A modeling method for ultrasonic transducer load equivalent model

Abstract

The present invention relates to a method for modeling an ultrasonic transducer load equivalent model. The present invention includes the following steps: S1, constructing an ultrasonic transducer electromechanical equivalent model based on equivalent circuit theory; S2, inputting the ultrasonic transducer electromechanical equivalent model into a MATLAB simulation environment; S3, determining the input impedance characteristics of the ultrasonic transducer under pressure load by a comparison method; S4, matching the optimal impedance under the pressure load by a cross value mapping method based on the determined input impedance characteristics; S5, using the least squares method to perform curve fitting on the pressure load applied by the ultrasonic transducer and the optimal impedance. The present invention finds the optimal impedance corresponding to the dynamic pressure load by the cross value mapping method, fits the series of data by the least squares method, and obtains the optimal functional relationship. Based on this transducer pressure load and impedance equivalent model, the impedance can be obtained quickly and accurately by only giving a pressure.

Description

Technical Field

[0001] The present invention relates to the technical field of ultrasonic machining, and in particular to a method for modeling an ultrasonic transducer load equivalent model based on an equivalent circuit model. Background Art

[0002] In recent years, with the diversification of machining materials and increasing precision requirements, ultrasonic machining systems have seen significant application. In precision machining systems, the use of ultrasonic technology offers advantages over conventional machining techniques, such as increased tool life, improved workpiece quality, and a wider range of machining materials. Understanding the load characteristics of ultrasonic transducers is crucial for designing effective controllers, a development that researchers in the field of ultrasonic machining are eagerly awaiting.

[0003] However, the impedance of an ultrasonic transducer is affected by factors such as material, structural dimensions, and load. Furthermore, much existing research on ultrasonic transducers has been conducted under no-load conditions. This no-load model analysis only reflects a portion of the system's performance. When the load increases, the existing no-load model fails to fully reflect the system's true state, leading to wear of the ultrasonic transducer tool head and significantly impacting ultrasonic machining. Furthermore, the dramatic dynamic load changes during ultrasonic machining make it difficult to accurately estimate the input impedance and resonant frequency, making it impossible to provide guidance for the design of ultrasonic toolholders and controllers. Therefore, research on the load characteristics of ultrasonic transducers is crucial. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for modeling an ultrasonic transducer load equivalent model based on an equivalent circuit model. Based on the theoretical basis of equivalent circuits, combined with experiments and simulations, an equivalent model of the ultrasonic transducer dynamic pressure load and input impedance is established.

[0005] In order to achieve the above object, the present invention comprises the following steps:

[0006] S1. Construct an electromechanical equivalent model of ultrasonic transducer based on equivalent circuit theory;

[0007] S2, inputting the electromechanical equivalent model of the ultrasonic transducer into the MATLAB simulation environment;

[0008] S3. Determine the input impedance characteristics of the ultrasonic transducer under pressure load by comparison method in MATLAB simulation environment;

[0009] S4. Based on the determined input impedance characteristics, matching the optimal impedance under the pressure load by a cross value mapping method;

[0010] S5. Use the least squares method to perform curve fitting between the pressure load applied by the ultrasonic transducer and the optimal impedance.

[0011] In S1, the equivalent circuit theory is applied to analyze the relationship between the pressure load and impedance of the ultrasonic transducer, and the equivalent models of the metal front and rear cover plates and the piezoelectric ceramic crystal stack are integrated. The formula is expressed as follows:

[0012]

[0013] Among them, Z l is the total impedance of the metal rear cover, Z r is the total impedance of the metal front cover, Z 3p′ is the series-parallel impedance of the equivalent six-terminal network of the piezoelectric ceramic ring, C0 is the chip cut-off capacitance, ω is the longitudinal wave angular frequency, Z i is the input impedance.

[0014] In S2, based on the relevant parameter information of the ultrasonic transducer piezoelectric ceramic sheet and the metal front and rear cover plates, such as cross-sectional area S, number of ceramic sheets m, and length l, the amplitude-frequency and phase-frequency curves corresponding to the ultrasonic transducer when loaded with different pressures are obtained in the MATLAB simulation environment. At the same time, a loading electrical characteristic experiment is conducted on the selected ultrasonic transducer: assuming that the input impedance characteristics during the loading process vary from purely resistive (0 to a), inductive (0 to a+bj), and capacitive (0 to a-bj), the amplitude-frequency and phase-frequency curves corresponding to the ultrasonic transducer under different characteristic input impedances can be obtained based on the ultrasonic transducer component parameter information and the equivalent model calculation formula.

[0015] In S3, through comparative analysis, it can be found that when the input impedance is purely resistive, as the input impedance value increases, the peak of the amplitude curve decreases, and the space occupied by the phase-frequency curve decreases. After reaching the set value, the ultrasonic transducer input impedance begins to show capacitive characteristics, and the load characteristic parameters at the half-power point do not exist. When the input impedance is capacitive, as its value increases, the amplitude curve decreases, and the amplitude-frequency and phase-frequency curves both shift to the right. The input impedance characteristics are capacitive throughout the entire frequency sweep range. When the input impedance is inductive, the amplitude-frequency and phase-frequency curves shift to the left. In summary, through comparative analysis, it can be found that the amplitude-frequency and phase-frequency characteristic curves of the ultrasonic transducer when loaded with different pressures and when the input impedance is capacitive shift slightly to the right, which means that the input impedance characteristics of the ultrasonic transducer under pressure load are capacitive.

[0016] In S4, the cross value mapping method in this embodiment is as follows. The frequency and impedance characteristics of the ultrasonic transducer are key factors affecting its working performance. Considering them comprehensively, the forward resonant frequency F is selected. sThe three load characteristic parameters, F1, half-power point, and dynamic resistance R, were studied. The input impedance of the ultrasonic transducer under pressure load is capacitive, as determined by S3. The capacitive impedance range of 0 to 1000-1000j was selected for discussion. In the MATLAB simulation environment, the parameters of the front and rear metal covers and the piezoelectric ceramic crystal stack of the ultrasonic transducer were input as basic information, and the component equivalent expressions were input as the calculation part. Based on this information, a series of load characteristic parameter values ​​corresponding to the ultrasonic transducer within the selected capacitive impedance range were calculated, and a three-dimensional spatial diagram consisting of the load characteristic parameter values ​​(Z-axis), the real part of the capacitive impedance (X-axis), and the imaginary part (Y-axis) was plotted.

[0017] By adding weights of 0~kN to the front cover of the ultrasonic transducer, m groups of experiments are conducted to measure m groups of load characteristic parameter data. One group of data is randomly selected, such as when applying a pressure of F=20N, according to the data F measured by the PV520A impedance analyzer s =20030.4Hz, F1 =19998.7Hz, R = 15.674Ω. To find the same values ​​for the load characteristic parameters under study within the capacitive impedance range of 0 to 1000-1000j, within this range, a fixed horizontal plane is drawn in the three-dimensional space system for each of the load characteristic parameter values ​​measured by the impedance meter when a force of 20N is applied. The three fixed horizontal planes are used to make horizontal equivalent sections of the drawn three-dimensional graph, resulting in three intersecting curves.

[0018] In order to visually observe the position of the intersection curve in the two-dimensional coordinate system (the X-axis is the real part of the capacitive impedance a-bj, and the Y-axis is the imaginary part of the capacitive impedance), the intersection curves obtained by the intersection of the two surfaces are mapped one by one to the two-dimensional coordinate system to obtain three mapping curves.

[0019] By merging the three mapping curves obtained through mapping, we can get the load characteristic parameter F s The three intersection points of the three mapping curves F1, F2, and R are points A, B, and C. To find points equidistant from the three mapping curves, mathematical knowledge shows that the maximum inscribed circle of the triangle can be drawn through the three intersection points. The center D of the inscribed circle can be obtained. This center value can be approximated as the optimal impedance of the ultrasonic transducer under the applied pressure load.

[0020] Based on the m groups of data measured by the PV520A impedance analyzer, the next group of data is selected and the steps (fixed value cross section, mapping intersection curve, merging intersection lines, and making inscribed circles) are repeated to obtain the optimal impedance of the ultrasonic transducer when different pressure loads are applied.

[0021] In S5, the optimal impedance (A real -B imagj) has a certain correlation with the applied pressure F. Through various fitting methods, such as least squares, interpolation, and weighted regression, it was ultimately found that the least squares method has a very good fitting effect for the curve fitting of the applied pressure of the ultrasonic transducer and the optimal impedance, and the resulting fitting function formula is as follows. At this point, the equivalent model of the dynamic pressure load and input impedance of the ultrasonic transducer has been established. By applying any pressure load, the input impedance can be obtained through the established equivalent model.

[0022] The present invention demonstrates the following beneficial effects: By constructing an electromechanical equivalent model of an ultrasonic transducer, the present invention concludes that the input impedance of an ultrasonic transducer under pressure load exhibits capacitive characteristics. Furthermore, the present invention uses a cross-value mapping method to find the optimal impedance corresponding to dynamic pressure loads. By fitting a series of data using the least squares method, the optimal functional relationship is obtained. Based on this transducer pressure load and impedance equivalent model, the impedance can be quickly and accurately determined simply by specifying a pressure, providing a theoretical foundation for the efficient and accurate design of transducer controllers. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A flow chart of a method for modeling an ultrasonic transducer load equivalent model based on an equivalent circuit model provided by the present invention;

[0024] Figure 2 is the electromechanical equivalent model of the ultrasonic transducer;

[0025] Figure 3(a) shows the forward resonant frequency F of the ultrasonic transducer s Three-dimensional spatial plot within the selected capacitive impedance range;

[0026] Figure 3(b) is a three-dimensional spatial diagram of the ultrasonic transducer half-power point F1 within the selected capacitive impedance range;

[0027] Figure 3(c) is a three-dimensional spatial diagram of the ultrasonic transducer's dynamic resistance R within the selected capacitive impedance range;

[0028] Figure 4(a) shows the F s The three-dimensional diagram and its corresponding fixed horizontal plane are cross-sectional views;

[0029] Figure 4(b) shows a three-dimensional diagram of F1 within the selected capacitive impedance range and a cross-sectional view of its corresponding constant-value horizontal plane;

[0030] Figure 4(c) shows a three-dimensional plot of R within the selected capacitive impedance range and a cross-section of the constant-value horizontal plane;

[0031] Figure 5(a) shows the F s The mapping process of intersecting curves;

[0032] Figure 5(b) shows the mapping process of the F1 intersection curve;

[0033] Figure 5(c) shows the mapping process of the R-intersection curve;

[0034] Figure 6(a) shows the F in the two-dimensional coordinate system composed of the real and imaginary parts of the capacitive impedance. s Mapping curve;

[0035] Figure 6(b) shows the F1 mapping curve in the two-dimensional coordinate system composed of the real and imaginary parts of the capacitive impedance;

[0036] Figure 6(c) shows the R mapping curve in the two-dimensional coordinate system composed of the real and imaginary parts of the capacitive impedance;

[0037] Figure 7 Merge graph of three mapping curves;

[0038] Figure 8 It is the inscribed circle diagram of the intersection of three mapping curves. DETAILED DESCRIPTION

[0039] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] like Figure 1 As shown, the process of the modeling method of the ultrasonic transducer load equivalent model based on the equivalent circuit model provided by the present invention is as follows:

[0041] S1. Construct an electromechanical equivalent model of ultrasonic transducer based on equivalent circuit theory;

[0042] S2, inputting the electromechanical equivalent model of the ultrasonic transducer into the MATLAB simulation environment;

[0043] S3. Determine the input impedance characteristics of the ultrasonic transducer under pressure load by comparison method in MATLAB simulation environment;

[0044] S4. Based on the determined input impedance characteristics, matching the optimal impedance under the pressure load by a cross value mapping method;

[0045] S5. Use the least squares method to perform curve fitting between the pressure load applied by the ultrasonic transducer and the optimal impedance.

[0046] In S1, the equivalent circuit theory is applied to analyze the relationship between the pressure load and impedance of the ultrasonic transducer, and the equivalent models of the metal front and rear cover plates and the piezoelectric ceramic crystal stack are integrated to obtain the electromechanical equivalent model of the ultrasonic transducer as shown in the figure. Figure 2 As shown, the formula is expressed as:

[0047]

[0048] Among them, Z l is the total impedance of the metal rear cover, Z 11 、Z 12 、Z13 is the impedance of each arm of the equivalent four-terminal network of the metal rear cover, Z r is the total impedance of the metal front cover, Z 21 、Z 22 、Z 23 is the impedance of each arm of the equivalent four-terminal network of the metal front cover, R m2 、R m1 are the mechanical series loss resistance between the front and rear metal covers and the sandwich transducer, Z ft Indicates the radiated acoustic impedance of the front cover, Z 1p′ 、Z 2p′ 、Z 3p′ is the series-parallel impedance of the equivalent six-terminal network of the piezoelectric ceramic ring, C0 is the chip cut-off capacitance, ω is the longitudinal wave angular frequency, Z i is the input impedance.

[0049] In S2, the parameter information related to the piezoelectric ceramic piece and the metal front and rear cover plates of the ultrasonic transducer designed in this embodiment is shown in Table 1.

[0050] Table 1 Materials and parameters

[0051]

[0052]

[0053] In the MATLAB simulation environment, the corresponding amplitude-frequency and phase-frequency curves of the ultrasonic transducer when loaded with different pressures are obtained. At the same time, the electrical characteristics of the selected ultrasonic transducer are tested: assuming that the input impedance characteristics change range from pure resistance (0 to a), inductance (0 to a+bj), and capacitive (0 to a-bj) during the loading process, the amplitude-frequency and phase-frequency curves of the ultrasonic transducer under different characteristic input impedances can be obtained based on the component parameter information of the ultrasonic transducer and the equivalent model calculation formula.

[0054] In S3, through comparative analysis, it can be found that when the input impedance is purely resistive, as the input impedance value increases, the peak of the amplitude curve decreases, and the space occupied by the phase-frequency curve decreases. After reaching the set value, the ultrasonic transducer input impedance begins to show capacitive characteristics, and the load characteristic parameters at the half-power point do not exist. When the input impedance is capacitive, as its value increases, the amplitude curve decreases, and the amplitude-frequency and phase-frequency curves both shift to the right. The input impedance characteristics are capacitive throughout the entire frequency sweep range. When the input impedance is inductive, the amplitude-frequency and phase-frequency curves shift to the left. In summary, through comparative analysis, it can be found that the amplitude-frequency and phase-frequency characteristic curves of the ultrasonic transducer when loaded with different pressures and when the input impedance is capacitive shift slightly to the right, which means that the input impedance characteristics of the ultrasonic transducer under pressure load are capacitive.

[0055] In S4, the cross value mapping method of the present invention is as follows. The frequency and impedance characteristics of the ultrasonic transducer are key factors affecting its working performance. Considering them comprehensively, the forward resonant frequency F is selected. s The three load characteristic parameters, F1, half-power point, and dynamic resistance R, were studied. The input impedance of the ultrasonic transducer under pressure load is capacitive, as determined by S3. The capacitive impedance range of 0 to 1000-1000j was selected for discussion. In the MATLAB simulation environment, the relevant parameters of the front and rear metal covers and the piezoelectric ceramic crystal stack of the ultrasonic transducer were input as basic information, and the component equivalent expressions were input as the calculation part. Based on the above information, a series of load characteristic parameter values ​​corresponding to the ultrasonic transducer within the selected capacitive impedance range were calculated. A three-dimensional spatial diagram consisting of the load characteristic parameter values ​​(Z-axis), the real part (X-axis), and the imaginary part (Y-axis) of the capacitive impedance was plotted, as shown in Figures 3(a), 3(b), and 3(c).

[0056] By adding weights of 0~kN to the front cover of the ultrasonic transducer, m groups of experiments are conducted to measure m groups of load characteristic parameter data. One group of data is randomly selected, such as when applying a pressure of F=20N, according to the data F measured by the PV520A impedance analyzer s =20030.4Hz, F1 =19998.7Hz, R =15.674Ω. In order to find the same values ​​of the load characteristic parameters in the capacitive impedance range of 0 to 1000-1000j, within this range, a fixed horizontal plane is drawn in the three-dimensional space system for each of the load characteristic parameter values ​​measured by the impedance meter when a force of 20N is applied. The three fixed horizontal planes respectively make horizontal isovalue sections of the drawn three-dimensional graph, and three intersecting curves are obtained, as shown in Figures 4(a), 4(b), and 4(c).

[0057] In order to visually observe the position of the intersection curve in the two-dimensional coordinate system (the X-axis is the real part of the capacitive impedance a-bj, and the Y-axis is the imaginary part of the capacitive impedance), the intersection curve obtained by the intersection of the two surfaces is mapped one by one to the two-dimensional coordinate system to obtain three mapping curves. The mapping process of the intersection curve is shown in Figure 5(a), Figure 5(b), and Figure 5(c).

[0058] The intersection curve is completely mapped to the two-dimensional coordinate system composed of the x-axis (real part of capacitive impedance) and the y-axis (imaginary part of capacitive impedance), and three mapping intersection lines are obtained as shown in Figure 6(a), Figure 6(b), and Figure 6(c).

[0059] The three mapping curves obtained by mapping are combined to obtain the graph as follows Figure 7 As shown. Figure 7 It can be obtained that the load characteristic parameter (F sThe three intersection points of the three mapping curves (A, B, and C) are obtained by intersecting the three mapping curves. To find the points with equal distances from the three mapping curves, we can draw the maximum inscribed circle of the triangle at the three intersection points according to the relevant mathematical knowledge, as shown in the following example: Figure 8 As shown, the center D of the inscribed circle can be obtained, and the value of this center can be approximately the optimal impedance of the ultrasonic transducer corresponding to the applied pressure load.

[0060] Based on the m groups of data measured by the PV520A impedance analyzer, the next group of data is selected and the steps (fixed value cross section, mapping intersection curve, merging intersection lines, and making inscribed circles) are repeated to obtain the optimal impedance of the ultrasonic transducer when different pressure loads are applied.

[0061] In S5, the optimal impedance (A real -B imag j) has a certain correlation with the applied pressure F. Through various fitting methods, such as least squares method, interpolation method, weighted regression, etc., it is finally found that the least squares method has a very good fitting effect for the curve fitting of the pressure applied by the ultrasonic transducer and the optimal impedance. The fitting function formula is:

[0062]

[0063] At this point, the equivalent model of the ultrasonic transducer's dynamic pressure load and input impedance has been established. By applying a pressure load at random, the input impedance can be obtained through the established equivalent model.

[0064] From the above results, it can be found that the method proposed in the present invention can quickly and accurately obtain the input impedance value corresponding to a certain pressure in the ultrasonic machining system, providing a solid theoretical basis for the subsequent design of the controller.

[0065] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will readily appreciate that other variations or modifications based on the above descriptions are possible. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for modeling an ultrasonic transducer load equivalent model, characterized in that The method comprises the following steps: S1. Construct an electromechanical equivalent model of ultrasonic transducer based on equivalent circuit theory; S2, inputting the electromechanical equivalent model of the ultrasonic transducer into the MATLAB simulation environment; S3. Determine the input impedance characteristics of the ultrasonic transducer under pressure load by comparison method in MATLAB simulation environment; S4. Based on the determined input impedance characteristics, matching the optimal impedance under the pressure load by a cross value mapping method; S5. Using the least square method to perform curve fitting between the pressure load applied by the ultrasonic transducer and the optimal impedance; The cross value mapping method is as follows: It is obtained from S3 that the input impedance of the ultrasonic transducer under pressure load presents a capacitive characteristic, and the capacitive impedance range of 0 to 1000-1000j is selected for analysis; in the MATLAB simulation environment, the relevant parameter information of the front and rear metal cover plates and the piezoelectric ceramic crystal stack of the ultrasonic transducer is input as the basic information, and the component equivalent expression is input as the calculation part. Based on the above information, the series of load characteristic parameter values ​​corresponding to the ultrasonic transducer in the selected capacitive impedance range are calculated, and a three-dimensional space diagram consisting of the load characteristic parameter value, the real part and the imaginary part of the capacitive impedance is drawn, wherein the load characteristic parameter value is the Z axis, the real part of the capacitive impedance is the X axis, and the imaginary part of the capacitive impedance is the Y axis; By adding weights of 0~kN to the front cover of the ultrasonic transducer, m groups of experiments were conducted to measure m groups of load characteristic parameter data. One group of data was randomly selected. When the pressure F=20N was applied, the data F measured by the PV520A impedance analyzer was obtained. s =20030.4Hz, F1=19998.7Hz, R=15.674Ω; For the load characteristic parameter values ​​measured by the impedance meter when a force of 20N is applied, a fixed horizontal plane is made in the three-dimensional space system. The three fixed horizontal planes respectively make horizontal equal-value sections of the drawn three-dimensional graph to obtain three intersecting curves. The intersection curves obtained by intersecting the two surfaces are mapped one by one to the two-dimensional coordinate system to obtain three mapping curves; The three mapping curves obtained by mapping are combined to obtain the load characteristic parameter F s The three intersection points of the three mapping curves F1, F2, and R are A, B, and C. The maximum inscribed circle of the triangle is drawn for the three intersection points, and the center D of the inscribed circle is obtained. The center value can be approximated as the optimal impedance of the ultrasonic transducer corresponding to the applied pressure load. According to the m groups of data measured by the PV520A impedance analyzer, the next group of data was selected, and the fixed cross section, mapping of the intersection curve, merging of the intersection lines, and inscribed circle were repeated to obtain the optimal impedance of the ultrasonic transducer when different pressure loads were applied.

2. The method for modeling an ultrasonic transducer load equivalent model according to claim 1, wherein: In S1, the equivalent circuit theory is applied to analyze the relationship between the pressure load and impedance of the ultrasonic transducer, and the equivalent models of the metal front and rear cover plates and the piezoelectric ceramic crystal stack are integrated. The formula is expressed as follows: Among them, Z l is the total impedance of the metal rear cover, Z r is the total impedance of the metal front cover, Z 3p′ is the series-parallel impedance of the equivalent six-terminal network of the piezoelectric ceramic ring, C0 is the chip cut-off capacitance, ω is the longitudinal wave angular frequency, Z i is the input impedance.

3. The method for modeling an ultrasonic transducer load equivalent model according to claim 1, wherein: In S2, based on the relevant parameter information of the piezoelectric ceramic sheet and the metal front and rear cover plates of the ultrasonic transducer used, the amplitude-frequency and phase-frequency curves corresponding to the ultrasonic transducer when loaded with different pressures are obtained in the MATLAB simulation environment; At the same time, the selected ultrasonic transducer is subjected to a loading electrical characteristics experiment: assuming that the input impedance characteristics change range during the loading process is purely resistive, inductive, and capacitive, according to the component parameter information of the ultrasonic transducer and the equivalent model calculation formula, the amplitude-frequency and phase-frequency curves corresponding to the ultrasonic transducer under different characteristic input impedances can be obtained.

4. The method for modeling an ultrasonic transducer load equivalent model according to claim 1, wherein: In S3, through comparative analysis, it is found that when the input impedance is purely resistive, as the input impedance value increases, the peak value of the amplitude curve decreases, and the space occupied by the phase-frequency curve decreases. After reaching the set value, the input impedance of the ultrasonic transducer begins to show capacitive characteristics and the load characteristic parameters of the half-power point do not exist; when the input impedance is capacitive, as its value increases, the amplitude curve decreases, and the amplitude-frequency and phase-frequency curves both move to the right. The input impedance characteristics are capacitive within the entire frequency sweep range; when the input impedance is inductive, the amplitude-frequency and phase-frequency curves move to the left.

5. The method for modeling an ultrasonic transducer load equivalent model according to claim 1, wherein: In S5, the least squares method is used to perform curve fitting between the pressure applied by the ultrasonic transducer and the optimal impedance to obtain a fitting function. At this point, the equivalent model of the dynamic pressure load and input impedance of the ultrasonic transducer is established. By applying a pressure load at will, the input impedance can be obtained through the established equivalent model.

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