A non-contact inductive displacement sensor based on planar meander coil

Abstract

The application discloses a non-contact inductive displacement sensor based on a planar bending coil, which comprises a cantilever base and a U-shaped base, the cantilever end of the cantilever base extends into the notch of the U-shaped base, and the upper and lower surfaces of the cantilever end are parallel to the inner upper and lower surfaces of the notch, two excitation coils symmetrically arranged are fixed on the upper and lower surfaces of the cantilever end of the cantilever base, a receiving coil group symmetrically arranged is fixed on the inner upper surface of the notch, each receiving coil group is composed of two receiving coils stacked in upper and lower layers, the excitation coil and the receiving coil are both square wave periodic grid structures, have good range expansion, and the periodic widths W are all the same, the positions of the two receiving coils in the same receiving coil group in the X direction are different by W / 4. The application solves the problem of low resolution commonly existing in the inductive scheme, simultaneously adopts a double-side compensation structure and an optimized design of the coil, and realizes displacement measurement against transverse interference error.

Description

Technical Field

[0001] This invention belongs to the field of sensor technology, specifically a non-contact inductive displacement sensor based on a planar bent coil. Background Technology

[0002] With the development of industrial automation and intelligent manufacturing, the demand for precision displacement measurement technology is increasing. As a key component in automated systems, the performance of displacement sensors directly affects the position control accuracy and stability of the entire system. In fields such as semiconductor manufacturing, high-precision positioning systems, and precision CNC machining, there is a significant demand for displacement measurements with millimeter-scale and nanometer-scale resolution. In particular, future large-aperture modular astronomical telescopes, such as the European Very Large Telescope (E-ELT) and the 30-meter Telescope (TMT), are equipped with precision displacement actuators to drive adjacent sub-mirrors for tracking and positioning, thereby ensuring the stability of focusing during telescope surveys. In open-loop control mode, the nonlinear characteristics and drift phenomena exhibited by the positioning system are mainly attributed to the inherent properties of the drive mechanism and mechanical structure. Introducing displacement sensors to achieve feedback control can effectively solve this problem. The actuators used in telescopes consist of millimeter-scale coarse adjustment mechanisms and nanometer-scale fine adjustment mechanisms; therefore, the displacement sensors need to have millimeter-scale range and nanometer-scale resolution feedback capabilities.

[0003] Currently, common high-precision displacement sensors mainly include capacitive, optical, and inductive types. Most optical and capacitive displacement sensors have advantages in resolution and accuracy, but they still face many challenges in practical applications. Capacitive displacement sensors are sensitive to environmental factors such as humidity, dust, and oil. Due to size and cost limitations, laser interferometers are difficult to integrate into compact systems, and beam interference in the optical path, as well as fluctuations in humidity and temperature, inevitably introduce measurement errors. Gratings are difficult to manufacture and have high installation requirements; lateral interference displacement may damage the grating ruler structure. Inductive sensors are less affected by harsh operating conditions, are low-cost, and have a long lifespan, making them widely used in military, aerospace, and industrial fields. However, current research on inductive sensors mostly focuses on micrometer-level resolution; therefore, developing large-range, high-resolution inductive displacement sensors has great application potential. Summary of the Invention

[0004] This invention primarily addresses the need for displacement measurement with millimeter-scale and nanometer-scale resolution in fields such as high-precision positioning systems. Unlike common large-range, high-precision grating rulers and laser displacement sensors, it provides a non-contact, large-range inductive displacement sensor, solving the common problem of low resolution in inductive solutions. Furthermore, it employs a bilateral compensation structure and optimized coil design to achieve displacement measurement resistant to lateral interference errors, giving it significant application potential. Numerical simulation models verify the feasibility of the measurement principle and provide guidance for structural design.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A non-contact inductive displacement sensor based on a planar bent coil includes a cantilever base and a U-shaped base. The cantilever end of the cantilever base extends into the slot of the U-shaped base, and the upper and lower surfaces of the cantilever end are parallel to the upper and lower inner surfaces of the slot. Two excitation coils are symmetrically arranged on the upper and lower surfaces of the cantilever end of the cantilever base, and a group of receiving coils is symmetrically arranged on the upper inner surface of the slot. Each group of receiving coils consists of two receiving coils stacked one on top of the other.

[0007] Both the excitation coil and the receiving coil are square-wave periodic grid structures with the same period width W. The positions of two receiving coils in the same receiving coil group differ by W / 4 in the X direction; the X direction is the periodic grid expansion direction.

[0008] By applying a sinusoidal signal of a certain frequency to the excitation coil, when the U-shaped base and the cantilever base move relative to each other, the mutual inductance coefficient between the excitation coil and the receiving coil changes, which in turn causes a change in the induced voltage on the receiving coil. After the induced electrical signal in the receiving coil is modulated and demodulated, it is digitally processed to finally achieve nanometer-level resolution X-direction displacement measurement.

[0009] Furthermore, an insulating layer is provided between the two receiving coils within the same receiving coil group.

[0010] Furthermore, the insulating layer is made of polyurethane film.

[0011] Furthermore, the frequency of the sinusoidal signal applied to the excitation coil is 1MHz, and the peak-to-peak voltage is 2V.

[0012] Furthermore, the horizontal projection area of ​​the receiving coil and its travel path completely covers the horizontal projection area of ​​the excitation coil.

[0013] Furthermore, the two receiving coils located in the upper layer of the two receiving coil groups form a double-sided compensation structure, and the two receiving coils located in the lower layer form a double-sided compensation structure, keeping the total vertical gap between the two coils in the double-sided compensation structure unchanged.

[0014] Furthermore, the detection model creation process for this non-contact inductive displacement sensor is as follows:

[0015] The excitation coil is simplified to The series connection of several rectangular excitation coils simplifies the receiving coil to The series connection of the first rectangular receiving coil, with the first... i The center of each rectangular excitation coil is the origin. A ray passing through the origin and along the direction of the period width W of the rectangular excitation coil is taken as the X-axis, and a ray passing through the origin and perpendicular to the X-axis is taken as the Y-axis. Then, the Z-axis is determined according to the right-hand rule, thus creating a Cartesian coordinate system. ;

[0016] Find the first The magnetic field distribution generated by the four straight line segments of a single rectangular excitation coil is obtained by applying the superposition theorem to obtain the spatial distribution of the magnetic induction intensity produced by the rectangular excitation coil. ;

[0017] Find the first The magnetic induction intensity of each straight segment of the rectangular excitation coil in the th... Any point within a rectangular receiving coil P magnetic induction intensity at the location Z The components, when added together, yield the first component. The rectangular excitation coil in the first... Any point within a rectangular receiving coil P Magnetic induction intensity at that location ;

[0018] Integrating over the spatial region where the rectangular receiving coil is located yields the first... The rectangular excitation coil in the first... The total magnetic flux generated in the plane of the rectangular receiving coil Thus, the first The rectangular excitation coil and the first Mutual inductance between rectangular receiving coils ;

[0019] When the excitation coil and the receiving coil move relative to each other only along the X direction, the mutual inductance coefficient between the excitation coil and the receiving coil can be obtained according to the superposition principle. ;

[0020] An approximately linear relationship is established between the change in electromotive force and the displacement between the excitation coil and the receiving coil.

[0021] Furthermore, the induced electromotive force is calculated to establish an approximately linear relationship between the change in electromotive force and displacement of the single-sided excitation coil and receiving coil. :

[0022] ;

[0023] Construct an approximately linear relationship between the change in electromotive force and displacement of the dual-sided excitation coil and receiving coil. :

[0024] ;

[0025] in, and These are the induced electromotive forces between the excitation coil on one side and the two receiving coils on the corresponding side. and These are the mutual inductance coefficients between the excitation coil on this side and the two receiving coils on the corresponding side, respectively. and These are the induced electromotive forces between the excitation coil on the other side and the two receiving coils on the corresponding side, respectively. and These are the mutual inductance coefficients between the excitation coil on this side and the two receiving coils on the corresponding side, respectively. and They are respectively and The values ​​of each variable after filtering out their DC components. .

[0026] Furthermore, the mutual inductance coefficient between the excitation coil and the receiving coil Represented as:

[0027] ;

[0028] in, Its DC component, for Fourier coefficients, A positive integer, representing the harmonic order in the expansion, to filter out this DC component. ,get Represented as:

[0029] .

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0031] This invention provides a non-contact inductive displacement sensor based on a planar bent coil. The coil is manufactured using FPC technology and employs a periodic cyclic structure, exhibiting good range scalability. A test platform was built in the laboratory to conduct actual tests on the sensor prototype. Experimental results show that the original measurement error of the sensor prototype within a single 8mm cycle is -24µm, which is reduced to 2.3µm after optimization and correction, while also exhibiting good repeatability better than 2.7µm. Ultra-low lateral effects are achieved by employing a bilateral compensation structure and optimizing the coil design.

[0032] Further evidence demonstrates that the double-sided structure effectively suppresses Z-direction disturbance errors compared to the single-sided structure, while the sensor prototype's measurement accuracy remains largely unaffected by Y-direction disturbances. Finally, long-period displacement measurements were conducted. Within the entire 25mm measurement range, the maximum measurement error was 5.6µm, with a resolution of 6.1nm RMS, demonstrating excellent measurement range period extension capabilities. Theoretically, increasing the number of excitation coil cycles could enable displacement measurements over an even wider range. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the overall three-dimensional structure of the non-contact inductive displacement sensor of the present invention;

[0034] Figure 2 This is an exploded structural diagram of the non-contact inductive displacement sensor of the present invention.

[0035] Figure 3 This is a simplified cross-sectional view of the non-contact inductive displacement sensor of the present invention.

[0036] Figure 4 This is a top view of the single-sided coil group of the non-contact inductive displacement sensor of the present invention.

[0037] Figure 5 A simplified model of a polygonal coil is provided, wherein (a) is a schematic diagram of the polygonal coil structure, (b) is a schematic diagram of the simplified rectangular coil structure, and (c) is a schematic diagram of the magnetic induction intensity calculation model of the mutual inductance between the rectangular coils.

[0038] Figure 6 The simulation shows the variation of the mutual inductance signals of the two orthogonal coils with respect to displacement X;

[0039] Figure 7 The relationship between the calculated function and displacement curves obtained from the simulation, as well as the fitting error;

[0040] Figure 8 The mutual inductance under different spacing Z (0.5mm~1.5mm, interval 0.1mm) obtained from simulation was calculated. Pattern of change;

[0041] Figure 9 The mutual inductance under different Y-axis center offsets (0 mm to 3 mm, with 1 mm intervals) obtained from simulation Pattern of change;

[0042] Figure 10 This is a wiring and dimension diagram of the sensor prototype FPC-processed coil in the embodiment;

[0043] Figure 11 Overall structural diagram of the sensor prototype testing system built for actual experiments;

[0044] Figure 12 for Figure 11 A magnified view of the selected area;

[0045] Figure 13 This is a schematic diagram of the signal processing flow of the sensor prototype testing system.

[0046] Figure 14 The induced voltage result is obtained after demodulating and filtering the signals from the four receiving coils of a single-cycle sensor.

[0047] Figure 15 The signal processing and region division results for the four receiving coils of a single-cycle sensor;

[0048] Figure 16 A comparison chart showing the single-cycle sensor displacement measurement error before and after correction;

[0049] Figure 17 A comparison of harmonic components before and after single-cycle sensor displacement measurement error correction;

[0050] Figure 18 The results of the repeatability test of sensor displacement measurement error are shown in part (a) as the original measurement error of five tests; part (b) as the optimized measurement error; and part (c) as a magnified view of the part with the worst repeatability.

[0051] Figure 19 The experimental results are shown for different Z-direction spacings under lateral perturbation. Part (a) shows the performance of the single-sided structure, and part (b) shows the performance of the double-sided compensation structure.

[0052] Figure 20 The experimental results show the center distances in different Y directions under lateral perturbations.

[0053] Figure 21 The results show the long-period displacement measurement error of the sensor prototype;

[0054] Figure 22The results are the resolution test results of the sensor prototype, where (a) is the static test result and (b) is the step response test result. Detailed Implementation

[0055] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby providing a clearer and more explicit definition of the scope of protection of the present invention.

[0056] It should be noted that when a component is said to be "installed on" another component, it can be directly on the other component or it may be in a component that is centered on it. When a component is said to be "set on" another component, it can be directly set on the other component or it may also be in a component that is centered on it. When a component is said to be "fixed to" another component, it can be directly fixed to the other component or it may also be in a component that is centered on it.

[0057] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the specification of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "or / and" as used herein includes any and all combinations of one or more of the associated listed items.

[0058] See appendix Figure 1 and Figure 2As shown, a non-contact inductive displacement sensor based on a planar bent coil includes a cantilever base 1 and a U-shaped base 2. The cantilever end of the cantilever base 1 extends into the slot of the U-shaped base 2, and the upper and lower surfaces of the cantilever end are parallel to the upper and lower inner surfaces of the slot. Two excitation coils 3 are fixedly fixed on the upper and lower surfaces of the cantilever end of the cantilever base 1, respectively. A receiving coil group is fixedly fixed on the upper inner surface of the slot, and each receiving coil group consists of two receiving coils 4 stacked on top of each other. For ease of description, the two excitation coils 3 are referred to as excitation coil Coil A and excitation coil Coil B, respectively, and are attached to the lower and upper surfaces of the cantilever base 1. The four receiving coils 4 are referred to as receiving coil Coil 1, receiving coil Coil 2, receiving coil Coil 3, and receiving coil Coil 4, respectively. Receiving coil Coil 1 and receiving coil Coil 2 (with receiving coil Coil 1 located above receiving coil Coil 2) are attached to the lower groove surface of the slot, while receiving coil Coil 3 and receiving coil Coil 4 (with receiving coil Coil 3 located above receiving coil Coil 4) are attached to the upper groove surface of the slot. Therefore, excitation coil Coil A and receiving coils Coil 1 and Coil 2 form one group of coils, while excitation coil Coil B and receiving coils Coil 3 and Coil 4 form another group of coils. This can be considered as a double-sided compensation structure composed of two identical groups of coils. Figure 3 As shown.

[0059] Preferably, an insulating layer is provided between the two receiving coils 4 in the same receiving coil group, that is, an insulating layer is provided between receiving coil Coil1 and receiving coil Coil2, and between receiving coil Coil3 and receiving coil Coil4, in order to achieve insulation protection. In this embodiment, the insulating layer is a polyurethane film (PI).

[0060] The receiving coils Coil1 and Coil3, and Coil2 and Coil4, are mutually compensating. Through a bilateral compensation structure, by keeping the total Z-direction gap between the coils constant, when the magnetic flux received by one receiving coil decreases, the magnetic flux received by the other receiving coil increases, achieving ultra-low lateral effects. This structure makes it insensitive to Z-direction movement within a certain range, has good anti-interference capabilities, and is easy to install. Figure 4As shown, all excitation coils 3 and receiving coils 4 are square-wave periodic grid structures, possessing good range extension capabilities, and all have the same period width W. The positions of two receiving coils within the same receiving coil group differ by W / 4 in the X direction (measurement direction), meaning that receiving coils Coil1 and Coil2 differ by W / 4 in the measurement direction, resulting in a 90° phase difference in the spatial domain. The same applies to receiving coils Coil3 and Coil4. Here, the X direction is defined as the periodic grid extension direction. The horizontal projection area of ​​receiving coil 4 and its travel path completely covers the horizontal projection area of ​​excitation coil 3. The width of excitation coil 3 (… ) is wider than the receiving coil 4 ( The large magnetic field strength of the excitation coil 3 along the Y direction is due to the abrupt change in magnetic induction intensity distribution at the edge of the coil, while the distribution in the central region is more gradual. Therefore, this design can effectively resist interference in the Y direction.

[0061] By applying a sinusoidal signal of a certain frequency to the excitation coil 3, when the U-shaped base 2 and the cantilever base 1 move relative to each other, the mutual inductance coefficient between the excitation coil 3 and the receiving coil 4 changes, which in turn causes the induced voltage on the receiving coil 4 to change. After the induced electrical signal in the receiving coil 4 is modulated and demodulated, it is digitally processed to finally achieve nanometer-level resolution X-direction displacement measurement.

[0062] By optimizing the coil design and implementing a double-sided compensation structure on the base, the sensor becomes insensitive to lateral disturbances in the Y and Z directions, reducing installation requirements while addressing potential lateral offsets during feedback, thus achieving completely non-contact measurement. Experimental results show that the sensor can achieve displacement measurement with a resolution of 6.1 nm RMS and a range of 25 mm, with an error of less than 5.6 µm and repeatability better than 2.7 µm.

[0063] The process of creating the detection model for the non-contact inductive displacement sensor of the present invention is as follows:

[0064] The inductive displacement sensor measures displacement by utilizing the relationship between the mutual inductance of the excitation coil 3 and the receiving coil 4 and their changing positions. Mutual inductance coefficient. It only depends on the external dimensions, relative position, and dielectric properties of the two coils. For example, Figure 4 The polygonal coil shown can simplify excitation coil 3 to... The series connection of several rectangular excitation coils simplifies the receiving coil 4 to... A series connection of rectangular receiving coils, such as Figure 5 As shown in parts (a) to (b), the mutual inductance of the two rectangular coils can be obtained by simply calculating the spatial magnetic field distribution of a single rectangular excitation coil and then solving for the magnetic flux in the spatial domain where the receiving coil is located.

[0065] Find the first i The magnetic field distribution generated by the four straight line segments of a single rectangular excitation coil is obtained by applying the superposition theorem to obtain the spatial distribution of the magnetic induction intensity produced by the rectangular excitation coil. Specifically, taking the first... i The center of each rectangular excitation coil is the origin. A ray passing through the origin and along the direction of the period width W of the rectangular excitation coil is taken as the X-axis, and a ray passing through the origin and perpendicular to the X-axis is taken as the Y-axis. Then, the Z-axis is determined according to the right-hand rule, thus creating a Cartesian coordinate system. .like Figure 5 As shown in section (c), the four vertices of a single rectangular excitation coil are respectively , , , Each rectangular excitation coil consists of four straight wires, which are line segments. , , , By calculating the magnetic field distribution generated by each segment of the conductor, and applying the superposition theorem, the spatial distribution law of the magnetic induction intensity generated by the rectangular excitation coil can be obtained.

[0066] Let the time-harmonic alternating current applied in the excitation coil be... ,

[0067] ; (1)

[0068] in, ω is the angular frequency of the alternating current, which characterizes the change in electrical angle per second of a sinusoidal alternating current. t For time, This represents the amplitude of the alternating current.

[0069] Correspondingly, the induced electromotive force generated in the rectangular receiving coil is called the mutual inductance electromotive force. ,

[0070] ; (2)

[0071] According to the Biot-Savart law, any point in the space of a rectangular receiving coil... magnetic induction intensity at the location It can be represented as:

[0072] ; (3)

[0073] in, For the differential of the length of the receiving coil on a certain segment of the conductor, For the corresponding differential point to The distance between the points. For the corresponding differential point to The spatial vector corresponding to the line connecting the points. ρ is the magnetic permeability in vacuum.

[0074] Find the first The magnetic induction intensity of each straight segment of the rectangular excitation coil in the th... Any point within a rectangular receiving coil P magnetic induction intensity at the location Z The components, when added together, yield the first component. The rectangular excitation coil in the first... Any point within a rectangular receiving coil P Magnetic induction intensity at that location Regarding magnetic flux density, we are only concerned with its... Z The directional component directly affects the magnetic flux in the rectangular receiving coil; therefore, the conductor segments are calculated separately. , At point magnetic induction intensity at the location Z Quantity.

[0075] (4)

[0076] (5)

[0077] In the formula, and , They are respectively P Point in Cartesian coordinate system The coordinates within.

[0078] Similarly, we can obtain the other two sides. , exist Magnetic induction intensity at point Z Quantity , The magnetic flux density of a single rectangular receiving coil at any point in space can be obtained by superimposing the components. Furthermore, integration over the spatial region where the rectangular receiving coil is located yields the first... The rectangular excitation coil in the first... The total magnetic flux generated in the plane of the rectangular receiving coil :

[0079] ; (6)

[0080] Therefore, according to the definition of mutual inductance coefficient, we can obtain the first... The rectangular excitation coil and the first Mutual inductance between rectangular receiving coils :

[0081] ; (7)

[0082] Since both the excitation coil and the receiving coil are periodic grid structures, their mutual inductance also exhibits a periodic variation. Therefore, when they move relative to each other only along the X direction, according to the superposition principle, the mutual inductance between the excitation coil and the receiving coil can be expressed as:

[0083] ; (8)

[0084] in, Its DC component, for Fourier coefficients, is a positive integer, representing the harmonic order in the expansion.

[0085] Obviously, the mutual inductance coefficient With displacement change The relationship is not linear; when When large enough, the presentation period is It is a complex even function containing multiple harmonics. To obtain the output's relationship with displacement linearization, further signal processing is required. First, regarding the mutual inductance coefficient... Filter out its DC component Get it Represented as:

[0086] ; (9)

[0087] If Taking the absolute value again leads to a new cycle. an even function.

[0088] An approximately linear relationship is established between the change in electromotive force (EMF) and displacement between the excitation and receiving coils. For an alternating excitation current with constant amplitude, the induced EMF is calculated, and an approximately linear relationship between the change in EMF and displacement between the single-sided excitation and receiving coils is established. :

[0089] ; (10)

[0090] Construct an approximately linear relationship between the change in electromotive force and displacement of the dual-sided excitation coil and receiving coil. :

[0091] ; (11)

[0092] in, and These are the induced electromotive forces between the excitation coil on one side and the two receiving coils on the corresponding side. and These are the mutual inductance coefficients between the excitation coil on this side and the two receiving coils on the corresponding side, respectively. and These are the induced electromotive forces between the excitation coil on the other side and the two receiving coils on the corresponding side, respectively. and These are the mutual inductance coefficients between the excitation coil on this side and the two receiving coils on the corresponding side, respectively. and They are respectively and The values ​​of each variable after filtering out their DC components. .

[0093] Equations (10) and (11), using a proportional form, can effectively suppress common-mode interference, such as temperature changes and fluctuations in the excitation source. Using a division by the signal can, to some extent, weaken the influence of the coil spacing in the Z direction, and... or Periodic normalization has been completed.

[0094] To more intuitively demonstrate the effectiveness of this solution method, the corresponding simulation results will be presented below.

[0095] A simulation model of the sensor was established in the numerical analysis software MATLAB to analyze the relationship between coil mutual inductance and relative position. For an ideal coil model, simulating a set of single-ended coils is sufficient to observe the sensor's performance. The excitation coil Coil A was set to consist of nine single-turn rectangular coils, with a coil length of... The receiving coils Coil1 and Coil2 consist of five single-turn rectangular coils, with a coil length of... The coil period width is The spatial positions of receiving coils Coil1 and Coil2 along the X direction are different. Alternating arrangement, positional relationship as follows Figure 4 As shown, the effects of line width and line thickness are ignored. The mutual inductance of the coils is calculated using the magnetic induction intensity method. The area enclosed by the receiving coil is divided into 0.05mm*0.05mm units and substituted into equation (6) to calculate the magnetic flux. Furthermore, the mutual inductance between the coils can be obtained through equations (7) and (8).

[0096] Figure 6 The receiving coil is set to move in a step of 0.02 mm in the X direction, the distance between the excitation coil and the receiving coil in the Z direction is 1 mm, and the centers in the Y direction coincide, meaning there is no deviation in the Y direction. The average of the maximum and minimum values ​​of the curve is used to replace the value in equation (8). Then we can obtain it through equation (9). .

[0097] The mutual inductance coefficient obtained from the simulation is obtained according to equation (10). The pattern of change is as follows Figure 7 As shown, it can be seen The value changes periodically within the interval [-1, 1], and according to its pattern, it varies within a single coil period. The space can be divided into four regions, and each region is divided according to different displacements. Reference, conduct and The linear fit yields equation (12). and The linear fitting coefficients for each region are... :

[0098] (12)

[0099] Different regional judgments are mainly based on and The sign of the value determines the positional error, as shown below. Figure 7 As shown on the right coordinate axis, the maximum error is approximately 20µm. Furthermore, it can be observed that the errors in different regions exhibit certain patterns and similarities. Therefore, Fourier series fitting can be used to further optimize and reduce the error, which will be discussed in detail in subsequent experiments.

[0100] Furthermore, by changing the Z-direction spacing between the excitation coil and the receiving coil, their effect on mutual inductance was observed. The simulation results show the influence of the variation law of displacement in the X direction (step size 0.1 mm). Figure 8 As shown, the spacing varies from 0.5mm to 1.5mm, with intervals of 0.1mm. It can be seen that the mutual inductance between coils is very sensitive to the spacing, and the smaller the spacing, the larger the mutual inductance coefficient. Subsequently, a differential compensation structure can be used to maintain the spacing and reduce interference in the Z direction.

[0101] With a Z-direction spacing of 1mm, the center distance between the excitation coil and the receiving coil in the Y-direction is varied, and the mutual inductance is observed. The simulation results show the variation of displacement in the X direction (step size 0.1 mm). Figure 9 As shown. Mutual inductance is not sensitive to changes in the Y direction, due to... Figure 4 It can be seen that the width of the excitation coil ( ) is greater than the width of the receiving coil ( The large size of this design is due to the fact that the magnetic induction intensity distribution of the excitation coil along the Y direction has abrupt changes at the edge of the coil, while it is more gradual in the central region. Therefore, this design can effectively resist interference in the Y direction.

[0102] I. Experimental Setup: The prototype of the non-contact inductive displacement sensor of this invention uses FPC (Flexible Printed Circuit) technology to manufacture the coils, which features light weight, thinness, and good flexibility. The excitation coil 3 and receiving coil 4 are respectively bonded to the surfaces of the cantilever base 1 and U-shaped base 2 made of acrylic material using silicone sealant. The excitation coil 3 is a single-layer circuit board, while the receiving coil assembly is a double-layer circuit board, with polyurethane film (PI) used for insulation protection between the layers. The structure and dimensions of the coils wound using FPC are as follows... Figure 10 The relevant parameter values ​​are listed in Table 1.

[0103] Table 1. Parameters for coil selection

[0104]

[0105] The overall structure of the assembled sensor testing system is as follows: Figure 11 As shown, it mainly consists of the following parts: a sensor prototype, a lock-in amplifier 10 (MFLI, Zurich Instruments), a host computer 20, a piezoelectric inertial displacement platform controller 30 (PE211, ACTUS TECH, China), a signal generator 40, an oscilloscope 50, an X-direction displacement stage 5, a Y-direction displacement platform 6, a Z-direction displacement platform 7, and a vibration isolation platform 8. The Y-direction displacement platform 6 and the Z-direction displacement platform 7 are fixedly mounted on the vibration isolation platform 8, the X-direction displacement stage 5 is connected to the Z-direction displacement platform 7, the cantilever base 1 of the sensor prototype is fixedly mounted on the top displacement output platform of the X-direction displacement stage 5, and the U-shaped base 2 is fixedly mounted on the top displacement output platform of the Y-direction displacement platform 6. The output terminal of the signal generator 40 is connected to the input terminal of the excitation coil 3 to apply an AC signal of a certain frequency and constant amplitude to the excitation coil 3. Simultaneously, the output terminal of the signal generator 40 is connected to the input terminal of the oscilloscope 50 to graphically display the waveform of the AC signal. The output terminal of the receiving coil 4 is connected to the host computer 20 via the lock-in amplifier 10. The output signal of the receiving coil 4 is demodulated and filtered by the lock-in amplifier 10 to obtain the induced voltage, which is then processed and displayed on the host computer 20.

[0106] An AC signal of a certain frequency and constant amplitude is applied to the excitation coil 3 by the signal generator 40, and the receiving coil 4 generates a corresponding induced electromotive force, which can represent the mutual inductance between the two. After demodulation by the lock-in amplifier 10, the DC signal obtained is transmitted to the host computer 20. After the data processing software built into the host computer 20 is processed by the signal post-processing formulas (6) to (9), the displacement can be obtained, and the corresponding waveform image is displayed on the host computer 20. In order to make the induced voltage in the receiving coil 4 as large as possible for easy detection, the excitation frequency of the output signal of the signal generator 40 can be increased. However, if the excitation frequency is too high, the signal disturbance will increase and the demodulation will be difficult. Therefore, in the experiment, a sinusoidal signal with a frequency of 1MHz and a peak-to-peak voltage of 2V is selected as the excitation source. In the experiment, a piezoelectric inertial displacement platform (i.e., X-direction displacement platform 5) with an accuracy of 1µm is used as the X-direction measurement reference. The Z-direction displacement platform 7 can adjust the distance between the receiving coil 4 and the excitation coil 3. The system simulates different installation spacings and potential Z-axis disturbances during practical applications. The Y-axis displacement platform 6 is used to change the Y-axis center offset of the excitation coil 3 and the receiving coil 4, allowing observation of the impact of different Y-axis installation errors on sensor performance.

[0107] II. Experiments and Results:

[0108] A. Sensor testing errors and optimization:

[0109] The designed sensor prototype adopts a multi-cycle structure, therefore the primary focus is on the sensor's error performance within a single cycle of 8mm. Testing was conducted using a piezoelectric inertial displacement platform that moved the excitation coil 3, with a selected movement interval of 0.02mm. The signals from the four receiving coils were demodulated and filtered by a lock-in amplifier 10 to obtain the magnitude of the induced voltage. , , , ,like Figure 14 As shown. You can see and There is no spatial phase difference, and the curves of their displacement change are basically the same. and Similarly, there is almost no spatial phase difference, but At the same location, it will be more The difference is greater because the same set of receiving coils are printed on different wiring layers of the FPC coil, with a PI layer between the two layers for insulation. If adjusted... Figure 3 If the receiving coils Coil1 and Coil3 are equidistant from their corresponding excitation coils in the Z-direction, then the distance between the receiving coil Coil4 and its corresponding excitation coil CoilB is... The distance between the receiving coil Coil2 and its corresponding excitation coil CoilA The smaller the value, the lower the induced voltage at the same location X. Larger. Furthermore, we can see that... and The phase difference in the X direction is approximately This refers to the phase angle of 90° in the spatial domain. As can be seen from the diagram, the four signals have certain similarities; therefore, one signal is selected. Its relation to displacement The average of the maximum and minimum values ​​of the variation curve is -3.09mV, which is used to replace the DC component. After filtering out the four signals, the following can be obtained: , , , Since a bilateral compensation unit is used, as mentioned above, the following points need attention: and The changing patterns and sign changes, such as Figure 15 As shown. and A 90° phase angle is maintained between them. Since the sum of the Z-direction distances of the receiving coils Coil1 and Coil3 with respect to the two excitation coils is the same as the sum of the Z-direction distances of the receiving coils Coil2 and Coil4 with respect to the two excitation coils, their peak values ​​are basically equivalent.

[0110] After signal processing according to equation (11), the following is obtained: Its relation to displacement It exhibits periodic changes between [-1, 1], such as Figure 15 As shown by the solid line; for each of the four regions, a linear fit based on the least squares method is performed to obtain equation (13), then the original error of the relative reference displacement sensor is as follows: Figure 16 As shown by the solid line of the middle circle mark, the maximum error peaks are -24.0µm and 23µm.

[0111] (13)

[0112] Observing the error curve, we find that the magnitude of the error is related to... It exhibits certain regularity and is consistent with simulation results. Figure 6 The error curves in the two samples show slight differences. The peak measurement error is mainly concentrated at the junctions of different regions, which is because at this point... or One of the signals changes with respect to X near its peak, and its trend slows down compared to other locations, resulting in lower signal sensitivity. The nonlinearity is concentrated near -1 or 1. The original errors in the four regions have some similarity; therefore, we can select the error in region I for analysis and perform a Fast Fourier Transform (FFT) analysis, yielding the following results: Figure 17 The circular markers indicate the various harmonic components, with the first-order harmonic having the largest error at 4.0µm, while the errors gradually decrease with each subsequent order. These errors primarily originate from the two signals from the receiving coil. or The errors include non-strict orthogonality, unequal amplitudes, and processing errors such as line width and spacing. Because these errors exhibit good regularity, to obtain a smaller measurement error, a Fourier series can be used to fit the error (Error) to region I. The changing pattern between them was found to be such that the fitting function could be obtained by applying the third order of magnitude. :

[0113] (14)

[0114] This compensation function is applicable to all four regions, and the compensated... Substitution (13) This allows for the calculation of displacement X in each region, thus completing error optimization. In practice, the optimized error curve is shown in the following figure. Figure 16 As indicated by the triangular markings, the maximum error peaks within a single period are -1.8µm and 2.3µm. An FFT is performed on the optimized error in region I as follows... Figure 17 As indicated by the triangular markings, all higher-order harmonic components are well suppressed, reduced to the level of hundreds of nanometers, and similar effects are observed in the other three regions.

[0115] To further test the sensor's performance and the effectiveness of the optimization scheme, five repeated experiments were conducted to test its repeatability. The repeatability criterion was defined as three times the standard deviation at each sampling point. Figure 18 (a) shows that the maximum peak values ​​of the original errors for five measurements within a single cycle of 8 mm are -26.5 µm and 24.5 µm. Figure 18 (b) The mean of each sampling point is shown as a dashed line, and its three standard deviations are shown as a solid line in the graph. It can be seen that the errors of all sampling points are within the area enclosed by three standard deviations. The maximum peak values ​​of the optimized errors are -4.0µm and 2.2µm, respectively. (Partial zoom-in) Figure 18 (c) shows the largest standard deviation. The error variation is 0.886µm, and the peak value of the error variation at each sampling point is less than three standard deviations, therefore the repeatability can be considered better than 2.66µm. Except for the error jumps at the region junctions, in... Figure 18 A sudden change in error can also be observed at X = -2.34 mm in (c), this region is located in Figure 14 middle and Near the zero voltage point, which is close to the critical point of change in the direction of total magnetic flux, the signal is weak and difficult to demodulate, and there is a large noise disturbance, resulting in error jumps.

[0116] B. Lateral disturbance error:

[0117] The non-contact inductive displacement sensor of this invention is used to measure displacement in the X direction. However, in practical industrial applications, some lateral disturbances are unavoidable, such as installation alignment errors and coupling errors in other directions during movement. If the measurement error caused by lateral disturbances is too large, the displacement sensor will fail. Furthermore, it is necessary to use guide rails to restrict the movement between sensor components to reduce interference, making truly non-contact measurement impossible and greatly limiting its application scenarios. To fully understand the performance of this sensor, displacement disturbances from the Y and Z directions must also be considered.

[0118] First, considering the disturbance error caused by the change in the Z-direction spacing between the excitation coil 3 and the receiving coil 4, tests were conducted and compared on both single-sided and double-sided compensation structures. The single-sided structure consists of... Figure 3 The system consists of excitation coil Coil A, receiving coil Coil 1, and receiving coil Coil 2. The spacing between the coils is set by adjusting the Z-direction displacement platform. The spacing options are 0.8mm, 1.0mm, and 1.2mm, with the test results at a spacing of 1.0mm used as a reference for calibration and optimization. Correspondingly, the coil spacing of the double-sided compensation structure... The spacing was set to (1.0mm, 1.0mm), (0.9mm, 1.1mm), and (0.8mm, 1.2mm), keeping the total spacing constant at 2.0mm. The above optimization scheme was used throughout the experiments, and the results are as follows: Figure 19 As shown. For a one-sided structure, by Figure 19 (a) It can be seen that changes in the spacing lead to an increase in the peak value of the measurement error. The maximum error increases from 3.7µm at 1.0mm to 25.6µm at 0.8mm and 22.6µm at 1.2mm, indicating that the sensor is highly sensitive to disturbances in the Z-direction. For the dual-sided compensation structure, from Figure 19 (b) It can be seen that the maximum error within the period measurement range caused by the change in spacing gradually increases from 2.6µm to -3.3µm and -6.2µm, while the lateral disturbance error remains relatively small. Furthermore, at the same location, the error fluctuation of the bilateral structure is also smaller. Overall, the bilateral structure offers higher measurement accuracy and better suppresses disturbance errors in the Z direction.

[0119] Further consideration is needed for this sensor, specifically the disturbance error caused by the change in the center distance in the Y direction between the excitation coil 3 and the receiving coil 4. The experimental results were obtained by adjusting the Y-direction displacement platform to distances of 0mm, 1mm, and 2mm. Figure 20 As shown, the maximum errors are -3.9µm, 2.1µm, and 2.9µm, respectively. The measurement accuracy is not affected by the disturbance in the Y direction. This is mainly due to the fact that the designed excitation coil structure is longer than the receiving coil, which makes the change in mutual inductance coefficient along the Y direction small and can effectively suppress the disturbance error caused by the Y direction.

[0120] Experiments have shown that the prototype sensor has good suppression capabilities for disturbance errors caused by variations in the Y and Z directions within a certain range, enabling high-precision non-contact measurement and facilitating installation.

[0121] C. Multi-cycle measurement error and resolution test:

[0122] Because the coil uses a periodic grid structure, long-period measurement error testing should also be performed. For the periodic extended structure, the edge effect will lead to increased error; therefore, the excitation coil was redesigned and fabricated, increasing only the number of periods. All other parameters and experimental conditions remained unchanged. The experimental results are as follows: Figure 21 As shown, the maximum peak values ​​of the measurement error over the entire 25mm measurement range are 5.6µm and -4.4µm, respectively. Due to the varying magnetic induction intensity across different periodic regions, the large-range measurement error is slightly larger than the single-cycle error. The error jumps shown in the figure are the same as those mentioned earlier, concentrated near the zero-crossing point of the electrical signal and at the junctions of different regions.

[0123] Sensor resolution testing is affected by the external environment; therefore, the entire testing setup was placed on a vibration-isolated platform. The low-pass filter bandwidth of the lock-in amplifier 10 was set to 20Hz, and the sampling rate was set to 100sps. Figure 22 As shown in (a), after the sensor stabilizes, the effective noise value is 6.1 nm RMS. Furthermore, tests were conducted by driving the piezoelectric displacement stage along ten steps in the X direction with step sizes of 10 nm, 30 nm, and 50 nm, respectively. The experimental results are as follows: Figure 22 As shown in (b), the sensor prototype has a good response output. Finally, the main performance parameters of the sensor prototype are summarized in Table 2.

[0124] Table 2. Sensor Performance Indicators

[0125] range accuracy Repeatability resolution 25mm 5.6µm 2.7µm 6.1nm RMS

[0126] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0127] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A non-contact inductive displacement sensor based on a planar bent coil, comprising a cantilever base and a U-shaped base, wherein the cantilever end of the cantilever base extends into the slot of the U-shaped base, and the upper and lower surfaces of the cantilever end are parallel to the inner upper and lower surfaces of the slot, characterized in that: Two excitation coils are fixed symmetrically on the upper and lower surfaces of the cantilever end of the cantilever base, and a group of receiving coils is fixed symmetrically on the inner upper surface of the slot. Each group of receiving coils consists of two receiving coils stacked on top of each other. Both the excitation coil and the receiving coil are square-wave periodic grid structures with the same period width W. The positions of two receiving coils in the same receiving coil group differ by W / 4 in the X direction; the X direction is the periodic grid expansion direction. By applying a sinusoidal signal of a certain frequency to the excitation coil, when the U-shaped base and the cantilever base move relative to each other, the mutual inductance coefficient between the excitation coil and the receiving coil changes, which in turn causes a change in the induced voltage on the receiving coil. After the induced electrical signal in the receiving coil is modulated and demodulated, it is digitally processed to finally achieve nanometer-level resolution X-direction displacement measurement.

2. The non-contact inductive displacement sensor based on a planar bent coil according to claim 1, characterized in that: An insulating layer is provided between two receiving coils within the same receiving coil group.

3. The non-contact inductive displacement sensor based on a planar bent coil according to claim 2, characterized in that: The insulating layer is made of polyurethane film.

4. The non-contact inductive displacement sensor based on a planar bent coil according to claim 1, characterized in that: The frequency of the sinusoidal signal applied to the excitation coil is 1MHz, and the peak-to-peak voltage is 2V.

5. The non-contact inductive displacement sensor based on a planar bent coil according to any one of claims 1 to 4, characterized in that: The horizontal projection area of ​​the receiving coil and its travel path completely covers the horizontal projection area of ​​the excitation coil.

6. The non-contact inductive displacement sensor based on a planar bent coil according to claim 5, characterized in that: The two receiving coils in the upper layer of the two receiving coil groups form a double-sided compensation structure, and the two receiving coils in the lower layer form a double-sided compensation structure, keeping the total vertical gap between the two coils in the double-sided compensation structure constant.

7. The non-contact inductive displacement sensor based on a planar bent coil according to claim 1, characterized in that, The process of creating the detection model for this non-contact inductive displacement sensor is as follows: The excitation coil is simplified to The series connection of several rectangular excitation coils simplifies the receiving coil to The series connection of the first rectangular receiving coil, with the first... i The center of each rectangular excitation coil is the origin. A ray passing through the origin and along the direction of the period width W of the rectangular excitation coil is taken as the X-axis, and a ray passing through the origin and perpendicular to the X-axis is taken as the Y-axis. Then, the Z-axis is determined according to the right-hand rule, thus creating a Cartesian coordinate system. ; Find the first The magnetic field distribution generated by the four straight line segments of a single rectangular excitation coil is obtained by applying the superposition theorem to obtain the spatial distribution of the magnetic induction intensity produced by the rectangular excitation coil. ; Find the first The magnetic induction intensity of each straight segment of the rectangular excitation coil in the th... Any point within a rectangular receiving coil The Z component of the magnetic field strength at a given location, when superimposed, yields the first Z component. The rectangular excitation coil in the first... Any point within a rectangular receiving coil Magnetic induction intensity at that location ; Integrating over the spatial region where the rectangular receiving coil is located yields the first... The rectangular excitation coil in the first... The total magnetic flux generated in the plane of the rectangular receiving coil Thus, the first The rectangular excitation coil and the first Mutual inductance between rectangular receiving coils ; When the excitation coil and the receiving coil move relative to each other only along the X direction, the mutual inductance coefficient between the excitation coil and the receiving coil can be obtained according to the superposition principle. ; An approximately linear relationship is established between the change in electromotive force and the displacement between the excitation coil and the receiving coil.

8. The non-contact inductive displacement sensor based on a planar bent coil according to claim 7, characterized in that: The induced electromotive force is calculated, and an approximately linear relationship is established between the change in electromotive force and displacement of the single-sided excitation coil and receiving coil. : ； Construct an approximately linear relationship between the change in electromotive force and displacement of the dual-sided excitation coil and receiving coil. : ； in, and These are the induced electromotive forces between the excitation coil on one side and the two receiving coils on the corresponding side. and These are the mutual inductance coefficients between the excitation coil on this side and the two receiving coils on the corresponding side, respectively. and These are the induced electromotive forces between the excitation coil on the other side and the two receiving coils on the corresponding side, respectively. and These are the mutual inductance coefficients between the excitation coil on this side and the two receiving coils on the corresponding side, respectively. and They are respectively and The values ​​of each variable after filtering out their DC components. .

9. The non-contact inductive displacement sensor based on a planar bent coil according to claim 7 or 8, characterized in that, Mutual inductance coefficient between the excitation coil and the receiving coil Represented as: ； in, Its DC component, for Fourier coefficients, A positive integer, representing the harmonic order in the expansion, to filter out this DC component. ,get Represented as: 。

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