DE102024100687A1 - Method for determining a speed - Google Patents

Abstract

A precise method for determining a (constant) speed (n) is proposed, which requires little prior information and is characterized by the determination of the phase spectrum (PS) of an oscillation time signal (TWF) using the Fourier transform (FFT), under:
- Calculation of at least three temporally consecutive Fourier transforms (FFT1, FFT2, FFT3, FFT4) and
- Determination of the fluctuation and/or difference of the phase values (DPS),
- Determination of the frequency value(s) at which the fluctuation and/or difference of the phase values over time does not exceed a predetermined threshold and/or is constant.

Description

The invention relates to a method for determining a rotational speed, preferably a rotational speed that remains constant or at least does not change highly dynamically.

From the EP 3 581 328 B1 For example, a method is known in the prior art in which a vibration time signal from a rotor unit of a machine tool is recorded using a measuring scale. The amplitude spectrum thus obtained via a Fourier transformation can provide information about the rotational speed and even insights into possible axial runout errors.

The object of the invention is to provide a method for determining the rotational speed which allows a particularly precise measurement and, in particular, requires as little prior information or assumptions as possible about the process or machine to be measured.

The object is achieved by the features of claim 1, starting from a method for determining a rotational speed of the type mentioned at the outset.

Advantageous embodiments and developments of the invention are possible by the measures mentioned in the dependent claims.

The method according to the invention is therefore used to determine a rotational speed, preferably a rotational speed that remains constant. The rotational speed does not necessarily have to remain exactly constant; rather, it is generally sufficient that the rotational speed is not subject to highly dynamic changes, i.e., the rotational speed can be recognized as remaining constant for a low single-digit second range (for a few seconds, e.g., 4 seconds), i.e., it does not exhibit a fluctuation of more than 10% within this time interval. The present description initially relates to the detection of a rotational speed that is approximately constant within this framework. It is also fundamentally possible to apply the method if the rotational speed does not remain constant but changes over time.

For rotating components, such as the rotor unit of an electrical machine, a drive, or the like, speeds are determined and, if necessary, information about imbalance is obtained by detecting a reference, a so-called dimensional standard, on the rotor as it repeatedly passes the sensor. To increase accuracy, and especially to determine imbalance, the sensors are advantageously arranged with a phase offset of 90°.

The use of three-axis sensors is particularly preferred. Axial detection can produce a noticeable signal in the case of large imbalances, allowing the method to more effectively detect the imbalance.

In the method according to the invention, a vibration time signal of an axis is recorded, preferably in a perpendicular orientation or radially to the rotation axis. The sample rate of the vibration sensor used is generally known and is typically provided by the vibration sensor. However, the sample rate does not necessarily have to be transmitted directly by the vibration sensor. A computing unit such as the data acquisition unit can also provide the sample rate. The sample rate can be available there as a parameter. Furthermore, parameterization by a user is possible.

Using a Fourier transformation, a phase spectrum is generated from the oscillation time signal using the sample rate. The invention is characterized by the fact that only the phase information is required to determine the rotational speed. The amplitude spectrum, which has so far formed the almost exclusive basis for determining the rotational speed in conventional prior art methods, is fundamentally not required for this purpose. Nevertheless, accuracy can be increased with the help of an amplitude spectrum. The amplitude spectrum can also be used to determine the correct frequency. During the analysis, the phase spectrum initially forms a basis for selecting the frequencies that are possible rotational speeds, while taking the amplitude spectrum into account allows for a more detailed evaluation because it can provide further information that can be used, for example, to exclude certain frequency values. For example, it can be checked whether the amplitudes remain constant at a certain frequency value. If this is not the case, there may be an artifact caused by noise. This means that these frequency values can be ignored, while with a constant amplitude the frequency value can correlate with an actual speed.

When determining the speed using a Fourier transformation, in addition to the speed at a specific frequency, multiples of the speed are always visible as spectral lines in the spectrum. However, the actual speed frequency is not always the most prominent line, which makes determining the speed difficult because several lines are visible and a selection of the frequency that describes the actual rotation. In the amplitude spectrum, even the line at the actual speed can be vanishingly small, meaning that the actual frequency must be inferred from multiples of the speed. When using an amplitude spectrum, special knowledge of the rotation to be measured and good resolution are necessary, for example, a speed range within which the frequency must be expected. If an automated selection of potential speeds is not possible, the user is sometimes presented with a selection of possible speeds, whereby the user must use their own knowledge to determine which of the frequencies is the correct one.

The longer the recorded oscillation time signal is or the more oscillation time signals that can be recorded, the more accurate the determination can be. The more Fourier transforms are used over a certain period of time, the more accurate the determination can be. According to the invention, at least three Fourier transforms with the same settings and the same time offset are generally required. The sample rate required for evaluation is basically always available as information from a measured time signal if the acceleration sensor is known, so the need to have this information does not entail any disadvantage and, above all, does not entail any additional effort. A window function, in particular a Hanning window, can be used to weight the time signal values. Other window functions can also be applied in principle. With an increasing width of the window function, the secondary maxima can be suppressed and the dynamics improved.

The fluctuations or differences in the phases are calculated from the phase spectra. For the frequency values at which the speed, a multiple of the speed, or possibly other oscillations are found, an essentially constant phase is to be expected, where "essentially" means that the phases are at least approximately constant due to statistical or systematic errors in the measurement, i.e., they can be assumed to be constant to within a difference of less than 20°. A further advantage of the method according to the invention is that no reference value is necessary for the absolute determination of the phase, because only the constancy of the phase relationships is taken into account in the evaluation. A key phasor for the exact determination of the speed is also advantageously not required. This advantageously eliminates the need to attach a measuring scale or key phasor to the rotor. The constancy of the phase at a constant speed is achieved, for example, by measuring the respective phase up to a specific point (e.g., an oscillation maximum) in each time interval over which a Fourier transformation is performed and determining the difference at successive time intervals. This is possible without a measuring scale/key phasor. Overall, the invention enables parameter-free speed determination.

To determine the constancy of the phase, the two-fold difference or derivative can also be determined, which should ideally result in zero if temporal constancy actually occurs.

When an approximately constant phase occurs in a certain spectral line range, a constant or synchronous frequency is associated.

According to the invention, even small imbalances can advantageously be detected, as long as the amplitude is significant enough and leads to a stable phase, i.e., a constant phase value can be expected over time at the corresponding frequency. If the result of the phase spectrum is additionally combined with information from the amplitude spectrum, the quality factor can be significantly increased. The amplitude spectrum results from the Fourier transformation anyway, so it is already present. A particular advantage resulting from the invention is the use of the evaluated phase and amplitude spectrum in combination with one another, which can significantly increase the quality factor.

For example, the ratio of consecutive or all spectra can be calculated to check whether the amplitudes are changing. In the case of noise, the jumps in amplitude are expected to be larger. A nearly constant amplitude, which leads to a stable phase, is most likely a relevant frequency value, which is correlated, for example, with a rotational speed.

In particular, when the ratio of consecutive amplitude spectra is evaluated, speeds can be detected which disappear in the noise but are significant enough to lead to a stable phase.

A further advantage is that this evaluation according to the method according to the invention can be carried out either permanently during operation, in real time depending on the processing unit used, or even downstream. For evaluation, the measurement data is stored in a memory and evaluated.

Nevertheless, in an evaluation according to the invention, frequencies and their multiples are found, similar to methods that exclusively use an amplitude spectrum. However, according to the invention, the lowest frequency and not just one of its multiples is generally detected in the phase spectrum. However, frequencies can also be detected that hardly differ from noise in terms of amplitude. In general, the lowest frequency can therefore be separated from its harmonics and assumed to be the frequency value to be determined. When using a phase spectrum, it may therefore be sufficient to identify a group of frequencies (fundamental frequency and its harmonics) and to identify the lowest of these frequencies as the fundamental frequency.

Connected spectral line ranges can thus be grouped, and the exact frequency is determined using advanced algorithms (e.g., spline interpolation). The amplitude spectrum may therefore also be required. Since the harmonics can usually also be found, the speed can then be identified using advanced logic. In the simplest case, it is sufficient to identify the lowest frequency within this logic, which is made easier with a phase spectrum rather than an amplitude spectrum.

• - Bei einer Ausführungsform der Erfindung kann überprüft werden, ob das quadratische Mittel bzw. der Effektivwert im Zeitbereich der spektralen Berechnung innerhalb einer bestimmten Schwankungsbreite liegt, damit annähernd konstante Bedingungen angenommen werden können. Ein entsprechender Filter kann bei der Prüfung der Messwerte implementiert werden.
• - Bei einer weiteren Ausführungsform können auch die erhaltenen Spektrallinien danach gefiltert werden, ob sie nah genug an einen quadratische Mittelwert bzw. Effektivwert herankommen.
• - Grundsätzlich ist zu unterscheiden, ob eine Spektrallinie bei niedrigster Frequenz, welche die eigentliche Schwingung widerspiegelt oder eine ihrer Harmonischen vorliegt. Bei einer Weiterbildung der Erfindung kann dies durch eine weiterführende Logik separiert werden, indem bestimmt wird, ob es sich um die niedrigste Frequenz in der Gruppe handelt. Ist bekannt, in welchem Bereich die Frequenz zu erwarten ist, kann diese Information bei einer Ausführungsvariante auch zusätzlich verwendet werden.
• - Bei einem Ausführungsbeispiel der Erfindung kann die Recheneinheit auch dazu ausgebildet sein, die dritte Ableitung zu bilden, die Aufschluss über die Differenzfrequenz bei nah beieinanderliegenden Frequenzen geben kann.
• - Weiterbildungen der Erfindung können Recheneinheiten aufweisen, die zum Auffinden der Harmonischen verschiedene Algorithmen nutzen. Statt eines Frequenzspektrums kann auch ein Cepstrum zur Erkennung periodisch auftretender Strukturen im Frequenzspektrum berechnet werden.
• - Eine Recheneinheit kann auch Autokorrelationen verwenden, um die Linien bzw. die Frequenzen zu identifizieren.
• - In der Akustik wird zur Bestimmung der Grundfrequenz mitunter ein YIN-Algorithmus verwendet, was auch auf die vorliegenden Spektren angewandt werden kann. Dieser Algorithmus lässt sich in der Regel einfach in eine Recheneinheit implementieren.
• - Ähnlich kann auch ein 2-way-mismatch-Algorithmus von Maher und Beauchamp zur Bestimmung der Grundfrequenz mit Hilfe der Recheneinheit implementiert werden.
• - Zudem sind weitere Analysen möglich, bei denen die am stärksten hervortretenden Linien aus dem Spektrum herausgefiltert werden. Eine weitere in die Recheneinheit implementierbare Variante nach Salamon und Gomez wird beschrieben in: www.coursera.org/lecture/audio-signalprocessing/f0-detection-tx630 .

Embodiments of the invention can initially be used particularly effectively in the determination of constant speeds or under constant conditions in order to obtain constant phase information. However, it is also conceivable to implement speed variability, in which case the constant phase information is immediately missing. Processing can also be difficult when frequencies are close to one another, provided they contribute significantly to the same spectral range, for example in the case of beats. In the case of beats, a higher resolution of the Fourier transform can be used. For this reason, in embodiments of the invention, more advanced logic can be used in the computing unit used for evaluation. In general, in Fourier analysis, the highest visible frequency and the number of lines found determine the frequency resolution and thus the accuracy.

• - In one embodiment of the invention, it is possible to check whether the root mean square or the effective value in the time domain of the spectral calculation lies within a certain fluctuation range, so that approximately constant conditions can be assumed. A corresponding filter can be implemented when checking the measured values.
• - In a further embodiment, the spectral lines obtained can also be filtered according to whether they come close enough to a root mean square or effective value.
• - Fundamentally, a distinction must be made between a spectral line at the lowest frequency, which reflects the actual oscillation, or one of its harmonics. In a further development of the invention, this can be separated using advanced logic by determining whether it is the lowest frequency in the group. If the frequency range is known, this information can also be used additionally in a variant.
• - In one embodiment of the invention, the computing unit can also be designed to form the third derivative, which can provide information about the difference frequency at frequencies that are close to one another.
• - Further developments of the invention can include computing units that use different algorithms to locate the harmonics. Instead of a frequency spectrum, a cepstrum can also be calculated to detect periodically occurring structures in the frequency spectrum.
• - A computing unit can also use autocorrelations to identify the lines or frequencies.
• - In acoustics, a YIN algorithm is sometimes used to determine the fundamental frequency, which can also be applied to the spectra at hand. This algorithm can usually be easily implemented in a computer.
• - Similarly, a 2-way mismatch algorithm by Maher and Beauchamp can be implemented to determine the fundamental frequency using the arithmetic unit.
• - In addition, further analyses are possible in which the most prominent lines are filtered out of the spectrum. Another variant, according to Salamon and Gomez, that can be implemented in the processing unit is described in: www.coursera.org/lecture/audio-signalprocessing/f0-detection-tx630 .

In principle, the measurement period of the oscillation time signal is finite or limited. In a Fourier analysis, therefore, in contrast to a theoretically infinitely long recorded signal, additional lines are visible at high lower frequencies. In an advantageous embodiment of the invention, the computing unit is therefore designed to calculate out this leakage effect by introducing evaluation criteria for window functions. The wider the selected window, the more the secondary maxima decrease. The dynamic range, which represents a measure of the ratio of the largest peak to the secondary maxima, can thus be improved, i.e., the secondary maxima are attenuated.

In a further embodiment of the invention, the computing unit is configured to determine the harmonics. For this purpose, a corresponding algorithm can be implemented, which, for example, determines whether, within a certain uncertainty, lines exist whose frequencies can be represented as multiples of a fundamental frequency.

For example, the differences between all frequencies are determined, and those that exceed a certain threshold are filtered out. The quotients of the frequencies and the resulting differences that differ only by a specified percentage are counted. Finally, the frequency with the highest match is searched for. This basic algorithm can be repeated, especially if no frequency is found, by calculating whether the differences between the frequencies are integer multiples of a fundamental frequency.

Furthermore, especially if the algorithms mentioned above do not lead to any results in finding harmonics, the processing unit can be configured to check for other indications of harmonics, from which an alternative algorithm can be found. These lines are generally expected to have a high amplitude. Furthermore, it can be checked which is the lowest frequency at which a constant phase can be found. While it has been found that in the experimentally determined amplitude spectrum, the line with the lowest frequency does not necessarily represent the fundamental frequency, but may also be a higher harmonic, in the phase spectrum the line with the lowest frequency can regularly be identified with the fundamental frequency. If many lines with the same constant phase are found, this indicates that this oscillation has a significant effect on the observed physical process. When monitoring a rotation, it can be assumed that the actual rotation is clearly visible in the spectrum. Therefore, when preselecting the lines, their width is quite relevant and provides an indication that it is not an artifact from the general noise.

The method according to the invention can be implemented as a computer-implemented method. The computing unit can therefore comprise at least one processor.

In one embodiment, the computing unit can be configured to group ranges with specific frequency values. This allows, for example, a pre-selection of frequencies that belong together as fundamental frequencies and harmonics. To locate harmonics, the cepstrum, for example, can be used, which uses a time variable instead of a frequency.

• - Auftretende Harmonische liegen bei Vielfachen der Grundfrequenz. Daher ist, gerade im Phasenspektrum, der niedrigste gefundene Frequenzwert ein Indiz, dass es ich um die Grundfrequenz der Drehung handeln könnte.
• - Ferner ist aber auch umgekehrt zu erwarten, dass zu der Grundfrequenz der Drehung auch weitere Harmonische zu finden sind, d.h. es kann zusätzlich nach dem niedrigsten Frequenzwert gesucht werden, für den weitere Harmonische auftreten.
• - Oftmals ist bekannt, in welchem Frequenzbereich die Drehfrequenz einer Maschine zu erwarten ist, d.h. es kann überprüft werden, ob der Frequenzwert tatsächlich unterhalb einer vorgegebenen Grenzfrequenz liegt.
• - Die zu untersuchende Rotation liefert in der Regel einen Frequenzwert, welcher der breitesten Gruppe angehört und welcher deutlich hervortritt.

Whether to find the fundamental frequency of the rotation or to check plausibility, the following criteria can be used in an embodiment:

• - Harmonics that occur are at multiples of the fundamental frequency. Therefore, especially in the phase spectrum, the lowest frequency value found is an indication that it could be the fundamental frequency of the rotation.
• - Furthermore, it is also to be expected that, in addition to the fundamental frequency of the rotation, further harmonics can be found, ie one can also search for the lowest frequency value for which further harmonics occur.
• - It is often known in which frequency range the rotational frequency of a machine is to be expected, ie it can be checked whether the frequency value is actually below a specified limit frequency.
• - The rotation to be examined usually provides a frequency value which belongs to the broadest group and which stands out clearly.

For drives, from vehicle drives to motor spindle drives in machine tools, but also for other speed measurements, the requirements for the measurements go beyond the actual recording of the speed. The basic rotational movement is often superimposed by unbalance. To a certain extent, unbalance can hardly be avoided. However, they can also occur due to errors, such as bearing damage. In machine tools, the tools (e.g. milling cutters, drills, but also workpieces, such as on a lathe) are clamped and replaced if necessary. Errors can arise, especially during manual changing, e.g. if the tool is clamped in the tool holder with positioning errors. Such an error, which creates an unbalance during rotation, can occur, for example, if the tool The chuck is then subjected to one or more vibrations. This not only places stress on the drives, the drive motors, and the bearings, but also impairs the quality of the rotary motion. Artifacts are particularly undesirable on machine tools, whose production results depend heavily on the axial runout of the machine.

In applications like this, it can be advantageous to have real-time monitoring available so that deviations can be detected immediately during the machining process. If necessary, immediate action can then be taken and readjusted. Serious deviations or the detection of major imbalances can require immediate action: If bearing damage occurs, the machining process may have to be interrupted so that repairs can be carried out. If the rotation of the tool or workpiece becomes majorly unbalanced, it may be necessary to re-clamp it or clean the chuck because chips or similar items are causing the tool or workpiece to be mounted at an angle or with an offset. For smaller deviations, it may only be necessary to make a position correction via the machine control system.

However, such deviations often occur gradually and become increasingly more pronounced. It is therefore possible to use the data to detect a recurring occurrence, extrapolate the abnormal behavior, and schedule maintenance and repairs once a certain, predefined threshold is reached to prevent damage.

For this reason, it may also be advantageous to provide a memory in which the data can be stored. In this embodiment, evaluation can then also be performed at a later time.

In a further development of the invention, a DFT (Discrete Fourier Transformation) can advantageously be used to transform a time-discrete oscillation time signal. In one embodiment, this can be efficiently calculated using an FFT (Fast Fourier Transformation).

To make the evaluation faster and more efficient, a certain noise level can be considered in advance. Frequency values that lie within this specified noise level can thus be ignored and filtered out from the outset when determining the speed.

As already mentioned, the resolution of the DFT depends on the length of the acquisition time window. To further increase the resolution, the computation unit can add additional values with a magnitude of zero to increase the number of values, i.e., apply a zero-padding method.

Furthermore, the above-mentioned advantages can be achieved with a measuring device according to the invention.

Depending on the design, the vibration sensor can be designed as a two- or three-axis sensor. Typically, the vibration component is measured perpendicular or radial to the rotation axis. However, with large imbalances, vibration components can also occur along the actual rotation axis. A three-axis sensor can therefore be used to improve detection.

Overall, a particularly significant advantage of the invention is that a sensor with an integrated computing unit can be provided as the measuring device, e.g., in a common housing. Due to the evaluation of the phase spectrum, possibly taking the amplitude spectrum into account, no parameterization of the sensor is required. The sensor can be mounted as a compact component on the housing of essentially any machine to be tested and still provide measurements of any resulting imbalances. This enables significant time and cost savings during use.

Examples of implementation

• 1: eine schematische Darstellung eines Motors mit einer Messvorrichtung gem. der Erfindung,
• 2: eine beispielhafte Darstellung von Amplitudenspektrum, Phasenspektrum und Differenzphasenspektrum,
• 3: eine Darstellung der Konstanz der Phasenunterschiede im Schwingungszeitsignal,
• 4: eine beispielhafte Darstellung der drei Spektren aus 2, bei denen durch Filterung die Linien herausgestellt wurden,
• 5: eine schematische Darstellung des Einflusses der Fensterfunktion auf die Phase, sowie
• 6: eine schematische Ablaufdarstellung des Verfahrens gem. der Erfindung.

Embodiments of the invention are illustrated in the drawings and are explained in more detail below, including further details and advantages. In detail:

• 1 : a schematic representation of an engine with a measuring device according to the invention,
• 2 : an exemplary representation of amplitude spectrum, phase spectrum and difference phase spectrum,
• 3 : a representation of the constancy of the phase differences in the oscillation time signal,
• 4 : an exemplary representation of the three spectra from 2 , where the lines were highlighted by filtering,
• 5 : a schematic representation of the influence of the window function on the phase, as well as
• 6 : a schematic flow diagram of the method according to the invention.

1 shows a typical measurement setup with a motor M whose rotor R has an unbalance IB. There are various ways of measuring the speed. For example, the rotor R can have a measuring embodiment in the form of a key phasor K. During rotation, a rotary encoder RPT measures the speed n, for example inductively or capacitively, because whenever the measuring embodiment / key phasor K passes the point at which the rotary encoder sensor RPT is located, the latter receives a signal and can therefore count the number of rotations. In addition, a further sensor S for recording an oscillation time signal, which is designed as a three-axis acceleration sensor S, is provided via a mounting adapter A. The rotary encoder RPT can be used as a reference for calibrating the acceleration sensor S. The oscillation time signals TWF are evaluated by a computing unit C, which is connected to the motor controller MC. For this purpose, the computing unit C also uses the sample rate SR, which is known for the corresponding acceleration sensor S. From these discrete measured values, the computing unit C calculates the fast Fourier transform FFT.

From the Fourier transformation FFT one obtains an amplitude spectrum AS and a phase spectrum PS (cf. 2 , left figure and middle figure). From the phase spectrum PS, a difference phase spectrum DPS can be calculated by subtracting the phases or by time derivative (right figure in 2 ) can be obtained. In all three spectra displays AS, PS, DPS a line can be seen in the time course at a frequency in the range of 100 Hz. Above all in the amplitude spectrum AS, but also in the phase and difference phase spectrum PS, DPS additional lines can be seen at 300 Hz, 400 Hz and 500 Hz. In addition a line is also visible in the difference phase spectrum at 50 Hz, so that this is also suitable for determining the fundamental frequency, even if it is only very weak. The lowest frequency in a group In the phase spectrum PS a line of almost constant phase (within a certain tolerance range) can be seen in the time course at 50 Hz. This line is particularly clear in the difference phase spectrum DPS because the lines are more clearly visible due to the difference formation or derivative, especially if the visibility of the lines is increased by, for example, filtering the difference spectrum again and setting all phase differences up to a certain amount to zero. Overall, however, the line at 100 Hz is significantly broader than the other lines, so it is at least evident that this line is related to the main rotation. However, according to the differential phase spectrum, the fundamental frequency appears to be 50 Hz.

The width of the line at 100 Hz alone provides an indication that there is a connection with the main rotation; however, it can also be an indication that this is the actual fundamental frequency. Furthermore, the higher-frequency lines, which are narrower or weaker as a computational artifact, are located at multiples of the fundamental frequency. Often, a frequency range is also known in which the rotational speed should be found. Connected spectral line ranges can be grouped by the processing unit; with the help of advanced algorithms (e.g., spline interpolation), the exact frequency can be determined.

In 3 Again, it is illustrated that the phase differences remain constant. Here, several Fourier transformations (fast Fourier transformations) FFT1 - FFT4 of the oscillation time signal TWF are carried out in temporal sequence over the same time periods T. The calculated absolute function values of the phase spectrum depend, as can be seen from 3 As is clear, this also depends on how phase-shifted the signal sections of FFT1-FFT4 are. However, the phase differences are constant, or the second derivative ideally results in zero. However, this requires that the machine under investigation runs at a constant speed and the time period T remains constant. At least three FFTs should be performed to obtain at least two difference values. With the second derivative, particular attention must be paid to the 360° phase jump.

If the phase is constant for the spectral line range, then this can be associated with a constant or synchronous frequency.

The speed can generally be detected even with low unbalance IB, as long as the amplitude is significant enough and leads to an approximately stable phase.
4 shows a spectrum representation in which the lines are more clearly visible due to filtering, by equating the differences up to a certain threshold. This also demonstrates the advantages of the phase spectrum PS, because the lines, in this case the harmonics at 300 Hz and 400 Hz, are more prominent than in the amplitude spectrum AS.

Mathematically, the harmonics arise by applying the FFT to a temporally limited sampled oscillation time signal TWF. For a theoretically infinitely long signal nal, these secondary maxima would be eliminated, while the time limitation would add multiples of the fundamental frequency. To attenuate these secondary maxima compared to the main maximum HMax, a window function W (left figure in 5 ) can be applied. The main maximum HMax can thus be spectrally broadened, which leads to a more rapid decay of the secondary maxima NMax. The ratio of the amplitude of the main maximum HMax to the secondary maxima NMax is thus increased, i.e. the dynamic range is increased and the leakage effect is weakened. At the same time, the frequency selectivity is also reduced. Window functions with a wide main maximum HMax are therefore referred to as non-selective, dynamic windows, and those with a narrow main maximum HMax are referred to as selective, non-dynamic windows. The width of the main maximum HMax is usually specified as the 3 dB cut-off frequency, i.e. at this frequency the amplitude of the main maximum HMax drops by 3 dB.

• - Sensorisch wird zunächst ein Schwingungszeitsignal TWF detektiert.
• - Dieses Signal TWF kann zunächst einer Plausibilitätsprüfung (sanity check) unterzogen werden, d.h. es wird geprüft, ob es sich um ein hinreichend stabiles Signal handelt und die Drehzahl als annähernd konstant angesehen werden kann.
• - Die Fourier-Transformation FFT, die auf das Schwingungszeitsignal angewandt wird, liefert ein Phasenspektrum (FFT Phase) und ein Amplitudenspektrum (FFT Amplitude).
• - Das Amplitudenspektrum AS muss nicht direkt ausgewertet werden, kann aber zu einer weiteren Plausibilitätsprüfung herangezogen werden, z.B. Stabilitätsprüfung, aber auch, ob/welche Linien im Amplitudenspektrum vorhanden sind. Ist eine Linie sichtbar, die der Grundfrequenz entsprechend könnte?
• - Das Phasenspektrum (PS) kann, wenn es sich z.B. um einen mehrachsigen Sensor handelt, uniaxial oder unter Berücksichtigung einer Cross-Phasen-Beziehung, untersucht werden. Z.B. kann eine Unwucht eine Rotation in Richtung einer der senkrechten Achsen, die senkrecht zur eigentlichen Drehachse verlaufen, bewirken. Weitere Parameter sind die Auswahl des Frequenzbereichs, die Anzahl der FFT (mind. 3), die Frequenzauflösung und Überlappungen im Zeitbereich.
• - Im nächsten Hauptschritt wird geprüft, ob annähernd konstante Phasenbeziehungen bei bestimmten Frequenzen vorliegen. Die Phasendifferenzen müssen oder können aus experimentellen Gründen nicht unbedingt exakt null ergeben, aber kleiner als ein bestimmter Schwellwert sein. Zur besseren Erkennung von Linien das Spektrum entsprechend gefiltert werden, also allen Werten unter einem gewissen Schwellwert wird der gleiche Wert (Null) zugeordnet.
• - Je nach Ergebnis, welche Linien gefunden werden, können einzelne Bereiche gruppiert werden, wobei die Anzahl an Linien in einer Gruppe darauf schließen lässt, ob sich daraus eine wichtige Frequenz, etwa die gesuchte Drehfrequenz gegebenenfalls herausfinden lässt.
• - In der Regel sind dann weitere Logikschritte notwendig, um die eigentliche Frequenz (z.B. die Drehzahl) herauszufinden. Zwei grundsätzliche Ansätze sind:
  • o Das Cepstrum, mit dem periodische Strukturen im Frequenzspektrum analysiert werden können. Die Drehzahl sollte im Allgemeinen als prominente Linie erscheinen, zu der weitere Harmonische sichtbar sind.
  • o und/oder: eine Drehzahl-Selektor-Logik, die mit Indizien arbeitet, welches die gesuchte Frequenz sein könnte, etwa:
    • ▪ die kleinste Frequenz, bei der es sich somit wahrscheinlich nicht um eine Harmonische handelt,
    • ▪ die Auswahl einer Frequenz aus der breitesten Gruppe
    • ▪ die Vorauswahl einer Frequenz mit maximaler Amplitude

An overall overview is in 6 shown:

• - First, a vibration time signal TWF is detected by the sensor.
• - This signal TWF can first be subjected to a plausibility check (sanity check), ie it is checked whether it is a sufficiently stable signal and whether the speed can be regarded as approximately constant.
• - The Fourier transform FFT, which is applied to the oscillation time signal, provides a phase spectrum (FFT Phase) and an amplitude spectrum (FFT Amplitude).
• - The amplitude spectrum AS does not need to be evaluated directly, but can be used for further plausibility checks, e.g., stability checks, but also to determine whether/which lines are present in the amplitude spectrum. Is a line visible that could correspond to the fundamental frequency?
• - The phase spectrum (PS) can be analyzed uniaxially or considering a cross-phase relationship, for example, if the sensor is multi-axis. For example, an imbalance can cause rotation in the direction of one of the vertical axes that run perpendicular to the actual axis of rotation. Other parameters include the selection of the frequency range, the number of FFTs (at least 3), the frequency resolution, and overlaps in the time domain.
• - The next main step is to check whether approximately constant phase relationships exist at certain frequencies. For experimental reasons, the phase differences may or may not necessarily be exactly zero, but they can be smaller than a certain threshold. To better detect lines, the spectrum is filtered accordingly, so all values below a certain threshold are assigned the same value (zero).
• - Depending on the result of which lines are found, individual areas can be grouped, whereby the number of lines in a group can be used to determine whether an important frequency, such as the rotational frequency being sought, can be found out.
• - Typically, further logic steps are then necessary to determine the actual frequency (e.g., the rotational speed). Two basic approaches are:
  • o The cepstrum, which can be used to analyze periodic structures in the frequency spectrum. The rotational speed should generally appear as a prominent line, with additional harmonics visible.
  • o and/or: a speed selector logic that works with clues as to what the desired frequency could be, for example:
    • ▪ the smallest frequency, which is therefore probably not a harmonic,
    • ▪ selecting a frequency from the widest group
    • ▪ the preselection of a frequency with maximum amplitude

Cepstrum and speed selector logic can be used alternatively or side by side and later combined via data fusion. A stability algorithm provides a reliable result for the desired speed.

What all embodiments and developments of the invention have in common is that the use of the phase spectrum enables parameter-free speed determination.

List of reference symbols

A

Mounting adapter

AS

Amplitude spectrum

C

Computing unit

DPS

Difference phase spectrum

FFT

Fast Fourier transform

HMax

Main maxima

NMax

Secondary maxima

IB

Imbalance

K

Keyphasor / Measuring scale

M

Motor

MC

Machine control

N

speed

PS

Phase spectrum

R

rotor

RPT

rotary encoder

S

3-axis acceleration sensor

SR

Sample rate

T

Time span

W

Window function (window)

φ1, ..., φ4

Phases

QUOTES CONTAINED IN THE DESCRIPTION

This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• EP 3 581 328 B1 [0002]

Cited non-patent literature

• www.coursera.org/lecture/audio-signalprocessing/f0-detection-tx630 [0022]

Claims (16)

Method for determining a rotational speed (n), preferably a rotational speed that remains constant or does not change highly dynamically, comprising: a. recording an oscillation time signal (TWF) by a oscillation sensor (S), in particular for radial oscillations with respect to the axis of rotation, b. providing the sample rate (SR) during the recording, c. calculating a Fourier transform (FFT) of the oscillation time signal (S) using the sample rate (SR) by a computing unit (C), d. determining the phase spectrum (PS) using the Fourier transform (FFT), e. calculating at least three chronologically successive Fourier transforms (FFT1, FFT2, FFT3, FFT4) and f. determining the difference between the phase values (DPS) as phase difference values Δφ _i+1,i (v _k ) =φ _i+1 (v _k ) -φ _i (v _k ) g. Determination of the changes in the phase difference values Δφ _i+1,i for individual frequency values v _k h. Determination of the frequency value(s) v _k for which the fluctuation of the phase difference values Δφ _i+1,i over time does not exceed a predetermined threshold value and/or is constant, and i. Output of a value for the speed (n) to be determined, wherein in particular the speed (n) is a frequency value from the set of determined frequency values. Procedure according to Claim 1 , characterized in that the computing unit (C) groups areas with certain frequency values. Method according to one of the preceding claims, characterized in that at least one harmonic to the determined frequency values is determined by the computing unit (C), wherein in particular the cepstrum is determined for determining the harmonic. Method according to one of the preceding claims, characterized in that the speed (n) is determined by the computing unit (C) according to at least one of the following criteria from the set of determined frequency values: a. lowest frequency value and/or b. lowest frequency value for which at least one further frequency value was determined which is a multiple of this frequency value in order to filter out the harmonics, and/or c. frequency value lies below a predetermined cut-off frequency and/or d. frequency value can be assigned to a maximum amplitude and/or e. the frequency value belongs to the broadest group. Method according to one of the preceding claims, characterized in that the calculation by the computing unit (C): a. is carried out during the recording by the vibration sensor (S) and/or b. is carried out on the basis of data stored in a memory, wherein the memory is provided for recording the vibration time signal (TWF) recorded by the vibration sensor and in particular the sample rate (SR). Method according to one of the preceding claims, characterized in that an FFT and/or a DFT is calculated as the Fourier transformation by the computing unit (C). Method according to one of the preceding claims, characterized in that the amplitude spectrum is determined using the Fourier transformation (FFT) and it is checked whether the amplitudes from the amplitude spectrum are constant at the determined frequency values within a confidence interval, the associated frequency values only being taken into account if their amplitudes are constant within the confidence interval. Method according to one of the preceding claims, characterized in that the frequency resolution is increased by the computing unit using a zero-padding method. Method according to one of the preceding claims, characterized in that the computing unit (C) applies a window function (W) to the oscillation time signal (TWF) to avoid leakage effects. Method according to one of the preceding claims, characterized in that the third derivative is formed from the phase spectrum (PS) by the computing unit (C) in order to determine the difference frequency at rotational speeds (n) which are close to one another. A measuring device for determining a rotational speed (n), comprising a vibration sensor (S) for recording a vibration time signal (TWF) and for providing the sample rate (SR) during recording, and a computing unit (C) for calculating a Fourier transformation (FFT) of the vibration time signal (TWF) using the sample rate (SR) and outputting the phase spectrum (PS), wherein the computing unit (C) is designed to: a. to calculate at least three temporally successive Fourier transforms (FFT1, FFT2, FFT3, FFT4) and b. to determine the fluctuation and/or difference (DPS) of the phase values, c. to determine the frequency value(s) at which the fluctuation and/or difference of the phase values from the phase spectra does not exceed a predetermined threshold value or is constant over time, and d. to output a value for the rotational speed (n) to be determined, wherein in particular the rotational speed (n) is a frequency value from the set of determined frequency values. Measuring device according to Claim 11 , characterized in that the measuring device and/or the computing unit (C) for carrying out the method according to one of the Claims 1 - 10 is trained. Measuring device according to one of the Claims 11 or 12 , characterized in that the vibration sensor is designed to record the vibration time signal in at least two, in particular three directions, wherein particularly preferably the directions are perpendicular to one another, wherein in particular one of the directions is parallel to the axis of rotation, wherein preferably the vibration sensor (S) is arranged such that it can measure at least radial vibrations with respect to the axis of rotation. Measuring device according to Claim 13 , characterized in that instead of evaluating the formed uniaxial Fourier transform (FFT), the cross (phase) spectrum is evaluated. Measuring device according to one of the Claims 11 until 14 , characterized in that from the phase spectrum (PS) certain speeds (n) are additionally selected with information and ratios from the amplitude spectrum Measuring device according to one of the Claims 11 until 15 , characterized in that the measuring device is designed as a sensor (S) with an integrated computing unit (C), wherein in particular the sensor (S) and computing unit (C) are arranged in a common housing.

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