Method and generator for characterizing an oscillatory system

Abstract

The present invention relates to a method for determining at least one physical characteristic value of an electromechanical oscillatory system, which comprises a piezoelectric element and at least one additional element coupled, with respect to oscillation, to the piezoelectric element, the piezoelectric element having an electrode and a counter electrode. The method comprises the following steps: (a) applying an electrical alternating voltage between the electrode and the counter electrode for the duration of an excitation interval in order to induce mechanical oscillation of the oscillatory system or of a sub-system of the oscillatory system, so that after the excitation interval has expired, the oscillatory system or the sub-system performs a free oscillation without excitation, (b) after the end of the excitation and during the free oscillation of the oscillatory system or of the sub-system without excitation: (i) measuring a time curve of a voltage U between the electrode and the counter electrode, or (ii) short-circuiting the electrode and the counter electrode with a line and measuring a time curve of a current I through the line, and (c) determining the at least one physical characteristic value of the electromechanical oscillatory system from the time curve of the voltage U, which time curve was measured in step b) i), or the time curve of the current I, which time curve was measured in step b) ii).

Claims

1. A method for determining an electric capacitance C.sub.sw of an electromechanical oscillatory system (100), which comprises a piezoelectric element (10) and at least one additional element coupled, with respect to oscillation, to the piezoelectric element (10), the piezoelectric element (10) having an electrode and a counter electrode, comprising the following steps: a) applying an electrical alternating voltage between the electrode and the counter electrode for the duration of an excitation interval in order to induce mechanical oscillation of the oscillatory system or of a sub-system of the oscillatory system so that after the excitation interval has expired, the oscillatory system or the sub-system performs a free oscillation without excitation, b) after the end of the excitation and during the free oscillation of the oscillatory system or of the sub-system without excitation: measuring a time curve of a voltage U (1) between the electrode and the counter electrode, and c) determining the electric capacitance C.sub.sw from the time curve of the voltage U (1), which time curve was measured in step b), wherein, in step b), a measuring device (30) having an internal capacitance C.sub.probe and an internal resistance R.sub.probe is used to measure the time curve of the voltage (1), and wherein step c) comprises the following sub-steps: aa) determining a time curve of a DC voltage portion U.sub.DC (2) from the time curve of the voltage U (1), which time curve was measured in step b), bb) determining a characteristic time interval T, within which an initial value of the DC voltage portion U.sub.DC,O measured in step b) has fallen to the value U.sub.DC,O/e, wherein e is Euler's number, cc) calculating the electric capacitance C.sub.sw with the characteristic time interval T.

2. The method according to claim 1, wherein in step cc), the electric capacitance C.sub.SW is calculated using the formula $C_{\mathrm{SW}}=\left(\frac{?}{R_{probe}}\right)-C_{probe}.$

3. The method according to claim 1, wherein in step a), excitation occurs at a frequency f close to or equal to a previously known resonance frequency of the oscillatory system (100).

4. The method according to claim 1, further comprising: d) short-circuiting the electrode and the counter electrode with a line (28) and measuring a time curve of a current I (3) through the line, wherein step b) occurs during a first measurement interval and step d) occurs during a second measurement interval, e) determining at least one further physical characteristic value from the time curve of the current I (3), which time curve was measured in step d).

5. The method according to claim 4, further comprising one or two of the following steps: f) determining a resonance frequency f.sub.res of the oscillatory system (100) from the time curve of the current I (3), which time curve was determined in step d), g) determining an anti-resonance frequency f.sub.antires of the oscillatory system (100) from the time curve of the voltage U (1), which time curve was determined in step b), h) step f), step g), and calculating the modal equivalent capacitance C.sub.m of the oscillatory system (100) from the capacitance C.sub.SW by means of the formula $C_m=C_{\mathrm{SW}}\left(\frac{f_{\mathrm{antires}}^2}{f_{res}^2}-1\right),$ i) step h) and calculating the modal equivalent inductance L.sub.m of the oscillatory system (100) from the modal equivalent capacitance C.sub.m, preferably by means of the formula $L_m=\frac{1}{4{?}^2{f}_{res}^2{C}_m},$ j) determining a resonant damping coefficient D.sub.res, which characterises a decrease of an envelope of the time curve of the current I (3), which decrease is a function of the time t, k) determining an anti-resonant damping coefficient D.sub.antires, which characterises a decrease of an envelope of the time curve of the voltage U (1), which decrease is a function of the time t, l) step f), step i), step j), and calculating the modal equivalent resistance R.sub.m by means of the formula R.sub.m=4? D.sub.res L.sub.m f.sub.res.

6. The method according to claim 5, wherein a complete characterization of the oscillatory system (100) is carried out by performing steps f) to j) and all necessary preceding steps, within a time interval of less than 300 ms.

7. A method for determining an electric capacitance C.sub.sw, of an ultrasonic oscillatory system (100) used for ultrasonic machining, the method being carried out during a machining break, the ultrasonic oscillatory system (100) comprising at least a generator (20), a converter comprising at least one piezoelectric element (10), and a sonotrode, the generator (20) supplying an alternating voltage that is converted by the piezoelectric element (10) of the converter into mechanical oscillation, the piezoelectric element (10) having an electrode and a counter electrode, wherein the sonotrode is brought into contact with a material to be machined in order to perform ultrasonic machining, and the sonotrode is not in contact with the material to be machined during the machining break, the method comprising the following steps: a) applying an electrical alternating voltage between the electrode and the counter electrode for the duration of an excitation interval in order to induce mechanical oscillation of the ultrasonic oscillatory system or of a sub-system of the ultrasonic oscillatory system so that after the excitation interval has expired, the ultrasonic oscillatory system or the sub-system performs a free oscillation without excitation, b) after the end of the excitation and during the free oscillation of the ultrasonic oscillatory system or of the sub-system without excitation: measuring a time curve of a voltage U (1) between the electrode and the counter electrode, and c) determining the electric capacitance C.sub.sw from the time curve of the voltage U (1), which time curve was measured in step b), wherein, in step b), a measuring device (30) having an internal capacitance C.sub.probe and an internal resistance R.sub.probe is used to measure the time curve of the voltage (1), and wherein step c) comprises the following sub-steps: aa) determining a time curve of a DC voltage portion U.sub.DC (2) from the time curve of the voltage U (1), which time curve was measured in step b), bb) determining a characteristic time interval ?, within which an initial value of the DC voltage portion U.sub.DC,O measured in step b) has fallen to the value U.sub.DC,O/e, wherein e is Euler's number, cc) calculating the electric capacitance C.sub.sw with the characteristic time interval I.

8. The method according to claim 7, wherein the following steps take place during the machining break: A) determining the electric capacitance C.sub.SW of the ultrasonic oscillatory system (100), B) adjusting the alternating voltage as a function of the electric capacitance C.sub.SW of the ultrasonic oscillatory system (100), which electric capacitance was determined in step A).

9. The method according to claim 8, wherein step B) comprises the following sub-steps: AA) determining the amplitude X of the mechanical oscillation of the ultrasonic oscillatory system (100) with the electric capacitance C.sub.SW of the ultrasonic oscillatory system (100), which electric capacitance was determined in step A), BB) comparing the amplitude X with a setpoint amplitude X.sub.0, CC) setting the frequency and/or amplitude of the alternating voltage supplied by the generator (20) so that an amplitude X equal to the setpoint amplitude X.sub.0 is reached.

Description

(1) FIG. 1 shows a simplified equivalent circuit diagram of a first ultrasonic oscillatory system,

(2) FIG. 2 shows a circuit diagram of a second ultrasonic oscillatory system with a generator according to the invention in a first state,

(3) FIG. 3 shows a circuit diagram of the ultrasonic oscillatory system of FIG. 2 in a second state,

(4) FIG. 4 shows a circuit diagram of the ultrasonic oscillatory system of FIG. 2 in a third state,

(5) FIG. 5 shows a curve of the measured course of the voltage of the second ultrasonic oscillatory system after excitation close to the resonance frequency,

(6) FIG. 6 shows a curve of the measured course of the current of the second ultrasonic oscillatory system after excitation close to the resonance frequency.

(7) The equivalent circuit diagram shown in FIG. 1 shows a case in which a piezoelectric element, namely a piezoelectric actuator 10, with the capacitance C.sub.p close to or equal to its resonance frequency, i.e., in an eigenmode, is excited with an alternating voltage U to an oscillation. The equivalent circuit diagram consequently shows an oscillatory system that does not have any electric or piezoelectric element other than the piezoelectric actuator.

(8) The term equivalent circuit diagram should be understood to mean that the behaviour of the pure electric circuit which is shown in the equivalent circuit diagram and which represents an electric oscillatory circuit, can describe the behaviour of the underlying piezoelectric ultrasonic oscillatory system, which in reality also comprises mechanical elements in addition to electric elements.

(9) Via a signal input 11, a voltage U is applied to the piezoelectric actuator 10 in the equivalent circuit diagram of FIG. 1. The circuit of the piezoelectric actuator 10 comprises a capacitor connected in parallel with the capacitance C.sub.p, the capacitor representing the electrical domain of the equivalent circuit diagram. The electrical domain is the area of the equivalent circuit diagram that represents the electrical properties of a piezoelectric element. In this sense, the piezoelectric element actually has the electrical properties of a capacitor. The current i.sub.Cm flowing in the electrical domain is consequently an electric current flowing in reality in a piezoelectric element.

(10) In contrast, the equivalent circuit diagram also has a mechanical domain comprising an equivalent resistance R.sub.M, a capacitor with the equivalent capacitance C.sub.M, and a coil with the equivalent inductance L.sub.M, these three elements being connected in series. The mechanical domain of the equivalent circuit diagram describes the mechanical properties of a piezoelectric element. The elements of the mechanical domain do not represent actual electrical components but equivalent elements. These equivalent elements are designed to form an electric oscillatory circuit in which the charge amplitude behaves the same as the actual mechanical amplitude of the piezoelectric element. In this sense, the portion of current flowing in the mechanical domain and thus called mechanical current is also not current actually flowing in the piezoelectric element. It thus represents the conversion of electrical energy into mechanical energy within a piezoelectric element.

(11) The electrical portion of the current I is denoted in FIG. 1 by i.sub.Cp and the mechanical portion of the current I is denoted in FIG. 1 by i.sub.Cm. The entire current I also shown is measured. The amplitude of the mechanical oscillation results from the mechanical portion i.sub.m so that the electrical portion i.sub.Cp must be known in order to be able to determine i.sub.m, thus the charge Q, and thus the amplitude X from a measurement of the entire current I. Since the electrical portion i.sub.Cp is a function of the capacitance of the oscillatory system, which is identical to the capacitance of the piezoelectric element in FIG. 1 (in FIG. 1: C.sub.p=C.sub.SW), the method according to the invention can be used in this case to determine this capacitance C.sub.p and thus improve the determinability and regulation of the oscillation amplitude.

(12) FIGS. 2 to 6 show the measurements, data, and steps an embodiment of the method according to the invention uses to achieve this goal.

(13) FIGS. 2, 3, and 4 respectively show a circuit diagram of an ultrasonic oscillatory system 100 having a generator, wherein FIGS. 2, 3, and 4 respectively show different states of the circuit within the generator 20. The ultrasonic oscillatory system 100 shown here also comprises a piezoelectric actuator 10, which is represented as an equivalent circuit diagram according to FIG. 1. The piezoelectric actuator is coupled, with respect to oscillation, to another element of the oscillatory system 100 (not shown here), for example a sonotrode, which is not shown here. The piezoelectric actuator 10 is connected to the generator 20 according to the invention via a cable 15, wherein the cable has a capacitance C.sub.cable. The generator 20 consists of an alternating voltage source 23, which supplies an alternating voltage U. The voltage source 23 is connected via a ground line 26 to the ground connection 24 and via a potential line 27 to the potential connection 24 of the generator. The potential line comprises a first switching device 21, with which the potential line can be interrupted, i.e., the electrically conductive function of the potential line can be switched off. Moreover, a short-circuit line 28 is provided, which connects the potential line 27 and the ground line 26, wherein this line also comprises a switching device 22, with which the short-circuit line 28 can be interrupted, i.e., the electrically conductive function of the short-circuit line can be switched off.

(14) The signal input 11 is connected to the electrode and the counter electrode of the piezoelectric actuator 10 in such a way that an alternating voltage applied to signal input 11 is applied between the electrode and the counter electrode of the piezoelectric actuator. Since the signal input is connected to the generator via a cable, the electrode and the counter electrode of the piezoelectric actuator can be short-circuited via the switching device 22 by connecting the potential line and the ground line.

(15) The generator 20 moreover comprises a measuring device 30 in the form of an oscilloscope, which is connected to the potential connection 24 and the ground connection 24 by a parallel circuit. As shown in the circuit diagram, the measuring device 30 has an internal capacitance C.sub.probe and an internal resistance R.sub.probe.

(16) In order to perform the method according to the invention, the generator 20 shown in FIGS. 2, 3, and 4 is set into different states by using switching devices 21 and 22.

(17) In FIG. 2, only the potential line is initially not interrupted so that the alternating voltage source is electrically conductively connected to the signal output, i.e., the switching device 21 is in a closed position. On the other hand, the switching device 22 is open so that there is a short-circuit current does not flow between the potential line and the ground line. The alternating voltage supplied by the voltage source 23 is thus applied to the potential connection 24. This alternating voltage is transmitted via the cable to the ultrasonic oscillatory unit so that it is applied via the signal input 11 to the piezoelectric actuator, i.e., between the electrode and the counter electrode of the piezoelectric actuator. The frequency of the applied alternating voltage is preferably selected to correspond a resonance frequency of the oscillatory system shown.

(18) The piezoelectric actuator is set into oscillation by the applied alternating voltage. Accordingly, FIG. 2 shows the state of the circuit within an excitation interval [t.sub.0,t.sub.1] according to step (a) of the method according to the invention.

(19) In order to proceed from step (a) to step (b) of the method according to the invention, the switching device 21 is actuated in such a way that the connection between the voltage source and the potential connection 24, i.e., the potential line 27, is interrupted so that the ultrasonic oscillatory system 10 performs a free, non-applied oscillation since alternating voltage is no longer applied between the electrode and the counter electrode of the piezoelectric actuator. The corresponding state of the circuit with a switching device 21 now opened is shown in FIG. 3 for alternative (b) (i) and in FIG. 4 for alternative (b) (ii).

(20) Starting from an embodiment of the method according to the invention, in which alternative (i) is initially performed in step (b), and then step (d), consequently alternative (ii) from step (b), is performed, the generator remains in the state shown in FIG. 3 with open switching devices 21 and 22 for a first measurement interval [t.sub.1,t.sub.2] in which the voltage is measured with the measuring device 30 according to alternative (b) (i).

(21) In order to measure the current or short-circuit current according to step (d) in a second measurement interval [t.sub.2,t.sub.3], the electrode and the counter electrode are short-circuited by actuating the switching device 22 to make a connection 28 between the potential line 27 and the ground line 26, as shown in FIG. 4. According to step (d), the short-circuit current is measured while the generator 20 according to the invention is in the state shown in FIG. 4, after which the switching device 21 is open and the switching device 22 is closed, and thus an electrically conductive, direct connection between the electrode and the counter electrode exists.

(22) FIG. 5 shows in a two-dimensional diagram the time curve 1 of the voltage U and the time curve 2 of the DC current portion of the voltage U in the excitation interval [t.sub.0,t.sub.1], in the first measurement interval [t.sub.1,t.sub.2], and in the second measurement interval [t.sub.2,t.sub.3]. For the measurement shown here, an ultrasonic oscillatory system was excited in the time interval [t.sub.0,t.sub.1] with a frequency close to the resonance frequency of the ultrasonic oscillatory system by applying an alternating current (see state of the circuit of FIG. 2). At time t.sub.1, the applied alternating current was switched off, whereupon a decay of the ultrasonic oscillatory system began (see state of the circuit of FIG. 3). In the course of this decay, an initially present DC voltage portion U.sub.DC,1 of the voltage at time t.sub.1 decreased exponentially until a DC voltage portion U.sub.DC,2 at time t.sub.2 was reached. The curve 1 of the voltage U results overall from this exponential decrease of the DC voltage portion U.sub.DC and the superimposed alternating voltage portion U.sub.AC, the amplitude of which likewise decreases over the course of the measurement interval [t.sub.1, t.sub.2]. At time t.sub.2, the electrode and the counter electrode are connected by the short-circuit line, i.e., are short-circuited, so that the voltage drops abruptly to zero at time t.sub.2 and remains there for the duration of the second measurement interval [t.sub.3,t.sub.4], wherein the case t.sub.2=t.sub.3 is shown here (see state of the circuit of FIG. 4).

(23) From the decrease of the DC voltage portion U.sub.DC over time, the characteristic time interval t can be determined according to step (c) (bb), for example by means of the formula:

(24) $t=\left(t2-t1\right)/\ln \left(\frac{U_{\mathrm{DC},1}}{U_{\mathrm{DC},2}}\right)$

(25) FIG. 6 shows the time curve of the current I for the same measurement for which the curve of the voltage U is shown in FIG. 2. Thus, the time ta of FIG. 5 corresponds to the time t.sub.2 of FIG. 2, at which the electrode and the counter electrode are short-circuited. In the measurement interval [t.sub.3,t.sub.4] shown in FIG. 6, a short-circuit current triggered by the short circuit is measured between the electrode and the counter electrode. The current has an alternating curve around the zero position, consequently a pure alternating current curve. The amplitude of the alternating current decreases exponentially. This can be seen by means of an imaginary envelope of the curve of the alternating current. From this exponential decrease, the resonant damping coefficient D.sub.res can be determined by a fit according to e.sup.?D.sup.res.sup.t. Accordingly, the anti-resonant damping coefficient D.sub.antires can be determined from the decrease of an envelope of the alternating voltage portion U.sub.AC by means of the curve of the voltage shown in FIG. 5.

LIST OF REFERENCE SIGNS

(26) 1 Time curve of the voltage U 2 Time curve of the DC voltage portion U.sub.DC 3 Time curve of the current I 10 Piezoelectric element/piezoelectric actuator 11 Signal input 15 Cable 20 Generator 21 First switching device 22 Second switching device 23 Alternating voltage source 24 Potential connection 24 Ground Connection 25 Ground 26 Ground line 27 Potential line 28 Short-circuit line 30 Measuring device/oscilloscope 40 Auxiliary line 100 Ultrasonic oscillatory system C.sub.P Electric capacitance of the piezoelectric element R.sub.m Equivalent resistance of ultrasonic oscillation system C.sub.m Equivalent capacitance of the ultrasonic oscillatory system L.sub.m Equivalent inductance of the ultrasonic oscillatory system C.sub.cable Electric capacitance of the cable C.sub.probe Internal capacitance of the measuring device (of the oscilloscope) R.sub.probe Internal resistance of the measuring device (of the oscilloscope) U Voltage U.sub.DC,1 DC voltage portion at time t.sub.1 U.sub.DC,2 DC voltage portion at time t.sub.2 I Current i Current (as vector quantity) i.sub.m Mechanical current portion i.sub.Cp Electrical current portion t Time s Seconds V Volts