DE102014100126A1 - Method for determining an imbalance of a rotor - Google Patents

Abstract

Method for determining an imbalance of a rotor (R) with known moment of inertia with a rotation axis unparallel to a gravitational field and / or a buoyancy field with the following steps: a) Definition of measurement points distributed over the circumference of the rotor (R) of u> 2 (Si, i = 1 ... u) and providing means for detecting the position of the measuring points (Si) as a function of the time t; b) rotating the rotor (R) and measuring the angle of rotation (φ) and the angular velocity (ω) of the rotor (1) at a non-fixed or incoupled drive torque and calculate the location-dependent angular acceleration (ω) as a function of the rotation angle (φ) in a range between two consecutive measuring points (Si-Si + 1, i = 1 ... u); c) transformation of the angular acceleration (ω) as a function of the angle of rotation (φ) in an image space; d) determining the complex amplitude (A1) as the intensity of the unbalanced angular acceleration in the image space of the transformed function; e) Evaluation of the complex amplitude (A1) for determining the angle (φu) of a static unbalance (m × r), where r is the distance of the imbalance mass (m) from the axis of rotation (D) of the rotor (R).

Description

The invention relates to a method for determining an imbalance of a rotor having the features of patent claim 1.

Rotatory movements can lead to unwanted speed-dependent suggestions in case of imbalance. All-round, unbalance-induced centrifugal forces can z. B. lead to premature bearing damage, failure of the suspension and bearing carrier, transmissions on neighboring machines and disturbing noises. Even the bending and failure of the rotor is possible.

An unbalance is composed of a static imbalance and a purely dynamic unbalance or moment unbalance. The present invention is concerned with the static imbalance of a rotor whose axis of rotation is arranged unparallel to a gravitational field or buoyancy field. The gravitational field is in particular the gravitational field of the earth. The rotor has an axis of rotation which is not parallel to this gravitational field, in particular perpendicular to the gravitational field. The axis of rotation is oriented in particular horizontally.

There are different methods for determining the balancing state of a rotor. Not all methods can be applied in situ with reasonable effort, but often only with a special bearing of the rotor on a balancing bench. Large rotors, which can not be brought to a balancing bank with reasonable effort or for which no drive is available, can only be balanced in-situ. The same applies to runners of turbomachines (aircraft engines, fans, etc.), in which the drive power of the balancing bank is sufficient only in an evacuated environment to bring the runners to a suitable speed.

In contrast to the balancing bank, the direct measurement of the forces caused by the imbalance on site is generally not possible, which is why the forces are determined in the conventional balancing operation via the vibrations measured on site. From the oscillation amplitude and the phase angle relative to a mark on the rotor, the imbalance is determined. Preferably, accelerations on the bearing housing or vibration paths between the bearing and shaft are measured. Since the transfer function of force into vibrations is generally not known, this is usually determined by setting a defined test mass at a defined location on the rotor and the associated changes in the vibrations.

In conventional balancing the rotors are often operated only at rated speed or it must be approached speeds close to resonance frequencies to perform vibration measurements. Often, large rotors lack a conventional conventional balancing drive that can bring the rotor to a constant speed suitable for conventional balancing. Even with rotors that have no prime mover and z. B. must be driven by currents, such as water turbines, wind turbines and impellers in flow meters, a balancing is required. Impellers in flowmeters require a high balancing quality to achieve a low starting torque and thus a low measurable minimum flow rate.

The greater the effort required for balancing, the greater the unavailability of the system. In particular, in wind turbines occur sufficiently large vibrations only at appropriate speeds and the necessary wind conditions. At these times, on the other hand, the loss of production due to balancing is high and the accessibility e.g. may be restricted in offshore installations. In addition, the setting of test weights here is very complex.

The invention is therefore based on the object to provide a method for determining the imbalance of a rotating rotor, which in-situ, d. H. without balancing bank, is applicable on site and which can be carried out at low speeds with little effort for measuring and drive technology.

The invention solves this problem by a method having the features of patent claim 1.

Advantageous developments of the method are the subject of the dependent claims.

The inventive method is based on the measurement of angular velocity fluctuations on the rotating rotor caused by the rotating torque. In this case, measured at an average over a revolution constant or transient speed and a decomposition carried out in those shares, which are generated by the imbalance, and on the other hand in those parts, which are due to other causes.

The inventive method requires that the moment of inertia of the rotor to be examined is known. If the moment of inertia is not known, it may, for. B. be determined relatively easily with the method of an additional weight. The method of determining the moment of inertia by means of additional weight is as such state of the art and may be upstream of the actual inventive method. It is therefore assumed that the moment of inertia is generally known by given data or by determining the data.

The method applies exclusively to rotors within a gravitational field with or without superimposed lift field, to which the axis of rotation is unparallel and which acts on the mass of the rotor. In particular, there are rotors with a horizontal axis of rotation in the gravitational field of the earth. A buoyancy field may in this context be given by rotors with a lower density than their working medium. If the axis of rotation is not perpendicular to the gravitational field, but at an angle smaller than 90 °, the method is also applicable, but taking into account the specific inclination angle with respect to the perpendicular to the gravitational field or buoyancy field.

The inventive method is based on the measurement of changing angular velocities of non-rigidly coupled rotors. If a sufficiently accurate angle of rotation measurement is not installed on the rotor, then in a first step at least three measuring points distributed over the circumference of the rotor are to be defined and / or markings are to be provided. The more measuring points distributed over the circumference, the greater the accuracy of the method. Since several measured values per revolution must be recorded depending on the number of measuring points, the resolution of the means used for detecting the position of the measuring points must be correspondingly high. The higher the speed of the measurement, the higher the resolution must be. More readings per revolution and a lower average speed increase the accuracy of the process.

For the actual measurement, the rotor has to rotate. In this case, the rotation angle φ is measured and the angular velocity ω of the rotor. The means for detecting the position of the measuring points can be light barriers, reflection light barriers, inductive and capacitive encoders, eddy current based encoders, incremental encoders, quadrature encoders or all types of imaging methods. The angular velocity ω is calculated from the measured values or measured directly. The angular acceleration ω can then be dependent on the angle of rotation from the detected angular velocity ω. are calculated as a function of the angle of rotation φ in a range between two successive measuring points. Important in this context is the determination of the angular acceleration as a function of the angle of rotation and not as a function of time.

For non-rigidly coupled rotors, the invention is based on the measurement of rotational angular velocity variations of the rotating rotor. In this case, it is necessary to avoid constraining forces which completely or almost completely suppress the fluctuations and which would set the speed of the rotor firmly. Therefore, here the rotor is rotated in such a way that no drive torque is present, that the drive torque is not firmly coupled or that the drive torque is soft coupled. The latter is the case with a drive by a flow, z. As long as these soft-coupled drive torques do not cause torsional vibrations that are similar to the effect of imbalance in the gravitational or buoyancy field, these drive torques pose no problem. The method according to the invention can therefore be particularly be carried out at the outlet of rotors which are decoupled from their drive, z. As expiring electric motors and fans.

The method according to the invention can therefore also be used at low speeds, which can often be realized without drive only by abutment of the rotor.

The inventive method can therefore also with very slow-running rotors, such. B. in wind turbines, performed. In wind turbines, the vibrations to be measured are in a very low for the conventional operating balancing frequency range of less than 1 Hz. In this area measurements with acceleration sensors are complex and often faulty due to the small accelerations to be measured. In addition, it must be balanced in wind conditions that allow a sufficient and constant speed, which usually lead to a corresponding loss of production.

By definition of the imbalance, the torque acting on a rotor in the gravitational field is equal to the unbalance times the acceleration constant of the gravitational field (in the gravitational field of the earth, therefore, the gravitational acceleration g). If no similarly acting additional moments act on the rotor and the rotor is not rigidly coupled to a drive that does not allow speed variations, therefore, the imbalance can be calculated from the resulting change in angular velocity.

1 shows a rotor R with a given moment of inertia J. An imbalance mass m rotates about the axis of rotation D with the distance r. There are four measuring points S ₁ to S _{4 arranged} as markers evenly distributed over the circumference. The measuring point S ₁ represents the start marking and therefore differs from the other measuring points S ₂ -S ₄ . The imbalance mass has an angular position φ _u to the measuring point S ₁ , ie to the start mark. A means 1 for detecting the position of the marker outputs a signal via a transmission channel to a signal processing unit 2 continue, which may be, for example, a counter or A / D converter. The signal processing unit 2 may also comprise a counting unit for detecting the measuring points S ₁ -S ₄ and a measuring unit for detecting the period t ₁ -t ₄ between two signals. By means of this information can be calculated at given angular distances of the measuring points S ₁ -S _4, the rotation angle-dependent angular velocities.

In simple terms, the torque M from the inertia of the rotor including its imbalance is equal to the torque M _u , which is generated by the imbalance in the gravitational field.

ω:

Winkelgeschwindigkeit

ω .:

Winkelbeschleunigung

φ:

Winkel des Rotors

φ_U:

Winkel der resultierenden Unwucht gegenüber der horizontalen, entgegen der Drehrichtung, wenn des Rotors bei 0° steht.

G = mg:

Schwerkraft

g:

Gravitationskonstante

J:

Massenträgheitsmoment des Rotors

r:

Radius der resultierenden Unwucht

m:

Masse der Unwucht

With reference to the following equation (1) to (4) and considering the illustration of 1 it can be seen that the rotational angular acceleration ω. a function of the angle of rotation φ is: M = M _u (1) With M = Jω. + mr ² ω. (2) and M = G · r cos (φ + φ _u ) = mg · r cos (φ + φ _u ) (3) With

ω:

angular velocity

ω.:

angular acceleration

φ:

Angle of the rotor

φ _U :

Angle of the resulting imbalance with respect to the horizontal, counter to the direction of rotation when the rotor is at 0 °.

G = mg:

gravity

G:

gravitational constant

J:

Moment of inertia of the rotor

r:

Radius of the resulting imbalance

m:

Mass of imbalance

From the equations (1) to (3) results in the rotation angle-dependent angular acceleration

mit

f_i:

gemessene Reihe der Winkelbeschleunigungen

a_i:

Drehbeschleunigung am Winkel iΔφ verursacht durch Unwucht

u_i:

Drehbeschleunigung oder Messfehler am Winkel iΔφ verursacht nicht durch Unwucht und nicht moduliert mit cos(φ_i + φ_v)

v_i:

Drehbeschleunigung oder Messfehler am Winkel iΔφ verursacht nicht durch Unwucht, aber moduliert mit cos(φ_i + φ_v)

V_i:

Modulationsfaktor

φ_v:

Phasenwinkel der Störung.

For discretely measured values ω _i at equidistant angular distances iΔφ follows:

With

f _i :

measured series of angular accelerations

a _i :

Spin at angle iΔφ caused by imbalance

u _i :

Spin or measurement error at angle iΔφ does not cause imbalance and is not modulated with cos (φ _i + φ _v )

v _i :

Spin or measurement error at angle iΔφ does not cause imbalance, but modulated with cos (φ _i + φ _v )

V _i :

modulation factor

φ _v :

Phase angle of the fault.

The special feature of this representation is that the angular acceleration is not shown as a function of time, but as a function of the angle of rotation φ. This function can be transformed into a picture space by a function f (φ) in F (1 / φ). In this transformed function F, the unbalance-based fraction is ideally concentrated on a function value, e.g. B. at A = F (1 / (2π)) in the case of a Fourier transform.

In the transformation, which is an integral transformation and in particular a Fourier transformation, the proportion of imbalance should concentrate on as few points as possible in the image space. In the case of Fourier transformation of a sequence of angular accelerations over one revolution, the imbalance concentrates on a point in the image space of the transformation. In the invention, the complex amplitude of this point is now determined as the intensity of the unbalanced angular acceleration. Analogous to the transformation of a cosine function as a time series, this point can be called the first harmonic and can be evaluated with regard to the peak value of the underlying cosine function. This results in the imbalance m × r and the angle φ _u . In other words, the complex coefficients of the first harmonic of the transformed function are calculated.

By setting a balancing imbalance of the same magnitude as the imbalance m × r at the effective angular position φ _u + 180 ° or by removing the imbalance m × r at the effective angular position φ _u , the imbalance can be compensated. Should there be relevant disturbances v _i , ie spin accelerations or measurement errors at the angle iΔφ, which are not caused by the unbalance but are modulated with cos (φ _i + φ _v ), these disturbances can be eliminated by a suitable model or with the setting a defined test mass with known moment of inertia are measured out.

In particular, when V _{i is} a function of the average speed ω - and the dependence on the speed is known, by measuring at different speeds, for. B. during the start or stop, V _{i are} determined and the function V _i of F _{i are} split off. Thus, in addition, the average angular velocity is measured or determined.

If the first harmonic A of the transform is represented as a function of the mean angular velocity, ideally a constant is obtained that is independent of the angular velocity ω. In practice, however, it is due to various angular velocity-dependent influences, usually a parabola or a polynomial of higher order. An adaptation function (fit function) allows the relationship between the mean angular velocity and the first harmonic to be represented as a continuous function. The adaptation function is in particular a polynomial function. The constant portion of the polynomial function is the desired angular acceleration, by means of which the angle φ _{u of} the imbalance mass can be calculated.

The method according to the invention makes it possible to measure the angular acceleration by means of signal analysis, portions which are based on measurement errors and actual changes in the angular acceleration or on other causes (friction, flow, etc.) being eliminated. This method is applicable in situ without the need to install additional sensors to measure the force. The method is particularly suitable for soft-coupled forces, such as aerodynamic buoyancy forces in a wind turbine or hydrodynamic driving forces in a water meter. Here, the torque is virtually unchanged due to the flow due to the small speed fluctuations from the imbalance. Rather, a constant torque over a revolution at a certain point with the friction canceled or generates a constant acceleration. In both cases, the frequency can be filtered out.

In addition to the fast Fourier transform (FFT), the discrete Fourier transform (DFT) and other base transformations of the vector space, which includes the vector given by the measured values on one revolution, are also suitable.

The continuous fit function is not necessarily a polynomial function, as under certain circumstances it may be necessary to use other fit functions than polynomial functions, such as polynomial functions. As exponential functions to use, depending on the nature of the disorders.

2 shows a schematic representation of a sequence of the method according to the invention for determining an imbalance of the rotor by means of the removal of disturbances. In the first step, the rotor is provided with at least three equidistant measuring points, ie markings on its circumference, which can be detected by a sensor. The first mark is recorded as a 0 ° mark. This can be done by providing a second sensor or by a mark that differs from other markings. Each segment extends over a defined circumferential area Δφ.

Subsequently, the rotor is rotated in the freewheel and the time t _i between the passing of two measuring points S _i-1 and S _i measured. The measured values are stored as a function of the revolution n and the angle of rotation φ _i . From these measured values, on the one hand, the average rotational speed ω - is calculated as a function of the revolution n and, on the other hand, the angular acceleration ω. as a function of the angle of rotation φ _i and the revolution n. The angular acceleration ω. as a function of the angle of rotation φ is transformed by means of Fourier transformation and the angular acceleration amplitude A _j at j = 1 (first harmonic) is calculated as a function of the revolution n. This measurement is carried out for different average angular velocities ω -, so that the complex angular acceleration amplitude A can be represented as a function of the average rotational speed ω -, ie separated according to real part and imaginary part. These two functions of the complex angular acceleration can be expressed as a continuous function by a fit function, eg a polynomial function. From the speed-independent component c _I and c _{R of} the adaptation function, in particular the polynomial function, the maximum angular acceleration, the resulting imbalance mass and of course the imbalance angle φ _u .

Claims (10)

Method for determining an imbalance of a rotor (R) with known moment of inertia with a rotation axis unparallel to a gravitational field and / or a buoyancy field with the following steps: a) definition of measurement points distributed over the circumference of the rotor (R) of u> 2 (S _i , i = 1 ... u) and providing means for detecting the position of the measuring points (S _i ) as a function of the time t; b) rotating the rotor (R) and measuring the angle of rotation (φ) and the angular velocity (ω) of the rotor ( 1 ) at a drive torque that is not or not permanently coupled and calculates the location-dependent angular acceleration (ω) as a function of the rotational angle (φ) in a region between two successive measurement points (S _i -S _{i + 1} , i = 1. ; c) transformation of the angular acceleration (ω) as a function of the angle of rotation (φ) in an image space; d) determination of the complex amplitude (A ₁ ) as intensity of the unbalanced angular acceleration in the image space of the transformed function; e) evaluation of the complex amplitude (A ₁ ) for determining the angle (φ _u ) of a static unbalance (m × r), where r is the distance of the imbalance mass (m) from the axis of rotation (D) of the rotor (R). Method according to claim 1, characterized in that the steps b) to d) of claim 1 are repeated for different average angular velocities (ω -) and representing the real and imaginary part of the complex amplitude (A ₁ ) as a function of the respective mean angular velocity: Re {A ₁ (ω -)} and Im {A ₁ (ω -)} and calculate the angular velocity independent fraction through a continuous fit function for Re {A ₁ (ω -)} and Im {A ₁ (ω -)} and evaluation the angular velocity-independent portion of the adaptation functions for determining the angle (φ _u ) and the amount of static unbalance (m × r). A method according to claim 1 or 2, characterized in that disturbing influences of the complex amplitude (A ₁ ) are determined by setting a test weight. Method according to one of claims 1 to 3, characterized in that the transformation takes place in the image space by means of a Fourier transformation. Method according to one of Claims 1 to 4, characterized in that the transformation into the image space takes place by means of a fast Fourier transformation. Method according to one of Claims 1 to 4, characterized in that the transformation into the image space takes place by means of a discrete Fourier transformation. Method according to one of claims 1 to 6, characterized in that the adaptation function is a polynomial function. Method according to one of claims 1 to 7, characterized in that the adaptation function is an exponential function. Method according to one of claims 1 to 8, characterized in that it is carried out at an outgoing, decoupled from a drive or driven rotor (R). Method according to one of claims 1 to 9, characterized in that it is carried out in a flow-driven rotor (R).

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