Unbalance Identification Research Articles

Threshing cylinder unbalance detection using a signal extraction method based on parameter-adaptive variational mode decomposition

The threshing cylinder will wear and deform during the threshing process, causing dynamic balance problems. The combine harvester has multiple vibration excitation sources and a complex vibration environment, making it challenging to extract weak unbalanced signals from strong background noise. A novel three-step filtering framework is proposed in this paper. A zero phase filter was used as the pre-processing layer to filter out the high frequency components in the original signal and reduce the number of parameter-adaptive variational mode decompositions (PAVMD) needed. The PAVMD was used to decompose the non-stationary vibration signal before Adaptive Neuron Linear (Adaline) function was used to fit sinusoidal signal parameters. A measurement index, termed the correlation amplitude (CA) index, is constructed. The parameterisation of PAVMD was guided by the CA index, and the modal component of the unbalanced fault features were located. The simulation and real cylinder signals proved that the proposed method could effectively extract unbalanced signals under noise interference, and the unbalance was identified accurately by the influence coefficient method. Experiments on a threshing cylinder showed that the amplitude identification error was <24 g in single-sided unbalance identification, and the amplitude identification error was <27 g in double-sided unbalance identification. The proposed method had high robustness and small identification error, especially under short-time working conditions, compared with other similar approaches.

Intelligent system design for identification of unbalance and misalignment using Fuzzy Logic methods

Intelligent system design for identification of unbalance and misalignment using Fuzzy Logic methods

A novel rotor dynamic balancing method based on blade tip clearance measurement without the once per revolution sensor

The existence of the aeroengine casing, limited monitoring points, and multi-fault characteristics make obtaining the rotor’s vibration transmission characteristics challenging, resulting in difficulties accurately identifying the rotor unbalance. This paper utilizes a high-frequency composite sensor to monitor the engine’s blade tip clearance (BTC) and extracts unbalanced information from BTC signals for rotor dynamic balancing, while avoiding the need for the once per revolution (OPR) sensor. First, the vibration characteristics of the rotor-blade system under multi-fault conditions are investigated. Then, based on BTC measurement, a none OPR method and an unbalance identification method are proposed, in which the radial vibration of the blade tip in the BTC signals at different speeds is extracted and operated in the time domain to obtain the rotor unbalanced vibration, the signal is reconstructed, and cross-correlation analysis is used to accurately identify the magnitude and phase of the unbalanced signal. Finally, a rotor test bench is utilized for experimental verification. The results reveal that the dynamic balancing method based on the BTC signal can more precisely identify the rotor unbalance than the traditional rotor dynamic balancing method. The application of this technique will effectively improve engine health management and fault prediction.

Balancing of Asymmetric Rotor‑Bearing Systems Using Modal Masses Array Calculated by Algebraic Identification of Modal Unbalance

Balancing of Asymmetric Rotor‑Bearing Systems Using Modal Masses Array Calculated by Algebraic Identification of Modal Unbalance

Unbalance identification for a practical turbofan engine using augmented Kalman filter improved with the convergence criterion

Kalman filter has emerged as a powerful tool for unbalance identification in rotating machinery. Recently, the augmented Kalman filter combined with the finite element model has grown up and projects its potential for complex rotor systems. This paper investigates the application of the augmented Kalman filter (AKF) to a practical turbofan engine. The current study reveals that using steady-state responses as measurements can cause fluctuation in the estimated results, even divergence for some cases, while the available signals in practice are steady-state responses generally. To the authors' knowledge, this practical problem is revealed for the first time. To address the problem, the convergence criterion is employed to improve the AKF and formulates the adaptive fading augmented Kalman filter (AFAKF) proposed in this paper. Results indicate that the increase of the amplification factor, the insufficient measurement points, and the complexity of the dynamic model can all lead to the deterioration of the estimated unbalance. The proposed AFAKF method shows favorable convergence and can achieve accurate estimation with less than 5% relative errors, and the superiority over AKF in computation cost is also observed.

Assessing the Contribution of ECa and NDVI in the Delineation of Management Zones in a Vineyard

Precision fertilization implies the need to identify the variability of soil fertility, which is costly and time-consuming. Remotely measured data can be a solution. Using this strategy, a study was conducted, in a vineyard, to delineate different management zones using two indicators: apparent soil electrical conductivity (ECa) and normalized difference vegetation index (NDVI). To understand the contribution of each indicator, three scenarios were used for zone definition: (1) using only NDVI, (2) only ECa, or (3) using a combination of the two. Then the differences in soil fertility between these zones were assessed using simple statistical methods. The results indicate that the most beneficial strategy is the combined use of the two indicators, as it allowed the definition of three distinct zones regarding important soil variables and crop nutrients, such as soil total nitrogen, Mg2+ cation, exchange acidity, and effective cation exchange capacity, and some relevant cation ratios. This strategy also allowed the identification of an ionic unbalance in the soil chemistry, due to an excess of Mg2+, that was harming crop health, as reported by NDVI. This also impacted ECa and NDVI relationship, which was negative in this study. Overall, the results demonstrate the advantages of using remotely sensed data, mainly more than one type of sensing data, and suggest a high potential for differential crop fertilization and soil management in the study area.

Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotor: A Theoretical and Numerical Investigation on the Continuous Model and Analytical Solution for Unbalance Responses

Continuous rotor dynamics remains stagnant. In this paper, aim at multi-span and multi-disc rotor-bearing system, the continuous rotor dynamic analysis method (CRDAM) is proposed. The force acting on the shaft by the rotating eccentric disc is simulated as a point force. The counterforce of bearing is also considered as a point force. The shaft is considered free-ended. A continuous rotor dynamic model is obtained and an analytical solution is proposed to express the unbalance response as function of the position, unbalance, support stiffness and damping. The proposed method is validated by numerical experiments in which unbalance responses obtained by it are compared with that obtained by the two classical methods the finite element method (FEM) and Ricatti method. The results indicate that the proposed method is applicable to calculating unbalance response of multi-disc and multi-span rotor. Moreover, it is closer to FEM than Ricatti and can be applied to actual high speed rotors. Among the three methods, the calculating speed of Ricatti is the fastest, CRDAM is the second fastest and FEM is the slowest. The proposed method, which solves the forward problems of the continuous rotor dynamics for the multi-disc and multi-span rotors, can provide theoretical basis for further studies on inverse problems such as identification of rotor unbalance and bearing stiffness and damping coefficients without test runs and external excitations.

Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotors: A Theoretical and Numerical Investigation of the Identification of Rotor Unbalance from Unbalance Responses

Rotor unbalance identification plays a critical role in balancing rotors. In this paper, concerned with multi-disc and multi-span rotor-bearing systems, two novel algorithms called the Single Direction Algorithm (SDA) and the Two Orthogonal Direction Algorithm (TODA) are proposed for identifying rotor unbalance from unbalance responses. A matrix method is proposed to solve the problem of the equations being non-linear transcendental, there being too many unknown variables in the equations, and rotor unbalances and bearing coefficients being coupled together. The unbalance responses at all the eccentric discs are necessary for identifying their unbalances. Numerical simulations are conducted to validate the proposed methods. Moreover, an adjustment point is found, and a proper sensor resolution is suggested to achieve high identification accuracy by means of numerical studies. In addition, the identification accuracy of SDA is better than TODA, and SDA is more practical and suitable for medium-speed and high-speed rotors. The proposed algorithms have the flexibility to incorporate any number of bearings and discs and provide a technique for monitoring rotor unbalance without test runs or external exciters.

Dynamic unbalance identification and quantitative diagnosis of cardan shaft in high-speed train based on improved TQWT-RBFNN-NSGA-II method

In order to identify and quantitatively diagnose the dynamic unbalance of the cardan shaft equipped in high-speed trains, firstly, a numerical simulation model of the vehicle considering the cardan shaft dynamic unbalance is established. Secondly, the vibration and acceleration response of the motor and gearbox under different cardan shaft offset conditions are calculated. In order to better extract the feature signal related to the shaft unbalance, a novel algorithm based on the improved tunable Q-factor wavelet transform (TQWT) method is proposed. On this basis, in order to build the relationship between the unbalance and the characteristic frequency amplitude intensity (AI) index, radial basis function neural network (RBFNN) is used. In addition, non-dominated sorting genetic algorithm II (NSGA-II) is used to find the optimum Pareto solution of a combination of offsets to quantitatively analyze the cardan shaft dynamic unbalance. The results show that the proposed method can identify dynamic unbalance effectively and its magnitude quantitatively with an error of less than 15 %.

Experimental and numerical investigations on an unbalance identification method for full-size rotor system based on scaled model

Perfect balance of rotor systems is difficult to achieved in practical engineering and some amount of unbalance is unavoidable. However, identifying the unbalance value of full-size rotor system is difficult, time-consuming and sometimes dangerous. Aiming at this issue, this paper proposes an unbalance identification method for full-size rotor systems. The unbalance value can be identified through the scaling laws and scaled model, where the scaling laws are developed by incorporating the least squares method and sensitivity analysis. The effectiveness of the proposed method is verified by the numerical and experimental case studies, where the distortion in geometrical dimension is taken into account. The numerical case identifies the unbalance value of a rotor system and evaluate the identification errors. Furthermore, the experimental testing for the prototype and model test rigs is carried out. The results show that the unbalance values can be accurately identified by the proposed method. This allows one to identify the unbalance value of full-size rotor system through a small scaled model.

Model-based initial residual unbalance identification for rotating machines in one and two planes using an iterative inverse approach

Model-based initial residual unbalance identification for rotating machines in one and two planes using an iterative inverse approach

An innovative virtual trial misalignment approach for identification of unbalance, sensor and active magnetic bearing misalignment along with its stiffness parameters in a magnetically levitated flexible rotor system

A model-based identification algorithm derived from an innovative virtual trial misalignment (VTM) strategy is developed to identify the rotor unbalance, active magnetic bearings (AMBs) residual misalignment and their displacement and current stiffness parameters. The VTM approach is aligned with the similar concept of trial unbalance utilized in balancing of the rotor. This virtual method for providing the trial misalignment to the rotor is more reliable and effective than the physical trial misalignment, as the method does not need test runs and a precise model of the rotor-sensor-bearing system. The mathematical modelling for the non-contact displacement sensors offset from the rotor center has also been presented and even the offset amounts are identified using this novel approach. To illustrate the proposed methodology, an unbalanced and misaligned flexible rotor system mounted on multiple AMBs has been considered. Non-collinearity between the rotor operating axis and the axis of supported AMBs is the prime cause of misalignment (combination of parallel and angular) fault. A finite element method with a gyroscopic dynamic condensation scheme is employed for acquiring the reduced form of system equations. The numerically generated frequency domain responses are further employed in the identification algorithm for estimating the rotor-AMB system and faults parameters. Besides this, the different levels of the random noise signal as well as rotor modelling errors are added in the developed VTM based methodology to check its efficacy and sensitiveness in a practical rotor model.

Axial unbalance identification of GyroWheel rotor based on multi-position calibration and CEEMDAN-IIT denoising

Axial unbalance of the rotor is an important origin of disturbance torque for the GyroWheel (GW), which leads to constant torque and measurement drift. This paper proposes a novel axial unbalance identification strategy based on multi-position calibration. Based on the gimbal assembly support characteristics of the tilting rotor, the disturbance torque model caused by the offset from the support center to the centroid is established. Combined with multi-position calibration, the least square method is introduced to estimate the drift error coefficients, which are taken as the equivalent vibration response. The relationship between the unbalanced excitation by adding trial weight and the vibration response helps to calculate the original unbalance. To avoid the non-stationarity of the current signal affecting the estimation accuracy of the drift error coefficients, a signal process with consideration of CEEMDAN-IIT denoising is exploited. The experiments are performed to verify the superior performance of the proposed identification method.

Unbalance identification method based on SINDy applied to an SFD rotordynamic system

In recent years, there has been an increasing interest in Data Science and Machine Learning in different topics like financial and health, this have led to start using these methods on engineer applications. This paper is focus on identify the equivalent unbalance on Squeeze Film Damper – SFD bearing using a recent machine learning technique “Sparse Identification of Nonlinear Dynamics – SINDy”. Four different cases will be examined from Bonello’s work, all of which we introduce 4 different conditions of noise to the acceleration of the system. The data for this work was obtained via a simulation of the SFD system reported on Bonello’s thesis. From the simulation only the last 20 cycles were used to feed the SINDy. This study uses a combinatorial polynomial search space over preselected functions with the purpose to identify the equivalent imbalances. Both hyperparameters: the degree of the combinatory k and the threshold value λ remaining static during all the study. There was no error between the original equations and the identified system.

Model based estimation of inertial parameters of a rigid rotor having dynamic unbalance on Active Magnetic Bearings in presence of noise

Unbalance in rotors is known as the primary source of excitation, the state of unbalance changes over time and, therefore, industrial rotors require online or smart identification and attenuation of unbalance for smooth operation. To begin with, this paper proposes the use of Active Magnetic Bearings (AMBs) to identify the unbalance. Unbalance is defined as the location of centre of mass of the rotor and orientation of the axes of principal mass moments of inertia, both with respect to the spin-axis, assumed as the geometric axis of symmetry of rotor. Non-uniform distribution of mass makes a rotor dynamically unbalanced. The centre of mass shifts from the spin-axis and none of the principal axes of inertia is aligned with it. Dynamic behaviour of such a rotor is modelled by a set of differential equations with time varying coefficients. A rigid rotor is assumed to be supported on two AMBs with all known characteristics. A methodology based on modelling and simulation is proposed to determine the eccentricity and the orientation of the principal axes of inertia (angles of its skewness) by utilizing the force and response of the rotor recorded by each AMB. The median of simulated inertial properties are shown to be in close agreement with their actual values. The proposed methodology is also found robust enough in the presence of different types of simulated noise used to pollute signals from the bearings. Therefore, the methodology is suitable for online identification of inertial properties of a rotor.

Investigation on transient dynamic balancing of the power turbine rotor and its application

In the dynamic balancing procedure of the rotor system, the unbalance is determined as a principal parameter which should be identified firstly. In actual engineering, the interference of external noise on the rotor is usually the main factor influencing the identification. In this paper, we focus on the unbalance identification of the power turbine rotor while the vibration response is influenced by signal interference during the balancing process in actual engineering. Fast Fourier Transform (FFT) and wavelet transform are used to analyze the collected original signal. Butterworth filter and Chebyshev type I filter are employed to test signal processing. The transient dynamic balancing method and the single plane influence coefficient method are used to balance the three balancing bosses of the rotor, and the balance efficiency is compared. The results show that, the signal fluctuation of boss 3 in high-frequency band is less than boss 1 and boss 2. Butterworth filter is more effective than Chebyshev type I filter in filtering the transient response data. The transient dynamic balancing method requires one test run without any trial-weights. More importantly, compared with the influence coefficient method, the transient dynamic balancing method has a better balancing effect.

Flexible rotor balancing without trial runs using experimentally tuned FE based rotor model

A method based on experimentally calibrated rotor model is proposed in this work for unbalance identification of flexible rotors without trial runs. Influence coefficient balancing method especially when applied to flexible rotors is disadvantaged by its low efficiency and lengthy procedure, whilst the proposed method has the advantage of being efficient, applicable to multi-operating spin speeds and do not need trial runs. An accurate model for the rotor and its supports based on rotordynamics and finite elements analysis combined with experimental modal analysis, is produced to identify the unbalance distribution on the rotor. To create digital model of the rotor, frequency response functions (FRFs) are determined from excitation and response data, and then modal parameters (natural frequencies and mode shapes) are extracted and compared with experimental analogies. Unbalance response is measured traditionally on rotor supports, in this work the response measured from rotating disks instead. The obtained results show that the proposed approach provides an effective alternative in rotor balancing. Increasing the number of balancing disks on balancing quality is investigated as well.

Fault parameter identification in rotating system: Comparison between deterministic and stochastic approaches

Fault identification is a recurrent topic in rotating machines field. The evaluation of fault parameters allows better maintenance of such expensive and, sometimes, large machines. Unbalance is one of the most common faults, and it is inherent to rotors functioning. Wear in journal bearings is another common fault, caused by several start/stop cycles – when at low rotating speed, there is still contact between shaft and bearing wall. Fault parameter identification generally uses deterministic model–based methods. However, these methods do not take into account the uncertainties inherently involved in the identification process. The stochastic approach by the Bayesian inference is, then, used to account the uncertainties of the fault parameters. The generalized polynomial chaos expansion is proposed to evaluate the inference, due to its faster performance regarding the Markov chain Monte Carlo methods. Deterministic and stochastic approaches were compared; all were based on experimental vibration measurements of the shaft inside the journal bearings. The Bayesian inference with the polynomial chaos showed reliable and promising results for identification of unbalance and bearing wear fault parameters.

Investigation into the influence of bearings nonlinear forces in unbalance identification

Rotating machines are key components in several industrial sectors, mainly, in energy generation. In this way, a rotating component supported on hydrodynamic bearings creates typical problems, being high vibrations amplitudes due to unbalance, one of the most common. To avoid failures and ensure a safe operation, the rotor should be balanced, and influence coefficient methods are usually used. Since balancing by the traditional influence coefficients method requires trial masses, the machine can sometimes experience a long setup time, causing financial losses. Also, this method assumes a linear rotor response that can hamper the balancing procedure for nonlinear situations, which happens when the rotor experiences high vibrational motion. Thus, this work proposes a balancing identification that considers nonlinear bearings and avoids trial masses. For this, a mixed-integer gradient-based optimization is presented. The theoretical model of a rotor supported by hydrodynamic bearings is obtained using the Finite Element method and solving the Reynolds equation. In order to save computational time, the bearing forces are approximated by a fifth order Taylor series expansion. The presented results show that nonlinear bearing consideration can improve the machine diagnosis.

Dynamic analysis and identification of unbalance and misalignment in a rigid rotor with two offset discs levitated by active magnetic bearings: a novel trial misalignment approach

Rotating machinery is an essential and crucial component of numerous mechanical systems in modern industries, transport vehicles, and in several other applications. Excessive vibrations on rotating equipment due to multiple faults may cause catastrophic failure in machines and lead to hazardous accidents. So, there is a need for perceiving the dynamic nature and identifying the faults for the safe, smooth and effective operation of machines. This paper proposes a novel trial misalignment approach to estimate the misalignment with a similar concept as the trial unbalance in the rotor balancing. Active magnetic bearing (AMB) misalignment with the rotor has been investigated with residual misalignment and additional trial misalignment cases. Additional trial misalignments are provided in addition to the unknown misalignments of the residual misalignment case. For the execution of this methodology, the dynamic model of a four-degree-of-freedom unbalanced and misaligned rigid rotor with two offset discs supported by two active magnetic bearings has been mathematically developed. The offset discs result in the gyroscopic effect at high rotor speeds. Equations of motion of the rotor-AMB system have been derived and solved to generate the time domain rotor displacement and controlling current responses at AMB positions. A fast Fourier transform technique has been utilized to convert the time domain responses into the frequency domain for estimation of unbalance eccentricities and phases together with force-displacement and force-current stiffnesses of misaligned AMBs as well as AMB's constant forces using the developed identification algorithm. Identified values of AMB's parameters for both residual and additional trial misalignment cases are evaluated to estimate the four unknown misalignments. Testing of the algorithm has also been carried out at multiple spin speeds against measurement signal noise in rotor responses and bias errors in rotor system parameters to check its effectiveness and robustness. The algorithm is found to be exhibiting excellent.