Unbalance detection in rotor systems with active bearings using self-sensing piezoelectric actuators
Introduction
Rotating machinery could be found in many engineering systems and exists in different forms such as in electromechanical machines and turbomachines. Though it is not desired vibration is found in every machine. This could cause discomfort to users, affects performance of the process it drives and might also lead to its failure.
The reason for vibrations stem from faults in the system. This article focuses on unbalance faults affecting a rotor system. An unbalance might originate during the manufacturing of rotor where additional mass could be present or removed at a location of rotating shaft. Due to erosion between parts there could be loss of material leading again to an unbalanced condition. They are compensated during commissioning by placing balancing weights. It is not possible to completely balance a rotating system, as there is a small amount of residual unbalance. The system can only be brought to acceptable vibration limits [1]. This engineering problem has been explored over years by many researchers. Earlier work in [2] estimates unbalance by least squares approach which was later extended in [3] by an equivalent load minimisation approach. Both articles used modal expansion method to identify unbalance in time domain. A much simpler detection is possible in frequency domain as demonstrated by [4] using parameter estimation techniques. Because of its scope to conveniently extend to other fault types this method is used in this present article as well. Other faults which occur in a rotor system are misalignment, cracks, bearing failures, etc. A detailed review of different faults which occur in rotor systems along with the techniques used to identify them are presented in [5]. From these articles it can be inferred that fault detection in rotor systems has been attempted by many researchers since decades. Basic necessity of a condition monitoring unit is to sense the state of the system with the help of sensors. Unlike the studies which have been done previously this article explores the possibility of condition monitoring using virtually reconstructed sensor signals.
Conventionally sensors input information about a system to a control unit in which an algorithm or a controller is incorporated. It takes appropriate action on the system through actuators. Within the context of vibration in rotor systems the controller could perform an active vibration control. Commonly used actuators are active magnetic bearings [6] or piezoelectric actuators [7], [8], both driven by auxiliary electric supply. In this article the functionality of a rotor test setup which is being investigated for vibration control is augmented to detect unbalance faults. Though both these problems have been solved only with physical sensors, the possibility to replace them with virtual signals has been explored in this article. This scientific work also forms an initial study towards simultaneous sensing of faults and actuation for vibration control in rotor systems.
Piezomaterials exhibit sensing and actuating capability due to the inherent coupling between their electrical and mechanical properties. Hence they are used to manufacture both sensors and actuators. Self-sensing in piezoelectric actuators eliminates the need for a sensor as the electrical signals could be reconstructed into mechanical signals with the help of an appropriate mechanism. These efforts began in 90s when capacitance of an actuator was estimated in [9], [10] and approximated to be linear. If the working range of the actuators is more than of its maximum operating voltage the capacitance is non-linear in nature [11]. In this present research work non-linear capacitance is estimated with the help of an experimental procedure. The procedure was suggested in [12], where self-sensing concept of piezoelectric actuators developed in [12] was applied to vibration control of a thin plate and simple beam structure. The reconstruction mechanism from it has been used in this study of a rotor system. In our present study displacement signals are reconstructed from electrical signals of actuators which are placed in bearings. The reconstructed displacement signals were used as control signals in a closed vibration control loop with the help of an adaptive algorithm [13]. This validates the simultaneous use of signals for actuation and sensing. However self-sensing concept in the above works was neither used in condition monitoring or for combined fault detection and vibration control.
The sensory signals used for fault detection in this article are displacement of bearings, reconstructed from actuators which are mounted there. In [14] multiple faults in a rotor were also detected using bearing displacement signals. However the displacement signals were integrated twice from accelerometer located at bearing, ultimately with the use of a sensor. In this article also displacement signal is used even without a sensor. In a previous work [15] faults were detected with self-sensing piezoelectric actuators where time domain methods are used. Because of computational complexity and requirement of a very accurate model time domain methods are not preferred. Instead faults are detected in frequency domain in the present article.
The novelty of this paper lies in the use of the virtual reconstructed signals in the field of fault diagnosis in rotordynamics. Conventional fault detection techniques need a sensor element which provides information about the system. In this research the sensor as a component is not needed, instead sensory signals are provided by actuator by an appropriate reconstruction mechanism. Another distinct topic is detection of faults in closed control loop. An integrated fault detection and vibration control is more close to a real implementation. Very few researchers such as [16] have investigated it. This research makes use of mechatronic system available for vibration control for simultaneous fault detection.
The rotor system subjected to fault diagnosis in this article is a test bench in our institute (Institute for Mechatronic systems in Mechanical Engineering). The test bench has been presented in Section 2. Apart from its construction its mathematical model has also been discussed based on which unbalance faults are detected. Signals to detect faults are reconstructed from electrical signals of piezoelectric actuators as explained in Section 3. The basic equations are presented and a two-step method of self-sensing reconstruction is described. The reconstructed virtual signals are also validated against physical sensors mounted in test bench. Section 4 explains the fundamentals of fault detection using parameter estimation which is then extended to a robust method by weighted least squares. The method is extended in this research to a case with simultaneous actuation and fault detection. Section 5 explains the different experiments performed in the actual test bench and the results are presented and discussed in Section 6.
Section snippets
Structure and components
The test bench employed in this research work has a rotor shaft with a rotating mass and mounted in three bearing planes. The shaft with a length of 1.17 m weighs 22.5 kg together with the rotating mass. This mass represents a turbine of a turbopropeller aircraft engine. A schematic of the test bench is shown in Fig. 1 and its CAD diagram can be seen in Fig. 2. It can also be observed from the figures that the shaft on one side is mounted on a double bearing assembly where each bearing plane has
Basic equations
Piezomaterials were first discovered by Marie and Pierre Curie in natural crystals such as Quartz. In commercial applications today artificial materials are created such as Lead-Zirconate-Titanium (PZT) which has much pronounced piezoelectric effect than natural crystals. The fundamental equations of piezoelectric materials are given in Eq. (1).
The individual variables and material parameters are defined in Table 1. The variables are tensors defined for a generalised coordinate
Equations of motion
In this research work unbalance faults are detected in rotor systems using a model-based approach. Parameter estimation method is used in frequency domain, where unbalance is the unknown parameter to be detected. The steps are explained below in detail.
The basic equation of motion is given in Eq. (9), where M, D, G and K are mass, damping, gyroscopic and stiffness matrices of the rotor system respectively. These matrices are the result of
Simulation and experiments in test bench
In order to determine the effectiveness of self-sensing piezoelectric actuators to detect unbalance parameters, simulation was carried out which are also performed experimentally in real test bench. In all cases unbalances of defined magnitude are placed in rings which are distributed along the length of shaft as shown in Fig. 11. A photo of a ring is shown in Fig. 11b in which unbalances could be screwed in any desired angular position.
The rotor was driven within the frequency range [133–200
Simulation results
The unbalances detected out of the three simulation cases as explained in Section 5.1 are presented in Table 2. In all cases a test unbalance of 100 gmm at an angular position 0° is placed in each ring one after the other. The table shows magnitude and phase of unbalance detected by the algorithm. Apart from them relative error in magnitude and absolute error in phase are also mentioned.
From Table 2 it is evident that an ideal model assumption could detect unbalances precisely whereas the
Conclusion
In this research work unbalance faults were detected in frequency domain using parameter estimation method. These faults are characterised by three parameters which are unbalance magnitude, phase and location. To overcome the problem of outliers in measured data weighted least squares method is used. The weights are generated from theory of M-estimators which make unbalance detection robust. Displacement of piezoelectric actuators reconstructed using their self-sensing property are used instead
Acknowledgments
The entire research work was financed by German Research Foundation (DFG) within their Research Training Group “GRK1344”, with support from Rolls-Royce Deutschland Ltd and Co. KG. The authors earnestly acknowledge and thank them.
References (19)
- et al.
Identification of unbalance in a rotor bearing system
J. Sound Vib.
(2011) - et al.
Simultaneous piezoelectric sensing/actuation: analysis and application to controlled structures
J. Sound Vib.
(1994) - et al.
Identification of multiple faults in rotor systems
J. Sound Vib.
(2002) - et al.
Self-sensing techniques of piezoelectric actuators in detecting unbalance faults in a rotating machine
Procedia Eng.
(2016) Robust estimate of excitations in mechanical systems using M-estimators-theoretical background and numerical applications
J. Sound Vib.
(2008)- International Standards Organisation, Mechanical Vibration – Rotor Balancing – Part 14: Procedures for Assessing...
- et al.
Model based fault identification in rotor systems by least squares fitting
Int. J. Rotating Mach.
(2001) - N. Bachschmid, P. Pennacchi, A. Vania, G. Zanetta, L. Gregori, Case studies of fault identification in power plant...
- et al.
Rotordynamic faults: recent advances in diagnosis and prognosis
Int. J. Rotating Mach.
(2013)
Cited by (27)
A multi-function integrated PVDF transducer for fault detection and speed measurement of cylindrical roller bearings
2024, Mechanical Systems and Signal ProcessingA modified sensorless position estimation approach for piezoelectric bending actuators
2021, Mechanical Systems and Signal ProcessingCitation Excerpt :In order to overcome the mentioned problems, sensorless position estimation approaches have been proposed. These methods use piezoelectric material as a sensor and actuator simultaneously [10]. They are mostly based on the charge measurement to cope with the piezoelectric inherent nonlinearities.
A new sensor inspired by the lateral-line system of fish using the self-powered d<inf>33</inf> mode piezoelectric diaphragm for hydrodynamic sensing
2020, Mechanical Systems and Signal ProcessingCitation Excerpt :Piezoelectric materials provide an interesting alternative to address this issue. Based on the piezoelectric effect, they have been widely used as energy harvesters [23–28] and sensors [29–31]. When piezoelectric material deforms, charges will be induced at the surface.
A method to minimize stage-by-stage initial unbalance in the aero engine assembly of multistage rotors
2019, Aerospace Science and TechnologyCitation Excerpt :But above methods only focused on the geometric error propagation and did not research the mass eccentric deviation propagation process in the assembly. Besides, the current researches only reduce the initial unbalance of final assembly using the balancing methods and devices [30–33], and not minimize stage-by-stage initial unbalance in the assembly. Therefore, it is necessary to solve the problem that the initial unbalance can not be controlled accurately in the aero engine assembly of multistage rotors.