Computer-implemented method for detecting and/or determining an anomaly in a centrifugal pump

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is based upon and claims the right of priority to BE Patent Application No. 2024/5267, filed May 6, 2024, the disclosure of which is hereby incorporated by reference herein in its entirety for all purposes.

TECHNICAL FIELD

The invention relates to a computer-implemented method for detecting and/or determining an anomaly in a centrifugal pump, including the steps: in a normal state, accelerating and/or decelerating a rotor of the centrifugal pump for quantifying at least one term of a dynamic rotor model of the centrifugal pump, and in a fault state differing from the normal state, accelerating and/or decelerating the rotor of the centrifugal pump for detecting at least one fault parameter.

BACKGROUND OF THE INVENTION

Centrifugal pumps are known from the prior art and are used to convey a liquid by means of a rotary movement of an impeller. The liquid to be conveyed enters a pump chamber of the centrifugal pump through a suction opening, is captured by the rotating impeller and subsequently conveyed into a pressure outlet. Any solids contained in the liquid can settle in the region of the impeller and on the inside of a pump housing and thus negatively affect the hydraulic and/or mechanical efficiency of the centrifugal pump or even cause the centrifugal pump to become blocked and fail.

Although several methods for detecting and/or determining an anomaly and in particular for unblocking centrifugal pumps are known from the prior art, current practice indicates that the known methods are not ideal for safely and reliably protecting a centrifugal pump from damage, due to possibly not detecting the blockage early enough, and in particular for reliably detecting and/or determining a corresponding anomaly in the centrifugal pump.

DESCRIPTION OF THE INVENTION

On the basis of this situation, an objective of the present invention is to provide a method for detecting and/or determining an anomaly in a centrifugal pump which can detect and classify the anomaly, and in particular a blockage, more reliably and more quickly than the solutions known from the prior art, and/or can initiate targeted measures for eliminating the anomaly, in particular to clear the blockage.

The objective of the invention is achieved by the features of the independent claim. Advantageous embodiments are specified in the subclaims.

Accordingly, the objective is achieved by a computer-implemented method for detecting, determining and/or classifying an anomaly in a centrifugal pump, including the steps:

• • in a normal state, accelerating and/or decelerating a rotor of the centrifugal pump to quantify at least one term of a dynamic rotor model of the centrifugal pump,
  • in a fault state differing from the normal state, accelerating and/or decelerating the rotor of the centrifugal pump for detecting at least one fault parameter, and
  • solving an inverse problem of the dynamic rotor model to identify the at least one fault parameter for detecting, determining and/or classifying the anomaly.

An essential aspect of the proposed solution is that a digital twin of the centrifugal pump is created by the dynamic rotor model, whereby a parameter estimation is carried out by solving the inverse problem, for example by solving an optimization problem, in order to thus be able to determine the anomaly, in particular a blockage situation of the centrifugal pump, using the identified parameters. The anomaly may be, for example, bearing damage including wear and/or ageing, seal damage including wear and/or ageing, a particularly large change in temperature, a consequence such as expansion and/or a change in viscosity, an incorrect alignment of pump components, a consequence such as misalignments and/or changes in gap sizes, a blockage inside the centrifugal pump, in particular at different points, a corrosion effect, a deposit effect, multi-component fluids in the impeller, multiphase or cavitating fluids in the impeller, an unknown increase in friction, etc. The dynamic rotor model determined in this way makes it much easier to detect or determine an anomaly more accurately. In other words, the proposed method makes it much easier to analyze a blockage situation or another possible type of mechanical malfunction relating to the rotation of the rotor of the centrifugal pump. In the event of a blockage as an anomaly, an unblocking routine suitable for the blockage situation can be selected in order to return the centrifugal pump to its normal state as quickly as possible.

In summary, the method provides a mathematical and/or physical analysis of an acceleration or deceleration phase of a motor, in particular including the shaft and all rotating components of the centrifugal pump, in comparison with a previously determined digital twin of the centrifugal pump for the purpose of identifying potential blockage situations and/or further resistance or resistance-related torques and forces. Based on such a classification of the blockage situation, for example with regard to the location of a blockage in the interior of a pump housing of the centrifugal pump, a problem-oriented unblocking routine suitable for the blockage can be selected. The method thus enables a faster and more efficient unblocking sequence for sewage or waste water pumps.

The proposed method can preferably be used to determine a blockage. In particular, the terms of the dynamic rotor model can be determined during a coordinated, preferably stepwise run-up sequence and/or run-down sequence. To detect the at least one fault parameter, the method takes into account in particular a breakaway and/or static frictional torque, a frictional torque directly proportional to the angle of rotation, in particular as stiffness, any number of frictional torques directly proportional to angular velocities with different exponents, in particular as damping of different orders, and/or allows the selection of a cleaning sequence which is optimally suited to the anomaly depending on the classification of the current blockage. The proposed method also allows the detection of a dry run, the detection of a total blockage in particular, and differentiation with regard to both directions of rotation of the rotor and/or pre-processing of raw time signals such as torque, angular velocity and/or angle of rotation, such as the smoothing and/or filtering of the signals for example.

The term ‘computer-implemented’ is defined to mean in particular that the proposed method can be or is executed by a computer, a computer-based control unit, a microprocessor, cloud-based or the like. Preferably, all steps of the method are carried out by the computer, i.e. computer-implemented. In particular, the normal state is defined as the state of the centrifugal pump in which the centrifugal pump delivers a fluid without increased friction and without any altered inertia of any origin, in particular without any problems. The acceleration and/or deceleration of the rotor can be conducted under laboratory conditions, for example using clear water. The term of the dynamic rotor model of the centrifugal pump described in the following is defined for example as a friction term, a hydraulic torque term and/or an inertia term. The acceleration and/or deceleration of the rotor of the centrifugal pump for detecting the at least one fault parameter preferably takes place during the regular operation of the centrifugal pump, for example when pumping waste water.

A centrifugal pump is generally referred to as a flow machine that utilizes a rotary motion and dynamic forces to convey predominantly liquids as fluid. The centrifugal pump is preferably configured as a waste water pump. In addition to a tangential acceleration of the liquid, a centrifugal force in radial flow is used for pumping in the centrifugal pump, so that such pumps are also referred to as centrifugal pumps. The centrifugal pump is preferably used for a hydraulic system in a building or other applications.

During the regular operation of the centrifugal pump, a housing of the motor of the centrifugal pump can be arranged above the pump housing, in which the impeller driven by the motor via the shaft is provided for conveying the liquid, whereby the housing of the motor can be connected to the pump housing in a fixed position and/or configured in one piece. The centrifugal pump and the motor can also each have their own shaft, wherein the shafts can be connected to one another via a coupling. Preferably, the shaft protrudes from the housing of the motor into the pump housing on a drive side and/or is fixed to the shaft on the drive side of the impeller. Accordingly, an inlet for the liquid to be conveyed can preferably be arranged below or at the bottom of the pump housing.

The liquid preferably includes water or another liquid medium such as waste water, for example. The liquid may contain solids such as impurities or waste of any kind, in particular feces, sediments, dirt, sand, or even small pieces of wood, undergrowth, textiles or rags or the like. Preferably, the housing of the motor and/or the pump housing is made of metal, in particular cast iron or stainless steel, ceramic and/or plastic. As already mentioned, in the context of the invention, the acceleration and/or deceleration of the rotor in the normal state for quantifying the at least one term of the dynamic rotor model of the centrifugal pump means in particular during a regular, fault-free operation of the centrifugal pump, namely when the centrifugal pump conveys a fluid as a liquid, which may be fresh water or may be mixed with the aforementioned portion of solids. The fault state includes, in particular, a malfunction, bearing damage including wear and/or ageing, seal damage including wear and/or ageing, a particularly large change in temperature, a consequence such as expansion and/or a change in viscosity, an incorrect alignment of pump components, a consequence such as misalignment and/or a change in gap size, a blockage inside the centrifugal pump, particularly at different points, a corrosion effect, a deposit effect, multi-component fluids in the impeller, multiphase or cavitating fluids in the impeller, an unknown increase in friction, etc.

According to a preferred development, the method includes the step:

• • based on the determined anomaly, in particular the automatic or manual transfer of the centrifugal pump from the fault state to the normal state.

According to this development, an unblocking routine suitable for correcting the anomaly or the blockage is selected based on the determined anomaly, for example in the case of a blockage, by means of which the centrifugal pump can be transferred from the fault state back to the normal state as quickly as possible. Preferably, the selection of the unblocking routine and/or the transfer of the centrifugal pump from the fault state to the normal state is automated, in particular by the computer-based control system. Such an automated transfer can be achieved, for example, by the unblocking routine includes multiple changes to the direction of rotation and/or rotational speed of the rotor. It may also be expedient for the centrifugal pump to be transferred from the fault state to the normal state manually, for example through the intervention of a user. For example, such a manual transfer can be achieved by replacing a damaged impeller.

According to a further preferred embodiment, quantifying the dynamic rotor model, which is in particular force-based, includes detecting a braking torque of the normal state, in particular at least one friction term, in particular a hydraulic torque term, and/or in particular time-dependent, as a function of an angular velocity of the rotor, and/or quantifying the dynamic rotor model, which is in particular force-based, includes detecting a total inertia of a rotating system of the centrifugal pump in the normal state, in particular including a liquid moved proportionally by the centrifugal pump. The quantification of the dynamic rotor model, in particular the force-based dynamic rotor model, is carried out for the normal state, in particular under laboratory conditions, wherein in particular all braking torques of the rotor or the centrifugal pump are determined or measured in advance. More preferably, quantifying the dynamic rotor model, in particular the force-based dynamic rotor model, includes detecting a braking torque of the normal state, consisting in particular of a total friction term and a torque term, in particular a hydraulic torque term, all in particular depending on the angular velocity of the rotor as a function of time, as well as detecting the total inertia of the rotating system in the normal state, including proportionally moved liquid.

According to another preferred development, the quantifying is carried out taking into account a pump characteristic curve, taking into account a system characteristic curve, in particular taking into account a geodetic height difference, and/or taking into account a gate valve, a valve, a bypass and/or a non-return flap and in particular a position of the valve and/or taking into account a filling level of a pipeline and/or length of the pipeline, a liquid temperature, a liquid viscosity, a liquid density, a pressure difference, a volume flow, a pump efficiency and/or a degree of valve opening. Data determined in this way can be stored in a database for a specific type of centrifugal pump in order to be used in a comparison with the normal state, in particular in the fault state. The proposed method can be used in particular with a closed pressure-side valve or closed non-return flap in order to produce a repeatable and comparable state, virtually independently of the system. Furthermore, machine learning or artificial intelligence methods can be used to further process the fault parameters, in particular for classification, after carrying out a plurality of experiments and subsequently analyzing the results.

According to a further preferred embodiment, the dynamic rotor model includes a braking torque of the normal state dependent on a rotational speed and/or angular velocity according to the following equation:

M R ( φ . ( t ) ) := ∑ i = 1 N k i ⁢ φ . r i ( t ) + M T ( φ . ⁢ ( t ) ) + M I ( φ . ⁢ ( t ) )

• • with
  • k_i coefficients of the angular velocity of the rotor,
  • r_i exponents of the angular velocity of the rotor,
  • M_T torque function of a transfer from static to sliding friction, in particular of the rotor, and
  • M_I torque of an impeller of the centrifugal pump.

The equation described above combines all braking torques of the centrifugal pump in the normal state to form a total braking torque.

According to another preferred development, the dynamic rotor model, according to the following equation, includes in the normal state an inertia term and a braking torque on the left-hand side of the equation and a time-dependent motor torque on the right-hand side of the equation,

J ⁢ φ ¨ ⁢ ( t ) + M R ( φ . ⁢ ( t ) ) = M M ( t )

• • with
  • J inertia moment, in particular as the sum of various inertia effects of rotating fixed parts, liquid in the impeller and/or liquid in the pump housing and/or in parts of a pipeline system.

According to a further preferred embodiment, detecting the dynamic rotor model in the normal state includes calculating and/or experimentally determining an inertia moment. In particular, the detection of the dynamic rotor model in the normal state includes detecting the inertia moment of an entire rotating system of the centrifugal pump, in particular including additive inertias due to liquid in the environment of the rotor, for example by experimental determination in the laboratory or on the basis of a calculation.

According to another preferred development, solving the inverse problem includes classifying the anomaly, the normal state and/or the fault state. Based on the classification of the anomaly, a suitable measure can be selected, manually or by automation, to correct the anomaly. According to a further preferred embodiment, the centrifugal pump is transferred from the fault state to the normal state based on the classification of the anomaly and/or the fault state. Ideally, based on the classification in the case of a blockage, for example, an unblocking routine suitable for the classification can be selected so that the centrifugal pump can be transferred from the fault state back to the normal state after the unblocking routine has been used.

According to another preferred embodiment, the at least one fault parameter includes a breakaway torque and/or a static frictional torque of the fault state and/or the acceleration of the rotor for detecting the fault parameter includes increasing a motor torque from zero until the rotor is moved for the first time, wherein a static frictional torque of the anomaly results from a current motor torque at the first movement minus a breakaway torque of the normal state. According to a further preferred embodiment, the at least one fault parameter includes a breakaway torque and/or a static frictional torque of the fault state and/or the acceleration of the rotor for detecting the fault parameter includes increasing a motor torque from zero up to a first movement of the rotor, wherein a static frictional torque of the anomaly results from a current motor torque at the first movement minus a breakaway torque of the normal state. Preferably, a potential additional breakaway torque of the anomaly is determined first of all. For this purpose, the motor torque can be slowly increased continuously from zero until the rotor moves for the first time. The breakaway torque of the normal state is subtracted from this current motor torque so that the static frictional torque of the anomaly is obtained.

According to another preferred development, the method includes the step:

• • after the initial movement of the rotor, in particular rapidly increasing an angular velocity of the rotor to an in particular constant but in particular vanishingly small value by controlling and/or adjusting the motor torque, and
  • after reaching the in particular constant but in particular vanishingly small angular velocity, measuring and/or calculating an angle of rotation of the rotor by means of an integration method, wherein the in particular angle-related at least one fault parameter is obtained as a derivative of the motor torque according to the angle of rotation.

Vanishingly small means in particular ≥1 and ≤100 rotations of the rotor per minute, preferably ≥1 and ≤10 rotations of the rotor per minute.

In particular, the initial movement of the motor represents a breakaway. The angle of rotation of the rotor can be measured directly or calculated using an integration method.

According to a further preferred embodiment, the method includes the step:

• • determining K coefficients for angular velocities with different exponents as well as the at least one fault parameter, as velocity-independent Coulomb friction, corresponding to a coefficient of an angular velocity with the exponent zero,
  • by solving a linear equation system with K+1 linearly independent equations, where the equations can be associated with pairwise different constant angular velocities in a range between low and high rotational speeds of the rotor.

According to another preferred development, the method includes the step:

• • calculating an additional inertia moment, in particular with a positive or negative sign, during positive or negative acceleration in a predetermined angular velocity range. The acceleration can be constant, according to a predefined function, according to any functions etc.

According to a further preferred embodiment, the method includes the step:

• • determining, based on a result of at least one of the four preceding embodiments, the fault state including in particular no blockage, blockage between a rotating and a fixed part of the centrifugal pump, blockage leading to the standstill of an impeller of the centrifugal pump or blockage inside an impeller channel and in particular in impeller side clearances, in different gaps, at blade edges, at a tongue and/or in a spiral of the centrifugal pump. Particularly preferably, the determination includes a mix of blockage locations, such as pump casing, impeller channel, impeller edge and/or gap between rotating and fixed parts, and/or consequences, such as no blockage, soft blockage and/or hard blockage for example.

According to another preferred development, the method includes the step:

• • storing the dynamic rotor model, in particular the normal state of the centrifugal pump, in a database, in particular as a characteristic curve and/or a characteristic diagram, and/or
  • detecting the dynamic rotor model and/or the fault parameter as a function of temperature, fluid viscosity, fluid density, pressure difference, volume flow, pump efficiency and/or degree of opening or position of valves or the non-return flap.

According to a further preferred embodiment, the method includes the step:

• • stepwise, periodic and/or repeated acceleration and/or deceleration.

According to another preferred embodiment, the method includes the step:

• • comparing the determined fault parameters with respective threshold values in categories of fault parameters, in particular including:
  • (a) fault parameters with a breakaway torque reference (static friction),
  • b) fault parameters with constant torque reference (Coulomb sliding friction),
  • c) fault parameters with angle of rotation reference (stiffness),
  • d) fault parameters with angular velocity reference (damping),
  • e) fault parameters with angular acceleration reference (inertia).

According to a further preferred embodiment, the method includes the step:

• • storing the at least one term of the dynamic rotor model in the normal state of the centrifugal pump in the form of a characteristic curve and/or a characteristic diagram in the database for comparing the fault state with the normal state, in particular as a function of fluid temperature, fluid viscosity, fluid density, pressure difference, volume flow, pump efficiency and/or as a function of a system, in particular of the geodetic height difference, position of the valve and/or the non-return flap, the filling level, in particular of all pipelines, lengths in particular of all pipelines, and/or existence of a bypass.

According to another preferred development, the method includes the step:

• • accelerating and/or decelerating over a sufficiently large speed range in particular, wherein the acceleration and/or deceleration can be with a positive or negative acceleration always unequal to zero, in particular a strictly monotonic speed curve, and/or in stages, in particular a monotonic speed curve, with time intervals of in particular almost constant angular velocity, in particular intermediate stabilization of the speed, and/or in particular constant or true acceleration intervals, in particular with acceleration unequal to zero, between individual stages, a starting speed and a final speed and/or in any sequence.

According to a further preferred embodiment, the normal state can be learned and/or the rotor model can be used to determine the fault parameters in different ways. The normal state of the centrifugal pump, in particular with regard to run-up and run-down, can be determined for each individual case and stored in the form of a characteristic curve. The normal state of the centrifugal pump, in particular with regard to run-up and run-down, can also be determined in advance for different applications and stored in the form of characteristic curves or characteristic diagrams for later selection. Finally, the normal state and the fault state of the centrifugal pump during run-up and/or run-down can always be analyzed when the slide valve is closed, in particular when the valve on one pressure side of the centrifugal pump is closed, wherein the normal state is saved and stored in the database.

According to another preferred development, the method includes the step:

• • reading from the determined fault parameters, which can be viewed as coordinates of a multidimensional parameter range, which type of anomaly or fault is present or to which class the respective anomaly or disturbance belongs. Such class formation can also be supported by artificial intelligence methods, in particular by machine learning methods, if there is a sufficient database.

According to a further preferred embodiment, the normal state can be defined by the fact that all fault parameters are smaller in value than the respective threshold values, i.e. the value is close to zero in particular. In particular, the normal state represents the centrifugal pump at the time of its delivery or when put into operation in a respective system or in regular operation without malfunctions and/or without ageing effects such as wear. According to another preferred development, the fault state is defined by the fact that at least one fault parameter is greater in value than or equal to a respective threshold value, i.e. its value is significantly different from zero.

The fault state can in particular represent bearing damage, including wear, seal damage including wear, and/or a particularly in temperature and its consequences such as expansion and/or changes in viscosity, incorrect alignment of pump components and consequences such as misalignments and/or changes in gap sizes, and/or blockages inside the centrifugal pump, in particular at different points, further wear effects, corrosion effects, deposit effects, and/or the presence of fluids with several components and/or phases inside the pump. The threshold values can be defined in advance experimentally or based on existing experience.

According to another preferred development, time signals of torque, angle of rotation and angular velocity can be recorded by hardware sensors and/or soft sensors. Hardware sensors are understood in particular to be sensors that measure variables directly as a function of time, wherein a sensor for the combined measurement of all relevant variables is also conceivable. In particular, soft sensors are understood to be sensors that allow the measurement of basic signals from the motor and/or the frequency inverter adapted to the respective motor technology. A combination of hardware sensors and soft sensors is also conceivable.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following, the invention is explained in more detail with reference to the accompanying drawings with reference to preferred exemplary embodiments.

In the drawings:

FIG. 1 shows a schematic view of a centrifugal pump for carrying out the proposed method according to a preferred exemplary embodiment of the invention, and

FIG. 2 shows a flow chart for carrying out the proposed method according to the preferred exemplary embodiment of the invention.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

FIG. 1 shows a schematic view of a centrifugal pump 1 for carrying out a method described in the following for detecting, determining and/or classifying an anomaly and, in particular, in the event of a blockage, for subsequently unblocking the centrifugal pump 1 according to a preferred exemplary embodiment of the invention.

In a conventional manner, the centrifugal pump 1 has a pump housing 2 with a suction opening 3 as the inlet, which is arranged at the bottom of the pump housing 2 in the Figure. A rotor 4 is provided in the pump housing 2, which rotor extends vertically in the drawing. The rotor 4 is part of a motor 5, only partially shown, which is arranged opposite the suction opening 3. An impeller 6 is provided facing the suction opening 3, which impeller is driven by the motor 5 via the rotor 4. Furthermore, the centrifugal pump 1 has a microprocessor-based control unit 7, which is only indicated in FIG. 1.

Lastly, the centrifugal pump 1 has one or more sensors 8 for quantifying at least one term of a dynamic rotor model and/or for detecting at least one fault parameter of the centrifugal pump 1. The sensor 8 is configured accordingly as an acceleration and/or vibration sensor, in particular as a 3-axis acceleration and/or vibration sensor, as a pressure sensor and/or as a current sensor, and/or as a sensor for determining a motor torque, an angle of rotation and/or an angular velocity or a rotational speed. In the case of a configuration as an acceleration and/or vibration sensor, the sensor 8 is provided in particular in contact, directly adjacent and/or rigid, with a metal plate for example, in particular close to a respective bearing point, on the motor 5, assigned to the rotor 4, on the pump housing 2, on a motor housing of the motor 5 and/or assigned to the impeller 6. In the case of a pressure sensor, the sensor 8 is provided on the pressure side and/or suction side, in particular at the suction opening 3. In the case of a current sensor, the sensor 8 measures a motor current received by the motor 5.

The computer-implemented method described below for detecting, determining and/or classifying the anomaly of the centrifugal pump 1 is carried out by a processor and/or computer, not shown, in particular the control unit 7. In principle, the method uses a mathematical-physical approach for analyzing pump behavior during the acceleration and/or deceleration of the rotor 4, in particular during a run-up or run-down time of the motor 5. The approach consists essentially of three components: training a digital twin with reference to a normal state, identifying anomaly parameters by solving an inverse problem and classifying anomalies using the identified parameters.

Specifically, the method for detecting and/or determining the anomaly of the centrifugal pump 1 includes the following steps:

• • in a normal state, accelerating and/or decelerating the rotor 4 of the centrifugal pump 1 to quantify at least one term of a dynamic rotor model of the centrifugal pump 1 100,
  • in a fault state differing from the normal state, accelerating and/or decelerating the rotor 4 of the centrifugal pump 1 to detect at least one fault parameter 200, and
  • solving an inverse problem of the dynamic rotor model to identify the at least one fault parameter for detecting and/or determining the anomaly 300.

Based on the determined anomaly, the centrifugal pump 1 can in particular be automatically or manually transferred from the fault state back to the normal state.

The dynamic rotor model of the centrifugal pump, which takes into account potential anomalies or malfunctions as variable terms, is described by the following physical equation of motion:

( J + λ ) ⁢ φ ¨ = M M - ∑ i = 1 N k i ⁢ φ .   r i - ∑ i = 1 K μ i ⁢ φ .   s i - γφ - M T - M ψ - M I ⁢ w ⁢ ith ⁢ k = ( k 1 , k 2 , … , k N ) , r = ( r 1 , r 2 , … , r N ) ⁢ μ = ( μ 1 , μ 2 , … , μ K ) , s = ( s 1 , s 2 , … , s K ) ⁢ M T = f 1 ( φ . ) , M ψ = f 2 ( φ . ) ⁢ and ⁢ M i - f 3 ( φ . )

Definition of the Variables

• • t time
  • φ angle of rotation
  • φ^⋅ angular velocity
  • φ^⋅⋅ angular acceleration

Definition of known parameters (normal state) (determined in particular during the final inspection of the centrifugal pump 1, when setting the centrifugal pump 1 into operation or at regular intervals).

• • J inertia moment (depending on the installation, valves, etc. of the centrifugal pump 1) as the sum of various inertia effects of rotating fixed parts of the centrifugal pump 1, liquid in the impeller 6, liquid in the pump housing 2 and pipeline system
  • M_M motor torque
  • k vector of coefficients for the angular velocity
  • r vector of exponents for the angular velocity
  • M_T resistance torque of a transfer from static to sliding friction
  • M_I impeller torque (depending on installation, valves, etc. of centrifugal pump 1)

Definition of Unknown (Fault) Parameters

• • λ additional inertia moment (negative values also possible)
  • μ vector of coefficients for the angular velocity
  • s vector of exponents for the angular velocity (estimated in particular by initial tests)
  • γ coefficient for the angle of rotation
  • M_ψ additional resistance torque of a transfer from static to sliding friction with the following boundary conditions:
    • M_ψ=ε . . . in the case of static friction with φ^⋅=0
    • M_ψ=δ . . . in the case of sliding friction after the transfer for φ^⋅>>0

The above equation basically corresponds to Newton's second law, according to which force equals mass times acceleration. In the case of the present rotation of the centrifugal pump 1, the force becomes a torque, the mass becomes an inertia moment and the acceleration becomes an angular acceleration.

All torques acting on the rotor 4, whether driving torques, braking frictional torques, etc., are on the right-hand side of the equation. These torques can depend on the time, the angle of rotation and angular velocity. The torques on the right-hand side of the equation can be divided into two groups. On the one hand, torques that always act or, in other words, always occur in the normal state of the centrifugal pump 1, and on the other hand, additional frictional torques that only occur in the event of a fault or an anomaly.

On the left-hand side of the equation, the sum of all inertia moments is multiplied by the angular acceleration. The sum of all inertia moments includes the inertia moments of the normal state on the one hand and the inertia moments of an anomaly, i.e. the fault state, on the other. An additional inertia moment of an anomaly can be positive or negative, depending on the case.

To quantify at least one term of the dynamic rotor model of the centrifugal pump 1 in the normal state, the aforementioned equation can be rearranged in such a way that only anomaly terms remain on the left-hand side, while only terms of the normal state, summarized as term M, remain on the right-hand side:

λ ⁢ φ ¨ ( t ) + ∑ i = 1 K μ i ⁢ φ ˙ s i ( t ) + γφ ⁢ ( t ) + M ψ ( φ ˙ ⁢ ( t ) ) = M ⁡ ( φ ˙ , φ ¨ , t ) ⁢ with ⁢ M ⁡ ( φ ˙ , φ ¨ , t ) = M M ( t ) - J ⁢ φ ¨ ⁢ ( t ) - ∑ i = 1 N k i ⁢ φ ˙ r i ( t ) - M T ( φ ˙ ⁢ ( t ) ) - M I ( φ ˙ ⁢ ( t ) ) ⁢ ∀ t ∈ I = ( 0 , T ] ⊂ ℝ 0 + ⁢ with ⁢ φ ⁢ ( 0 ) = 0 ⁢ and ⁢ φ ˙ ⁢ ( 0 ) = 0

As a result, the anomaly terms are set to zero, so that only terms of the normal state remain, which will be analyzed in more detail in the following.

λ = 0 , μ i = 0 ⁢ ∀ i ∈ { 1 , 2 , … , K } , γ = 0 ⁢ and ⁢ ⁢ M ψ = 0

The decelerating torque can be defined as follows by combining all braking torques of the centrifugal pump 1 into a total braking torque. The result is an equation with an inertia term and a braking torque on the left-hand side and the motor torque on the right-hand side.

J ⁢ φ ¨ ⁢ ( t ) + ∑ i = 1 N k i ⁢ φ ˙   r i ( t ) + M T ( φ ˙ ⁢ ( t ) ) + M I ( φ ˙ ⁢ ( t ) ) = M M ( t ) ⁢ M R ( φ ˙ ⁢ ( t ) ) := ∑ i = 1 N k i ⁢ φ ˙   r i ( t ) + M T ( φ ˙ ⁢ ( t ) ) + M I ( φ ˙ ⁢ ( t ) ) ⁢ J ⁢ φ ¨ ⁢ ( t ) + M R ( φ ˙ ⁢ ( t ) ) = M M ( t )

The inertia moment of the entire rotating system in the normal state, see above description of the formula symbols, can either be calculated in advance or determined experimentally by measuring quasi-stationary curves of torque and angular velocity.

M R ( φ ˙ ⁢ ( t ) ) = f 4 ( φ ˙ ) ⁢ with ⁢ φ ¨ = 0

All braking torques that have been combined to form a total braking torque can now be measured in advance under laboratory conditions as a function of the angular velocity. The following boundary conditions should be taken into account:

• • pump characteristic curve or pump characteristic diagram
  • system characteristic curve, in particular geodetic height difference
  • gate valve or non-return flap and their position (%)

Other boundary conditions can include temperature, fluid viscosity, fluid density, pressure difference, volume flow, pump efficiency, valve opening status, etc. Such data determined in characteristic curve or diagram form can be stored in a database for a specific pump type and/or a specific centrifugal pump 1. The data is subsequently required for comparison with the normal state and is retrieved again.

To identify the at least one fault parameter, a stepwise method is used during the acceleration, whereby unknown fault parameters can be determined step-by-step. Alternatively, other methods are possible that can be used both for an acceleration or deceleration phase and for solving general or special inversion, optimization or parameter identification problems. In particular, there are other mathematical methods for parameter identification or for solving such an inverse problem. The method described in the following is therefore only one of many possible methods and is therefore given merely by way of example.

Basic initial value problem for estimating the fault parameters:

λ ⁢ φ ¨ ⁢ ( t ) + ∑ i = 1 K μ i ⁢ φ ˙ s i ( t ) + γφ ⁢ ( t ) + M ψ ( φ ˙ ⁢ ( t ) ) = M M ( t ) - J ⁢ φ ¨ ⁢ ( t ) - M R ( φ ˙ ⁢ ( t ) ) ⁢ ∀ t ∈ I = ( 0 , T ] ⊂ ℝ 0 + ⁢ with ⁢ φ ⁢ ( 0 ) = 0 ⁢ and ⁢ φ ˙ ⁢ ( 0 ) = 0

Step 1—Estimating the Fault Parameters for an Initial Fault (Breakaway)

Continuous increase of the motor torque until the breakaway of the rotor 4

φ ¨ ⁢ ( t B ) = 0 , φ ˙ ⁢ ( t B ) = 0 , φ ⁢ ( t B ) = 0 ⁢ M B := M M ( t B ) ⁢ M ψ ( 0 ) = M B ( 0 ) - M R ( 0 ) = M B - M T ( 0 ) ⁢ ε := M ψ ( 0 )

First of all, a (potential) additional breakaway torque of the anomaly is determined (the breakaway torque of the normal state is already known). For this purpose, the motor torque is slowly increased continuously from zero until the rotor 4 moves for the first time. The breakaway torque of the normal state is subtracted from this current motor torque. The result is the static frictional torque of the anomaly.

Step 2—Estimating the Constant Fault Parameter (See Also Notes and Calculation Method in Step 4)

This fault parameter is implicitly calculated in step 4, since in step 4 a fault parameter of an occurring velocity-independent constant friction is considered as a coefficient of an angular velocity with the exponent zero. The result is a sliding frictional torque (Coulomb friction) of the anomaly.

Step 3—Estimating the Angle-Related Fault Parameter

After the breakaway, the angular velocity of centrifugal pump 1 is quickly increased to a very small but constant value. The motor torque is then adjusted so that this angular velocity remains constant. Once this angular velocity has been reached, the angle of rotation is measured directly or calculated using an integration method. The angle-related fault parameter is derived from the motor torque according to the angle of rotation.

φ = ∫ t 1 t 2 φ ˙ ⁢ ( t ) ⁢ dt ⁢ where ⁢ ⁢ φ ¨ ⁢ ( t ) = 0 ⁢ and ⁢ φ ˙ ⁢ ( t ) = const ⁢ M M ( t ) = ∑ i = 1 K μ i ⁢ φ ˙ s i ( t ) + γφ ⁢ ( t ) + M ψ ( φ ˙ ⁢ ( t ) ) + M R ( φ ˙ ⁢ ( t ) ) = const + γφ ⁢ ( t ) ⁢ | γ ≈ dM M d ⁢ φ

At the end of this step, a decision is made on further identification based on a comparison with a predefined threshold value.

If the angle-related fault parameter is greater than or equal to a certain threshold value, it can be assumed that the centrifugal pump 1 will come to a rapid or brief standstill after a certain number of revolutions or a certain time period (in particular limited rotation of the rotor 4). In this case, the identification procedure can be aborted.

If the angle-related fault parameter is below a certain threshold value, continue with the following steps (which in particular allows infinite free rotation of the rotor 4). In the following, it is assumed that γ is zero.

In an alternative solution, which can be used for different types of motors, it is firstly assumed that γ is zero and the subsequent step 4 is carried out. If the rotor 4 can rotate freely, step 4 can be carried out completely; the assumption was therefore correct. If the rotor 4 cannot rotate freely (recognizable in particular on reaching the maximum motor torque or a certain threshold value), the execution of step 4 is aborted; the assumption was therefore incorrect. In this alternative solution, γ is simply interpreted as a Boolean variable that indicates an angle-related malfunction. Since such an anomaly ultimately leads to a total blockage, the exact value of γ in terms of a real-valued variable is not important, so that the representation of a Boolean variable is sufficient.

Step 4—Estimating the Speed-Related Fault Parameters

The coefficients for the angular velocities with different exponents and the constant fault parameter can be determined according to the definition of a linear system of equations with K+1 linearly independent equations. The equations are associated with pairwise different constant angular velocities in a certain range between low and high velocities.

It is assumed that all of these angular velocities are greater than a transitional range from static friction to sliding friction (completely subsided breakaway effect) with respect to the potential anomaly. In this way, the additional resistance torque M_ψ is constant and corresponds in the following to the constant fault parameter 8 from step 2. This still unknown fault parameter on the left-hand side can also be interpreted as a coefficient for an angular velocity with the exponent of zero.

φ ¨ ⁢ ( t ) = 0 , φ . ⁢ ( t ) = stepwise ⁢ constant , γ = 0 ⁢ ∑ i = 1 K μ i ⁢ φ . s i ⁢ ( t j ) + δ = ∑ i = 1 K μ i ⁢ φ . s i ⁢ ( t j ) + δ ⁢ φ .   0 ⁢ ( t j ) = M M ( t j ) - M R ( φ ˙ ⁢ ( t j ) ) ⁢ for ⁢ j ∈ { 1 , … , K + 1 } ⁢ and ⁢ t 1 < … < t j < … < t K + 1 ⁢ with ⁢ l ≠ m ⇒ φ ˙ ⁢ ( t l ) ≠ φ ˙ ( t m ) ⁢ for ⁢ ⁢ l , m ∈ { 1 , … , K + 1 }

One possible method is to accelerate the centrifugal pump 1 stepwise with K+1 stages of constant angular velocities, wherein the angular velocity of a current stage is greater than the angular velocity of the previous stage. Thus, each individual time t_j can be associated with a specific stage and a specific constant angular velocity. A standard solver can be used for the final solution of this system of linear equations.

Basically, a system of linear equations with K+1 linear independent equations is formulated to determine the K+1 unknown parameters. The K+1 equations can be associated with the K+1 steps with constant angular velocity. The angular velocities with exponents, on the other hand, form the known or measured entries of the coefficient matrix. The right-hand side of the system of equations corresponds to the vector of the known differences between the motor torque and braking torque at specific points in time.

Another way to solve this linear system of equations, or another way to calculate parameters, could be to consider a larger number of steps in order to (intentionally) define an overdetermined system of equations that is solved approximately in the end.

Step 5—Estimating the Acceleration-Related Fault Parameter

Estimating an additional inertia moment using a high acceleration (e.g. constant acceleration, predefined function, arbitrary function, etc.) in a given angular velocity range

λ ⁢ φ ¨ ⁢ ( t ) ≈ M M ( t ) - J ⁢ φ ¨ ⁢ ( t ) - M R ( φ ˙ ⁢ ( t ) ) - ∑ i = 1 K μ i ⁢ φ .   s i ⁢ ( t ) - δ ⁢ where ⁢ γ = 0

For the angular velocity range under consideration, it was again assumed that the breakaway effect has completely subsided.

In particular, the following three methods can be used for step 5:

• • After step 4, the centrifugal pump 1 can be accelerated from a final speed stage to an operating speed or a maximum speed.
  • After step 4, the motor torque can be briefly reduced or set to zero, whereby the angular speed of the rotor 4 decreases. After a short waiting time, the centrifugal pump can be accelerated to the operating speed or the maximum speed. An advantage over the first variant is that a larger speed range is available for acceleration.
  • After step 4, the motor torque can be set to zero. The run-down behavior of the centrifugal pump 1 is then analyzed directly afterwards. In this case, negative rather than positive acceleration is used to determine the inertia. This method would represent a certain time saving for the determination of all fault parameters.

Classification of the Anomalies

By comparing the K+4 estimated fault parameters with the corresponding threshold values, various anomalies can now be classified. This classification is explained individually for each parameter in the following.

Classification	Normal state	Fault state

initial	Criterion	0 ≤ ε < ε0	0 < ε0 ≤ ε
fault parameter	Result	no additional	static friction
		initial effect	(breakaway)
constant fault	Criterion	0 ≤ δ < δ0	0 < δ0 ≤ δ
parameter	Result	no additional	sliding friction
		constant effect	(independent of speed)
angle-related fault	Criterion	0 ≤ γ < γ0	0 < γ0 ≤ γ
parameter	Result	no additional	required torque too high,
		stiffness effect	no start-up possible, stop
			classification
speed-related	Criterion	∀ i ∈ {1, . . . , K}:	∃ i ∈ {1, . . . , K}:
fault		0 ≤ μi < μi, 0	0 < μi, 0 ≤ μi
parameter	Result	no additional	speed-dependent
		damping effect	friction effects with
			different exponents
acceleration-	Criterion	λ0− < λ < λ0+	0 < λ0+ ≤ λ
related fault			λ ≤ λ0− < 0
parameter	Result	no additional	added or subtracted
		inertia effect	mass in the rotating
			system

The following two methods are particularly suitable for solving the inverse problem. On the one hand, for identifying in particular all fault parameters in steps 2 and 4, the centrifugal pump 1 or the motor 5 of the centrifugal pump 1 can be accelerated in stages and in step 5 the centrifugal pump 1 or the motor 5 of the centrifugal pump 1 can be finally accelerated over a sufficiently wide speed range to the actual operating speed of the motor 5. In each stage of the stepwise acceleration sequence, the system waits until the speed has reached a respective steady-state value. These individual speed values are used to subsequently set up the system of equations for steps 2 and 4. On the other hand, with regard to an acceleration sequence, all speed values can be analyzed as a function of time. In this way, dynamic progressions or accelerations between successive steps can be used. Depending on the resolution of the speed-time curves, this results in a large number of equations and, as a consequence, an overdetermined system of equations. This can then be solved using a least squares method, for example. The advantage of this method relates to the simultaneous processing of steps 2, 4 and 5.

The described embodiments are simply examples, which can be modified and/or added to in a variety of ways within the scope of the claims. Each feature, which has been described for a particular exemplary embodiment, can be used independently or in combination with other features in any other exemplary embodiment. Each feature, which has been described for an exemplary embodiment of a certain category, can also be used in a corresponding manner in an exemplary example of another category.

LIST OF REFERENCE SIGNS

• • Centrifugal pump 1
  • Pump housing 2
  • Suction opening 3
  • Rotor 4
  • Motor 5
  • Impeller 6
  • Control unit 7
  • Sensor 8

In a normal state, accelerating and/or decelerating a rotor of the centrifugal pump for quantifying at least one term of a dynamic rotor model of the centrifugal pump 100 In a fault state differing from the normal state, accelerating and/or decelerating the rotor of the centrifugal pump to detect at least one fault parameter 200 Solving an inverse problem of the dynamic rotor model to identify the at least one fault parameter for detecting and/or determining the anomaly 300