sensor is 1xN.

[0039] Compared with the prior art, the present application can achieve the following beneficial effects:

[0040] On the basis of the existing cylindrical grating angular displacement measurement technology, the different axis error calculation module and the ruling error detection module are designed, the shortest transmission distance of the point light source spherical wave in the multi-angle detection spherical wave exposure device reflected to the linear array image sensor through the cylindrical grating is calculated, and then based on the spatial geometric relationship, the shortest transmission distance is converted into the vertical distance variation, and then the amplitude and phase information of the different axis error are accurately calculated according to the variation; then the ruling error is detected by the difference operation between the positioning error and the different axis error, which can effectively suppress the interference of the different axis error in the ruling error detection process, effectively improve the inherent precision of the cylindrical grating displacement measurement, and is suitable for high-precision industrial, aerospace and other scenes. BRIEF DESCRIPTION OF DRAWINGS

[0041] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The illustrations, together with the description, serve to explain the application, but are not intended to limit the application in any way.

[0042] Figure 1 Structure schematic diagram of cylindrical grating ruling error detection system according to an embodiment of the present application;

[0043] Figure 2 Spherical wave transmission schematic diagram of spherical wave exposure detection device according to an embodiment of the present application;

[0044] Figure 3 Schematic diagram of vertical distance variation caused by different shafts according to an embodiment of the present application;

[0045] Figure 4 Schematic diagram of geometric relationship between vertical distance variation and shortest spherical wave transmission distance according to an embodiment of the present application;

[0046] Figure 5 Schematic diagram of different shaft error generation principle according to an embodiment of the present application.

[0047] The reference signs in the drawings include:

[0048] 1, read head; 2, cylindrical grating; 3, spherical wave exposure detection device; 31, point light source; 32, linear array image sensor; 4, angle reference; 5, motor; 6, main shaft; 7, positioning error calibration module; 8, different shaft error calculation module; 9, ruling error detection module. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and do not constitute a limitation on the present application.

[0050] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0051] In the description of the present application, it should be understood that the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation of the present application. In addition, the terms "first", "second" and the like are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined with "first", "second" and the like can be explicitly or implicitly included one or more. In the description of the present application, unless otherwise specified, the meaning of "a plurality of" is two or more.

[0052] In the description of the present application, it should be noted that unless otherwise specified and limited, the terms "mounting", "connection", "connection" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium, or it can be connected inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood through specific circumstances.

[0053] The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0054] Embodiment 1

[0055] In an embodiment of the present application, a cylindrical grating ruling error detection method comprises the following contents:

[0056] Step one, positioning error calibration of cylindrical grating 2;

[0057] The reading head 1 can obtain the rotation angle of the detection position on the cylindrical grating 2, which is denoted as the measured angle The angle output by the angle reference 4 coaxially connected with the cylindrical grating 2 is denoted as Then the positioning error of the cylindrical grating 2 is :

[0058] ;

[0059] Step two, calculation of cylindrical grating 2 misalignment error (this part is a misalignment error calculation method based on the spherical light exposure amplitude inversion method);

[0060] The spherical wave emitted by the point light source 31 is irradiated on the cylindrical grating 2, and then reflected to the linear array image sensor 32 through the cylindrical grating 2. The shortest transmission distance of the spherical wave of the pixel point with the maximum gray value on the linear array image sensor 32 is calculated according to the gray value data of the pixel on the linear array image sensor 32 , and specifically includes the following contents:

[0061] S1: The shortest transmission distance of the spherical wave of the pixel point with the maximum gray value on the linear array image sensor 32 is calculated according to the gray value data of the pixel on the linear array image sensor 32, that is, the shortest transmission distance of the spherical wave of the pixel point with the maximum gray value on the linear array image sensor 32 when the spherical wave emitted by the point light source 31 is irradiated on the cylindrical grating 2 and then reflected to the linear array image sensor 32 through the cylindrical grating 2 (defined according to the pixel gray value, when the gray value is maximum, the light ray emitted by the point light source 31 is reflected to the pixel point with the maximum gray value through a point on the cylindrical grating 2, and the light ray transmission distance is the shortest), and the calculation steps are as follows:

[0062] S11: For any pixel point on the linear array image sensor 32 , the expression of the spherical wave transmission distance of the spherical wave emitted by the point light source 31 and reflected to any pixel point on the linear array image sensor 32 through the cylindrical grating 2 is established

[0063] ;

[0064] Wherein, there are 1×N pixels on the linear array image sensor 32, the center pixel is taken as the reading reference, that is, the origin, and the arrangement direction of the pixels is taken as the X axis. The position of any pixel point on the linear array image sensor 32 can be uniquely determined by a one-dimensional coordinate, and in the formula, is the coordinate of any pixel point, that is, the corresponding pixel point is represented by the coordinate value of the pixel point, =0 represents the center pixel, represents the distance of the center pixel and the pixel point with the maximum gray value on the linear array image sensor 32 on the X axis, that is, the interval of the two pixel points; the pixel points include all the pixel points on the left and right sides of the center pixel.

[0065] S12: The expression between the spherical wave transmission distance and the gray value of the corresponding pixel point is established

[0066] ;

[0067] Wherein represents the sum of the shortest distance from the point light source 31 (the point light source 31 is approximated as a point) to the outer cylindrical surface of the cylindrical grating 2 and the shortest distance from the pixel point with the maximum gray value on the linear array image sensor 32 to the outer cylindrical surface of the cylindrical grating 2, ​​​Exposure coefficient of the linear array image sensor 32 (exposure coefficient is the product of exposure time and system reference gain, determined by the linear array image sensor 32 itself performance), Pixel physical size constant of the linear array image sensor 32;

[0068] Gray value of the pixel point The following processing is performed to obtain a quadratic function expression about any pixel point :

[0069] ;

[0070] Wherein , the maximum value of the gray value, the constant term, the first-order polynomial coefficient and the second-order polynomial coefficient of the quadratic function expression are , and ;

[0071] S13: read the gray value of all pixel points by the linear array image sensor 32, combine the gray value expression and the normalization processing flow of S12, and use the least square method to fit the quadratic function expression obtained in step S12 to obtain the values of coefficients , and (both and can be read by the linear array image sensor 32, so the least square method can be used to fit the quadratic function expression according to the actual pixel gray value read by the linear array image sensor 32);

[0072] According to the values of coefficients , and , the shortest transmission distance of the spherical wave emitted by the point light source 31 and reflected by the cylindrical grating 2 to the pixel point with the maximum gray value on the linear array image sensor 32 is calculated ;

[0073] S2: calculate , wherein , represents the distance between the point light source 31 and the pixel point with the maximum gray value on the linear array image sensor 32, i.e. the longitudinal distance between the point light source 31 and the linear array image sensor 32, represents the shortest distance from the point light source 31 to the outer cylindrical surface of the cylindrical grating 2, i.e. the vertical distance constant between the point light source 31 and the cylindrical grating 2, represents the shortest distance from the pixel point with the maximum gray value on the linear array image sensor 32 to the outer cylindrical surface of the cylindrical grating 2, i.e. the vertical distance constant between the linear array image sensor 32 and the cylindrical grating 2, The distance variation caused by the different rotation axes of the cylindrical grating 2 and the angle reference 4; that is, the rotation axes of the cylindrical grating 2 and the angle reference 4 are different when rotating, so and will cause the same distance variation; and will cause the same distance variation;

[0074] S3: Calculate the corresponding at multiple measurement angles , where the calculated at the measurement angle is denoted as , and is fitted with as the reference to obtain , the amplitude of the curve, , the phase of the curve (i.e., the decentering phase), , the DC component of the curve, where , ; , the decentering distance, i.e., the distance between the O point and the O1 point, ; where the position of the field center of the reading head 1 on the outer cylindrical surface of the cylindrical grating 2 on one side of the reading head 1 is defined as a theoretical reference point, denoted as the P point, and a cross section perpendicular to the rotation axis of the cylindrical grating 2 is drawn through the P point, which intersects the cylindrical grating 2 to obtain a circular cross section, and the center of the circular cross section is set as the O point. A normal projection is made from the bottom surface of the angle reference 4 to the circular cross section, and a circle is formed through the normal projection, and the center of the circle is set as the O1 point;

[0075] S4: Calculate the decentering error of the cylindrical grating 2 with a radius of at a measurement angle of , a decentering distance of , and a decentering phase of .

[0076] ;

[0077] Step three, by subtracting the positioning error from the decentering error , the ruling error of the cylindrical grating 2 is obtained.

[0078] A cylindrical grating ruling error detection system, as shown in Figure 1 , comprising:

[0079] The reading head 1 is used to read the measurement angle of the cylindrical grating 2 detection position, and the angle positioning error includes different axis error and ruling error;

[0080] The angle reference 4 rotates synchronously with the cylindrical grating 2 under the driving of the motor 5, and can output the rotation angle of its own rotation axis;

[0081] The positioning error calibration module 7 is used to calculate the difference between the measurement angle and the rotation angle to obtain the positioning error;

[0082] The spherical wave exposure detection device 3 includes a point light source 31 and a linear array image sensor 32, wherein the point light source 31 emits a spherical wave to illuminate the cylindrical grating 2, and the linear array image sensor 32 receives the reflected light after the cylindrical grating 2 reflects the light, and the linear array image sensor 32 generates pixel gray value data;

[0083] The different axis error calculation module 8 calculates the different axis error according to the spherical wave characteristics of the point light source 31 and the gray value of the pixels on the linear array image sensor 32 according to the method described in step two;

[0084] The ruling error detection module 9 detects the ruling error by removing the different axis error from the positioning error.

[0085] Preferably, the angle reference 4 is an absolute encoder or an incremental encoder, and the angle reference 4 is coaxially connected with the cylindrical grating 2 and rotates synchronously.

[0086] Preferably, the cylindrical grating 2 is an absolute single code track grating.

[0087] Preferably, the pixel arrangement of the linear array image sensor 32 is 1×N.

[0088] Embodiment 2

[0089] A cylindrical grating ruling error detection system includes a reading head 1, a cylindrical grating 2, a spherical wave exposure detection device 3, and an angle reference 4, wherein the cylindrical grating 2 and the angle reference 4 are connected through a main shaft 6 and are driven to rotate through a driving mechanism, the reading head 1 is arranged opposite to the cylindrical grating 2 through a support and is used to read the rotation angle of the cylindrical grating 2; and the angle reference 4 is an encoder in a high-precision servo motor with a brand of SEROTECH and a model of ADRS-200-M-A-NS-AS.

[0090] The spherical wave exposure detection device 3 includes a point light source 31 and a linear array image sensor 32, wherein the point light source 31 is used to emit a light beam to the cylindrical grating 2, the light beam is reflected by the cylindrical grating 2 and then enters the linear array image sensor 32, and the linear array image sensor 32 outputs the gray value data of each pixel point. The spatial positions of the point light source 31 and the linear array image sensor 32 are relatively fixed, and they are arranged on one side of the cylindrical grating 2.

[0091] The cylindrical grating 2 is an absolute single code grating.

[0092] The read head 1 is specifically a British Renishaw RESOLUTE absolute circular grating BiSS communication read head RA26BBA075B50A, which is arranged opposite to the cylindrical grating 2, and is used to read the rotation angle of a specific detection position on the cylindrical grating 2.

[0093] The light emitted by the point light source 31 is a spherical wave.

[0094] The cylindrical grating 2 and the angle reference 4 are sequentially sleeved on the outer periphery of the main shaft 6 in the axial direction, and the driving mechanism is the motor 5, which is a disc motor.

[0095] The main shaft 6 passes through the shaft of the angle reference 4, i.e., the encoder, and then penetrates into the cylindrical grating 2, and the disc motor drives the synchronous rotation of the cylindrical grating 2 and the angle reference 4 through the main shaft 6.

[0096] The main shaft 6 is sleeved in the rotor disc of the disc motor.

[0097] The pixel arrangement of the linear array image sensor 32 is 1×N.

[0098] The point light source 31 and the linear array image sensor 32 are fixed on one side of the motor 5 through a support, and the read head 1 is fixed on the other side of the motor 5 through a support.

[0099] The read head 1 outputs a measured angle , and the angle reference 4 outputs a rotation angle ; the positioning error calibration module 7 subtracts the measured angle from the rotation angle to realize the calibration of the positioning error , and the calculation formula is as follows:

[0100] ;

[0101] The spherical wave exposure detection device 3 includes a point light source 31 and a linear array image sensor 32, the spatial position of the point light source 31 and the linear array image sensor 32 is fixed relative to each other, and the point light source 31 and the linear array image sensor 32 are arranged on one side of the cylindrical grating 2. The pixel arrangement on the linear array image sensor 32 is 1×N. The light emitted by the point light source 31 is a spherical wave, the spherical wave emitted by the point light source 31 is irradiated on the cylindrical grating 2, and after being reflected by the cylindrical grating 2, it is received by the linear array image sensor 32. The gray value data on the linear array image sensor 32 can be used to calculate different axis errors, and the specific steps are as follows:

[0102] S1: First, it is necessary to determine the shortest transmission distance of the spherical wave from the point light source 31 to the pixel point with the maximum gray value on the linear array image sensor 32 after being reflected by the cylindrical grating 2 . To this end, a different axis error calculation method based on the spherical light exposure amplitude inversion method is proposed, and the steps are as follows:

[0103] S11: As shown in Figure 2 , the center pixel point on the linear array image sensor 32 is marked as m point, and the pixel point with the maximum pixel gray value on the linear array image sensor 32 is marked as v point. The X axis is established with the m point as the origin, so that all pixel points on the linear array image sensor 32 are located on the X axis, wherein the direction of the v point moving along the X axis to the m point is the positive direction, and vice versa. The v point is located on the negative direction of the X axis; , the distance between the v point and the m point, the transmission distance of the spherical wave emitted by the point light source 31 and reflected by the cylindrical grating 2 to any pixel point on the linear array image sensor 32 , can be expressed as:

[0104] ;

[0105] S12: Let the sum of the shortest distance from the point light source 31 to the outer cylindrical surface of the cylindrical grating 2 and the shortest distance from the pixel point with the maximum gray value on the linear array image sensor 32 to the outer cylindrical surface of the cylindrical grating 2 be , the transmission distance of the spherical wave emitted by the point light source 31 and reflected by the cylindrical grating 2 to any pixel point on the linear array image sensor 32 is ; then the angle between the light beam of the spherical wave to any pixel point on the linear array image sensor 32 and the light beam to the center pixel point can be expressed as: ;

[0106] Since the intensity of the point light source 31 decreases with the cosine of the angle according to the Lambert cosine law, the pixel photosensitive area decreases with the increase of the angle ; the intensity of the spherical wave emitted by the point light source 31 decreases inversely with the square of the transmission distance; by analyzing the relationship between the spherical wave transmission distance and the change of pixel gray value, the relationship equation between the spherical wave transmission distance from the point light source 31 to the linear array image sensor 32 and the gray value of the corresponding pixel point is established:

[0107] ;

[0108] wherein This represents the exposure coefficient of the linear image sensor 32. This represents the pixel physical size constant of the linear image sensor 32.

[0109] grayscale value of a pixel Maximum grayscale value Normalization based on the baseline can yield results for any pixel. The quadratic function expression:

[0110] ;

[0111] The constant term, first-order polynomial coefficients, and second-order polynomial coefficients of the quadratic function expression are respectively... , and ;

[0112] S13: The grayscale values ​​of all pixels are read by the linear image sensor 32, and the coefficients are obtained by fitting the quadratic function expression using the least squares method. , and .

[0113] Here, in order to obtain the grayscale value of the pixel... Relative to any pixel To analyze the variation pattern, the 640 pixels on the linear image sensor 32 were divided into 16 groups of 40 pixels each. The pixel with the highest grayscale value in each group was selected as the fitting pixel. The grayscale values ​​corresponding to the 16 fitting pixels were used as the final data. The quadratic function expression was then fitted using the least squares method with the final data and the maximum grayscale value. , and .

[0114] Based on coefficient , and The value was calculated. .

[0115] S2: To determine the shortest transmission distance of the cylindrical grating 2 for spherical waves under different rotational degrees. The influence can be transformed into analyzing the changes in the vertical distance between the point light source 31 and the linear image sensor 32 and the cylindrical grating 2, respectively.

[0116] like Figure 3As shown, for ease of description and calculation, the position aligned with the center of the field of view of the reading head 1 on the outer cylindrical surface of the cylindrical grating 2 on one side of the reading head 1 is defined as a theoretical reference point, denoted as point P (this point P represents the theoretical position of the center of the field of view of the reading head 1 on the surface of the cylindrical grating 2). A cross section perpendicular to the rotation axis of the cylindrical grating 2 is made through point P. This cross section intersects with the cylindrical grating 2 to obtain a circular cross section. The center of this circular cross section is set as point O. An orthographic projection is made from the bottom of the angle reference 4 onto the circular cross section. A circle is formed by the orthographic projection, and the center of this circle is set as point O1. Theoretically, points O and O1 should completely coincide, but in reality, there is a deviation between them.

[0117] The theoretical perpendicular distance constant from point light source 31 to cylindrical grating 2 is: (i.e., the shortest distance from point light source 31 to the outer cylindrical surface of cylindrical grating 2), the theoretical vertical distance constant from the pixel with the highest grayscale value on linear image sensor 32 to cylindrical grating 2 is... (That is, the shortest distance from the pixel with the highest grayscale value on the linear image sensor 32 to the outer cylindrical surface of the cylindrical grating 2); because the cylindrical grating 2 and the angle reference 4 have micron-level misalignment during actual installation (their theoretical rotation axes are different), point O1 does not coincide with point O. and The angle will change with the direction of rotation of point O. It changes with the change (point O revolves around point O1, the radius of rotation is e, and the included angle is...). It is the angle between OO1 and the horizontal direction during the rotation. It is the offset distance between different axes, that is, the length of OO1. This indicates that the misalignment of the cylindrical grating 2 and the angular reference 4 during rotation leads to... and The change in distance that will occur is expressed as:

[0118] ;

[0119] like Figure 4 As shown, the shortest propagation distance of a spherical wave can be obtained through S1 based on spatial geometric relationships. To calculate , This represents the distance between the point light source 31 and the pixel with the highest grayscale value on the linear image sensor 32, i.e., the vertical distance between the point light source 31 and the linear image sensor 32. This represents the radius of cylindrical grating 2.

[0120] S3: In order to obtain the result during rotation Regarding the measurement angle The change curve is obtained by repeating the exposure and calculation process of S1 and S2 every 9° rotation to obtain the results at multiple measurement angles. ， wherein the is calculated when the measurement angle is is fitted by curve, and the is the amplitude of the curve, is the phase of the curve (i.e. the off-axis phase), is the DC component of the curve.

[0121] Comparing the expressions of the sum of the two groups of distances in S2 and S3 , we can get: , ;

[0122] Comparing the expressions of the two groups of distances in S2 and S3 , we can get the off-axis offset distance of cylindrical grating 2 , and the offset angle .

[0123] S4: As shown in Figure 5 , during the installation of cylindrical grating 2, when the O1 point does not completely coincide with the O point, the measurement angle obtained by the reading head 1 has an off-axis error . The off-axis offset distance of the O1 point relative to the O point is , and the off-axis phase is (i.e. the angle between OZ and OO1). Wherein, Figure 5 , OP is the horizontal direction, F point represents the intersection point of the extension line of OO1 extending to point O1 and the outer wall of cylindrical grating 2, that is, the intersection point of the extension line of OO1 extending to point O1 and the circular cross-section circumference where the O point is located, and Z point represents a fixed reference point on the absolute zero position area of cylindrical grating 2, and is located on the circular cross-section of cylindrical grating 2 passing through P point, that is, on the circular cross-section where the O point is located.

[0124] Let ∠OPO1 be , ∠POO1 be , and ∠PO1F be , then the off-axis error of cylindrical grating 2 is obtained by the difference between and :

[0125] ;

[0126] The radius of the cylindrical grating 2 OP= , ∠POZ represents the measurement angle , and the offset distance OO1 of the O1 point relative to the O point is​​​​ , the off-axis phase ∠O1OZ= . Draw OQ perpendicular to PO1(the foot is Q), OQ is expressed as:

[0127] ;

[0128] The cylindrical grating 2 with a radius of measures the angle , the off-axis offset distance is , and the off-axis error of the cylindrical grating 2 is , the expression is:

[0129] ;

[0130] S5: The cylindrical grating line error detection method and system provided by the application, the line error detection module 9 obtains the line error by subtracting the positioning error obtained by the positioning error calibration module 7 from the off-axis error obtained by the off-axis error calculation module 8.

[0131] Finally, the detected line error is substituted into the angular displacement measurement system of the cylindrical grating 2 to compensate for the line error of the measurement angle , and the calibrated angle output by the system can be expressed as:

[0132] .

[0133] The embodiment of the application effectively suppresses the interference of the off-axis error of the cylindrical grating 2 in the line error detection process, further improves the inherent measurement accuracy of the cylindrical grating 2, and enhances the ability of the small-volume cylindrical grating 2 to achieve high-precision measurement, thereby providing support for its reliable application in the measurement scene of industrial precision equipment and aerospace core components with limited space and high precision requirements.

[0134] Although the embodiments of the application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the application. Those skilled in the art can make changes, modifications, replacements and variations to the above embodiments within the scope of the application.

[0135] The specific embodiments of the application described above do not constitute a limitation on the scope of protection of the application. Any various other corresponding changes and modifications made according to the technical concept of the application should be included in the protection scope of the claims of the application.

Claims

1. A method for detecting errors in cylindrical grating scribing, characterized in that, Includes the following: Step 1, Cylindrical Grating Positioning Error Calibration: ,in To measure the angle, specifically the rotation angle of the cylindrical grating is read through the reading head. The rotation angle of the cylindrical grating is output as an angular reference that is coaxially connected to it. Step two, calculation of the misalignment error of the cylindrical grating, specifically includes the following: S1: Calculate the shortest transmission distance of the spherical wave emitted from the point light source, reflected by the cylindrical grating, to the pixel with the highest grayscale value on the linear image sensor. The calculation steps are as follows: S11: Establish the spherical wave emitted by the point light source, which is reflected by the cylindrical grating to any pixel on the linear image sensor. spherical wave transmission distance The expression: ； in, = 0 represents the center pixel. This represents the distance between the center pixel and the pixel with the highest grayscale value on a linear image sensor. S12: Establish spherical wave transmission distance and the grayscale value of the corresponding pixel Expressions between: ； in This represents the exposure coefficient of the linear image sensor. This represents the pixel physical size constant of a linear image sensor; grayscale values Perform the following processing to obtain information about The quadratic function expression: ； in , where is the maximum grayscale value, and the constant term, first-order polynomial coefficients, and second-order polynomial coefficients of the quadratic function expression are respectively , and ; S13: Based on the grayscale values ​​of all pixels on the linear array image sensor, the least squares method is used to fit the data and obtain the coefficients. , and The value; Based on coefficient , and The value was calculated. ; S2: Calculation ,in This represents the distance between the point light source and the pixel with the highest grayscale value on the linear image sensor. This represents the shortest distance from the point light source to the outer cylindrical surface of the cylindrical grating. This represents the shortest distance from the pixel with the highest grayscale value on the linear image sensor to the outer cylindrical surface of the cylindrical grating. express and The amount of distance change that will occur in all of them; S3: Calculate at multiple measurement angles Below ,by Fitting to the baseline yields... The amplitude of the curve. For the phase of the curve, This represents the DC component of the curve. S4: Calculation radius is The cylindrical grating at the measurement angle is Different axis errors under different conditions : ； in For different axis offset distances, ; Step 3: Obtain the engraving error of the cylindrical grating by subtracting the positioning error from the errors of different axes. .

2. A cylindrical grating engraving error detection system applied to the cylindrical grating engraving error detection method of claim 1, characterized in that, include: Cylindrical grating; Reading head: Used to read the rotation angle of the cylindrical grating, denoted as the measurement angle; Angle reference: Under the drive of the motor, the angle reference rotates synchronously with the cylindrical grating and outputs its own rotation angle; Positioning error calibration module: used to calculate the difference between the measured angle and the rotation angle to obtain the positioning error; Spherical wave exposure detection equipment: includes a point light source and a linear array image sensor. The spherical wave emitted by the point light source illuminates the cylindrical grating. After being reflected by the cylindrical grating, it is received by the linear array image sensor, which generates pixel grayscale data. Different axis error calculation module: Calculates different axis errors based on the spherical wave characteristics of the point light source and the grayscale values ​​of the pixels on the linear array image sensor; Grating error detection module: It detects grading errors by eliminating errors of different axes from the positioning errors.

3. The cylindrical grating engraving error detection system according to claim 2, characterized in that, The angle reference is an absolute encoder or an incremental encoder, and the angle reference is coaxially connected to the cylindrical grating and rotates synchronously.

4. The cylindrical grating engraving error detection system according to claim 2, characterized in that, The cylindrical grating is an absolute single-track grating.

5. The cylindrical grating engraving error detection system according to claim 2, characterized in that, The pixel arrangement of the linear image sensor is 1×N.

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