DE102019109311B3 - Arrangement and method for the calibration and operation of capacitive actuators - Google Patents

Abstract

The invention relates to an arrangement and a method for traceable calibration of an electrostatic actuator. In addition to a guided mechanical frame, the arrangement has at least one device for electrostatic force generation. With the arrangement proposed here and the associated method, the electrical parameters prevailing at the devices for electrostatic force generation can be resonated simultaneously and without the arrangement or measurement-relevant parts of the device to move, the level of force generation to be determined. This calibration can take place during force generation.

Description

The invention relates to an arrangement and a method for traceable calibration of an electrostatic actuator.

The minimal example of an electrostatic actuator is a plate capacitor. A plate capacitor is an arrangement of two plane-parallel plates of the same geometry, which are contacted in an electrically conductive manner. This arrangement is thus able to store electrical energy in the form of an electrical field caused by electrical charge carriers. The measure of the capacity of a capacitor for electrical charge carriers is the capacity. The capacitance of a plate capacitor depends on the plate size, the plate spacing and the material between the plates, the dielectric. If the plate size, the plate spacing or the dielectric is changed while the electrical voltage is constantly applied, the resulting change in capacitance is compensated for by the flow of an electrical current. The measurement of these electrical currents is used in a variety of ways, for example to measure movements of the capacitor plates and thus to be used by sensors, for example to demonstrate the smallest changes in travel or speeds. On the other hand, it can also be used as a capacitive actuator for generating electrostatic force.

In the US 4,963,829 A discloses a "tachometer", which is to be understood fundamentally as a capacitive structure. A second associated plate is attached to a shaft above a plate of a plate capacitor. The second plate is rotated. Both plates are connected to a DC voltage and the changes in capacitance, caused by the geometrical peculiarities of the second capacitor plate, result in a measurable current flow. This is the actual measured variable and allows conclusions to be drawn about the angular velocity. With the recorded signal curve of the current strength, however, only the measured variable “speed” can be determined.

In the US 2004/0113514 A1 Both a method and a device for the electrical damping of mechanical vibrations are disclosed. This is used to electrostatically compensate for unpleasant vibrations from piezo actuators. A piezo actuator is an arrangement in which the energy of the resulting electrical field is converted into mechanical energy by the application of an electrical voltage to a so-called piezoelectric crystal. In the arrangement described in the patent, the speed and the position of a movable capacitor plate of a plate capacitor are measured. A suitable electrical voltage signal is then applied to this capacitor and the unpleasant movements are compensated. The monitoring of the compensation is solved by a control loop.

In the DE 10 2015 104 696 B3 discloses an electrodynamic levitation device. In this, the position of a flotator is maintained by suitable electrical fields, while external forces and torques act on the flotor. The position control is accomplished by active regulation. During the position control, the external forces and torques can be measured by measuring the applied voltage.

However, none of these known documents explicitly determine the coupling constant between the generation of force and the electrical voltage used for it.

In contrast, in the US 2006/0267596 A1 described a force standard for the measuring tips (cantilever) of an atomic force microscope. The magnitude of the forces to be determined is a few nanonewtons. The force standard disclosed replaces the measurement by means of a direct comparison between the cantilever to be calibrated and a reference cantilever by a traceable calibration method. Thus, the coupling constant of force generation and the electrical voltage used for it is explicitly determined in a traceable manner. This calibration method for the measuring tips (cantilever) of AFM microscopes works according to the resonance method, but has the disadvantage that this can result in a larger version of the resonance catastrophe and the associated destruction of the mechanically executed force coupling. In addition, the calibration on the normal and the actual measurement are carried out separately and therefore cannot be carried out simultaneously.

In addition to the measurement methods mentioned, the capacitance and thus the coupling constant can be determined using mathematical models and with the aid of a length measurement A. M. Thompson & D. G. Lampard: A new theorem in electrostatics and its application to calculable standards of capacitance. In: Nature volume 177, page 888 (1956)). However, this method can only be implemented with high accuracy for certain electrode arrangements.

The object of the present invention is to provide an arrangement and a device for simultaneously and without causing the arrangement or measurement-relevant parts of the arrangement to resonate, during the generation of force using electrical parameters to calibrate the actuator constant without resonance.

The object is achieved by the features of the independent claims. Preferred embodiments are the subject of the respective back-related claims.

A first aspect of the invention relates to an arrangement for traceable calibration of an electrostatic actuator.
The arrangement for traceable calibration of an electrostatic actuator has at least one frame for holding at least one movable electrode, at least one electrode fixed to the frame, at least one voltage source, at least one electrical consumer, at least two measuring devices for electrical parameters and at least one measuring device for position measurement and one measuring device Velocity measurement, the arrangement being designed to calibrate the actuator constant without resonance.
The calibration at the same time as the generation of the electrostatic force is achieved when the frequency of the relative movement of the electrodes on the frame is far above the mechanical resonance frequency of the guide system connected to the actuator, so that the change in force generated due to the relative movement only moves in a range that is negligible for the application mechanical system leads. A suitable movement frequency is, for example, above 10 times the resonance frequency.

• Elektrode: Hierbei wird vorliegend das offene Ende eines elektrischen Leiters verstanden. Werden zwei dieser Leiterenden elektrisch gegenpolig geladen und in einen geometrischen Abstand zueinander gesetzt, so ist dies ein allgemeiner Kondensator. Als spezielle und besonders einfache Ausführung gilt der Plattenkondensator. Bei diesem sind die Platten die hier definierten Elektroden. Die Elektroden sind mit einer Spannungsquelle verbunden.

In the following, certain terms are defined for a better understanding of the invention:

• Electrode: Here the open end of an electrical conductor is understood. If two of these conductor ends are charged with opposite polarity and placed at a geometric distance from one another, this is a general capacitor. The plate capacitor is a special and particularly simple version. The plates are the electrodes defined here. The electrodes are connected to a voltage source.

Constant voltage source: This is the special case of a voltage source. In this version of a voltage source, a constant value of the output electrical voltage is set over a given period of time. This value of the voltage can also be measured during the movement of the capacitor plates to one another over the specified period.

Frequency of movement: This is synonymous with the excitation frequency, or excitation frequency, of a system suitable for mechanical vibration. After a short settling phase, the system capable of oscillation assumes the excitation frequency and is forced to oscillate with it. Every system capable of oscillation has a natural frequency. If the excitation frequency is equal to the natural frequency, there is a special case of resonance.

Resonance frequency: This is the frequency at which the vibrational energy of an exciter is coupled into an oscillatory system without the damping being sufficient to convert the supplied energy back into heat and to dissipate it. It is possible and likely that this will destroy the vibrating system.

1. 1. $F\left(x\left(t\right)\right)=\frac{\text{d}}{\text{d}x}W$
   
   und mit
2. 2. x(t) = Δx(t) + x₀, wobei Δx die relative Änderung des Abstandes der Kondensatorplatten zueinander und x₀ die Position der Ruhelage der Kondensatorplatten symbolisiert. Die elektrische Feldenergie mit
3. 3. $W=\frac{1}{2}C\left(x\left(t\right)\right)U^2$
   
   kann nach Gl. 1. durch Ableitung in eine Kraft überführt werden
4. 4. $\frac{\text{d}}{\text{d}x}W=\frac{\text{d}}{\text{d}x}C\left(x\left(t\right)\right)\cdot \frac{1}{2}{U}^2.$
   
   Unter Hinzunahme der elektrischen Stromstärke
5. 5. $i\left(t\right)=\frac{\text{d}}{\text{d}t}Q=\frac{\text{d}}{\text{d}t}C\left(x\left(t\right)\right)\cdot U$
   
   und den Regeln für partielle Ableitungen
6. 6. $\frac{\text{d}}{\text{d}t}C\left(x\left(t\right)\right)=\frac{\partial }{\partial x}C\left(x\left(t\right)\right)\cdot \frac{\text{d}x}{\text{d}t}$
   
   kann unter Ausnutzung des Spezialfalles eines Plattenkondensators die Identität
7. 7. $\frac{d}{dx}C\left(x\left(t\right)\right)=\frac{\partial }{\partial x}C\left(x\left(t\right)\right)=k\left(x\right)$
   
   ausgenutzt werden um aus den Gl. 1., 4. und 7. auf
8. 8. F(x(t)) = k(x)U² zu folgern.

Actuator constant: The actuator constant k specifies the value at which an applied electrical voltage generates the resulting amount of the expected force. Physically, this is based on the following equations, which are exemplary for the plate capacitor:

1. 1. $F\left(x\left(t\right)\right)=\frac{\text{d}}{\text{d}x}W$
   
   and with
2. 2. x (t) = Δx (t) + x ₀ , where Δx symbolizes the relative change in the distance between the capacitor plates and x ₀ symbolizes the position of the rest position of the capacitor plates. The electric field energy with
3. 3rd $W=\frac{1}{\mathrm{2nd}}\mathrm{C.}\left(x\left(t\right)\right)U^{\mathrm{2nd}}$
   
   according to Eq. 1. be transformed into a force by derivation
4. 4th $\frac{\text{d}}{\text{d}x}W=\frac{\text{d}}{\text{d}x}\mathrm{C.}\left(x\left(t\right)\right)\cdot \frac{1}{\mathrm{2nd}}{U}^{\mathrm{2nd}}.$
   
   With the addition of electrical current
5. 5. $i\left(t\right)=\frac{\text{d}}{\text{d}t}Q=\frac{\text{d}}{\text{d}t}\mathrm{C.}\left(x\left(t\right)\right)\cdot U$
   
   and the rules for partial derivatives
6. 6. $\frac{\text{d}}{\text{d}t}\mathrm{C.}\left(x\left(t\right)\right)=\frac{\partial }{\partial x}\mathrm{C.}\left(x\left(t\right)\right)\cdot \frac{\text{d}x}{\text{d}t}$
   
   Identity can be exploited using the special case of a plate capacitor
7. 7. $\frac{d}{dx}\mathrm{C.}\left(x\left(t\right)\right)=\frac{\partial }{\partial x}\mathrm{C.}\left(x\left(t\right)\right)=k\left(x\right)$
   
   be exploited to derive from Eq. 1st, 4th and 7th on
8. 8. To conclude F (x (t)) = k (x) U ² .

Where F (x) the force between two capacitor plates, x (t) the distance between the capacitor plates, W the stored field energy of the capacitor, U the constant electrical voltage applied to the capacitor plates, C the capacitance of the plate capacitor, i (t) the electrical Current, Q is the amount of charge stored in the capacitor and k (x) is the actuator constant that depends on the plate spacing.

Electrical parameters: In the sense of the present document, these are understood to mean the values of the electrical voltage U and the electrical current strength i (t). The electrical parameters describe an electrical consumer.
An electrical consumer is able to convert electrical energy into heat and another form of energy, e.g. B. in the magnetic field of an electromagnet. Theoretically, each consumer can be represented and described in a suitable combination using an equivalent circuit diagram of ideally ohmic, ideally inductive and ideally capacitive components. This real consumer shows different behavior at different frequencies of the applied voltage or of the electrical current flowing through it. For example, any consumer can show predominantly ohmic behavior for a specific frequency range. An electrical consumer is thus a real shape of a physical ohmic component in accordance with its electrical characteristics, which predominantly show ohmic behavior.

The arrangement according to the invention, which is designed to calibrate the actuator constant in the range from 10 μHz to 20 kHz, with the exception of a 3 dB wide range around the resonance frequency, has a frame which can accommodate force-generating devices, such as, for. B. electrostatic actuators and piezoelectric actuators is suitable. Furthermore, the frame is suitable for power-converting devices, such as. B. to hold mechanical or magnetic bearings or gears. Thus, in embodiments of the invention, the guidance of the movable electrode is carried out mechanically or magnetically.
The exception of the 3 dB wide range around the resonance frequency is chosen because in the case of resonance, the feedback of the effect on the measurement object influences the measurand beyond recognition and at the same time destroys the measurement or the arrangement.
The frame is also able to power storage devices such. B. mechanical coil or leaf springs. The frame of the arrangement has at least two electrodes of a capacitor, preferably a plate capacitor. The at least two electrodes of the capacitor are movable relative to one another. At least one electrode is preferably designed to be fixed to the frame and the other, second electrode is movable.
In embodiments of the invention, the voltage of the voltage source applied over the measurement period is constant.
The electrodes are electrically conductively connected to a voltage source to generate an electric field between them. In embodiments of the invention, this voltage source is a constant voltage source. The voltage source or constant voltage source is preferably connected to a measuring device for electrical parameters. The parameter of the electrical voltage is preferably measured.
An electrical consumer with predominantly ohmic behavior in the desired frequency range from 10 µHz to 20 kHz is attached and electrically conductively connected to the capacitor plates in such a way that the electrical current flow resulting from the movement of the capacitor plates must flow through this consumer, in whole or in part. At least one measuring device for measuring the electrical parameter is suitably connected to this consumer.

The parameter to be measured is preferably the electrical current. Therefore, a current measuring device is used to measure the current signal.

The electrical voltage signal falling across the predominantly ohmic behavior consumer is particularly preferably measured.

At least one fastening system for attaching an actuator is mechanically attached to the frame of the arrangement. Furthermore, at least one voltage source is connected, at least one measuring device for electrical parameters, at least one measuring device for position measurement and / or at least one measuring device for speed and an actuator for generating a relative movement of the electrodes to one another and the position or speed measuring system for measuring the relative movement of the electrodes appropriate. When used as an actuator, one of the electrodes is attached to the stationary frame, the other to a movable part, the electrode mounted on the frame preferably being set in motion. A constructive advantage of the movement of the frame-side electrode is that, apart from a ground connection, no further electrical connections are required for the actuator located on the movable part of the system.

In embodiments of the invention, the electrical consumer shows predominantly ohmic behavior in the given frequency range.

1. a. Beschalten eines Kondensators mit elektrischer Spannung wobei die Elektroden (Kondensatorplatten) beweglich und/oder drehbar zueinander angeordnet sind,
2. b. Beschaltung eines Aktors mit verschiedenen Betriebsspannungen zur Erzeugung einer Relativbewegung der Elektroden (Kondensatorplatten) zueinander,
3. c. Einstellung der Bewegungsfrequenz, sodass die Relativbewegung der Elektroden (Kondensatorplatten) oberhalb der Resonanzfrequenz des mit einer der Elektroden (Kondensatorplatten) verbundenen mechanischen Systems liegt,
4. d. Messung der Geschwindigkeit der Relativbewegung der Elektroden (Kondensatorplatten) bei gleichzeitiger Messung des durch die Kapazitätsänderung bedingten elektrischen Stromes oder der daraus resultierenden elektrischen Spannung über einem elektrischen Verbraucher und
5. e. Berechnung der Aktorkonstante aus den gemessenen elektrischen und mechanischen Größen.

The method according to the invention has the following steps for simultaneously measuring and calibrating the actuator constant from the traceably measured variables:

1. a. Wiring a capacitor with electrical voltage, the electrodes (capacitor plates) being arranged to be movable and / or rotatable relative to one another,
2. b. Wiring an actuator with different operating voltages to generate a Relative movement of the electrodes (capacitor plates) to each other,
3. c. Setting the movement frequency so that the relative movement of the electrodes (capacitor plates) lies above the resonance frequency of the mechanical system connected to one of the electrodes (capacitor plates),
4. d. Measurement of the speed of the relative movement of the electrodes (capacitor plates) while simultaneously measuring the electrical current caused by the change in capacity or the resulting electrical voltage across an electrical consumer and
5. e. Calculation of the actuator constant from the measured electrical and mechanical quantities.

In contrast to classic calibration methods, such as B. Watt scales, no reference weights are required in the proposed solution. An advantageous traceability of the force coupling constant without mass standard is thus made possible. The calibration at the same time as the generation of the electrostatic force is achieved when the frequency of the relative movement of the electrodes on the frame side is in a range of 3 dB from the mechanical resonance frequency of the guide system connected to the actuator. The resonance-free calibration of the force coupling constant offers the advantage that it can be carried out independently of the force generation.

The method is based on the generation of the electrostatic force and simultaneous measurement of the relative speed of the electrodes (capacitor plates) to one another and of the electrical current flowing simultaneously in the circuit during the generation of a force on the rack side. Furthermore, knowledge of the voltage applied to the electrodes is necessary for the method.
The actuator constant of the electrostatic actuator can be determined by evaluating the ratio of the electrical current strength and speed of the moving electrodes (capacitor plates) according to the above-mentioned equations, in particular according to equations (1, 4 and 8). For this purpose, the distance between the capacitor plates in the rest position x ₀ is preferably known. In the event of an unknown distance, this can be reconstructed from the measurement data of location change, speed and current. This is preferably carried out by a computer program product using a data processing repository.

To implement the invention, it is also expedient to combine the above-described configurations, embodiments and features of the claims with one another in any arrangement.

The invention will be explained in more detail below using an exemplary embodiment. The exemplary embodiment relates to a force measuring system in the form of a torsion balance and is intended to describe the invention without restricting it.

• 1: In der Abbildung ist schematisch das vereinfachte Modell der Messapparatur eingezeichnet. Die schematische Abbildung weist alle minimalen Merkmale der erfindungsseitigen Anordnung auf. Diese sind: eine bewegliche Elektrode und eine gestellfeste Elektrode eines Plattenkondensators (101), ein mechanisches Führungssystem zur Befestigung eines Aktors (701), eine Spannungsquelle (401), eine Messeinrichtung für elektrische Kenngrößen (601), geeignet zur Messung des Spannungsabfalls am elektrischen Verbraucher (501), sowie eine Messeinrichtung zur Positionsmessung und eine Messeinrichtung für Geschwindigkeit (301).
• 2: In der Abbildung ist schematisch das vereinfachte Modell der Messapparatur eingezeichnet. Die schematische Abbildung weist alle minimalen Merkmale der erfindungsseitigen Anordnung auf. Diese sind: eine bewegliche Elektrode und eine gestellfeste Elektrode eines Plattenkondensators (101), ein mechanisches Führungssystem zur Befestigung eines Aktors (701), eine Spannungsquelle (401), eine Messeinrichtung für elektrische Kenngrößen (601), geeignet zur Messung der Stromstärke, sowie eine Messeinrichtung zur Positionsmessung und eine Messeinrichtung für Geschwindigkeit (301).
• 3: In der Abbildung ist das Diagramm der Messung der relativen Position der Kondensatorplatten dargestellt. Aus dem Diagramm kann die Frequenz, mit welcher die Messung des Ausführungsbeispiels durchgeführt wurde, von 0,06 Hz entnommen werden.
• 4: In der Abbildung ist ein Diagramm mit Messdaten der mechanischen Kenngrößen Geschwindigkeit und relative Position der Kondensatorplatten zueinander dargestellt. Dabei ist die relative Position der Kondensatorplatten gegen die Geschwindigkeit abgetragen, mit welcher die Änderung der Position der Kondensatorplatten vollzogen wird.
• 5: In der Abbildung ist ein Diagramm abgebildet, welches die gemessenen Werte der Stromstärke in Beziehung zur gemessenen Geschwindigkeit der Änderung der Position der Kondensatorplatten veranschaulicht. Diese Korrelation ist maßgeblich für das Bestimmen der gesuchten Aktorkonstante.
• 6: In der Abbildung ist die Verteilung des Verhältnisses aus gemessener Stromstärke i(t) und Geschwindigkeit über der relativen Position der Kondensatorplatten zueinander dargestellt. Die Asymmetrie bzgl. der relativen Ruhelage ist aus Gleichung (2.) sowie durch Annäherung und Entfernung der Kondensatorplatten zueinander erklärbar.
• 7: In der Abbildung ist ein Diagramm abgebildet, welches eine vorläufige Kalibrierkonstante (Hilfskonstante) f^f = kU zeigt.

The invention is explained in more detail with reference to drawings. Show:

• 1 : The simplified model of the measuring apparatus is shown schematically in the figure. The schematic illustration has all the minimal features of the arrangement according to the invention. These are: a movable electrode and a fixed electrode of a plate capacitor ( 101 ), a mechanical guide system for fastening an actuator ( 701 ), a voltage source ( 401 ), a measuring device for electrical parameters ( 601 ), suitable for measuring the voltage drop at the electrical consumer ( 501 ), as well as a measuring device for position measurement and a measuring device for speed ( 301 ).
• 2nd : The simplified model of the measuring apparatus is shown schematically in the figure. The schematic illustration has all the minimal features of the arrangement according to the invention. These are: a movable electrode and a fixed electrode of a plate capacitor ( 101 ), a mechanical guide system for fastening an actuator ( 701 ), a voltage source ( 401 ), a measuring device for electrical parameters ( 601 ), suitable for measuring the current, as well as a measuring device for position measurement and a measuring device for speed ( 301 ).
• 3rd : The diagram shows the measurement of the relative position of the capacitor plates. The frequency at which the measurement of the exemplary embodiment was carried out, 0.06 Hz, can be seen from the diagram.
• 4th : The figure shows a diagram with measurement data of the mechanical parameters speed and relative position of the capacitor plates to each other. The relative position of the capacitor plates is plotted against the speed at which the change in the position of the capacitor plates is carried out.
• 5 : The figure shows a diagram which shows the measured values of the current intensity in relation to the measured speed of the change in the position of the capacitor plates. This Correlation is decisive for determining the actuator constant sought.
• 6 : The figure shows the distribution of the ratio of the measured current i (t) and speed over the relative position of the capacitor plates to each other. The asymmetry with respect to the relative rest position can be explained from equation (2) and by the approximation and distance of the capacitor plates from one another.
• 7 : The figure shows a diagram showing a provisional calibration constant (auxiliary constant) f ^f = kU.

This is a preliminary calibration constant, since the constant electrical voltage used for the measurement is still contained in size f '. The measured values were sorted according to the measured relative position of the capacitor plate and an average with measurement uncertainty was formed. The value of f 'is presented without units and was measured as 9.85 (2) in this example.

The arrangement in this exemplary embodiment is aimed at the purpose of compensating a force generated by a remote measurement object by generating an electrostatic counterforce. The electrical voltage used for electrostatic compensation can be converted into a force if the calibration factor is known. For this purpose, the calibration device for resonance-free calibration of the actuator constant is attached to the frame for measurement, a spring joint being arranged on a mounting plate. A metal wheel is arranged horizontally on this spring joint. Lying here means that the axis of the rotational symmetry of the wheel is aligned in the direction of the acceleration due to gravity. The wheel is made of aluminum. The wheel has four spokes arranged symmetrically and radially to the central axis. The devices for measuring the force on the measurement object, for measuring position and speed, for generating movement and for generating force are arranged along the spokes of the wheel. The force to be measured is exerted magnetically on the measurement object by generating eddy currents in a moving, electrically conductive liquid. For this purpose, a spacer in the form of a rod is attached along the spoke on a spoke of the wheel. At the end of the rod, which is inclined to the center of the wheel, magnets for generating force by means of eddy current induction are arranged. A spacer is also arranged in the opposite direction, along the spoke running opposite. This serves on the one hand as a counterweight and on the other hand as a base for a piezoelectric actuator for generating movement. In this exemplary embodiment, a plate of the force-compensating plate capacitor is also attached along this weight-balancing holding device.

The mounting of the second capacitor plate, the mounting of the piezoelectric actuator and the mounting of the measuring device for measuring the position and speed of the wheel are attached to the mounting plate.

Both plates of the plate capacitor form the electrostatic actuator to be calibrated, since the electrical voltage applied to the plates to generate an electrostatic counterforce must be converted into the resulting force. The electrical voltage is provided by an Agilent 3245A constant voltage source. The actuator, which is additionally attached to this arrangement, is supplied with its own voltage signal with suitably high frequencies to excite mechanical vibration.

bestimmt. Eine resonante Kalibrierung der Kraftkopplungskonstante bei gleichzeitiger Messung ist in diesem Ausführungsbeispiel nicht möglich, da im Resonanzfall die Rückkopplung des Magnetfeldes auf das Messobjekt die Messgröße bis zur Unkenntlichkeit beeinflusst und gleichsam die Messung zerstört.The natural frequency of the arrangement measured by means of a torsional vibration test is 0.6 Hz and the frequency of the set voltage signal is (0.06) Hz, see the figure 3rd . The frequency of the excitation signal is only 10% of the previously measured resonance frequency of the arrangement. At this frequency, various values of speed and electrical current were measured in addition to the position. The relationships from equations 1, 4 and 8 make an actuator constant of $$k\left(x=0\right)=1.16\cdot {\mathrm{10th}}^{-7}\frac{\text{N}}{{\text{v}}^{\mathrm{2nd}}}$$

certainly. A resonant calibration of the force coupling constant with simultaneous measurement is not possible in this exemplary embodiment, since in the case of resonance the feedback of the magnetic field to the measurement object influences the measurement variable beyond recognition and, as it were, destroys the measurement.

Reference list

101 -

Plate capacitor with variable distance between the capacitor plates

201 -

Current flow

301 -

Measuring device for position and / or speed measurement

401 -

Voltage source (especially constant voltage source)

501 -

Electrical consumer with predominantly ohmic behavior

601 -

Device for measuring electrical parameters

701 -

Actuator

Claims (11)

Arrangement for calibrating an electrostatic actuator (701), comprising at least one frame for holding at least one movable electrode, at least one electrode fixed to the frame, at least one voltage source (401), at least one electrical consumer (501), at least two measuring devices for electrical parameters (601) and at least one measuring device (301) for position measurement and one measuring device (301) for speed measurement, the arrangement being designed to calibrate the actuator constant k without resonance. Arrangement after Claim 1 , characterized in that the voltage of the voltage source (401) present over the measurement period is constant. Arrangement after Claim 2 , characterized in that the voltage source (401) is a constant voltage source. Arrangement after Claim 1 , characterized in that the arrangement is designed to calibrate the actuator constant k in the range from 10 µHz to 20 kHz, with the exception of a 3 dB wide environment around the resonance frequency. Arrangement after Claim 1 or 4th , characterized in that the electrical consumer (501) shows predominantly ohmic behavior in the given frequency range. Arrangement after Claim 1 , characterized in that the guide of the movable electrode is carried out mechanically. Arrangement after Claim 1 , characterized in that the guide of the movable electrode is magnetic. Arrangement according to one of the Claims 1 to 5 , characterized in that a measuring device (301) is designed for position measurement. Arrangement according to one of the Claims 1 to 6 , characterized in that a measuring device (301) is designed for speed measurement. Using an arrangement after Claim 1 for calibration of the actuator constant k that can be traced back at the same time as the force is being generated. Method for calibrating the actuator constant k of an electrostatic actuator (701), which can be traced back during the generation of force, comprising the following steps: a. Wiring a capacitor (101) with electrical voltage, the capacitance-defining assemblies being arranged to be movable and / or rotatable relative to one another, b. Wiring an actuator with different operating voltages to generate a relative movement of the capacitance-defining assemblies to each other, c. Setting the movement frequency so that the relative movement of the capacity-defining assemblies lies above the resonance frequency of the mechanical system connected to one of the capacity-defining assemblies, d. Measuring the speed of the relative movement of the capacity-defining assemblies while simultaneously measuring the electrical current caused by the change in capacity or the resulting electrical voltage across an electrical load (501) and e. Calculation of the actuator constant k from the measured electrical and mechanical quantities.

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