Oil Film Force Research Articles

The effect of lubricating oil temperature on the stability of rubbing rotor-bearing system

Based on the interaction between oil film force and rub impact force of fault rotor bearing system, the nonlinear dynamic equation of rotor bearing system is established to explore the influence of lubricating oil temperature on system stability. The Runge-Kutta method was used to solve the dynamic equations to analyze the steady-state characteristics of the system. The bifurcation diagrams, frequency-waterfall diagrams, time-series diagrams, axis orbit diagrams, poincare map diagrams, frequency spectra dia-grams of the system at oil temperatures of 0 ° C, 40 ° C, 80 ° C were used to reveal the nonlinear behavior of the system. The results show that the temperature mainly affects the speed and amplitude of the oil whirl. When the speed increases to oil whirl, the vibration of the system is mainly oil whirl.

Nonlinear Dynamic Characteristics of Multidisk Rod Fastening Rotor with Axial Unbalance Mass Distribution

During long-term operation, the blades of rod fastening rotor are very prone to fault and may cause uneven axial mass distribution. The dynamic characteristics of a multidisk rod fastening rotor with axial unbalance mass distribution are studied. A four-disk rod fastening rotor model was established by the lumped mass method. The mass unbalance on different disks was used to simulate blade faults in different parts, and nonlinear factors such as oil film force and disk contact effect were considered. The fourth-order Runge-Kutta method was used to solve the model, and the spectrum and axis trajectory curves were obtained. The influence of fault location and rotating speed on rotor dynamic characteristics was analysed when there were blade faults on two disks. The results show that a large, unbalanced mass will bring strong nonlinear characteristics. The rod fastening rotor may be in different motion states at different rotating speeds. When the fault position of two disks changes, the changes of bearing spectrum, axis trajectory, and phase difference have regularity. The results can provide a theoretical basis for condition monitoring and fault diagnosis of rod fastening rotor.

Dynamic performance of a novel integral magnetorheological damper-rotor system

Magnetorheological dampers (MRDs), as active damping devices, show superior performances in vibration control in rotor systems. However, MRDs tend to cause nonlinear behaviors of rotor systems under a large eccentricity, and the direction of the output damping force cannot be controlled. To overcome these deficiencies of MRDs, this paper proposes an integral magnetorheological damper (IMRD). In the proposed IMRD, the damper combines the elastic support and the squeeze film as a whole, where both magnitude and direction of oil film force are adjustable. Firstly, by employing bilinear constitutive equations to represent the magnetorheological fluid (MRF), the implicit form Reynolds equations of IMRD are established. Then, by implementing the proposed IMRD model into a flexible rotor system, the nonlinear dynamic model of a flexible rotor system with IMRD is developed by finite element (FE) method. The mechanical characteristics of IMRD are revealed from the view of oil film pressure and dynamic coefficients, and the nonlinear dynamic responses of the rotor system with IMRD are investigated and compared with those of rotor system with traditional MRD. The results indicate that oil film pressure in each bearing region can be adjusted independently with the current, which can lead to changes in both the direction and magnitude of the oil film force. Moreover, different oil film bearing regions have different contributions to the stiffness and damping of IMRD. Under certain situations, IMRD can provide pure damping with negligible stiffness. Besides, the over-squeezed MRF with large journal eccentricity ratio tends to produce strong nonlinearity; whereas, the IMRD proposed here can significantly reduce the level of nonlinearity compared with traditional MRDs.

Research on fault signal detection method of mechanical vibration based on Kalman filtering algorithm

There are some problems in traditional mechanical fault signal detection, such as large fault detection error and is time-consuming. A mechanical vibration fault signal detection method based on Kalman filter algorithm is proposed. The time-varying nonlinear oil film force of mechanical equipment under different working conditions is analysed. The piezoelectric acceleration sensor is set in the mechanical equipment to obtain the mechanical vibration fault signal. The energy difference between the normal signal and the fault signal is obtained by arranging them according to the acquisition time sequence. The mechanical vibration fault signal is pre-processed by Kalman filtering algorithm to obtain the state prediction of the fault signal. The frequency and amplitude characteristics of mechanical vibration fault signal are obtained to complete the detection of mechanical vibration fault signal. The results show that the error of the proposed method is small and the detection time is 2 s.

Nonlinear vibration behaviors of marine rotor system coupled with floating raft-airbag-displacement restrictor under ship heaving motion

To study the nonlinear vibration behaviors of rotor system coupled with floating raft-airbag-displacement restrictor under ship heaving motion, the dynamic model is established considering the effect of heaving motion, its steady-state responses are numerically obtained using Runge-Kutta method and the results are surveyed by tools such as the spectrum waterfall diagram, time-domain response, frequency-domain response, axis orbit, and Poincaré map. The effects of rotating speed, ship heaving amplitude, and its frequency on the nonlinear dynamic behavior of the system are mainly studied. The results show that the responses of the rotor and raft are of obvious nonlinear behaviors such as amplitude jumping, bifurcation, and chaos due to the effects of nonlinear oil film force and ship heaving motion. With the increase of rotating speed, the motion of rotor and raft presents quasi-periodic and chaotic vibrations. Ship heaving amplitude and its frequency all have great effect on the vibration of rotor and raft; as heaving amplitude or frequency increases, the motion state of rotor and raft changes, and the amplitude of raft increases significantly. The displacement restrictor can effectively limit the vibrating displacements of the raft when ship heaving amplitude or its frequency is large.

Nonlinear dynamics of marine rotor-bearing system coupled with vibration isolation structure subject to ship rolling motion

This study focuses on the nonlinear dynamic behavior of a marine rotor-bearing system coupled with vibration isolation structure under ship rolling motion. After considering the effect of the nonlinear oil film force and the ship rolling motion, a mathematical model is established based on Lagrange's equation. By employing a numerical method, the dynamic steady-state response of the system is analyzed, such as the orbits of the rotor and its Poincaré maps, spectrum waterfall diagram, and the displacements and frequency spectrum diagram of the raft frame. We also studied the effects of the rotor speed, the amplitude and frequency of ship rolling on the marine rotor-bearing system coupled with isolation structure under ship rolling motion. The results indicates that response of the rotor shows obvious nonlinear dynamic behaviors such as amplitude jumping, bifurcation and chaos due to the influence of the nonlinear oil film force and the ship rolling motion. As the rotor speed increases, the motion of the rotor experiences the process of quasi-periodic and chaos vibration. Both the amplitude and frequency of ship rolling have effects on the amplitude of the rotor and the raft frame. Moreover, the rotation angle of the raft frame is greatly influenced by the amplitude and frequency of ship rolling, and it is necessary to control the vibration attitude of the raft frame.

Dynamic Response Analysis of Tilting Pad Journal Bearing Considering Fluid-Structure Interaction

The transient hydrodynamic lubrication model of tilting pad journal bearings (TPJBs) was established by the computational fluid dynamics (CFD) method and the self-developed dynamic grid program. The fluid-structure interaction between the flow field and the rotor motion, the pads rotations was realized. The feasibility of the model is proved by comparing with the experimental data. The dynamic response of TPJBs under the various unbalance, the loading modes and the rotating speeds was studied. The dynamic response of TPJBs is further analyzed through a research of the relationships among the shaft whirl orbits, transient force acting on the shaft, rotation angles of the pads and transient oil film force of the pads. With the increase of unbalance, the whirl orbits expand and whirl orbits centers rise continuously. The whirl orbits and orbit center attitude angles of TPJBs are smaller than those of fixed-pad journal bearings. Compare with the load between pads, the whirl orbits are smaller and whirl orbits centers drop slightly under the load on pads. With the increase of rotating speed, the whirl orbits expand nonlinearly, whirl orbit center rises nonlinearly. The transient force acting on the shaft, the rotation angles of the pads and the transient oil film force of the pads change periodically, and the period and frequency of these changes are the same as that of the shaft rotation. The maximum force acting on the shaft appear before the maximum shaft center position (the vertexes of the whirl orbit).

Effects of journal static eccentricity on dynamic responses of a rotor system under base motions using FDM inertia model

When an oil-lubricated rotor-bearing system is subjected to base motions, it will inevitably be affected by oil-film forces, base excitations, and inertial forces. The alignment state cannot be guaranteed over time, resulting in a static eccentricity. An inertia model for open-ended SFD incorporated three-dimensional fluid velocities and pressure distribution represented by the Reynolds number. In addition to viscous pressure, the inertial pressure distribution was also solved by finite difference method (FDM), and the oil-film forces were determined by numerical integration. Using transient modal integration method, dynamic responses of a rotor-SFD-support system considering oil-film inertia were simulated. The effects of oil-film inertia, static eccentricity, and base motions on transient responses and bifurcation behavior were discussed. The results indicate that for large eccentricity ratio, the oil-film inertia increases the reaction forces. For medium and large static eccentricity, the journal performs quasi-periodic motions. Under base harmonic translation, a series of sub- and super-harmonic frequencies kΩ±Ωz are stimulated along with the multiples of rotational frequency kΩ and base harmonic frequency Ωz. The bifurcation motion of journal with static eccentricity fluctuates seriously in resonance. Overall, nonlinear dynamic responses of rotor-damping-support systems subjected to base motions can be evaluated during dynamics design and vibration suppression.

Nonlinear vibration response of a complex aeroengine under the rubbing fault

Rolling bearing and squeeze film damper will introduce structural nonlinearity into the dynamic model of aeroengine. Rubbing will occur due to the clearance reduction design of the engine. The coupling of structural nonlinearity and fault nonlinearity will make the engine present rich vibration responses. This paper aims to analyze the nonlinear vibration behavior of the whole aeroengine including rolling bearing and squeeze film damper under rubbing fault. Firstly, the dynamic model of a turboshaft engine with nonlinear support and rubbing fault is established; The rolling bearing force, the oil film force and the rubbing force are introduced into a dual-rotor–casing model with six support points. Secondly, the linear part of the model is verified by the dynamic characteristics of the three-dimensional finite element model. Finally, the varying compliance vibration, the damping effect and the bifurcation mechanism are analyzed in detail in which the bearing clearance, speed ratio and rubbing stiffness are considered. Results show that the rubbing fault in the nonlinear support case will excite more significant varying compliance vibration in the low-speed region and expand the rotating speed range of the chaotic region in the high-speed region compared with that in the linear support case.

Numerical and experimental study of gear rattle based on a refined dynamic model

A refined single pair gear dynamic model is established to accurately predict the gear rattle. The model considers various key parameters, such as backlash, time-varying mesh stiffness, nonlinear oil film force between teeth and drag torque. The time-varying mesh stiffness of helical gears is calculated by using the potential energy method. The nonlinear oil film force is introduced into the model by considering the entrainment and squeeze effects of the lubricating oil between the teeth. In addition, the friction resistance caused by the squeeze of lubricating oil between the teeth is considered in the proposed model. The rotation speed and angular acceleration of the loose gear were measured on the bench, and compared with the simulation results, which proved the accuracy of the model. The results of the parametric analysis show that excessive torque fluctuation and backlash may lead to severe impact of the gear pair. Increasing the drag torque has a positive effect on the control of the gear rattle. Larger viscosity will make faster attenuation of high frequency impact and reduce the impact strength.

Nonlinear characteristic investigation of tribo-crack-dynamic rotor system based on full spectrum analysis

The tribo-crack-dynamic model and experimental method to research dynamic mechanism are proposed based on the full spectrum in this paper. In view of the nonlinear characteristics from rub-impact forces, oil-film forces and time-varying stiffness of crack shaft, the tribo-crack-dynamic rotor model is established to serve the analysis of dynamic mechanism and characteristics. The numerical simulation is developed to obtain the precession signal and bifurcation diagram for the tribo-crack-dynamic rotor system. The results show that the negative frequency components are more abundant and their amplitudes increase in the full spectrum, showing obvious reverse precession characteristics when cracks and rub-impact faults occur at the same time. Experiment investigation on nonlinear dynamics is designed, which verifies the tribo-crack-dynamic model and the positive and negative precession characteristics in multi-fault rotor system.

Transient TEHD Analysis of a Thrust Bearing Based on Two-Way Fluid-Solid-Thermal Interaction

Thrust bearing is a key component of hydroelectric generator and bears the axial load of the unit. During transient processes, such as start and stop of the unit, thrust bearing usually occurs wear phenomenon at pad surface, which affects the stable operation of the unit and reduces service life of the bearing. Based on two-way fluid-solid-thermal interaction, this paper did transient thermal-elastic-hydrodynamic (TEHD) analysis of a tilting pad thrust bearing under the pump mode. For the fluid region, the Reynolds equation and the viscosity-temperature equation are solved. For the solid region, transient heat conduction equation and basic thermal-elasticity equation are considered. The data transferred in the fluid-solid interface satisfy the fluid-solid-thermal interaction equation. The variation of the lubricant oil temperature, the oil film force, the pad surface inclination angle and axial velocity of pad and mirror plate are analysed, which provide theoretical basis for the design of bearing and the safe operation of the unit.

Stability analysis of rotating shaft under electromagnetic and bearing oil-film forces

The stability of the fixed pints of a flexible rotor supported by journal bearings is investigated through the Bifurcation diagrams. In this paper the effect of nonlinear electromagnetic harmonic force is added to the simultaneous consideration of the effects of the nonlinearity in curvature and inertia, mass eccentricity and hydrodynamic forces of the journal bearings. Solution of the Reynolds equation renders the pressure distribution in the bearings. The bearing forces are found from integrating the pressure distribution on the surface of bearings. Derivation of the equations is performed using the Hamilton's principle and the nonlinearity terms are related to the eccentricity and the curvature of shaft. Primary and combination resonances are imposed to the rotor-bearing system and steady state responses show the effects of magnetic and bearing forces on the stability of amplitudes. In combination resonance, frequency of the electromagnetic load is tuned as the average of the forward and backward natural frequencies of the rotor. Existence of unstable Hopf points demonstrates that periodic, quasi-periodic and chaotic motions may be arisen in the nonlinear behavior of rotor.

Nonlinear modeling and simulation of flywheel energy storage rotor system with looseness and rub-impact coupling hitch

Abstract Flywheel energy storage system as a new energy source is widely studied. This paper establishes a dynamic model of a single disk looseness and rub-impact coupling hitch flywheel energy storage rotor system firstly. Then dynamic differential equations of the system under the condition of nonlinear oil film force of the sliding bearing are given. Runge–Kutta method is used to solve the simplified dimensionless differential equations. The effect of variable parameters such as disk eccentricity, stator stiffness and bearing support mass on the system are analyzed. With the increase of eccentricity, the range of period-three motion is significantly reduced and the range of chaotic motion begins to appear in the bifurcation diagram. Meanwhile, stiffness of the stator and mass of the bearing support have a significant influence on the flywheel energy storage rotor system.

Nonlinear Dynamic Behaviors of the Arc Tooth Connected Rotor under Different Loads

Due to the wear of wheels during operation, the unbalance is induced. To study the nonlinear vibration of the arc tooth connected rotor under different loads, the motion equation was built based on Lagrange equation, considering contact property of the arc tooth and the oil-film force. From the GW rough surface model, the interface contact stiffness for the arc end-tooth was calculated. The eventual contact force was simulated by a nonlinear spring. Rich nonlinear dynamic phenomena, such as periodic doubling bifurcation phenomenon, multiperiodic motion, quasi periodic motion, oil whirl, etc., were observed. The results show distinct phenomena caused by the load variations. To reduce the nonsynchronous vibration, the relative phase is suggested to be kept at 120°.

Influence of contact interface friction of bolted disk joint on motion stability of rotor-bearing system

In rotating machines, bolted joints are widely employed to connect adjacent disks to make multiple parts into an integrated one. The contact interface, subjected to tangential force introduced by unbalanced forces during normal operation, influencing the rotor dynamics, especially in the presence of relative speed, is of interest for investigations. However, there are little researches on the rotor dynamics considering the contact interface friction of the bolted disk joint. Thus, a dynamic model of the rotor-bearing system is established, which considers the friction at the contact interface between disks, nonlinear oil-film force, etc. The nonlinear dynamic phenomena of the rotor system were investigated using the fourth-order Runge–Kutta method. Bifurcation diagrams, vibration waveforms, frequency spectrums, shaft orbits, and Poincare maps are used to demonstrate the diversity of the system responses. The results indicate that the rotor system exhibits a rich diversity motion states, such as periodic-1 motion, multiple periodic motion, and quasi-periodic motion. The parametric study about the effect of friction coefficient on rotor dynamics is also conducted in the present work, which shows that a larger friction coefficient will lead the system enters into an unstable motion state at high rotating speed, and make the system enters into multiple periodic bifurcations at a higher rotating speed. The corresponding results can contribute to the further understanding of the nonlinear dynamic characteristics of the bolted joint rotor-bearing system.

Study on tribo-dynamic behaviors of rolling bearing-rotor system based on neural network

The tribo-dynamic model of the rolling bearing-rotor (RBR) system based on the radial basis function neural network (RBFNN) is proposed to effectively obtain tribo-dynamic performances of the system. In doing so, the thermal elastohydrodynamic lubrication (TEHL) and motion equations of the rolling bearing are solved simultaneously for the oil film forces, and the fast Fourier transform (FFT) is employed to accelerate the deformation computation. Further, the RBFNN is well trained to reconstruct the oil film forces of the bearing. By incorporating the oil film forces into the dynamic simulation module of the RBR system, its transient tribological and dynamic performances are predicted using the Matlab/Simulink module. Meanwhile, the efficiency and accuracy of the RBFNN in predicting the oil film forces are verified. Then, the tribo-dynamic performances of the RBR system such as the spiral structures of the film thickness, film pressure and film temperature are revealed.

Nonlinear forced vibration analysis of spinning shaft‐disk assemblies under sliding bearing supports

This paper presents an investigation on nonlinear forced vibration characteristics of a spinning shaft‐disk assembly resting on sliding bearing supports. Based on the Timoshenko beam theory and Kirchhoff plate theory, the coupled model of the rotor is established. The present model is validated through comparison with the experiment results for different structure parameters. Considering the gyroscopic effect and nonlinear oil film force, the equations of motion are derived by employing the Lagrange equation. Then, the modal synthesis method and the Runge‐Kutta method are adopted to obtain forced vibration responses of the spinning assembly. Special attention is paid to examine the effect of spinning speed on the nonlinear vibration behaviors of the shaft‐disk rotor system, which can play an especially important role in an actual project.

Mathematical modeling of vibration failure caused by balancing effect in hydraulic turbines

This article discusses the causes of vibrations depending on unbalanced hydraulic forces in rotating and non-rotating equipment in hydraulic plants within the scope of vibration measurement standards. The radial and axial positions of the turbine shaft, normal operating conditions, the absolute vibration of the signal output velocity during startup and shutdown during unbalance condition of the turbine, the proximity probes have been measured by TMO 793 accelerometer sensor and TMO 793 velocity sensor. The results obtained from the monitoring are analyzed and the first discussion is over the comparison of the current operating levels and vibration standards. Secondly, the comparison is analyzed in order to examine the improvement in vibration level of the elimination of hydraulic imbalance more comprehensively, considering the stability of the hydro turbine-generator unit, a proportional row damping force, proportional-order oil-film force and a hydraulic force and by creating a new non-linear proportional-order mathematical model. Changes in vibration levels and spectral bands for failure types are stated as well. The solution of this integrated and accurate mathematical model shows that it is useful and concise in the diagnosis and prediction of faults in hydropower plants.

Vibration analysis of ship propulsion shafting bearings

The ship power propulsion system is the "heart" of the ship, and the ship propulsion shafting is the core unit of the ship power propulsion system, and it is an indispensable part of the ship's propulsion torque and thrust transmission. The operating status of the propulsion shafting directly affects the operating conditions of the ship, and even the life of the ship. Bearing load is one of the most important manifestations of the operating state of the propulsion shafting. Focusing on changes in the bearing load can better study the operating state of the propulsion shafting. The research on the steady-state load of ship propulsion shafting meets the needs of ship development and has great value for practical engineering applications. This paper takes the ship propulsion shafting-oil film-bearing structure system as the research object. Through the steady-state load mathematical model of ship propulsion shafting bearings, it reveals the coupling relationship among ship propulsion shafting bearing load, oil film force, and journal position, and establishes the ship The steady-state load calculation method of the propulsion shafting bearings solves the basic theoretical problems of modeling and analysis of the steady-state operating state of the ship's propulsion shafting, and provides theoretical support for the safety prediction, management and evaluation of the ship's propulsion shafting operation.