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

Abstract

The application discloses a kind of transducer small-angle emission models based on ultrasonic cavitation field foot care, including installation in foot container single transducer or double transducer, the included angle of ultrasonic wave emission direction of the single transducer or double transducer and sole is small angle;And in the offset emission mode of double transducer, increase the coupling physical field for realizing the energy and distribution accurate control of ultrasonic cavitation field to the foot care at any place on the propagation path of ultrasonic wave in foot container.The application is analyzed by selecting the most suitable transducer small-angle model of ultrasonic cavitation field to care foot, can facilitate the popularization and application of the equipment or product that ultrasonic cavitation field acts on foot care foot, with good application prospect.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ultrasonic cavitation effect, and particularly relates to a transducer small-angle emission model for foot care based on an ultrasonic cavitation field. BACKGROUND

[0002] In the prior art, it is known that the ultrasonic cavitation effect has a fungicidal effect, 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, the ultrasonic cavitation sound field can be applied to the foot, and the foot can be cared for through the physical method of ultrasonic cavitation, which will bring revolutionary changes to the traditional foot care industry and is a blessing for all tinea patients, without the worry of drug side effects and the trouble of drug resistance caused by the use of various chemical drugs.

[0003] However, the current application of the 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 device or product for caring for the feet by applying the ultrasonic cavitation field to the feet. Some patents or papers only outline the ultrasonic cavitation foot care and the ultrasonic cavitation field fungicidal experiment, but only propose the concept without research on the applicable scope. From the perspective of whether the 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-focusing category. When human tissues are placed in the ultrasonic cavitation field, part of the measurement will enter the human tissues when the ultrasonic wave propagates in water, which will produce a certain mechanical effect. Because of the non-focusing sound field, the thermal effect is very weak. Due to the mechanical effect, shear stress and other mechanical effects will occur in the human tissues. When the stress is large enough, the direct response of the tissue is swelling pain or stabbing pain. The stronger the sound intensity, the greater the stress, and the stronger the swelling pain and stabbing pain. Because the impedance of different human tissues ρ×c (ρ refers to the density of human tissues, and c refers to the sound speed) is different, the absorption of sound waves is different, and at the same time, each person has different feelings of swelling pain and stabbing pain. Therefore, it is impossible to give a safe output power value for ultrasonic cavitation, so as to ensure that the ultrasonic cavitation field is comfortable in the composition of people's foot care, and therefore, the technical difficulty leads to the fact that the device or product for caring for the feet by applying the ultrasonic cavitation field to the feet has no good prospect for popularization;

[0005] 2. If the output power of the ultrasonic wave is continuously reduced to achieve safe use by most people, but blindly reducing the output power will reduce the cavitation intensity and the fungicidal effect, which will inevitably affect the foot care effect, and even cannot produce the care effect.

[0006] Therefore, how to overcome the above problems, construct an ultrasonic cavitation field output model for foot care, can output the appropriate ultrasonic cavitation output power value, ensure the effect of foot care, and avoid the swelling pain or strong pain caused by the ultrasonic into the elastic tissue of the foot, and improve the comfort of the user, is the current urgent problem, so as to promote the application of the equipment or product of the ultrasonic cavitation field acting on the foot care foot. SUMMARY

[0007] The technical problem solved by the present application is to overcome the existing concept of ultrasonic cavitation foot care, without studying the application scope, and how to apply the cavitation field angle analysis to realize the foot care. The transducer small-angle emission model based on the ultrasonic cavitation field foot care of the present application analyzes the influence of the layout of the transducer and the emission direction of the ultrasonic wave when the ultrasonic cavitation field acts on the foot, and the included angle between the emission direction of the single transducer or double transducer and the sole is a small angle, which is the best nursing effect, and the double transducer is applied to the sole through the opposite emission mode, the parameters of the coupled physical field are set, the energy and distribution of the ultrasonic cavitation field for nursing the foot are precisely controlled, then the frequency of the double transducer after the coupled physical field is added is analyzed, the application of the double transducer opposite emission mode can reduce the influence of the load and the hydrostatic pressure on the matching circuit, realize the stability of the entire ultrasonic cavitation field, complete the construction of the small-angle emission model of the ultrasonic cavitation field foot care, 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 the equipment or product of the ultrasonic cavitation field acting on the foot care foot.

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

[0009] A transducer small-angle emission model based on the ultrasonic cavitation field foot care, comprising a single transducer or double transducer installed in a foot container, and the included angle between the emission direction of the single transducer or double transducer and the sole is a small angle β.

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

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

[0012] Preferably, the included angle between the emission direction of the single transducer or double transducer and the sole is a small angle β, and through the analysis of the cavitation intensity distribution characteristics of the ultrasonic cavitation field, the opposite emission mode of the double transducer acting on the sole is optimized.

[0013] The small angle β is preferably selected in the range of 0°≤β≤15° as follows:

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

[0015] In step (A1), when the ultrasonic cavitation field acts on the foot,

[0016] According to the reflection and refraction formula of the Rayleigh acoustic wave, as shown in formula (1):

[0017]

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

[0019] Since the density and the acoustic speed of the elastic tissue of the human foot are approximately equal to those of water, the characteristic impedance of medium 1 and 2 is equal, as shown in formula (2):

[0020] ρ1c1=ρ2c2 (2)

[0021] According to formula (1) and formula (2), θ i = θ t , that is, the incident angle of the incident wave in water is equal to the transmission angle of the transmission wave in the human tissue.

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

[0023]

[0024] Wherein, t P is the transmission coefficient.

[0025] When 0≤θ i <90°, because θ i = θ t and ρ1c1=ρ2c2, t P is always equal to 1, that is, as long as the incident angle θ i of the incident wave is not equal to 90°, when the incident acoustic intensity of the transducer is constant, the measurement of the ultrasonic wave into the foot is the same and does not change with the change of the incident angle θ i of the incident wave.

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

[0027]

[0028] wherein, r P is the reflection coefficient, when the incident angle θ i of the incident wave in water is equal to 90°, then the small angle β = 0°, the control of the ultrasonic emission area is not higher than the sole, and the grazing incidence phenomenon of |r P ≈1 will occur, the incident wave is completely reflected, and the expansion or stinging pain of the incident wave into the elastic tissue of the human foot is avoided, i.e. the feasibility of the single transducer or the double transducer ultrasonic emission direction and the small angle β = 0° of the sole is analyzed.

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

[0030] Step (A3), when the density and the sound speed of the elastic tissue of the human foot are taken according to the actual value, the sound speed of the elastic tissue of the human foot is taken as c2≈1540m / s, the sound speed of water under normal temperature and pressure is taken as c1≈1500m / s, and according to formula (1), the following is obtained:

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

[0032] Step (A4), if the incident angle continues to increase, then sinθ t >1, i.e. 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 a complex number, and the absolute value is always equal to 1, the energy of the incident wave is completely reflected back into water, only a phase jump is generated relative to the incident wave, therefore, when the sound speed of the elastic tissue of the human foot is taken according to the actual value, when the incident angle is 90°>θ i ≥75°, i.e. 0°<β≤15°, in this incident direction range, the single transducer or the double transducer ultrasonic wave occurs total reflection at the sole tissue interface in the transmission process, no ultrasonic energy is transmitted into the elastic tissue of the human foot, the expansion or stinging pain of the incident wave into the elastic tissue of the human foot is avoided, i.e. the rationality of the single transducer or the double transducer ultrasonic emission direction and the small angle 0°<β≤15° of the sole is analyzed.

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

[0034] In step (B1), the sound wave excited by the single transducer forms a standing wave as follows:

[0035] By simplifying the foot container wall as a rigid boundary through a single transducer installed in parallel with the foot container, the ultrasonic wave emitted by the transducer propagates in the water in the foot container, which can be described by a one-dimensional wave equation as shown in formula (5),

[0036]

[0037] Wherein, p is the sound pressure, and c is the propagation speed of the ultrasonic wave in water.

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

[0039] p=2Acos(kx)e j(ωt) (6)

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

[0041] In step (B2), the standing wave formed by the sound wave excited by the dual transducer pair emission is as shown in formula (7),

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

[0043] Comparing formula (6) and formula (7), it can be seen that the single transducer has a node and cannot excite cavitation effect; and the dual transducer pair emission structure, if L satisfies

[0044] n=0,1,2,L, then at the node formed by the single transducer x=(2n+1)λ / 4, the sound pressure of the dual transducer pair emission mode is as shown in formula (8) according to formula (7),

[0045] p=2A[cos(nπ)+sin(nπ)]e jωt

[0046] =2Acos(nπ)e jωt

[0047] = ±2Ae jωt (8) ;

[0048] Step (B3), according to formula (6) and formula (8), the standing wave node generated by the 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, and the envelope is approximately a straight line, indicating that the double transducer opposite shooting mode acts on the foot palm without amplitude zero area, the sound pressure distribution of the entire propagation domain is uniform, thereby optimizing the double transducer opposite shooting mode acting on the foot palm.

[0049] Preferably, in the double transducer opposite shooting mode, a coupling physical field for precise control of ultrasonic cavitation field energy and distribution is added at any position on the ultrasonic propagation path in the foot container. The specific analysis implementation process is as follows:

[0050] Step (C1), during the process of the double transducer opposite shooting mode acting on the foot palm, noise is generated due to the existence of standing wave, and a coupling physical field is continuously added at any position on the ultrasonic propagation path in the ultrasonic water;

[0051] Step (C2), adding a coupling physical field

[0052] Since the entire ultrasonic emission area or cavitation area is below the foot palm area, by adding a coupling physical field between the ultrasonic propagation areas, through the reflection surface form of the coupling physical field, and the adjustment of the mass M m , force order C m and force resistance R m of the coupling physical field, the energy and distribution of the entire cavitation sound field are precisely controlled, and the ultrasonic cavitation field is effectively utilized for foot care;

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

[0054]

[0055] and

[0056]

[0057] Where 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 sound speed, ρ1 is the density of water, and ρ2 is the density of the coupling physical field material, thereby obtaining different transmission coefficients t P , which can precisely control the coupling physical field parameters to control the ultrasonic wave into the coupling physical field and the propagation loss through the coupling physical field, and can obtain a precise traveling wave field;

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

[0059]

[0060] wherein:

[0061]

[0062]

[0063] wherein, is the initial phase angle, p is the superimposed sound pressure, p1 is the incident sound pressure, p2 is the reflected sound pressure, w t instantaneous phase, p 1a is the sound pressure real part absolute value, p 2a sound pressure imaginary part absolute value, is the reflected sound phase angle, incident sound phase angle, through the reflection coefficient r p and the setting of the physical field emission surface, appropriately increase the sound pressure in different regions of the cavitation field, and by setting the parameters of the coupled physical field, the precise control of the ultrasonic cavitation field energy and distribution of the foot care is realized.

[0064] Preferably, through the frequency analysis of the double transducer after the coupling physical field is increased, it is further illustrated that the application of the double transducer in the opposite emitting mode can reduce the influence of the load and the hydrostatic pressure on the matching circuit, specifically, in the process of reducing the influence of the hydrostatic pressure on the transducer performance, the frequency equation at the front cover of the one-half wavelength transducer is as shown in equation (14):

[0065]

[0066] wherein, the subscript E represents the piezoelectric wafer, p E , p3 are the densities of the piezoelectric wafer and the front cover respectively; S E , S are the cross-sectional areas of the piezoelectric wafer and the front cover respectively, c E , c are the longitudinal equivalent sound speeds of the piezoelectric wafer and the front cover respectively, l E , l are half of the thickness of the piezoelectric wafer and the length of the front cover respectively, and the wave number is k E = ω / c E , k = ω / c, and the front cover length l' is:

[0067] l' = l + Δl

[0068] wherein, the change of the hydrostatic pressure P0 can be equivalent to the length change amount of the front cover, that is, p w is the density of water, and it is found through analysis that the greater the hydrostatic pressure, the lower the resonance frequency; according to equation (14), when l' increases, the resonance frequency ω decreases under the condition that the equivalent electrical parameters remain unchanged, which indicates that the increase of the water static pressure P0 is equivalent to the increase of l'.

[0069] The beneficial effects of the present application are: the transducer small-angle emission model for foot care based on ultrasonic cavitation field of the present application, by analyzing the traditional way, the transducer is fixed at the bottom of the groove, or the inclined angle layout, or the bottom groove, wall layout and other ways, the immersion object (palm or foot) will change the liquid height H, and the water surface work will also fluctuate, which will cause the change of transducer static pressure p0, frequent power fluctuation, and easy to weaken the steady cavitation effect; the installation method of the small-angle emission model for foot care based on ultrasonic cavitation field constructed, only located in the groove wall, H is lower, compared with the traditional installation method, the power fluctuation is smaller, the stability is better, which is beneficial to the establishment of transient cavitation and the continuation of steady cavitation, and the following advantages are also set:

[0070] (1) The transducer is installed in the small-angle emission model, which can make the sound field distribution tend to be uniform in the propagation area, the standing wave node area is less, the cavitation field is stably distributed in a wide area, and there is no obvious cavitation dead zone, which can avoid the problems of cleaning blind area and incomplete cleaning caused by the installation of traditional transducer at the bottom, and is beneficial to the full range cleaning and care of the foot;

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

[0072] (3) The output power is stable, the current change is small, the foot is effectively and continuously cared, the pain and compression caused by the power of the foot sound radiation are avoided, the discomfort and strong radiation damage caused by the power fluctuation of the traditional transducer are solved, and the popularization and application of the equipment or product for foot care by ultrasonic cavitation field are realized. BRIEF DESCRIPTION OF DRAWINGS

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

[0074] Figure 2 is a schematic diagram of the ultrasonic wave emission direction perpendicular to the palm surface.

[0075] Figure 3 is a schematic diagram of the ultrasonic wave emission direction and the small angle β formed by the angle between the palm.

[0076] Figure 4 is a schematic diagram of the incident angle θ i equal to 90 degrees, that is, the small angle β of the ultrasonic wave emission direction and the palm is 0.

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

[0078] Figure 6is a schematic diagram of interference superposition of double transducer sound field.

[0079] Figure 7 is a schematic diagram of relationship curve between static pressure generated Δl change and resonance frequency. DETAILED DESCRIPTION

[0080] The application will be further described below in conjunction with the drawings of the specification.

[0081] The transducer small-angle emission model for foot care based on ultrasonic cavitation field of the application comprises a single transducer or a double transducer installed in a foot container, and the included angle between the ultrasonic wave emission direction of the single transducer or the double transducer and the sole is a small angle β, as shown in Figure 1 As shown in the figure, the foot is cared for in the mode of double transducers, and a coupling physical field for realizing precise control of ultrasonic cavitation field energy and distribution is added at any position on the ultrasonic wave propagation path in the foot container in the mode of double transducer butt-shooting, as shown in Figure 6 As shown in the figure, the coupling physical field for realizing precise control of ultrasonic cavitation field energy and distribution of the foot container is more beneficial to the care of the foot.

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

[0083] Preferably, the included angle between the ultrasonic wave emission direction of the single transducer or the double transducer and the sole is a small angle β, and the double transducer butt-shooting mode is optimized to act on the sole more preferably by analyzing the cavitation intensity distribution characteristics of the ultrasonic cavitation field.

[0084] By analyzing the ultrasonic cavitation field acting on the foot, under normal circumstances, if the ultrasonic cavitation field of a certain water area is used to act on the foot, a foot container containing a certain volume of water must be provided, the foot container can have any shape, and the transducer has numerous arrangement and combination modes. No matter any arrangement, after the sound wave is emitted, it propagates in the water and enters the foot tissue, either vertically to the sole or with a certain small angle β to the sole, as shown in Figure 2 and Figure 3 As shown in the figures, the layout of the transducer and the influence of the ultrasonic wave emission direction, the layout mode of the transducer is selected as the grazing incidence mode (small-angle emission direction), therefore, the included angle between the ultrasonic wave emission direction of the single transducer or the double transducer and the sole is a small angle β,

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

[0086] Under the condition that the impedance of the elastic tissue of the human foot and the impedance of the 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 reflection and refraction formula of Rayleigh acoustic wave, as shown in formula (1):

[0089]

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

[0091] Since the density and acoustic speed of human foot elastic tissue are approximately equal to those of water, the characteristic impedance of medium 1 and 2 is equal, as shown in formula (2):

[0092] ρ1c1=ρ2c2 (2)

[0093] According to formula (1) and formula (2), θ i = θ t , that is, the incident angle of incident wave in water is equal to the transmission angle of transmission wave in human tissue;

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

[0095]

[0096] Wherein, 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, as long as the incident angle θ i of incident wave is not equal to 90°, when the incident sound intensity of transducer is constant, the measurement of ultrasonic wave into the foot is the same and does not change with the change of incident angle θ i of incident wave;

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

[0099]

[0100] Wherein, r P is the reflection coefficient, when the incident angle θ i of incident wave in water is equal to 90°, then the small angle β = 0°, the control of ultrasonic emission area is not higher than the sole, and |r PThe grazing incidence phenomenon of ≈1, the incident wave is completely reflected, avoiding the incident wave into the human foot elastic tissue to produce swelling pain or tingling, that is, the feasibility of the analysis of the single transducer or double transducer ultrasonic emission direction and the angle of the foot palm is a small angle β = 0°;

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

[0102] Step (A3), when the density and sound speed of the human foot elastic tissue are actual values, the sound speed of the human foot elastic tissue can be taken as c2≈1540m / s, and the sound speed of water under normal temperature and pressure can be taken as c1≈1500m / s, according to formula (1):

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

[0104] Step (A4), if the incident angle continues to increase, then sinθ t >1, that is, there is no real angle sinθ t , so there is no refracted wave in the human foot elastic tissue in the usual sense. At this time, the reflection angle is still equal to the incident angle, and the reflection coefficient is equal to a complex number, and its absolute value is always equal to 1. The energy of the incident wave is completely reflected back into the water. Only with respect to the incident wave, a phase jump is produced. Therefore, when the actual sound speed of the human foot elastic tissue is normally taken as the value, when the incident angle is 90°>θ i ≥75°, that is, 0°<β≤15°, in this incident direction range, the single transducer or double transducer ultrasonic wave in the transmission process, at the foot palm tissue interface, occurs total reflection, no ultrasonic energy transmits into the human foot elastic tissue, avoiding the incident wave into the human foot elastic tissue to produce swelling pain or tingling, that is, the analysis is completed. In the real situation, the single transducer or double transducer ultrasonic emission direction and the angle of the foot palm is a small angle 0°<β≤15°.

[0105] The single transducer or double transducer ultrasonic emission direction and the angle of the foot palm is a small angle β, by analyzing the cavitation intensity distribution characteristics of the ultrasonic cavitation field, it is optimized to obtain that the double transducer opposite firing mode is better for acting on the foot palm, and the specific analysis process is as follows:

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

[0107] By single transducer installed in parallel with foot container, as shown in Figure 5 simplified foot container wall rigid boundary, the ultrasonic wave emitted by the transducer in the water in the foot container, can be described by a one-dimensional wave equation, as shown in equation (5),

[0108]

[0109] Where p is the sound pressure, c is the speed of ultrasonic wave in water;

[0110] Single transducer installed in parallel with foot container to excite acoustic wave formation, as 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 single transducer installed in parallel with foot container in the propagation, x = (2n + 1) λ / 4 there is a node area of zero amplitude of sound pressure, not to produce cavitation, where n is an integer, λ is the wavelength, that is, single transducer installed in parallel with foot container has not cavitation region exists, as shown in the shadow. Figure 5

[0113] Step (B2), double transducer installation method, as shown in Figure 6 Double transducer emits acoustic wave formation, as shown in equation (7),

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

[0115] Comparing equation (6) and equation (7) can be known that single transducer exists node, can not excite cavitation effect; and double transducer emits structure, if L satisfies

[0116] n = 0, 1, 2, L, then the single transducer x = (2n + 1) λ / 4 formation node, according to equation (7) double transducer emits sound pressure, 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 formula (6) and formula (8) analysis of single transducer generated by the wave node is compensated by another transducer wave crest, thereby reducing cavitation dead zone, and improving the sound field distribution uniformity, as Figure 6 As shown in the figure, the envelope is approximately a straight line, indicating that the double transducer opposite transmission mode acts on the foot palm without amplitude zero region, the whole propagation domain sound pressure distribution is uniform, thereby optimizing the scheme of double transducer opposite transmission mode acting on the foot palm.

[0121] In the double transducer opposite transmission mode, a coupling physical field is added at any position in the ultrasonic wave propagation path in the foot container to realize precise control of the energy and distribution of the ultrasonic cavitation field for nursing feet, and the implementation process is analyzed as follows:

[0122] Step (C1), in the process of double transducer opposite transmission mode acting on the foot palm, noise is generated due to the existence of standing wave, and a coupling physical field is continuously added at any position in the ultrasonic wave propagation path in the water;

[0123] Step (C2), increase the coupling physical field

[0124] Since the entire ultrasonic emission area or cavitation area is below the foot palm area, by increasing the coupling physical field between the ultrasonic propagation area, through the reflection surface form of the coupling physical field, and the adjustment of the mass M m , force order C m and force resistance R m of the coupling physical field, the energy and distribution of the entire cavitation sound field are precisely controlled, and the ultrasonic cavitation field is effectively used for foot care;

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

[0126]

[0127] and

[0128]

[0129] Where 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 sound speed, ρ1 is the density of water, and ρ2 is the density of the coupling physical field material, so as to obtain different transmission coefficients t P , which can precisely control the coupling physical field parameters to control the ultrasonic wave into the coupling physical field, and the propagation loss through the coupling physical field, so as to obtain a precise traveling wave field;

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

[0131]

[0132] wherein:

[0133]

[0134] wherein, is the initial phase angle, p is the superimposed sound pressure, p1 is the incident sound pressure, p2 is the reflected sound pressure, w t instantaneous phase, p 1a is the sound pressure real part absolute value, p 2a sound pressure imaginary part absolute value, is the reflected sound phase angle, incident sound phase angle, through the reflection coefficient r p and the physical field emission surface is set, the sound pressure in different areas of the cavitation field is appropriately increased, and the energy and distribution of the ultrasonic cavitation field for nursing the foot are precisely controlled by setting the parameters of the coupled physical field;

[0135] Through frequency analysis of the double transducer after the coupling physical field is increased, it is further illustrated that the application of the double transducer in the way of opposite emission can reduce the influence of the load and the hydrostatic pressure on the matching circuit, specifically, the process of reducing the influence of the hydrostatic pressure on the transducer performance, the frequency equation at the front cover of the one-half wavelength transducer is as shown in formula (14):

[0136]

[0137] wherein, the subscript E represents a piezoelectric wafer, p E , and p3 are the densities of the piezoelectric wafer and the front cover respectively; S E , and S are the cross-sectional areas of the piezoelectric wafer and the front cover respectively, c E , and c are the longitudinal equivalent sound speeds of the piezoelectric wafer and the front cover respectively, l E , and l are half the thickness of the piezoelectric wafer and the length of the front cover respectively, and the wave number is k E = ω / c E , k = ω / c, and the front cover length l' is:

[0138] l' = l + Δl

[0139] wherein, the change of the hydrostatic pressure P0 can be equivalent to the length change amount of the front cover, that is, p w is the density of water, and it is found through analysis that the greater the hydrostatic pressure, the lower the resonance frequency; according to formula (14), when l' increases, the resonance frequency ω decreases under the condition that the equivalent electrical parameters are unchanged, which indicates that the increase of the water static pressure P0 is equivalent to the increase of l', and a specific implementation process is as follows: Figure 7As shown, specifically represented (45# steel, l = 30mm; PZT-8 piezoelectric ceramic, single piece thickness is 6mm, outer diameter D1 = 50mm, inner diameter D2 = 20mm)

[0140] Obviously, the static pressure p0 changes, the optimal frequency of the transducer changes, thereby causing the matching circuit efficiency to decrease, resulting in output current fluctuation, power instability.

[0141] In summary, the transducer small-angle emission model for foot care based on the ultrasonic cavitation field of the application, by analyzing the influence of the layout of the transducer and the ultrasonic wave emission direction when the ultrasonic cavitation field acts on the foot, the angle between the ultrasonic wave emission direction of the single transducer or double transducer and the sole is a small angle, and the optimal nursing effect is obtained, and the double transducer is applied to the sole through the counterattack emission mode, the parameters of the coupled physical field are set, the energy and distribution of the ultrasonic cavitation field for nursing the foot are precisely controlled, then the frequency of the double transducer after the coupled physical field is added is analyzed, and it is further illustrated that the application of the double transducer counterattack emission mode can reduce the influence of the load and the hydrostatic pressure on the matching circuit, realize the stability of the entire ultrasonic cavitation field, complete the construction of the small-angle emission model of the ultrasonic cavitation field for foot care, select the most suitable small-angle model of the transducer of the ultrasonic cavitation field to nurse the foot, and moreover, through the analysis of the traditional way, the transducer is fixed at the bottom of the groove, or the layout of the inclined angle, or the layout of the bottom groove and wall surface, the immersion object (the sole or the foot) will change the liquid height H, and the water surface will also fluctuate, which will cause the change of the static pressure p0 of the transducer, frequent power fluctuation, and easy weakening of the steady-state cavitation effect; the installation mode of the small-angle emission model for foot care based on the ultrasonic cavitation field constructed has the following advantages:

[0142] (1) The transducer is installed in the small-angle emission model, the sound field distribution in the propagation area tends to be uniform, there are fewer standing wave nodes, the cavitation field is stably distributed in a wide area, and there is no obvious cavitation dead zone, which avoids the cleaning blind area and incomplete cleaning problem caused by the traditional transducer bottom installation, and is beneficial to the full-range cleaning and nursing of the foot;

[0143] (2) The coupled physical field can be arbitrarily set in the propagation area, and the distribution of the cavitation energy field is further precisely controlled through the control of the parameters of the physical field;

[0144] (3) The output power is stable, the current change is small, the foot is effectively and continuously nursed, the pain and compression caused by the excessive power of the foot sound radiation are avoided, the discomfort and strong radiation damage caused by the power fluctuation of the traditional transducer are solved, and the popularization and application of the equipment or product for foot care by the ultrasonic cavitation field acting on the foot are realized.

[0145] The foregoing is considered as illustrative only of the principles of the application and the forms thereof which are demonstrated by the described embodiments. Further, those skilled in the art will readily recognize that certain of the above described embodiments can include, inter alia, alternate configurations and steps thereof known in the art. Therefore, there is no intention that this application be limited as described unless by the recitations of the claims that follow, or by appropriate words taken in the broader and / or more general sense.

Claims

1. The transducer small-angle emission model for foot care based on ultrasonic cavitation field is characterized by: The device comprises a single transducer or a dual transducer installed in the foot container, wherein the ultrasonic emission direction of the single transducer or the dual transducer is at an angle β to the sole of the foot, and the value range of the small angle β is 0°≤β≤15°; 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. Since the entire ultrasonic emission area or cavitation area is below the sole of the foot, the coupled physical field is added between the ultrasonic propagation areas, and the reflection surface form of the coupled physical field and the mass M of the coupled physical field are used. m , Lishun C m and resistance R m Through the adjustment of the ultrasonic cavitation field, 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.

2. The transducer small-angle emission model for foot care based on ultrasonic cavitation field according to claim 1 is 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 has a better effect on the sole of the foot.

3. The transducer small-angle emission model for foot care based on ultrasonic cavitation field according to claim 1 is characterized in that: The selection process of the small angle β within 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; 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 speed of sound 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 formula (1) and formula (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 It 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 measurement of ultrasonic waves entering the foot is the same, and does not change with the incident wave 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 θ of the incident wave in water 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 The incident wave is completely reflected to avoid the incident wave entering the elastic tissue of the human foot and causing swelling or tingling, that is, the ultrasonic emission of the single transducer or dual transducer is completed. The feasibility of the direction with a small angle β = 0° with the sole of the foot; In real life, 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 average sound velocity of the elastic tissue of the human foot can be taken as c2≈1540 m / s; the average sound velocity of water at normal temperature and pressure is taken as c1≈1500 m / s, and according to formula (1), the following is obtained: The speed of sound of the elastic tissue of the human foot is greater than the speed of sound of water, and the refraction angle is always greater than the incident angle. When the incident angle gradually 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 of the foot. 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, then 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 a complex number, its absolute value is always equal to 1. The energy of the incident wave is completely reflected back into the water, but a phase jump is generated relative to the incident wave. Therefore, when the sound velocity of the actual elastic tissue of the human foot is taken as the normal value, when the incident angle is 90°>θ i When the angle is ≥75°, that is, 0°<β≤15°, within the range of the incident direction, the ultrasonic wave of the single transducer or the 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, the rationality of the angle between the ultrasonic emission direction of the single transducer or the dual transducer and the sole of the foot being a small angle of 0°<β≤15° is completed.

4. 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 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 is more effective for the sole of the foot. The specific analysis process is as follows: In step (B1), the sound waves excited by the single transducer form standing waves as follows: By installing a single transducer parallel to 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 ultrasonic waves in water; The standing wave formed by the acoustic wave excited by a single transducer installed in parallel with the foot container is shown in formula (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 parallel foot containers is propagating, there is a node region with zero sound pressure amplitude at x = (2n + 1)λ / 4, where n is an integer and λ is the wavelength. That is, a single transducer with parallel foot containers has a region where no cavitation occurs. In step (B2), the standing wave formed by the dual transducers colliding with the transmitted sound waves is shown in formula (7). p=2A{cos(kx)+cos[k(Lx)]}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, the sound pressure of the dual transducer radiation mode is expressed as p = 2A[cos(nπ) + sin(nπ)]e according to equation (7), as shown in equation (8). jωt =2Acos(nπ)e jωt =±2Ae jωt (8); In step (B3), according to the analysis of equations (6) and (8), 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.

5. The transducer small-angle emission model for foot care based on ultrasonic cavitation field according to claim 1 is 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 along the ultrasonic wave propagation path in the foot container. The specific analysis and implementation process is as follows: In step (C1), during the process of the 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 a coupled physical field is further set at any point in the ultrasonic wave propagation path in water; Step (C2), add coupled physics 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 a precise traveling wave field; Step (C3), according to the superposition formula (11) of ultrasonic waves: 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 sound pressure part, p 2a Absolute value of the imaginary part of sound pressure, is the reflected sound phase angle, The incident sound phase angle, through 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.

6. The transducer small-angle emission model for foot care based on ultrasonic cavitation field according to claim 5, characterized in that: The frequency analysis of the dual transducer after adding the coupled physical field further illustrates the application of the dual transducer counter-emission mode, 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 level static pressure on the transducer performance is as shown in Equation (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 and the length of the front cover, and the wave number is k E =ω / c E , k=ω / c, the front end cover length l′ is: l′=l+Δl Among them, the change of hydrostatic pressure P0 can be equivalent to the change of 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 hydrostatic pressure P0 is equivalent to the increase in l′.

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