Rotor-bearing System Research Articles

Fault diagnosis in rotors using adaptive neuro-fuzzy inference systems

Condition monitoring of rotor dynamic systems is emerging research in recent years. The proposed research is a condition monitoring methodology based on Adaptive Neuro-Fuzzy Inference Systems (ANFIS) to detect the open cracks in the single disk rotor-bearing system. Condition monitoring systems generally requires a large amount of processed data for a specific output. The proposed methodology uses the same input data to train two different ANFIS without compromising on the accuracy of the results. The response of rotor-bearing system is generated by using finite element model analysis and harmonic balance method. All simulations are programed in MATLAB programing software. The effects of open groove or wedge cracks (notch crack) on natural frequency and resultant operational response (nodal deflections) of rotor-bearing systems are analyzed. Response orbit at 3× resonance of first natural frequency is analyzed to diagnose the crack in rotor shaft. Resultant operational response (Absolute response due to crack) is recorded for various crack locations and crack depths. Continuous Wavelet Transforms (CWT) are used, to extract the features from operational deflection shape (from operational response) to detect the crack location and their severity (depth). Location of maximum CWT coefficients provides the close vicinity of crack and their magnitude provides the severity of crack. Crack as small as 1% of crack depth to diameter ratio can be identified by CWT. ANFIS are used as a machine condition monitoring methodology to diagnose the crack and predict the crack parameters (crack location and depth). Two Parallel ANFIS are trained to predict the crack parameters. ANFIS-1 is trained for crack location and ANFIS-2 is trained for crack depth. CWT coefficients, maximum response amplitude at the vicinity of crack, and first three natural frequencies are provided as input to both ANFIS-1 and ANFIS-2 for training. The trained condition monitoring methodology accurately detects (predict) the crack location (ANFIS-1) and crack depth (ANFIS-2) with root mean squared error of 0.0833 and 0.137916 respectively.

Nonlinear Analysis of Rotor-Bearing-Seal System with Varying Parameters Muszynska Model Based on CFD and RBF

The computational fluid dynamics (CFD) combined with radial basis function (RBF) method were adopted to obtain the response surface of the Muszynska nonlinear seal force model coefficient with two variables: eccentricity and rotation speed. During the implementation of the simulation, three coefficients of the seal force model were calculated in each sub-step according to the current state of the rotor-bearing seal system; following which the rotor dynamics analysis with varying parameters was realized. As with the traditional constant coefficient method, the first-order critical speed of the system was obtained, and the bifurcation point and oil film whirl of the system response were identified. The difference is that the coefficients of the traditional method ordinarily do not change with the state of the system. Comparing the results of the varying parameter method with those of the traditional method, it can be seen that the speeds of the system corresponding to the bifurcation and oil film whirl are different. The varying parameter rotor dynamics simulation method proposed in this paper provides a new way of analyzing the nonlinear characteristics of rotor-bearing-seal systems.

Active Balancing Disk of Rotor-Bearing Systems Based on Vibration Amplitude Data: MATLAB-Aided Wireless Control

Active Balancing Disk of Rotor-Bearing Systems Based on Vibration Amplitude Data: MATLAB-Aided Wireless Control

Stability of a Rotor Partially Filled With Fluid: Test Facility and Experimental Results

Abstract Fluid trapped in a hollow, rotating component may lead to subsynchronous vibrations, resulting in high vibration amplitudes. This asynchronous response is observed around 0.55–0.92× after passing through the first critical frequency and affects large rotating equipment such as centrifuges, fluid-cooled gas turbines, and jet engines. A test rig is designed to evaluate this self-excited asynchronous vibration. The high-speed rig comprises of a flexibly-mounted rotor partially filled with fluid, with an overhung test chamber providing an unobstructed view of the liquid surface. A squeeze film damper provides external damping and allows operation through the asynchronous response when the test chamber contains a large amount of fluid. The results show the rotor response with different fluid depths and external damping values as the rotor-bearing system transverses the first critical speed (cylindrical mode). The experiments show that only a small amount of oil (∼20 mL) is required to induce asynchronous excitations, and increasing the fluid depth increases the amplitude of vibration. External damping slightly decreases the response, but it also expands the range of frequencies where asynchronous vibrations occur. At a given speed ratio, the vibrations reach a limit cycle, and subsequently, begin to drop as the rotor speed increases past the first critical speed.

Modal balancing for ball bearing-rotor system using nonlinear normal modes

Rotor dynamic balancing procedure relies on the linearisation hypothesis of the rotor system. However, some mechanical elements constituting a rotor system behave in various nonlinearities, such as the contact force and radial internal clearance between rolling balls and races for a rotor-bearing system. To balance a nonlinear rotor system, the traditional modal balancing method must be extended. This paper investigates the modal balancing method for a rotor-bearing system based on nonlinear normal modes (NNMs). The proposed algorithm includes three main steps. First, compute the NNMs and express nonlinear modal shapes using complex Fourier series. Second, describe the unbalance response as a complex amplitude containing higher harmonics. Third, estimate the correction coefficient of each harmonic, then compute the unbalance correction of each mode of interest until the total unbalance corrections are obtained. Hertz contact force and two different sizes of radial internal clearances of the ball bearings are considered during the balancing simulation. The responses after balancing with NNMs are present and compared with the linear modal method to demonstrate the accuracy and effectiveness of the proposed method.

The Effects of Interval Uncertainties on Dynamic Characteristics of a Rotor System Supported by Oil-Film Bearings

Rotating systems equipped with oil-film bearings are critical and common in many industrial machines. There are various non-random uncertainties in such fluid-lubricated dynamic systems. It is important to quantify the effects of uncertainties without adequate statistical information on the dynamics of rotor-bearing systems. In this paper, a rotor system with oil-film bearings at both ends is investigated considering many interval uncertainties. The rotating system is modeled in a deterministic sense. The Chebyshev interval method is used to track the propagation of different uncertainties. Deviations in the steady state responses, time history, and shaft orbits are calculated and comparatively discussed. Influence patterns of different interval parameters and dispersions in various dynamics are presented in detail. It is found that there can be global and local impacts as well as cumulative effects caused by multi-source uncertainties. The findings of the present study could be helpful for a more insightful dynamic analysis of rotor-bearing systems as well as their optimal design and maintenance.

Simulation and experimental analysis of rotor-bearing system with rolling element bearing fault in axial piston pump under churning condition

Axial piston pumps have been widely studied and applied in engineering applications. Generally, traditional simulation models are established to analyze the vibration characteristics of the pump without the churning effect of the gap annular flow. A new vibration model of a rotor-bearing system considering the oil churning effect and time-varying excitation introduced by localized faults on the rolling element bearing is proposed in this work. External forces on rotor-bearing system are solved to obtain time-varying displacement and contact stiffness coefficient based on lump mass method. The dynamic model has constructed to analyze the dynamic characteristics of rotor-bearing system with bearing faults. The validity of the model is verified by comparing the simulation results with the analysis results and the experimental results. The findings reveal that rolling element bearing with localized faults alters the vibration characteristics of the rotor-bearing system. Both the simulation results and the experimental results show the fault characteristic frequency of the rotor-bearing system and the explicit component of its harmonics. The fault characteristic frequency of rotor-bearing system with bearing faults is consistent with the simulation result, and the error is less than 10%. The spectrum of the experimental and simulated signals is similar and indicates the validity of the dynamical model.

Torsional vibration feature extraction method from lateral vibrations based on decomposed forward and backward whirl motions

The high-speed turbomachinery rotor-bearing system faces potential torsional vibration problems due to its large span, flexible structure, and the wildly use of variable frequency drive systems. In this paper, a method based on the Hilbert technique to extract weak torsional vibration signals from measured lateral vibration signals is proposed, and the forward whirl signal is constructed to make full use of the information contained in lateral vibration signals. Furthermore, it was found that the forward whirl signal has better stability and stronger anti-noise ability after comparing the utilization of horizontal, vertical, forward, and backward vibration signals applied to the proposed method to extract the torsional vibration signal from simulated vibration responses of a rotor system. Numerical simulation and experimental results indicate that the method can detect torsional vibration signals accurately, with a high resolution in frequency estimation. This method enables additional monitoring of torsional vibrations for machines without dedicated torsional vibration testers and provides a convenient way to measure torsional vibrations in engineering applications.

Transient nonlinear dynamics of the rotor system supported by low viscosity lubricated bearing.

This paper clarifies the mechanism of the dynamic characteristics of the water-lubricated bearing-rotor coupling system at different operating stages. Dynamic models of the water-lubricated bearing-rotor system under fluid lubrication are developed. The influences of different operating modules on the dynamic characteristics are investigated. The effects of different speeds, different loads, and different impacts are analyzed. The time domain responses, axis orbits, and phase diagram are gained. Velocity has impacts on the vibration performance of the shaft. The external load has slight effects on the vibration characteristics. Different forms of transient impacts have different effects on the vibration characteristics. The validity of the new-built models is verified by experiments. Results provide theoretical foundations for the optimum design for such bearing-rotor systems.

Rotor vibration control using tilting-pad journal bearing with active pads — Numerical and experimental results

Rotating machines are elements of great importance to the production chain, and they can eventually operate under unpredicted or off-the-norm conditions, thus causing failure and significant economic losses. One way of reducing the consequences of such off-the-norm operation of these machines is the modification of the characteristics of the bearings that support the rotor. Active bearings can be a solution to this problem because they can change the dynamic characteristics of the machine during operation without needing machine stops. The present work presents a tilting-pad journal bearing whose pads are controlled by electromagnetic actuators (an innovative design solution). By mounting the electromagnetic actuators in the bearing casing behind the pads, one can exert electromagnetic forces on the pads and make them change their angular position about the bearing. Hence, one can modify the dynamic characteristics of the rotor-bearing system for desired and more appropriate values for a given operational condition, thus reducing the need for machine stops and the consequent economic losses. In this work, we present the system in a test rig designed for the system’s proof of concept, and both numerical and experimental results are provided for open- and closed-loop operating conditions. The bearing and the rotor are modeled by rigid-body dynamics, and the lubricant interface is modeled by the Reynolds equation. The dynamics of the electromagnetic actuators are identified experimentally and used in the model as an empirical model. A proportional–derivative controller is adopted in the closed-loop conditions. The results show the effectiveness of the system in reducing the lateral vibrations of the rotor during operation, and one observed a good correlation between the numerical and the experimental results.

A review on deep learning based condition monitoring and fault diagnosis of rotating machinery

Rotating machine faults are unavoidable; thus, early diagnosis is essential to avoid further damage to the machine or other machine attached to it. Various signal analysis based conventional techniques have been developed and used in the industries to identify various defects in the rotating machines. In last two decades, researchers have shifted their focus to automated or intelligent fault diagnosis based on Artificial Intelligence (AI) techniques due to a variety of issues in conventional fault analysis techniques, such as a dependence on machine operating circumstances, human interference, and expert abilities. In AI based techniques, various machine learning (ML) and deep learning (DL) techniques have been successfully applied for fault diagnosis of various rotating machines. From last half decade DL have been gaining popularity due to its attractive characteristic of automated feature learning and solving big data, unbalanced data, big computational burden and over-fitting problems of conventional ML techniques. Advances in DL methodologies have prompted interest in DL based intelligent fault diagnosis in the industry in the last five to 6 years. This review paper summarizes recent research and developments on DL based fault diagnosis in the last five to 6 years for various critical rotating machineries in industry such as electric motors, rotor-bearing systems, gear and gearbox, wind turbines, pumps, and compressors.

Nonlinear Dynamic Analysis of Gas Bearing-Rotor System by the Hybrid Method Which Combines Finite Difference Method and Differential Transform Method

Gas bearings have been widely applied to high-speed rotating machines due to their low friction and high rotational speed advantages. Nevertheless, gas lubrication is low viscosity and compressible. It causes the gas bearing-rotor system easy to produce self-excited vibration, which leads to instability of the rotor system and hinders the increase of rotor system speed. It is necessary to study the nonlinear behaviors of the aerostatic bearing-rotor system and the nonlinear vibration of the gas bearing-rotor system, especially considering the distribution mass and flexible and gyroscopic effects of the real rotor. In this paper, the nonlinear behavior of the gas bearing-rotor system is investigated from the viewpoint of nonlinear dynamics. Firstly, the dynamics model of a gas bearing rotor is established by combining the transient Reynolds equation and rotor dynamic equation obtained by finite element method (FEM). The transient Reynolds equation is solved using a hybrid method combining the differential transform method (DTM) and finite difference method (FDM). Then the transient gas force is substituted into the FEM rotor dynamic equation. In the end, based on the bifurcation diagram, the orbit of the rotor center, the frequency spectrum diagram and Poincaré map, the rotor system’s nonlinear behaviors are studied using a solution for the rotor dynamic equation with the Newmark method. Results show that there exists a limited cycle motion in the autonomous rotor system and half-speed whirl in the nonautonomous rotor system.

General-purpose controller for multiple types of magnetic bearing rotor systems

With the increasingly widespread application of magnetic bearings (MBs) in high-speed motors, turbomachinery, and machine tools, the development of magnetic bearing controllers (MBCs) is becoming increasingly significant. Conventional MBCs are designed specifically for a particular type of MB and have poor generality. Given this, an MBC with a digital signal processor (TMS320F28377S) as the core is developed. Meanwhile, a generality calculation method for the circuit module is proposed. The displacement conditioning circuit designed in this paper can match most MB displacement sensors, and the generality is improved to 91.66%. The designed power amplifier can realize the switching of two-level and three-level pulse width modulation (PWM). It can also realize the switching of unidirectional and bidirectional power amplifier control. Therefore, it can apply to most MB rotor systems, and the generality is improved to 66.67%. In addition, the proposed dual closed-loop control strategy based on linear active disturbance rejection control (LADRC) makes the system’s anti-interference capability, robustness and self-adaptive capability enhanced, further improving the generality of the controller. Simulation and experimental results show that the MBC is highly general and has good dynamic performance, and the electrical control system of the MB is optimized.

Nonlinear dynamic mechanical response analysis of dual-segment single-span rotor-bearing system under normal condition and misalignment fault

Nonlinear dynamic mechanical response analysis of dual-segment single-span rotor-bearing system under normal condition and misalignment fault

Fractional-order model and nonlinear vibration analyses of hybrid gas journal bearing–rotor system

It is important to propose a reasonable nonlinear dynamic model of gas dynamic bearing–rotor system for the stable operation of turbocharger. This paper presents a hybrid gas journal bearing (HGJBs)–rotor system with flexible supporting structure. A fractional-order dynamic model of the symmetrical flexible HGJB–rotor system is established. A tracking–alarming method is proposed to obtain the rotational speed ratio at the bifurcation point. The stable and unstable regions of the rotational speed ratio Ωω for both the rigid bearing–rotor system and flexible HGJB–rotor system are analyzed. The nonlinear dynamic behaviors of HGJB–rotor system versus the fractional order αd and rotational speed ratio Ωω are studied. Results show the fractional-order dynamic model can realize the reasonable prediction of nonlinear dynamic behaviors. An increase in the rotational speed ratio Ωω and the decrease of fractional order αd result in a growth of the vibration amplitude. The adoption of flexible supporting structure is a good strategy to increase the size of stable region.

Nonlinear dynamic analysis of ceramic motorized spindle considering bearing preload and span

Ceramic motorized spindle is more suitable for high-precision and high-speed machining because of its material with high stiffness, low deformation, and other excellent characteristics. The ceramic bearing assembly and support location are critical elements influencing the stiffness and dynamic characteristics of ceramic motorized spindle. In order to investigate the influence of bearing assembly on the dynamic characteristics of spindle, the relationship between preload and bearing stiffness is determined and a dynamic model of ceramic motorized spindle bearing rotor system is established taking the comprehensive impact of bearing span and preload into account. The bearing stiffness fluctuation caused by bearing preload and bearing thermal deformation is calculated, and the effect of bearing preload and span on the dynamic characteristics is investigated. The results show that the rotor amplitude firstly decreases with the bearing preload and span vary, and then increases. The best assembly combination of ceramic spindle is a preload of 400 N and a span of 190 mm in the speed of 12,000–18,000 r/min. The vibration experiments are conducted on the ceramic motorized spindle, and the average error between experimental date and calculated date is 2.49%, which verifies the accuracy of the model. This study lays a theoretical foundation for further investigation of the dynamic characteristics of ceramic motorized spindle and its structural optimization.

Non-uniform roller-race contact performance of bearings along width in the rotor-bearing system under dynamic loads

Under complex dynamic loads, the motions of the rotor and bending of the shaft can make the inner and outer races being of support bearings nonparallel in the rotor-bearing system, which will significantly affect the contact performance between the roller and race of support bearings. In this study, a rotor-bearing system with a cantilevered pinion is established by coupling the kinematic equations of the rotor with the determination of deflection deformation of the shaft. The time-varying mesh stiffness of gear pair, interactions between the roller and race of support bearings, and dynamic forces induced by dynamic rotor eccentricity are comprehensively considered in this model. In addition, a spatial rolling bearing dynamics model considering the radial load distribution along width and flexible roller is especially involved in this dynamic system using the slice method. The effect of traction torque, rotor eccentricity, and external excitation is analyzed. The results indicate that the non-uniform loads induced by gear engagement, dynamic rotor eccentricity, and external excitation will lead to local fatigue failures for support bearings. The fatigue lives of bearings are significantly lower than those calculated based on the static loads. Taking the traction motor of a railway locomotive as an example, this study is proven to be capable to provide a more reasonable method to investigate the service conditions of rolling bearings and assess the corresponding fatigue lives.

Computational fluid dynamics-based investigation of the static and dynamic characteristic of hydrostatic bearing with nanolubricant: A theoretical method

The objective of this work is to study the characteristics of the hydrostatic bearing with nanolubricant. To investigate the effect of nanoparticle additives on the performance of hydrostatic bearings, a coupled heat transfer finite-element model of the hydrostatic bearing is developed, and the results of the static and dynamic performance of the hydrostatic bearing with lubricant and nanolubricant are evaluated based on computational fluid dynamics methods at different eccentricity ratios. The results show that the rotation error of the bearing–rotor system is reduced by using nanolubricant at a high eccentricity ratio.

Multi-sensor optimal placement of rotor-bearing system based on fault diagnosability

In view of the current situation that there are few studies on whether the fault signals that may occur in the rotor bearing system can be identified and analyzed in the sensor arrangement, fault diagnosability is applied to the optimal arrangement of the sensors in the rotor bearing system. The preliminary layout of the multi-sensor is carried out by analyzing the transmission path of the vibration signals in the rotor bearing system and based on the minimum path. Secondly, the nonparametric kernel density estimation method calculates the state information’s probability density function. The K-L divergence value is further used to measure fault detectability, fault separability, and fault diagnosability. Then, the correlation function method is used to fuse the multi-sensor information, and the optimal sensor layout is given with the fault diagnosability as an index. Finally, the validity of the method is proved by the experimental laboratory data and the correlation coefficient.

Investigation on the misalignment of full ceramic ball bearing rotor system caused by varying gap in wide temperature ranges

The temperature-varying gap between the full ceramic ball bearings and the steel pedestal in wide temperature ranges leads to misalignment of the bearing rotor system, and there is a significant impact on the vibration of the rotor system. In this paper, the dynamic model considering the temperature-varying gap and time-varying contact between the full ceramic ball bearing and the steel pedestal in wide temperature ranges is proposed. The rigid body elements and the inner rings are coupled in the model, and the influence of the temperature-varying gap is analyzed. Results show that the increased gap at high temperatures brings about the looseness of the full ceramic ball bearing, the misalignment occurs between the axes of the two full ceramic ball bearings due to the looseness. The interaction between the full ceramic ball bearing and the steel pedestal becomes more significant, which causes the vibration of the rotor system to rise. Appropriately increase the interference between the full ceramic ball bearing and the steel pedestal helps reduce the gap at high temperature, thus avoiding the excessive vibration caused by misalignment and improving the rotation accuracy of the rotor system. The research results provide a reference basis for the use of full ceramic ball bearings in wide temperature ranges.