Analytic model of eddy current angular position sensor and high signal-to-noise ratio optimization design method

Abstract

The invention discloses a high signal-to-noise ratio optimization design method of an eddy current angular position sensor, and relates to the field of eddy current angular position sensors. Firstly, a three-dimensional equivalent magnetic circuit model of a sensor is established, rotor eddy current equivalent average flux density of a receiving coil surface is defined, and a receiving coil induced voltage calculation formula represented by the equivalent average flux density is given according to the Faraday's law of electromagnetic induction. Then, establishing a two-dimensional simplified electromagnetic model of an excitation coil-rotor, and solving magnetic fields of a rotor region and an air gap region by using a Fourier transform method; introducing an equivalent average flux density correction coefficient, calculating and correcting the rotor eddy current equivalent average flux density according to the air gap flux density distribution to obtain a corrected receiving coil induced voltage calculation formula, and further obtaining an analytical model from each design parameter to the receiving coil induced voltage; by means of the analytical model, it can be determined that under different size requirements and excitation conditions, the sensor outputs voltage signals to obtain the optimal design parameter combination with the high signal-to-noise ratio.

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. According to the excitation mode of the signal, magnetic sensors can be divided into two categories. Sensors based on the Hall effect, with magnetic encoders as typical representatives, are vulnerable to external harsh environments; resolvers 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 and 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] Existing design methods for sine coil eddy current angular position sensors are all based on the finite element analysis method, with large computational amounts and long required times, and cannot explicitly represent the relationship between the sensor design parameters and their performance. 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, clarifying the quantitative relationship between its output voltage and structural parameters and electromagnetic parameters, and providing an effective method for optimization design aiming to improve 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 higher 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: 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: 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; In the three-dimensional magnetic circuit model, the equivalent average magnetic density of the rotor eddy current in the rotor projection area within the receiving coil plane is defined, and 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 according to Faraday's law of electromagnetic induction; 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 area and the magnetostatic equation satisfied by the magnetic field in the air gap area through Maxwell's equations, and solve them using the Fourier transform method to calculate the air gap magnetic density distribution; 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 corrected induced voltage calculation formula for each phase of the receiving coil; From the induced voltage calculation formula of each phase of the receiving coil, construct an analytical model from each design parameter to the induced voltage of the receiving coil.

[0006] 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: 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, 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.

[0007] Furthermore, in the three-dimensional magnetic circuit model, the equivalent average magnetic density of the rotor eddy current in the rotor projection area within the receiving coil plane is defined, and 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: In the three-dimensional magnetic circuit model, give the definition formula of the equivalent average magnetic density of the rotor eddy current in the rotor projection area within the receiving coil plane, which is calculated from the air gap magnetic density distribution; From 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, calculate the induced voltage of each clockwise turn of the receiving coil according to Faraday's law of electromagnetic induction V R+ ; The induced voltage of each phase of the counterclockwise turn of the receiving coil is calculated according to Faraday's law of electromagnetic induction based on the number of sensor pole pairs, air gap thickness, PCB layer spacing, inner and outer diameter size parameters of the receiving coil and the equivalent average magnetic flux density of the rotor eddy current. V R- ; Due to the reverse series relationship between the clockwise and counterclockwise turns of each phase of the receiving coil, the induced voltage of each phase of the receiving coil is V R = V R+ - V R- , and the calculation formula for the induced voltage of each phase of the receiving coil is obtained.

[0008] Furthermore, for the excitation coil-air gap-rotor system, a radial cross section is taken to 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 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 flux density expression includes two additions, the first one is the rotor eddy current flux density, and the second one is the excitation current flux density, thus obtaining the rotor eddy current air gap flux density z Towards quantity.

[0009] Furthermore, according to the air gap magnetic flux distribution, an equivalent average magnetic flux correction coefficient is introduced, and the equivalent average magnetic flux is calculated and corrected to obtain the corrected average magnetic flux, and then the corrected calculation formula of the induced voltage of each phase receiving coil is obtained, including: According to the rotor eddy current air gap flux density z The distribution of the axial component in the plane of the two layers of receiving coils is calculated, and the equivalent average magnetic flux density of the rotor eddy current in the plane of the two layers of receiving coils is calculated; According to the distribution of the z-component of the rotor eddy current air gap flux density in the plane of the two layers of receiving coils, the equivalent average flux density correction coefficient is introduced to correct the rotor eddy current equivalent average flux density to obtain the corrected average flux density, and then the corrected induced voltage calculation formula of each phase receiving coil is obtained.

[0010] Furthermore, an analytical model of 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 the amplitude term, the high-frequency carrier term, and the low-frequency modulation term; Among them 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 excitation current angular frequency, T is the rotation time of the rotor starting from the zero position angle; The sine-phase and cosine-phase induced voltages have the same amplitude term V m , which is a function of six design parameters, namely Among them 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 excitation current angular frequency, I f is the effective value of the excitation current, σ c is the electrical conductivity of the rotor material.

[0011] On the second aspect, the present invention provides a high signal-to-noise ratio optimization design method based on this analytical model. It can be known from this analytical model that the output voltage amplitude of this sensor is related to the following six parameters: a) Size parameters k 1 , H a , H l ; b) Electromagnetic parameters ω f , I f ,σ c ; Among them, 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 excitation current angular frequency,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 operating 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 dimension 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.

[0012] Advantages of the present invention: 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 dimension 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, structural parameters, and electromagnetic parameters, has strong universality, and provides an effective method for the optimization design aiming to improve its signal-to-noise ratio. Description of the Drawings

[0013] Figure 1 is a schematic structural diagram of a 3-pole sinusoidal coil eddy current angular position sensor provided by an embodiment of the present invention; 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; Figure 3 is a schematic diagram of the calculation of a three-dimensional magnetic circuit model provided by an embodiment of the present invention; Figure 4 is a schematic diagram of the calculation of a two-dimensional simplified electromagnetic model of an excitation coil - air gap - rotor system provided by an embodiment of the present invention; Figure 5 is a high signal-to-noise ratio optimization design flow chart of the sinusoidal coil eddy current angular position sensor provided by an embodiment of the present invention. Detailed Embodiment

[0014] 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.

[0015] Figure 1Schematic diagram of the 3-pole sinusoidal coil eddy current angular position sensor provided by the embodiment of the present invention, as shown in Figure 1 shown, the number of pole pairs is p of the eddy current sensor, and its excitation coil is printed on the Bottom layer of the PCB. The sinusoidal receiving coil is printed in segments through vias on the Bottom layer and the Top layer of the same PCB, and is composed 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 sector is π / p , covering the coil in the z direction and separated by an air gap. The clockwise turns and counterclockwise turns of the cosine phase of the receiving coil are in a reverse series relationship.

[0016] The process of establishing the analytical model of the present invention is as shown in Figure 2 shown, including the following steps: S101. Based on the cylindrical coordinate system, establish a three-dimensional magnetic circuit model of the excitation coil, the receiving coil, and the rotor in space ( xyz coordinate system), and give the coordinate expressions of the trajectories of the excitation coil and the receiving coil, including: Taking the cosine-phase receiving coil as an example, the expressions of the trajectories of the clockwise turns and counterclockwise turns of the cosine-phase receiving coil in the cylindrical coordinate system ( rz coordinate system) are respectively:

[0017] where r + and z + represent the coordinates of the clockwise turns of the cosine-phase receiving coil, r - and z - represent the coordinates of the counterclockwise turns of the cosine-phase receiving coil, θ is the rotation angle of the rotor, k 1 , k 2 are the size parameters of the receiving coil, the inner diameter of the receiving coil is k 2 - k 1 , 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.

[0018] The exciting coil trajectory is expressed in the cylindrical coordinate system ( rz coordinate system) as:

[0019] where, R F is the exciting coil radius, r F 、z F represents the coordinates of the exciting coil.

[0020] The PCB layer spacing 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:

[0021] 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.

[0022] 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 its xy plane projection range. As Figure 3 shown, the area linked by a single rotor eddy current magnetic field and the clockwise turns of the cos-phase receiving coil is S cover . According to the law of electromagnetic induction, the induced voltage V R+ of the clockwise turns of the cos-phase receiving coil is:

[0023] where: is the z-component of the rotor eddy current magnetic density, T is the rotor rotation time starting from the zero position angle.

[0024] The projections of the rotor on z = t and z = b planes are respectively , at z =t and z = b The rotor eddy current magnetic flux density in the z direction components are respectively , that is, in z = t the rotor eddy current magnetic flux density in the z direction component is , in z = b the rotor eddy current magnetic flux density in the z direction component is .

[0025] The average value of the z - direction component of the rotor eddy current magnetic flux density in the region at each moment is a sine wave with the same frequency and opposite phase as the excitation current, and its amplitude remains constant at any moment of rotor rotation. Its expression is:

[0026] where is its amplitude, defined as the equivalent average magnetic flux 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.

[0027] Furthermore, S cover The part in the z = t plane is S t , the part in the z = b plane is S b , that is , then V R+ The expression can be rewritten as:

[0028] S t , S b and their calculation formulas for the derivatives with respect to the rotor rotation angle θ are:

[0029] where represents the integration variable in this integral formula.

[0030] Furthermore, the rotor mechanical angular velocity is ωm , there is θ = ω m T, T the rotor rotation time starting from the zero position angle ， then V R+ can be calculated by the following formula:

[0031] Similarly, the induced voltage expression of the cosine-phase counterclockwise turns of the receiving coil is:

[0032] 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, it can be obtained that the induced voltage of the cosine phase of the receiving coil can be calculated by the following formula:

[0033] 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:

[0034] 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:

[0035] S103. For the excitation coil - air gap - rotor system, establish a simplified two-dimensional Cartesian coordinate system electromagnetic model for its radial cross-section and calculate the air gap magnetic density distribution.

[0036] Figure 4 is the 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 cross-section of the excitation coil - air gap - rotor system as 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 of any radial cross-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 the Maxwell equations, and the magnetic density in the conductor region satisfies the diffusion equation:

[0037] where is the vacuum permeability (H / m).

[0038] Regarding the electromagnetic field in the air-gap region as a magnetoquasistatic field, the magnetic flux density in the air-gap region satisfies the equation:

[0039] where is the line current density of the exciting current, expressed by the following formula:

[0040] 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.

[0041] Introduce the vector magnetic potential A , and take the Coulomb gauge . It can be easily known from the model structure that , (where, A x、 A y and A z are A of x direction, y and z direction component magnitudes, e x is x direction unit vector). Therefore, the following vector magnetic potential A is all expressed as a scalar . From the diffusion equation of , the vector magnetic potential y <0) in the conductor region can be derived to satisfy the diffusion equation: Satisfies the diffusion equation:

[0042] 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:

[0043] where, j is the imaginary unit.

[0044] To solve it, introduce the Fourier transform and inverse transform, k is the frequency variable of the Fourier transform, for The Fourier transform is performed on both sides of the equation to obtain the corresponding spatial frequency domain function The spatial frequency domain equation satisfied is:

[0045] From the general solution structure of the homogeneous linear differential equation with constant coefficients, by discarding the divergent terms therein, the general solution of this equation can be obtained as:

[0046] where , are undetermined coefficients.

[0047] By the inverse Fourier transform, we can obtain The general solution is:

[0048] From the equation can derive the vector magnetic potential y >0) in the air region that satisfies the Poisson equation: The spatial frequency domain equation satisfied is:

[0049] Performing the Fourier transform on both sides of it, we get The corresponding spatial frequency domain function The spatial frequency domain equation satisfied is:

[0050] From the structure of the solution of the non-homogeneous linear differential equation with constant coefficients, it can be known that the solution of this equation consists of a particular solution and the homogeneous general solution of its corresponding homogeneous differential equation, corresponding to the excitation current field and the eddy current field respectively.

[0051] From the general solution structure of the homogeneous linear differential equation with constant coefficients, by discarding the divergent terms therein, we can obtain :

[0052] where,[[]] are undetermined coefficients.

[0053] Next, solve the particular solution of this equation. Due to the existence of the Dirac function in the equation, it is necessary to perform regional processing on z . At z ≠ h , the equation becomes a homogeneous equation , and the general solution of this homogeneous equation is:

[0054] Among them, , are undetermined coefficients.

[0055] By discarding the divergent term at infinity, we can obtain

[0056] According to the boundary conditions

[0057] where z → h + and z → h - respectively represent approaching z = h infinitely from the positive and negative directions.

[0058] We can obtain , so can be expressed as:

[0059] Among them, are updated undetermined coefficients.

[0060] Due to the z = h first-order derivative jump property at

[0061] We can obtain , that is The particular solution of the spatial frequency domain equation satisfied by is:

[0062] Therefore, the solution of the spatial frequency domain equation in the air region is:

[0063] By the inverse Fourier transform, we can obtain The general solution is:

[0064] Next, we solve the undetermined coefficients , from the boundary conditions. From the continuity condition of the vector magnetic potential

[0065] where z → 0 + and z → 0 - respectively represent approaching z = 0 infinitely from the positive and negative directions.

[0066] and the magnetic flux density y radial component Continuity condition

[0067] wherein, and respectively represent the magnetic flux density in regions Ⅰ and Ⅱ y in the tangential direction.

[0068] The undetermined coefficients and can be obtained to satisfy

[0069] Solving gives and which are respectively

[0070] wherein .

[0071] Therefore, it can be obtained that and The final expressions are:

[0072] From , the tangential component of the air-gap magnetic flux density y in the tangential direction and z the tangential component are respectively:

[0073] wherein, , .

[0074] wherein, is the permeability of vacuum, σ c is the conductivity of the rotor material, I f is the effective value of the excitation current, k is the frequency variable of the Fourier transform, j is the imaginary unit.

[0075] In the expressions of the tangential and radial components of the air-gap magnetic flux density y in the tangential direction and z in the radial direction, the former term is the rotor eddy-current magnetic flux density and the latter term is the excitation-current magnetic flux density. Therefore, the tangential component of the rotor eddy-current air-gap magnetic flux density y in the tangential direction and z the tangential component are respectively:

[0076] S104. According to the air-gap magnetic flux density distribution, introduce an equivalent average magnetic flux density correction coefficient to calculate and correct the equivalent average magnetic flux density of the rotor eddy current defined in S102 to obtain the corrected average magnetic flux density, and further obtain the calculation formula for the induced voltage of each phase of the receiving coil after correction.

[0077] For the two-dimensional model z the direction is the same as that of the three-dimensional model described in S102 z direction, h the same as the air-gap height H a . Then the equivalent average magnetic flux density of the rotor eddy current in the plane of the two-layer receiving coil can be calculated by the following formula:

[0078] The magnetic flux density of the part actually linked with the receiving coil needs to be corrected from the above equivalent average magnetic flux density. Therefore, introduce the equivalent average magnetic flux density correction coefficient K B , to obtain the corrected average magnetic flux density

[0079] From the corrected average magnetic flux density, obtain the calculation formula for the induced voltage of each phase of the receiving coil after correction:

[0080] where

[0081] S105. The above calculation formulas for the sine-phase and cosine-phase induced voltages can be written as the following relationship:

[0082] It contains three factors, namely the amplitude term, the high-frequency carrier term, and the low-frequency modulation term; 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 excitation current angular frequency, T is the rotation time of the rotor starting from the zero position angle; The sine-phase and cosine-phase induced voltages have the same amplitude term V m, which is a function of six design parameters, namely , 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 excitation current, I f is the effective value of the excitation current, σ c is the conductivity of the rotor material.

[0083] The said relational expression is the analytical model from each design parameter to the induced voltage of each phase of the receiving coil.

[0084] S201, Figure 5 is the flowchart for 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: a) Size parameters k 1 , H a , H l ; b) Electromagnetic parameters ω f , I f ,σ c .

[0085] Among them, 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 excitation current, I f is the effective value of the excitation current, σ c is the conductivity of the rotor material.

[0086] S202. According to the specific size 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 dimensions as the objective function, and 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.

[0087] Under certain specific assembly and operation conditions, the embodiments of the present application provide a set of fixed design parameters as shown in the following table:

[0088] The embodiments of the present application provide the requirements ranges of a set of target parameters (output voltage amplitude) and variable design parameters as shown in the following table:

[0089] 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; meanwhile, 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 containing and only containing the variable design parameters and its constraint conditions:

[0090] where represents a function about k 1 and , represents a function about Ha, V Rm represents the output voltage amplitude.

[0091] 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 that 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.

[0092] 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. The analytical model of the eddy current angular position sensor is 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 the receiving coil of each phase, an analytical model of the induced voltage of the receiving coil from various design parameters is constructed.

2. The analytical model of the eddy current angular position sensor according to claim 1, characterized in that: 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 3D 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; According to the main parameters of the three-dimensional magnetic circuit model, the trajectory of the excitation coil and the sinusoidal receiving coil is determined in the cylindrical coordinate system by the rotor rotation angle. θ The coordinate expression represented by .

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. The induced voltage of each clockwise turn of the receiving coil is calculated based on the number of sensor pole pairs, air gap thickness, PCB layer spacing, inner and outer diameter size parameters of the receiving coil, and the equivalent average magnetic flux density of the rotor eddy current according to Faraday's law of electromagnetic induction. V R+ ; The induced voltage of each phase of the counterclockwise turn of the receiving coil is calculated according to Faraday's law of electromagnetic induction based on the number of sensor pole pairs, air gap thickness, PCB layer spacing, inner and outer diameter size parameters of the receiving coil and the equivalent average magnetic flux density of the rotor eddy current. V R- ; Due to the reverse series relationship between the clockwise and counterclockwise turns of each phase of the receiving coil, the induced voltage of each phase of the receiving coil is 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 flux density expression includes two additions, the first one is the rotor eddy current flux density, and the second one is the excitation current flux density, thus obtaining the rotor eddy current air gap flux density z Towards quantity.

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 rotor eddy current air gap flux density z The distribution of the axial component in the plane of the two layers of receiving coils is calculated, and the equivalent average magnetic flux density of the rotor eddy current in the plane of the two layers of receiving coils is calculated; According to the distribution of the z-component of the rotor eddy current air gap flux density in the plane of the two layers of receiving coils, the equivalent average flux density correction coefficient is introduced to correct the rotor eddy current equivalent average flux density to obtain the corrected average flux density, and then the corrected induced voltage calculation formula of each phase receiving coil is obtained.

6. The analytical model of the eddy current angular position sensor according to claim 5, characterized in that: 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, 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; in V m is the amplitude term, is the low frequency modulation phase of the sinusoidal 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 excitation current angular frequency, T is the rotation time of the rotor starting from zero position angle; The sine and cosine induced voltages have the same amplitude V m , is a function of 6 design parameters, namely ,in 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 excitation current angular frequency, I f is the effective value of the excitation current, σ c is the electrical conductivity of the rotor material.

7. A high signal-to-noise ratio optimization design method for an eddy current angular position sensor, based on the analytical model described in claim 6, characterized in that The following steps are involved: According to the analytical model, the output voltage amplitude of the sinusoidal coil eddy current angular position sensor is simplified to be related to the following six parameters: a) Size parameters k 1, H a , H l ; b) Electromagnetic parameters ω f , I f , σ c ; in, 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 excitation current angular frequency, I f is the effective value of the excitation current, σ c is the electrical conductivity of the rotor material; According to the specific dimensional requirements and excitation conditions under different assembly and operation conditions, the fixed design parameters in the above parameters and the feasible domain 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 dimensions as the objective function and the feasible domain of the variable design parameters as the constraint conditions, a nonlinear programming problem is established and solved to obtain the variable design parameter combination that satisfies the objective function, that is, to obtain 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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