Novel ultrasonic transducer design method for resisting nonlinearity caused by load fluctuation through energy beam coverage

Abstract

The invention discloses a novel ultrasonic transducer design method for resisting nonlinearity caused by load fluctuation through energy beam coverage, and relates to the technical field of ultrasonic transducer design optimization. Comprising the following steps: performing preliminary design of an ultrasonic transducer by taking a theorem in a valley hanging problem as a guiding thought; mathematical parameters in the valley hanging problem are matched with transducer parameters; determining a parameter for establishing an inequality in a valley hanging problem, and carrying out optimization design on the transducer; the method comprises the following steps of: defining coverage and overlapping penalty, realizing frequency drift minimization by establishing an objective function and constraint conditions, optimizing the transducer, and finishing the design of the novel ultrasonic transducer with high load capacity. According to the invention, a novel transducer design with load fluctuation resistance and low frequency drift is realized.

Description

Technical Field

[0001] This invention relates to the field of ultrasonic transducer design optimization technology, and more specifically to a novel ultrasonic transducer design method that uses energy beam coverage to resist nonlinearity caused by load fluctuations. Background Technology

[0002] With the rapid development of the aerospace, military, and automotive industries, the demand for machining difficult-to-machine materials such as optical glass, titanium alloys, silicon carbide, carbon fiber reinforced plastics, and ceramic matrix composites is constantly expanding. Ultrasonic-assisted machining, by superimposing ultrasonic vibrations onto the tool or workpiece to achieve intermittent cutting, thereby improving machining performance, has become an effective method for machining difficult-to-machine materials and is receiving increasing attention.

[0003] As a key component in ultrasonic-assisted machining systems, the ultrasonic transducer is crucial for converting electrical energy into mechanical vibration energy. Its performance stability and output energy consistency directly determine the machining quality and energy utilization efficiency of the entire ultrasonic system. Traditional transducers often employ piezoelectric ceramic materials, achieving energy concentration and mechanical amplification through a resonant structure. However, in practical applications, the transducer output is often affected by complex load conditions. Especially under non-uniform media, transient contact, or dynamic load changes, fluctuations in output amplitude and energy transfer path can easily occur, causing nonlinear response and frequency drift in the system. This leads to decreased energy transfer efficiency or even system detuning.

[0004] Currently, to address issues such as nonlinearity and amplitude instability in transducers under load, common techniques involve introducing frequency tracking or adaptive control algorithms (e.g., fuzzy PID, PLL, etc.) to dynamically adjust the drive signal frequency, thereby keeping the transducer operating near its resonant point. However, the response speed of frequency tracking control is limited by the sampling and calculation delays of the control loop, making it difficult to offset high-speed load fluctuations in real time and ensure stable amplitude. Therefore, it is crucial to improve the transducer's load capacity and reduce the impact of nonlinearity under load by focusing on the transducer itself. Due to limitations in theoretical methods and materials, ensuring output stability under load by enhancing the transducer's load capacity remains a challenge.

[0005] Therefore, proposing a novel ultrasonic transducer design method that uses energy beam coverage to resist nonlinearity caused by load fluctuations is an urgent problem to be solved by those skilled in the art to address the difficulties existing in the prior art. Summary of the Invention

[0006] In view of this, the present invention provides a novel ultrasonic transducer design method that uses energy beam coverage to resist nonlinearity caused by load fluctuations. Inspired by the valley problem in mathematics, it is introduced into engineering to guide the design of ultrasonic transducers, enhance the load capacity of ultrasonic transducers, reduce the nonlinearity generated under load, minimize frequency drift, and ensure amplitude stability during processing.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A novel ultrasonic transducer design method for energy beam coverage to resist nonlinearity caused by load fluctuations includes the following steps: S1. The preliminary design of the ultrasonic transducer is carried out based on the theorem in the valley hanging problem; S2. Match the mathematical parameters in the hanging valley problem with the transducer parameters; S3. Determine the parameters that make the inequalities in the valley problem hold true, and optimize the design of the transducer. S4. Define coverage and overlap penalty, and optimize the transducer by establishing objective function and constraints to minimize frequency drift, thus completing the design of a new type of ultrasonic transducer with high load capacity.

[0008] Optionally, when designing the ultrasonic transducer in S1 using the theorem from the valley problem as a guide, a non-point-concentrated acoustic energy distribution form is adopted to increase the lateral energy coverage of the ultrasonic energy field and ensure the lower bound of the ultrasonic energy coverage volume in three-dimensional space.

[0009] Optionally, the specific details of matching the mathematical parameters in the hanging valley problem with the transducer parameters in S2 are as follows: Geometric and Quantitative Distribution: The energy beam radius parameter δ in the valley-hanging problem corresponds to the actual radius of the transducer's energy beam, and satisfies δ≈0.5λ, where λ is the ultrasonic wave length; the direction number parameter in the valley-hanging problem... (#T) corresponds to the actual number of directions of the transducer's energy beam; Directional concentration: A constant related to the Kakeya-type inequality and the Córdoba-Wolff inequality in the valley problem. , The minimum angular spacing between the energy beams of the corresponding transducers And satisfy ; Materials and Coupling: The parameter ε in the valley problem corresponds to the control parameters of the acoustic impedance gradient layer and backing energy dissipation of the transducer; Phase and amplitude control: Configure the transducer with a multi-point closed-loop control module and an independently adjustable amplitude and phase control module, and limit the total power of the transducer to not exceed a preset threshold.

[0010] Optionally, the inequality in the hanging valley problem in S3 is: Determine if the inequality Established The transducer parameters were optimized and improved, and the transducer was remodeled.

[0011] Optionally, the specific details of coverage and overlap penalty defined in S4 are as follows: Coverage The calculation formula is:

[0012] in, The size of the space effectively covered by the sound field. To cover the target space; Overlapping penalty factor The calculation formula is:

[0013] in, The sum of the local energy coverage areas. This refers to the size of the space effectively covered by the sound field.

[0014] Optionally, the specific details of establishing the objective function and constraints in S4 are as follows: The objective function is , The corresponding constraints are: Geometric-frequency consistency constraint: any two energy beams , The included angle between them satisfies ; Covering lower bound constraints: ,in ; Energy homogenization constraint: The corresponding transducer parameters are further optimized to achieve the ultrasonic transducer design.

[0015] Optionally, the ultrasonic transducer is a hybrid drive structure, including: a main transducer, a first auxiliary compensation transducer, a second auxiliary compensation transducer, an acoustic impedance gradient layer, a backing layer, and a base plate; the main transducer and the first and second auxiliary compensation transducers are at a preset angle, with the initial value of the angle being 30°, and the size and number of the first and second auxiliary compensation transducers are matched with the energy beam radius and number of directions in the valley problem, respectively.

[0016] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a novel ultrasonic transducer design method that uses energy beam coverage to resist nonlinearity caused by load fluctuations, and its beneficial effects are as follows: By introducing the problem of hanging valleys from mathematics into engineering, and guiding transducer design, the transverse properties of the beam are increased by dividing the space and arranging the number of directions and beam width of the energy beam, thus avoiding excessively dense collinear beams. This enables the design of a new type of transducer that is resistant to load fluctuations and has low frequency drift. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This invention provides two scenarios: satisfying and not satisfying the non-centralization assumption in the valley hanging problem. Figure 2 A flowchart illustrating a novel ultrasonic transducer design method for resisting nonlinearity caused by load fluctuations, provided by this invention; Figure 3 A schematic diagram illustrating the design principle of an ultrasonic transducer for solving the problem of grain hanging in the valley, as provided in this invention; Figure 4 A geometrical diagram illustrating one of the theorems for the hanging valley problem provided by this invention; Figure 5 This is an isometric schematic diagram of the overall structure of the transducer provided by the present invention; Figure 6 This is a schematic front view of the various parts of the transducer provided by the present invention; Among them, 1-main transducer; 2-acoustic impedance gradient layer; 3-first auxiliary compensation transducer; 4-backing layer; 5-second auxiliary compensation transducer; 6-main amplitude transformer; 7-main transducer electrode; 8-auxiliary transducer electrode; 9-base plate; 10-main piezoelectric ceramic; 11-auxiliary piezoelectric ceramic; 12-auxiliary amplitude transformer. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] See Figure 2 As shown, this invention discloses a novel ultrasonic transducer design method that uses energy beam coverage to resist nonlinearity caused by load fluctuations, comprising the following steps: S1. The preliminary design of the ultrasonic transducer is carried out based on the theorem in the valley hanging problem; S2. Match the mathematical parameters in the hanging valley problem with the transducer parameters; S3. Determine the parameters that make the inequalities in the valley problem hold true, and optimize the design of the transducer. S4. Define coverage and overlap penalty, and optimize the transducer by establishing objective function and constraints to minimize frequency drift, thus completing the design of a new type of ultrasonic transducer with high load capacity.

[0021] Specifically, under the high-frequency approximation, the sound field can be represented as several "wave packets" or "energy tubes," each with a principal direction, position, and lateral scale. Strong overlap of different directions / wave packets in the same region increases the sensitivity to local stress peaks, temperature hotspots, nonlinear domain wall motion, and frequency drift. Reducing the overlap of high-energy wave packets from different directions within a small volume in the same space can lower local energy peaks and the probability of rapid nonlinear triggering, thereby improving the system's linearity and frequency robustness.

[0022] See Figure 1 The figure shows two cases where the non-centrality assumption in the valley hanging problem is satisfied and not satisfied, as provided by the present invention.

[0023] See Figure 3 The diagram shown illustrates the design principle of an ultrasonic transducer for addressing the grain-hanging problem provided by this invention; see also... Figure 4 The figure shown is a geometric schematic diagram of one of the theorems for the hanging valley problem provided by the present invention.

[0024] Furthermore, in the preliminary design of the ultrasonic transducer in S1, guided by the theorem in the valley problem, a non-point-concentrated acoustic energy distribution is adopted to increase the lateral energy coverage of the ultrasonic energy field and ensure the lower bound of the ultrasonic energy coverage volume in three-dimensional space.

[0025] Furthermore, the specific details of matching the mathematical parameters in the hanging valley problem with the transducer parameters in S2 are as follows: Geometric and Quantitative Distribution: The energy beam radius parameter δ in the valley-hanging problem corresponds to the actual radius of the transducer's energy beam, and satisfies δ≈0.5λ, where λ is the ultrasonic wave length; the direction number parameter in the valley-hanging problem... (#T) corresponds to the actual number of directions of the transducer's energy beam; Directional concentration: A constant related to the Kakeya-type inequality and the Córdoba-Wolff inequality in the valley problem. , The minimum angular spacing between the energy beams of the corresponding transducers And satisfy ; Materials and Coupling: The parameter ε in the valley problem corresponds to the control parameters of the acoustic impedance gradient layer and backing energy dissipation of the transducer; Phase and amplitude control: Configure the transducer with a multi-point closed-loop control module and an independently adjustable amplitude and phase control module, and limit the total power of the transducer to not exceed a preset threshold.

[0026] Furthermore, the inequality in the valley problem in S3 is: Determine if the inequality Established The transducer parameters were optimized and improved, and the transducer was remodeled.

[0027] Furthermore, the specific details of coverage and overlap penalty defined in S4 are as follows: Coverage The calculation formula is:

[0028] in, The size of the space effectively covered by the sound field. To cover the target space; Overlapping penalty factor The calculation formula is:

[0029] in, The sum of the local energy coverage areas. This refers to the size of the space effectively covered by the sound field.

[0030] Furthermore, the specific details of establishing the objective function and constraints in S4 are as follows: The objective function is , The corresponding constraints are: Geometric-frequency consistency constraint: any two energy beams , The included angle between them satisfies ; Covering lower bound constraints: ,in ; Energy homogenization constraint: The corresponding transducer parameters are further optimized to achieve the ultrasonic transducer design.

[0031] Furthermore, the ultrasonic transducer is a hybrid drive structure, including: a main transducer 1, a first auxiliary compensation transducer 3, a second auxiliary compensation transducer 5, an acoustic impedance gradient layer 2, a backing layer 4, and a base plate 9; the main transducer 1 forms a preset angle with the first auxiliary compensation transducer 3 and the second auxiliary compensation transducer 5, with the initial value of the angle being 30°. The size d and the number n of the first auxiliary compensation transducer 3 and the second auxiliary compensation transducer 5 are respectively related to the energy beam radius δ and the number of directions in the valley problem. (#T) matches.

[0032] See Figure 5 The diagram shown is an isometric schematic of the overall structure of the transducer provided by this invention; see also... Figure 6 The image shown is a schematic front view of the various parts of the transducer provided by the present invention. The structural components are named as follows: main transducer 1; acoustic impedance gradient layer 2; first auxiliary compensation transducer 3; backing layer 4; second auxiliary compensation transducer 5; main amplitude transformer 6; main transducer electrode 7; auxiliary transducer electrode 8; base plate 9; main piezoelectric ceramic 10; auxiliary piezoelectric ceramic 11; and auxiliary amplitude transformer 12.

[0033] Specifically, according to the description in the hanging valley problem: for each x∈Y0(P0), P has a prism that intersects P0 at x, with an included angle of at least 0. θ min The combination of these prisms fills a large portion of each b-sphere centered at P0. A hybrid drive transducer is employed, consisting of a single high-power transducer and a small array of auxiliary compensation transducers, with an initial angle of 30°, and the transducer is modeled using SolidWorks.

[0034] The constructed transducer model was imported into the multiphysics simulation software COMSOL, and the sound field generated by the ultrasonic transducer was calculated and simulated. The sound field was spatially divided into several energy beams, with the energy beam radius, number of directions, and minimum angular interval corresponding to... , , .

[0035] Write a MATLAB program to apply transducer optimization indices to the valley problem. The parameters are matched, and the MATLAB program is called from COMSOL. The correspondence is: auxiliary compensation transducer size. With quantity distribution : Corresponding energy beam radius With direction number Angle between transducers: ,correspond Materials and Coupling: Acoustic Impedance Gradient Layer, Backing Energy Dissipation Control .

[0036] Determine if the inequality Established Based on this, the transducer parameters were optimized and improved, and the transducer was remodeled.

[0037] Define coverage in COMSOL ; Overlapping penalties ; Objective function: , ; Constraints: Geometric-frequency consistency condition: ; Covering the lower bound: ; Energy homogenization: The corresponding transducer parameters are further optimized to achieve an ultrasonic transducer design with high load resistance and low frequency drift.

[0038] The optimized transducer was designed by simulating different load conditions. , , The impedance characteristics are evaluated to verify the designed transducer, and the frequency drift constraint is redefined based on coverage and overlap penalty.

[0039] Any adaptive changes made according to actual needs are within the scope of protection of this invention.

[0040] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0041] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A novel ultrasonic transducer design method for energy beam coverage to resist nonlinearity caused by load fluctuations, characterized in that, Includes the following steps: S1. The preliminary design of the ultrasonic transducer is carried out based on the theorem in the valley hanging problem; S2. Match the mathematical parameters in the hanging valley problem with the transducer parameters; S3. Determine the parameters that make the inequalities in the valley problem hold true, and optimize the design of the transducer. S4. Define coverage and overlap penalty, and optimize the transducer by establishing objective function and constraints to minimize frequency drift, thus completing the design of a new type of ultrasonic transducer with high load capacity.

2. The novel ultrasonic transducer design method according to claim 1, characterized in that, In the preliminary design of the ultrasonic transducer in S1, guided by the theorem in the valley problem, a non-point-concentrated acoustic energy distribution is adopted to increase the lateral energy coverage of the ultrasonic energy field and ensure the lower bound of the ultrasonic energy coverage volume in three-dimensional space.

3. The novel ultrasonic transducer design method according to claim 1, characterized in that, The specific details of matching the mathematical parameters in the hanging valley problem with the transducer parameters in S2 are as follows: Geometric and Quantitative Distribution: The energy beam radius parameter δ in the valley-hanging problem corresponds to the actual radius of the transducer's energy beam, and satisfies δ≈0.5λ, where λ is the ultrasonic wave length; the direction number parameter in the valley-hanging problem... (#T) corresponds to the actual number of directions of the transducer's energy beam; Directional concentration: A constant related to the Kakeya-type inequality and the Córdoba-Wolff inequality in the valley problem. , The minimum angular spacing between the energy beams of the corresponding transducers And satisfy ; Materials and Coupling: The parameter ε in the valley problem corresponds to the control parameters of the acoustic impedance gradient layer and backing energy dissipation of the transducer; Phase and amplitude control: Configure the transducer with a multi-point closed-loop control module and an independently adjustable phase and amplitude control module, and limit the total power of the transducer to not exceed a preset threshold.

4. The novel ultrasonic transducer design method according to claim 1, characterized in that, The inequality in the valley-hanging problem in S3 is: Determine if the inequality Established The transducer parameters were optimized and improved, and the transducer was remodeled.

5. A novel ultrasonic transducer design method according to claim 1, characterized in that, The specific details of coverage and overlap penalty defined in S4 are as follows: Coverage The calculation formula is: in, The size of the space effectively covered by the sound field. To cover the target space; Overlapping penalty factor The calculation formula is: in, The sum of the local energy coverage areas. This refers to the size of the space effectively covered by the sound field.

6. A novel ultrasonic transducer design method according to claim 1, characterized in that, The specific details of establishing the objective function and constraints in S4 are as follows: The objective function is , The corresponding constraints are: Geometric-frequency consistency constraint: any two energy beams , The included angle between them satisfies ; Covering lower bound constraints: ,in ; Energy homogenization constraint: The corresponding transducer parameters are further optimized to achieve the ultrasonic transducer design.

7. A novel ultrasonic transducer design method according to claim 1, characterized in that, The ultrasonic transducer is a hybrid drive structure, including: a main transducer, a first auxiliary compensation transducer, a second auxiliary compensation transducer, an acoustic impedance gradient layer, a backing layer, and a base plate; the main transducer is at a preset angle with the first and second auxiliary compensation transducers, with an initial angle of 30°; the size and number of the first and second auxiliary compensation transducers are matched with the energy beam radius and number of directions in the valley problem, respectively.

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