Disclosure of Invention
In view of the above, the present invention provides an electrostatic voltage measurement apparatus and method, for solving the problems that the area and the area amplitude of an electrode, the distance between the electrode and a measured electrostatic body, and the distance amplitude need to be corrected, a comparison voltage with the same amplitude as the voltage of the measured electrostatic body needs to be generated, and the shape, the installation position, and the installation angle of the electrode affect the measurement result in the existing vibration capacitance non-contact measurement, and the technical scheme is as follows:
an electrostatic voltage measurement apparatus comprising: the device comprises electrodes, a vibrator, a voltage source, a current sampling device and a processor;
the voltage source outputs alternating current and direct current superposed voltage to the tested static body;
the processor controls the vibrator to vibrate so as to drive the electrode connected with the vibrator to vibrate, wherein the electrode is arranged close to the tested electrostatic body, and the coupling capacitance between the electrode and the tested electrostatic body alternates due to the vibration of the electrode;
the voltage source, the measured electrostatic body, the electrode and the current sampling device form a series loop, the current sampling device samples the current of the measured electrostatic body coupled through the electrode to obtain a sampling current, and a sampling current signal containing the sampling current is sent to the processor;
the processor extracts a current component from the sampled current signal and obtains an electrostatic voltage parameter of the measured electrostatic body according to the extracted current component.
The sampling current is specifically as follows: the voltage source, the measured electrostatic body, the electrode and the current sampling device form a series loop.
The processor extracts a current component from the sampling current signal and acquires an electrostatic voltage parameter of the measured electrostatic body according to the extracted current component, specifically:
the processor extracts j times of current component amplitude values from the sampling current signals, extracts j + i, j-i or i-j times of current component amplitude values, and acquires the electrostatic voltage amplitude value and the electrostatic voltage polarity of the tested electrostatic body according to the extracted current component amplitude values, wherein j is a positive integer greater than or equal to 1, i is a positive integer greater than or equal to 1, and j is not equal to i.
The current of a series loop formed by the voltage source, the measured electrostatic body, the electrode and the current sampling device is as follows:
wherein, CcIs the coupling capacitance, U, between the electrode and the measured electrostatic bodycAnd t is the total voltage between the electrode and the measured electrostatic body, and t is the time.
The coupling capacitance between the electrode and the measured electrostatic body is as follows:
<math>
<mrow>
<msub>
<mi>C</mi>
<mi>c</mi>
</msub>
<mo>=</mo>
<msub>
<mi>C</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>α</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
</math>
wherein, C0Is the average value of the coupling capacitance between the electrode and the measured electrostatic body, N is a positive integer greater than or equal to 1, j is a positive integer greater than or equal to 1 and less than or equal to N, CjAmplitude of change of capacitance, ω, for the jth harmonic componentjAs electricity of the j-th harmonic componentVolume-varying angular frequency, alphajIs the phase of the capacitance variation of the jth harmonic component, and t is time.
The voltage output by the voltage source is as follows:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>r</mi>
</msub>
<mo>=</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>β</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
</math>
total voltage U between the electrode and the measured electrostatic bodycThe electrostatic voltage U charged by the detected electrostatic bodysAnd the voltage U output by the voltage sourcerSumming;
wherein, UdcDirect current voltage, M is a positive integer greater than or equal to 1, i is a positive integer greater than or equal to 1 and less than or equal to M, UiAmplitude of voltage variation, ω, for the ith harmonic componentiAngular frequency of voltage change, beta, of the ith harmonic componentiIs the voltage phase of the ith harmonic component, and t is time.
The amplitude of the j times current component is angular frequency omegajThe amplitude of the current component of (1) is an angular frequency of ωj+ωiThe amplitude of the current component of (a) j-i times is an angular frequency of omegaj-ωiThe amplitude of the current component of (a) is ω for i-j timesi-ωjThe magnitude of the current component of (a).
The j times of current component amplitude is as follows:
I0=Cjωj(Us+Udc);
the amplitude of the j + i times current component is as follows:
<math>
<mrow>
<msub>
<mi>I</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
</math>
the amplitude of the current component of j-i or i-j times is as follows:
<math>
<mrow>
<msub>
<mi>I</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<mo>.</mo>
</mrow>
</math>
the method comprises the following steps of obtaining the electrostatic voltage amplitude and the electrostatic voltage polarity of the measured electrostatic body according to the amplitude of the extracted current component, specifically:
when U is turneddcWhen the current component amplitude is greater than or equal to 0, if the current component amplitude I is measured j times0Following UdcIs increased, the static electricity charged in the tested static electricity body is increasedThe voltage is positive, and the electrostatic voltage amplitude is:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>,</mo>
</mrow>
</math>
or,
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>|</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>;</mo>
</mrow>
</math>
when U is turneddcWhen the current component amplitude is greater than or equal to 0, if the current component amplitude I is measured j times0Following UdcThe voltage of the electrostatic voltage charged on the detected electrostatic body is negative, and the amplitude of the electrostatic voltage is as follows:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>,</mo>
</mrow>
</math>
or,
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>|</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>;</mo>
</mrow>
</math>
when U is turneddcIf the current component amplitude I is less than 0 times j0Following UdcIf the voltage is decreased and increased, the electrostatic voltage charged by the measured electrostatic body is negative, and the amplitude of the electrostatic voltage is:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mo>|</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>|</mo>
<mo>,</mo>
</mrow>
</math>
or,
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>|</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mo>|</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>|</mo>
<mo>;</mo>
</mrow>
</math>
when U is turneddcIf the current component amplitude I is less than 0 times j0Following UdcIf the voltage is decreased, the electrostatic voltage charged by the measured electrostatic body is positive, and the amplitude of the electrostatic voltage is:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<mo>|</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>|</mo>
<mo>,</mo>
</mrow>
</math>
or,
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>|</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<mo>|</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>|</mo>
<mo>.</mo>
</mrow>
</math>
an electrostatic voltage measuring method applied to an electrostatic voltage measuring apparatus including an electrode, a vibrator, a voltage source, a current sampling device, and a processor, comprising:
the voltage source outputs alternating current and direct current superposed voltage to the tested static body;
the processor controls the vibrator to vibrate so as to drive the electrode to vibrate, wherein the electrode is arranged close to the tested electrostatic body, and the coupling capacitance between the electrode and the tested electrostatic body alternates due to the vibration of the electrode;
the current sampling device samples the current of the tested electrostatic body coupled through the electrode to obtain a sampling current, and sends a sampling current signal containing the sampling current to the processor;
the processor extracts a current component from the sampled current signal and obtains an electrostatic voltage parameter of the measured electrostatic body according to the extracted current component.
In the electrostatic voltage measuring device provided by the invention, a voltage source outputs alternating current and direct current superposed voltage to a measured electrostatic body, a processor controls a vibrator to vibrate so as to drive an electrode to vibrate, the electrode is arranged close to the measured electrostatic body, a coupling capacitor between the electrode and the measured electrostatic body is alternated due to the vibration of the electrode, the voltage source, the measured electrostatic body, the electrode and a current sampling device form a series loop, the current sampling device samples a current signal coupled by the electrode of the measured electrostatic body, and the processor extracts a current component from the sampled current signal and obtains an electrostatic voltage parameter of the measured electrostatic body according to the extracted current component. Compared with the measuring device in the prior art, the electrostatic voltage measuring device and the method provided by the invention do not need to correct the area and the area amplitude of the electrode and the distance amplitude between the electrode and the measured electrostatic body, do not need to generate a comparison voltage with the same amplitude as the measured electrostatic voltage, and simultaneously have no influence on the measuring result by the shape, the installation position and the angle of the electrode, so long as the electrode is close to the measured electrostatic body.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
An embodiment of the present invention provides an electrostatic voltage measurement apparatus, and fig. 1 is a schematic structural diagram of the apparatus, where the apparatus includes: processor 101, vibrator 102, electrodes 103, voltage source 104, and current sampling device 105.
The voltage source 104 outputs alternating current and direct current superposed voltage to the tested electrostatic body 100, the processor 101 controls the vibrator 102 to vibrate so as to drive the electrode 103 connected with the vibrator 102 to vibrate, wherein the electrode 103 is arranged close to the tested electrostatic body 100, the coupling capacitance between the electrode 103 and the tested electrostatic body 100 is alternated due to the vibration of the electrode 103, the voltage source 104, the tested electrostatic body 100, the electrode 103 and the current sampling device 105 form a series loop, the voltage of the current sampling device 105 is reduced to zero or the voltage between the tested electrostatic body 100 and the electrode 103 is ignored, the current sampling device 105 samples the current coupled by the electrode 103 of the tested electrostatic body 100, so as to obtain sampling current, and a sampling current signal containing the sampling current is sent to the processor 101; the processor 101 extracts a current component from the sampled current signal and obtains an electrostatic voltage parameter of the measured electrostatic body 100 according to the extracted current component.
The voltage source 104 in this embodiment outputs the ac/dc superimposed voltage to the measured electrostatic object 100 under the control of the processor 101, but the embodiment does not limit the voltage source 104 to be controlled by the processor 101, and it is within the protection scope of the present invention as long as the voltage source 104 outputs the ac/dc superimposed voltage required by the embodiment of the present invention to the measured electrostatic object.
In this embodiment, the current sampling device 105 may be a resistor, a current sensor, or a transconductance amplifier, where the current sensor may be an ac current transformer or a hall current sensor. The current sampling device 105 samples a current signal coupled to the electrostatic body 100 through the electrode 103, and the obtained sampling current is a current in which the voltage source 104, the electrostatic body 100, the electrode 103, and the current sampling device 105 form a series circuit.
Let the electrostatic voltage of the measured electrostatic body 100 be UsThe coupling capacitance between the electrode 103 and the electrostatic body 100 to be measured is CcAnd the voltage drop of the current sampling device 105 is ignored.
In the present embodiment, the vibration of the vibrator 102 causes the coupling capacitance between the electrode 103 and the electrostatic body 100 to be:
<math>
<mrow>
<msub>
<mi>C</mi>
<mi>c</mi>
</msub>
<mo>=</mo>
<msub>
<mi>C</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>α</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
wherein, C0Is the average value of the coupling capacitance between the electrode 103 and the measured electrostatic body 100, N is a positive integer of 1 or more, j is a positive integer of 1 or more and N or less, CjAmplitude of change of capacitance, ω, for the jth harmonic componentjAngular frequency of change of capacitance, alpha, of the jth harmonic componentjIs the phase of the capacitance variation of the jth harmonic component, and t is time.
The ac/dc superimposed voltage output by the voltage source 104 is set as:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>r</mi>
</msub>
<mo>=</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>β</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
wherein, UdcDirect current voltage, M is a positive integer greater than or equal to 1, i is a positive integer greater than or equal to 1 and less than or equal to M, UiAmplitude of voltage variation, ω, for the ith harmonic componentiAngular frequency of voltage change, beta, of the ith harmonic componentiIs the voltage phase of the ith harmonic component, and t is time.
The total voltage between the measured electrostatic body 100 and the electrode 103 is:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>c</mi>
</msub>
<mo>=</mo>
<msub>
<mi>U</mi>
<mi>s</mi>
</msub>
<mo>+</mo>
<msub>
<mi>U</mi>
<mi>r</mi>
</msub>
<mo>=</mo>
<msub>
<mi>U</mi>
<mi>s</mi>
</msub>
<mo>+</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>β</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>.</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
the current of the series loop formed by the voltage source 104, the measured electrostatic body 100, the electrode 103 and the current sampling device 105, i.e. the sampling current, is:
<math>
<mrow>
<mo>=</mo>
<mo>[</mo>
<msub>
<mi>C</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>α</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>]</mo>
<mo>×</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mi>cos</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>β</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</math>
<math>
<mrow>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mi>cos</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>α</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mo>[</mo>
<msub>
<mi>U</mi>
<mi>s</mi>
</msub>
<mo>+</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>+</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>β</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>]</mo>
</mrow>
</math>
<math>
<mrow>
<mo>=</mo>
<msub>
<mi>C</mi>
<mn>0</mn>
</msub>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mi>cis</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>β</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>{</mo>
<mi>sin</mi>
<mo>[</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>α</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>β</mi>
<mi>i</mi>
</msub>
<mo>]</mo>
</mrow>
</math>
<math>
<mrow>
<mo>+</mo>
<mi>sin</mi>
<mo>[</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>α</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>β</mi>
<mi>i</mi>
</msub>
<mo>]</mo>
<mo>}</mo>
<mo>+</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>U</mi>
<mi>s</mi>
</msub>
<mo>+</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>)</mo>
</mrow>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mi>cos</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>α</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
</mrow>
</math>
<math>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>{</mo>
<mi>sin</mi>
<mo>[</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>α</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>β</mi>
<mi>i</mi>
</msub>
<mo>]</mo>
<mo>-</mo>
<mi>sin</mi>
<mo>[</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>t</mi>
<mo>+</mo>
<msub>
<mi>α</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>β</mi>
<mi>i</mi>
</msub>
<mo>]</mo>
<mo>}</mo>
</mrow>
</math>
in this example, the processor 101 extracts a current component from the sampled current signal and obtains an electrostatic voltage parameter of the measured electrostatic body 100 according to the extracted current component, specifically: the processor 101 obtains a sampling current i from the sampling current signalcThen from the sampled current icExtracting j times of current component amplitude, extracting j + i, j-i or i-j times of current component amplitude, and then obtaining the electrostatic voltage parameter of the tested electrostatic body 100 according to the extracted current component amplitude, wherein j is a positive integer greater than or equal to 1, i is a positive integer greater than or equal to 1, and j is not equal to i. The electrostatic voltage parameters of the measured electrostatic body 100 include: electrostatic voltage magnitude and electrostatic voltage polarity.
Processor 101 samples current i fromcExtracting j times of current component amplitude, i.e. from sampled current icMiddle extraction angular frequency of omegajThe amplitude of the current component (c) is given by the equation (4) that the angular frequency is ωjThe current component amplitudes of (a) are:
I0=Cjωj(Us+Udc) (5)
processor 101 samples current i fromcExtracting the amplitude of the current component of j + i times, i.e. from the sampled current icMiddle extraction angular frequency of omegaj+ωiThe amplitude of the current component (c) is given by the equation (4) that the angular frequency is ωj+ωiThe current component amplitudes of (a) are:
<math>
<mrow>
<msub>
<mi>I</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
processor 101 samples current i fromcExtracting the amplitude of the current component j-i or i-j times, i.e. from the sampled current icMiddle extraction angular frequency of omegaj-ωiOr ωi-ωjThe amplitude of the current component (c) is given by the equation (4) that the angular frequency is ωj-ωiOr ωi-ωjThe current component amplitudes of (a) are:
<math>
<mrow>
<msub>
<mi>I</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
in this embodiment, the obtaining, by the processor 101, the electrostatic voltage parameter of the detected electrostatic body 100 according to the extracted current component amplitude specifically includes:
when U is turneddcWhen it is greater than or equal to 0, if the sampling current icJ times the current component amplitude I0Following UdcIs increased, the electrostatic voltage U charged on the electrostatic object 100 is increasedsPositive, the electrostatic voltage amplitude obtained according to equations (5) and (6) is:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
alternatively, the electrostatic voltage amplitude can be found according to equations (5) and (7) as:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>|</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
when U is turneddcWhen it is greater than or equal to 0, if the sampling current icJ times the current component amplitude I0Following UdcIs increased or decreased, the electrostatic voltage U of the measured electrostatic body 100 is increased or decreasedsNegative, the electrostatic voltage amplitude is obtained according to equations (5) and (6):
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
alternatively, the electrostatic voltage amplitude can be found according to equations (5) and (7) as:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>|</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
when U is turneddcWhen less than 0, if the sampling current icJ times the current component amplitude I0Following UdcIs decreased and increased, the electrostatic voltage U charged on the electrostatic object 100 to be measuredsNegative, the electrostatic voltage amplitude is obtained according to equations (5) and (6):
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mo>|</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>|</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
alternatively, the electrostatic voltage amplitude can be found according to equations (5) and (7) as:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>|</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mo>|</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>|</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
when U is turneddcWhen less than 0, if the sampling current icJ times the current component amplitude I0Following UdcIs decreased, the electrostatic voltage U of the measured electrostatic body 100 is decreasedsPositive, the electrostatic voltage amplitude obtained according to equations (5) and (6) is:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<mo>|</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>|</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
alternatively, the electrostatic voltage amplitude can be found according to equations (5) and (7) as:
<math>
<mrow>
<msub>
<mi>U</mi>
<mi>sam</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>|</mo>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>ω</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msub>
<mi>I</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>ω</mi>
<mi>j</mi>
</msub>
<msub>
<mi>I</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<mo>|</mo>
<msub>
<mi>U</mi>
<mi>dc</mi>
</msub>
<mo>|</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
the embodiment of the invention also provides an electrostatic voltage measuring method, which is applied to an electrostatic voltage measuring device comprising an electrode, a vibrator, a voltage source, a current sampling device and a processor, and comprises the following steps:
s11: the voltage source outputs the voltage of alternating current and direct current superposition to the tested static body.
S12: the processor controls the vibrator to vibrate so as to drive the electrode to vibrate, wherein the electrode is arranged close to the tested electrostatic body, and the coupling capacitance between the electrode and the tested electrostatic body alternates due to the vibration of the electrode.
S13: the current sampling device samples a current signal of the tested electrostatic body coupled through the electrode to obtain a sampling current, and sends the sampling current signal containing the sampling current to the processor.
S14: the processor extracts a current component from the sampled current signal and obtains an electrostatic voltage parameter of the measured electrostatic body according to the extracted current component.
In this embodiment, the processor extracts a current component from the sampled current signal and obtains an electrostatic voltage parameter of the measured electrostatic body according to the extracted current component, specifically: the processor obtains sampling current from the sampling current signal, extracts j times of current component amplitude from the sampling current, extracts j + i, j-i or i-j times of current component amplitude, and obtains the electrostatic voltage parameter of the tested electrostatic body according to the extracted current component amplitude, wherein j is a positive integer larger than or equal to 1, i is a positive integer larger than or equal to 1, and j is not equal to i. The electrostatic voltage parameters of the measured electrostatic body 100 include: electrostatic voltage magnitude and electrostatic voltage polarity.
In the electrostatic voltage measuring device provided by the invention, a voltage source outputs alternating current and direct current superposed voltage to a measured electrostatic body, a processor controls a vibrator to vibrate so as to drive an electrode to vibrate, the electrode is arranged close to the measured electrostatic body, a coupling capacitor between the electrode and the measured electrostatic body is alternated due to the vibration of the electrode, the voltage source, the measured electrostatic body, the electrode and a current sampling device form a series loop, the voltage of the current sampling device is reduced to zero or the voltage between the electrodes of the measured electrostatic body is ignored, the current sampling device samples a current signal coupled by the electrode of the measured electrostatic body, and the processor extracts a current component from the sampled current signal and obtains an electrostatic voltage parameter of the measured electrostatic body according to the extracted current component. Compared with the measuring device in the prior art, the electrostatic voltage measuring device and the method provided by the invention do not need to correct the area and the area amplitude of the electrode and the distance amplitude between the electrode and the measured electrostatic body, and do not need to generate a comparison voltage with the same amplitude as the measured electrostatic voltage, meanwhile, the shape, the installation position and the angle of the electrode have no influence on the measuring result, and the electrode is only close to the measured electrostatic body, so that the consistency of the electrostatic voltage measuring product is ensured.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.