Analytical Model of Eddy Current Angular Position Sensor and High Signal-to-Noise Ratio Optimization Design Method

Abstract

The present invention discloses a high signal-to-noise ratio optimization design method for an eddy current angular position sensor, which relates to the field of eddy current angular position sensors. First, a three-dimensional equivalent magnetic circuit model of the sensor is established, the equivalent average magnetic density of the rotor eddy current on the receiving coil surface is defined, and the calculation formula of the induced voltage of the receiving coil expressed by the equivalent average magnetic density is given according to Faraday's law of electromagnetic induction. Then, a two-dimensional simplified electromagnetic model of the exciting coil-rotor is established, and the Fourier transform method is used to solve the magnetic fields in the rotor region and the air gap region; an equivalent average magnetic density correction coefficient is introduced, and the equivalent average magnetic density of the rotor eddy current is calculated and corrected according to the air gap magnetic density distribution, and the corrected calculation formula of the induced voltage of the receiving coil is obtained, and then an analytical model from each design parameter to the induced voltage of the receiving coil is obtained; through this analytical model, the optimal design parameter combination that enables the sensor output voltage signal to obtain a high signal-to-noise ratio under different size requirements and excitation conditions can be determined.

Description

Technical Field

[0001] The present invention relates to the field of eddy current angular position sensors, and particularly to an analytical model of an eddy current angular position sensor and a high signal-to-noise ratio optimization design method for an eddy current angular position sensor based on the analytical model. Background Art

[0002] Absolute angular position measurement is a key factor affecting the performance in a wide range of motor closed-loop control systems. Magnetic sensors are one of the most commonly used position sensors, and according to the excitation method of the signal, magnetic sensors can be divided into two categories. Hall effect-based sensors, typified by magnetic encoders, are vulnerable to harsh external environments; resolver transformers based on electromagnetic induction have stronger environmental robustness, but their large size and weight limit their application scenarios. Eddy current sensors based on electromagnetic induction overcome the above disadvantages and have obvious advantages of small size, light weight, low cost, and strong robustness. Among eddy current angular position sensors with different structures, the sine-shaped coil structure has the advantages of through-axis installation and arc design, and can meet the needs of more diverse installation environments.

[0003] The existing design methods for sine coil eddy current angular position sensors are all based on the finite element analysis method, which has a large amount of calculation and requires a long time, and cannot explicitly represent the relationship between the sensor design parameters and their performance. In order to improve the design and optimization efficiency of this sensor, the present invention proposes an analytical model and a corresponding high signal-to-noise ratio optimization design method, clarifies the quantitative relationship between its output voltage and structural parameters and electromagnetic parameters, and provides an effective method for optimization design aiming at improving its signal-to-noise ratio. Summary of the Invention

[0004] The purpose of the present invention is to provide an analytical model of an eddy current angular position sensor and a high signal-to-noise ratio optimization design method for an eddy current angular position sensor based on the analytical model. Through this analytical model, the optimal design parameter combination that enables the sensor output voltage signal to obtain a high signal-to-noise ratio under different size requirements and excitation conditions can be determined.

[0005] To achieve the above purpose, the present invention adopts the following technical solutions:

[0006] In the first aspect, the present invention provides an analytical model of an eddy current angular position sensor. The eddy current angular position sensor is a sine coil eddy current angular position sensor. The establishment of the analytical model includes the following steps:

[0007] Based on the cylindrical coordinate system, establish a three-dimensional magnetic circuit model of the exciting coil, receiving coil, and rotor in space, and give the coordinate expressions of the trajectories of the exciting coil and the sine-shaped receiving coil;

[0008] In the three-dimensional magnetic circuit model, the equivalent average magnetic density of the rotor eddy current in the projected area of the rotor within the plane of the receiving coil is defined, and according to Faraday's law of electromagnetic induction, the induced voltage expression of each phase of the receiving coil represented by the equivalent average magnetic density of the rotor eddy current is obtained;

[0009] For the excitation coil - air gap - rotor system, take its radial cross-section, establish a simplified two-dimensional Cartesian coordinate system electromagnetic model, derive the diffusion equation satisfied by the magnetic field in the rotor conductor region and the magneto-quasi-static equation satisfied by the magnetic field in the air gap region through Maxwell's equations, and solve them using the Fourier transform method to calculate the air gap magnetic density distribution;

[0010] According to the air gap magnetic density distribution, introduce an equivalent average magnetic density correction coefficient, calculate and correct the equivalent average magnetic density of the rotor eddy current to obtain the corrected average magnetic density, and further obtain the calculation formula for the induced voltage of each phase of the receiving coil after correction;

[0011] From the calculation formula for the induced voltage of each phase of the receiving coil, construct an analytical model from each design parameter to the induced voltage of the receiving coil.

[0012] Furthermore, based on the cylindrical coordinate system, establish a three-dimensional magnetic circuit model of the excitation coil, receiving coil, and rotor in space, and give the coordinate expressions of the trajectories of the excitation coil and the sinusoidal receiving coil, including:

[0013] Select the main parameters of the three-dimensional magnetic circuit model, including the number of pole pairs of the eddy current sensor p , air gap thickness H a , the PCB layer spacing where the receiving coil is located H l , the size parameters of the receiving coil k 1. k 2;

[0014] According to the main parameters of the three-dimensional magnetic circuit model, determine the coordinate expressions of the trajectories of the excitation coil and the sinusoidal receiving coil represented by the rotor rotation angle θ in the cylindrical coordinate system.

[0015] Furthermore, in the three-dimensional magnetic circuit model, the equivalent average magnetic density of the rotor eddy current in the projected area of the rotor within the plane of the receiving coil is defined, and according to Faraday's law of electromagnetic induction, the induced voltage expression of each phase of the receiving coil represented by the equivalent average magnetic density of the rotor eddy current is obtained, including:

[0016] In the three-dimensional magnetic circuit model, give the definition formula of the equivalent average magnetic density of the rotor eddy current in the projected area of the rotor within the plane of the receiving coil, which is calculated from the air gap magnetic density distribution;

[0017] Calculate the induced voltage of each clockwise turn of the receiving coil according to Faraday's law of electromagnetic induction based on the number of pole pairs of the sensor, air gap thickness, PCB layer spacing, inner and outer diameter size parameters of the receiving coil, and the equivalent average magnetic density of the rotor eddy current. V R+ ;

[0018] Calculate the induced voltage of each counterclockwise turn of the receiving coil according to Faraday's law of electromagnetic induction based on the number of pole pairs of the sensor, air gap thickness, PCB layer spacing, inner and outer diameter size parameters of the receiving coil, and the equivalent average magnetic density of the rotor eddy current. V R- ;

[0019] Based on the reverse series relationship between the clockwise turns and counterclockwise turns of each phase of the receiving coil, the induced voltage of each phase of the receiving coil V R = V R+ - V R- , and obtain the calculation formula for the induced voltage of each phase of the receiving coil.

[0020] Furthermore, for the excitation coil - air gap - rotor system, take its radial cross-section, establish a simplified two-dimensional Cartesian coordinate system electromagnetic model, derive the diffusion equation satisfied by the magnetic field in the rotor conductor region and the magnetostatic equation satisfied by the magnetic field in the air gap region through Maxwell's equations, solve using the Fourier transform method, and calculate the air gap magnetic density distribution, including:

[0021] For the excitation coil - air gap - rotor system, take its radial cross-section to establish a simplified two-dimensional Cartesian coordinate system electromagnetic model, write the diffusion equation for the magnetic field in the rotor conductor region and the magnetostatic equation for the magnetic field in the air gap region, and solve them simultaneously through boundary conditions to calculate the magnetic density in the air gap region;

[0022] The air gap magnetic density expression contains the sum of two terms. The first term is the rotor eddy current magnetic density, and the second term is the exciting current magnetic density. Thus, obtain the z radial component of the rotor eddy current air gap magnetic density.

[0023] Furthermore, according to the air gap magnetic density distribution, introduce an equivalent average magnetic density correction coefficient, calculate and correct the equivalent average magnetic density to obtain the corrected average magnetic density, and then obtain the corrected calculation formula for the induced voltage of each phase of the receiving coil, including:

[0024] According to the z radial component distribution of the rotor eddy current air gap magnetic density in the plane of the two-layer receiving coil, calculate the equivalent average magnetic density of the rotor eddy current in the plane of the two-layer receiving coil;

[0025] According to the distribution of the z - component of the rotor eddy - current air - gap magnetic density in the plane of the two - layer receiving coils, an equivalent average magnetic density correction coefficient is introduced to correct the equivalent average magnetic density of the rotor eddy - current, obtaining the corrected average magnetic density, and further obtaining the calculation formula for the induced voltage of each phase of the receiving coil after correction.

[0026] Furthermore, from the calculation formula for the induced voltage of each phase of the receiving coil, an analytical model from each design parameter to the induced voltage of the receiving coil is constructed, including:

[0027] The induced voltages of the sine - phase and cosine - phase of the receiving coil are calculated by the following formulas respectively:

[0028] ;

[0029] Among them, there are three factors, namely the amplitude term, the high - frequency carrier term, and the low - frequency modulation term;

[0030] Where V m is the amplitude term, is the low - frequency modulation phase of the sine - phase induced voltage, is the low - frequency modulation phase of the cosine - phase induced voltage, is the high - frequency carrier term, ω m is the rotor mechanical angular frequency, ω f is the angular frequency of the exciting current, T is the rotation time of the rotor starting from the zero - position angle;

[0031] The sine - phase and cosine - phase induced voltages have the same amplitude term V m , which is a function of six design parameters, that is where k 1 is the receiving - coil size parameter, H a is the air - gap thickness, H l is the PCB layer - spacing where the receiving coil is located, ω f is the angular frequency of the exciting current, I f is the effective value of the exciting current, σ c is the conductivity of the rotor material.

[0032] On the second aspect, the present invention provides a high - signal - to - noise ratio optimization design method based on this analytical model. From this analytical model, it can be known that the output - voltage amplitude of this sensor is related to the following six parameters:

[0033] a) Size parameter k 1, H a ,H l ;

[0034] b) Electromagnetic parameters ω f , I f ,σ c ;

[0035] Among them, k 1 is the size parameter of the receiving coil, H a is the air gap thickness, H l is the PCB layer spacing where the receiving coil is located, ω f is the angular frequency of the excitation current, I f is the effective value of the excitation current, σ c is the conductivity of the rotor material;

[0036] According to the specific size requirements and excitation conditions under different assembly and operation conditions, determine the fixed design parameters among the above parameters, as well as the feasible region of the variable design parameters; substitute the fixed design parameters into the analytical model to obtain the relationship between the target parameter output voltage amplitude and the variable design parameters; take the maximization of the output voltage amplitude under the same outer dimensions as the objective function, and the feasible region of the variable design parameters as the constraint condition, establish a nonlinear programming problem and solve it to obtain the combination of variable design parameters that satisfies the objective function, that is, obtain the optimal design parameter combination that enables the sensor output voltage signal to obtain a higher signal-to-noise ratio under this condition.

[0037] Advantages of the present invention:

[0038] Through the analytical model of the eddy current angular position sensor of the present invention, the optimal design parameter combination that enables the sensor output voltage signal to obtain a higher signal-to-noise ratio under different size requirements and excitation conditions can be determined. Compared with the prior art, the analytical model proposed by the present invention explicitly represents the relationship between the design parameters of the eddy current angular position sensor and its performance, improves the design and optimization efficiency of the sensor, provides a quantitative relationship between its output voltage and structural parameters and electromagnetic parameters, has strong universality, and provides an effective method for the optimization design aiming at improving its signal-to-noise ratio. Description of the drawings

[0039] Figure 1 is a structural schematic diagram of a 3-pole sinusoidal coil eddy current angular position sensor provided by an embodiment of the present invention;

[0040] Figure 2 is a schematic diagram of the establishment process of the analytical model of the sinusoidal coil eddy current angular position sensor provided by an embodiment of the present invention;

[0041] Figure 3 It is a schematic diagram for calculating the three-dimensional magnetic circuit model provided by an embodiment of the present invention;

[0042] Figure 4 It is a schematic diagram for calculating the two-dimensional simplified electromagnetic model of the excitation coil - air gap - rotor system provided by an embodiment of the present invention;

[0043] Figure 5 It is a high signal-to-noise ratio optimization design flow chart of the sine coil eddy current angular position sensor provided by an embodiment of the present invention. Detailed implementation manners

[0044] In order to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions in the specific embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0045] Figure 1 It is a schematic structural diagram of a 3-pole pair sine coil eddy current angular position sensor provided by an embodiment of the present invention. As Figure 1 shown, for the eddy current sensor with the number of pole pairs being p , its excitation coil is printed on the Bottom layer of the PCB. The sine-shaped receiving coil is printed in segments through vias on the Bottom layer and the Top layer of the same PCB, and consists of sine and cosine two phases, with a phase difference of π / p between the two phases; each phase is composed of two turns connected in reverse series, and the phase difference between the two turns is π . The conductive material rotor is a uniformly distributed p sectors, and the central angle corresponding to each is π / p , covering the coil in the z direction and separated by an air gap. The clockwise turn and the counterclockwise turn of the cosine phase of the receiving coil are in a reverse series relationship.

[0046] The establishment process of the analytical model of the present invention is as Figure 2 shown and includes the following steps:

[0047] S101. Establish a three-dimensional magnetic circuit model of the excitation coil, the receiving coil, and the rotor in space based on the cylindrical coordinate system ( xyz coordinate system), and give the coordinate expressions of the trajectories of the excitation coil and the receiving coil, including:

[0048] Taking the cosine-phase receiving coil as an example, give the expressions of the trajectories of the clockwise turn and the counterclockwise turn of the cosine-phase receiving coil in the cylindrical coordinate system ( rz coordinate system), which are respectively:

[0049]

[0050] Among them,r + and z + represent the coordinates of the clockwise turns of the cos-phase receiving coil, r - and z - represent the coordinates of the counterclockwise turns of the cos-phase receiving coil, θ is the rotor rotation angle, k 1, k 2 are the size parameters of the receiving coil. The inner diameter of the receiving coil is k 2 - k 1, and the outer diameter of the receiving coil is k 2 + k 1, t 、 b are the z coordinates of the upper and lower layers of the PCB respectively.

[0051] The excitation coil trajectory is represented in the cylindrical coordinate system ( rz coordinate system) as:

[0052]

[0053] where, R F is the radius of the excitation coil, r F 、z F represents the coordinates of the excitation coil.

[0054] The layer spacing of the PCB where the receiving coil is located is H l , and the distance from the rotor surface to the lower layer of the PCB is the air gap thickness H a , then t , b satisfies:

[0055]

[0056] S102. In the three-dimensional magnetic circuit model, define the equivalent average magnetic density of the rotor eddy current in the projected area of the rotor in the plane of the receiving coil. According to Faraday's law of electromagnetic induction, obtain the induced voltage expression of each phase of the receiving coil represented by the equivalent average magnetic density.

[0057] The surfaces enclosed by the clockwise turns of the cos-phase receiving coil are distributed in segments on z = t and z = b planes, and the normal direction is z direction. It is considered that the rotor eddy current magnetic field is only distributed within the range of its xy plane projection. AsFigure 3 As shown, the area of the single-rotor eddy current magnetic field linked with the clockwise turns of the cos-phase receiving coil is S cover . According to the electromagnetic induction law, the induced voltage of the clockwise turns of the cos-phase receiving coil V R+ is:

[0058]

[0059] Where: is the z-component of the rotor eddy current magnetic density, T is the rotor rotation time starting from the zero position angle.

[0060] The projections of the rotor on the z = t and z = b planes are respectively . In the z = t and z = b planes, the z-components of the rotor eddy current magnetic density z are respectively . That is, in the z = t plane, the z-component of the rotor eddy current magnetic density z is . In the z = b plane, the z-component of the rotor eddy current magnetic density z is .

[0061] The average value of the z-component of the rotor eddy current magnetic density in the region at each moment is a sine wave with the same frequency and opposite phase as the excitation current. Its amplitude remains constant at any moment during the rotor rotation, and its expression is:

[0062]

[0063] Where is its amplitude, defined as the equivalent average magnetic density of the rotor eddy current; ω f is the angular frequency of the excitation current, T is the rotor rotation time starting from the zero position angle.

[0064] Furthermore, S cover The part in the z = t plane is S t . In thez = b The part on the plane is S b , that is , then V R+ The expression can be rewritten as:

[0065]

[0066] S t , S b and their respective calculation formulas for the derivative of the rotor rotation angle θ are:

[0067]

[0068] where represents the integration variable in this integral formula.

[0069] Furthermore, the mechanical angular velocity of the rotor is ω m , there is θ = ω m T, T is the rotor rotation time starting from the zero position angle ， then V R+ can be calculated by the following formula:

[0070]

[0071] Similarly, the induced voltage expression of the cosine-phase counterclockwise turns of the receiving coil is:

[0072]

[0073] From the reverse series relationship between its counterclockwise turns and clockwise turns, and the definition of the equivalent average magnetic density of the rotor eddy current mentioned above, the induced voltage of the cosine phase of the receiving coil can be calculated by the following formula:

[0074]

[0075] Furthermore, since at the operating speed of the sensor there is , the first term in the above formula can be ignored. Therefore, the induced voltage expression of the cosine phase of the receiving coil is:

[0076]

[0077] Since there is a spatial phase difference of π / 2p between the sine phase and the cosine phase in the circumferential direction of the sensor, the induced voltage expression of the sine phase of the receiving coil is:

[0078]

[0079] S103. For the excitation coil - air gap - rotor system, establish a simplified two - dimensional Cartesian coordinate system electromagnetic model for its radial section, and calculate the air gap magnetic flux density distribution.

[0080] Figure 4 It is a calculation schematic diagram of the two - dimensional simplified electromagnetic model of the excitation coil - air gap - rotor system. As Figure 4 shown, in the Cartesian coordinate system, take any radial section of the excitation coil - air gap - rotor system as the yz plane. Ignoring the edge effect, the rotor can be regarded as an infinitely large flat plate relative to the excitation coil, and the air gap can be regarded as an infinitely large air region. Therefore, the electromagnetic field calculation for any radial section of the coil - air gap - rotor system is equivalent. The conductive rotor (hereinafter referred to as the conductor) satisfies , where and are the conductivity and permittivity of the conductor respectively. Therefore, the displacement current in the conductor region can be ignored. Substitute the constitutive equation of the conductor into Maxwell's equations, and the magnetic flux density in the conductor region satisfies the diffusion equation:

[0081]

[0082] where is the vacuum permeability (H / m).

[0083] Regard the electromagnetic field in the air gap region as a magnetoquasistatic field, and the magnetic flux density in the air gap region satisfies the equation:

[0084]

[0085] where is the line current density of the excitation current, which is expressed by the following formula:

[0086]

[0087] where, and are the line current coordinates represented by the Dirac function, h is the z - coordinate of the line current; is the unit vector in the z - direction.

[0088] Introduce the vector magnetic potential A , and take the Coulomb gauge . It is easy to know from the model structure that , (where, A x、 A y andA z For A of x the direction towards, y and z the modulus of the component in the direction towards, e x is x the unit vector in the direction). Thus, the following vector magnetic potential A is all expressed as a scalar . From the diffusion equation of, the vector magnetic potential y in the conductor region (<0) satisfies the diffusion equation:

[0089]

[0090] When the rotor is stationary, in an ideal situation, the electromagnetic field in the exciting coil - air gap - rotor system is a non - harmonic time - harmonic field. Therefore the equation of can be expressed as:

[0091]

[0092] where, j is the imaginary unit.

[0093] To solve it, the Fourier transform and inverse transform are introduced, k is the frequency variable of the Fourier transform. Taking the Fourier transform of both sides of the equation of gives the corresponding spatial frequency - domain function satisfying the spatial frequency - domain equation:

[0094]

[0095] From the general solution structure of the homogeneous linear differential equation with constant coefficients, discarding the divergent terms, the general solution of this equation can be obtained as:

[0096]

[0097] where , are undetermined coefficients.

[0098] From the inverse Fourier transform, the general solution is:

[0099]

[0100] From the equation of, the vector magnetic potential y in the air region (>0) satisfies the Poisson equation:

[0101]

[0102] Taking the Fourier transform of both sides, we get The corresponding spatial frequency domain function The spatial frequency domain equation satisfied by:

[0103]

[0104] From the structure of the solution of the non - homogeneous linear differential equation with constant coefficients, it can be seen that the solution of this equation consists of a particular solution and the homogeneous general solution of its corresponding homogeneous differential equation which respectively correspond to the exciting current field and the eddy current field.

[0105] From the general solution structure of the homogeneous linear differential equation with constant coefficients, discarding the divergent terms therein, we can obtain :

[0106]

[0107] where are undetermined coefficients.

[0108] Next, we solve the particular solution of this equation. Due to the existence of the Dirac function in the equation, we need to perform a regional treatment on z . At z ≠ h , the equation becomes a homogeneous equation , and the general solution of this homogeneous equation is:

[0109]

[0110] where , are undetermined coefficients.

[0111] Discarding the divergent terms at infinity, we can obtain

[0112]

[0113] According to the boundary conditions

[0114]

[0115] where z→h + and z→h - respectively represent approaching z = h infinitely from the positive and negative directions.

[0116] We can obtain , so can be expressed as:

[0117]

[0118] Among them, is the updated undetermined coefficient.

[0119] brought by the Dirac function z = h first-order derivative jump property at

[0120]

[0121] It can be obtained that , that is particular solution of the spatial frequency domain equation satisfied is:

[0122]

[0123] Therefore, the solution of the spatial frequency domain equation in the air region is:

[0124]

[0125] By inverse Fourier transform, it can be obtained that The general solution is:

[0126]

[0127] Next, solve the undetermined coefficients , from the boundary conditions. From the continuity condition of the vector magnetic potential

[0128]

[0129] where z → 0 + and z → 0 - respectively represent approaching z = 0 infinitely from the positive and negative directions.

[0130] and the magnetic flux density y radial component continuity condition

[0131]

[0132] where and respectively represent the radial components of the magnetic flux density in regions Ⅰ and Ⅱ y .

[0133] It can be obtained that the undetermined coefficients , satisfy

[0134]

[0135] The solution is , respectively

[0136]

[0137] wherein .

[0138] Therefore, it can be obtained that 、 The final expression is:

[0139]

[0140] From , the air-gap magnetic density of y the component in the and z the component in the directions are respectively:

[0141]

[0142] wherein, , .

[0143] wherein, is the permeability of free space, σ c is the conductivity of the rotor material, I f is the effective value of the exciting current, k is the frequency variable of the Fourier transform, j is the imaginary unit.

[0144] For the expressions of the components of the air-gap magnetic density in the y direction and z the direction, the first term in the expression is the rotor eddy current magnetic density, and the second term is the exciting current magnetic density. Therefore, the components of the rotor eddy current air-gap magnetic density in the y direction and z the component in the directions are respectively:

[0145]

[0146] S104. According to the air-gap magnetic density distribution, an equivalent average magnetic density correction coefficient is introduced to calculate and correct the rotor eddy current equivalent average magnetic density defined in S102, so as to obtain the corrected average magnetic density, and further obtain the calculation formula of the induced voltage of each phase receiving coil after correction.

[0147] The z direction of the two-dimensional model is the same as that of the three-dimensional model described in S102z direction h same air-gap height H a Then, the equivalent average magnetic density of the rotor eddy current in the plane of the two-layer receiving coils can be calculated by the following formula:

[0148]

[0149] The magnetic density of the actual interlinked part with the receiving coils needs to be corrected from the above equivalent average magnetic density. Therefore, an equivalent average magnetic density correction coefficient K B is introduced to obtain the corrected average magnetic density

[0150]

[0151] The calculation formula for the induced voltage of each phase of the receiving coils after correction is obtained from the corrected average magnetic density:

[0152]

[0153] where

[0154]

[0155] S105. The calculation formulas for the induced voltages of the above sine phase and cosine phase can be written as the following relationship:

[0156]

[0157] It contains three factors, namely the amplitude term, the high-frequency carrier term, and the low-frequency modulation term;

[0158] where V m is the amplitude term, is the low-frequency modulation phase of the sine-phase induced voltage, is the low-frequency modulation phase of the cosine-phase induced voltage, is the high-frequency carrier term, ω m is the mechanical angular frequency of the rotor, ω f is the angular frequency of the exciting current, T is the rotation time of the rotor starting from the zero position angle;

[0159] The sine-phase and cosine-phase induced voltages have the same amplitude term V m which is a function of six design parameters, i.e., where k 1 is the size parameter of the receiving coil, H a is the air-gap thickness, Hl is the PCB layer spacing where the receiving coil is located, ω f is the angular frequency of the exciting current, I f is the effective value of the exciting current, σ c is the conductivity of the rotor material.

[0160] The above relationship is the analytical model from each design parameter to the induced voltage of each phase of the receiving coil.

[0161] S201, Figure 5 is the flowchart of the high signal-to-noise ratio optimization design of the eddy current angular position sensor. It can be seen from this analytical model that the output voltage amplitude of this sensor is related to the following six parameters:

[0162] a) Dimension parameters k 1, H a , H l ;

[0163] b) Electromagnetic parameters ω f , I f ,σ c .

[0164] Among them, k 1 is the dimension parameter of the receiving coil, H a is the air gap thickness, H l is the PCB layer spacing where the receiving coil is located, ω f is the angular frequency of the exciting current, I f is the effective value of the exciting current, σ c is the conductivity of the rotor material.

[0165] S202. According to the specific dimension requirements and excitation conditions, determine the fixed design parameters among the above parameters, as well as the feasible region of the variable design parameters. Take the maximization of the output voltage amplitude under the same outer dimension as the objective function, and take the feasible region of the variable design parameters as the constraint condition to establish a nonlinear programming problem. This application takes a set of design parameters as an example to illustrate the implementation process of this method.

[0166] Under certain specific assembly and operation conditions, the embodiments of this application provide a set of fixed design parameters as shown in the following table:

[0167]

[0168] The requirements for a set of target parameters (output voltage amplitude) and variable design parameters provided by the embodiments of this application are shown in the following table:

[0169]

[0170] Under the conditions of the fixed design parameters, it is necessary to determine the variable design parameters k 1 and H a effective value ranges such that the target parameter output voltage amplitude meets the upper and lower limit requirements; at the same time, one or more groups of k 1 and H a values can be selected such that the output voltage signal has the maximum signal-to-noise ratio within the allowable range. Substitute the fixed parameters into the analytical model to obtain the objective function and its constraint conditions containing and only containing the variable design parameters:

[0171]

[0172] where represents a function of k 1 and , represents a function of Ha, V Rm represents the output voltage amplitude.

[0173] S203. Solve this non-linear programming problem to obtain the k 1 and H a values that satisfy the objective function: k 1 = 6mm, H a = 0.8mm. Calculate the output voltage amplitude V Rm = 63.8mV at this time, which meets the requirement range and has a relatively high signal-to-noise ratio under the conditions.

[0174] The above embodiments are only used to illustrate rather than limit the technical solutions of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the present invention can still be modified or equivalently replaced, and any modification or partial replacement without departing from the spirit and scope of the present invention shall be covered by the scope of the claims of the present invention.

Claims

1. Analytical model of an eddy current angular position sensor, characterized in that, The eddy current angular position sensor is a sinusoidal coil eddy current angular position sensor. The establishment of the analytical model includes the following steps: A three-dimensional magnetic circuit model of the excitation coil, receiving coil and rotor in space is established based on the cylindrical coordinate system, and the coordinate expressions of the excitation coil and sinusoidal receiving coil trajectories are given; In the three-dimensional magnetic circuit model, the rotor eddy current equivalent average magnetic flux density of the rotor projection area in the receiving coil plane is defined, and the expression of the induced voltage of each phase receiving coil represented by the rotor eddy current equivalent average magnetic flux density is obtained according to Faraday's law of electromagnetic induction; For the excitation coil-air gap-rotor system, take its radial section and establish a simplified two-dimensional Cartesian coordinate system electromagnetic model. The diffusion equation satisfied by the magnetic field in the rotor conductor area and the magnetic quasi-static equation satisfied by the magnetic field in the air gap area are derived through the Maxwell equations. The Fourier transform method is used to solve them and calculate the air gap magnetic flux distribution. According to the air gap flux distribution, the equivalent average flux correction coefficient is introduced to calculate and correct the rotor eddy current equivalent average flux to obtain the corrected average flux, and then the corrected calculation formula of the induced voltage of each phase receiving coil is obtained; Based on the calculation formula of the induced voltage of each phase receiving coil, an analytical model of the induced voltage of the receiving coil from each design parameter is constructed; Among them, the analytical model of each design parameter to the induced voltage of the receiving coil is constructed based on the calculation formula of the induced voltage of each phase receiving coil, including: The sine phase and cosine phase induced voltages of the receiving coil are calculated by the following formulas: It contains three factors, namely, amplitude term, high-frequency carrier term and low-frequency modulation term; wherein V m is the amplitude term, is the low-frequency modulation phase of the sine-phase induced voltage, is the low-frequency modulation phase of the cosine-phase induced voltage, is the high-frequency carrier term; ω m is the rotor mechanical angular frequency, ω f is the exciting current angular frequency, T is the rotation time of the rotor starting from the zero position angle; The induced voltages in sine and cosine phases have the same magnitude terms V m , which are functions of six design parameters, namely , where k 1 is the size parameter of the receiving coil, H a is the air-gap thickness, H l is the PCB layer spacing where the receiving coil is located, ω f is the angular frequency of the exciting current, I f is the effective value of the exciting current, σ c is the conductivity of the rotor material.

2. The analytical model of the eddy current angular position sensor according to claim 1, wherein Based on the cylindrical coordinate system, a three-dimensional magnetic circuit model of the excitation coil, the receiving coil and the rotor in space is established, and the coordinate expressions of the excitation coil and the sinusoidal receiving coil trajectory are given, including: Select the main parameters of the three-dimensional magnetic circuit model, including the number of pole pairs of the eddy current sensor p , the air gap thickness H a , the PCB layer spacing where the receiving coil is located H l , the size parameters of the receiving coil k 1、 k 2; According to the main parameters of the three-dimensional magnetic circuit model, the coordinate expressions of the excitation coil and the sinusoidal receiving coil trajectories are determined in the cylindrical coordinate system by the rotation angle of the rotor θ represented.

3. The analytical model of the eddy current angular position sensor according to claim 2, characterized in that In the three-dimensional magnetic circuit model, the rotor eddy current equivalent average magnetic flux of the rotor projection area in the receiving coil plane is defined. According to Faraday's law of electromagnetic induction, the expression of the induced voltage of each phase receiving coil represented by the rotor eddy current equivalent average magnetic flux is obtained, including: In the three-dimensional magnetic circuit model, the definition of the rotor eddy current equivalent average magnetic flux in the rotor projection area in the receiving coil plane is given, which is calculated from the air gap magnetic flux distribution. According to Faraday's law of electromagnetic induction, the induced voltage of each clockwise turn of the receiving coil is calculated based on the number of pole pairs of the sensor, the air gap thickness, the PCB layer spacing, the inner and outer diameter dimensions of the receiving coil, and the equivalent average magnetic density of the rotor eddy current. V R+ ; According to the number of pole pairs of the sensor, the air gap thickness, the PCB layer spacing, the inner and outer diameter size parameters of the receiving coil, and the equivalent average magnetic density of the rotor eddy current, the induced voltage of each counterclockwise turn of the receiving coil is calculated according to Faraday's law of electromagnetic induction. V R- ; Due to the reverse series relationship between the clockwise turns and counterclockwise turns of each phase of the receiving coil, the induced voltage of each phase of the receiving coil V R = V R+ - V R- , and the calculation formula for the induced voltage of each phase of the receiving coil is obtained.

4. The analytical model of the eddy current angular position sensor according to claim 3, characterized in that, For the excitation coil-air gap-rotor system, take its radial section and establish a simplified two-dimensional Cartesian coordinate system electromagnetic model. The diffusion equation satisfied by the magnetic field in the rotor conductor area and the magnetic quasi-static equation satisfied by the magnetic field in the air gap area are derived through the Maxwell equations. The Fourier transform method is used to solve and calculate the air gap magnetic flux density distribution, including: For the excitation coil-air gap-rotor system, take its radial cross section to establish a simplified two-dimensional Cartesian coordinate electromagnetic model, write the diffusion equation for the magnetic field in the rotor conductor area, write the magnetic quasi-static equation for the magnetic field in the air gap area, and calculate the magnetic flux density in the air gap area by solving the boundary conditions simultaneously; The air-gap magnetic density expression consists of two terms added together. The first term is the rotor eddy current magnetic density, and the second term is the exciting current magnetic density. Thus, the rotor eddy current air-gap magnetic density is obtained. z The component in the direction.

5. The analytical model of the eddy current angular position sensor according to claim 4, characterized in that, According to the air gap magnetic flux distribution, the equivalent average magnetic flux correction coefficient is introduced, the equivalent average magnetic flux is calculated and corrected, and the corrected average magnetic flux is obtained, and then the corrected calculation formula of the induced voltage of each phase receiving coil is obtained, including: According to the distribution of the tangential component of the rotor eddy current air-gap magnetic density z in the plane of the two-layer receiving coils, calculate the equivalent average magnetic density of the rotor eddy current in the plane of the two-layer receiving coils; According to the distribution of the z - component of the rotor eddy - current air - gap magnetic density in the plane of the two - layer receiving coils, an equivalent average magnetic density correction coefficient is introduced to correct the equivalent average magnetic density of the rotor eddy - current, and the corrected average magnetic density is obtained. Furthermore, the calculation formula for the induced voltage of each - phase receiving coil after correction is obtained.

6. Optimization design method for high signal-to-noise ratio of eddy current angular position sensor, based on the analytical model described in claim 5, characterized in that It includes the following steps: According to the analytical model, the output voltage amplitude of the sine - coil eddy - current angular position sensor is simplified to be related to the following six parameters: a) Dimension parameters k 1, H a , H l ; b) Electromagnetic parameters ω f , I f , σ c ; Among them k 1 is the size parameter of the receiving coil, H a is the air gap thickness, H l is the PCB layer spacing where the receiving coil is located, ω f is the angular frequency of the excitation current, I f is the effective value of the excitation current, σ c is the conductivity of the rotor material; According to the specific dimension requirements and excitation conditions under different assembly and operation conditions, the fixed design parameters among the above - mentioned parameters and the feasible region of the variable design parameters are determined; the fixed design parameters are substituted into the analytical model to obtain the relationship between the target parameter output voltage amplitude and the variable design parameters; Taking the maximization of the output voltage amplitude under the same outer dimension as the objective function and the feasible region of the variable design parameters as the constraint condition, a non - linear programming problem is established and solved to obtain the combination of variable design parameters that satisfies the objective function, that is, the optimal design parameter combination that enables the sensor output voltage signal to obtain a higher signal - to - noise ratio under this condition.

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