Oil Film Force Research Articles

Nonlinear Coupled Dynamics of a Rod Fastening Rotor under Rub-Impact and Initial Permanent Deflection

A nonlinear coupled dynamic model of a rod fastening rotor under rub-impact and initial permanent deflection was developed in this paper. The governing motion equation was derived by the D’Alembert principle considering the contact characteristic between disks, nonlinear oil-film force, rub-impact force, unbalance mass, etc. The contact effects between disks was modeled as a flexural spring with cubical nonlinear stiffness. The coupled nonlinear dynamic phenomena of the rub-impact rod fastening rotor bearing system with initial permanent deflection were investigated by the fourth-order Runge-Kutta method. Bifurcation diagram, vibration waveform, frequency spectrum, shaft orbit and Poincaré map are used to illustrate the rich diversity of the system response with complicated dynamics. The studies indicate that the coupled dynamic responses of the rod fastening rotor bearing system under rub-impact and initial permanent deflection exhibit a rich nonlinear dynamic diversity, synchronous periodic-1 motion, multiple periodic motion, quasi-periodic motion and chaotic motion can be observed under certain conditions. Larger radial stiffness of the stator will simplify the system motion and make the oil whirl weaker or even disappear at a certain rotating speed. With the increase of initial permanent deflection length, the instability speed of the system gradually rises, and the chaotic motion region gets smaller and smaller. The corresponding results can provide guidance for the fault diagnosis of a rub-impact rod fastening rotor with initial permanent deflection and contribute to the further understanding of the nonlinear dynamic characteristics of the rod fastening rotor bearing system.

Numerical modeling of the flow in the squeeze film dampers with oil feed groove by computational fluid dynamic analysis

Squeeze film dampers are widely applied in high rotating speed machinery to reduce vibration, add damping and increase the stability of the system. The traditional method of squeeze film dampers analysis usually involves a complicated calculation program that is limited to a simplified physical model. In this study, the feasibility of applying commercial code ANSYS-FLUENT to study the characteristics of the squeeze film damper is investigated, where the dynamic mesh method is employed. The Zwart–Gerber–Belamri model is applied to simulate the cavitation phenomenon in squeeze film damper. By numerical simulation, the dynamic pressure distribution and oil film force are obtained and then the damping coefficients are acquired. The effect of the cavitation model on the damping coefficients and inertia coefficients is obtained. The parametric study including the squeeze film damper clearance, length and whirl frequency is carried out. The result indicates that the use of the cavitation model will reduce the amplitude of the dynamic oil film force and the hysteresis phenomenon can be observed. It leaves room for further improvement on this method.

Manufacturing and study on influence of changes in center distance in circle arc-involute-circle arc gear pump operating at high pressure and high speed

This study examined the effect of changes in center distance on a circular-arc gear pump that operates at high pressure and high speed. In principal these types of gear pumps have no trapped-oil and flow ripples. The effect of changes in center distance caused by assembly, machining, radial force and oil film force on the performance of circular-arc gear pumps was studied. The results show that the flow rate, axial force and torque increased linearly with an increase in variables [Formula: see text]. Computer aided manufacturing for ball end milling has been developed to simulate the process of numerical control of the rotors of circular-arc gear pumps. Two methods for assessing interference are provided. The trajectories of the centers of ball end milling for rough and finish machining are simulated.

Oil film boundary analysis of spiral oil wedge sleeve bearing based on the dynamic loading conditions

The area and location of cavitation change with time in the condition of dynamic loading. The cavitation location of sleeve bearing not only depends on axis location and velocity at a certain moment but also is affected by cavitation history, so the boundary condition need to be defined in the solution of lubrication equation. Based on the balance of axial inertia force, oil film force, and dynamic loading, the motion equation, generalized Reynolds equation and oil film thickness equation of spiral oil wedge sleeve bearing are established. The results show that the cavitation location and carrying capacity vary periodically with the change in time. The effect of dynamic loading and rotational speed on the oil film cavitation and carrying capacity is studied.

A new dynamic mesh algorithm for studying the 3D transient flow field of tilting pad journal bearings

A new dynamic mesh algorithm is developed in this paper to realize the three-dimensional (3D) computational fluid dynamics (CFD) method for studying the small clearance transient flow field of tilting pad journal bearings (TPJBs). It is based on a structured grid, ensuring that the total number and the topology relationship of the grid nodes remain unchanged during the dynamic mesh updating process. The displacements of the grid nodes can be precisely recalculated at every time step. The updated mesh maintains high quality and is suitable for transient calculation of large journal displacement in FLUENT. The calculation results, such as the static equilibrium position and the dynamic characteristic coefficients, are consistent with the two-dimensional (2D) solution of the Reynolds equation. Furthermore, in the process of transient analysis, under conditions in which the journal is away from the static equilibrium position, evident differences appear between linearized and transient oil film forces, indicating that the nonlinear transient calculation is more suitable for studying the rotor-bearing system.

Experimental Analysis of Dynamic Oil Film Pressure of Tilting-Pad Journal Bearings

With the increase in capacity demand, the development of rotating machinery is toward larger scale, higher speed, and intellectualization. In order to achieve a safer and more reliable operation, a better vibration performance of the rotor-bearing system is expected. Tilting-pad journal bearings have many advantages such as improved dynamic performance and drastic reduction in instability; therefore, they are widely used in rotating machinery. The nonlinearity of the dynamic oil film force is one of the fundamental parameters for an oil film bearing supported rotor system. A mounts of scholars and technicians have conducted theoretical research in this field. This paper focuses on the experimental research of the nonlinearity of dynamic oil film force. Oil film force was measured in various experiments, where relevance and sensitivity to vibration responses were evaluated under different operation speeds and excitation frequencies. The research was mainly divided into three steps. Firstly, experimental measurements data of oil film pressure under different speeds and static loads were verified by theoretical numerical calculation. Secondly, the feature information of displacement and pressure under different dynamic loads and excitation frequency was obtained from experiments. In addition, the frequency compositions of displacement and pressure were compared. Finally, a newly developed time–frequency analysis tool, named the synchrosqueezing wavelet transform, was employed to characterize the displacement and pressure features. Through the comparison between the time–frequency compositions of these two features,there are more signal characteristics presented in the time–frequency spectrums of dynamic oil film force. Characteristics like amplitude of both excitation frequency and half-frequency whirl frequency are more obvious in those spectrums. It can be concluded that the measurement of dynamic oil film force is an effective method to monitor the real-time status of the rotor-bearing system vibration.

Design and modeling of a novel active squeeze film damper

Rotating machinery support design with the aim of reducing the amplitude vibration and force transmitted to the foundation has significant importance regarding the various applications of these machineries. In this paper, a theoretical model for an active squeeze film damper (ASFD) is introduced as an option in the vibration control field. The design is based on the SFD with the controllability characteristics of magnetic bearing, which allows the development of a variable force, and a change in fluid film stiffness and damping. It is assumed that the SFD and the AMB are collocated, whether adjacent or integrated in a single unit. Expressions for the oil film forces and magnetic force are obtained. Then, the dynamic equations of the combine both bearings in a single bearing are presented. The vibration control of a rigid rotor is taken as an example of the application of the new design. The possibility of suppressing rotor vibrations and transmitted forces is demonstrated by means of numerical experiments. The simulation shows that in this type of application, good vibration control can be achieved by using new active squeeze-film damper. The potential benefits of varying the magnetic bearing parameters can thus be examined for any given rotor bearing configuration.

Nonlinear dynamics of an asymmetric rotor-bearing system with coupling faults of crack and rub-impact under oil-film forces

The parametric instability of a rotor-bearing system with coupling faults of crack and rub-impact under nonlinear oil-film force is studied in this paper. A model considering time-varying crack stiffness, rub-impact force and nonlinear oil-film force is put forward to analyze the complicated nonlinear behaviors of the rotor-bearing system. The numerical simulation focuses on the effects of crack depth and the stator stiffness on the onset of instability and nonlinear responses of the rotor-bearing system by using bifurcation diagrams, Poincare maps, largest Lyapunov exponent and frequency spectrum. The multiple periodic, quasiperiodic and chaotic motions are observed in this study. The results indicate that crack depth and stator stiffness have influences on the vibration and instability of the rotor-bearing system with varied rotating speed. The motion of the system with coupling faults shows strong nonlinearity and instability in high speed region. Moreover, crack depth and stator stiffness interfere with the formation of oil whirl, thus, making the oil whirl appear later. There also exists interaction among coupling multiple faults. The research discloses the worthy energy exchange phenomenon of multi-fault system and is helpful for fault diagnosis and vibration control of real rotor-bearing systems.

Nonlinear dynamic response of a rub-impact rod fastening rotor considering nonlinear contact characteristic

The nonlinear dynamic characteristics of a rub-impact rod fastening rotor have been investigated in this paper. A model of the rod fastening rotor bearing system under rub-impact condition is proposed considering nonlinear contact characteristic between disks, nonlinear oil-film force, unbalance mass, etc. The equation of motion of the system has been derived by D’Alembert principle. The contact effects between disks are modeled as a flexural spring with nonlinear stiffness. The dynamic equations of motion are solved using fourth-order Runge–Kutta method. Bifurcation diagram, vibration waveform, frequency spectrum, shaft orbit and Poincare map are used to illustrate the rich diversity of the system response with complicated dynamics. The studies indicate that it is unsuitable to take the rod fastening rotor as an integral rotor in analyzing the rub-impact dynamic response of the system. The subharmonic periodic motion, multiple periodic motion, quasi-periodic motion and chaotic motion are observed in this study. Larger radial stiffness of stator will simplify the system motion and make the oil whirl weaker or even disappear at a certain rotating speed. The corresponding results can provide the guidance for the fault diagnosis of a rub-impact rod fastening rotor; meanwhile, the study may contribute to the further understanding of the nonlinear dynamic characteristics of a rub-impact rod fastening rotor.

Global Dynamics Analysis of a Continuum Rotor through G-Function and LFunction Method

The global dynamics of a continuum rotor excited by nonlinear oilfilm force and electromagnetic force is investigated. The governing equation of the system is obtained using the Galerkin’s method. The dynamical systems are reduced into two 2-dimensional systems in Yand Z-directions. The analytical conditions for global transversality and tangency to the separatrix are presented. The global and local dynamics of the system is determined through the G-function and G(1)-function and is compared to numerical solution. The periodicity of periodic flow of the rotor is determined by the L-function. The complexity of the nonlinear continuum rotor system is demonstrated through global transversality and tangency of the periodic motions to separatrix.

Nonlinear dynamic behaviors of circumferential rod fastening rotor under unbalanced pre-tightening force

A nonlinear dynamic model of the rod fastening rotor bearing system is established considering nonlinear oil-film force, unbalanced mass, unbalanced rod pre-tightening force, etc. The motion equation of the system has been deduced from Lagrange’s equations. The nonlinear dynamic and bifurcation characteristic is investigated using fourth-order Runge–Kutta method. Bifurcation diagram, vibration waveform, frequency spectrum, phase trajectory and Poincare map are applied to analyze the nonlinear dynamic phenomena of the rod fastening rotor. The numerical results indicated that the initial deflection caused by the unbalanced pre-tightening force, nonlinear oil-film force and rotational speed has a great influence on the nonlinear dynamic characteristics of the rod fastening rotor bearing system. The corresponding results can provide the guidance for the fault diagnose of a rod fastening rotor with unbalanced pre-tightening force; meanwhile, the study may contribute to the further understanding of the nonlinear dynamic characteristics of a rod fastening rotor with unbalanced pre-tightening force.

Nonlinear Dynamics Analysis of a Continuum Rotor through Generalized Harmonic Balance Method

The dynamics of a continuum rotor system excited by nonlinear oilfilm force and electromagnetic force is investigated through the Generalized Harmonic Balance Method. The governing differential equation of the continuum rotor system is reduced through the Galerkin’s approximation method. Firstly, the motion in Y-direction is considered as the response of a planar continuum rotor. The analytical periodic motion is obtained and the bifurcation and stability is determined. Secondly, the dynamical model of a spatial continuum rotor is studied. The stability and bifurcation of the analytical periodic motion is obtained and compared to numerical results to show the accuracy of the Generalized Harmonic Balance Method.

Study on Misalignment-rubbing Coupling Fault of Rotor System Supported by Oil Film Force

针对滑动轴承支撑下的转子系统发生不对中故障进而引起不对中-碰摩耦合故障的诊断问题,基于非线性有限元法,应用短轴承油膜力、等效不对中力矩及Hertz接触理论建立双盘不对中-碰摩耦合故障转子系统动力学模型,并通过增广的拉格朗日方法来处理接触约束条件,以保证转盘和机匣相互接触时满足边界渗透深度在规定的容差范围内。同时,结合试验研究分析了在不同转速条件时,滑动轴承支撑下的耦合故障转子系统的相关动力学特性。研究表明碰摩故障在耦合故障中处于主导地位,不对中故障主要会激发高倍频谱处于从属地位;并且随着转速的提高,系统频率成分以高倍频为主,逐步由拟周期运动进入混沌运动状态,同时由于不对中力矩与碰摩力的作用,油膜失稳现象局部被抑制,一、二阶油膜振荡现象均滞后显现。研究结果可为滑动轴承支撑下耦合故障转子系统故障诊断提供依据。

スクイズフィルムダンパのモデル化と実験的検証

Squeeze film damper is used in high-speed rotating machinery such as aircraft engines and gas turbine to suppress the vibration amplitudes of rotor response. However, non-linear characteristics of SFD has a large influence on the vibration characteristics of the system. This paper deals with the vibration analysis of a flexible shaft supported by SFD. Particularly, the case that the oil supply system is oil bath type is considered. In such case, the existing range of the oil film of SFD is limited to the bottom 120 degree of the SFD. This paper calculated the nonlinear oil film force of this type of SFD, and analyzed the rotor vibration by numerical simulation. The obtained results were compared with experimental results, and discussed.

Effects of unbalance location on dynamic characteristics of high-speed gasoline engine turbocharger with floating ring bearings

For the high-speed gasoline engine turbocharger rotor, due to the heterogeneity of multiple parts material, manufacturing and assembly errors, running wear in impeller and uneven carbon of turbine, the random unbalance usually can be developed which will induce excessive rotor vibration, and even lead to nonlinear vibration accidents. However, the investigation of unbalance location on the nonlinear high-speed turbocharger rotordynamic characteristics is less. In order to discuss the rotor unbalance location effects of turbocharger with nonlinear floating ring bearings(FRBs), the realistic turbocharger of gasoline engine is taken as a research object. The rotordynamic equations of motion under the condition of unbalance are derived by applied unbalance force and nonlinear oil film force of FRBs. The FE model of turbocharger rotor-bearing system is modeled which includes the unbalance excitation and nonlinear FRBs. Under the conditions of four different applied locations of unbalance, the nonlinear transient analyses are performed based on the rotor FEM. The differences of dynamic behavior are obvious to the turbocharger rotor systems for four conditions, and the bifurcation phenomena are different. From the results of waterfall and transient response analysis, the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different from the different unbalance locations, and the non-synchronous vibration does not occur in the turbocharger and the amplitude is relative stable and minimum under the condition 4. The turbocharger vibration and non-synchronous components could be reduced or suppressed by controlling the applied location of unbalance, which is helpful for the dynamic design, fault diagnosis and vibration control of the high-speed gasoline engine turbochargers.

Nonlinear coupled dynamics of an asymmetric double-disc rotor-bearing system under rub-impact and oil-film forces

The nonlinear dynamic behavior of an asymmetric double-disc rotor-bearing system with interaction between rub-impact and oil-film forces is addressed in this paper. Using dynamics theory, the mathematical model of an asymmetric double-disc rotor-bearing system is established, considering nonlinear oil-film force and rub-impact force. The nonlinear oil-film force model is presented in Reynolds equation, and the rub-impact is assumed with a Hertz contact and a Coulomb friction. The dynamic equations with coupled rub-impact and oil-film forces are numerically solved using the Runge–Kutta method. Bifurcation diagrams, largest Lyapunov exponent, Poincaré maps, and three-dimension spectral plots are employed to analyze the dynamic behavior of the system. The sub-harmonic, multiple periodic, quasi-periodic and chaotic motions are observed in this study. A special phenomenon is occurring that the motion of system becomes simple and the oil-whirl is restrained or even removed with an increasing imbalance by magnifying the eccentricity. Another special phenomenon is also occurring that the oil-whirl gets diminished or even disappeared with increasing stator stiffness, but the oil-whip is uninfluenced. The discoveries will have a considerable value as diagnostic tools in settling oil-film instability. The numerical results show that the nonlinear dynamic behavior of the system varies with the rotational speed and model parameters.

Dynamic simulation and experimental study of an asymmetric double-disk rotor-bearing system with rub-impact and oil-film instability

This study deals with numerical analysis and experimental investigations where the nonlinear dynamic behaviors of an asymmetric double-disk rotor-bearing system are reproduced considering rub-impact and oil-film instability. A dedicated experimental setup was designed to validate the interaction between rubs and oil-film vibration. A model considering nonlinear rub-impact forces and nonlinear oil-film forces is put forward to analyze the complicated nonlinear vibrations of the rotor-bearing system. The experimental study focuses on the interaction of oil-whirl/whip and rub-impact faults, and the results show that the oil-whirl is restrained or even removed, but the whip is uninfluenced when the rub becomes heavy contact. The numerical simulation focuses on the effect of eccentricity and the stator stiffness on the onset of instability and nonlinear responses of the rotor-bearing system by using bifurcation diagrams, Poincare maps, frequency spectrum and three-dimension spectral plots. Agreeing with the experimental results, the results from simulation indicate that the motion of system becomes simple and the oil-whirl gets diminished or even disappeared, but the whip keeps unchanged when the eccentricity or the stator stiffness increases. The research discloses the worthy energy exchange phenomenon of multi-fault system and presents the nonlinear dynamical characteristics of the interaction between rub-impact and oil-film instability for such a rotor-bearing system.

Lubrication Characteristics of Electric Sliding Contacts Consisting of Rotating Circular Grooved Disk and Stationary Rider With Spherical Surface Under Lubricated Condition

Electric sliding contacts are widely used in various electrical components such as for home appliances and automobiles. The purpose of the present study is to improve the performance characteristics of the electric sliding contacts operating under the lubricated condition by the combination of circular grooved disk and rider with a spherical surface. The experimental and theoretical analyses have been carried out to investigate the effect of cross-sectional area of circular grooves provided in the rotating disk surface on the frictional characteristics and the electrical conductivity. The experimental analysis is conducted with a pin-on-disk friction tester to measure the frictional force and the contact voltage between the sliding contacts under the lubricated condition. The oil-film force and the frictional force between the rider and disk are also calculated with the Reynolds equation and they are found to be closely corresponding to the experimental results. The results obtained in the present study show that increasing the cross-sectional area of the circular grooves on the disk extends the operation condition yielding the metal contact to a higher value of the bearing characteristic number S, which is defined by ηU0L0λ/W (η is the lubricant oil viscosity, U0 is the sliding velocity, L0 is the rider arc length in the sliding direction at the middle of radial width, W is the applied load, and λ is the aspect ratio of rider), and also decreases the frictional force at the maximum value of S at which the rider could contact with the disk surface. These are expected since upstream lubricant oil dragged into the contact region tends to easily leak out along the circular grooves, yielding a lower oil-film force between the rider and disk and enhancing the metal contact.

Rotor Dynamics Behavior of Tilting Pad Bearing Supported Turbo-Expander Considering Temperature Gradient

This paper dedicates on the rotor dynamics behavior analysis on a tilting pad bearing supported turbo-expander rotor system considering temperature gradient. Both numerical and experimental investigations are conducted intensively. The influence of the temperature gradient is modeled as the change of the lubrication oil viscosity and the length variation of the clearance due to the cryogenic thermal expansion of the journal. The analytical expressions of the tilting pad bearing oil-film force are then amended and substitute into the lumped parameter model of the turbo-expander rotor dynamics. Linear analysis based on this model indicates that the existence of the temperature gradient can stabilize the turbo-expander rotor system to an extent, while the nonlinear analyses reveal that the temperature gradient will advance the occurrence of the quasi-periodic motion and break the equilibrium of the vibration between the expander side and the compressor side. Furthermore, an experimental system is established and the experimental results show that the temperature of the tilting pad bearing is influenced by the environment temperature greatly; the spectrum of the displacement of the rotor is dominated by the synchronous frequency of the impellers and bearings. The experiment results also observe the vibration amplitude decreases when the environment temperature gets down and grows when the rotating speed increases. At the same time, the sensitivity of the vibration amplitude versus rotating speed decreases as the environment temperature rises, and vice versa.

Nonlinear model identification of oil-lubricated tilting pad bearings

A new method of modeling and identification of weak nonlinear behavior of tilting pad journal bearings (TPJBs) is proposed. A novel nonlinear model of a TPJB based on a Taylor series expansion of oil film forces, consistent with the transient form of Reynolds differential equation (the original model), is developed. The least mean square technique in time domain is employed to identify Taylor series coefficients of the nonlinear model. The terms with dominant effects on the nonlinear oil film forces are chosen using the subset selection method. Good agreement is achieved between the predicated response obtained from the original model and the one evaluated through using the identified nonlinear model.