Oil Whirl Research Articles

Special issue on recent advances in nonlinear rotordynamics

This issue of Nonlinear Dynamics is devoted to actual problems in rotordynamics. Rotating machinery plays an important role in many disciplines of engineering. The dynamics of such machines are rich in nonlinearity so that a survey on topics concerning nonlinear phenomena in rotor dynamics is interesting for theory and practice. In organizing this issue, we did not intend to target one special topic within this field. We simply wanted to reflect its breadth of interests. The results of this informal survey are published in this issue indicating that many different problems occur. Nine contributions are collected from all over the world. Okabe and Cavalca investigate the dynamics of systems with a nonlinear model of tilting pad bearings including turbulence effects. Boyaci et al. perform an analytical bifurcation analysis of a rotor supported by floating ring bearings while Schweizer studies oil whirl, oil whip and whirl/whip synchronization occurring in such systems. Szolc et al. examine the nonlinear and parametric vibrations of rotor-shaft systems as fault identifi-

On the Bifurcation and Stability of Periodic Motion of the Rotor-Bearing System with Rub-Impact and Oil Whirl

In this paper, the dynamic model of rotor bearing system with rub-impact and oil whirl is formulated. Continuation-shooting method for the periodic solution of nonlinear non-autonomous system is used to obtain the bifurcation and stability of the periodic motion of the rotor-bearing system. The effect of the unbalance and rotor/stator clearance on the bifurcation and stability of the periodic motion of the rotor bearing system are analyzed respectively. The results obtained are compared with those of rotor-bearing system with oil whirl fault.

Oil whirl, oil whip and whirl/whip synchronization occurring in rotor systems with full-floating ring bearings

High-speed rotors are often supported in floating ring bearings because of their good damping behavior. In contrast to conventional hydrodynamic bearings with a single oil film, full-floating ring bearings consist of two oil films: An inner and an outer oil film. As single oil-film bearings, full-floating ring bearings also show the typical fluid-film-induced instabilities (self-excited vibrations). Both inner and outer oil films can become unstable and exhibit oil whirl/whip instabilities.

Numerical and experimental analysis of the rotor—bearing—seal system

The rotor—bearing—seal system is simulated by a model consisting of the rotor, the bearing, the foundation, and the labyrinth seal. Governing equations are set up theoretically using the finite-element method. The equivalent model of the bearing—foundation support system is analysed. Forces from the bearing—foundation support and gas-excited forces in the labyrinth seal are imposed in the finite-element equations. Then an experimental rotor—bearing—seal device is designed and many tests are carried out. The Bode, orbit, and waterfall plots are all constructed from the experimental data. An experimental rotor system is studied using the developed equations. Theoretical results from the developed model are in agreement with the ones from the experiment. Analysis proves that although the gas-excited force in the labyrinth seal can improve the stable region of the rotor—bearing—seal system, it makes the rotor vibrate more violently and initiates destructive impacts within the rotor system when the rotor running speed reaches a certain level. Oil whirl and oil whip of journal bearings are found in both the theoretical calculation and the experiment.

Whirl and whip instabilities in rotor-bearing system considering a nonlinear force model

Linear models and synchronous response are generally adequate to describe and analyze rotors supported by hydrodynamic bearings. Hence, stiffness and damping coefficients can provide a good model for a wide range of situations. However, in some cases, this approach does not suffice to describe the dynamic behavior of the rotor-bearing system. Moreover, unstable motion occurs due to precessional orbits in the rotor-bearing system. This instability is called “oil whirl” or “oil whip”. The oil whirl phenomenon occurs when the journal bearings are lightly loaded and the shaft is whirling at a frequency close to one-half of rotor angular speed. When the angular speed of the rotor reaches approximately twice the natural frequency (first critical speed), the oil whip phenomenon occurs and remains even if the rotor angular speed increases. Its frequency and vibration mode correspond to the first critical speed. The main purpose of this paper is to validate a complete nonlinear solution to simulate the fluid-induced instability during run-up and run-down. A flexible rotor with a central disk under unbalanced excitation is modeled. A nonlinear hydrodynamic model is considered for short bearing and laminar flow. The effects of unbalance, journal-bearing parameters and rotor arrangement (vertical or horizontal) on the instability threshold are verified. The model simulations are compared with measurements at a real vertical power plant and a horizontal test rig.

Identification of nonlinear dynamic coefficients in plain journal bearings

This work proposes a framework to the numerical identification of nonlinear fluid film bearing parameters from large journal orbital motion (20–60% of the bearing clearance). Nonlinear coefficients are defined by a third order Taylor expansion of bearing reaction forces and are evaluated through a least mean square in time domain technique. The journal response is obtained from a computational fluid dynamic (CFD) model of a plain journal bearing on high dynamic loading conditions. The model considers fluid–structure interaction between the fluid flow and the journal. The case in study considers a laboratory test rig. Results indicate that nonlinear coefficients have an important effect on stiffness and damping. It was found a change on nonlinear behavior occurred when the Oil Whirl phenomenon starts, which it is not seen in classical linear models.

Response and bifurcation of rotor with squeeze film damper on elastic support

This paper investigates the nonlinear response and bifurcation of rotor with Squeezed Film Damper (SFD) supported on elastic foundation. The motion equations are derived. To analyze the bifurcation of nonlinear response of SFD rotor, the Floquet Multipliers is obtained by solving the perturbation equations with numerical method. For computing Floquet Multipliers, a novel method is presented in this paper, which can begin integration at the stable solution. Simulation results are given in two figures. One figure, which consists of eight subfigures, gives the effect of rotating speed on the response of SFD damper supported on elastic foundation: with increasing rotating speed, the nonlinear response evolves from quasi-period to period, then jumps between different periods, and finally returns to quasi-period; the corresponding bifurcations are saddle-node bifurcation and secondary Hopf bifurcation. The second figure, which consists of six subfigures, shows that: the support stiffness has large influence on the response of bearings and film force in SFD; large support stiffness can lead to oil whirl in SFD.

Decision tree and PCA-based fault diagnosis of rotating machinery

After analysing the flaws of conventional fault diagnosis methods, data mining technology is introduced to fault diagnosis field, and a new method based on C4.5 decision tree and principal component analysis (PCA) is proposed. In this method, PCA is used to reduce features after data collection, preprocessing and feature extraction. Then, C4.5 is trained by using the samples to generate a decision tree model with diagnosis knowledge. At last the tree model is used to make diagnosis analysis. To validate the method proposed, six kinds of running states (normal or without any defect, unbalance, rotor radial rub, oil whirl, shaft crack and a simultaneous state of unbalance and radial rub), are simulated on Bently Rotor Kit RK4 to test C4.5 and PCA-based method and back-propagation neural network (BPNN). The result shows that C4.5 and PCA-based diagnosis method has higher accuracy and needs less training time than BPNN.

Singularity analysis of the vibration signals by means of wavelet modulus maximal method

Machine fault diagnosis is vital for safe services and non-interrupted production. The key issue in fault diagnosis is the pattern recognition. A set of valid features will simplify the classifying operations and enhance the accuracy in diagnosis. In this paper, a novel singularity based fault features is presented. Vibration signals collected under different machine health conditions will show different patterns of singularities that can be measured quantitatively by the Lipschitz exponents. The wavelet transforms modulus maximal (WTMM) method provides a simple but accurate method in calculating the Lipschitz exponents. Therefore, the WTMM based Lipschitz exponent calculation as well as the method to select the appropriate wavelet function for WTMM and its range of scale are introduced. Three parameters about the singularity analysis are recommended. They are the number of Lipschitz exponents per rotation N ¯ , the mean value μ α and the relative standard deviation s ¯ α of the Lipschitz exponents that are obtained from the extracted features. To verify the usefulness of the proposed methods, simulated signals and vibration signals generated by four types of faults commonly occurred in a rotating machine, including the imbalance, the oil whirl, the coupling misalignment and the rub-impact, had been used for testing purpose. The results show that the signal from the rub-impact possesses the highest singular value and the widest range of singularity. The signal of the coupling misalignment ranked the second. Whilst, the signal of imbalance is more regular or having the smallest singular value and the narrowest range of singularity. The results also prove that the three parameters are excellent fault features for pattern recognition as they can well separate the four fault patterns.

Experimental study on the characteristics of pad fluttering in a tilting pad journal bearing

The fluttering characteristics of the upper unloaded pads in a tilting pad journal bearing were studied experimentally. In order to investigate the fluttering phenomena of the pad, the absolute vibration of the pad, the relative vibration between the bearing and the shaft, and the circumferential film thickness/film pressure were measured with the variation of the supply oil flow rate, the shaft speed, and bearing load. By analyzing the circumferential distributions of the film thickness, it was identified that the film shape of the upper pad continuously alternates between the wedge shape and the diverged shape in the rotational direction while the shaft is rotating. And it was discovered that the pads tend to a representative sub-synchronous self-excited vibration exactly like classical rotor-bearing instability, defined as the oil whirl and oil whip phenomena, with the increase of rotating speed from the cascade plot of the pad. The major finding was that the incipient fluttering velocity of the pad increased with the increase of the supply oil flow rate but decreased with the increase of the bearing load. The experimental results also showed that the fluttering amplitudes of the pad can be effectively suppressed by controlling the supply oil flow rate.

터보회전기기의 진동모니터링 및 진단을 위한 이산 은닉 마르코프 모델에 관한 연구

Condition monitoring is very important in turbo machinery because single failure could cause critical damages to its plant. So, automatic fault recognition has been one of the main research topics in condition monitoring area. We have used a relatively new fault recognition method, Hidden Markov Model(HMM), for mechanical system. It has been widely used in speech recognition, however, its application to fault recognition of mechanical signal has been very limited despite its good potential. In this paper, discrete HMM(DHMM) was used to recognize the faults of rotor system to study its fault recognition ability. We set up a rotor kit under unbalance and oil whirl conditions and sampled vibration signals of two failure conditions. DHMMs of each failure condition were trained using sampled signals. Next, we changed the setup and the rotating speed of the rotor kit. We sampled vibration signals and each DHMM was applied to these sampled data. It was found that DHMMs trained by data of one rotating speed have shown good fault recognition ability in spite of lack of training data, but DHMMs trained by data of four different rotating speeds have shown better robustness.

Some Experiments on Oil Whirl and Oil Whip

The oil whirl and oil whip phenomena have been well known since the early twentieth century. However, there is a lot of confusion on the parameters that affect the onset of instability. In this study, we investigate the onset of instability on a flexible rotor mounted on two plain cylindrical journal bearings. The rotor is run through the first critical speed, the instability, and the second critical speed. Tests are conducted at various unbalance levels, pressures, and misalignment conditions on the coupling. It is shown that, by far, the misalignment of the coupling is the parameter that is most effective on the onset of instability. In particular angular misalignment resulted in the smoothest rotor response.

은닉 마르코프 모형을 이용한 회전체 결함신호의 패턴 인식

Hidden Markov Model(HMM) has been widely used in speech recognition, however, its use in machine condition monitoring has been very limited despite its good potential. In this paper, HMM is used to recognize rotor fault pattern. First, we set up rotor kit under unbalance and oil whirl conditions. Time signals of two failure conditions were sampled and translated to auto power spectrums. Using filter bank, feature vectors were calculated from these auto power spectrums. Next, continuous HMM and discrete HMM were trained with scaled forward/backward variables and diagonal covariance matrix. Finally, each HMM was applied to all sampled data to prove fault recognition ability. It was found that HMM has good recognition ability despite of small number of training data set in rotor fault pattern recognition.

Half-frequency whirl of pistons in axial piston pumps and motors under mixed lubrication

Dynamic lubrication characteristics between a piston and a cylinder in an axial piston pump and motor have been calculated under mixed-lubrication conditions. The calculated results have shown that half-frequency whirling of the piston occurs under some operating conditions and specifications such as low supply pressure, narrow clearance and long sealing length between the piston and the cylinder, in a manner similar to the oil whirl phenomenon in journal bearings. The whirl phenomenon has been confirmed by measurements of piston motion.

IDENTIFICATION OF THE SHAFT ORBIT FOR ROTATING MACHINES USING WAVELET MODULUS MAXIMA

In this paper, a novel approach for the identification of the shaft centre orbits is proposed, which is based on wavelet modulus maxima. For this approach, continuous wavelet transform is utilised upon the Θ–S diagram of the shaft centre orbits, and then, maxima lines are extracted and Lipschitz exponents α of every maxima line are calculated by non-linear least-squares method. The number of maxima lines with positive α, the mean of the positive α, the number of maxima lines with negative α and the mean of the negative α are used as features of the shaft orbits. In succession, the four features are used as the inputs of the back-propagation network to classify the shaft orbits for the fault diagnosis for the rotating machines. The experimental data of four classes of faults (rub-impact, oil whirl, coupling misalignment and unbalance) are used to test the performance of the proposed method. The test result indicates that the proposed method is very effective with the advantages of fewer features used and faster training of the network, and can fulfil classification of the shaft centre orbit with satisfactory accuracy.

VIBRATION SIGNAL ANALYSIS AND FEATURE EXTRACTION BASED ON REASSIGNED WAVELET SCALOGRAM

The wavelet scalogram has been widely used for vibration signal analysis, but it has low frequency concentration at small scales and low time concentration at large scales owing to the limitation of Heisenberg–Gabor inequality. In addition, misleading interference terms would appear in the scalogram at some conditions. All of these would influence scalogram analysis seriously. In this paper, a reassignment method is used, which can improve the concentration of the scalogram and weaken the interference terms to a certain extent; thus, the readability of the scalogram can be improved. The experimental data for three kinds of faults in rotating machinery: rotor-to-stator rub, oil whirl, coupling misalignment and the actual measurement data from a Pumped Storage Power Generator Unit are analyzed by the scalogram and the reassigned scalogram, and the results by FFT analysis are also given. A comparison among three kinds of analysis results is carried out, and the comparison results indicate that the scalogram can not only reveal the time–frequency features of vibration signal but also highlight the components of low energy. Therefore, it is suitable to extract features of faults at an early stage.

Relationship between Stiffness of Sliding Part End and Friction Characteristics in Oil Hydraulics Equipment.

Effects of stiffness of sliding part end between piston and cylinder on the friction characteristics have been investigated experimentally for rotating-swash plate type piston pump and motor. The friction forces were measured by means of Piezo-type load washers under several stiffness of the sliding part end and forcing the piston to rotate. Since the oil whirl phenomena may occur on the piston for certain working conditions, the friction forces were evaluated during two rotations of the swash plate. The friction losses were estimated on the basis of the experimental results. It was clarified that the maximum friction forces and the mean friction losses decreased markedly with decreasing the stiffness, and that the maximum friction forces were almost independent of supply pressure, rotational speed of the swash plate and overhang ratio (bearing width) with low stiffness of the sliding part end.

Hopf bifurcation to a short porous journal-bearing system using the Brinkman model: weakly nonlinear stability

On the basis of the Brinkman model, the weakly nonlinear stability characteristics of short porous journal-bearing systems are presented. By applying the Hopf bifurcation theory, the weakly nonlinear behaviors near the critical stability boundary are predicted. According to results, the onset of oil whirl for porous bearings is a bifurcation phenomenon; it can exhibit supercritical limit cycles or subcritical limit cycles for journal speeds in the vicinity of the bifurcation point. With a fixed permeability parameter, such supercritical limit cycles for journal speeds in excess of the threshold speed are confined to a specific region in the ( ω, ϵ s) plane; and outside this region subcritical limit cycles exist for journal speeds below the threshold speed. In addition, increasing the value of system parameter, S p, may change supercritical bifurcation into the more complicated subcritical bifurcation.

ON GEARED ROTORDYNAMIC SYSTEMS WITH OIL JOURNAL BEARINGS

This study investigates response and stability characteristics of rotordynamic systems interconnected with gear pairs and supported on oil journal bearings. The systems examined are driven by a motor providing a known torque, which is transferred to a load element through shafts and a gear box. Initially, the emphasis is placed on the gear-pair action, by assuming that the interconnecting shafts are rigid. This results in low order mechanical models with strongly non-linear characteristics, whose long-time dynamics are then effectively studied by applying appropriate numerical methodologies. In this way, useful information is obtained about the influence of the loading, the gear mesh and the journal parameters on the system dynamic behaviour, including periodic, quasi-periodic and chaotic response. Efforts are also directed towards predicting the onset of oil whirl instability and investigating its effects on the system dynamics. The focus is then shifted to more realistic models, including the flexibility of the interconnecting shafts. In this case, the order of the system is first reduced by applying a component mode synthesis method, which takes advantage of the fact that the non-linearities are located at the journal bearings and the gear mesh only. As a result, it is possible to study the dynamics of the reduced rotor-bearing model by employing the methodology that was developed for the gear-pair models.

Experimental Verification of Oil Whirl of Piston in Axial Piston Pump and Motor.

Piston motion which interacts with lubrication characteristics including friction force between the piston and cylinder has been measured by means of eddy current displacement sensors in order to prove the oil whirl phenomena in axial piston pump and motor which had been found theoretically in the previous paper, and been compared with the calculated results. It has been verified that the piston has whirled in the cylinder under certain operating conditions and specifications, similar to the oil whirl phenomena in journal bearings as a self-excited vibration. The phenomena have not occurred for large clearance and narrow bearing width between the piston and the cylinder as the predicated results in the previous paper. The period of the piston whirl has coincided with that of friction force variation.