DE102010063812B4 - Method for balancing a shaft for a rotating machine, in particular for a turbocharger - Google Patents

Abstract

Method for balancing a shaft (1) for a rotating machine, in which the shaft is supported by a number of bearings, in which: a) the shaft (1) is rotated in the installed state in the machine and at least one measuring point (M1 , M2) the deflection (ux, 1, uy, 1, ux, 2, uy, 2) of the shaft (1) in the radial direction during rotation is measured; b) from the measured deflection (ux, 1, uy, 1, ux, 2, uy, 2) one or more unbalance parameters (A1, A2) for characterizing the imbalance of the shaft (1) and from this one or more compensation parameters to compensate for Imbalance can be determined; c) the shaft (1) is balanced in the installed state based on the or the compensation parameters; wherein the shaft (1) is rotated at one or more rotational speeds in at least one speed range in which the first or a higher bending mode of a bending vibration of the shaft (1) occurs, and for this bending mode of the unbalance parameter (A1, A2) and the or the compensation parameters are determined, whereby a rotor-dynamic simulation model of the shaft (1) is adapted to the determined unbalance parameter (s) (A1, A2) and the compensating parameter (s) are derived from the adapted rotor-dynamic simulation model, wherein the amplitude values (A1, A2 ) of the deflections (ux, 1, uy, 1, ux, 2, uy, 2) of the shaft (1) at the at least one measuring point (M1, M2) for a plurality of rotational speeds in the at least one rotational speed range are determined and to this Amplitude values (A1, A2) is fitted a predetermined resonance curve, which is then used to adapt the rotordynamischen simulation model, wherein in the fitting of the Res onanzkurve the resonance frequency is determined as a parameter of the resonance curve.

Description

The invention relates to a method and a device for balancing a shaft for a rotating machine, in particular for a turbocharger.

Various concepts are known from the prior art, such as waves can be stored properly in rotating machines. For fast rotating machines, such as B. turbocharger, z. B. active magnetic bearings are used, via which the shaft is supported by magnetic force without touching the surrounding mechanical structures.

Of crucial importance for the safe functioning of a shaft in a rotating machine is its precise and careful balancing. In the publication DE 10 2008 034 342 A1 a method for balancing a magnetically mounted shaft in an exhaust gas turbocharger is described, wherein in the installed state of the shaft, the imbalance is determined based on the determination of the position or deflection of the shaft via the magnetic bearing. Subsequently, the balance of the shaft takes place via a removal or application of material, for which purpose the shaft may not have to be removed from the exhaust gas turbocharger.

With the method of the publication DE 10 2008 034 342 A1 can be reduced by wobbling caused by imbalance of a wave. However, this method does not take into account imbalances that occur during operation of the rotating machine with supercritical speeds. At such speeds, the rotor shaft can no longer be regarded as a rigid body, but there are bending vibrations. In this case, a first bending mode and possibly also higher bending modes of vibrations is excited. This results in further unbalance effects that do not occur in the subcritical rotational speed range of the rotor shaft.

The publication DE 41 33 787 A1 discloses a balancing method for determining the balancing weights of elastic rotors on dynamometric balancing machines. Among other things, unbalance measured values for a rotor speed in the range of the resonant frequency of a modal imbalance are determined and from this compensation parameters are determined.

In the document R. Gasch, J. Drechsler: "Modal Balancing elastic runners without test weight settlements", in: VDI reports, No. 320, 1978, pages 45 to 54, ISSN 0083-5560, is the modal balancing elastic runners without test weightings described in which a mathematical evaluation of the imbalance measured modal imbalances are determined. In this method, no determination of the resonance frequency takes place.

The object of the invention is to balance the shaft in a rotating machine so that imbalances are compensated for supercritical rotational speeds of the shaft with improved accuracy.

This object is achieved by the method according to claim 1 and the device according to claim 7. Further developments of the invention are defined in the dependent claims.

The method according to the invention serves to balance a shaft for a rotating machine, wherein the rotating machine is in particular a turbocharger and particularly preferably an exhaust-gas turbocharger which is used, for example, in motor vehicles. The shaft is stored over a number of bearings in the rotating machine. According to the invention, in a step a) the shaft is rotated in the installed state in the machine, during which rotation the deflection of the shaft in the radial direction is measured at at least one measuring point and preferably at two measuring points. From this measured deflection, one or more imbalance parameters for characterizing the unbalance of the shaft and, therefrom, one or more compensation parameters for compensating the imbalance are then determined in a step b). Finally, the shaft is balanced in the installed state based on the or the compensation parameters. The inventive method is characterized in that the shaft is rotated in step a) with one or more speeds in at least one speed range in which the first or a higher bending mode of a bending vibration of the shaft occurs, for this bending mode of the imbalance or the parameters the compensation parameter or parameters are determined.

In the method according to the invention, the determination of the compensation parameters takes place in such a way that a rotordynamic simulation model of the shaft is adapted to the determined imbalance parameter (s) and the compensating parameter (s) are derived from the adapted rotor dynamic simulation model. The description of the dynamics of a wave via rotordynamic simulation models is in itself known in the art. According to the wave to be balanced is first described with such a simulation model, but this model is not yet adapted to the actual imbalances of the wave. These imbalances are thus represented by free parameters in the model. These free parameters are adapted to the determined imbalance parameters, whereupon corresponding compensating parameters for compensating the imbalance can be determined with the adapted rotor dynamic simulation model. The determination of corresponding compensation parameters using a rotor dynamic simulation model, in particular in the form of a material application or removal at suitable locations in the radial or axial direction of the shaft, is known per se to the person skilled in the art.

According to the invention, the amplitude values of the deflections of the shaft at the at least one measuring point for a plurality of rotational speeds in the at least one rotational speed range are determined as unbalance parameters, wherein a predetermined resonance curve is fitted to these amplitude values, which is then used to adapt the rotor dynamic simulation model. One makes use of the fact that the shape of a resonance curve in supercritical operation with excitation of the first or higher bending modes is known. It should be noted that for each bending mode resonance occurs at a corresponding resonance frequency, which is also referred to as supercritical resonance frequency. In the context of the invention, the imbalance parameters are preferably determined in a speed range below the resonance frequency of the corresponding bending mode. In the detailed description, a concrete embodiment will be explained how to fit a resonance curve based on detected amplitude values.

The invention is based on the finding that a classical balancing of a shaft for speeds at which the shaft represents a rigid body is no longer sufficient for machines that rotate rapidly. In this case, it is necessary that the occurring at high speeds unbalances, which are caused by bending oscillations of the shaft, are compensated suitable.

In a particularly preferred embodiment of the method according to the invention, a shaft is balanced, which is mounted in the machine via one or more active magnetic bearings, wherein the magnetic force of a respective active magnetic bearing is controlled based on a measurement of the deflection of the shaft in the magnetic bearing. In this case, this measurement of the deflection is also used to determine the unbalance parameters of the shaft. Thus, according to this embodiment, it is not necessary to separately mount measuring devices on the shaft to determine unbalance parameters. Rather, the already provided in the context of storage of the shaft measuring means can be used to determine the imbalance.

The magnetic bearings described above can be sensorless magnetic bearings which detect the deflection of the shaft in the magnetic bearing without separate sensors. This detection takes place z. B. via an inductance measurement with the help of or the magnetic force generating electromagnet of the camp. Optionally, however, there is also the possibility that one or more of the magnetic bearings comprise one or more separate sensors for measuring the deflection of the magnetic bearing. Such sensors can, for. B. optical sensors, capacitive sensors or eddy current sensors.

In a particularly preferred embodiment, the balance of the shaft in step c) takes place during the rotation of the removal of material, for. B. by laser and / or spark erosion. In this way, a fast balance in the installed state of the shaft can be achieved. Optionally, however, there is also the possibility that the rotation of the shaft is stopped in step c) and then carried out by drilling the shaft and / or the attachment of Balastgewichten the balance of the shaft.

In a further embodiment of the method according to the invention, imbalances in the subcritical operation of the shaft are also compensated. In this case, the shaft is further rotated at a speed in a speed range in which no bending vibrations of the shaft occur, for which speed the static and / or dynamic imbalance is determined and is then compensated in the context of balancing in a conventional manner.

In addition to the method described above, the invention further relates to a device for balancing a shaft for a rotating machine, in particular for a turbocharger, in which the shaft is mounted over a number of bearings. The device comprises a rotation and measuring device for rotating the shaft in the installed state in the machine and for measuring the deflection of the shaft in the radial direction at at least one measuring point during rotation. Furthermore, a calculation device is provided with which one or more unbalance parameters for characterizing the imbalance of the shaft and from this one or more compensation parameters for compensating for the unbalance are determined from the measured deflection. The device further includes a balancing device with which the shaft is balanced in the installed state based on the or the compensation parameters.

The device according to the invention is characterized in that it rotates the shaft with one or more rotational speeds in at least one rotational speed range in which the first or a higher bending mode a bending vibration of the shaft occurs, for this bending mode of the imbalance or the parameters and the one or more parameters to compensate for the unbalance, wherein a rotordynamischen simulation model of the wave is adapted to the one or more unbalance parameters and from the adapted rotor dynamic simulation model or the compensation parameters are derived as unbalance parameters, the amplitude values of the deflections of the wave at the at least one measuring point for a Variety of speeds in the at least one speed range are determined and to these amplitude values a predetermined resonance curve is fitted, which is then used to adapt the rotor dynamic simulation model. The device is preferably designed such that one or more of the above-described preferred variants of the method according to the invention can be carried out with the device. In particular, the measuring device of the device by itself in the rotating machine components, d. H. by position sensors in magnetic bearings or sensorless magnetic bearings formed.

Embodiments of the invention are described below with reference to the attached 1 and 2 described in detail.

Show it:

1 a schematic representation of a sensorless magnetic bearing mounted shaft of a turbocharger to explain a variant of the balancing invention; and

2 a schematic representation, which is based on the wave of 1 illustrates the occurring at higher speeds first bending mode of a bending vibration.

The following is based on the in 1 shown wave 1 an embodiment of the balancing invention described. The wave 1 is part of a turbocharger, not shown, wherein at the ends of the shaft, a turbine wheel 101 or a compressor wheel 102 of the loader are attached. The shaft comprises a flange in its central area 103 to which a schematically indicated magnetic bearing 4 is provided, with which the shaft is mounted in the axial direction. Further, on the shaft, two magnetic bearings also shown schematically 2 and 3 arranged, with which the shaft is mounted in the radial direction. These magnetic bearings are sensorless magnetic bearings which, without further external sensors, suitably support the shaft via a corresponding current supply by electromagnets. In this case, the deflection of the shaft is determined by means of an inductance measurement with the aid of the electromagnets and, based thereon, the magnetic field of the electromagnets is suitably regulated, so that the shaft is held in position in the radial direction. It may also be possible, instead of or in addition to sensorless magnetic bearings, to use other types of magnetic bearings with position sensors integrated therein, which separately measure the position of the shaft.

In the embodiment of the 1 the position of the shaft in the radial direction is determined at the measuring points M1 and M2. For the measuring position M1, the deflection components u _{x, 1} and u _{y, 1} and for the measuring position M1, the deflection components u _{x, 2} and u _{y, 2 are} determined. The x-axis is the axis running into the leaf plane and the y-axis is the axis that is perpendicular to the x-axis. The z-axis corresponds to the axial direction of the shaft. The positions of the shaft at the individual measuring points can be determined as described above either via the sensorless magnetic bearings or optionally via additional position sensors.

An essential aspect of the invention is the balance of the shaft in a speed range in which bending vibrations of the shaft occur. In addition, however, it is also possible to determine corresponding imbalance parameters in lower rpm ranges and also to carry out a balancing in these rpm ranges. First, such balancing will be explained in lower speed ranges.

From the above position values u _{x, 1} (t), u _{x, 2} (t), u _{y, 1} (t) and u _{y, 2} (t), which during the rotation of the shaft at low speed and thus low angular frequency w can be determined, the following time-dependent complex variable can be determined for each of the measurement positions i (i = 1, 2): z _i (t) = u _{x, i} (t) + j · u _{y, i} (t) (1).

This quantity z _i (t) is measured over a period t = 0,..., T, where T corresponds to the period of the angular frequency ω according to the rotational speed. From the size, the following displacement signal W _i can be determined:

If, instead of the period T integrated over a multiple of this period, W _i delivers a signal of high quality. It is important that the circle sequence ω is known precisely. This can, for. B. be determined by optical measurements on prominent structures of the shaft (eg., Co-rotating parts).

Based on the above deflection signal W _i , a static unbalance parameter S and a dynamic unbalance parameter D can now be determined in a manner known per se as follows: S = 1/2 · (W ₁ + W ₂ ), (3) D = 1/2 · (W ₁ - W ₂ ) (4).

bestimmt werden Dabei bezeichnet

den Realteil und

den Imaginärteil der statischen Unwucht. Analog kann der Betrag der dynamischen Unwucht (in Kilogramm pro Quadratmeter) als m·b·|D| und die Position der dynamischen Unwucht als Orientierungswinkel Φ(D) bestimmt werden. Mit Hilfe der Orientierungswinkel Φ(S) bzw. Φ(D) der statischen und dynamischen Unwucht kann dann in an sich bekannter Weise eine Wuchtung der Welle erfolgen. In einer bevorzugten Ausführungsform wird die Wuchtung während der Rotation der Welle durch Materialabtrag (z. B. mittels eines Lasers oder Funkenerosion) erreicht. Gegebenenfalls besteht auch die Möglichkeit, dass die Rotation der Welle gestoppt wird und anschließend zum Ausgleich der Unwucht an geeigneten Positionen Bohrlöcher vorgesehen werden. Eine entsprechende Berechnung, an welcher Stelle in Abhängigkeit der ermittelten Unwuchtungen Material abzutragen ist bzw. Bohrlöcher vorzusehen sind, ist dabei an sich bekannt bzw. liegt im Rahmen von fachmännischem Handeln.With the aid of the known mass m of the rotor and the known distance b between the measuring points M1 and M2, the magnitude of the static unbalance (in kilograms per meter) as m | IS | and the position of the static imbalance as an angle value

to be determined

the real part and

the imaginary part of the static imbalance. Similarly, the amount of dynamic unbalance (in kilograms per square meter) can be expressed as m · b · | D | and the position of the dynamic imbalance can be determined as the orientation angle Φ (D). With the aid of the orientation angle Φ (S) or Φ (D) of the static and dynamic imbalance, a balancing of the shaft can then take place in a manner known per se. In a preferred embodiment, the balance is achieved during the rotation of the shaft by material removal (eg by means of a laser or spark erosion). Optionally, there is also the possibility that the rotation of the shaft is stopped and then provided to compensate for the imbalance at appropriate positions drilled holes. A corresponding calculation, at which point material is to be removed depending on the determined imbalances or boreholes are to be provided, is known per se or is within the scope of expert action.

The above-described balancing in a low speed range, in which the shaft is essentially a rigid body, is no longer sufficient in the so-called supercritical operation of the shaft, in which the shaft is excited to flexural vibrations. In supercritical operation, the excitation of the first bending mode and possibly higher bending modes is extremely problematic and can lead to undesirable large deflections of the shaft at a balancing, which does not take into account these bending modes, which may cause damage to the turbocharger under certain circumstances.

A variant of a balancing according to the invention is described below, with which the imbalance generated when the first bending mode occurs is compensated. For better understanding is in 2 schematically shows the amplitude curve of the deflection of the shaft for the first bending mode along the axis of rotation of the shaft. The amplitude is denoted by A and the axial position along the shaft with z, wherein the shaft 1 again at the top of the 2 is reproduced and also the corresponding measurement positions M1 and M2 are indicated on the shaft. The amplitude curve A (z) of the first bending mode comprises two oscillation nodes N1 and N2 with a deflection of 0, whose position on the shaft is indicated by the arrows P1 and P2. Usually, the positions P1 and P2 correspond to the locations of the bearing of the shaft. When using an active magnetic bearing, however, these vibration nodes are not located exactly at the location of the bearing, so that the corresponding amplitude values can be detected by means of the magnetic bearings. According to 2 occur at the measuring positions M1 and M2, the amplitude values A1 and A2.

When the first bending mode occurs, the shaft is 1 no longer to be regarded as a rigid body. Rather, the shaft comprises three oscillating sections, with a first section ranging from z = 0 to Vibration node N1, a second portion between vibration node M1 and vibration node N2, and a third portion extending from vibration node N2 to the end of the shaft. The individual sections are flexurally coupled to each other. Consequently, the simple static and dynamic balancing described above no longer has the desired effect, since it can compensate for an imbalance only for a rigid body, but not for a mass distribution, as is the case in supercritical operation in the case of excited bending vibrations. Thus, to suppress the excitation of bending vibrations due to imbalance to such an extent that a stable operation of the rotor is also possible in the supercritical region, the method for balancing must be able to influence a possibly complex mass distribution. This is achieved by the embodiment of the invention described below, which allows a balancing of the shaft for the first bending mode.

In the context of the method according to the invention, it should be taken into account that for the first and also for higher bending modes a so-called supercritical frequency exists according to which the corresponding bending vibration is set in resonance. The first bending mode already occurs at frequencies below the resonance frequency. In an appropriately selected speed range of the shaft below the resonant frequency, but in which the bending mode of the first mode already occurs, in the embodiment described here, in analogy to the above-described determination of the static and dynamic unbalance, the deflection signals W _i (ω) and the corresponding Imbalances S (ω) and D (ω) determined. The course of the deflection signals as a function of the rotational speed and thus the angular velocity ω corresponds to the course of a resonance curve, which can be described by the following equation:

ω₀ bezeichnet dabei die Resonanzfrequenz. Im Falle, dass eine Welle mit moderater Dämpfung zum Einsatz kommt, wird die Auswertung im Rahmen der Durchführung der Wuchtung vereinfacht, da der Verlauf von A(ω) offensichtlich nicht von der individuellen Dämpfung der Welle abhängig ist.With moderate damping ξ, the curve below the resonance frequency can be simplified to a good approximation as follows:

ω ₀ denotes the resonant frequency. In the case where a wave with moderate damping is used, the evaluation is simplified in the implementation of the balance, since the course of A (ω) is obviously not dependent on the individual damping of the shaft.

Taylor's development further simplifies the course of A (ω) as follows:

A correction of the higher order terms not considered in the above formula provides an even more detailed description of the course of the resonance curve based on the following equation:

According to the invention, the values of the amplitude A ₀ or of the resonance frequency ω _{0 of} the above function (5) are now adapted to the correspondingly measured values of the deflection signals W _i (ω) or optionally S (ω) and Dω). For adaptation, the approximate functions according to equations (6), (7) or (8) can also be used with moderate attenuation. In this way one obtains for the measured W _i (ω), S (ω) and D (ω) the corresponding amplitude values W ₀ , S ₀ and D ₀ as well as the resonance frequency ω ₀ . These variables can be classified as imbalance parameters in the sense of the claims.

Based on these quantities, a rotordynamic simulation model can then be tuned so that its behavior coincides with the measured wave. Rotor dynamic simulation models for describing the dynamic behavior of rotating bodies are known per se from the prior art. An adaptation of such a model to the variables W ₀ , S ₀ , D ₀ and ω ₀ described above is within the scope of expert action and is therefore not described in detail. Based on the adapted simulation model, the dynamics of the considered rotor shaft can then be determined by means of a finite element calculation, from which the modal mass m, the modal rigidity k and the gyroscopic factor g and also the above, in 2 shown bending line A (z) of the first bending mode results. With this knowledge, those points or sections on the rotor shaft can then be determined, at which material for balancing in supercritical operation is to be removed or, if appropriate, to be attached.

In summary, according to the embodiment of the invention described above, the deflection amplitude of the shaft is determined as a function of the rotational speed in supercritical operation at two measuring points on the rotor shaft and from this with the aid of a rotor-dynamic simulation model corresponding compensating parameters for balancing are derived. The method is not limited to use for the first bending mode, but may optionally be used analogously for higher bending modes.

The inventive method has a number of advantages. In particular, a balance on the installed and functional rotor shaft is made possible. That is, the drive system can be fully assembled and then balanced in the assembled state. This has the consequence that the drive system can be made significantly cheaper than is the case with classical balancing technology, in which the balancing of the rotor shaft is done with a separate balancing machine. According to the embodiment described above, in which the turbocharger's high-speed rotation system is balanced at rotational speeds of up to 300,000 revolutions per minute, significant manufacturing costs can be saved because up to 30% of the turbocharger's manufacturing cost can be balanced.

If the method according to the invention is used in combination with a bearing of the rotor shaft via sensorless magnetic bearings, in addition no external sensors are required for determining the position of the shaft, since in this case the magnetic bearing simultaneously acts as a suspension and as a sensor. On the other hand, if active magnetic bearings using sensors are used for supporting the shaft, then these sensors can also be used for balancing. Thus, there is no need for temporary mounting of sensors specifically for balancing in the rotation system. In contrast to conventional methods, corresponding imbalances in the supercritical operation of the shaft at high rotational frequencies are compensated based on the invention. In addition, also the static and dynamic imbalance can be compensated.

Claims (8)

Method for balancing a shaft ( 1 ) for a rotating machine in which the shaft is supported by a number of bearings, in which: a) the shaft ( 1 ) is rotated in the installed state in the machine and at at least one measuring point (M1, M2) the deflection (u _{x, 1} , u _{y, 1} , u _{x, 2} , u _{y, 2} ) of the shaft ( 1 ) is measured in the radial direction during the rotation; b) from the measured deflection (u _{x, 1} , u _{y, 1} , u _{x, 2} , u _{y, 2} ) one or more unbalance parameters (A1, A2) for characterizing the imbalance of the wave ( 1 ) and from this one or more compensation parameters are determined to compensate for the imbalance; c) the wave ( 1 ) is balanced in the installed state based on the or the compensation parameters; where the wave ( 1 ) is rotated at one or more speeds in at least one speed range in which the first or a higher bending mode of a bending vibration of the shaft ( 1 ) and, for this bending mode, the imbalance parameter (s) (A1, A2) and the compensating parameter (s) are determined, whereby a rotor dynamic simulation model of the shaft ( 1 ) is adapted to the one or more unbalance parameters (A1, A2) and the compensating parameter (s) are derived from the adapted rotor dynamic simulation model, the amplitude values (A1, A2) of the deflections (u _{x, 1} , u _{y, 1} , u _{x, 2} , u _{y, 2} ) of the wave ( 1 ) are determined at the at least one measuring point (M1, M2) for a multiplicity of rotational speeds in the at least one rotational speed range and a predetermined resonance curve is fitted to these amplitude values (A1, A2), which is then used to adapt the rotor dynamic simulation model, wherein Fitting the resonance curve, the resonance frequency is determined as a parameter of the resonance curve. Method according to claim 1, characterized in that the shaft ( 1 ) via one or more active magnetic bearings ( 2 . 3 ) is stored in the machine, wherein the magnetic force of a respective active magnetic bearing ( 2 . 3 ) based on a measurement of the deflection of the shaft ( 1 ) in the magnetic bearing ( 2 . 3 ) and this measurement of the deflection is also used to determine the imbalance parameter (s) (A1, A2). Method according to claim 2, characterized in that one or more of the magnetic bearings ( 2 . 3 ) are sensorless magnetic bearings, which without separate sensors, the deflection of the shaft ( 1 ) in the magnetic bearing ( 2 . 3 ), and / or one or more of the magnetic bearings ( 2 . 3 ) one or more separate sensors for measuring the deflection of the shaft ( 1 ) in the magnetic bearing ( 2 . 3 ) Method according to one of the preceding claims, characterized in that the shaft ( 1 ) in step c) is balanced during the rotation via a removal of material. Method according to one of the preceding claims, characterized in that the rotation of the shaft ( 1 ) is stopped in step c) and then the balance of the shaft ( 1 ) about drilling the shaft ( 1 ) and / or the attachment of ballast weights to the shaft ( 1 ) he follows. Method according to one of the preceding claims, characterized in that the shaft ( 1 ) is further rotated at a speed in a speed range in which no bending vibrations of the shaft ( 1 ) occur, and for this speed, the static and / or dynamic imbalance is determined, which are compensated in the context of balancing. Device for balancing a shaft ( 1 ) for a rotating machine in which the shaft ( 1 ) over a number of warehouses ( 2 . 3 ), comprising: - a rotating and measuring device for rotating the shaft ( 1 ) in the installed state in the machine and for measuring the deflection (u _{x, 1} , u _{y, 1} , u _{x, 2} , u _{y, 2} ) of the shaft ( 1 ) in the radial direction at at least one measuring point (M1, M2) during the rotation; A calculation device with which from the measured deflection (u _{x, 1} , u _{y, 1} , u _{x, 2} , u _{y, 2} ) one or more unbalance parameters (A1, A2) for characterizing the imbalance of the shaft ( 1 ) and from this one or more compensation parameters are determined to compensate for the imbalance; - a balancing device with which the shaft ( 1 ) is balanced in the installed state based on the or the compensation parameters; the device being designed such that the shaft ( 1 ) is rotated at one or more speeds in at least one speed range in which the first or a higher bending mode of a bending vibration of the shaft ( 1 ), and for this bending mode the unbalance parameter (s) and the compensation parameter (s) are determined, wherein a rotor dynamic simulation model of the shaft ( 1 ) is adapted to the one or more unbalance parameters (A1, A2) and the compensating parameter (s) are derived from the adapted rotor dynamic simulation model, the amplitude values (A1, A2) of the deflections (u _{x, 1} , u _{y, 1} , u _{x, 2} , u _{y, 2} ) of the wave ( 1 ) are determined at the at least one measuring point (M1, M2) for a multiplicity of rotational speeds in the at least one rotational speed range and a predetermined resonance curve is fitted to these amplitude values (A1, A2), which is then used to adapt the rotor dynamic simulation model, wherein Fitting the resonance curve, the resonance frequency is determined as a parameter of the resonance curve. Apparatus according to claim 7, characterized in that the device is designed such that with the device, a method according to one of claims 2 to 6 is feasible.

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