Transducer small-angle emission model based on ultrasonic cavitation field foot care

Abstract

The invention discloses a transducer small-angle emission model for foot care based on an ultrasonic cavitation field, which comprises a single transducer or a double transducer arranged in a foot container, and the included angle between the ultrasonic emission direction of the single transducer or the double transducer and the sole is a small angle; and when the double-transducer hedging emission mode is adopted, a coupling physical field used for accurately controlling the energy and distribution of an ultrasonic cavitation field for nursing feet is added at any position on the propagation path of ultrasonic waves in the foot container. According to the method, the most suitable transducer small-angle model of the ultrasonic cavitation field is analyzed and selected to nurse the foot, so that popularization and application of equipment or products for foot nursing under the action of the ultrasonic cavitation field can be facilitated, and the method has a good application prospect.

Description

Technical Field

[0001] The invention relates to the technical field of ultrasonic cavitation effect, and in particular to a transducer small-angle emission model for foot care based on ultrasonic cavitation field. Background Art

[0002] In the prior art, people know that the ultrasonic cavitation effect has the effect of killing fungi, and can also kill fungi on the surface of the skin. Based on theoretical analysis, the ultrasonic cavitation effect has a certain effect on foot care. Therefore, if the ultrasonic cavitation sound field can be applied to the feet, foot care can be performed through the physical method of ultrasonic cavitation, which will bring revolutionary changes to the traditional foot care industry and is also good news for all athlete's foot patients, who do not need to use various chemical drugs and worry about drug side effects and drug resistance.

[0003] However, the current application of ultrasonic cavitation sterilization effect is mainly concentrated in industrial sterilization, agricultural and sideline product sterilization, and household food sterilization. So far, there is still no equipment or product that uses ultrasonic cavitation field to care for the feet. Some patents or papers only outline ultrasonic cavitation foot care and ultrasonic cavitation field fungus killing experiments, but they only put forward concepts without conducting research on the scope of application. From the perspective of whether cavitation field can be applied (for foot care), the reasons are as follows:

[0004] 1. The ultrasonic cavitation field in a certain water area belongs to the non-focused category. When human tissue is placed in the ultrasonic cavitation field, when ultrasound propagates in the water, some of the ultrasound will enter the human tissue, which will produce certain mechanical effects. Because of the non-focused sound field, the thermal effect is very weak. Due to the mechanical effect, there will be mechanical effects such as shear stress in the human tissue. When the stress is large enough, the direct reaction of the tissue is swelling or piercing pain. The greater the sound intensity, the greater the stress, and the stronger the swelling and tingling. Since the impedance ρ×c (ρ refers to the density of human tissue, c refers to the speed of sound) of different human tissues is different, the impedance is different, and the absorption of sound waves is different. At the same time, everyone has different feelings about swelling and tingling. Therefore, it is impossible to give a safe output power value for ultrasonic cavitation, and thus, it is impossible to ensure that ultrasound enters the skin of the foot to produce swelling or tingling, so as to ensure the comfort of the ultrasonic cavitation field in the foot care for people. Therefore, this technical difficulty leads to the ultrasonic cavitation field acting on the foot care foot equipment or products, there is no good promotion prospect;

[0005] 2. If the ultrasonic output power is continuously reduced to achieve safe use by most people, however, if the output power is reduced blindly, the cavitation intensity will decrease as the power value decreases, and the effect of killing fungi will decrease, which will inevitably affect the effect of foot care, or even fail to produce the care effect.

[0006] Therefore, how to overcome the above-mentioned problems and construct an output model for foot care using ultrasonic cavitation field, which can not only output a suitable output power value of ultrasonic cavitation to ensure the effect of foot care, but also avoid the swelling or strong tingling caused by ultrasonic input into the elastic tissue of the foot, thereby improving the user's comfort level, is an issue that needs to be urgently solved, so as to promote the application of equipment or products that use ultrasonic cavitation field to care for the feet. Summary of the invention

[0007] The technical problem solved by the present invention is to overcome the existing concept of merely outlining ultrasonic cavitation foot care without conducting research on the scope of application, and the problem of how to use cavitation field angle analysis to achieve foot care. The transducer small-angle emission model for foot care based on ultrasonic cavitation field of the present invention analyzes the influence of the layout of the transducer and the ultrasonic emission direction when the ultrasonic cavitation field acts on the foot. The angle between the ultrasonic emission direction of a single transducer or a dual transducer and the sole of the foot is the best for the care effect. It is obtained that the dual transducer counter-emission mode acts on the sole of the foot, and the precise control of the ultrasonic cavitation field energy and distribution for foot care is achieved by setting the parameters of the coupled physical field. Then, through the analysis of the dual transducer frequency after adding the coupled physical field, the application of the dual transducer counter-emission mode is further explained, which can reduce the influence of the load and the static pressure of the water level on the matching circuit, achieve the stability of the entire ultrasonic cavitation field, complete the construction of the small-angle emission model for foot care of the ultrasonic cavitation field, and select the most suitable transducer small-angle model of the ultrasonic cavitation field to care for the foot, which can facilitate the promotion and application of equipment or products for foot care using the ultrasonic cavitation field.

[0008] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0009] A transducer small-angle emission model for foot care based on ultrasonic cavitation field, comprising a single transducer or a double transducer installed in a foot container, wherein the ultrasonic emission direction of the single transducer or the double transducer is at a small angle β with the sole of the foot;

[0010] In the dual-transducer counter-emission mode, a coupled physical field for precise control of the energy and distribution of the ultrasonic cavitation field is added at any point on the propagation path of the ultrasonic wave in the foot container.

[0011] Preferably, the small angle β has a value range of 0°≤β≤15°.

[0012] Preferably, the angle between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is a small angle β, and by analyzing the cavitation intensity distribution characteristics of the ultrasonic cavitation field, the dual transducer counter-emission mode is optimized to act better on the sole of the foot.

[0013] Preferably, the value range of the small angle β is 0°≤β≤15°, and the selection process is as follows:

[0014] Assuming that the impedance of the elastic tissue of the human foot and the impedance of water are equal, the specific analysis process of the small angle β is as follows:

[0015] Step (A1), analyzing the ultrasonic cavitation field acting on the foot,

[0016] According to the Reisler sound wave reflection and refraction formula, as shown in formula (1):

[0017]

[0018] Where, k1 and k2 are the wave numbers of medium 1 and medium 2 respectively; c1 and c2 are the sound speeds of medium 1 and medium 2 respectively, and medium 1 and medium 2 are water and elastic tissue of human foot respectively; θ i ,θ t The incident angle of the incident wave in water and the transmission angle of the transmitted wave in human tissue respectively;

[0019] Since the density and sound velocity of the elastic tissue of the human foot are approximately equal to those of water, the characteristic impedances of media 1 and 2 are equal, as shown in formula (2):

[0020] ρ1c1=ρ2c2 (2)

[0021] From equation (1) and equation (2), we can get: i =θ t , that is, the incident angle of the incident wave in water is equal to the transmission angle of the transmitted wave in human tissue;

[0022] According to the transmission coefficient formula (3) at any angle of incidence:

[0023]

[0024] Among them, t P is the transmission coefficient;

[0025] When 0≤θ i <90°, because θ i =θ t ,ρ1c1=ρ2c2, so t P is always equal to 1, that is, no matter how the transducer is arranged, as long as the incident angle θ of the incident wave i Not equal to 90°, when the incident sound intensity of the transducer is constant, the amount of ultrasound entering the foot is the same, and does not change with the incident angle θ of the incident wave i changes with the changes;

[0026] Step (A2), according to the reflection coefficient formula (4):

[0027]

[0028] Among them, r P is the reflection coefficient, when the incident angle of the incident wave in water is θ i When it is equal to 90°, the small angle β = 0°, and the ultrasonic emission area is controlled not to be higher than the sole of the foot, and |r P |≈1 grazing incidence phenomenon, the incident wave is completely reflected, avoiding the incident wave entering the elastic tissue of the human foot to produce swelling or tingling, that is, the feasibility of completing the analysis of the angle between the ultrasonic emission direction of the single transducer or the dual transducer and the sole of the foot is a small angle β=0°;

[0029] In real situations, the impedance of the elastic tissue of the human foot and the impedance of water are similar but not equal. The specific analysis process of the small angle β is as follows:

[0030] In step (A3), when the density and sound velocity of the elastic tissue of the human foot are taken according to actual values, the sound velocity of the elastic tissue of the human foot can be taken as c2≈1540m / s, and the sound velocity of water at normal temperature and pressure can be taken as c1≈1500m / s. According to formula (1), the following is obtained:

[0031] The speed of sound in the elastic tissue of the human foot is greater than the speed of sound in water, and the refraction angle is always greater than the incident angle. When the incident angle increases from 0°, the refraction angle also increases. When the incident angle increases to 90°, the refracted wave propagates along the interface, that is, parallel to the sole surface. At this time, according to formula (1), the incident angle θ i ≈75°, that is, the small angle β between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is ≈15°;

[0032] Step (A4), if the incident angle continues to increase, sinθ t >1, that is, there is no real angle sinθ t , so there is no refracted wave in the elastic tissue of the human foot in the usual sense. At this time, the reflection angle is still equal to the incident angle, and the reflection coefficient is equal to the complex number, whose absolute value is always equal to 1. The energy of the incident wave is all reflected back into the water, but a phase jump is generated relative to the incident wave. Therefore, when the sound velocity of the elastic tissue of the actual human foot is taken as normal, when the incident angle is 90°>θ i When ≥75°, that is, 0°<β≤15°, within the range of the incident direction, the ultrasonic wave of the single transducer or dual transducer is totally reflected at the tissue interface of the sole of the foot during transmission, and no ultrasonic energy is transmitted into the elastic tissue of the human foot, thereby avoiding the incident wave entering the elastic tissue of the human foot to cause swelling or tingling. That is, the analysis is completed under real circumstances, and the rationality of the angle between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is a small angle of 0°<β≤15°.

[0033] Preferably, the angle between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is a small angle β. By analyzing the cavitation intensity distribution characteristics of the ultrasonic cavitation field, it is optimized that the dual transducer counter-emission mode acts better on the sole of the foot. The specific analysis process is as follows:

[0034] Step (B1), the sound wave excited by the single transducer forms a standing wave:

[0035] By installing a single transducer in parallel with the foot container, the wall of the foot container is simplified as a rigid boundary. Then, the ultrasonic wave emitted by the transducer propagates in the water in the foot container and can be described by a one-dimensional wave equation, as shown in equation (5):

[0036]

[0037] Among them, p is the sound pressure, c is the propagation speed of ultrasound in water;

[0038] The standing wave formed by the sound wave excited by a single transducer installed in parallel with the foot container is shown in equation (6):

[0039] p=2Acos(kx)e j(ωt) (6)

[0040] Where A is a constant, k is the wave number, It can be seen that when a single transducer with a foot container installed in parallel propagates, there is a node area with zero sound pressure amplitude at x = (2n + 1)λ / 4, and no cavitation occurs, where n is an integer and λ is the wavelength, that is, a single transducer with a foot container installed in parallel has an area where no cavitation occurs;

[0041] Step (B2), the standing wave formed by the double transducers colliding with the emitted sound waves is shown in formula (7):

[0042] p=2A{cos(kx)+cos[k(Lx)]}e jωt (7)

[0043] Comparing equations (6) and (7), it can be seen that a single transducer has wave nodes and cannot excite the cavitation effect; and for the structure of dual transducers colliding with each other, if L satisfies

[0044] n=0,1,2,L, then at the node formed by the single transducer x=(2n+1)λ / 4, according to equation (7), the sound pressure of the dual transducer beam-to-be-radiated method is as shown in equation (8),

[0045] p=2A[cos(nπ)+sin(nπ)]e jωt

[0046] =2Acos(nπ)e jωt

[0047] = ±2Ae jωt (8);

[0048] Step (B3), according to the analysis of equations (6) and (8), it is obtained that the standing wave node generated by the single transducer is compensated by the standing wave peak of the other transducer, thereby reducing the cavitation dead zone and improving the uniformity of the sound field distribution. Its envelope is approximately a straight line, indicating that there is no zero amplitude area when the dual transducer counter-emission mode acts on the sole of the foot, and the sound pressure distribution in the entire propagation domain is uniform, thereby optimizing the dual transducer counter-emission mode to act on the sole of the foot.

[0049] Preferably, in the dual transducer counter-emission mode, a coupled physical field for precise control of ultrasonic cavitation field energy and distribution is added at any point on the propagation path of the ultrasonic wave in the foot container. The specific analysis and implementation process is as follows:

[0050] Step (C1), in the process of dual transducers acting on the sole of the foot in a counter-emission mode, noise is generated due to the existence of standing waves, and the coupled physical field is continuously added at any point in the ultrasonic wave propagation path in water;

[0051] Step (C2), add coupled physics

[0052] Since the entire ultrasound emission area or cavitation area is below the sole of the foot, by adding the coupled physical field between the ultrasound propagation areas, the reflection surface form of the coupled physical field, and the mass M of the coupled physical field m , Lishun C m And resistance R m Through the adjustment, the energy and distribution of the entire cavitation sound field can be precisely controlled, and the ultrasonic cavitation field can be effectively used for foot care;

[0053] According to the characteristic impedance, as shown in equations (9) and (10):

[0054]

[0055] and

[0056]

[0057] Among them, z m is the characteristic impedance, ω is the angular frequency of the sound wave, ρ is the density of the physical field material, c is the speed of sound, ρ1 is the density of water, and ρ2 is the density of the coupled physical field material, thereby obtaining different transmission coefficients t P , can accurately control various parameters of the coupled physical field to control the measurement of ultrasonic waves entering the coupled physical field, and the propagation loss through the coupled physical field, and can obtain accurate traveling wave fields;

[0058] Step (C3), according to the ultrasonic superposition formula (11):

[0059]

[0060] in:

[0061]

[0062]

[0063] in, is the initial phase angle, p is the sound pressure after superposition, p1 is the incident sound pressure, p2 is the reflected sound pressure, w t Instantaneous phase, p 1a is the absolute value of the acoustic pressure part, p 2a The absolute value of the imaginary part of the sound pressure, is the reflected sound phase angle, The incident sound phase angle is reflected by the reflection coefficient r p By setting the emitting surface of the physical field, the sound pressure in different areas of the cavitation field can be appropriately increased, and by setting the parameters of the coupled physical field, precise control of the energy and distribution of the ultrasonic cavitation field for foot care can be achieved.

[0064] Preferably, by analyzing the frequency of the dual transducer after adding the coupled physical field, the application of the dual transducer counter-emission mode is further explained, which can reduce the influence of the load and the water level static pressure on the matching circuit. Specifically, the process of reducing the influence of the water static pressure on the transducer performance, the frequency equation at the front end cover of the half-wavelength transducer is as shown in formula (14):

[0065]

[0066] Where, the subscript E represents the piezoelectric chip, ρ E , ρ3 are the densities of the piezoelectric chip and the front end cover respectively; S E , S are the cross-sectional areas of the piezoelectric chip and the front end cover, c E , c are the longitudinal equivalent sound velocities of the piezoelectric crystal stack and the front end cover, l E , l is half of the thickness of the piezoelectric crystal stack, the length of the front cover, and the wave number is k E =ω / c E , k = ω / c, the length of the front cover l' is:

[0067] l′=l+Δl

[0068] The change in the hydrostatic pressure P0 can be equivalent to the change in the length of the front cover, that is, ρ w is the density of water. The analysis shows that the greater the hydrostatic pressure, the lower the resonant frequency. According to formula (14), when the equivalent electrical parameters remain unchanged, the resonant frequency ω will be reduced when l′ increases, indicating that the increase in the hydrostatic pressure P0 is equivalent to the increase in l′.

[0069] The beneficial effects of the present invention are as follows: the transducer small-angle emission model for foot care based on ultrasonic cavitation field of the present invention, by analyzing the traditional method, fixes the transducer at the bottom of the tank, or arranges it at an inclined angle, or arranges it at the bottom tank and the wall, etc., the soaked object (sole or foot) will change the liquid height H, and the water surface will also fluctuate during operation, which will cause the static pressure ρ0 of the transducer to change, the power fluctuates frequently, and the steady-state cavitation effect is easily weakened; the installation method of the constructed small-angle emission model for foot care based on ultrasonic cavitation field is only located on the tank wall, H is lower, and its power fluctuation is smaller than the traditional installation method, and the stability is better, which is conducive to the establishment of transient cavitation and the continuation of steady-state cavitation, and also has the following advantages:

[0070] (1) The transducer is installed in the opposite direction of the small-angle emission model, which can make the sound field distribution in the propagation area tend to be uniform, with fewer standing wave node areas, a wide stable distribution area of ​​the cavitation field, and no obvious cavitation dead zone. It avoids the cleaning blind area and incomplete cleaning problems caused by the bottom installation of the traditional transducer, which is conducive to the full range of foot cleaning and care;

[0071] (2) The coupled physical field can be set arbitrarily in the propagation area, and the distribution of the cavitation energy field can be further accurately controlled by controlling the various parameters of the physical field;

[0072] (3) It is less affected by the volume change of the medium and the addition of substances, has a stable output power, and a small current change, which can effectively and continuously care for the feet, avoid the tingling and pressure caused by excessive power radiation to the feet, and solve the discomfort caused by power fluctuations and strong radiation damage of traditional transducers, thereby realizing the promotion and application of equipment or products that use ultrasonic cavitation fields to care for the feet. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a schematic diagram of the transducer small-angle emission model for foot care based on ultrasonic cavitation field.

[0074] Figure 2 It is a schematic diagram showing that the ultrasonic emission direction is perpendicular to the sole surface of the foot.

[0075] Figure 3 It is a schematic diagram showing that the ultrasonic emission direction and the sole of the foot form a small angle β.

[0076] Figure 4 is the angle of incidence θ i When it is equal to 90 degrees, that is, the angle β between the ultrasonic emission direction and the sole of the foot is a small angle = 0.

[0077] Figure 5 It is a schematic diagram of standing wave in sound field transmission of a single transducer.

[0078] Figure 6It is a schematic diagram of the interference and superposition of the sound fields of dual transducers.

[0079] Figure 7 It is a schematic diagram of the relationship between the change in Δl caused by static pressure and the resonant frequency. DETAILED DESCRIPTION

[0080] The present invention will be further described below in conjunction with the accompanying drawings.

[0081] The transducer small-angle emission model for foot care based on ultrasonic cavitation field of the present invention comprises a single transducer or a double transducer installed in a foot container, wherein the ultrasonic emission direction of the single transducer or the double transducer is at a small angle β with the sole of the foot, such as Figure 1 As shown, a dual-transducer method is used to care for the foot. When the dual-transducer counter-emission method is used, a coupled physical field for realizing precise control of the energy and distribution of the ultrasonic cavitation field is added at any point on the propagation path of the ultrasonic wave in the foot container, such as Figure 6 As shown, the coupled physical field with precise control of the ultrasonic cavitation field energy and distribution of the foot container is more conducive to foot care.

[0082] Preferably, the small angle β has a value range of 0°≤β≤15°.

[0083] Preferably, the angle between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is a small angle β, and by analyzing the cavitation intensity distribution characteristics of the ultrasonic cavitation field, the dual transducer counter-emission mode is optimized to act better on the sole of the foot.

[0084] By analyzing the effect of ultrasonic cavitation field on the foot, under normal circumstances, if the ultrasonic cavitation field in a certain water area is applied to the foot, there must be a foot container with a certain volume of water. The foot container can be of any shape. The transducer has countless arrangements and combinations. No matter how it is arranged, after the sound wave is emitted, it propagates through the water and enters the foot tissue, either perpendicular to the sole of the foot or at a certain small angle β with the sole of the foot, such as Figure 2 and Figure 3 As shown in the figure, the layout of the transducer and the influence of the ultrasonic emission direction, the layout of the transducer is selected as the grazing incidence mode (small angle emission direction), therefore, the angle between the ultrasonic emission direction of the single transducer or the dual transducer and the sole of the foot is a small angle β,

[0085] The selection process of the small angle β in the range of 0°≤β≤15° is as follows:

[0086] Assuming that the impedance of the elastic tissue of the human foot and the impedance of water are equal, the specific analysis process of the small angle β is as follows:

[0087] Step (A1), analyzing the ultrasonic cavitation field acting on the foot,

[0088] According to the Reisler sound wave reflection and refraction formula, as shown in formula (1):

[0089]

[0090] Where, k1 and k2 are the wave numbers of medium 1 and medium 2 respectively; c1 and c2 are the sound speeds of medium 1 and medium 2 respectively, and medium 1 and medium 2 are water and elastic tissue of human foot respectively; θ i ,θ t The incident angle of the incident wave in water and the transmission angle of the transmitted wave in human tissue respectively;

[0091] Since the density and sound velocity of the elastic tissue of the human foot are approximately equal to those of water, the characteristic impedances of media 1 and 2 are equal, as shown in formula (2):

[0092] ρ1c1=ρ2c2 (2)

[0093] From equation (1) and equation (2), we can get: i =θ t , that is, the incident angle of the incident wave in water is equal to the transmission angle of the transmitted wave in human tissue;

[0094] According to the transmission coefficient formula (3) at any angle of incidence:

[0095]

[0096] Among them, t P is the transmission coefficient;

[0097] When 0≤θ i <90°, because θ i =θ t ,ρ1c1=ρ2c2, so t P is always equal to 1, that is, no matter how the transducer is arranged, as long as the incident angle θ of the incident wave i Not equal to 90°, when the incident sound intensity of the transducer is constant, the amount of ultrasound entering the foot is the same, and does not change with the incident angle θ of the incident wave i changes with the changes;

[0098] Step (A2), according to the reflection coefficient formula (4):

[0099]

[0100] Among them, r P is the reflection coefficient, when the incident angle of the incident wave in water is θ i When it is equal to 90°, the small angle β = 0°, and the ultrasonic emission area is controlled not to be higher than the sole of the foot, and |r P|≈1 grazing incidence phenomenon, the incident wave is completely reflected, avoiding the incident wave entering the elastic tissue of the human foot to produce swelling or tingling, that is, the feasibility of completing the analysis of the angle between the ultrasonic emission direction of the single transducer or the dual transducer and the sole of the foot is a small angle β=0°;

[0101] In real situations, the impedance of the elastic tissue of the human foot and the impedance of water are similar but not equal. The specific analysis process of the small angle β is as follows:

[0102] In step (A3), when the density and sound velocity of the elastic tissue of the human foot are taken according to actual values, the sound velocity of the elastic tissue of the human foot can be taken as c2≈1540m / s, and the sound velocity of water at normal temperature and pressure can be taken as c1≈1500m / s. According to formula (1), the following is obtained:

[0103] The speed of sound in the elastic tissue of the human foot is greater than the speed of sound in water, and the refraction angle is always greater than the incident angle. When the incident angle increases from 0°, the refraction angle also increases. When the incident angle increases to 90°, the refracted wave propagates along the interface, that is, parallel to the sole surface. At this time, according to formula (1), the incident angle θ i ≈75°, that is, the small angle β between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is ≈15°;

[0104] Step (A4), if the incident angle continues to increase, sinθ t >1, that is, there is no real angle sinθ t , so there is no refracted wave in the elastic tissue of the human foot in the usual sense. At this time, the reflection angle is still equal to the incident angle, and the reflection coefficient is equal to the complex number, whose absolute value is always equal to 1. The energy of the incident wave is all reflected back into the water, but a phase jump is generated relative to the incident wave. Therefore, when the sound velocity of the elastic tissue of the actual human foot is taken as normal, when the incident angle is 90°>θ i When ≥75°, that is, 0°<β≤15°, within the range of the incident direction, the ultrasonic wave of the single transducer or dual transducer is totally reflected at the tissue interface of the sole of the foot during transmission, and no ultrasonic energy is transmitted into the elastic tissue of the human foot, thereby avoiding the incident wave entering the elastic tissue of the human foot to cause swelling or tingling. That is, the analysis is completed under real circumstances, and the rationality of the angle between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is a small angle of 0°<β≤15°.

[0105] The angle between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is a small angle β. By analyzing the cavitation intensity distribution characteristics of the ultrasonic cavitation field, it is optimized that the dual transducer counter-emission mode acts better on the sole of the foot. The specific analysis process is as follows:

[0106] Step (B1), the sound wave excited by the single transducer forms a standing wave:

[0107] By means of a single parallel mounted foot container transducer, e.g. Figure 5 As shown, if the wall of the foot container is simplified as a rigid boundary, the ultrasonic wave emitted by the transducer propagates in the water in the foot container and can be described by a one-dimensional wave equation, as shown in equation (5):

[0108]

[0109] Among them, p is the sound pressure, c is the propagation speed of ultrasound in water;

[0110] The standing wave formed by the sound wave excited by a single transducer installed in parallel with the foot container is shown in equation (6):

[0111] p=2Acos(kx)e j(ωt) (6)

[0112] Where A is a constant, k is the wave number, It can be seen that when a single transducer with a foot container installed in parallel propagates, there is a node area with zero sound pressure amplitude at x = (2n + 1)λ / 4, and no cavitation occurs, where n is an integer and λ is the wavelength. That is, a single transducer with a foot container installed in parallel has a region where no cavitation occurs, such as Figure 5 The shaded area shown.

[0113] Step (B2), installation method of dual transducer hedge, such as Figure 6 As shown in the figure, the standing wave formed by the double transducers colliding with the transmitted sound waves is shown in formula (7):

[0114] p=2A{cos(kx)+cos[k(Lx)]}e jωt (7)

[0115] Comparing equations (6) and (7), it can be seen that a single transducer has wave nodes and cannot excite the cavitation effect; and for the structure of dual transducers colliding with each other, if L satisfies

[0116] n=0,1,2,L, then at the node formed by the single transducer x=(2n+1)λ / 4, according to equation (7), the sound pressure of the dual transducer beam-to-be-radiated method is as shown in equation (8),

[0117] p=2A[cos(nπ)+sin(nπ)]e jωt

[0118] =2Acos(nπ)e jωt

[0119] = ±2Ae jωt (8);

[0120] Step (B3), according to equations (6) and (8), the standing wave node generated by a single transducer is compensated by the standing wave peak of another transducer, thereby reducing the cavitation dead zone and improving the uniformity of the sound field distribution, such as Figure 6 As shown, its envelope is approximately a straight line, indicating that there is no area with zero amplitude when the dual-transducer counter-emission mode acts on the sole of the foot, and the sound pressure distribution in the entire propagation domain is uniform. Therefore, the optimization results show that the dual-transducer counter-emission mode acting on the sole of the foot is the best.

[0121] In the dual transducer counter-emission mode, a coupled physical field is added at any point on the propagation path of the ultrasonic wave in the foot container to achieve precise control of the energy and distribution of the ultrasonic cavitation field for foot care. The specific analysis and implementation process is as follows:

[0122] Step (C1), in the process of dual transducers acting on the sole of the foot in a counter-emission mode, noise is generated due to the existence of standing waves, and the coupled physical field is continuously added at any point in the ultrasonic wave propagation path in water;

[0123] Step (C2), add coupled physics

[0124] Since the entire ultrasound emission area or cavitation area is below the sole of the foot, by adding the coupled physical field between the ultrasound propagation areas, the reflection surface form of the coupled physical field, and the mass M of the coupled physical field m , Lishun C m And resistance R m Through the adjustment, the energy and distribution of the entire cavitation sound field can be precisely controlled, and the ultrasonic cavitation field can be effectively used for foot care;

[0125] According to the characteristic impedance, as shown in equations (9) and (10):

[0126]

[0127] and

[0128]

[0129] Among them, z m is the characteristic impedance, ω is the angular frequency of the sound wave, ρ is the density of the physical field material, c is the speed of sound, ρ1 is the density of water, and ρ2 is the density of the coupled physical field material, thereby obtaining different transmission coefficients t P , can accurately control various parameters of the coupled physical field to control the measurement of ultrasonic waves entering the coupled physical field, and the propagation loss through the coupled physical field, and can obtain accurate traveling wave fields;

[0130] (C3), according to the superposition formula of ultrasound (11):

[0131]

[0132] in:

[0133]

[0134] in, is the initial phase angle, p is the sound pressure after superposition, p1 is the incident sound pressure, p2 is the reflected sound pressure, w t Instantaneous phase, p 1a is the absolute value of the acoustic pressure part, p 2a The absolute value of the imaginary part of the sound pressure, is the reflected sound phase angle, The incident sound phase angle is reflected by the reflection coefficient r p By setting the physical field emission surface, the sound pressure in different areas of the cavitation field can be appropriately increased, and the energy and distribution of the ultrasonic cavitation field for foot care can be precisely controlled by setting the parameters of the coupled physical field.

[0135] Through the frequency analysis of the dual transducer after adding the coupling physical field, the application of the dual transducer counter-emission method is further explained, which can reduce the influence of the load and the water level static pressure on the matching circuit. Specifically, the process of reducing the influence of the water static pressure on the transducer performance, the frequency equation at the front end cover of the half-wavelength transducer is shown in formula (14):

[0136]

[0137] Where, the subscript E represents the piezoelectric chip, ρ E , ρ3 are the densities of the piezoelectric chip and the front end cover respectively; S E , S are the cross-sectional areas of the piezoelectric chip and the front end cover, c E , c are the longitudinal equivalent sound velocities of the piezoelectric crystal stack and the front end cover, l E , l is half of the thickness of the piezoelectric crystal stack, the length of the front cover, and the wave number is k E =ω / c E , k = ω / c, the length of the front cover l' is:

[0138] l′=l+Δl

[0139] The change in the hydrostatic pressure P0 can be equivalent to the change in the length of the front cover, that is, ρ w is the density of water. The analysis shows that the greater the hydrostatic pressure, the lower the resonant frequency. According to formula (14), when the equivalent electrical parameters remain unchanged, the resonant frequency ω will be reduced when l′ increases, indicating that the increase in the hydrostatic pressure P0 is equivalent to the increase in l′. A specific implementation process, such as Figure 7As shown, specifically (45# steel, l = 30mm; PZT-8 piezoelectric ceramic, single piece thickness is 6mm, outer diameter D1 = 50mm, inner diameter D2 = 20mm)

[0140] Obviously, when the static pressure ρ0 changes, the optimal frequency of the transducer changes accordingly, which leads to a decrease in the efficiency of the matching circuit, causing output current fluctuations and power instability.

[0141] In summary, the transducer small-angle emission model for foot care based on ultrasonic cavitation field of the present invention analyzes the influence of the layout of the transducer and the ultrasonic emission direction when the ultrasonic cavitation field acts on the foot. The angle between the ultrasonic emission direction of a single transducer or a dual transducer and the sole of the foot is small, which has the best care effect. The dual transducer counter-emission mode is applied to the sole of the foot, and the precise control of the ultrasonic cavitation field energy and distribution for foot care is achieved by setting the parameters of the coupled physical field. Then, the application of the dual transducer counter-emission mode is further explained by analyzing the dual transducer frequency after adding the coupled physical field. The influence of the load and the static pressure of the water level on the matching circuit can be reduced, and the stability of the entire ultrasonic cavitation field can be achieved. The small-angle emission model of ultrasonic cavitation field foot care is constructed, and the most suitable small-angle model of ultrasonic cavitation field transducer is selected to care for the feet. Moreover, by analyzing the traditional method, the transducer is fixed on the bottom of the tank, or arranged at an inclined angle, or arranged at the bottom tank and the wall. The immersed object (sole or foot) will change the liquid height H, and the water surface will also fluctuate during work, which will cause the static pressure ρ0 of the transducer to change, and the power fluctuates frequently, which is easy to weaken the steady-state cavitation effect; the installation method of the constructed small-angle emission model for foot care based on ultrasonic cavitation field is only located on the tank wall, H is lower, and its power fluctuation is smaller than the traditional installation method, and the stability is better, which is conducive to the establishment of transient cavitation and the continuation of steady-state cavitation. It also has the following advantages:

[0142] (1) The transducer is installed in the opposite direction of the small-angle emission model, which can make the sound field distribution in the propagation area tend to be uniform, with fewer standing wave node areas, a wide stable distribution area of ​​the cavitation field, and no obvious cavitation dead zone. It avoids the cleaning blind area and incomplete cleaning problems caused by the bottom installation of the traditional transducer, which is conducive to the full range of foot cleaning and care;

[0143] (2) The coupled physical field can be set arbitrarily in the propagation area, and the distribution of the cavitation energy field can be further accurately controlled by controlling the various parameters of the physical field;

[0144] (3) It is less affected by the volume change of the medium and the addition of substances, has a stable output power, and a small current change, which can effectively and continuously care for the feet, avoid the tingling and pressure caused by excessive power radiation to the feet, and solve the discomfort caused by power fluctuations and strong radiation damage of traditional transducers, thereby realizing the promotion and application of equipment or products that use ultrasonic cavitation fields to care for the feet.

[0145] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. The transducer small angle emission model for foot care based on ultrasonic cavitation field is characterized by: It includes a single transducer or a double transducer installed in the foot container, and the ultrasonic emission direction of the single transducer or the double transducer is at a small angle β with the sole of the foot; In the dual-transducer counter-emission mode, a coupled physical field for precise control of the energy and distribution of the ultrasonic cavitation field is added at any point on the propagation path of the ultrasonic wave in the foot container.

2. The transducer small-angle emission model for foot care based on ultrasonic cavitation field according to claim 1, characterized in that: The small angle β has a value range of 0°≤β≤15°.

3. The transducer small-angle emission model for foot care based on ultrasonic cavitation field according to claim 2, characterized in that: The angle between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is a small angle β. By analyzing the cavitation intensity distribution characteristics of the ultrasonic cavitation field, it is optimized that the dual transducer counter-emission mode acts better on the sole of the foot.

4. The transducer small-angle emission model for foot care based on ultrasonic cavitation field according to claim 2, characterized in that: The selection process of the small angle β in the range of 0°≤β≤15° is as follows: Assuming that the impedance of the elastic tissue of the human foot and the impedance of water are equal, the specific analysis process of the small angle β is as follows: Step (A1), analyzing the ultrasonic cavitation field acting on the foot, According to the Reisler sound wave reflection and refraction formula, as shown in formula (1): Where, k1 and k2 are the wave numbers of medium 1 and medium 2 respectively; c1 and c2 are the sound speeds of medium 1 and medium 2 respectively, and medium 1 and medium 2 are water and elastic tissue of human foot respectively; θ i ,θ t The incident angle of the incident wave in water and the transmission angle of the transmitted wave in human tissue respectively; Since the density and sound velocity of the elastic tissue of the human foot are approximately equal to those of water, the characteristic impedances of media 1 and 2 are equal, as shown in formula (2): ρ1c1=ρ2c2 (2) From equation (1) and equation (2), we can get: i =θ t , that is, the incident angle of the incident wave in water is equal to the transmission angle of the transmitted wave in human tissue; According to the transmission coefficient formula (3) at any angle of incidence: Among them, t P is the transmission coefficient; When 0≤θ i <90°, because θ i =θ t ,ρ1c1=ρ2c2, so t P is always equal to 1, that is, no matter how the transducer is arranged, as long as the incident angle θ of the incident wave i Not equal to 90°, when the incident sound intensity of the transducer is constant, the amount of ultrasound entering the foot is the same, and does not change with the incident angle θ i changes with the changes; Step (A2), according to the reflection coefficient formula (4): Among them, r P is the reflection coefficient, when the incident angle of the incident wave in water is θ i When it is equal to 90°, the small angle β = 0°, and the ultrasonic emission area is controlled not to be higher than the sole of the foot, and |r P |≈1 grazing incidence phenomenon, the incident wave is completely reflected, avoiding the incident wave entering the elastic tissue of the human foot to produce swelling or tingling, that is, the feasibility of completing the analysis of the angle between the ultrasonic emission direction of the single transducer or the dual transducer and the sole of the foot is a small angle β=0°; In real situations, the impedance of the elastic tissue of the human foot and the impedance of water are similar but not equal. The specific analysis process of the small angle β is as follows: In step (A3), when the density and sound velocity of the elastic tissue of the human foot are taken according to actual values, the sound velocity of the elastic tissue of the human foot can be taken as c2≈1540m / s, and the sound velocity of water at normal temperature and pressure can be taken as c1≈1500m / s. According to formula (1), the following is obtained: The speed of sound in the elastic tissue of the human foot is greater than the speed of sound in water, and the refraction angle is always greater than the incident angle. When the incident angle increases from 0°, the refraction angle also increases. When the incident angle increases to 90°, the refracted wave propagates along the interface, that is, parallel to the sole surface. At this time, according to formula (1), the incident angle θ i ≈75°, that is, the small angle β between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is ≈15°; Step (A4), if the incident angle continues to increase, sinθ t >1, that is, there is no real angle sinθ t , so there is no refracted wave in the elastic tissue of the human foot in the usual sense. At this time, the reflection angle is still equal to the incident angle, and the reflection coefficient is equal to the complex number, whose absolute value is always equal to 1. The energy of the incident wave is all reflected back into the water, but a phase jump is generated relative to the incident wave. Therefore, when the sound velocity of the elastic tissue of the actual human foot is taken as normal, when the incident angle is 90°>θ i When ≥75°, that is, 0°<β≤15°, within the range of the incident direction, the ultrasonic wave of the single transducer or dual transducer is totally reflected at the tissue interface of the sole of the foot during transmission, and no ultrasonic energy is transmitted into the elastic tissue of the human foot, thereby avoiding the incident wave entering the elastic tissue of the human foot to cause swelling or tingling. That is, the analysis is completed under real circumstances, and the rationality of the angle between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is a small angle of 0°<β≤15°.

5. The transducer small-angle emission model for foot care based on ultrasonic cavitation field according to claim 3, characterized in that: The angle between the ultrasonic emission direction of the single transducer or dual transducer and the sole of the foot is a small angle β. By analyzing the cavitation intensity distribution characteristics of the ultrasonic cavitation field, it is optimized that the dual transducer counter-emission mode acts better on the sole of the foot. The specific analysis process is as follows: Step (B1), the sound wave excited by the single transducer forms a standing wave as follows: By installing a single transducer in parallel with the foot container, the wall of the foot container is simplified as a rigid boundary. Then, the ultrasonic wave emitted by the transducer propagates in the water in the foot container and can be described by a one-dimensional wave equation, as shown in equation (5): Among them, p is the sound pressure, c is the propagation speed of ultrasound in water; The standing wave formed by the sound wave excited by a single transducer installed in parallel with the foot container is shown in equation (6): p=2Acos(kx)e j(ωt) (6) Where A is a constant, k is the wave number, It can be seen that when a single transducer with a foot container installed in parallel propagates, there is a node area with zero sound pressure amplitude at x = (2n + 1)λ / 4, and no cavitation occurs, where n is an integer and λ is the wavelength, that is, a single transducer with a foot container installed in parallel has an area where no cavitation occurs; Step (B2), the standing wave formed by the double transducers colliding with the emitted sound waves is shown in formula (7): p=2A{cos(kx)+cos[k(L-x)]}e jωt (7) Comparing equations (6) and (7), it can be seen that a single transducer has wave nodes and cannot excite the cavitation effect; and for the dual transducer counter-emission structure, if L satisfies Then at the node formed by the single transducer x = (2n + 1)λ / 4, according to equation (7), the sound pressure of the dual transducer radiation mode is as shown in equation (8): p=2A[cos(nπ)+sin(nπ)]e jωt =2Acos(nπ)e jωt =±2Ae jωt (8); Step (B3), according to the analysis of equations (6) and (8), it is obtained that the standing wave node generated by the single transducer is compensated by the standing wave peak of the other transducer, thereby reducing the cavitation dead zone and improving the uniformity of the sound field distribution. Its envelope is approximately a straight line, indicating that there is no zero amplitude area when the dual transducer counter-emission mode acts on the sole of the foot, and the sound pressure distribution in the entire propagation domain is uniform, thereby optimizing the dual transducer counter-emission mode to act on the sole of the foot.

6. The transducer small-angle emission model for foot care based on ultrasonic cavitation field according to claim 1, characterized in that: In the dual-transducer counter-emission mode, a coupled physical field for precise control of the ultrasonic cavitation field energy and distribution is added at any point on the propagation path of the ultrasonic wave in the foot container. The specific analysis and implementation process is as follows: Step (C1), in the process of dual transducers acting on the sole of the foot in a counter-emission mode, noise is generated due to the existence of standing waves, and the coupled physical field is continuously added at any point in the ultrasonic wave propagation path in water; Step (C2), add coupled physics Since the entire ultrasound emission area or cavitation area is below the sole of the foot, by adding the coupled physical field between the ultrasound propagation areas, the reflection surface form of the coupled physical field, and the mass M of the coupled physical field m , Lishun C m And resistance R m Through the adjustment, the energy and distribution of the entire cavitation sound field can be precisely controlled, and the ultrasonic cavitation field can be effectively used for foot care; According to the characteristic impedance, as shown in equations (9) and (10): and Among them, z m is the characteristic impedance, ω is the angular frequency of the sound wave, ρ is the density of the physical field material, c is the speed of sound, ρ1 is the density of water, and ρ2 is the density of the coupled physical field material, thereby obtaining different transmission coefficients t P , can accurately control various parameters of the coupled physical field to control the measurement of ultrasonic waves entering the coupled physical field, and the propagation loss through the coupled physical field, and can obtain accurate traveling wave fields; Step (C3), according to the ultrasonic superposition formula (11): in: in, is the initial phase angle, p is the sound pressure after superposition, p1 is the incident sound pressure, p2 is the reflected sound pressure, w t Instantaneous phase, p 1a is the absolute value of the acoustic pressure part, p 2a The absolute value of the imaginary part of the sound pressure, is the reflected sound phase angle, The incident sound phase angle is reflected by the reflection coefficient r p By setting the emitting surface of the physical field, the sound pressure in different areas of the cavitation field can be appropriately increased, and by setting the parameters of the coupled physical field, precise control of the energy and distribution of the ultrasonic cavitation field for foot care can be achieved.

7. The transducer small-angle emission model for foot care based on ultrasonic cavitation field according to claim 6, characterized in that: Through the frequency analysis of the dual transducer after adding the coupling physical field, the application of the dual transducer counter-emission method is further explained, which can reduce the influence of the load and the water level static pressure on the matching circuit. Specifically, the process of reducing the influence of the water static pressure on the transducer performance, the frequency equation at the front end cover of the half-wavelength transducer is shown in formula (14): Where, the subscript E represents the piezoelectric chip, ρ E , ρ3 are the densities of the piezoelectric chip and the front cover respectively; S E , S are the cross-sectional areas of the piezoelectric chip and the front cover, c E , c are the longitudinal equivalent sound velocities of the piezoelectric crystal stack and the front end cover, l E , l is half of the thickness of the piezoelectric crystal stack, the length of the front cover, and the wave number is k E =ω / c E , k = ω / c, the length of the front cover l' is: l′=l+Δl The change in the hydrostatic pressure P0 can be equivalent to the change in the length of the front cover, that is, ρ w is the density of water. The analysis shows that the greater the hydrostatic pressure, the lower the resonant frequency. According to formula (14), when the equivalent electrical parameters remain unchanged, the resonant frequency ω will be reduced when l′ increases, indicating that the increase in the hydrostatic pressure P0 is equivalent to the increase in l′.

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