Three-degree-of-freedom measurement method based on planar two-dimensional time grating sensor

Abstract

This invention discloses a three-degree-of-freedom measurement method based on a planar two-dimensional time grating sensor, comprising the following steps: A moving scale base and a fixed scale base are installed parallel to each other with a certain gap; after applying sinusoidal excitation signals of the same frequency and amplitude with a phase difference of π / 2 to the four-phase excitation electrode group on the fixed scale base, the moving scale base moves relative to the fixed scale base along the X and Y directions and deflects around the Z-axis; a single sensing unit on the moving scale base can calculate the output signals along the X and Y directions and around the axis deflection; by combining the output signals of each sensing unit, the displacement values ​​of the moving scale base along the X and Y directions and the deflection angle θ can be decoupled. This method can realize displacement measurement in the X direction, Y direction, and around the Z-axis deflection angle through the combined calculation between sensing units on the moving scale base, with fast calculation speed, further elimination of interference, and improved measurement accuracy.

Description

Technical Field

[0001] This invention relates to precision displacement measurement, specifically to a three-degree-of-freedom measurement method based on a planar two-dimensional time grating sensor, belonging to the field of measurement and sensing technology. Background Technology

[0002] Precision displacement measurement technology is fundamental to the development of industries such as large-scale integrated circuit manufacturing and precision machining of machine tools. Improving the accuracy of precision displacement measurement requires positioning systems with high-precision sensors. Currently, widely used three-degree-of-freedom measurement methods include those using a combination of gratings and laser interferometers for measurement and calculation with a magnetic field Hall sensor. While the combination of gratings and laser interferometers offers high accuracy, the grating is limited by the engraving process, preventing further refinement. The laser interferometer is also affected by ambient light and temperature, introducing nonlinear errors. Furthermore, the combination of both methods makes the measurement system more complex. Using a Hall sensor for magnetic field-based three-degree-of-freedom calculation, while offering fast response and strong anti-interference capabilities, is limited by its own magnetic field coil and environmental factors, hindering high-precision measurement. A capacitive planar two-dimensional time-grating sensor (publication number CN109631735A) offers advantages such as high precision, high resolution, and non-contact measurement, and is expected to overcome the bottleneck of large-range, high-precision two-dimensional planar measurement in fields such as precision machining of machine tools and precision positioning of workpiece stages.

[0003] However, capacitive planar two-dimensional time grating sensors have extremely stringent installation requirements for the moving scale. Even a slight deflection error during installation can lead to distortion of the output signal, resulting in significant measurement errors during sensor measurements. This installation deviation is unavoidable in practical applications. Although it can be calibrated using high-precision equipment such as gratings and lasers, this makes the measurement system more complex, increases the cost of system construction, and makes implementation and maintenance difficult. Summary of the Invention

[0004] To address the shortcomings of the aforementioned three-degree-of-freedom measurement techniques, this invention aims to provide a three-degree-of-freedom measurement method based on a planar two-dimensional time-grating sensor. Based on the measurement principle of a planar two-dimensional time-grating sensor, this invention achieves measurement in the X and Y directions. Simultaneously, it utilizes the output displacement values ​​of sensing units arranged on a moving scale base for combined calculations to resolve the minute displacement caused by the deflection angle θ of the moving scale base. Then, through arcsine calculation, it obtains the deflection angle θ of the moving scale base relative to the fixed scale base, thus realizing the measurement and resolution of the sensor's three degrees of freedom (XY-θ). This method offers high measurement accuracy, simple structure, low cost, and ease of maintenance.

[0005] The technical solution of this invention is implemented as follows:

[0006] A three-degree-of-freedom measurement method based on a planar two-dimensional time grating sensor includes a moving scale base and a fixed scale base arranged parallel to each other with a gap. An excitation electrode is disposed on the upper surface of the fixed scale base, and all excitation electrodes constitute a four-phase excitation electrode group. An induction electrode is disposed on the lower surface of the moving scale base, and the induction electrode on the moving scale base faces the excitation electrode on the fixed scale base. The method is characterized by:

[0007] The sensing electrodes consist of four identical groups, each group forming a sensing unit, for a total of four sensing units, referred to as a, b, c, and d, arranged in a 2×2 array. Each sensing unit is composed of four identical square sensing electrodes arranged in a 2×2 array. The left and right sensing units arranged along the X direction are spaced half a cycle apart at the initial spatial position of the cycle, forming a differential structure. The output signals of the left and right sensing units differ in phase by π to eliminate nonlinear interference in the X direction. Similarly, the upper and lower sensing units arranged along the Y direction are spaced half a cycle apart at the initial spatial position of the cycle, forming a differential structure. The output signals of the upper and lower sensing units differ in phase by π to eliminate nonlinear interference in the Y direction.

[0008] During measurement, equal-amplitude, same-frequency sinusoidal excitation signals with a phase difference of π / 2 are sequentially applied to the four-phase excitation electrode group;

[0009] Scenario 1: When the moving scale base moves relative to the fixed scale base in the X or Y direction, each sensing unit outputs a corresponding traveling wave signal. The traveling wave signals output by all sensing units are transmitted to the signal processing circuit for calculation to obtain the displacement value of the moving scale base in the X or Y direction.

[0010] Scenario 2: When the geometric center of the moving scale base deflects at an angle θ relative to the fixed scale base around the Z-axis, the moving scale base will simultaneously produce a small displacement along the X and Y directions relative to the fixed scale base. This small displacement is measured, and the inverse trigonometric function is performed on the small displacement produced by the moving scale base along either the X or Y direction to obtain the deflection angle θ produced by the moving scale base relative to the fixed scale base around the Z-axis. This achieves the three-degree-of-freedom measurement of the moving scale base along the X, Y, and Z-axis deflection angle θ.

[0011] Furthermore, the excitation electrodes are arranged in 2m rows side by side along the upper surface of the fixed-length substrate. Each row of excitation electrodes consists of n identical square excitation plates evenly arranged along the X-axis. The distance I2 between two adjacent square excitation plates is greater than the width I1 of one square excitation plate. The distance between two adjacent rows of excitation electrodes along the Y-axis is (I2-I1) / 2, and their starting positions along the X-axis are staggered by (I2+I1) / 2. The starting positions of the excitation electrodes in odd-numbered rows along the X-axis are the same, and the starting positions of the excitation electrodes in even-numbered rows along the X-axis are the same. Wherein, n = 4k1, m = 4k2, and k1 and k2 are both positive integers.

[0012] In the excitation electrode array consisting of all odd-numbered rows of excitation electrodes, all excitation electrodes in each row are connected to form row excitation groups, thus forming m rows of row excitation groups; starting from the first row, every four rows form a cycle, which are respectively called row excitation group Y1, row excitation group Y2, row excitation group Y3 and row excitation group Y4;

[0013] In the excitation electrode array consisting of all even-numbered rows of excitation electrodes, all excitation electrodes in each column are connected to form column excitation groups, thus forming m column excitation groups; starting from the first column, every four columns form a cycle, which are respectively called column excitation group X1, column excitation group X2, column excitation group X3 and column excitation group X4;

[0014] All X1 column excitation groups and all Y1 row excitation groups are connected to form phase A excitation electrode group; all X2 column excitation groups and all Y2 row excitation groups are connected to form phase B excitation electrode group; all X3 column excitation groups and all Y3 row excitation groups are connected to form phase C excitation electrode group; all X4 column excitation groups and all Y4 row excitation groups are connected to form phase D excitation electrode group; thus, the four-phase excitation electrode group is obtained.

[0015] Furthermore, in scenario one, the displacement value of the moving scale base along the X or Y direction is obtained as follows:

[0016] Let the geometric centers of sensing units a, b, c, and d coincide with the origin of the XOY coordinate system, and let sensing units a, b, c, and d be located in the second, third, first, and fourth quadrants of the XOY coordinate system, respectively. When the moving scale base moves along the X direction, sensing units a, b, c, and d all output traveling wave signals in the measurement direction. The phase of the traveling wave signals output by sensing units a and b lags behind the phase of the traveling wave signals output by sensing units c and d by 1 / 2 cycle. The traveling wave signals output by sensing units c and d are superimposed by an adder, and then the sum of the traveling wave signals output by sensing units a and b is subtracted by a subtractor, which is the output traveling wave signal when the moving scale base moves along the X direction. When the moving scale base moves along the Y direction, sensing units a, b, c, and d all output traveling wave signals in the measurement direction. The phase of the traveling wave signals output by sensing units a and c leads the phase of the traveling wave signals output by sensing units b and d by 1 / 2 cycle. The traveling wave signals output by sensing units a and c are superimposed by an adder, and then the sum of the traveling wave signals output by sensing units b and d is subtracted by a subtractor. This gives the traveling wave signal when the moving scale base moves along the Y direction. The displacement values ​​of the moving scale base along the X and Y directions are calculated by comparing the output traveling wave signal moving along the measurement direction with a reference signal with a fixed phase.

[0017] Furthermore, in scenario two, when the geometric center of the moving scale base rotates clockwise relative to the fixed scale base around the Z-axis, sensing units a, b, c, and d all output traveling wave signals with minute displacements in both the X and Y directions. In the positive X direction, the traveling wave signal output by sensing unit c leads the phase of the traveling wave signal output by sensing unit a by 1 / 2 cycle; in the negative X direction, the traveling wave signal output by sensing unit b leads the phase of the traveling wave signal output by sensing unit d by 1 / 2 cycle; in the positive Y direction, the traveling wave signal output by sensing unit a leads the phase of the traveling wave signal output by sensing unit b by 1 / 2 cycle; and in the negative Y direction, the traveling wave signal output by sensing unit d leads the phase of the traveling wave signal output by sensing unit c by 1 / 2 cycle.

[0018] The traveling wave signal output from sensing unit c is subtracted from the traveling wave signal output from sensing unit a by a subtractor to obtain the output signal along the positive X direction; the traveling wave signal output from sensing unit d is subtracted from the traveling wave signal output from sensing unit b by a subtractor to obtain the output signal along the negative X direction; the phase of the output signals along the positive X direction and the negative X direction is calculated to solve their small displacements, and the difference between the small displacements along the positive X direction and the negative X direction is averaged to cancel the nonlinear interference and the first harmonic error in the X direction, and finally obtain the small displacement value in the X direction;

[0019] The traveling wave signal output from sensing unit a is subtracted from the traveling wave signal output from sensing unit b by a subtractor to obtain the output signal along the positive Y direction; the traveling wave signal output from sensing unit c is subtracted from the traveling wave signal output from sensing unit d by a subtractor to obtain the output signal along the negative Y direction; the phase of the output signals along the positive Y direction and the negative Y direction is calculated to solve their small displacements, and the difference between the small displacements along the positive Y direction and the negative Y direction is averaged to cancel the nonlinear interference and the first harmonic error in the Y direction, and finally obtain the small displacement value in the Y direction;

[0020] The deflection angle of the moving scale base rotating around the Z-axis can be obtained by solving for any small displacement value output in the X and Y directions using arcsine.

[0021] Furthermore, the initial values ​​of the deflection angle of the moving scale base rotating around the Z-axis are obtained by solving the small displacement values ​​output in the X and Y directions respectively. Then, the average value of the two initial deflection angles is taken as the final deflection angle value of the moving scale base rotating around the Z-axis.

[0022] Furthermore, the planar two-dimensional time grating sensor comprises two sets; the two sets of planar two-dimensional time grating sensors share a moving scale base, a fixed scale base, and an excitation electrode; each set of planar two-dimensional time grating sensors has its own sensing electrode; the sensing electrode of one set of planar two-dimensional time grating sensors is formed by rotating it 90° relative to the sensing electrode of the other set of planar two-dimensional time grating sensors around the center of the sensing electrode, and the four sensing units of each of the two planar two-dimensional time grating sensors are staggered and non-overlapping on the shared moving scale base.

[0023] To ensure that the eight sensing units are staggered and do not overlap, one approach is to ensure that the spacing between the four sensing units of each planar two-dimensional time grating sensor in the Y direction is greater than the overall size of the sensing electrode in the X direction.

[0024] During measurement, two sets of planar two-dimensional time grating sensors output signals through their respective sensing electrodes to calculate the displacement values ​​of the moving scale base along the X and Y directions, as well as the deflection angle of the moving scale base relative to the fixed scale base around the Z axis. Then, the corresponding values ​​obtained by the two sets of planar two-dimensional time grating sensors are averaged to obtain the final displacement values ​​of the moving scale base along the X and Y directions, as well as the deflection angle of the moving scale base relative to the fixed scale base around the Z axis.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] In this invention, during three-degree-of-freedom measurement, equal-amplitude, same-frequency sinusoidal excitation signals with a phase difference of π / 2 are sequentially applied to each row and column excitation electrode. As the moving scale substrate moves, each sensing unit outputs measurement signals along the X and Y directions. When the moving scale substrate is measured along the X direction, the displacement measurement values ​​output by each sensing unit in the X direction are summed to obtain the displacement measurement value of the moving scale substrate along the X direction. When the moving scale substrate is measured along the Y direction, the displacement measurement values ​​output by each sensing unit in the Y direction are summed to obtain the displacement measurement value of the moving scale substrate along the Y direction. When the moving scale base rotates clockwise (or counterclockwise) around the Z-axis by a small angle θ, the measured displacement values ​​output by each sensing unit along the X and Y directions are summed to obtain the minute displacement values ​​generated by the moving scale base in the X and Y directions when it rotates. After performing an arcsine operation on these minute displacement values ​​along the X and Y directions and converting them, the displacement value of the moving scale base rotating around the Z-axis by a small angle θ is obtained. This method can achieve displacement measurement in the X, Y directions and around the Z-axis by a small angle θ.

[0027] This invention can further reduce the impact of rotation measurement caused by manufacturing and installation deviations, and has high deflection measurement accuracy, simple structure, low cost and easy maintenance. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the moving ruler base structure in Example 1.

[0029] Figure 2 This is a schematic diagram showing the correspondence between the fixed-length base and the moving-length base in Example 1.

[0030] Figure 3 This is a schematic diagram of the structure of the fixed-length base in Example 1.

[0031] Figure 4 This is a schematic diagram of the induction electrode signal calculation of the moving scale substrate in Example 1.

[0032] Figure 5 This is a schematic diagram illustrating the calculation of the measured displacement value of the moving ruler in Example 1.

[0033] Figure 6 This is a schematic diagram showing the deflection angle θ of the moving scale base relative to the fixed scale base around the Z-axis in Example 1.

[0034] Figure 7 This is a schematic diagram of the arrangement of the sensing units on the moving ruler substrate in Example 2. Detailed Implementation

[0035] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0036] See Figures 1-3The three-degree-of-freedom measurement method of this invention is based on a planar two-dimensional time grating sensor with the following structure, see [link to relevant documentation]. Figure 2 The planar two-dimensional time grating sensor includes a movable scale base 1 and a fixed scale base 2 arranged parallel to each other with a gap h. An excitation electrode 1-1 is provided on the upper surface of the fixed scale base 1, and an induction electrode 2-1 is provided on the lower surface of the movable scale base 2. The induction electrode on the movable scale base is directly opposite to the excitation electrode on the fixed scale base.

[0037] See Figure 3 The excitation electrodes 1-1 are arranged in 2m rows along the upper surface of the fixed-length substrate. Each row of excitation electrodes consists of n identical square excitation plates evenly arranged along the X-axis. The distance I2 between two adjacent square excitation plates is greater than the width I1 of one square excitation plate. The distance between two adjacent rows of excitation electrodes along the Y-axis is (I2-I1) / 2, and the starting positions along the X-axis are staggered by (I2+I1) / 2. The starting positions of the excitation electrodes in odd-numbered rows along the X-axis are the same, and the starting positions of the excitation electrodes in even-numbered rows along the X-axis are the same. Wherein, n = 4k1, m = 4k2, and k1 and k2 are both positive integers.

[0038] In the excitation electrode array consisting of all odd-numbered rows of excitation electrodes, all excitation electrodes in each row are connected to form row excitation groups, thus forming m rows of row excitation groups; starting from the first row, every four rows form a cycle, which are respectively called row excitation group Y1, row excitation group Y2, row excitation group Y3 and row excitation group Y4.

[0039] In the excitation electrode array consisting of all even-numbered rows of excitation electrodes, all excitation electrodes in each column are connected to form column excitation groups, thus forming m column excitation groups; starting from the first column, every four columns form a cycle, which are respectively called column excitation group X1, column excitation group X2, column excitation group X3 and column excitation group X4.

[0040] All X1 column excitation groups and all Y1 row excitation groups are connected to form phase A excitation electrode group; all X2 column excitation groups and all Y2 row excitation groups are connected to form phase B excitation electrode group; all X3 column excitation groups and all Y3 row excitation groups are connected to form phase C excitation electrode group; all X4 column excitation groups and all Y4 row excitation groups are connected to form phase D excitation electrode group; thus, a four-phase excitation electrode group is obtained.

[0041] See Figure 1The induction electrodes 2-1 on the moving ruler base 2 are in four identical groups, each group constituting a sensing unit, for a total of four sensing units, referred to as a, b, c, and d, arranged in a 2×2 array. Each sensing unit consists of four square sensing electrodes of the same size arranged in a 2×2 array; for example, the four sensing electrodes corresponding to sensing unit a are a1, a2, a3, and a4. The width of the sensing unit is W, and the center-to-center distance between adjacent sensing units is 2L2 along the X direction and 2L1 along the Y direction, where 2L2 = nW + W / 2 and 2L1 = mW + W / 2 (n and m are both positive integers), and L2 = L1. The width of the sensing electrode is I3, and the spacing between adjacent sensing electrodes in each sensing unit is I4. The left and right sensing units arranged along the X direction are spaced half a cycle apart at the initial spatial position of the cycle, forming a differential structure. The output signals of the left and right sensing units are π phase apart to eliminate nonlinear interference in the X direction. The upper and lower sensing units arranged along the Y direction are spaced half a cycle apart at the initial spatial position of the cycle, forming a differential structure. The output signals of the upper and lower sensing units are π phase apart to eliminate nonlinear interference in the Y direction.

[0042] During measurement, equal-amplitude, same-frequency sinusoidal excitation signals with a phase difference of π / 2 are sequentially applied to the four-phase excitation electrode group;

[0043] Scenario 1: When the moving scale base moves relative to the fixed scale base in the X or Y direction, each sensing unit outputs a corresponding traveling wave signal. The traveling wave signals output by all sensing units are transmitted to the signal processing circuit for calculation to obtain the displacement value of the moving scale base in the X or Y direction.

[0044] Scenario 2: When the geometric center of the moving scale base deflects at an angle θ relative to the fixed scale base around the Z-axis, the moving scale base will simultaneously produce a small displacement along the X and Y directions relative to the fixed scale base. This small displacement is measured, and the inverse trigonometric function is performed on the small displacement produced by the moving scale base along either the X or Y direction to obtain the deflection angle θ produced by the moving scale base relative to the fixed scale base around the Z-axis. This achieves the three-degree-of-freedom measurement of the moving scale base along the X, Y, and Z-axis deflection angle θ.

[0045] In actual processing, the displacement output signals of a single sensing unit along the X and Y directions are first transmitted to the signal processing circuit for decoupling. Then, the decoupled output signals of the differentially arranged sensing units moving along the X and Y directions are differentially calculated in the processing circuit to obtain the X and Y direction output signals after eliminating nonlinear interference. Based on these output signals, displacement calculation is performed to obtain the displacement value in the X or Y direction.

[0046] In scenario one, the displacement value of the moving scale base along the X or Y direction is obtained as follows:

[0047] Let the geometric centers of sensing units a, b, c, and d coincide with the origin of the XOY coordinate system, and let sensing units a, b, c, and d be located in the second, third, first, and fourth quadrants of the XOY coordinate system, respectively. When the moving scale base moves along the X direction, sensing units a, b, c, and d all output traveling wave signals in the measurement direction. The phase of the traveling wave signals output by sensing units a and b lags behind the phase of the traveling wave signals output by sensing units c and d by 1 / 2 cycle. The traveling wave signals output by sensing units c and d are superimposed by an adder, and then the sum of the traveling wave signals output by sensing units a and b is subtracted by a subtractor, thus outputting the traveling wave signal when the moving scale base moves along the X direction. When the moving scale base moves along the Y direction, sensing units a, b, c, and d all output traveling wave signals in the measurement direction. The phase of the traveling wave signals output by sensing units a and c leads the phase of the traveling wave signals output by sensing units b and d by 1 / 2 cycle. The traveling wave signals output by sensing units a and c are superimposed by an adder, and then the sum of the traveling wave signals output by sensing units b and d is subtracted by a subtractor. This gives the traveling wave signal when the moving scale base moves along the Y direction. The displacement values ​​of the moving scale base along the X and Y directions are calculated by comparing the output traveling wave signal moving along the measurement direction with a reference signal with a fixed phase.

[0048] In scenario two, when the geometric center of the moving scale base rotates clockwise relative to the fixed scale base around the Z-axis, sensing units a, b, c, and d all output traveling wave signals with minute displacements in both the X and Y directions. In the positive X direction, the traveling wave signal output by sensing unit c leads the phase of the traveling wave signal output by sensing unit a by 1 / 2 cycle. In the negative X direction, the traveling wave signal output by sensing unit b leads the phase of the traveling wave signal output by sensing unit d by 1 / 2 cycle. In the positive Y direction, the traveling wave signal output by sensing unit a leads the phase of the traveling wave signal output by sensing unit b by 1 / 2 cycle. In the negative Y direction, the traveling wave signal output by sensing unit d leads the phase of the traveling wave signal output by sensing unit c by 1 / 2 cycle.

[0049] The traveling wave signal output from sensing unit c is subtracted from the traveling wave signal output from sensing unit a by a subtractor to obtain the output signal along the positive X direction; the traveling wave signal output from sensing unit d is subtracted from the traveling wave signal output from sensing unit b by a subtractor to obtain the output signal along the negative X direction; the phase of the output signals along the positive X direction and the negative X direction is calculated to solve their small displacements, and the difference between the small displacements along the positive X direction and the negative X direction is averaged to cancel the nonlinear interference and the first harmonic error in the X direction, and finally obtain the small displacement value in the X direction;

[0050] The traveling wave signal output from sensing unit a is subtracted from the traveling wave signal output from sensing unit b by a subtractor to obtain the output signal along the positive Y direction; the traveling wave signal output from sensing unit c is subtracted from the traveling wave signal output from sensing unit d by a subtractor to obtain the output signal along the negative Y direction; the phase of the output signals along the positive Y direction and the negative Y direction is calculated to solve their small displacements, and the difference between the small displacements along the positive Y direction and the negative Y direction is averaged to cancel the nonlinear interference and the first harmonic error in the Y direction, and finally obtain the small displacement value in the Y direction;

[0051] The deflection angle of the moving scale base rotating around the Z-axis can be obtained by solving for any small displacement value output in the X and Y directions using arcsine.

[0052] like Figure 4 As shown, the output signals Ua1, Ua2, Ua3, and Ua4 are generated by the coupling of sensing electrodes a1, a2, a3, and a4 in a single sensing unit a. By combining the operations Uxa = Ua2 + Ua4 - Ua1 - Ua3 and Uya = Ua1 + Ua2 - Ua3 - Ua4, the measurement output signals Uxa and Uya of sensing unit a along the X and Y directions can be obtained. Similarly, the measurement output signals Uxb and Uyb, Uxc and Uyc, and Uxd and Uyd of the other sensing units b, c, and d along the X and Y directions can be obtained. The relationship between the output signals of a single sensing unit a, b, c, and d and the displacement value can be expressed as follows:

[0053]

[0054] In this embodiment, the excitation voltage amplitude U0 = 27V, the frequency f = 20kHz, and the angular frequency ω = 2πf = 4 × 10⁻⁶. 4 π, K e denoted as the electric field coupling coefficient, and x and y as displacement measurements along the X and Y directions, respectively.

[0055] like Figure 4 and Figure 5 As shown, during three-degree-of-freedom measurement, when the moving scale base moves relative to the fixed scale base along the X direction, the output signals of sensing units a, b, c, and d along the X direction are combined and calculated to obtain the measurement output signal Ux and displacement value X of the moving scale base along the X direction: Uxc + Uxd - Uxa - Uxb. The calculation formula is as follows:

[0056]

[0057] When the moving scale base moves relative to the fixed scale base along the Y direction, the output signals of sensing units a, b, c, and d along the Y direction are combined and calculated as Uya + Uyc - Uyb - Uyd to obtain the measurement output signal Uy and displacement value Y of the moving scale base along the Y direction. The calculation formula is as follows.

[0058]

[0059] like Figure 6 As shown, when the movable scale base rotates clockwise by an angle θ around the Z-axis, it will generate small displacement values ​​along the X and Y directions. The differential operation Uxc-Uxa is performed on the X-direction measurement output signals Uxb and Uxd of the movable scale base's sensing units a and c, respectively. Similarly, Uxd-Uxb is performed on the X-direction measurement output signals Uya and Uyb of the movable scale base's sensing units a and b, respectively. Uya-Uyb is performed on the Y-direction measurement output signals Uyc and Uyd of the movable scale base's sensing units a and b, respectively. Finally, Uyc-Uyd is performed on the Y-direction measurement output signals Uyc and Uyd of the sensing units c and d, respectively.

[0060]

[0061] By solving the differential signal using trigonometric functions, the minute displacement values ​​Xac, Xbd, Yab, and Ycd generated when the moving scale base rotates around the Z-axis by an angle θ can be obtained. The deflection angle θ generated by the moving scale base around the Z-axis can then be obtained by performing inverse trigonometric function calculations on these minute displacement values ​​along the X or Y directions in the signal circuit processing system. The calculation formula is as follows:

[0062]

[0063] This method can achieve displacement measurement in the X direction, Y direction and around the Z axis by combining the calculations between the sensing units on the moving scale substrate. It can eliminate nonlinear interference and first harmonic error when measuring in the X and Y directions, and reduce the influence of rotation measurement caused by manufacturing and installation deviations. Its calculation method is effective, has high measurement accuracy and fast calculation speed.

[0064] To further improve measurement accuracy, the initial values ​​of the deflection angle of the moving scale base rotating around the Z-axis can be obtained by solving the small displacement values ​​output in the X and Y directions respectively. Then, the average value of the two initial deflection angles is taken as the final deflection angle value of the moving scale base rotating around the Z-axis.

[0065] Example 2: As Figure 7As shown, the measurement principle and most of the structure of Embodiment 2 are the same as those of Embodiment 1, except that: there are two sets of planar two-dimensional time grating sensors; the two sets of planar two-dimensional time grating sensors share a set of moving scale base, fixed scale base and excitation electrode; the two sets of planar two-dimensional time grating sensors have their own sensing electrodes; the sensing electrode of one set of planar two-dimensional time grating sensors is rotated 90° around the center of the sensing electrode relative to the sensing electrode of the other set of planar two-dimensional time grating sensors, and the four sensing units of each of the two planar two-dimensional time grating sensors are staggered and do not overlap on the shared moving scale base.

[0066] To ensure that the eight sensing units are staggered and do not overlap, one approach is to have the spacing between the four sensing units of each planar two-dimensional time grating sensor in the Y direction be greater than the overall size of the sensing electrode in the X direction.

[0067] During measurement, two sets of planar two-dimensional time grating sensors output signals through their respective sensing electrodes to calculate the displacement values ​​of the moving scale base along the X and Y directions, as well as the deflection angle of the moving scale base relative to the fixed scale base around the Z axis. Then, the corresponding values ​​obtained by the two sets of planar two-dimensional time grating sensors are averaged to obtain the final displacement values ​​of the moving scale base along the X and Y directions, as well as the deflection angle of the moving scale base relative to the fixed scale base around the Z axis.

[0068] Since the two sets of sensors are identical and share the same structure except for the sensing unit, and the excitation signal is also the same, this invention uses the output signals of the sensing electrodes of the two sets of sensors to measure separately, and then takes the average, which can minimize the measurement error to the greatest extent.

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the applicant has described the present invention in detail with reference to preferred embodiments, those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A three-degree-of-freedom measurement method based on a planar two-dimensional time grating sensor, wherein the planar two-dimensional time grating sensor includes a moving scale base and a fixed scale base arranged parallel to each other with a gap between them; an excitation electrode is provided on the upper surface of the fixed scale base, and all excitation electrodes constitute a four-phase excitation electrode group; an induction electrode is provided on the lower surface of the moving scale base, and the induction electrode on the moving scale base is directly opposite the excitation electrode on the fixed scale base; characterized in that: The sensing electrodes consist of four identical groups, each group forming a sensing unit, for a total of four sensing units, referred to as a, b, c, and d, arranged in a 2×2 array. Each sensing unit is composed of four identical square sensing electrodes arranged in a 2×2 array. The left and right sensing units arranged along the X direction are spaced half a cycle apart at the initial spatial position of the cycle, forming a differential structure. The output signals of the left and right sensing units differ in phase by π to eliminate nonlinear interference in the X direction. Similarly, the upper and lower sensing units arranged along the Y direction are spaced half a cycle apart at the initial spatial position of the cycle, forming a differential structure. The output signals of the upper and lower sensing units differ in phase by π to eliminate nonlinear interference in the Y direction. During measurement, equal-amplitude, same-frequency sinusoidal excitation signals with a phase difference of π / 2 are sequentially applied to the four-phase excitation electrode group; Scenario 1: When the moving scale base moves relative to the fixed scale base in the X or Y direction, each sensing unit outputs a corresponding traveling wave signal. The traveling wave signals output by all sensing units are transmitted to the signal processing circuit for calculation to obtain the displacement value of the moving scale base in the X or Y direction. Scenario 2: When the geometric center of the moving scale base deflects at an angle θ relative to the fixed scale base around the Z-axis, the moving scale base will simultaneously produce a small displacement along the X and Y directions relative to the fixed scale base. This small displacement is measured, and the inverse trigonometric function is performed on the small displacement produced by the moving scale base along either the X or Y direction to obtain the deflection angle θ produced by the moving scale base relative to the fixed scale base around the Z-axis. This achieves the three-degree-of-freedom measurement of the moving scale base along the X, Y, and Z-axis deflection angle θ.

2. The three-degree-of-freedom measurement method based on a planar two-dimensional time grating sensor according to claim 1, characterized in that: The excitation electrodes are arranged in 2m rows along the upper surface of the fixed-length substrate. Each row of excitation electrodes consists of n identical square excitation plates evenly arranged along the X-axis. The distance I2 between two adjacent square excitation plates is greater than the width I1 of one square excitation plate. The distance between two adjacent rows of excitation electrodes along the Y-axis is (I2-I1) / 2, and their starting positions along the X-axis are staggered by (I2+I1) / 2. The starting positions of the excitation electrodes in odd-numbered rows along the X-axis are the same, and the starting positions of the excitation electrodes in even-numbered rows along the X-axis are the same. Wherein, n = 4k1, m = 4k2, and k1 and k2 are both positive integers. In the excitation electrode array consisting of all odd-numbered rows of excitation electrodes, all excitation electrodes in each row are connected to form row excitation groups, thus forming m rows of row excitation groups; starting from the first row, every four rows form a cycle, which are respectively called row excitation group Y1, row excitation group Y2, row excitation group Y3 and row excitation group Y4; In the excitation electrode array consisting of all even-numbered rows of excitation electrodes, all excitation electrodes in each column are connected to form column excitation groups, thus forming m column excitation groups; starting from the first column, every four columns form a cycle, which are respectively called column excitation group X1, column excitation group X2, column excitation group X3 and column excitation group X4; All X1 column excitation groups and all Y1 row excitation groups are connected to form phase A excitation electrode group; all X2 column excitation groups and all Y2 row excitation groups are connected to form phase B excitation electrode group; all X3 column excitation groups and all Y3 row excitation groups are connected to form phase C excitation electrode group; all X4 column excitation groups and all Y4 row excitation groups are connected to form phase D excitation electrode group; thus, the four-phase excitation electrode group is obtained.

3. The three-degree-of-freedom measurement method based on a planar two-dimensional time grating sensor according to claim 1, characterized in that: In scenario one, the displacement value of the moving scale base along the X or Y direction is obtained as follows: Let the geometric centers of sensing units a, b, c, and d coincide with the origin of the XOY coordinate system, and let sensing units a, b, c, and d be located in the second, third, first, and fourth quadrants of the XOY coordinate system, respectively. When the moving scale base moves along the X direction, sensing units a, b, c, and d all output traveling wave signals in the measurement direction. The phase of the traveling wave signals output by sensing units a and b lags behind the phase of the traveling wave signals output by sensing units c and d by 1 / 2 cycle. The traveling wave signals output by sensing units c and d are superimposed by an adder, and then the sum of the traveling wave signals output by sensing units a and b is subtracted by a subtractor, which is the output traveling wave signal when the moving scale base moves along the X direction. When the moving scale base moves along the Y direction, sensing units a, b, c, and d all output traveling wave signals in the measurement direction. The phase of the traveling wave signals output by sensing units a and c leads the phase of the traveling wave signals output by sensing units b and d by 1 / 2 cycle. The traveling wave signals output by sensing units a and c are superimposed by an adder, and then the sum of the traveling wave signals output by sensing units b and d is subtracted by a subtractor. This gives the traveling wave signal when the moving scale base moves along the Y direction. The displacement values ​​of the moving scale base along the X and Y directions are calculated by comparing the output traveling wave signal moving along the measurement direction with a reference signal with a fixed phase.

4. The three-degree-of-freedom measurement method based on a planar two-dimensional time grating sensor according to claim 3, characterized in that: In scenario two, when the geometric center of the moving scale base rotates clockwise relative to the fixed scale base around the Z-axis, sensing units a, b, c, and d all output traveling wave signals with minute displacements in both the X and Y directions. In the positive X direction, the traveling wave signal output by sensing unit c leads the phase of the traveling wave signal output by sensing unit a by 1 / 2 cycle. In the negative X direction, the traveling wave signal output by sensing unit b leads the phase of the traveling wave signal output by sensing unit d by 1 / 2 cycle. In the positive Y direction, the traveling wave signal output by sensing unit a leads the phase of the traveling wave signal output by sensing unit b by 1 / 2 cycle. In the negative Y direction, the traveling wave signal output by sensing unit d leads the phase of the traveling wave signal output by sensing unit c by 1 / 2 cycle. The traveling wave signal output from sensing unit c is subtracted from the traveling wave signal output from sensing unit a by a subtractor to obtain the output signal along the positive X direction; the traveling wave signal output from sensing unit d is subtracted from the traveling wave signal output from sensing unit b by a subtractor to obtain the output signal along the negative X direction; the phase of the output signals along the positive X direction and the negative X direction is calculated to solve their small displacements, and the difference between the small displacements along the positive X direction and the negative X direction is averaged to cancel the nonlinear interference and the first harmonic error in the X direction, and finally obtain the small displacement value in the X direction; The traveling wave signal output from sensing unit a is subtracted from the traveling wave signal output from sensing unit b by a subtractor to obtain the output signal along the positive Y direction; the traveling wave signal output from sensing unit c is subtracted from the traveling wave signal output from sensing unit d by a subtractor to obtain the output signal along the negative Y direction; the phase of the output signals along the positive Y direction and the negative Y direction is calculated to solve their small displacements, and the difference between the small displacements along the positive Y direction and the negative Y direction is averaged to cancel the nonlinear interference and the first harmonic error in the Y direction, and finally obtain the small displacement value in the Y direction; The deflection angle of the moving scale base rotating around the Z-axis can be obtained by solving for any small displacement value output in the X and Y directions using arcsine.

5. The three-degree-of-freedom measurement method based on a planar two-dimensional time grating sensor according to claim 1, characterized in that: The initial values ​​of the deflection angle of the moving scale base around the Z-axis are obtained by solving the small displacement values ​​output in the X and Y directions respectively. Then, the average value of the two initial deflection angles is taken as the final deflection angle value of the moving scale base around the Z-axis.

6. The three-degree-of-freedom measurement method based on a planar two-dimensional time grating sensor according to claim 1, characterized in that: The planar two-dimensional time grating sensor consists of two sets; both sets share a moving scale base, a fixed scale base, and an excitation electrode; each set has its own sensing electrode; the sensing electrode of one set is formed by rotating the sensing electrode of the other set by 90° around its center, and the four sensing units of each of the two sets are staggered and non-overlapping on the shared moving scale base. To ensure that the eight sensing units are staggered and do not overlap, one approach is to ensure that the spacing between the four sensing units of each planar two-dimensional time grating sensor in the Y direction is greater than the overall size of the sensing electrode in the X direction. During measurement, two sets of planar two-dimensional time grating sensors output signals through their respective sensing electrodes to calculate the displacement values ​​of the moving scale base along the X and Y directions, as well as the deflection angle of the moving scale base relative to the fixed scale base around the Z axis. Then, the corresponding values ​​obtained by the two sets of planar two-dimensional time grating sensors are averaged to obtain the final displacement values ​​of the moving scale base along the X and Y directions, as well as the deflection angle of the moving scale base relative to the fixed scale base around the Z axis.

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