Ferromagnetic rod radial displacement detection method based on differential multi-saddle detection coil voltage

Abstract

The application provides a ferromagnetic rod radial deviation detection method based on a multi-saddle detection coil voltage difference, and comprises the following steps: establishing a magnetic vector potential of a ferromagnetic rod in a sensor under a non-deviation condition; calculating a reference induced voltage of a saddle detection coil under the non-deviation condition according to the magnetic vector potential; constructing an induced voltage model under a deviation condition according to the reference induced voltage of the saddle detection coil and a deviation parameter; constructing a deviation characteristic component according to the induced voltage model under the deviation condition, and calculating a deviation distance and a deviation angle. The application regards the rod radial deviation as a state parameter which can be directly represented by a multi-channel induced voltage circumferential distribution characteristic, so that quantitative detection of the rod deviation distance and the deviation angle can be realized; the first harmonic component of the detection coil in the y-axis direction and the x-axis direction can be used to simultaneously give the deviation amplitude and the deviation direction, the common-mode error can be effectively suppressed, the deviation sensitive term can be enhanced, and the identification stability is improved.

Description

Technical Field

[0001] This invention relates to the field of sensor measurement technology, and in particular to a method for detecting radial offset of a ferromagnetic rod based on voltage differential of multiple saddle-shaped detection coils. Background Technology

[0002] Electromagnetic induction displacement sensors are widely used in metal rod position detection, actuator displacement feedback, and displacement monitoring under special working conditions due to their advantages such as non-contact measurement, strong anti-pollution ability, relatively simple structure, and suitability for complex environments.

[0003] Existing electromagnetic induction displacement sensors typically use an excitation coil to generate an alternating magnetic field and measure displacement by detecting the change in induced voltage in the coil with the position of the conductor or ferromagnetic body being measured. For most existing technologies, sensor modeling, structural design, and signal processing are largely based on the ideal condition that the measured rod and the sensor are coaxial, that is, it is assumed that the electromagnetic field distribution and electromagnetic coupling relationship inside the sensor have circular symmetry. Therefore, the output signal mainly reflects the displacement change of the rod along the axial direction.

[0004] However, in practical engineering applications, it is often difficult for the measured rod to maintain strict alignment with the sensor's central axis during movement. Affected by factors such as assembly errors, guide clearances, machining deviations, thermal deformation, mechanical vibration, and long-term wear, the measured rod often experiences varying degrees of radial displacement relative to the sensor's central axis. After this radial displacement, the axisymmetric magnetic field distribution established under concentric conditions is disrupted, leading to differences in the induced voltage response of the detection coil at different circumferential positions. This results in the output signal reflecting axial displacement information while also incorporating disturbance components related to the measured rod's offset distance and direction.

[0005] In existing technologies, the methods for dealing with the eccentricity problem of the measured rod mainly focus on improving the mechanical assembly accuracy, reducing the guide clearance, setting up guide support structures, or making empirical corrections to the output signal. These methods can only reduce the offset error to a certain extent and are difficult to accurately distinguish the combined effect of axial displacement changes and radial offset disturbances on the detection results. This can easily lead to a decrease in displacement measurement sensitivity, a deterioration in linearity, and output distortion.

[0006] Furthermore, existing technologies typically treat the radial offset of the measured rod as an error factor that should be suppressed or compensated for, lacking effective methods for online detection and quantitative identification, making it difficult to simultaneously obtain the offset distance and direction of the measured rod. For electromagnetic induction displacement sensors containing circumferential excitation coils and multiple radial detection coils, how to effectively identify the radial offset state during the axial displacement detection of the measured rod, and further improve the sensor's measurement accuracy and anti-interference capability under complex working conditions, remains a pressing technical problem to be solved in this field. Summary of the Invention

[0007] To address the technical problem in existing technologies where it is difficult to accurately distinguish the combined effects of axial displacement changes and radial offset disturbances on the detection results of the measured rod, leading to a decrease in displacement measurement sensitivity, this invention proposes a radial offset detection method for ferromagnetic rods based on voltage differential across multiple saddle-shaped detection coils. By establishing a correspondence between the radial offset parameters of the ferromagnetic rod and the induced voltage of the saddle-shaped detection coils, the method enables the identification of the offset amount and direction of the ferromagnetic rod, improving displacement measurement sensitivity and thus enhancing the accuracy of displacement measurement. This method is applicable to electromagnetic induction structures comprising a circumferential excitation coil, a saddle-shaped detection coil, and a ferromagnetic material.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A method for detecting radial offset of a ferromagnetic rod based on voltage differential of multiple saddle-shaped detection coils includes the following steps: S1: Establish the magnetic vector potential under the condition that the ferromagnetic rod in the sensor has no offset; S2: Calculate the reference induced voltage of the saddle-shaped detection coil under the condition of no offset based on the magnetic vector potential; S3: Construct an induced voltage model under offset conditions based on the reference induced voltage and offset parameters of the saddle-shaped detection coil; S4: Construct offset characteristic components based on the induced voltage model under offset conditions, and calculate the offset distance and offset angle.

[0009] Preferably, in S1, the sensor includes a ferromagnetic rod 1 located in the central region, a circumferential excitation coil 2, and multiple saddle-shaped detection coils; Among them, the circumferential excitation coil 2 is set on the outer surface of the ferromagnetic rod 1, and multiple saddle-shaped detection coils are circumferentially distributed on the outer surface of the circumferential excitation coil 2.

[0010] Preferably, the saddle-shaped detection coil includes a first group of coils and a second group of coils; the first group of coils is distributed at the lower end of the circumferential excitation coil 2, and the second group of coils is distributed at the upper end of the circumferential excitation coil 2, with a certain interval distance d1 between the first group of coils and the second group of coils, where d1>0.

[0011] Preferably, the first group of coils includes a first saddle-shaped detection coil 301, a second saddle-shaped detection coil 302, a third saddle-shaped detection coil 303, and a fourth saddle-shaped detection coil 304; The first saddle-shaped detection coil 301 and the second saddle-shaped detection coil 302 are arranged opposite each other in the y-axis direction, and the third saddle-shaped detection coil 303 and the fourth saddle-shaped detection coil 304 are arranged opposite each other in the x-axis direction.

[0012] Preferably, the second group of coils includes a fifth saddle-shaped detection coil 401, a sixth saddle-shaped detection coil 402, a seventh saddle-shaped detection coil 403, and an eighth saddle-shaped detection coil 404; The fifth saddle-shaped detection coil 401 and the sixth saddle-shaped detection coil 402 are arranged opposite each other in the y-axis direction, and the seventh saddle-shaped detection coil 403 and the eighth saddle-shaped detection coil 404 are arranged opposite each other in the x-axis direction.

[0013] Preferably, in S1, the magnetic vector potential expression is: (1) In formula (1), This represents the magnetic vector potential at a radial coordinate of r and an axial coordinate of z. Indicates the first constant coefficient; Indicates the second constant coefficient; Represents the first-order Bessel function of the first kind; denoted as the first-order Bessel function of the second kind; n represents a positive integer, n=1,2,3……; h represents the solution boundary of the magnetic vector potential equation in the z direction.

[0014] Preferably, in step S2, the reference induced voltage of the saddle-shaped detection coil under no-offset conditions is: , in, This represents the reference induced voltage of the k-th saddle-shaped detection coil under no-offset conditions; j represents the imaginary unit. Angular frequency; This represents the average circumferential span angle of the saddle-shaped detection coil in the sensor; Indicates the number of turns of the saddle-shaped detection coil; Indicates the radial width of the saddle-shaped detection coil; Indicates the axial width of the saddle-shaped detection coil; Indicates the axial starting position coordinates of the second group of coils; Indicates the inner diameter of the saddle-shaped detection coil; Indicates the outer diameter of the saddle-shaped detection coil; The magnetomotive force represents the induced voltage at a radial coordinate of r and an axial coordinate of z under the condition of no offset. This indicates the axial starting position coordinates of the first group of coils.

[0015] Preferably, in S3, the induced voltage model of the k-th saddle-shaped detection coil under the offset condition is expressed as: (2) In formula (2), This represents the first-order model of the induced voltage of the k-th saddle-shaped detection coil under offset conditions. This represents the reference induced voltage of the k-th saddle-shaped detection coil. This represents the first harmonic coefficient corresponding to the k-th saddle-shaped detection coil; This represents the circumferential center angle of the k-th radial saddle-shaped detection coil.

[0016] Preferably, in step S4, when the ferromagnetic rod 1 deflects, the deflection response term satisfies: , , (3) , In formula (3), This represents the voltage offset of the saddle-shaped coil located in the positive x-axis direction. This represents the voltage offset of the saddle coil located in the negative x-axis direction. This represents the voltage offset of the saddle coil located in the positive y-axis direction. The voltage offset of the saddle-shaped coil located in the negative y-axis direction; e represents the offset distance of the ferromagnetic rod relative to the central axis of the saddle-shaped detection coil; , , , These represent the first-order induced voltage response coefficients of the saddle-shaped coils located in the positive x-axis direction, negative x-axis direction, positive y-axis direction, and negative y-axis direction, respectively, to the radial displacement of the ferromagnetic rod. Indicates the offset angle; Then, the responses of the saddle-shaped detection coils in the y-axis and x-axis directions are differentially processed to construct the first offset characteristic component in the x-axis direction. and the second offset characteristic component in the y-axis direction ,Right now: (4) In formula (4), This represents the first offset characteristic component in the x-axis direction; This represents the second offset characteristic component in the y-axis direction.

[0017] Preferably, in step S4, the offset distance and offset angle are calculated as follows: (5) In formula (5), This indicates the offset distance of the ferromagnetic rod 1 relative to the central axis of the saddle-shaped detection coil; Indicates the offset angle; Represents the azimuth function; This represents the first offset characteristic component in the x-axis direction; This represents the second offset characteristic component in the y-axis direction.

[0018] In summary, by adopting the above technical solution, the present invention has at least the following beneficial effects compared with the prior art: (1) The present invention regards the radial offset of the rod as a state parameter that can be directly characterized by the circumferential distribution characteristics of the multi-channel induced voltage, thereby enabling quantitative detection of the rod offset distance and offset angle; (2) By subtracting the detection coils in the positive and negative directions (y-axis direction and x-axis direction), the offset amplitude and offset direction can be given simultaneously by the first harmonic components in the two orthogonal directions. This can effectively suppress common mode error and enhance the offset sensitivity, thereby improving identification stability. (3) The present invention is based on clear electromagnetic physical relationships and circumferential modulation characteristics. The calculation structure is clear and easy to implement in real time in a microcontroller or host computer system. It has good engineering application value. (4) No additional eccentricity detection sensor is required, making it easy to apply directly to existing displacement sensor systems based on multi-saddle-shaped detection coils. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of a radial offset detection method for a ferromagnetic rod based on voltage difference of multiple saddle-shaped detection coils according to an exemplary embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of a sensor structure according to an exemplary embodiment of the present invention.

[0021] Figure 3 This is a top view schematic diagram of a sensor structure according to an exemplary embodiment of the present invention. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to embodiments and specific implementation methods. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0023] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0024] like Figure 1As shown, this invention provides a method for detecting the radial offset of a ferromagnetic rod based on the voltage difference of multiple saddle-shaped detection coils, specifically including the following steps: S1: Establish the magnetic vector potential under the condition of no offset of the ferromagnetic rod in the sensor.

[0025] In this embodiment, as Figure 2 , Figure 3 As shown, the sensor includes a ferromagnetic rod 1 located in the central region, a circumferential excitation coil 2 arranged along the axial direction of the ferromagnetic rod 1, and multiple saddle-shaped detection coils distributed circumferentially. The circumferential excitation coil 2 is used to establish an alternating magnetic field around the ferromagnetic rod 1; the saddle-shaped detection coils are used to extract the induced voltage.

[0026] The circumferential excitation coil 2 is coaxially sleeved on the outside of the ferromagnetic rod 1, and a preset radial gap is maintained between it and the ferromagnetic rod 1; multiple saddle-shaped detection coils are attached and fixed to the outer surface of the circumferential excitation coil 2 along the circumferential direction.

[0027] In this embodiment, the saddle-shaped detection coil includes a first group of coils and a second group of coils. The first group of coils is located at the lower end of the circumferential excitation coil 2, and the second group of coils is located at the upper end of the circumferential excitation coil 2. That is, there is a certain interval d1 between the first group of coils and the second group of coils, and d1 > 0. The purpose of setting up two groups of saddle-shaped detection coils is to provide multi-position magnetic field response information, thereby effectively reducing the influence of factors such as local magnetic field distortion, coil manufacturing errors, installation errors, and environmental disturbances on the detection results, and improving the stability of radial offset feature extraction of the ferromagnetic rod 1 and the accuracy of radial offset direction and offset calculation.

[0028] The first set of coils includes a first saddle-shaped detection coil 301, a second saddle-shaped detection coil 302, a third saddle-shaped detection coil 303, and a fourth saddle-shaped detection coil 304. The first saddle-shaped detection coil 301, the third saddle-shaped detection coil 303, the second saddle-shaped detection coil 302, and the fourth saddle-shaped detection coil 304 are distributed circumferentially and evenly at the lower end of the circumferential excitation coil 2. The first saddle-shaped detection coil 301 and the second saddle-shaped detection coil 302 are arranged opposite each other, and the third saddle-shaped detection coil 303 and the fourth saddle-shaped detection coil 304 are arranged opposite each other. The purpose of this arrangement is to extract the response characteristics of the induced voltage of the saddle-shaped coils when the ferromagnetic rod 1 is radially offset in different directions.

[0029] The second group of coils includes a fifth saddle-shaped detection coil 401, a sixth saddle-shaped detection coil 402, a seventh saddle-shaped detection coil 403, and an eighth saddle-shaped detection coil 404. These coils are distributed circumferentially and evenly on the upper end of the circumferential excitation coil 2. The fifth saddle-shaped detection coil 401 and the sixth saddle-shaped detection coil 402 are arranged opposite each other, as are the seventh saddle-shaped detection coil 403 and the eighth saddle-shaped detection coil 404. This arrangement is intended to extract the response characteristics of the induced voltage of the saddle-shaped coils when the ferromagnetic rod 1 is radially offset in different directions.

[0030] In this embodiment, to facilitate the establishment of an analytical model, the electromagnetic field distribution of the sensor is described in a cylindrical coordinate system.

[0031] Based on Maxwell's electromagnetic field theory, the governing equations and boundary conditions for the circumferential component of the magnetic vector potential are established, and the expression for the magnetic vector potential is obtained using the method of separation of variables. The magnetic vector potential can be expressed as a first-order Bessel function containing the first and second kinds. , If the magnetic vector potential is in series form, then the expression for the magnetic vector potential is: (1) In formula (1), This represents the magnetic vector potential at a radial coordinate of r and an axial coordinate of z. Indicates the first constant coefficient. The second constant coefficient is determined by the governing equations, boundary conditions, and continuity conditions of adjacent regions. and These are constant coefficients determined by solving the boundary conditions of the magnetic vector potential equation; Represents the first-order Bessel function of the first kind; denoted as the first-order Bessel function of the second kind; n represents a positive integer, n=1,2,3……; h represents the solution boundary of the magnetic vector potential equation in the z direction.

[0032] S2: Calculate the reference induced voltage of the saddle-shaped detection coil based on the magnetic vector potential.

[0033] When the central axis of the ferromagnetic rod 1 coincides with the central axis of the saddle-shaped detection coil, the entire sensor structure can be equivalent to an axisymmetric structure.

[0034] Since the saddle-shaped coil is an arc, let the central angle of the k-th radial saddle-shaped detection coil be . Then the average circumferential span angle of the saddle-shaped detection coil in the entire sensor is: (2) In formula (2), This represents the average circumferential span angle of the saddle-shaped detection coil in the sensor; Represented as the span angle of the inner circumference, It represents the span angle of the outer circumference.

[0035] In this embodiment, each saddle-shaped detection coil has the same structure and the number of turns is... The radial width is axial width is The axial z-positions corresponding to the top and bottom of a saddle-shaped coil are respectively and The inner and outer radii of the saddle-shaped detection coil are respectively , The reference induced voltage of the k-th saddle-shaped detection coil under no-offset conditions can be obtained in the following general form: , in This represents the reference induced voltage of the k-th saddle-shaped detection coil under no-offset conditions; j represents the imaginary unit. Angular frequency; This represents the average circumferential span angle of the saddle-shaped detection coil in the sensor; Indicates the number of turns of the saddle-shaped detection coil; Indicates the radial width of the saddle-shaped detection coil; Indicates the axial width of the saddle-shaped detection coil; Indicates the axial starting position coordinates of the second group of coils; Indicates the inner diameter of the saddle-shaped detection coil; Indicates the outer diameter of the saddle-shaped detection coil; The magnetomotive force represents the induced voltage at a radial coordinate of r and an axial coordinate of z under the condition of no offset. This indicates the axial starting position coordinates of the first group of coils.

[0036] As can be seen from the above formula, the reference induced voltage of the k-th saddle-shaped detection coil under the condition of no offset is jointly determined by the number of coil turns, the average span angle of the circumference, the radial width, the axial width, and the non-offset magnetic vector potential within its coverage area.

[0037] S3: Construct an induced voltage model under offset conditions based on the reference induced voltage and offset parameters of the saddle-shaped detection coil; the offset parameters include offset distance and offset angle.

[0038] In this embodiment, let the offset vector of the ferromagnetic rod 1 relative to the central axis of the saddle-shaped detection coil be defined. for: (3) In formula (3), Represents the offset vector; This indicates the offset distance of the ferromagnetic rod 1 relative to the central axis of the saddle-shaped detection coil; Indicates the offset angle.

[0039] Then, under the offset condition (offset angle is...), The first-order model of the induced voltage of the k-th saddle-shaped detection coil can be expressed as: (4) In formula (4), Indicates the offset condition (offset angle is) The first-order model of the induced voltage of the k-th saddle-shaped detection coil; This represents the reference induced voltage of the k-th saddle-shaped detection coil; This represents the first harmonic coefficient corresponding to the k-th saddle-shaped detection coil; This represents the circumferential center angle of the k-th radial saddle-shaped detection coil; This represents the induced voltage offset of the k-th saddle-shaped detection coil when the ferromagnetic rod undergoes radial displacement.

[0040] It can be seen that after the ferromagnetic rod 1 undergoes radial displacement, the induced voltage of the saddle-shaped detection coil exhibits an angular modulation pattern dominated by the first harmonic along the circumferential direction.

[0041] Correspondingly, the first harmonic coefficient of the k-th saddle-shaped detection coil can be expressed in the following general form: (5) In formula (5), This represents the first harmonic coefficient corresponding to the k-th saddle-shaped detection coil; denoted by r, which represents the partial derivative of the magnetic vector potential with respect to the radial coordinate under the condition of no offset; r represents the radial coordinate.

[0042] Therefore, it can be seen that a first-order model of the offset voltage can be established based solely on the magnetic vector potential and its radial coordinate derivative under the condition of no offset.

[0043] S4: Construct offset characteristic components based on the induced voltage model under offset conditions, and calculate the offset distance and offset angle.

[0044] In this embodiment, as Figure 3 As shown, the explanation will be based on the first group of coils.

[0045] The first saddle-shaped detection coil 301, the third saddle-shaped detection coil 303, the second saddle-shaped detection coil 302, and the fourth saddle-shaped detection coil 304 are distributed circumferentially and evenly at the lower end of the circumferential excitation coil 2. The first saddle-shaped detection coil 301 and the second saddle-shaped detection coil 302 are arranged opposite each other in the y-axis direction (symmetrically arranged at 180° intervals) to extract the y-axis offset feature. The y-axis offset feature is constructed by the differential induced voltage of the first saddle-shaped detection coil 301 and the second saddle-shaped detection coil 302 and is used to characterize the radial offset component of the ferromagnetic rod in the y-axis direction. The third saddle-shaped detection coil 303 and the fourth saddle-shaped detection coil 304 are arranged opposite each other in the x-axis direction (symmetrically arranged at 180° intervals) to extract the x-axis offset feature. The x-axis offset feature is constructed by the differential induced voltage of the third saddle-shaped detection coil 303 and the fourth saddle-shaped detection coil 304 and is used to characterize the radial offset component of the ferromagnetic rod in the x-axis direction.

[0046] Furthermore, based on the x-axis offset characteristics and y-axis offset characteristics, the radial offset distance and offset angle of the ferromagnetic rod can be further determined.

[0047] In this embodiment, when the ferromagnetic rod 1 is not deflected, the reference induced voltages of the relatively positioned saddle-shaped detection coils are equal (i.e., the reference induced voltages of the first saddle-shaped detection coil 301 and the second saddle-shaped detection coil 302 are equal). The reference induced voltages of the third saddle-shaped detection coil 303 and the fourth saddle-shaped detection coil 304 are equal. ; When the ferromagnetic rod 1 deflects, the changes in the induced voltages of the four saddle-shaped coils 303, 304, 301, and 302 satisfy a relationship of opposite signs: , , (6) , In formula (6), This represents the voltage change of the saddle-shaped coil 303 located in the positive x-axis direction. This represents the voltage change of the saddle-shaped coil 304 located in the negative x-axis direction. This represents the voltage change of the saddle-shaped coil 301 located in the positive y-axis direction. The voltage change of the saddle-shaped coil 302 located in the negative y-axis direction; e represents the offset distance of the ferromagnetic rod 1 relative to the central axis of the saddle-shaped detection coil; , , , The first-order induced voltage response coefficients of the saddle coil located in the positive and negative directions of the x-axis (x+, x-) and the positive and negative directions of the y-axis (y+, y-) to the radial displacement of the ferromagnetic rod are respectively calculated using formula (5) in this embodiment. Indicates the offset angle.

[0048] Specifically, The offset voltage response coefficient of the saddle-shaped coil 303 in the positive x-axis direction is represented by... This represents the offset voltage response coefficient of the saddle-shaped coil 304 in the negative x-axis direction. This represents the offset voltage response coefficient of the saddle-shaped coil 301 in the positive y-axis direction. This represents the offset voltage response coefficient of the saddle-shaped coil 302 in the negative y-axis direction; To mitigate the common-mode effects of concentric residuals, power supply fluctuations, and manufacturing errors, and to enhance the first harmonic term caused by offset, the responses of the saddle-shaped detection coils in the y-axis and x-axis directions are differentially processed to construct the first offset characteristic component in the x-axis direction. and the second offset characteristic component in the y-axis direction ,Right now: (7) In formula (7), This represents the first offset characteristic component in the x-axis direction; This represents the second offset characteristic component in the y-axis direction.

[0049] When the structure and winding parameters of the radial saddle-shaped detection coil satisfy the symmetry condition, it is often true that... , Then formula (6) can be further simplified to: (8) In formula (8), The first-order equivalent induced voltage response coefficient of a pair of saddle-shaped detection coils located in the positive and negative x-axis directions to the x-axis offset component of the ferromagnetic rod is represented. This represents the first-order equivalent induced voltage response coefficient of a pair of saddle-shaped detection coils located in the positive and negative y-axis directions to the y-axis offset component of the ferromagnetic rod.

[0050] Then, based on the first offset feature component in the x-axis direction... and the second offset characteristic component in the y-axis direction The magnitude and direction of the offset of the ferromagnetic rod 1 were determined: (9) In formula (9), This indicates the offset distance of the ferromagnetic rod 1 relative to the central axis of the saddle-shaped detection coil; Indicates the offset angle; This represents the azimuth function.

[0051] The physical meaning of formula (8) is that after the ferromagnetic rod 1 undergoes radial displacement, the circumferential symmetry of the original concentric structure is destroyed, and the induced voltage of the saddle-shaped detection coil along the circumferential direction exhibits angular modulation dominated by the amplitude of the first harmonic. Its variation law can be approximately expressed as cos(θ−β). Since the first saddle-shaped detection coil 301, the third saddle-shaped detection coil 303, the second saddle-shaped detection coil 302, and the fourth saddle-shaped detection coil 304 are located in four orthogonal orientations, it is equivalent to sampling four typical points of the circumferential distribution. Therefore, by subtracting the y-axis direction and the x-axis direction, the cosine component and sine component of the first harmonic can be extracted respectively. Then, by synthesizing the amplitude and phase angle relationship, the displacement amount and displacement direction can be obtained.

[0052] Those skilled in the art will understand that the above embodiments are specific examples of implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.

Claims

1. A method for detecting radial offset of a ferromagnetic rod based on voltage differential of multiple saddle-shaped detection coils, characterized in that, Includes the following steps: S1: Establish the magnetic vector potential under the condition that the ferromagnetic rod in the sensor has no offset; S2: Calculate the reference induced voltage of the saddle-shaped detection coil under the condition of no offset based on the magnetic vector potential; S3: Construct an induced voltage model under offset conditions based on the reference induced voltage and offset parameters of the saddle-shaped detection coil; S4: Construct offset characteristic components based on the induced voltage model under offset conditions, and calculate the offset distance and offset angle.

2. The radial offset detection method for a ferromagnetic rod based on voltage differential of multiple saddle-shaped detection coils as described in claim 1, characterized in that, In S1, the sensor includes a ferromagnetic rod (1) located in the central region, a circumferential excitation coil (2) and multiple saddle-shaped detection coils; Among them, the circumferential excitation coil (2) is set on the outer surface of the ferromagnetic rod (1), and multiple saddle-shaped detection coils are circumferentially distributed on the outer surface of the circumferential excitation coil (2).

3. The radial offset detection method for ferromagnetic rods based on voltage differential of multi-saddle-shaped detection coils as described in claim 2, characterized in that, The saddle-shaped detection coil includes a first group of coils and a second group of coils; the first group of coils is located at the lower end of the circumferential excitation coil (2), and the second group of coils is located at the upper end of the circumferential excitation coil (2). There is a certain interval distance d1 between the first group of coils and the second group of coils, where d1 > 0.

4. The radial offset detection method for a ferromagnetic rod based on voltage difference of multiple saddle-shaped detection coils as described in claim 3, characterized in that, The first group of coils includes a first saddle-shaped detection coil (301), a second saddle-shaped detection coil (302), a third saddle-shaped detection coil (303), and a fourth saddle-shaped detection coil (304). The first saddle-shaped detection coil (301) and the second saddle-shaped detection coil (302) are arranged opposite each other in the y-axis direction, and the third saddle-shaped detection coil (303) and the fourth saddle-shaped detection coil (304) are arranged opposite each other in the x-axis direction.

5. The radial offset detection method for a ferromagnetic rod based on voltage differential of multiple saddle-shaped detection coils as described in claim 3, characterized in that, The second group of coils includes a fifth saddle-shaped detection coil (401), a sixth saddle-shaped detection coil (402), a seventh saddle-shaped detection coil (403), and an eighth saddle-shaped detection coil (404). The fifth saddle-shaped detection coil (401) and the sixth saddle-shaped detection coil (402) are arranged opposite each other in the y-axis direction, and the seventh saddle-shaped detection coil (403) and the eighth saddle-shaped detection coil (404) are arranged opposite each other in the x-axis direction.

6. The radial offset detection method for a ferromagnetic rod based on voltage differential of multiple saddle-shaped detection coils as described in claim 1, characterized in that, In S1, the expression for the magnetic vector potential is: （1） In formula (1), This represents the magnetic vector potential at a radial coordinate of r and an axial coordinate of z. Indicates the first constant coefficient; Indicates the second constant coefficient; Represents the first-order Bessel function of the first kind; denoted as the first-order Bessel function of the second kind; n represents a positive integer, n=1,2,3……; h represents the solution boundary of the magnetic vector potential equation in the z direction.

7. The radial offset detection method for a ferromagnetic rod based on voltage differential of multiple saddle-shaped detection coils as described in claim 1, characterized in that, In S2, the reference induced voltage of the saddle-shaped detection coil under the condition of no offset is: ， in, This represents the reference induced voltage of the k-th saddle-shaped detection coil under no-offset conditions; j represents the imaginary unit. Angular frequency; This represents the average circumferential span angle of the saddle-shaped detection coil in the sensor; Indicates the number of turns of the saddle-shaped detection coil; Indicates the radial width of the saddle-shaped detection coil; Indicates the axial width of the saddle-shaped detection coil; Indicates the axial starting position coordinates of the second group of coils; Indicates the inner diameter of the saddle-shaped detection coil; Indicates the outer diameter of the saddle-shaped detection coil; The magnetomotive force represents the induced voltage at a radial coordinate of r and an axial coordinate of z under the condition of no offset. This indicates the axial starting position coordinates of the first group of coils.

8. The radial offset detection method for a ferromagnetic rod based on voltage differential of multiple saddle-shaped detection coils as described in claim 1, characterized in that, In S3, the induced voltage model of the k-th saddle-shaped detection coil under the offset condition is expressed as: （2） In formula (2), This represents the first-order model of the induced voltage of the k-th saddle-shaped detection coil under offset conditions. This represents the reference induced voltage of the k-th saddle-shaped detection coil. This represents the first harmonic coefficient corresponding to the k-th saddle-shaped detection coil; This represents the circumferential center angle of the k-th radial saddle-shaped detection coil.

9. The radial offset detection method for a ferromagnetic rod based on voltage differential of multiple saddle-shaped detection coils as described in claim 1, characterized in that, In S4, when the ferromagnetic rod (1) is deflected, the deflection response term satisfies: ， ， ，（3） ， In formula (3), This represents the voltage offset of the saddle-shaped coil located in the positive x-axis direction. This represents the voltage offset of the saddle coil located in the negative x-axis direction. This represents the voltage offset of the saddle coil located in the positive y-axis direction. The voltage offset of the saddle-shaped coil located in the negative y-axis direction; e represents the offset distance of the ferromagnetic rod relative to the central axis of the saddle-shaped detection coil; , , , These represent the first-order induced voltage response coefficients of the saddle-shaped coil located in the positive x-axis direction, negative x-axis direction, positive y-axis direction, and negative y-axis direction, respectively, to the radial displacement of the ferromagnetic rod. Indicates the offset angle; Then, the responses of the saddle-shaped detection coils in the y-axis and x-axis directions are differentially processed to construct the first offset characteristic component in the x-axis direction. and the second offset characteristic component in the y-axis direction ,Right now: （4） In formula (4), This represents the first offset characteristic component in the x-axis direction; This represents the second offset characteristic component in the y-axis direction.

10. The radial offset detection method for a ferromagnetic rod based on voltage differential of multiple saddle-shaped detection coils as described in claim 1, characterized in that, In step S4, the offset distance and offset angle are calculated as follows: （5） In formula (5), This indicates the offset distance of the ferromagnetic rod (1) relative to the central axis of the saddle-shaped detection coil; Indicates the offset angle; Represents the azimuth function; This represents the first offset characteristic component in the x-axis direction; This represents the second offset characteristic component in the y-axis direction.

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