EP0340470A1 - Verfahren und Schaltung zur Anregung eines Ultraschallschwingers und deren Verwendung zur Zerstäubung einer Flüssigkeit - Google Patents

Verfahren und Schaltung zur Anregung eines Ultraschallschwingers und deren Verwendung zur Zerstäubung einer Flüssigkeit Download PDF

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Publication number
EP0340470A1
EP0340470A1 EP89106106A EP89106106A EP0340470A1 EP 0340470 A1 EP0340470 A1 EP 0340470A1 EP 89106106 A EP89106106 A EP 89106106A EP 89106106 A EP89106106 A EP 89106106A EP 0340470 A1 EP0340470 A1 EP 0340470A1
Authority
EP
European Patent Office
Prior art keywords
frequency
oscillator
voltage
ultrasonic
ultrasonic oscillator
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP89106106A
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German (de)
English (en)
French (fr)
Inventor
Frank-Peter Jagdt
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Satronic AG
Original Assignee
Satronic AG
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Filing date
Publication date
Application filed by Satronic AG filed Critical Satronic AG
Publication of EP0340470A1 publication Critical patent/EP0340470A1/de
Withdrawn legal-status Critical Current

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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B06—GENERATING OR TRANSMITTING MECHANICAL VIBRATIONS IN GENERAL
    • B06B—METHODS OR APPARATUS FOR GENERATING OR TRANSMITTING MECHANICAL VIBRATIONS OF INFRASONIC, SONIC, OR ULTRASONIC FREQUENCY, e.g. FOR PERFORMING MECHANICAL WORK IN GENERAL
    • B06B1/00—Methods or apparatus for generating mechanical vibrations of infrasonic, sonic, or ultrasonic frequency
    • B06B1/02—Methods or apparatus for generating mechanical vibrations of infrasonic, sonic, or ultrasonic frequency making use of electrical energy
    • B06B1/0207—Driving circuits
    • B06B1/0223—Driving circuits for generating signals continuous in time
    • B06B1/0238—Driving circuits for generating signals continuous in time of a single frequency, e.g. a sine-wave
    • B06B1/0246—Driving circuits for generating signals continuous in time of a single frequency, e.g. a sine-wave with a feedback signal
    • B06B1/0253—Driving circuits for generating signals continuous in time of a single frequency, e.g. a sine-wave with a feedback signal taken directly from the generator circuit
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B05—SPRAYING OR ATOMISING IN GENERAL; APPLYING FLUENT MATERIALS TO SURFACES, IN GENERAL
    • B05B—SPRAYING APPARATUS; ATOMISING APPARATUS; NOZZLES
    • B05B17/00—Apparatus for spraying or atomising liquids or other fluent materials, not covered by the preceding groups
    • B05B17/04—Apparatus for spraying or atomising liquids or other fluent materials, not covered by the preceding groups operating with special methods
    • B05B17/06—Apparatus for spraying or atomising liquids or other fluent materials, not covered by the preceding groups operating with special methods using ultrasonic or other kinds of vibrations
    • B05B17/0607—Apparatus for spraying or atomising liquids or other fluent materials, not covered by the preceding groups operating with special methods using ultrasonic or other kinds of vibrations generated by electrical means, e.g. piezoelectric transducers
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B06—GENERATING OR TRANSMITTING MECHANICAL VIBRATIONS IN GENERAL
    • B06B—METHODS OR APPARATUS FOR GENERATING OR TRANSMITTING MECHANICAL VIBRATIONS OF INFRASONIC, SONIC, OR ULTRASONIC FREQUENCY, e.g. FOR PERFORMING MECHANICAL WORK IN GENERAL
    • B06B2201/00—Indexing scheme associated with B06B1/0207 for details covered by B06B1/0207 but not provided for in any of its subgroups
    • B06B2201/70—Specific application
    • B06B2201/77—Atomizers

Definitions

  • the invention relates to a method for exciting an ultrasonic vibrator according to the preamble of claim 1, a circuit for exciting the ultrasonic vibrator according to this method, and the use of the method for atomizing a liquid.
  • Such parameters are, for example, the manufacturing tolerances of the mechanical components of the ultrasonic vibrator and in particular its atomizing plate, the variations in the mechanical and electrical parameters of the piezoceramic used in its manufacture, the operating temperature of the ultrasonic transducer (very important when used in burners), the aging of the ultrasonic transducer, the deposits that form on it (such as soot and resins during use) in burners), the properties of the medium to be atomized, and also the manufacturing, adjustment and other tolerances in the excitation circuit.
  • the cessation of atomization must be reliably recognized. If the exposure is caused by droplets remaining on the atomizing plate, it must also be ensured that they are thrown off the atomizing plate.
  • a practical requirement for industrial applicability is the free interchangeability of the excitation circuit and the ultrasonic oscillator itself or, if applicable, its atomizing plate, and without any adjustment work and without high tolerance requirements on the spare parts or on the components of the circuit (which is particularly important when individual components are replaced due to repairs is).
  • the active power of the ultrasonic vibrator or its atomizing plate must be adjustable in the largest possible dynamic range, and the control of active power and frequency must not influence each other. Furthermore, changes in the aforementioned parameters and the operating voltage must have little or no influence on the function of the control loops.
  • the disadvantage of this solution is that the circuit has to be matched to the ultrasonic vibrator and in particular to its resonance target frequency, so that the operation of the ultrasonic vibrator cannot be tracked to the changes in some of the parameters listed above and the easy interchangeability of components is not guaranteed .
  • a reliable function is not guaranteed when starting up, especially under load and with changing operating conditions, since the impedance and thus the phase relationships between the current and voltage of the ultrasonic transducer change significantly with changes in load, and thus a tracking of the optimal oscillation frequency, derived from the phase relationships between current and Voltage in the ultrasonic transducer is not possible. It is not possible to achieve a real compensation of the capacitance of the ultrasonic vibrator by means of an inductor, because of the capacitance which changes during operation and in particular when there are changes in load.
  • the disadvantage here is that with ultrasonic transducers that do not reach the maximum adjustable power, the excitation circuit no longer locks onto the desired operating frequency when there is a high power requirement can.
  • a further disadvantage is that the current / frequency characteristic near the parallel resonance, that is to say at low powers, has a low slope, which leads to the control oscillation being interrupted and, consequently, to the wobble generator being switched on for no reason. The dynamic range of the power control is severely limited by these two phenomena.
  • the object of the invention is to avoid the aforementioned disadvantages and to enable cost-effective and reliable control of an ultrasonic vibrator.
  • the An Excitation of the ultrasonic vibrator 1 takes place via an output stage 2, which is supplied with a current I from a source of a direct voltage U.
  • the output stage 2 is controlled by a driver stage 3, which in turn receives a signal of frequency f from a voltage-controlled oscillator 4.
  • the voltage-controlled oscillator 4 is known per se (“VCO”) and is constructed using commercially available components.
  • the permissible voltage swing at its control input is predetermined, the corresponding frequency swing at its signal output can be adjusted in a known manner by the value of frequency-determining components that can be connected to the oscillator 4 and are not shown in FIG. 1, which can be resistors and / or capacitors when using analog technology , when using digital technology can include a crystal oscillator and signal inputs to corresponding programming inputs.
  • the control input of the oscillator 4 receives a signal from a triangular generator 5, so that the frequency f is wobbled depending on the output voltage of the triangular generator 5.
  • the triangle generator 5 increases or decreases its output voltage and the oscillator 4 its frequency f.
  • FIG. 2 shows an example of an embodiment of the output stage 2 of the circuit according to FIG. 1.
  • the ultrasonic vibrator 1 is excited via a transformer 21, which ensures galvanic isolation of the ultrasonic vibrator 1 and, if necessary (depending on its winding conditions), the excitation with different voltage ranges Voltage U allowed.
  • the output stage 2 comprises two transistors 22 and 23, which are driven by the driver stage 3 in push-pull and alternately switch the current I through to one half of the primary winding of the transformer 21.
  • the driver stage 3 supplies the phases necessary for the transistors 22 and 23 correct signals depending on the signal of the frequency f fed to the driver stage 3.
  • Such a driver stage is well known to the person skilled in the art and need not be described in more detail here.
  • the excitation circuit for the ultrasonic oscillator 1 is closed via a current measuring resistor 24.
  • a capacitor 25 leads the changes in the current I occurring at the frequency f directly from the transistors 22 and 23 back to the source of the voltage U, and thereby causes the voltage drop V occurring at the current measuring resistor 24 to be proportional to the temporal mean value of the current I, ie has no significant variation on frequency f.
  • the excitation frequency f is plotted on the abscissa and the voltage drop V measured at the current measuring resistor 24 is plotted on the ordinate.
  • the frequency range 32 of the control oscillation of a resonance detection control circuit of the circuit described below is also indicated in FIG. 3 when it is in the state locked onto the desired resonance frequency f r .
  • the voltage drop V across the current measuring resistor 24 is also a direct measure of the electrical power supplied to the ultrasonic oscillator 1. This in turn is a useful measure of the atomizing power of the ultrasonic vibrator 1 when it is provided with an atomizing plate and is used to atomize a liquid.
  • the characteristic curve 31 shown in FIG. 3 corresponds to the well-known impedance curve (ie here also the reactance curve) of a resonance system like that of a piezo oscillator.
  • the maximum 33 recognizable on the characteristic curve 31 corresponds to the series resonance resulting from the known equivalent circuit diagram of an oscillator, the recognizable minimum 34 corresponds to the parallel resonance resulting from the same equivalent circuit diagram.
  • the ratio of the currents I at the maximum 33 and at the minimum 34 is essentially determined by the impedance behavior of the ultrasonic oscillator 1.
  • the output voltage of the triangle generator 5 is fed to a window comparator 6. As will be seen from the following, this output voltage is always between the two window limits of the window comparator 6. If the output voltage of the triangle generator 5 now reaches the upper or lower window limit of the window comparator 6, this controls a set input or the set window or Reset input of a D flip-flop 7, which causes this flip-flop 7 to tilt (the conversion of the output signal of a window comparator into control signals for the inputs of a flip-flop is well known to the person skilled in the art and need not be described in more detail here).
  • the window comparator 6 monitors the wobble direction of the oscillator 4, and the flip-flop 7 serves as a memory for the wobble direction.
  • An output of the flip-flop 7 supplies a signal to a control input of the triangle generator 5. This signal determines the wobble direction.
  • the tilting of the flip-flop 7 causes the wobble direction to be reversed, and the ultrasonic oscillator 1 is operated at a frequency which is between a lower frequency f and an upper frequency f o (see FIG. 3) is wobbled uniformly as long as the clock input of the flip-flop 7 receives no pulses.
  • the voltage drop V across the current measuring resistor 24 is delayed in an all-pass filter 8 by a frequency-dependent amount of time.
  • the voltage drop V and the voltage drop delayed in the all-pass filter 8 are each fed to an input of a comparator 9, if appropriate after they have been freed from interference signals by filtering (not shown) and converted into suitable signals by an amplification (not shown).
  • the comparator 9 supplies a signal to the clock input of the flip-flop 7, which causes the flip-flop 7 to tilt and thus the signal at the control input of the triangle generator 5 changes and reverses the respective wobble direction of the oscillator 4.
  • the wobble direction is thus determined by the value of the instantaneous difference between the delayed voltage drop and the undelayed voltage drop, or by comparing this difference with a threshold.
  • the ultrasonic oscillator 1 If the ultrasonic oscillator 1 is operated in a state in which there is no resonance peak 33 or an insufficiently pronounced resonance peak, inter alia if the ratio of the currents I at the maximum 33 and the minimum 34 corresponds to an excessively damped impedance behavior of the ultrasonic oscillator 1, the wobble direction is reversed , when the triangle generator 5 delivers an output voltage which corresponds to the lower frequency limit f u or the upper frequency limit f o . This is the case, for example, if the ultrasonic vibrator 1 is used to atomize a liquid and is too strongly dampened by attached drops.
  • the wobble frequency can usefully be set in the area of the natural resonance of the attached drop in order to throw it off.
  • the ultrasonic oscillator 1, the output stage 2, the current measuring resistor 24, the all-pass filter 8, the comparator 9, the flip-flop 7, the triangle generator 5, the oscillator 4 and the driver stage 3 form a control circuit which, due to its design, regulates the excitation frequency of the excitation frequency Ultrasonic vibrator 1 around its series resonance frequency f r executes.
  • the delay in the all-pass filter 8 and the switching thresholds in the comparator 9 it is achieved that only the course of the resonance curve, which is typical for proper atomization, is recognized as real resonance. This suitable choice results from the wobble frequency used, the frequency spacing between the series resonance 33 and the parallel resonance 34 of the ultrasonic oscillator, and from the control properties of the assemblies contained in the control loop.
  • the wobble direction is reversed when the delayed voltage drop is greater than the undelayed voltage drop V by a predetermined amount. This has the result that the excitation frequency f of the ultrasonic vibrator 1 changes periodically in a region 32 around the resonance frequency, that is, this frequency control loop has a constant amplitude swings.
  • the instantaneous frequency and amplitude of the current I depend on the damping of the ultrasonic oscillator in the region of the resonance (cf. FIG. 3) in accordance with the selected sweep speed.
  • a low attenuation corresponds to a high instantaneous amplitude and high instantaneous frequency, with a correspondingly large difference between the undelayed and the delayed voltage drop.
  • the circuit thus causes the excitation frequency f of the ultrasonic oscillator to sweep through a predetermined frequency range, namely until the resonance detection snaps into place, ie the wobble direction is reversed before the frequency limit f u or f o is reached. Then the excitation frequency f of the ultrasonic oscillator locks into its resonance frequency f r , provided that this resonance is of a sufficiently high quality (for example, the ultrasonic oscillator is not dampened by attached drops).
  • the criterion for the engagement is the rate of change of the current I flowing through the output stage 2, which is in a first approximation proportional to the active power of the ultrasonic vibrator 1.
  • the desired power of the ultrasonic vibrator can be set by setting the operating voltage U of the output stage 2, for example using an adjustable voltage source (not shown). If the active power of the ultrasonic vibrator is also to be controlled, e.g. the current I is multiplied by the operating voltage U and the result of this multiplication is compared with the desired power.
  • the method described here has the advantage, among other things, that the functions of the resonance detection and the power control are separate, ie the resonance detection can work over a dynamic range of more than 1:10.
  • the process also works continuously, so it is not external time processes bound and can therefore easily follow changes such as changes in operational damping, power, resonance frequency, etc. Attached drops are shaken off faster than with the use of previously known methods, since wobbling is not rigid across the entire frequency range, but the switching between a frequency of the highest and the highest at a certain level of damping, for example, even with a partially shaken off drop Active power and one of the two frequency limits wobbles.
  • the analysis of the characteristic curve 31 can also be carried out by directly deriving the current I or the voltage drop V according to the frequency f. This is again equivalent to deriving the current I or the voltage drop V over time, since the frequency f determined by the triangle generator 5 varies linearly with time. Such a derivation is only the limiting case of the previously described difference formation in the event of a time delay tending towards zero at the all-pass filter 8.
  • the invention has been described in connection with an ultrasonic oscillator, in particular a piezoelectric ultrasonic oscillator, the use of which, e.g. is atomizing a liquid.
  • the invention is also advantageously applicable to other resonance systems, the resonance of which lies in a defined frequency range and can change depending on various parameters and in particular on the usual variation in the properties of ultrasonic oscillators and circuit components produced in series.

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Special Spraying Apparatus (AREA)
  • Apparatuses For Generation Of Mechanical Vibrations (AREA)
EP89106106A 1988-05-06 1989-04-07 Verfahren und Schaltung zur Anregung eines Ultraschallschwingers und deren Verwendung zur Zerstäubung einer Flüssigkeit Withdrawn EP0340470A1 (de)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CH172888 1988-05-06
CH1728/88 1988-05-06

Publications (1)

Publication Number Publication Date
EP0340470A1 true EP0340470A1 (de) 1989-11-08

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EP89106106A Withdrawn EP0340470A1 (de) 1988-05-06 1989-04-07 Verfahren und Schaltung zur Anregung eines Ultraschallschwingers und deren Verwendung zur Zerstäubung einer Flüssigkeit

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US (1) US4901034A (cs)
EP (1) EP0340470A1 (cs)
CS (1) CS274553B2 (cs)

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE3933300A1 (de) * 1989-10-05 1991-04-18 Eberspaecher J Ultraschallzerstaeuber
US5216338A (en) * 1989-10-05 1993-06-01 Firma J. Eberspacher Circuit arrangement for accurately and effectively driving an ultrasonic transducer
GB2279535A (en) * 1993-06-30 1995-01-04 Hielscher Gmbh The safe oscillation build-up of ultrasonic disintegrators
DE4412900A1 (de) * 1994-04-14 1995-10-26 Eberspaecher J Verfahren und Vorrichtung zum Feststellen des Einsetzens einer Überflutung eines Ultraschallzerstäubers
US6212936B1 (en) 1997-09-01 2001-04-10 Fresenius Ag Ultrasonic transmitter particularly for an air bubble detector
CN105988387A (zh) * 2015-02-16 2016-10-05 台达电子工业股份有限公司 喷雾驱动装置及喷雾系统
DE112017004833B4 (de) 2016-09-27 2022-11-24 Omron Healthcare Co., Ltd. Vernebler vom Netztyp

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EP0401802B1 (en) * 1989-06-07 1995-02-08 Nippondenso Co., Ltd. Drive system of actuator having piezoelectric device for use in motor vehicle
DE3925459A1 (de) * 1989-08-01 1991-02-14 Ferton Holding Ultraschallerzeuger mit einem piezoelektrischen wandler
US5097171A (en) * 1989-10-24 1992-03-17 Nippondenso Co., Ltd. Piezo-actuator shock absorber damping force controlling system having abnormality detection function
SE9804484D0 (sv) * 1998-12-22 1998-12-22 Siemens Elema Ab Förfarande för avsökning och inställning av en resonansfrekvens samt en tuner
US6288473B1 (en) * 2000-03-31 2001-09-11 Sandia Corporation Frequency modulation drive for a piezoelectric motor
US6539937B1 (en) * 2000-04-12 2003-04-01 Instrumentarium Corp. Method of maximizing the mechanical displacement of a piezoelectric nebulizer apparatus
DE102005030777B4 (de) * 2005-07-01 2016-10-20 Martin Walter Ultraschalltechnik Ag Verfahren und Schaltungsanordnung zum Betreiben eines Ultraschall-Schwingers
FR2903331B1 (fr) * 2006-07-07 2008-10-10 Oreal Generateur pour exciter un transducteur piezoelectrique
US8006918B2 (en) * 2008-10-03 2011-08-30 The Proctor & Gamble Company Alternating current powered delivery system
US20110130560A1 (en) * 2009-05-29 2011-06-02 Bio-Rad Laboratories, Inc. Sonication cartridge for nucleic acid extraction
US8798950B2 (en) 2010-08-20 2014-08-05 Bio-Rad Laboratories, Inc. System and method for ultrasonic transducer control
WO2012025833A2 (en) * 2010-08-27 2012-03-01 Socpra- Sciences Et Génie, S.E.C. Mechanical wave generator and method thereof
US9242263B1 (en) * 2013-03-15 2016-01-26 Sono-Tek Corporation Dynamic ultrasonic generator for ultrasonic spray systems

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US4275363A (en) * 1979-07-06 1981-06-23 Taga Electric Co., Ltd. Method of and apparatus for driving an ultrasonic transducer including a phase locked loop and a sweep circuit
DE3428523A1 (de) * 1983-08-05 1985-02-14 Taga Electric Co., Ltd., Tokyo Verfahren zur steuerung des betriebs eines ultraschallwandlers
DE3331896A1 (de) * 1983-09-03 1985-03-21 Gerhard Prof. Dr.-Ing. 8012 Ottobrunn Flachenecker Leistungsgenerator fuer einen ultraschallwandler
EP0254237A2 (de) * 1986-07-25 1988-01-27 Herbert Gässler Verfahren zur phasengesteuerten Leistungs- und Frequenzregelung eines Ultraschallwandlers sowie Vorrichtung zur Durchführung des Verfahrens

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DE3401735C1 (de) * 1984-01-19 1985-05-02 Herbert 7909 Bollingen Gässler Vorrichtung zum Betrieb eines piezoelektrischen Ultraschallwandlers
US4642581A (en) * 1985-06-21 1987-02-10 Sono-Tek Corporation Ultrasonic transducer drive circuit
US4808948A (en) * 1987-09-28 1989-02-28 Kulicke And Soffa Indusries, Inc. Automatic tuning system for ultrasonic generators

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4275363A (en) * 1979-07-06 1981-06-23 Taga Electric Co., Ltd. Method of and apparatus for driving an ultrasonic transducer including a phase locked loop and a sweep circuit
DE3428523A1 (de) * 1983-08-05 1985-02-14 Taga Electric Co., Ltd., Tokyo Verfahren zur steuerung des betriebs eines ultraschallwandlers
DE3331896A1 (de) * 1983-09-03 1985-03-21 Gerhard Prof. Dr.-Ing. 8012 Ottobrunn Flachenecker Leistungsgenerator fuer einen ultraschallwandler
EP0254237A2 (de) * 1986-07-25 1988-01-27 Herbert Gässler Verfahren zur phasengesteuerten Leistungs- und Frequenzregelung eines Ultraschallwandlers sowie Vorrichtung zur Durchführung des Verfahrens

Cited By (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE3933300A1 (de) * 1989-10-05 1991-04-18 Eberspaecher J Ultraschallzerstaeuber
US5216338A (en) * 1989-10-05 1993-06-01 Firma J. Eberspacher Circuit arrangement for accurately and effectively driving an ultrasonic transducer
US5532539A (en) * 1993-06-30 1996-07-02 Dr. Hielscher Gmbh Method and circuitry for the safe oscillation build-up of ultrasonic disintegrators
DE4322388A1 (de) * 1993-06-30 1995-01-12 Hielscher Gmbh Schaltungsanordnung zum sicheren Anschwingen von Ultraschalldesintegratoren
FR2708487A1 (fr) * 1993-06-30 1995-02-10 Hielscher Gmbh Procédé et disposition de montage pour l'amorçage sûr de désintégrateurs d'ultrasons.
GB2279535A (en) * 1993-06-30 1995-01-04 Hielscher Gmbh The safe oscillation build-up of ultrasonic disintegrators
GB2279535B (en) * 1993-06-30 1997-06-04 Hielscher Gmbh Method and circuitry for the safe oscillation build-up of ultrasonic disintegrators
DE4412900A1 (de) * 1994-04-14 1995-10-26 Eberspaecher J Verfahren und Vorrichtung zum Feststellen des Einsetzens einer Überflutung eines Ultraschallzerstäubers
US5588592A (en) * 1994-04-14 1996-12-31 J. Eberspacher Method and apparatus for detecting the onset of flooding of an ultrasonic atomizer
EP0677335A3 (de) * 1994-04-14 1997-05-21 Eberspaecher J Verfahren und Vorrichtung zum Feststellen des Einsetzens einer Überflutung eines Ultraschallzerstäubers.
DE4412900C2 (de) * 1994-04-14 2000-04-27 Eberspaecher J Gmbh & Co Verfahren und Vorrichtung zum Feststellen des Einsetzens einer Überflutung eines Ultraschallzerstäubers
US6212936B1 (en) 1997-09-01 2001-04-10 Fresenius Ag Ultrasonic transmitter particularly for an air bubble detector
CN105988387A (zh) * 2015-02-16 2016-10-05 台达电子工业股份有限公司 喷雾驱动装置及喷雾系统
CN105988387B (zh) * 2015-02-16 2019-11-01 台达电子工业股份有限公司 喷雾驱动装置及喷雾系统
DE112017004833B4 (de) 2016-09-27 2022-11-24 Omron Healthcare Co., Ltd. Vernebler vom Netztyp

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Publication number Publication date
US4901034A (en) 1990-02-13
CS274553B2 (en) 1991-08-13
CS258489A2 (en) 1990-10-12

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