A method and system for semi-active acoustic and vibration control of a permanent magnet synchronous motor

Abstract

The present invention relates to a semi-active control method for acoustic vibration of a permanent magnet synchronous motor, which is applicable to a motor, wherein a piezoelectric ceramic sheet is provided inside and / or on the surface of the motor housing, and the method comprises: during the operation of the motor, the operation information of the motor is collected by a sensor to obtain the motor operation information, and the actual voltage value at both ends of the piezoelectric ceramic is collected by a sampling circuit; an acoustic vibration estimation model of the motor noise and vibration is created, and the collected motor operation information is input into the acoustic vibration estimation model to obtain the voltage estimation value at both ends of the piezoelectric ceramic; the noise and vibration of the motor are suppressed according to the voltage estimation value and the actual voltage value at both ends of the piezoelectric ceramic. Compared with the prior art, the present invention can suppress the vibration and noise of the motor without changing the electromagnetic parameters of the motor; the semi-active vibration control method based on the synchronous switch damping technology is adopted, which eliminates the external vibration sensor, power amplifier and power supply, reduces the volume and mass, and meets the actual application requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of AC motor vibration control, and in particular to a method and system for semi-active acoustic vibration control of a permanent magnet synchronous motor. Background Art

[0002] The vibration and noise of permanent magnet synchronous motors come from mechanical vibration, aerodynamic noise and electromagnetic vibration, among which electromagnetic vibration is the main factor, which is caused by the torque pulsation and radial electromagnetic force fluctuation of the motor. Existing motor vibration suppression methods mainly focus on stator skew slots, optimizing pole-slot ratios, changing structural modal parameters, injecting compensation currents, and using spread spectrum modulation drive technology. However, the permanent magnet synchronous motor is a complex electromechanical coupling system. Therefore, if the method of modifying the motor structure and electromagnetic parameters is used to suppress the vibration and noise of the motor, there will be problems such as complex design, cumbersome processing, and reduced motor output torque. If the method of changing the drive control strategy is used to suppress the vibration and noise of the motor, there will be problems such as high requirements for the computing power of the main control chip and complex supporting circuits.

[0003] Therefore, there is an urgent need to provide a solution that can effectively suppress the vibration and noise of the permanent magnet synchronous motor while basically not changing the electromagnetic parameters and driving mode of the motor. Summary of the invention

[0004] Based on this, it is necessary to provide a permanent magnet synchronous motor acoustic vibration semi-active control method and system that can effectively suppress the vibration and noise of the permanent magnet synchronous motor without basically changing the electromagnetic parameters and driving mode of the motor in order to address the above technical problems.

[0005] An embodiment of the present invention provides a method for semi-active acoustic vibration control of a permanent magnet synchronous motor, the method comprising:

[0006] During the operation of the motor, the real-time speed, drive current, back electromotive force and other operating parameters of the motor are collected through sensors to obtain the motor operation information; the piezoelectric ceramics arranged inside and / or on the surface of the motor housing are deformed by the vibration of the motor surface, and the actual voltage value at both ends of the piezoelectric ceramics is collected through the sampling circuit;

[0007] Creating an acoustic vibration estimation model for motor noise and vibration, and inputting the collected motor operation information into the acoustic vibration estimation model to obtain an estimated value of the voltage across the piezoelectric ceramic;

[0008] The noise and vibration of the motor are suppressed according to the estimated voltage value and the actual voltage value at both ends of the piezoelectric ceramic.

[0009] Furthermore, the acoustic vibration estimation model includes:

[0010] An electromagnetic model, used to obtain the electromagnetic force acting on the stator of the motor according to the acquired motor operation information;

[0011] A structural dynamics model for obtaining the surface vibration displacement of the motor under electromagnetic force excitation;

[0012] an acoustic radiation model, used to obtain the noise level of the motor according to the surface vibration displacement of the motor under electromagnetic force excitation, and to adjust the variables of the structural dynamics model according to the noise level;

[0013] The piezoelectric effect model is used to obtain an estimated value of the voltage across the piezoelectric ceramic arranged on the motor according to the surface vibration displacement of the motor under the excitation of the electromagnetic force.

[0014] Furthermore, the step of creating the electromagnetic model includes:

[0015] The stator and rotor of the motor are divided into subdomains, partial differential equations of different subdomains are established, and general solutions of the partial differential equations under different subdomains are obtained; wherein the subdomains of the stator and rotor of the motor include a slot domain, a slot opening domain, an air gap domain, and a permanent magnet domain;

[0016] Based on the principle that the vertical component of the magnetic flux density vector in the magnetic field is continuous at the interface between two adjacent media and the parallel component of the magnetic field intensity vector on one side of the boundary is equal to the parallel component of the magnetic field intensity vector on the other side, boundary conditions between different subdomains are created;

[0017] Based on the winding arrangement and power-on strategy of the motor, an armature current distribution equation is obtained. Based on the arrangement, shape and magnetization direction parameters of the permanent magnet, a permanent magnet magnetization vector equation is obtained through Fourier decomposition. According to the armature current distribution equation and the permanent magnet magnetization vector equation of the motor, and the boundary conditions between different subdomains, the integral constant in the general solution of the partial differential equation is solved to obtain the radial and tangential magnetic field distribution in the air gap of the motor;

[0018] The electromagnetic model is established according to the radial and tangential magnetic field distributions in the air gap of the motor.

[0019] Furthermore, the radial electromagnetic force density acting on the stator teeth is obtained from the electromagnetic model as follows:

[0020]

[0021] Among them, σ r is the radial electromagnetic force density, B rs is the radial air gap flux density on the inner surface of the stator, B θs is the tangential air gap magnetic flux density on the inner surface of the stator, μ0 is the vacuum magnetic permeability, and the electromagnetic force acting on the motor stator is the product of the radial electromagnetic force density and the effective area.

[0022] Furthermore, the step of creating the structural dynamics model includes:

[0023] Obtaining the vibration equation of the motor, performing modal decoupling on the vibration equation of the motor, and obtaining the transfer function of each mode,

[0024] Establishing a structural model of the motor in finite element software, and extracting the node coordinates, modal matrix and natural frequency of the motor from the motor structural model through the finite element software;

[0025] Input the node coordinates, modal matrix, natural frequency and electromagnetic force acting on the motor stator of the motor into the transfer function of each mode to obtain the corresponding modal response vector;

[0026] The modal response vector of each mode is converted into a physical displacement through a modal matrix, a dynamic displacement matrix of the motor structure model is established according to the physical displacement of each mode, and the structural dynamics model is obtained according to the dynamic displacement matrix.

[0027] Furthermore, the structural dynamics model is:

[0028]

[0029] Where S(φ,t) is the vibration displacement of the motor surface, is the h-th order amplitude of the displacement of the motor outer surface after two-dimensional Fourier transform in time and space, v S,(h) is the spatial order of the h-th surface displacement, f S,(h) is the time order of surface displacement, φ S,(h) is the phase of the h-th order surface displacement, φ represents the angular position of the motor outer surface in the stator polar coordinate system, and t represents the time. Since the motor structure has low damping and high stiffness, it deforms little under the action of electromagnetic force, so the frequency of the motor surface vibration displacement in steady-state operation is consistent with the frequency of the electromagnetic force density.

[0030] Furthermore, the sound radiation model is:

[0031]

[0032]

[0033] Among them, L P,total is the total sound pressure level of all vibrations, L P,(h) is the sound pressure level generated by vibration of a single frequency, f (h) is the frequency of the h-th order vibration, is the displacement amplitude of the h-th order surface vibration, is the composite relative radiated power.

[0034] Furthermore, the piezoelectric effect model of the piezoelectric ceramic is:

[0035]

[0036] u(t)=S(φ p ,t)

[0037] Among them, F is the mechanical force, K E is the short-circuit elastic constant, U is the piezoelectric voltage, α is the global piezoelectric voltage coefficient, u is the displacement of the piezoelectric ceramic, S(φ,t) is the surface φ of the motor p The vibration displacement at p is the angular position of the piezoelectric ceramic piece in the motor stator polar coordinate system.

[0038] Further, according to the voltage estimation value and the actual voltage value at both ends of the piezoelectric ceramic, the noise and vibration of the motor are suppressed, specifically including:

[0039] A vibration control signal module generates a switch signal according to the estimated voltage value and the actual voltage value at both ends of the piezoelectric ceramic, and transmits the switch signal to a vibration suppression module connected to the piezoelectric ceramic;

[0040] The vibration suppression module generates a driving signal according to the switch signal to suppress the noise and vibration of the motor;

[0041] The target model for suppressing the noise and vibration of the motor is:

[0042]

[0043] Among them, f switch is the switching frequency, is the maximum frequency of the electromagnetic force density, is the minimum frequency of the electromagnetic force density.

[0044] Another embodiment of the present invention provides a control system for implementing a method for semi-actively controlling acoustic vibration of a permanent magnet synchronous motor, which is applicable to a motor, wherein a piezoelectric ceramic sheet deformed by motor vibration is provided inside and / or on the surface of the motor housing, and the system comprises:

[0045] The information acquisition module is used to acquire parameters such as rotation speed, driving current, back electromotive force, etc. through sensors during the operation of the motor to obtain the motor operation information; the actual voltage value at both ends of the piezoelectric ceramic is acquired through a sampling circuit; the acoustic vibration estimation module is used to input the motor operation information acquired by the information acquisition module into the acoustic vibration estimation model to obtain the voltage estimation value at both ends of the piezoelectric ceramic;

[0046] A vibration control signal module, used for generating a switch signal according to the estimated voltage value and the actual voltage value at both ends of the piezoelectric ceramic;

[0047] A vibration suppression module is used to generate a drive signal according to the switch signal to suppress the noise and vibration of the motor; the vibration suppression module includes a voltage detection unit arranged at both ends of the piezoelectric ceramic, and an adjustable inductance unit, a switch circuit unit and a voltage source unit connected in series with the piezoelectric ceramic.

[0048] In the above-mentioned permanent magnet synchronous motor acoustic and vibration semi-active control method, during the operation of the motor, the sensor collects the motor's real-time speed, drive current, back electromotive force and other operating parameters to obtain the motor's operating information; the piezoelectric ceramics arranged inside and / or on the surface of the motor casing are deformed by the vibration of the motor surface, and the actual voltage value at both ends of the piezoelectric ceramics is collected through a sampling circuit; a motor vibration and noise estimation model is created, and the collected motor operation information is input into the acoustic and vibration estimation model to obtain an estimated voltage value at both ends of the piezoelectric ceramics; based on the estimated voltage value and the actual voltage value at both ends of the piezoelectric ceramics, the noise and vibration of the motor are suppressed. Compared with the prior art, the present invention uses piezoelectric ceramics to suppress the vibration and noise of the motor, which has the advantages of wide suppression bandwidth, fast response speed and good robustness; the motor vibration and noise can be suppressed without changing the electromagnetic parameters of the motor; a semi-active vibration control method based on synchronous switching damping technology is adopted, which eliminates the external vibration sensor, power amplifier and power supply, and reduces the volume and mass; the piezoelectric ceramics are arranged inside or (and) on the surface of the motor casing, which can more accurately sense the actual vibration level of the motor than when arranged on the stator, and obtain better vibration reduction and noise reduction effects; a new synchronous switching control technology based on the motor vibration model applies the synchronous switching damping technology to solve the problem of suppressing the wide-band vibration of the motor, meeting the actual application needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A schematic diagram of a permanent magnet synchronous motor sound and vibration suppression system according to an embodiment of the present invention;

[0050] Figure 2 It is a structural schematic diagram of the vibration suppression module;

[0051] Figure 3 A schematic diagram of the structure of the semi-active acoustic and vibration control of a permanent magnet synchronous motor provided by an embodiment of the present invention;

[0052] Figure 4 A schematic diagram of the geometric shape of the stator and rotor of a surface-embedded motor provided by an embodiment of the present invention;

[0053] Figure 5 A flow chart of a method for semi-active acoustic and vibration control of a permanent magnet synchronous motor provided by an embodiment of the present invention;

[0054] Figure 6 This is a structural block diagram of a permanent magnet synchronous motor acoustic vibration semi-active control system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0055] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the technical field without creative work are within the scope of protection of the present invention. It should be noted that the step numbers in the text are only for the convenience of explanation of specific embodiments and do not serve to limit the order of execution of the steps.

[0056] The semi-active acoustic vibration control method for a permanent magnet synchronous motor provided in the embodiment of the present invention can be used for permanent magnet synchronous motors with different magnetic pole configurations, including rotary motors, linear motors, radial flux motors, axial flux motors, and transverse flux motors. Figure 1 Taking the motor structure shown in the figure as an example, the motor includes a motor housing 1, a piezoelectric material placement groove 2, a piezoelectric ceramic 3, a stator silicon steel sheet 4, a rotating shaft 5, a coil groove 6, a permanent magnet 7, a rotor sleeve 8 and a rotor silicon steel sheet 9. The piezoelectric ceramic is placed in the piezoelectric material placement groove and is fixed to the motor housing 1 by means of high-strength glue to sense motor vibration. Figure 2 The piezoelectric ceramic is driven by a vibration suppression module based on synchronous switch damping technology, and the vibration suppression module includes a voltage detection unit disposed at both ends of the piezoelectric ceramic, and an adjustable inductance unit, a switch circuit unit and a voltage source unit connected in series with the piezoelectric ceramic. The adjustable inductance unit includes an inductor and an operational amplifier circuit, the switch circuit unit includes a triode switch circuit, and the voltage detection unit includes a voltage detection sensor or a voltage detection circuit.

[0057] like Figure 3 to Figure 4 As shown, the semi-active acoustic vibration control method of a permanent magnet synchronous motor provided by an embodiment of the present invention is applicable to a motor, wherein a piezoelectric ceramic sheet deformed by the vibration of the motor is provided inside and / or on the surface of the motor housing, and the method comprises:

[0058] Step S11, during the operation of the motor, the operation information of the motor is collected by a sensor to obtain the motor operation information, and the actual voltage value across the piezoelectric ceramic is collected by a sampling circuit.

[0059] The motor operation information includes the three-phase current information and the speed information of the motor.

[0060] Step S12, creating an acoustic vibration estimation model for motor noise and vibration, and inputting the collected motor operation information into the acoustic vibration estimation model to obtain an estimated value of the voltage across the piezoelectric ceramic.

[0061] The acoustic vibration estimation model includes an electromagnetic model, a structural dynamics model, an acoustic radiation model, and a piezoelectric effect model. The electromagnetic model is used to obtain the electromagnetic force acting on the motor stator based on the motor operation information obtained. The structural dynamics model is used to obtain the surface vibration displacement of the motor under the excitation of the electromagnetic force. The acoustic radiation model is used to obtain the noise level of the motor based on the surface vibration displacement of the motor under the excitation of the electromagnetic force, and adjust the variables of the structural dynamics model according to the noise level. The piezoelectric effect model is used to obtain the voltage estimation value across the piezoelectric ceramic arranged on the motor based on the structural deformation of the piezoelectric ceramic caused by the surface vibration displacement of the motor under the excitation of the electromagnetic force.

[0062] It should be noted that the vibration and noise of the motor are mainly caused by the electromagnetic force acting on the stator. In order to design a synchronous switch control law for motor vibration suppression, it is necessary to establish a functional relationship between the motor operating parameters and the surface vibration. The following takes a surface-embedded three-phase permanent magnet synchronous motor as an example to explain the modeling methods of the electromagnetic model, structural dynamics model, acoustic radiation model and piezoelectric effect model, as well as the model-based vibration control law design method.

[0063] When modeling electromagnetic models:

[0064] Since the stator and rotor geometry of the surface embedded motor is Figure 5 As shown, in order to calculate the electromagnetic force acting on the stator inner diameter (stator teeth) of the motor under different rotor positions and input voltages and currents, it is necessary to first calculate the air gap magnetic field distribution. When the stator and rotor of the motor are sub-divided into sub-domains, the stator and rotor are geometrically divided into Q slot domains (sl), Q slot opening domains (so), air gap domains (a) and 2p permanent magnet domains (m), based on Ampere's law and Gauss's law of magnetic field In the polar coordinate system ({r,θ,z}), partial differential equations in different subdomains can be written:

[0065]

[0066] In the formula, r is the polar diameter, θ is the polar angle, is the magnetic vector potential in the slot domain, is the magnetic vector potential of the permanent magnet domain, is the magnetic vector potential in the air gap domain, is the magnetic vector potential of the slot opening, μ0 is the vacuum permeability, J is the armature current density vector, M is the permanent magnet remanence vector, M θis the tangential component of the permanent magnet remanence vector, M r is the radial component of the permanent magnet remanent magnetization vector.

[0067] From this, the general solution of the partial differential equation in different subdomains can be obtained as follows:

[0068] ① The general solution of Poisson's equation in the slot subdomain is

[0069]

[0070] In the formula, r is the polar diameter, θ is the polar angle, is the characteristic parameter of the jth slot domain determined by the boundary conditions, For a special solution, is the integration constant, R sl is the groove bottom radius, R so is the slot opening radius, δ is the slot span angle, v is the harmonic order calculated in the slot domain, θ j is the angular position of the center of the jth slot.

[0071] The special solution is

[0072]

[0073] Where r is the pole diameter, θ is the pole angle, μ0 is the vacuum permeability, is the DC component coefficient of the Fourier series expansion of the winding current density in the jth slot, is the coefficient of the vth component of the Fourier series expansion of the winding current density in the jth slot, v is the harmonic order calculated in the slot domain, δ is the slot span angle, θ j is the angular position of the center of the jth slot.

[0074] According to the boundary conditions (1.12.7), the solution is

[0075]

[0076] Where r is the pole diameter, θ is the pole angle, μ0 is the vacuum permeability, is the DC component coefficient of the Fourier series expansion of the winding current density in the jth slot, R sl is the groove bottom radius, is the integration constant, R so is the slot opening radius, δ is the slot span angle, v is the harmonic order calculated in the slot domain, θ j is the angular position of the center of the jth slot.

[0077] ②The solution of the Laplace equation in the slot opening subdomain is

[0078]

[0079] In the formula, r is the polar diameter, θ is the polar angle, is the characteristic parameter of the jth slot opening domain determined by the boundary conditions, is the integration constant, R so is the slot opening radius, R s is the stator inner diameter, u is the harmonic order calculated in the slot opening domain, β is the slot opening span angle, θ j is the angular position of the center of the jth slot.

[0080] ③The general solution of the Laplace equation in the air gap subdomain is

[0081]

[0082] In the formula, r is the polar diameter, θ is the polar angle, R s is the inner diameter of the stator, R m is the outer diameter of the permanent magnet, is the integration constant, u is the harmonic order calculated in the slot opening domain, β is the slot opening span angle, θ j is the angular position of the center of the jth slot.

[0083] ④The general solution of Poisson's equation in the permanent magnet subdomain is

[0084]

[0085] in,

[0086]

[0087]

[0088] In the formula, r is the polar diameter, θ is the polar angle, is the characteristic parameter of the kth permanent magnet domain determined by the boundary conditions, is the integration constant, w is the harmonic order calculated in the permanent magnet domain, R m is the outer diameter of the permanent magnet, R r is the inner diameter of the rotor back iron, p is the number of pole pairs, α p is the pole arc coefficient, α is the rotor angular position, is the wth harmonic amplitude of the radial component of the permanent magnet remanence vector in the kth permanent magnet domain, is the wth harmonic amplitude of the tangential component of the permanent magnet remanence vector in the kth permanent magnet domain.

[0089] According to the boundary conditions (1.12.1), the general solution can be simplified to

[0090]

[0091] in,

[0092]

[0093]

[0094]

[0095] In the formula, r is the polar diameter, θ is the polar angle, is the integration constant, R m is the outer diameter of the permanent magnet, R r is the inner diameter of the rotor back iron, w is the harmonic order calculated in the permanent magnet domain, p is the number of pole pairs, α p is the pole arc coefficient, α is the rotor angular position, μ0 is the vacuum permeability, is the wth harmonic amplitude of the radial component of the permanent magnet remanence vector in the kth permanent magnet domain, is the wth harmonic amplitude of the tangential component of the permanent magnet remanence vector in the kth permanent magnet domain.

[0096] With N, V, U and W representing the number of harmonics calculated in the air gap, slot, slot opening and permanent magnet subdomains respectively, the number of integral constants that need to be determined is 4N+Q(2U+V+1)+2pW, including

[0097]

[0098]

[0099]

[0100]

[0101] These integral constant variables can be determined based on the boundary conditions between adjacent subdomains.

[0102] The vertical component of the magnetic flux density vector B in the magnetic field (B ⊥ ) is continuous at the interface between two adjacent media. If the interface is passive, the parallel component of the magnetic field intensity vector H on one side of the boundary (H || ) is equal to the parallel component of the magnetic field intensity vector on the other side. According to the above principle, the boundary conditions between different subdomains can be written as:

[0103] At the interface between the rotor back iron and the permanent magnet, the tangential component of the magnetic field strength is 0; at the interface between the iron pole and the permanent magnet, the radial component of the magnetic field strength is 0, that is,

[0104]

[0105] In the formula, r is the polar diameter, θ is the polar angle, R r is the inner diameter of the rotor back iron, k = 0, 1, ..., 2p-1 represents the permanent magnet domain number, α is the rotor angular position, α pis the pole arc coefficient and p is the number of pole pairs.

[0106] At the interface between the air gap and the permanent magnet, the radial component of the magnetic flux density and the tangential component of the magnetic field intensity are continuous. At the interface between the iron pole and the air gap, the tangential component of the magnetic field intensity is 0, that is,

[0107]

[0108] In the formula, r is the polar diameter, θ is the polar angle, R m is the outer diameter of the permanent magnet, k = 0, 1, ..., 2p-1 represents the permanent magnet domain number, α is the rotor angular position, α p is the pole arc coefficient and p is the number of pole pairs.

[0109] The radial component of the magnetic field intensity on both sides of each slot opening is 0, that is,

[0110]

[0111] Where r is the polar diameter, θ is the polar angle, j=1,…Q represents the slot opening domain number, β is the slot opening span angle, is the angular position of the center of the jth slot.

[0112] At the interface between the air gap and the slot opening, the radial component of the magnetic flux density and the tangential component of the magnetic field intensity are continuous; at the boundary between the air gap and the stator with infinite magnetic permeability, the tangential component of the magnetic field intensity is 0, that is,

[0113]

[0114] In the formula, r is the polar diameter, θ is the polar angle, R s is the inner diameter of the stator, j=1,…Q represents the slot opening domain number, β is the slot opening span angle, is the angular position of the center of the jth slot.

[0115] At the interface between each slot opening and its adjacent slot, the radial component of the magnetic flux density and the tangential component of the magnetic field intensity are continuous; the tangential component of the magnetic field intensity between the slot and the adjacent stator with infinite magnetic permeability is 0, that is,

[0116]

[0117] In the formula, r is the polar diameter, θ is the polar angle, R so is the slot opening radius, j=1,…Q represents the slot opening domain and the slot domain number, β is the slot opening span angle, is the angular position of the center of the jth slot, and δ is the slot span angle.

[0118] The radial component of the magnetic field strength on both sides of each slot is 0, that is,

[0119]

[0120] Where r is the polar diameter, θ is the polar angle, j=1,…Q represents the slot number, is the angular position of the center of the jth slot, and δ is the slot span angle.

[0121] The tangential component of the magnetic field strength at the bottom of each slot is 0, that is,

[0122]

[0123] In the formula, r is the polar diameter, θ is the polar angle, R sl is the groove bottom radius, is the angular position of the center of the jth slot, and δ is the slot span angle.

[0124] For a q-phase motor, the armature current distribution equation of the motor can be expressed as follows using the Fourier series:

[0125]

[0126] In the formula, I v is the vth harmonic amplitude of the phase current, θ v is the vth harmonic phase shift of the phase current, is the time phase shift angle of the κth phase relative to the 1st phase, p is the number of pole pairs, and ω is the rotor rotation angular velocity.

[0127] Write the connection matrix according to the winding arrangement of the motor (concentrated winding, distributed winding, lapped winding, non-lapped winding). For example, for the alternating tooth non-lapped winding (single layer) winding, the current in all slots is

[0128]

[0129] In the formula, k f is the winding filling factor, A c is the cross-sectional area of ​​the conductor, and

[0130] J(t)=[J 1 (t) J 2 (t)…J Q (t)], i(t)=[i1(t) i2(t)…i q (t)].

[0131] For a full-tooth non-lapped (double-layer) winding, the current density in each slot is

[0132]

[0133] For a double-layer non-overlapped winding, the coefficients of the Fourier series expansion of the current density are

[0134]

[0135]

[0136] In the formula and They are the current densities of the coils on the left and right sides of the j-th slot at time t (observed from the center of the motor), which can be defined as

[0137]

[0138]

[0139] In the formula C r and C l are the connection matrices on the left and right sides of the slot, respectively.

[0140] For motors with different magnetizing methods, the permanent magnet vector can be decomposed into radial and tangential components according to the permanent magnet magnetization vector equation:

[0141]

[0142] And expand the radial and tangential components according to the Fourier series:

[0143]

[0144]

[0145] Combining the above boundary conditions, the armature current distribution equation and the permanent magnet magnetization vector equation can be solved to obtain the integral constant in the general solution:

[0146]

[0147] From this, the radial and tangential magnetic field distributions in the motor air gap can be obtained as follows:

[0148]

[0149]

[0150] In addition to using the above analytical analysis method to obtain the air gap magnetic field distribution of the motor, the finite element method can also be used. The commercial electromagnetic field finite element software (Maxwell, COMSOL, FEMAG, etc.) can take into account the nonlinear magnetization characteristics of ferromagnetic materials and more complex thermal field characteristics. Compared with the above analytical method, the results are more accurate, but time-consuming and require high computer performance. In the design of control laws, the electromagnetic field analytical modeling method is more recommended.

[0151] Regardless of whether the analytical method or the finite element method is used, the radial electromagnetic force density acting on the stator tooth surface can be obtained according to the Maxwell stress tensor equation, which can be expressed by the electromagnetic model as follows:

[0152]

[0153] Among them B rs is the radial air gap flux density on the inner surface of the stator, B θs is the tangential air gap flux density on the inner surface of the stator, and μ0 is the vacuum magnetic permeability. Since the tangential air gap flux density is much smaller than the radial air gap flux density, the above formula can be expressed as

[0154]

[0155] When modeling a structural dynamics model:

[0156] It should be noted that the structural vibration modeling of the motor can adopt an equivalent analytical modeling method and a finite element modeling method. The equivalent analytical modeling method regards the stator and housing of the motor as a cylindrical barrel structure, and uses the Hamiltonian method in analytical mechanics to establish a structural dynamics model. This method ignores the influence of stator slotting, motor base clamping and complex shape housing, so the accuracy is low and it is difficult to accurately reflect the vibration characteristics of the structure. Compared with the analytical modeling method, the finite element modeling method can take into account complex structures and boundary constraints, but it is time-consuming. In the present invention, the characteristics of the two are combined, and finite element modeling is used to solve the characteristic frequency and modal vibration shape of the motor. Based on the modal decoupling theory of multi-degree-of-freedom vibration system, the analytical calculation of the surface vibration of the motor is realized.

[0157] The structural dynamics problem of the motor is a typical multi-degree-of-freedom system problem. The system can be described by a finite number of mass points, which are coupled to each other through the spring-damper principle. At this time, the vibration equation is expressed in matrix form:

[0158]

[0159] The number of degrees of freedom and the number of elements of the vector correspond to the number n of moving masses describing the system. When torsion is not considered, the mass matrix and stiffness matrix satisfy M = Μ T , K=K T , that is, both matrices are symmetric matrices and positive definite matrices.

[0160] In the case of undamped free vibration (D = 0, ), the system vibrates freely and the response of the system is described by the harmonic motion in the time domain:

[0161]

[0162] Substituting into equation 1.28, we get the characteristic equation

[0163]

[0164] Solve the corresponding eigenvalues ​​and eigenvectors, arrange the corresponding eigenvectors in order from small to large eigenvalues, and construct the eigenvector matrix of the undamped system

[0165]

[0166] And normalize it according to the mass matrix in the following form

[0167]

[0168] The normalized modal matrix of the undamped system is constructed as

[0169]

[0170] Under the normalized modal matrix, the mass matrix and stiffness matrix satisfy

[0171]

[0172] Where i=1,2,…,n(0.34)

[0173] Under the assumption of Rayleigh damping, the damping satisfies

[0174] D=αM+βK(0.35)

[0175] Where α and β are the proportional factors of the mass matrix M and the stiffness matrix K. After orthogonalization, we can get

[0176]

[0177] make

[0178]

[0179] This allows equation (1.37) to be rewritten as

[0180]

[0181] Define a congruence transformation using a modal matrix:

[0182]

[0183] Through it, the vibration equation (Equation 1.28) can be converted to modal coordinates

[0184]

[0185] Transpose of the modal matrix multiplied on the left Available

[0186]

[0187] The orthogonal relations (1.34), (1.35), (1.39) are used to decouple the equations, where the degrees of freedom of each mode or each mode i = 1, 2, ..., n can be calculated separately:

[0188]

[0189] In the case of forced vibration, the external excitation is expressed as

[0190]

[0191] The corresponding system response is

[0192]

[0193] Substituting (1.44) and (1.45) into the decoupled vibration equation (1.42), we can obtain

[0194]

[0195] After transformation, the transfer function of each mode can be obtained as follows:

[0196]

[0197] Based on the above modal decoupling theory, the structural model of the motor is established in the finite element software, and the characteristic frequency and vibration mode of the motor are calculated. Since the vibration and noise of the motor mainly consider the radial vibration of the motor surface, the radial modal matrix can be constructed by extracting the radial displacement of the nodes on the outer surface of the structure and the inner surface of the stator. That is, the node coordinates, normalized radial modal matrix and natural frequency are extracted by the finite element software:

[0198]

[0199]

[0200]

[0201] Apply electromagnetic forces on nodes that are inside the stator

[0202]

[0203] Among them, the amplitude It represents the force exerted on the finite element node by the harmonic amplitude of the electromagnetic force density of order h.

[0204]

[0205] in A represents the harmonic amplitude of the radial electromagnetic force density of order h (i.e., the h-th order amplitude after Fourier transformation of equation (1.27)). Since the mesh at the force-bearing surface is usually divided in a uniform distribution in the finite element method, the force on the area near the node can be regarded as a concentrated force acting on the node. node Represents a small area near the node.

[0206] For different spatial orders h of electromagnetic force density, the radial modal response vector of the system is

[0207]

[0208]

[0209] Each radial modal displacement vector can be converted back to a physical radial displacement vector (indicating the displacement of the motor surface) using the radial modal matrix:

[0210]

[0211] By adding up the displacement vectors of all electromagnetic force excitations, the total radial displacement of each relevant node in time t can be obtained:

[0212]

[0213] When calculating t1 to t end After several time points, the dynamic displacement matrix of the model nodes is established. The columns show the displacement of the nodes (first the internal nodes, then the external nodes) at a specific time point, and the rows show the displacement of a specific node at different time points:

[0214]

[0215] For the real part of the above formula Re{ ξ outside} Perform two-dimensional Fourier analysis, and the surface vibration displacement at any time t can be mathematically described in the form of a cosine function:

[0216]

[0217] Where S(φ,t) is the vibration displacement of the motor surface, is the h-th order amplitude of the displacement of the motor outer surface after two-dimensional Fourier transform in time and space, v S,(h) is the spatial order of the h-th surface displacement, f S,(h) is the time order of surface displacement, φ S,(h)is the phase of the h-th order surface displacement, φ represents the angular position of the motor outer surface in the stator polar coordinate system, and t represents the time. Since the motor structure has low damping and high stiffness, it deforms little under the action of electromagnetic force, so the frequency of the motor surface vibration displacement in steady-state operation is consistent with the frequency of the electromagnetic force density.

[0218] At this point, the vibration conditions on the motor surface are obtained, that is, the structural dynamics model of the motor is established.

[0219] When modeling the acoustic radiation model:

[0220] The acoustic radiation model of the motor can be regarded as the acoustic propagation model of a finite-length cylindrical sound source. Under the condition of a far-field sound field, it can be regarded as a spherical acoustic radiation model. The relative acoustic radiation power is

[0221]

[0222] where c Luft is the speed of sound in air (343m / s), r a is the outer surface radius of the motor, ρ is the spatial order of the free vibration of the equivalent circular ring of the motor stator, u is the spatial order of the actual vibration, and ω is the angular frequency of the surface vibration. It can be seen that the relative sound radiation power only depends on the outer radius r of the radiator. a (which can be approximated as the outer radius of the stator), and the angular frequency ω of the surface vibration S , which corresponds to an angular frequency of ω σ The exciting force wave.

[0223] Due to the complexity of the motor structure, or when considering the near-field acoustic radiation, the relative acoustic radiation power can be weighted to obtain the composite relative radiation power: At this time, the sound pressure level on the motor surface (the noise level of the motor) generated by the single frequency vibration can be expressed as

[0224]

[0225] Calculation, where the sound pressure reference value P0 = 2 × 10 5 Pa, acoustic impedance Z = 4074 kg / m 2 s,f (h) is the frequency of the h-th order vibration, is the displacement amplitude of the h-th order surface vibration. The total sound pressure level of all vibrations is

[0226]

[0227] When modeling the piezoelectric effect:

[0228] When the two ends of the piezoelectric ceramic are excited by the vibration of the motor surface, a voltage with the same phase as the strain will be generated at both ends of the piezoelectric ceramic. The piezoelectric effect and inverse piezoelectric effect of piezoelectric ceramics can be described by the following constitutive equations:

[0229]

[0230] Where [c E ](6×6) represents the open circuit elastic stiffness coefficient when the electric field strength E is zero or constant; [e](3×6) is the piezoelectric stress constant; [ε S ](3×3) represents the strain S p When axial or transverse strains and stresses are considered along with appropriate elastic and piezoelectric coefficients, the simplified scalar expression is obtained:

[0231]

[0232] For the case below the resonant frequency of the piezoelectric ceramic, the above formula can be expressed as a function of displacement u, piezoelectric voltage U, and mechanical force F

[0233]

[0234] where t p is the thickness between the electrodes, ω p is the width in the strain direction, and A is the electrode surface area.

[0235] therefore

[0236] F=K E u+αU (0.61)

[0237] in is the short-circuit elastic constant, is the piezoelectric voltage coefficient, from which the piezoelectric effect model of piezoelectric ceramics can be obtained

[0238]

[0239] The displacement u of the piezoelectric ceramic pasted on the motor surface can be derived from the motor surface vibration displacement S(φ,t) (Equation 1.55) at the pasting position:

[0240] u(t)=S(φ p ,t) (0.63)

[0241] where φ p represents the angular position of the piezoelectric ceramic in the motor stator polar coordinate system. From equation (1.63), the voltage U(t) across the piezoelectric ceramic can be obtained, which is U 估计 .

[0242] Step S13, suppressing the noise and vibration of the motor according to the estimated voltage value and the actual voltage value across the piezoelectric ceramic.

[0243] Specifically, according to the estimated voltage value and the actual voltage value at both ends of the piezoelectric ceramic, a switch signal is generated by the vibration control signal module, and the switch signal is transmitted to a vibration suppression module connected to the piezoelectric ceramic; the vibration suppression module generates a drive signal according to the switch signal to suppress the noise and vibration of the motor. The vibration suppression module includes a voltage detection unit arranged at both ends of the piezoelectric ceramic, and an adjustable inductance unit, a switch circuit unit and a voltage source unit connected in series with the piezoelectric ceramic.

[0244] It should be noted that in piezoelectric vibration control based on synchronous switch damping technology, when the voltage of the piezoelectric material is opposite to the speed, the efficiency of synchronous switch damping is the highest. However, due to the mechanical hysteresis effect and the delay of the processor, the on-off moment of the switch cannot always be kept at the extreme value of the voltage. At the same time, due to the large number of harmonics generated by the surface vibration of the motor on both ends of the piezoelectric ceramic, that is, the vibration of the motor is a coupling of multiple modes, it is difficult to determine the appropriate time of the switch to maximize the damping.

[0245] In the multi-modal vibration suppression of the motor, how to switch the switch to maximize the vibration control efficiency is a difficult point in the research. The present invention establishes the vibration model of the motor and the voltage model of the piezoelectric ceramic, analyzes the coupling relationship between the two, and designs a model-based switch advance control method to achieve the optimization of the motor vibration control.

[0246] Based on the piezoelectric equation, the calculated motor surface vibration acceleration can be converted into the charge at both ends of the piezoelectric ceramic, and the voltage U caused by the motor vibration on both ends of the piezoelectric ceramic calculated based on the model can be obtained. 估计 (Obtained by formula (1.65)). By arranging the voltage detection circuit at both ends of the piezoelectric ceramic, the voltage U at both ends of the piezoelectric ceramic under different motor vibration levels can be measured. 实际 (obtained from measurement). Based on the following objective function, the optimal control law is designed:

[0247]

[0248] where f switch is the switching frequency. Since the motor structure has low damping and high stiffness, the deformation caused by electromagnetic force is small. Therefore, the frequency of surface vibration of the motor during stable operation is consistent with the frequency of electromagnetic force. Therefore, the switching frequency range should be within the maximum frequency of electromagnetic force density. and minimum frequency The design of the control algorithm can be based on displacement gradient, least mean square algorithm, artificial neural network, etc.

[0249] The present invention provides a semi-active acoustic and vibration control method for a permanent magnet synchronous motor. During the operation of the motor, a sensor collects the real-time rotation speed, drive current, back electromotive force and other operating parameters of the motor to obtain the operating information of the motor; the piezoelectric ceramics arranged inside and / or on the surface of the motor casing are deformed by the vibration of the motor surface, and the actual voltage value at both ends of the piezoelectric ceramics is collected by a sampling circuit; a motor vibration and noise estimation model is created, and the collected motor operation information is input into the acoustic and vibration estimation model to obtain the voltage estimation value at both ends of the piezoelectric ceramics; and the noise and vibration of the motor are suppressed according to the voltage estimation value and the actual voltage value at both ends of the piezoelectric ceramics. Compared with the prior art, the present invention uses piezoelectric ceramics to suppress the vibration and noise of the motor, which has the advantages of wide suppression bandwidth, fast response speed and good robustness; the motor vibration and noise can be suppressed without changing the electromagnetic parameters of the motor; a semi-active vibration control method based on synchronous switching damping technology is adopted, which eliminates the external vibration sensor, power amplifier and power supply, and reduces the volume and mass; the piezoelectric ceramics are arranged inside or (and) on the surface of the motor casing, which can more accurately sense the actual vibration level of the motor than when arranged on the stator, and obtain better vibration reduction and noise reduction effects; a new synchronous switching control technology based on the motor vibration model applies the synchronous switching damping technology to solve the problem of suppressing the wide-band vibration of the motor, meeting the actual application needs.

[0250] See also Figure 6 The present invention also provides a permanent magnet synchronous motor acoustic vibration semi-active control system applicable to the above-mentioned permanent magnet synchronous motor acoustic vibration semi-active control method, wherein a piezoelectric ceramic sheet deformed by the vibration of the motor is provided inside and / or on the surface of the motor housing, and the system comprises:

[0251] The information acquisition module 21 is used to collect the operation information of the motor through the sensor and the voltage value across the piezoelectric ceramic through the sampling circuit during the operation of the motor.

[0252] An acoustic vibration estimation module 22, used for inputting the motor operation information collected by the information collection module into an acoustic vibration estimation model to obtain an estimated value of the voltage across the piezoelectric ceramic;

[0253] A vibration control signal module 23, used to generate a switch signal according to the estimated voltage value and the actual voltage value at both ends of the piezoelectric ceramic;

[0254] The vibration suppression module 24 is used to generate a driving signal according to the switching signal to suppress the noise and vibration of the motor; the vibration suppression module includes a voltage detection unit arranged at both ends of the piezoelectric ceramic, and an adjustable inductance unit, a switching circuit unit and a voltage source unit connected in series with the piezoelectric ceramic.

[0255] The semi-active acoustic and vibration control system for a permanent magnet synchronous motor provided by the present invention collects the real-time rotation speed, driving current, back electromotive force and other operating parameters of the motor by a sensor during the operation of the motor to obtain the operating information of the motor; the piezoelectric ceramics arranged inside and / or on the surface of the motor casing are deformed by the vibration of the motor surface, and the actual voltage value at both ends of the piezoelectric ceramics is collected by a sampling circuit; an acoustic and vibration estimation model is created, and the collected motor operation information is input into the acoustic and vibration estimation model to obtain the voltage estimation value at both ends of the piezoelectric ceramics; and the noise and vibration of the motor are suppressed according to the voltage estimation value and the actual voltage value at both ends of the piezoelectric ceramics. Compared with the prior art, the present invention uses piezoelectric ceramics to suppress the vibration and noise of the motor, which has the advantages of wide suppression bandwidth, fast response speed and good robustness; the motor vibration and noise can be suppressed without changing the electromagnetic parameters of the motor; a semi-active vibration control method based on synchronous switching damping technology is adopted, which eliminates the external vibration sensor, power amplifier and power supply, and reduces the volume and mass; the piezoelectric ceramics are arranged inside or (and) on the surface of the motor casing, which can more accurately sense the actual vibration level of the motor than when arranged on the stator, and obtain better vibration reduction and noise reduction effects; a new synchronous switching control technology based on the motor vibration model applies the synchronous switching damping technology to solve the problem of suppressing the wide-band vibration of the motor, meeting the actual application needs.

[0256] It should be understood that, although the various steps in the above-mentioned flow chart are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps is not strictly limited in order, and these steps can be executed in other orders. Moreover, at least a part of the steps in the above-mentioned flow chart may include a plurality of sub-steps or a plurality of stages, and these sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages does not have to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the sub-steps or stages of other steps.

[0257] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for semi-active acoustic vibration control of a permanent magnet synchronous motor, applicable to a motor, characterized in that: A piezoelectric ceramic sheet that is deformed by the vibration of the motor is provided inside and / or on the surface of the motor housing, and the method comprises: During the operation of the motor, the operating information of the motor is collected by a sensor to obtain the motor operating information, and the actual voltage value at both ends of the piezoelectric ceramic is collected by a sampling circuit; Creating an acoustic-vibration estimation model for motor noise and vibration, and inputting the collected motor operation information into the acoustic-vibration estimation model to obtain an estimated value of the voltage across the piezoelectric ceramic; The acoustic vibration estimation model includes: An electromagnetic model, used to obtain the electromagnetic force acting on the stator of the motor according to the acquired motor operation information; A structural dynamics model for obtaining the surface vibration displacement of the motor under electromagnetic force excitation; an acoustic radiation model, used to obtain the noise level of the motor according to the surface vibration displacement of the motor under electromagnetic force excitation, and to adjust the variables of the structural dynamics model according to the noise level; A piezoelectric effect model, used to obtain an estimated value of the voltage across the piezoelectric ceramic arranged on the motor according to the surface vibration displacement of the motor under the excitation of the electromagnetic force; Wherein, the structural dynamics model is: Where S(φ,t) is the vibration displacement of the motor surface, is the h-th order amplitude of the displacement of the motor outer surface after two-dimensional Fourier transform in time and space, v S,(h) is the spatial order of the h-th surface displacement, f S,(h) is the time order of surface displacement, φ S,(h) is the phase of the h-th order surface displacement, φ represents the angular position of the motor outer surface in the stator polar coordinate system, and t represents the time; Suppressing noise and vibration of the motor according to the estimated voltage value and the actual voltage value across the piezoelectric ceramic; The step of suppressing the noise and vibration of the motor according to the voltage estimation value and the actual voltage value at both ends of the piezoelectric ceramic specifically includes: A vibration control signal module generates a switch signal according to the estimated voltage value and the actual voltage value at both ends of the piezoelectric ceramic, and transmits the switch signal to a vibration suppression module connected to the piezoelectric ceramic; The vibration suppression module generates a driving signal according to the switch signal to act on the piezoelectric ceramic to suppress the noise and vibration of the motor; The target model for suppressing the noise and vibration of the motor is: Among them, f switch is the switching frequency, is the maximum frequency of the electromagnetic force density, is the minimum frequency of the electromagnetic force density.

2. The method for semi-active acoustic vibration control of a permanent magnet synchronous motor according to claim 1, characterized in that: The steps of creating the electromagnetic model include: The stator and rotor of the motor are divided into subdomains, partial differential equations of different subdomains are established, and general solutions of the partial differential equations under different subdomains are obtained; wherein the subdomains of the stator and rotor of the motor include a slot domain, a slot opening domain, an air gap domain, and a permanent magnet domain; Based on the principle that the vertical component of the magnetic flux density vector in the magnetic field is continuous at the interface between two adjacent media and the parallel component of the magnetic field intensity vector on one side of the boundary is equal to the parallel component of the magnetic field intensity vector on the other side, boundary conditions between different subdomains are created; Based on the winding arrangement and power-on strategy of the motor, an armature current distribution equation is obtained. Based on the arrangement, shape and magnetization direction parameters of the permanent magnet, a permanent magnet magnetization vector equation is obtained through Fourier decomposition. According to the armature current distribution equation and the permanent magnet magnetization vector equation of the motor, and the boundary conditions between different subdomains, the integral constant in the general solution of the partial differential equation is solved to obtain the radial and tangential magnetic field distribution in the air gap of the motor; The electromagnetic model is established according to the radial and tangential magnetic field distributions in the air gap of the motor.

3. The method for semi-active acoustic vibration control of a permanent magnet synchronous motor according to claim 2, characterized in that: The electromagnetic force density acting on the stator teeth is obtained from the electromagnetic model: Among them, σ r is the radial electromagnetic force density, B rs is the radial air gap flux density on the inner surface of the stator, B θs is the tangential air gap magnetic flux density on the inner surface of the stator, μ0 is the vacuum magnetic permeability, and the electromagnetic force acting on the motor stator is the product of the radial electromagnetic force density and the effective area.

4. The method for semi-active acoustic vibration control of a permanent magnet synchronous motor according to claim 3, characterized in that: The steps of creating the structural dynamics model include: Obtaining the vibration equation of the motor, performing modal decoupling on the vibration equation of the motor, and obtaining the transfer function of each mode, Establishing a motor structure model of the motor in finite element software, and extracting the node coordinates, modal matrix and natural frequency of the motor from the motor structure model through the finite element software; Input the node coordinates, modal matrix, natural frequency and electromagnetic force acting on the motor stator of the motor into the transfer function of each mode to obtain the corresponding modal response vector; The modal response vector of each mode is converted into a physical displacement through a modal matrix, a dynamic displacement matrix of the motor structure model is established according to the physical displacement of each mode, and the structural dynamics model is obtained according to the dynamic displacement matrix.

5. The method for semi-active acoustic and vibration control of a permanent magnet synchronous motor according to claim 1, characterized in that: The acoustic radiation model is: Among them, L P,total is the total sound pressure level of all vibrations, L P,(h) is the sound pressure level generated by vibration of a single frequency, f (h) is the frequency of the h-th order vibration, is the displacement amplitude of the h-th order surface vibration, is the composite relative radiated power.

6. The method for semi-active acoustic and vibration control of a permanent magnet synchronous motor according to claim 1, characterized in that: The piezoelectric effect model of the piezoelectric ceramic is: u(t)=S(φ p ,t) Among them, F is the mechanical force, K E is the short-circuit elastic constant, U is the piezoelectric voltage, α is the global piezoelectric voltage coefficient, u is the displacement of the piezoelectric ceramic, S(φ p ,t) is the motor surface φ p The vibration displacement at p is the angular position of the piezoelectric ceramic piece in the motor stator polar coordinate system.

7. A semi-active acoustic vibration control system for a permanent magnet synchronous motor, applicable to a motor, characterized in that: A piezoelectric ceramic sheet that is deformed by the vibration of the motor is provided inside and / or on the surface of the motor housing. The system comprises: An information acquisition module is used to acquire the operation information of the motor through a sensor during the operation of the motor to obtain the motor operation information, and to acquire the actual voltage value at both ends of the piezoelectric ceramic through a sampling circuit; An acoustic vibration estimation module, used for inputting the motor operation information collected by the information collection module into an acoustic vibration estimation model to obtain an estimated value of the voltage across the piezoelectric ceramic; A vibration control signal module, used for generating a switch signal according to the estimated voltage value and the actual voltage value at both ends of the piezoelectric ceramic; A vibration suppression module is used to generate a drive signal according to the switch signal to suppress the noise and vibration of the motor; the vibration suppression module includes a voltage detection unit arranged at both ends of the piezoelectric ceramic, and an adjustable inductance unit, a switch circuit unit and a voltage source unit connected in series with the piezoelectric ceramic.

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