DE102017220385A1 - Method for indirectly determining the rotational speed of a rotating shaft - Google Patents

Abstract

Provided is a method for indirectly determining the rotational speed of a rotating shaft. The conversion is carried out in two steps. In the first step, the measured values of the normal acceleration and the tangential acceleration of the shaft orthogonal thereto are determined. In the second step, the observer state is updated.

Description

The present invention relates to a method for indirectly determining the rotational speed of a rotating shaft.

For monitoring or process control of stationary transmissions, e.g. of wind power transmissions, it is necessary to know and monitor the motion quantities of the rotating shaft. For this purpose, e.g. Rotary encoder can be used. Examples of such rotary encoders are optical or magnetic incremental or absolute encoders, or generator-operated electrical machines, for example permanent-magnet DC machines. This type of rotary encoder is expensive, susceptible to contamination and wear due to moving parts, and / or requiring tight positional tolerances because magnetic sensors often require a relatively narrow air gap.

Furthermore, methods are known for calculating the movement quantities of a shaft according to the invention indirectly from acceleration or force measurements. Such sensors can do without moving mechanical parts and are therefore cheaper than encoders and less sensitive to contamination.

From the German patent application DE 10 2007 030 268 A1 For example, a method for determining the rotational speed by means of a discrete Fourier transformation of a force or acceleration signal is known. This has the disadvantage that the achievable resolution depends on the measurement duration and the rotational speed should ideally not change during the measurement. If low rotational speeds are to be determined with high accuracy, then a long measurement time is required and a rotational speed which is almost constant during this measurement period. This limits the practicality of the process at low rotational speeds. Furthermore, there is described a second method for the indirect determination of motion quantities of a rotating shaft from force or acceleration measurements. This method is based on a so-called phase-locked loop (PLL). Such phase locked loops have the disadvantage that they may become unstable due to the need for feedback of the estimated values outside the rotational speed interval for which they were designed. This limits the practicality of this method in applications where both very low and very high angular velocities occur.

From the US patent US 6,940,940 B2 A method is known for reconstructing the rolling movement of a wheel from two co-rotating acceleration sensors. To evaluate the acceleration signals adaptive filters are used in combination with a PLL, so that this method can be unstable in applications with very different rotational speeds.

Furthermore, in an application filed simultaneously with this application, the Applicant proposes a simultaneous estimation of the motion quantities, ie the angle of rotation, the angular velocity and the angular acceleration. However, because of the required approximate numerical inversion of a nonlinear system of equations, this method is relatively computation-time intensive.

Therefore, it is an object of this invention to provide a method of indirectly determining the rotational speed of a rotating shaft which requires little computing time. This object is achieved by the features of the independent claims. Advantageous embodiments are the subject of the dependent claims.

Stationary transmissions such as wind power transmissions have a shaft rotating about their longitudinal axis, wherein the longitudinal axis is oriented horizontally in the gravitational field of the earth. Movements beyond the longitudinal rotation are subsequently assumed to be negligible.

The aim of the invention is thus the estimation of the rotational speed of the shaft about its longitudinal axis by using as measured variables only the tangential and normal acceleration of a point on the shaft outside its axis of rotation. The reconstruction of the angular velocity is performed according to the nonlinear observer described below.

Proposed is a method for indirectly determining the rotational speed of a rotating shaft. The conversion is carried out in two steps. In the first step, the measured values of the normal acceleration and the tangential acceleration of the shaft orthogonal thereto are determined. In the second step, the observer state is updated.

In one embodiment, the updating of the observer state takes place via an approximately numerical solution of the observer state's state differential equations dependent on the observer error and observer gains of the normal acceleration and described below.

In one embodiment, adjustment of the low-pass effect occurs via the choice of the observer gains, which are greater than zero.

By the proposed method, an accurate, i. especially independent of the duration of the measurement, as well as stable and cost-effective determination of the rotational speed of a rotating shaft can be performed. In addition, due to the only two required variables, it is less time-intensive and easy to parameterize.

In one embodiment, the method is implemented as a software program.

Furthermore, a control device is provided, which is configured to execute the described method cyclically or event-controlled.

There is no need for additional hardware, since the process can be performed as a software program usually on an existing controller. Thus, an improvement or change of the calculation method can be easily implemented.

Furthermore, a wind turbine is provided, comprising a rotating shaft, acceleration sensors and a described control unit, wherein the control unit receives from the acceleration sensors measured values of the normal acceleration and the orthogonal tangential acceleration of the shaft for processing.

The detailed implementation will be described in more detail below with reference to the associated calculation rules.

Further features and advantages of the invention will become apparent from the following description of embodiments of the invention, with reference to the figures of the drawing, the inventive details shows, and from the claims. The individual features can be realized individually for themselves or for several in any combination in a variant of the invention.

• 1 zeigt ein Diagramm der Kräfte und zugehörigen Mess-Signale einer rotierenden Welle.
• 2 zeigt ein Ablaufdiagramm des Verfahrens gemäß einer Ausführung der vorliegenden Erfindung.

Preferred embodiments of the invention are explained below with reference to the accompanying drawings.

• 1 shows a diagram of the forces and associated measurement signals of a rotating shaft.
• 2 FIG. 3 shows a flowchart of the method according to an embodiment of the present invention.

• r: Abstand des Beschleunigungssensors von der Rotationsachse der Welle
• g: Erdbeschleunigung
• t: Zeitpunkt
• <p (t): Drehwinkel der Welle zum Zeitpunkt t
• φ̇ (t): Winkelgeschwindigkeit der Welle zum Zeitpunkt t
• φ̈ (t): Winkelbeschleunigung der Welle zum Zeitpunkt t
• a_n (t): Normalbeschleunigung (Zentripetalbeschleunigung) der Welle im Abstand r von der Rotationsachse zum Zeitpunkt t
• a_t (t): Tangentialbeschleunigung der Welle im Abstand r von der Rotationsachse zum Zeitpunkt t
• α_̇n (t): Zeitliche Ableitung von a_n zum Zeitpunkt t
• α_̂n (t): Schätzwert von a_n zum Zeitpunkt t (Zustandsvariable des Zustandsbeobachters)
• $\widehat{\dot{\phi }}\left(t\right):$
  
  Schätzwert von φ̇ zum Zeitpunkt t
• α_̃n := α̂_n-a_n: Beobachterfehler (Schätzfehler) der Normalbeschleunigung
• $\tilde{\dot{\phi }}:=\widehat{\dot{\phi }}-\dot{\phi }:$
  
  Beobachterfehler (Schätzfehler) der Winkelgeschwindigkeit
• $\frac{d{\widehat{a}}_n}{dt}:$
  
  Zeitliche Ableitung von α_̂n
• $\frac{d\widehat{\dot{\phi }}}{dt}:$
  
  Zeitliche Ableitung von $\widehat{\dot{\phi }}$
  
• $\frac{d\widetilde{a_n}}{dt}:$
  
  Zeitliche Ableitung von α_̃̃n
• $\frac{d\tilde{\dot{\phi }}}{dt}:$
  
  Zeitliche Ableitung von $\tilde{\dot{\phi }}$
  
• k₁, k₂ > 0: Beobachterverstärkungen

The following terms and abbreviations are used below:

• r: Distance of the acceleration sensor from the axis of rotation of the shaft
• g: acceleration of gravity
• t: time
• <p (t): angle of rotation of the shaft at time t
• φ̇ (t): angular velocity of the wave at time t
• φ̈ (t): Angular acceleration of the shaft at time t
• a _n (t): normal acceleration (centripetal acceleration) of the shaft at a distance r from the axis of rotation at time t
• a _t (t): Tangential acceleration of the wave at a distance r from the axis of rotation at time t
• α _̇n (t): time derivative of a _n at time t
• α _n (t): estimated value of a _n at time t (state variable of state observer)
• $\widehat{\dot{\phi }}\left(t\right):$
  
  Estimated value of φ̇ at time t
• α _n : = α _n -a _n : observer error (estimation error) of the normal acceleration
• $\tilde{\dot{\phi }}:=\widehat{\dot{\phi }}-\dot{\phi }:$
  
  Observer error (estimation error) of angular velocity
• $\frac{d{\widehat{a}}_n}{dt}:$
  
  Time derivative of α _n
• $\frac{d\widehat{\dot{\phi }}}{dt}:$
  
  Temporal derivative of $\widehat{\dot{\phi }}$
  
• $\frac{d\widetilde{a_n}}{dt}:$
  
  Temporal derivative of α _n
• $\frac{d\tilde{\dot{\phi }}}{dt}:$
  
  Temporal derivative of $\tilde{\dot{\phi }}$
  
• k ₁ , k ₂ > 0: observer gains

As in 1 are shown on a rotating shaft at a distance r from the axis of rotation, the outward normal acceleration a _n (t) and the orthogonal tangential acceleration a _t (t) measured by appropriate sensors. These acceleration signals are related to the sought motion quantities <p (t), φ̇ (t) and φ̈ (t) of the shaft via the following equations: $$a_{\text{t}}\left(t\right)=G\text{cos}\phi \left(t\right)+r\ddot{\phi }\left(t\right).a_{\text{n}}\left(t\right)=-G\text{sin}\phi \left(t\right)+r{\dot{\phi }}^2\left(t\right)$$

If the second equation in (1a) is derived once again according to time, then one obtains in addition: $${\dot{a}}_{\text{n}}\left(t\right)=\left(-G\text{cos}\phi \left(t\right)+2r\ddot{\phi }\left(t\right)\right)\dot{\phi }\left(t\right)$$

If the first equation in (1a) is inserted into the parenthesis term in (1b), the result is: $${\dot{a}}_{\text{n}}\left(t\right)=\dot{\phi }\left(t\right)\left(3r\ddot{\phi }\left(t\right)-a_{\text{t}}\left(t\right)\right)$$

This is simplified for small angular accelerations φ̈ (t) ≈ 0 to: $${\dot{a}}_{\text{n}}\left(t\right)\approx -\dot{\phi }\left(t\right)a_{\text{t}}\left(t\right),$$

With this background knowledge, the following steps are carried out according to the invention in order to obtain an indirect determination of the rotational speed of the rotating shaft.

The conversion is carried out in two steps, as in 2 shown. In the first step S1, the measured values of the normal acceleration are determined a _n (t) and the orthogonal tangential acceleration a _t (t) advantageously with already existing sensors, as mentioned above.

wobei α_̂n ein Schätzwert von a_n und $\widehat{\dot{\phi }}$

Schätzwert von φ̇ ist, durch näherungsweise numerische Lösung der Zustandsdifferentialgleichungen $$\frac{\text{d}{\widehat{a}}_{\text{n}}}{\text{d}t}\left(t\right)=-\widehat{\dot{\phi }}\left(t\right)a_{\text{t}}\left(t\right)-k_1{\tilde{a}}_{\text{n}}\left(t\right)$$

$$\frac{\text{d}\widehat{\dot{\phi }}}{\text{d}t}\left(t\right)=k_2{\tilde{a}}_{\text{n}}\left(t\right)a_{\text{t}}\left(t\right)$$

In the second step S2, the observer state is updated $\left({\widehat{a}}_{\text{n}};\widehat{\dot{\phi }}\right).$

where α _{n is} an estimate of a _n and $\widehat{\dot{\phi }}$

Estimate of φ̇ is by approximate numerical solution of the state differential equations $$\frac{\text{d}{\widehat{a}}_{\text{n}}}{\text{d}t}\left(t\right)=-\widehat{\dot{\phi }}\left(t\right)a_{\text{t}}\left(t\right)-k_1{\tilde{a}}_{\text{n}}\left(t\right)$$

$$\frac{\text{d}\widehat{\dot{\phi }}}{\text{d}t}\left(t\right)=k_2{\tilde{a}}_{\text{n}}\left(t\right)a_{\text{t}}\left(t\right)$$

Here, α _n : = α _n - a _{n is} the observer error (estimation error) of the normal acceleration. Numerous methods for approximate numerical solution of initial value problems are familiar to the person skilled in the art for this update. About the choice of observer gains k1; k2> 0, the low-pass effect of the method can be set. This is also familiar to the person skilled in the art.

The described two steps S1 and S2 can be performed cyclically or event-controlled on the electrical control unit, which is used to determine the movement variables. In this case, the control unit receives the measured variables to be processed for step S1, preferably from corresponding sensors. In step S2, the processing of the measured quantities obtained in the control unit then takes place according to the proposed method. The method can be executed as a software program on a control unit, wherein the control unit receives the necessary input signals and carries out the calculations for this purpose.

die nachfolgend dargestellte Dynamik auf: $$\frac{\text{d}{\tilde{a}}_{\text{n}}}{\text{d}t}\left(t\right)=-\tilde{\dot{\phi }}\left(t\right)a_{\text{t}}\left(t\right)-k_1{\tilde{a}}_{\text{n}}\left(t\right),$$

$$\frac{\text{d}\tilde{\dot{\phi }}}{\text{d}t}\left(t\right)=k_2{\tilde{a}}_{\text{n}}\left(t\right)a_{\text{t}}\left(t\right)$$

The following is a representation of a stability analysis of the observer, which shows that the proposed method is stable. According to the above equations (2) and (3), the observer error $\left({\tilde{a}}_n;\tilde{\dot{\phi }}\right)=\left({\widehat{a}}_{\text{n}}-{\text{a}}_{\text{n}};\widehat{\dot{\phi }}-\dot{\phi }\right)$

the dynamics shown below: $$\frac{\text{d}{\tilde{a}}_{\text{n}}}{\text{d}t}\left(t\right)=-\tilde{\dot{\phi }}\left(t\right)a_{\text{t}}\left(t\right)-k_1{\tilde{a}}_{\text{n}}\left(t\right).$$

$$\frac{\text{d}\tilde{\dot{\phi }}}{\text{d}t}\left(t\right)=k_2{\tilde{a}}_{\text{n}}\left(t\right)a_{\text{t}}\left(t\right)$$

lautet $$\dot{V}\left(t\right)=-{\tilde{a}}_{\text{n}}^2\left(t\right)$$

und ist somit positiv semidefinit bezüglich des Beobachterfehlers. Für at ≠ 0 folgt die Stabilität von $\left({\widehat{a}}_{\text{n}};\widehat{\dot{\phi }}\right)=\left(0;0\right)$

aus dem Invarianzprinzip von Krassovskii-LaSalle.The temporal derivative of the positive definite function with respect to the observer error $$V\left(t\right):=\frac{1}{2}\left(\frac{{\tilde{a}}_{\text{n}}^2\left(t\right)}{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="DE102017220385A1\_0029.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}+\frac{{\tilde{\dot{\phi }}}^2\left(t\right)}{k_1{k}_2}\right)$$

reads $$\dot{V}\left(t\right)=-{\tilde{a}}_{\text{n}}^2\left(t\right)$$

and thus is positively semidefinite with respect to the observer error. For at ≠ 0, the stability of $\left({\widehat{a}}_{\text{n}};\widehat{\dot{\phi }}\right)=\left(0;0\right)$

from the invariance principle of Krassovskii-LaSalle.

The described method can be used for stationary transmissions, in particular for wind turbines. It can also be used for transmissions in mobile applications in which the acceleration of the transmission housing - in relation to the inertial system - in comparison to the normally occurring measured normal and tangential accelerations is low.

In all other transmission applications, ie in particular in transmission applications in which the accelerations of the transmission housing in comparison to the measured normal and tangential accelerations is no longer negligible, the accelerations of the transmission housing can be measured with additional acceleration sensors and excluded from the measured normal and tangential accelerations.

The advantages of the method described are that the acceleration sensors required to acquire the measured values for the indirect determination of the rotational speed are both cost-effective and robust, above all insensitive to dirt. In addition, large positional tolerances for the position of the acceleration sensors are possible, in particular in combination with an easily performed calibration. In addition, the angle, the rotational speed and acceleration of the shaft are determined simultaneously, and the speed resolution is independent of the measurement duration, in contrast to methods based on a Fourier transformation of the measurement signals. Furthermore, in contrast to PLL-based methods, no feedback of past estimates is required, which means that the method can not become unstable. Compared to known methods for indirect reconstruction, the inventive method is much more computationally efficient, since only a few elementary algebraic arithmetic operations are needed and no trigonometric functions must be evaluated. In addition, the method has only two parameters and is therefore easy to parameterize in practice.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The 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

• DE 102007030268 A1 [0004]
• US 6940940 B2 [0005]

Claims (6)

Method for the indirect determination of the rotational speed of a rotating shaft, wherein the following steps are carried out: - first step (S1): determination of the measured values of the normal acceleration (a _n (t)) and the orthogonal tangential acceleration (a _t (t)) of the shaft, - second step (S2): update the observer state. Method according to Claim 1 in which, in the second step (S2), the updating of the observer state takes place via an approximately numerical solution of the observer error state differential equations dependent on the observer error and observer gains of the normal acceleration, the state differential equations being: $$\frac{\text{d}{\widehat{a}}_{\text{n}}}{\text{d}t}\left(t\right)=-\widehat{\dot{\phi }}\left(t\right)a_{\text{t}}\left(t\right)-k_1{\tilde{a}}_{\text{n}}\left(t\right)$$

$$\frac{\text{d}\widehat{\dot{\phi }}}{\text{d}t}\left(t\right)=k_2{\tilde{a}}_{\text{n}}\left(t\right)a_{\text{t}}\left(t\right)$$

with: t: time φ (t): angle of rotation of the shaft at time t φ̇ (t): angular speed of the shaft at time t a _n (t): normal acceleration (centripetal acceleration) of the shaft at a distance r from the axis of rotation at time t a _t (t ): Tangential acceleration of the wave at a distance r from the axis of rotation at time t _n (t): estimated value of a _n at time t (state variable of the state observer) $\widehat{\dot{\phi }}\left(\text{t}\right):$

Estimated value of φ̇ at time t ã _n : = â _n -a _n : observer error (estimation error) of the normal acceleration k ₁ , k ₂ > 0: observer gains $\frac{{\text{d}\widehat{\text{a}}}_{\text{n}}}{\text{dt}}:$

Temporal derivative of A _n $\frac{\text{d}\widehat{\dot{\phi }}}{\text{dt}}:$

Temporal derivative of $\widehat{\dot{\phi }},$

Method according to Claim 2 , wherein an adjustment of the low-pass effect on the choice of the observer gains (k ₁ , k ₂ ) takes place. Method according to one of the preceding claims, wherein the method is implemented as a software program. Control device adapted to perform the procedure according to one of Claims 1 to 4 cyclically or event-driven. Wind turbine, comprising a rotating shaft, acceleration sensors and a controller after Claim 5 in which the control unit receives from the acceleration sensors measured values of the normal acceleration (a _n (t)) and the orthogonal tangential acceleration (a _t (t)) of the shaft for processing.

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