A method for predicting and controlling the motion frequency of an ultrasonically suspended object under eccentricity

Abstract

The invention discloses a method for predicting and controlling the motion frequency of an ultrasonic suspended object under eccentricity. The method comprises the following steps: constructing a finite element model of a near-field acoustic suspension vibration system, and obtaining the surface amplitude distribution of a vibration disk based on the model; constructing a theoretical motion analysis model, and obtaining the control equation of the dimensionless air pressure in an extruded film based on the theoretical motion analysis model; solving the dimensionless air film pressure distribution in the extruded film based on the control equation by using an eight-point discrete method and a Newton-Raphson method; calculating the motion trajectory and frequency of the suspended object based on the dimensionless air film pressure distribution by force analysis and a time advancement method; constructing the relationship between the frequency and peak-to-peak value of an excitation voltage and the reciprocating motion frequency based on the control equation, the dimensionless air film pressure distribution, and the motion trajectory and frequency of the suspended object, and changing the frequency and peak-to-peak value of the excitation voltage in the finite element model to realize the control of the motion frequency of the suspended object.

Description

Technical Field

[0001] The invention relates to the technical field of non-contact suspension, and in particular to a method for predicting and controlling the movement frequency of an ultrasonically suspended object under eccentricity. Background Art

[0002] As a non-contact suspension technology, near-field acoustic suspension mainly uses the suspension force generated by the nonlinear extrusion flow field generated by high-frequency vibration (usually with a frequency greater than 20kHz, in the ultrasonic frequency range) to act on the suspended object to overcome the gravity of the suspended object. When the suspension force generated by the acoustic suspension is balanced with the gravity of the suspended object, if the suspension height is in the range of tens to hundreds of microns, it is much smaller than the wavelength of the sound wave and is in the near field range, so this kind of acoustic suspension is called near-field acoustic suspension.

[0003] Compared with other suspension technologies, such as magnetic levitation and air cushion suspension, near-field acoustic levitation has no restrictions on the materials of the suspended object and does not require additional air supply equipment. Therefore, near-field acoustic levitation has the advantages of a wide range of applications, compact structure and high controllability. Therefore, near-field acoustic levitation has broad application prospects in the fields of positioning transmission of precision components or gas-lubricated bearings.

[0004] At present, there are two major problems that need to be solved in the practical application of near-field acoustic suspension. The first is the problem of the small carrying capacity of near-field acoustic suspension, which can be solved by optimizing the transducer to produce a larger vibration amplitude or optimizing the surface to improve the lubrication properties. Secondly, since near-field acoustic suspension has a self-recovery characteristic, when the suspended object is slightly eccentric relative to its equilibrium position, the squeezed air in the squeeze film will produce a viscous force to force the suspended object to return to its equilibrium position. This causes the suspended object to oscillate when the near-field acoustic suspension encounters a disturbance, affecting its positioning or transmission accuracy. Most scholars' theoretical research on this oscillation phenomenon is based on the restoring force. For example, based on the spring oscillator model of near-boundary acoustic flow theory, the restoring force F of the near-field acoustic suspension when the preset eccentricity is e0 is first calculated. r , and then simplify the suspended object into an oscillator with a mass of m, then the oscillation frequency of the suspended object is f e equal However, this model has two disadvantages: first, it cannot obtain the specific distribution of the squeezing flow field in the near-field acoustic levitation over time; second, because this model has a linear assumption, the error in the analysis is large when the eccentricity is large. Therefore, this theoretical model cannot make an accurate prediction of the oscillation position of the suspended object, which will affect the precise control of its positioning or transmission. Therefore, establishing a mathematical motion model under the eccentricity of near-field acoustic levitation is of great significance for accurately predicting the motion trajectory of the suspended object and realizing precise motion control.

[0005] In addition, if no other equipment or tools are added during the suspension process, the motion control of the suspended object can only be carried out by changing the operating parameters of the vibration system, that is, by changing the frequency and peak-to-peak value of the excitation voltage to change the amplitude distribution of the vibration disk, further affecting the pressure distribution in the extruded film. Therefore, establishing the relationship between the frequency and peak-to-peak value of the excitation voltage and the reciprocating motion frequency of the suspended object has guiding significance for the motion trajectory control of the suspended object. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a method for predicting and controlling the motion frequency of an ultrasonically suspended object under eccentricity, the method comprising:

[0007] S1. Constructing a finite element model of a near-field acoustic suspension vibration system using finite element analysis software, and obtaining the amplitude distribution of the vibration disk surface based on the finite element model;

[0008] S2. constructing a theoretical motion analysis model based on the amplitude distribution on the surface of the vibration disk and the eccentric tilt angle of the suspended object, and obtaining a control equation for the dimensionless air pressure in the extruded film based on the theoretical motion analysis model;

[0009] S3. Based on the control equation, the dimensionless air film pressure distribution in the extruded film is solved using the eight-point discretization method and the Newton-Raphson method;

[0010] S4. Based on the dimensionless air film pressure distribution, the motion trajectory and frequency of the suspended object are calculated by force analysis and time advancement method;

[0011] S5. Based on the control equation, the dimensionless air film pressure distribution, and the motion trajectory and frequency of the suspended object, the relationship between the frequency and peak-to-peak value of the excitation voltage and the reciprocating motion frequency is constructed, and the frequency and peak-to-peak value of the excitation voltage in the finite element model are changed to achieve control of the motion frequency of the suspended object.

[0012] Optionally, in S1, a finite element model of a near-field acoustic suspension vibration system is constructed using finite element analysis software, and a method for obtaining the amplitude distribution on the surface of a vibration disk based on the finite element model specifically includes:

[0013] S11. Establish a three-dimensional solid model of a near-field acoustic suspension vibration system, wherein the near-field acoustic suspension vibration system includes a Langevin transducer, a horn and a vibration disk;

[0014] S12. Importing the three-dimensional solid model into the finite element analysis software to establish a three-dimensional solid finite element model;

[0015] S13. Perform harmonic response analysis on the three-dimensional solid finite element model to obtain the amplitude distribution on the surface of the vibration disk.

[0016] Optionally, in S2, the method of constructing a theoretical motion analysis model based on the amplitude distribution on the surface of the vibration disk and the eccentric tilt angle of the suspended object, and obtaining a control equation of the dimensionless air pressure in the extruded film based on the theoretical motion analysis model specifically includes:

[0017] The amplitude distribution on the surface of the vibration plate is set to remain unchanged. When the eccentricity between the suspended object and the vibration plate is e and the inclination angle is α, the introduction depth is h. g A hypothetical suspended object with a groove is obtained, and the dimensionless expression of the air film thickness is obtained;

[0018] Based on the dimensionless air film thickness expression, a control equation of the dimensionless air pressure in the extruded film is obtained.

[0019] Optionally, the dimensionless air film thickness expression H is:

[0020]

[0021] Among them, r and θ are the coordinates of any point in the solution domain, h m is the average distance between the center of the suspended object and the center of the vibration disk in the z direction, τ=ωt=2πft is the dimensionless time, t is the time since the near-field acoustic suspension system starts working, κ is the groove depth coefficient, and V(r) is the amplitude distribution.

[0022] Optionally, the governing equation for the dimensionless air pressure in the extruded film is:

[0023]

[0024] Among them, σ is the extrusion number, μ a is the dynamic viscosity coefficient of air, Λ v and Λ a They represent the influence of the reciprocating velocity and acceleration of the suspended object on the pressure distribution, P, H, and R are the dimensionless air film pressure distribution, air film thickness, and radial position, respectively. a is the ambient air density, p a is the ambient air pressure, L is the radius of the vibrating disk and the suspended object, p and h represent the air pressure and thickness of the extruded film, respectively, and e(t) is the eccentricity of the suspended object at time t. and are the velocity and acceleration of the reciprocating motion of the suspended object at time t respectively.

[0025] Optionally, in S4, based on the dimensionless air film pressure distribution, the method for calculating the motion trajectory and frequency of the suspended object by force analysis and time advancement method specifically includes:

[0026] Calculating the balance of suspension force and the balance of restoring moment based on the dimensionless air film pressure distribution;

[0027] Based on the balance of the suspension force and the balance of the restoring moment, the shear stress generated by the gas flow acting on the lower surface of the suspended object is obtained;

[0028] Obtaining a restoring force based on the shear stress, and obtaining an acceleration of horizontal motion of the suspended object according to the restoring force;

[0029] The time advancement method is used to obtain the movement speed and eccentricity at a preset time, and the movement trajectory and frequency of the suspended object are obtained based on the movement speed and eccentricity.

[0030] Optionally, the suspension force balance formula is:

[0031]

[0032] Among them, m and g are the mass of the suspended object and the local gravitational acceleration, respectively, P is the dimensionless air film pressure distribution, and G is the gravity of the suspended object.

[0033] Optionally, the restoring torque balance formula is:

[0034]

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] (1) The prediction method proposed in the present invention establishes a fluid-solid coupling model of a vibration system-extrusion air film-suspended object, calculates the actual pressure distribution in the extrusion film to predict the motion trajectory and frequency of the suspended object, and provides a theoretical basis for the flow field to control the motion of the suspended object. (2) The theoretical analysis model proposed in the present invention simultaneously considers the eccentricity and inclination of the suspended object, which is closer to the actual physical situation. Therefore, this model can accurately predict the motion trajectory of the suspended object at different eccentricities. (3) The control method proposed in the present invention is based on the suspension of the suspended object, without the need for additional tools, and is practical and convenient. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0038] Figure 1 It is a flowchart of a method for predicting and controlling the motion frequency of a suspended object under near-field acoustic suspension eccentricity according to an embodiment of the present invention;

[0039] Figure 2 It is a schematic diagram of a finite element model of a vibration system in a near-field acoustic suspension according to an embodiment of the present invention;

[0040] Figure 3 It is a schematic diagram of a motion trajectory analysis model of a suspended object under eccentricity according to an embodiment of the present invention;

[0041] Figure 4 Schematic diagram of the position and structure of an imaginary suspended object with a groove in an embodiment of the present invention;

[0042] Figure 5 A flow chart of the calculation of the motion trajectory of a suspended object in an embodiment of the present invention;

[0043] Figure 6 A comparison diagram of the reciprocating motion frequency calculation result and the experimental result of the prediction method proposed in the embodiment of the present invention;

[0044] Figure 7 A graph showing the relationship between the reciprocating motion frequency calculation result and the excitation voltage frequency of the prediction method proposed in an embodiment of the present invention;

[0045] Figure 8 A graph showing the relationship between the reciprocating motion frequency calculation result and the peak-to-peak value of the excitation voltage according to the prediction method proposed in the embodiment of the present invention;

[0046] Figure numerals: 1-vibration plate; 2-amplifier, 2-1-amplifier flange structure; 3-Langevin transducer, 3-1-front cover plate, 3-2 piezoelectric vibration unit, 3-3 rear cover plate, 3-4 fastening bolts. Specific implementation methods

[0047] 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 of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] Embodiment 1

[0050] A method for predicting and controlling the motion frequency of an ultrasonically suspended object under eccentricity, such as Figure 1 As shown, specifically including:

[0051] S1. Use finite element analysis software to construct a finite element model of the near-field acoustic suspension vibration system, and obtain the amplitude distribution on the surface of the vibration disk based on the finite element model.

[0052] S1.1: Establish a three-dimensional solid model of a near-field acoustic suspension vibration system including a Langevin transducer, a horn and a vibration plate, wherein the Langevin transducer mainly includes a front cover, a piezoelectric vibration unit, a rear cover and fastening bolts.

[0053] S1.2: Import the above three-dimensional solid model into the finite element analysis software Workbench, define the material parameters and connection relationships of each component, divide the grid, and establish its finite element model.

[0054] S1.3: Apply a voltage with an excitation frequency of f and a peak-to-peak value of U, set boundary conditions, perform harmonic response analysis on the above finite element model, and obtain the amplitude distribution V(r) on the surface of the vibration disk.

[0055] In this embodiment, if Figure 2 As shown, in step S1, the near-field acoustic suspension vibration system mainly includes a vibration disk 1, a horn 2 and a Langevin transducer 3. Among them, the Langevin transducer mainly includes a front cover 3-1, a piezoelectric vibration unit 3-2, a rear cover 3-3 and a fastening bolt 3-4. The excitation frequency is f, and a voltage with a peak-to-peak value of U is applied to the piezoelectric vibration unit 3-2. According to the inverse piezoelectric effect, the piezoelectric vibration unit 3-2 generates vibrations, which are amplified by the horn 2, so that the vibration disk 1 generates vibrations of the same frequency. The finite element model of the entire vibration system adopts a free meshing method. In order to save calculation time, the minimum mesh size is set to 5mm. Since the entire vibration system is mounted and fixed on the base through the flange structure 2-1 on the horn, the node displacement at the flange is set to 0. The piezoelectric vibration unit defines its piezoelectric properties by using the PiezoAndMEMS plug-in in Workbench. The excitation voltage applied is U and the frequency is f. By using harmonic response analysis, the vibration characteristics of the entire near-field acoustic suspension vibration system under the above excitation parameters can be calculated, and the amplitude distribution V(r) on the surface of the vibration disk can be further obtained.

[0056] S2. A theoretical motion analysis model is constructed based on the amplitude distribution on the surface of the vibration disk and the eccentric tilt angle of the suspended object, and a control equation of the dimensionless air pressure in the extruded film is obtained based on the theoretical motion analysis model.

[0057] Further, such as Figure 3 As shown, in step S2, the entire excitation system, including the piezoelectric transducer, excitation power supply, amplitude transformer, vibration disk, etc., is simplified to a vibration disk with the same vibration characteristics. The vibration frequency f and amplitude distribution V(r) of the vibration disk obtained in step S1 remain unchanged. Figure 3 As shown in (a), when the suspended object and the vibrating plate have a preset eccentricity e0, the restoring force generated by the squeeze film is in the same direction as the positive direction of the x-axis, causing the suspended object to accelerate to the right. LWhen the center O of the vibration plate is on the z-axis, Figure 3 As shown in (b), the suspended object reaches the equilibrium position, at which point the restoring force is almost zero. Due to its inertia, the suspended object will continue to move to the right, and the direction of the restoring force is the negative direction of the x-axis, causing the suspended object to decelerate until the speed reaches zero and reaches the rightmost end, as shown in Figure 3 (c) After that, the restoring force in the negative direction of the x-axis will cause the suspended object to move to the left until the speed is zero, and then continue to repeat the above movement process, and finally the suspended object will show reciprocating motion. During the reciprocating motion, the eccentricity of the suspended object will be accompanied by tilt, and its tilt angle is represented by α.

[0058] Further, such as Figure 4 As shown, in step S3, the suspended object is freely suspended on the vibration disk, and the eccentricity at this time is e and the inclination angle is α. It can be seen that since the radius of the suspended object and the vibration disk are equal, the eccentricity of the suspended object will cause a non-overlapping area between it and the vibration disk (from the perspective of the top view). Since the area of ​​the vibration disk is used as the solution domain, in order to facilitate the expression of the air film thickness on the entire solution domain, an imaginary suspended object with a groove is introduced. This imaginary suspended object has the same radius and mass as the suspended object. The area of ​​the groove is equal to the non-overlapping area, and its depth is h g . Then the dimensionless gas film thickness H is expressed as:

[0059]

[0060] In the formula, r and θ are the coordinates of any point in the solution domain, h m is the average distance between the center of the suspended object and the center of the vibration disk in the z direction, τ=ωt=2πft is the dimensionless time, t is the time since the near-field acoustic suspension system started working, κ is the groove depth coefficient, which is 1 in the groove domain and 0 in the rest of the area. Based on the gas lubrication theory, refer to step S2 Figure 3 , the governing equation for the dimensionless air pressure in the extruded film is:

[0061]

[0062] Where, σ = 12μ a ωL 2 / p a h a 2 is the extrusion number, which indicates the influence of the extrusion effect on the pressure distribution, μ a is the dynamic viscosity coefficient of air, and They represent the influence of the reciprocating velocity and acceleration of the suspended object on the pressure distribution, P = p / p a ,H=h / h aand R = r / L are the dimensionless film pressure, film thickness and radial position, respectively, where ρ a is the ambient air density, p a is the ambient air pressure, L is the radius of the vibrating disk and the suspended object, p and h represent the air pressure and thickness of the extruded film, respectively, and e(t) is the eccentricity of the suspended object at time t. and are the velocity and acceleration of the reciprocating motion of the suspended object at time t respectively.

[0063] S3. Based on the control equation, the dimensionless air film pressure distribution in the extruded film is solved using the eight-point discretization method and the Newton-Raphson method.

[0064] Considering the inclination of the suspended object, there is a position near the center O where the air film thickness H takes a minimum value and satisfies Therefore, the squeezing effect is most obvious at this position, and the pressure change satisfies In addition, if Figure 3 As shown, at the junction of the squeezed film and the outside atmosphere, the air pressure value should be equal to the outside air pressure, satisfying P(r=L)=1. Due to the eccentricity of the suspended object, the air film thickness H is discontinuous, and the conventional finite difference method is not convenient to solve. Therefore, the eight-point discretization method and Newton-Raphson method are used to solve formula (2) to obtain the dimensionless air film pressure distribution P in the squeezed film.

[0065] S4. Based on the dimensionless air film pressure distribution, the motion trajectory and frequency of the suspended object are calculated through force analysis and time advancement method.

[0066] Further, in step S4, the air pressure P in the squeezed film obtained in step S3 will generate a suspension force, a restoring force and a restoring torque on the suspended object. When the suspended object is in a balanced state at time t, the gravity of the suspended object and the suspension force generated by the squeezed film are balanced, which is:

[0067]

[0068] Where m and g are the mass of the suspended object and the local gravitational acceleration, respectively. The mass of the suspended object can be measured by a precision balance. The tilt caused by the eccentricity of the suspended object satisfies the restoring moment balance of the membrane force distribution relative to the center of the suspended object, expressed as:

[0069]

[0070] Since the suspension height and tilt angle are unknown at this time, it is necessary to use the double spline interpolation method to process the suspension force balance equation (3) and the restoring moment balance equation (4) respectively. The air pressure distribution that satisfies the above balance equations (3) and (4) at time t can be obtained. The shear stress τ generated by the gas flow acting on the lower surface of the suspended object is zr and τ zθ for

[0071]

[0072] In the formula, shear stress τ zr and τ zθ The restoring force due to shear stress originating from the gas flow in the r and θ directions within the extruded film is expressed as:

[0073]

[0074] Where θ1 is the distance between the infinitesimal element rdrdθ and the center of the actual suspended object O L The angle of the line.

[0075] After a small time increment dt, the restoring force F at time t+dt can be obtained in the same way. r (t+dt). Because it takes time for the film to be squeezed to satisfy formulas (3) and (4), this time increment should be several dozen times the squeezing period 1 / f. The acceleration of the horizontal motion of the suspended object caused by the restoring force is:

[0076]

[0077] Using the time advancement method, the velocity and eccentricity at time t+dt can be expressed as:

[0078]

[0079] In this way, the change of the eccentricity of the suspended object over time, that is, the motion trajectory, can be obtained. At the initial moment, that is, t = 0, the eccentricity of the suspended object is equal to the preset eccentricity e0, and the squeezing effect has not yet taken effect, so the speed and acceleration at this moment are both 0. Based on the above analysis, the motion trajectory prediction flow chart under near-field acoustic suspension eccentricity is as follows Figure 5 As shown, when the calculation time reaches the preset time, the entire calculation process stops.

[0080] By changing the preset eccentricity e0, the reciprocating motion frequency f of the suspended object can be established. e and the mathematical relationship of the preset eccentricity, such as Figure 6As shown. The calculation results of the prediction method proposed by the present invention are very close to the experimental results. Therefore, this method can predict the motion trajectory of the suspended object by calculating the actual flow field distribution in the squeezed air film, and provide a theoretical basis for the flow field to control the motion of the suspended object.

[0081] S5. Based on the control equation, the dimensionless air film pressure distribution, and the motion trajectory and frequency of the suspended object, the relationship between the frequency and peak-to-peak value of the excitation voltage and the reciprocating motion frequency is constructed, and the frequency and peak-to-peak value of the excitation voltage in the finite element model are changed to achieve control of the motion frequency of the suspended object.

[0082] Further, in step S5, by using the finite element model in step S1, keeping the peak-to-peak value U of the excitation voltage and the preset eccentricity e0 unchanged, changing the frequency f of the excitation voltage, the surface amplitude distribution V(r) of the vibration disk under this excitation frequency can be obtained, and by repeating steps S2-S4, the relationship between the excitation voltage frequency and the reciprocating motion frequency of the suspended object can be established, such as Figure 7 Similarly, by keeping the excitation voltage frequency f and the preset eccentricity e0 unchanged and changing the peak-to-peak value U of the excitation voltage, the relationship between the excitation voltage amplitude and the reciprocating motion frequency of the suspended object can be established, as shown in Figure 8 shown.

[0083] It can be seen that the reciprocating frequency of the suspended object under eccentricity is the largest when the excitation voltage frequency is 19kHz. This is because this excitation frequency is close to the resonant frequency of the near-field acoustic suspension vibration system, so the amplitude of the vibration disk is the largest at this time, and the squeezing effect is obvious. In addition, the reciprocating frequency of the suspended object under eccentricity will increase with the increase of the peak-to-peak value of the excitation voltage. This is because the larger the peak-to-peak value of the excitation voltage, the larger the amplitude of the vibration disk, and the stronger the squeezing effect. Therefore, in order to obtain a higher reciprocating frequency of the suspended object, the excitation voltage frequency can be set near the resonant frequency of the vibration system or the peak-to-peak value of the excitation voltage can be increased. By establishing the relationship between the frequency and peak-to-peak value of the excitation voltage and the reciprocating frequency, a direction is provided for the control of the motion frequency of the suspended object.

[0084] Based on finite element theory and air film lubrication theory, the present invention establishes a fluid-solid coupling model of vibration system-squeezed air film-suspended object, and proposes a motion trajectory prediction method based on near-field acoustic suspension under eccentricity. The method can accurately predict the motion trajectory of the suspended object after eccentricity and propose corresponding control directions, providing a theoretical basis for motion optimization of near-field acoustic suspension in the fields of precision positioning and transmission.

[0085] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for predicting and controlling the motion frequency of an ultrasonically suspended object under eccentricity, characterized in that: The method comprises: S1. Constructing a finite element model of a near-field acoustic suspension vibration system using finite element analysis software, and obtaining the amplitude distribution of the vibration disk surface based on the finite element model; S2. constructing a theoretical motion analysis model based on the amplitude distribution on the surface of the vibration disk and the eccentric tilt angle of the suspended object, and obtaining a control equation for the dimensionless air pressure in the extruded film based on the theoretical motion analysis model; S3. Based on the control equation, the dimensionless air film pressure distribution in the extruded film is solved using the eight-point discretization method and the Newton-Raphson method; S4. Based on the dimensionless air film pressure distribution, the motion trajectory and frequency of the suspended object are calculated through force analysis and time advancement method, specifically including: Calculating the balance of suspension force and the balance of restoring moment based on the dimensionless air film pressure distribution; Based on the balance of the suspension force and the balance of the restoring moment, the shear stress generated by the gas flow acting on the lower surface of the suspended object is obtained; Obtaining a restoring force based on the shear stress, and obtaining an acceleration of horizontal motion of the suspended object according to the restoring force; Using the time advancement method, the motion speed and eccentricity at a preset time are obtained, and the motion trajectory and frequency of the suspended object are obtained based on the motion speed and eccentricity; The suspension force balance formula is: Where m and g are the mass of the suspended object and the local gravitational acceleration, respectively, P is the dimensionless air film pressure distribution, G is the gravity of the suspended object, and p a is the ambient air pressure, L is the radius of the vibrating disk, H is the air film thickness, R is the radial position; τ is the dimensionless time; The restoring moment balance formula is: Where, e is the eccentricity; The suspension force balance equation and the restoring moment balance equation are processed by the quadratic spline interpolation method respectively, and the air pressure distribution that satisfies the suspension force balance equation and the restoring moment balance equation at time t is obtained, and the shear stress τ generated by the gas flow acting on the lower surface of the suspended object zr and τ zθ for: In the formula, shear stress τ zr and τ zθ The restoring force due to shear stress originating from the gas flow in the r and θ directions within the extruded film is expressed as: Among them, θ1 is the distance between the infinitesimal element rdrdθ and the center of the actual suspended object O L The angle of the connecting line; After a small time increment dt, the restoring force F at time t+dt can be obtained in the same way. r (t+dt); because it takes time for the extruded film to satisfy the suspension force balance equation and the restoring torque balance equation, this time increment should be several dozen times the extrusion cycle 1 / f; the acceleration of the horizontal motion of the suspended object caused by the restoring force is: Using the time advancement method, the velocity and eccentricity at time t+dt can be expressed as: Among them, e(t) is the eccentricity of the suspended object at time t, and are the velocity and acceleration of the reciprocating motion of the suspended object at time t respectively; Thus, the change of the eccentricity of the suspended object with time, i.e., the motion trajectory, is obtained; S5. Based on the control equation, the dimensionless air film pressure distribution, and the motion trajectory and frequency of the suspended object, the relationship between the frequency and peak-to-peak value of the excitation voltage and the reciprocating motion frequency is constructed, and the frequency and peak-to-peak value of the excitation voltage in the finite element model are changed to achieve control of the motion frequency of the suspended object.

2. The method for predicting and controlling the motion frequency of an ultrasonically suspended object under eccentricity according to claim 1, characterized in that: In S1, a finite element model of a near-field acoustic suspension vibration system is constructed using finite element analysis software, and a method for obtaining the amplitude distribution on the surface of a vibration disk based on the finite element model specifically includes: S11. Establish a three-dimensional solid model of a near-field acoustic suspension vibration system, wherein the near-field acoustic suspension vibration system includes a Langevin transducer, a horn and a vibration disk; S12. Importing the three-dimensional solid model into the finite element analysis software to establish a three-dimensional solid finite element model; S13. Perform harmonic response analysis on the three-dimensional solid finite element model to obtain the amplitude distribution on the surface of the vibration disk.

3. The method for predicting and controlling the motion frequency of an ultrasonically suspended object under eccentricity according to claim 1, characterized in that: In S2, a method of constructing a theoretical motion analysis model based on the amplitude distribution on the surface of the vibration disk and the eccentric tilt angle of the suspended object, and obtaining a control equation of the dimensionless air pressure in the extruded film based on the theoretical motion analysis model specifically includes: The amplitude distribution on the surface of the vibration plate is set to remain unchanged. When the eccentricity between the suspended object and the vibration plate is e and the inclination angle is α, the introduction depth is h. g A hypothetical suspended object with a groove is obtained, and the dimensionless expression of the air film thickness is obtained; Based on the dimensionless air film thickness expression, a control equation of the dimensionless air pressure in the extruded film is obtained.

4. The method for predicting and controlling the motion frequency of an ultrasonically suspended object under eccentricity according to claim 3, characterized in that: The dimensionless gas film thickness expression H is: Among them, h m is the average distance between the center of the suspended object and the center of the vibration disk in the z direction, τ=ωt=2πft is the dimensionless time, t is the time since the near-field acoustic suspension system starts working, κ is the groove depth coefficient, and V(r) is the amplitude distribution.

5. The method for predicting and controlling the motion frequency of an ultrasonically suspended object under eccentricity according to claim 4, characterized in that: The governing equation for the dimensionless air pressure in the extruded film is: Where σ=12μ a ωL 2 / p a h a 2 , is the extrusion number, μ a is the dynamic viscosity coefficient of air, and They represent the influence of the reciprocating velocity and acceleration of the suspended object on the pressure distribution, P = p / p a ,H=h / h a and R = r / L are the dimensionless film pressure distribution, film thickness and radial position, respectively, where ρ a is the ambient air density, p a is the ambient air pressure, L is the radius of the vibrating disk, p and h represent the air pressure and thickness of the extruded film, respectively, and e(t) is the eccentricity of the suspended object at time t. and are the velocity and acceleration of the reciprocating motion of the suspended object at time t respectively.

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