Nonlinear Oil-film Force Research Articles

Stability analysis of multi-leaf oil-lubricated foil bearings with back springs based on nonlinear oil film force model

Stability analysis of multi-leaf oil-lubricated foil bearings with back springs based on nonlinear oil film force model

A comprehensive multi-parameter optimization method of squeeze film damper-rotor system using hunter-prey optimization algorithm

The squeeze film damper (SFD) is a damping device that is widely used in turbomachinery. A well-designed SFD structure can effectively mitigate vibration at critical speeds, while a poorly designed SFD may increase vibration. The comprehensive multi-parameter optimization method is used for optimizing the vibration response at critical speed and improving the reliability and overall performance by designing the crucial structural parameters of the SFD. Firstly, the coupling dynamic model is proposed for the rotor and SFD, taking into account the influence of non-linear oil film forces of SFD. The test rig is used to verify the vibration response in a typical SFD-rotor system. To provide the optimal vibration reduction effect within a specific SFD parameter range for a particular rotor, a method for comprehensive multi-parameter optimization is introduced. This method introduces the hunter-prey intelligent optimization (HPO) algorithm and compares its results with the PSO algorithm. The comprehensive optimization method revealed that the key parameters of the SFD, when designed using this approach, can effectively alleviate the vibration response of the entire rotor system, achieving the rotor system amplitude reduction ratio of up to13.89%.

Dynamic analysis of slant cracked rotor system considering nonlinear oil film force.

In this paper, considering the combined effects of nonlinear oil film forces and cracks on the rotor-bearing system, the differential equations of motion with 4 degrees of freedom are established by Lagrangian method. Then, the Lundgren-Kutta method is used to solve them and the results of the model are compared with the experimental data. The study demonstrate that the cracked rotor-bearing system is relatively stable at subcritical speeds, mostly in the period-1 motion. But near 1/3 of the critical speed, there is an inner loop in its whirl orbit and a significant increase in the 2x frequency component. When the system speed rises to the region near 1/2 of the critical speed, though the bifurcation motion and a relatively high 2x frequency can be observed, there are no other reliable fault characteristics. The study proves that the rotor crack fault diagnosis method based on the whirl orbits is convincing for slant cracked rotors.

Nonlinear response of hydraulic turbine generator set caused by unbalanced magnetic pull and oil film force

Hydraulic turbine generator sets are crucial for harnessing water energy. However, the nonlinear phenomena resulting from the combination of unbalanced magnetic pull (UMP) and oil film forces remain unclear. A mathematical model of the rotor-bearing system is introduced to investigate the effects of UMP and the nonlinear oil film force on system. The UMP and nonlinear oil film force are derived from the air-gap magnetic energy and short bearing theory, respectively. The proposed model is verified by the stability experiments of hydraulic turbine generator set in the idling, no-load, and load conditions. The results show that, firstly, the system turns unstable for oil whip and oil swirl, and which experiences bifurcation and undergoes dynamical motions such as period-1 to period-5, quasi-periodic, and chaotic motions. Then, at moderate speeds, the rotor eccentricity has the greatest effect on the bifurcation at idle. While the nonlinear characteristics of the system are most sensitive to the rotor eccentricity at loaded condition. Finally, the existence of UMP reduces the instability caused by oil film forces.

Effect of laminate parameters on nonlinear dynamic characteristic of the composite rotor-bearing system with pedestal looseness

The nonlinear dynamics of the composite shaft rotor-bearing system are greatly affected by the orientation angle layer and its proportion of the ply, i.e., the ratio of the orientation angle layer in the laminate. This paper presents a nonlinear dynamic analysis of a composite rotor-bearing system with pedestal looseness that considers the nonlinear oil film force and the pedestal looseness. Nonlinear phenomena including periodic, quasi-periodic, and chaotic motions are analyzed. The analysis results indicate that the stiffness and damping coefficients of a composite shaft tube can be influenced strongly by the laminate parameters, which can in turn affect the instability speed of the rotor system. To enhance the oil film instability speed of the composite rotor system, it is essential to maximize the ratio of the small orientation angle layer or the ±45° layer. Additionally, increasing the ratio of the small orientation angle layers in the shaft tube leads to a higher rotational speed for loosening instability. The research results obtained in this paper have important theoretical value for the design of composite rotor-bearing systems.

Vibration attenuation characteristics of squeeze film dampers in spiral bevel gear systems

A central drive bevel gear system of aero-engines extracts power from a high-pressure rotor. The high speed of the high-pressure rotor aggravates the gear system's vibration. This work adopts squeeze film dampers (SFD) as damping devices to suppress excessive vibration of the spiral bevel gear rotor system. This paper establishes the general Reynolds equation of SFD and calculates the nonlinear oil-film force of SFD in real-time based on the finite element method. Besides, the finite element method and Timoshenko beam element are employed to model the flexible gear shaft. Then, the dynamic model of the spiral bevel gear system supported by SFDs is established, including the nonlinear oil-film force of SFD and time-varying meshing stiffness of the gear system. The dynamic response of the spiral bevel gear system is analyzed theoretically and experimentally to study the vibration attenuation characteristics of SFD. The findings indicate that SFD can effectively suppress the vibration amplitude of the system at high speeds. The theoretical analysis and experimental amplitude are within an order of magnitude, and the changing trend is consistent.

Numerical and experimental study of the preload induced period-1 and chaotic vibration of a rotor system considering contact effects

Contact effects are one of the primary nonlinear sources of vibrations in the gas turbine rotor systems. Specifically, the nonlinear stiffness between the disk interface from the contact effects has an important influence on the vibration characteristics. In this study, a contact model that accounts for the elastoplastic deformation of asperity is established based on the contact theory. To improve the macroscopic contact model of the bolted structure, we integrate the tested morphology results and modified the skewed distribution function. Subsequently, a dynamic model of the rod fastened rotor-bearing system that incorporates the nonlinear oil film force is established. The influence of the preload on the vibration characteristics of the rotor bearing system is analyzed. The results demonstrate that the improved contact model accurately describes the distribution of asperities on rough surface. The contact effects weaken the rotor lateral stiffness to a certain extent. According to the numerical results and experimental results, it can be found that changes in preload significantly affects the occurrence conditions from periodic vibration to chaotic vibration, a higher preload is conducive to maintaining the stable period-1 motion state at high speed. Additionally, as the preload is decreased, the speed range with obvious periodic-doubling frequencies gradually increases and the amplitude of vibration response decreases. This work provides a practical guidance for the dynamic design and preload adjustment of gas turbine rod-fastened rotor considering contact effects.

Dynamical modeling and experimental validation for squeeze film damper in bevel gears

Squeeze film damper (SFD) effectively reduces rotor motion amplitude while crossing critical speeds for vibration and noise reduction in a wide application of aero-engine rotor system. The squirrel cage elastic support (SCES) as an essential component of SFD, accurate modelling of SCES using component modal synthesis (CMS) to account for its flexibility, and calculation of nonlinear oil film forces for SFD using the finite difference method. The CMS method is also used to model the bevel gear wheel body and to establish a finite element nodal dynamics model of the gear-rotor-bearing-SFD system considering time-varying mesh stiffness, tooth clearance, gyroscopic effects, transmission error excitation and SFD oil film forces. The modal frequency of the gear shaft in aero-engine power transmission is exercised to verify the established bevel gear model. Moreover, a bevel gear test platform with SFD is established to study the vibration reduction effect of SFD. It is found that SFD can effectively improve the transmission of the bevel gear system, and the flexibility of the SCES makes the critical speed shift. Actually, the smaller the stiffness of SCES, the more the critical speed is moved to the left. By using CMS to determine the flexibility of bevel gear and SCES, it can show the complete phenomenon of the dynamic behaviors of the bevel gear system with SFD.

Dynamic analysis of grinding electric spindle bearing-rotor system under eccentric action

To study the influence of eccentricity on the dynamic characteristics of grinding electric spindle, firstly, the nonlinear oil film force (NOFF) expression of sliding bearing is established based on the boundary condition of adhesion pressure. Then, the expression of the unbalanced magnetic pull (UMP) under the eccentricity of the air gap is derived. Finally, the bearing-rotor dynamics equation of the grinding electric spindle considering the NOFF and UMP is established, and the dimensionless processing is carried out. The nonlinear dynamics study of the bearing-rotor system under the influence of geometric eccentricity and mass eccentricity is carried out through the shaft center trajectory and the shaft center vibration spectrum. The research results can provide reference for the optimal design of grinding electric spindle.

Nonlinear dynamic characteristics of a power-turbine rotor system with branching structure

The branching structure is commonly utilized in the rotor system due to several merits, such as enabling a more compact structure and achieving a higher power-weight ratio, and also usually omitted or concentrated on a disk in the form of lumped mass during modeling, resulting in an inability to achieve the desired modeling accuracy. The aim of this paper is to investigate the nonlinear dynamic characteristics of a power-turbine rotor system with branching structure in turbo-shaft engine. Considering the branching structure and the effect of nonlinear oil-film force due to the squeeze film damper (SFD), the dynamic model of the power-turbine rotor system with branching structure is developed by means of finite element method. Meanwhile the critical speeds and mode shapes of the power-turbine rotor system are achieved by numerical calculation, simulation and experiment. The results reveal that the calculation results of the critical speeds and mode shapes are in good agreement with the simulation and experimental results. Moreover, the detailed comparison of vibration responses of the power-turbine rotor system with and without SFD is conducted, and the effects of oil-film clearance, length and viscosity on vibration responses are further investigated, respectively. The numerical results reveal that when the oil-film clearance goes up, the vibration amplitude at resonance goes down and the opposite is also true, moreover, increasing the oil-film length or decreasing the oil-film viscosity will improve the vibration-reduction performance of SFD.

Effect of the unbalanced magnetic pull force and oil-film force on nonlinearity of a dual-rotor bearing system

Turbogenerator sets, the indispensible rotating machinery in thermal power plants, can be simplified into a dual-rotor bearing system. In this case, its nonlinear phenomenon largely results from the unbalanced magnetic pull (UMP) and the nonlinear oil film forces, which, however, are not well understood. In this study, a mathematical model for a dual-rotor bearing system is established, the effects of the UMP and the oil-film forces on its nonlinear phenomenon are investigated creatively. Of which, the UMP force is initially calculated by the integration of the air-magnetic energy, and the short journal bearing assumption is employed to derive the oil-film force. The fitness of the developed model is validated through the stability experiments of a 660 MW turbogenerator set. Results indicate that in the idling condition, nonlinear phenomenon of the system can be described as the period-1 and quasi-periodic motions as the rotational speed rises. At low speeds, the amplitude of oil whirl appears. With the rising rotational speed, the oil whirl turns into oil whip in the second quasi-periodic. Interestingly, the electromagnetic force can greatly alleviate the system amplitude and enhance its stability considering the UMP force. The nonlinear effect of air-gap distance of the system under load conditions is also investigated. The system is still in the quasi-periodic state with the increasing air-gap distance at low/high speed. But the system is still unstable owing to oil whirl/whip and UMP force, causing the system experiences multiple states and becomes more stable at the intermediate speed.

Dynamic Analysis of Gear Rattling of a Certain Type of Dual-Clutch Transmission

In order to accurately explore the transmission rattling phenomenon and the influence of different factors on the dynamic characteristics of the gear rattling of the dual-clutch transmission under the condition of preselected gears, this paper establishes the gear rattling dynamics model of the transmission with the 1st gear without preselection and the preselected 4th gear, respectively; The model takes into account factors such as time-varying mesh stiffness, mesh damping, nonlinear oil film force, nonlinear backlash, and the drag torque generated by the clutch in the unengaged state. In addition, the feasibility of the dynamic model was verified by the bench test. On this basis, we took the gear meshing power and system power loss as quantitative indexes to analyze the influence of the preselected gear state and different parameters on the rattle vibration of the transmission. The results show that the pre-selected gear will not have a significant effect on the gears that have been rattled in the non-pre-selected state, and the torque fluctuation of the non-power flow shaft is aggravated by the influence of the transmission power flow branch and transmission ratio at different levels, which makes the overall rattling strength increase. In order to improve the transmission efficiency of the gear, the torque fluctuation of the input end of the system should be reduced as much as possible, and a larger lubricant viscosity can be appropriately selected, the inertia of the empty gear can be properly reduced, and the tooth clearance can be relaxed for selection.

Bifurcation and Stability Analysis of a Bolted Joint Rotor System Contains Multi-Discs Subjected to Rub-Impact Effect

In aero-engines, the rotor systems are frequently designed with multistage discs, in which the discs are fastened together through bolted joints. During operation, rotating machines are susceptible to rotor–stator rubbing faults. Those bolted joints are subjected to friction and impact forces during a rubbing event, leading to a dramatic change in mechanical properties at the contacting interfaces, influencing the rotor dynamics, which have attracted the attention of scholars. In the present work, a mathematical model, which considers the unbalance force, rotor dimensional properties, nonlinear oil-film force and rub-impact effect, is developed to study the bifurcation and stability characteristics of the bolted joint rotor system containing multi-discs subjected to the rub-impact effect. The time-domain waveforms of the system are obtained numerically by using the Runge–Kutta method, and a bifurcation diagram, time domain waveforms, spectrum plots, shaft orbits and Poincaré maps are adopted to reveal the rotor dynamics under the effect of the rub-impact. Additionally, the influences of rubbing position at the multi-discs on rotor dynamic properties are also examined through bifurcation diagrams. The numerical simulation results show that the segments of the rotating speeds for rubbing are wider and more numerous, and the middle disc is subjected to the rub-impact. When the rub-impact position is far away from disc 1, the rubbing force has little effect on the response of disc 1. The corresponding results can help to understand the bifurcation characteristics of a bolted joint rotor system containing multi-discs subjected to the rub-impact effect.

Nonlinear characteristic analysis of gear rattle based on refined dynamic model

In order to explore the vibration response and the nonlinear behavior of gear rattle, a nonlinear dynamic model is developed in this paper considering the nonlinear oil film force, time-varying meshing stiffness, dragging torque and friction and gear backlash with time-varying characteristics. The time-varying meshing stiffness is calculated using the potential energy method. Considering the convolution and extrusion of the lubricant between the teeth, it is modeled as a nonlinear spring-damped element and a nonlinear oil film force is introduced. The drag torque is calculated numerically using fluid dynamics theory, friction principle, momentum conservation principle, and Bernoulli's principle. The model is verified by comparing the bench test results with the simulation results, and the parametric study is performed to investigate the nonlinear system characteristics by means of fast Fourier transform, Poincare map, and bifurcation diagram. The results show that as the excitation frequency increases, the system enters chaotic state under multiple frequency jumps. Excessive torque fluctuation may lead to severe rattling phenomenon of the gear pair and making the system enter a chaotic state; as the lubricant viscosity increases, the system shows periodic, bifurcation and chaotic behavior alternately, and when the viscosity is large enough, the high-frequency shock intensity decays more rapidly due to large drag torque, which is beneficial to reduce the percussion strength and prevent the system into chaos.

Nonlinear characteristic investigation of magnetorheological damper-rotor system with local nonlinearity

Magnetorheological (MR) dampers show superior performance in reducing rotor vibration, but their high nonlinearity will cause nonsynchronous response, resulting in fatigue and instability of rotors. Herein, we are devoted to the investigation of the nonlinear characteristics of MR damper mounted on a flexible rotor. First, Reynolds equations with bilinear constitutive equations of MR fluid are employed to derive nonlinear oil film forces. Then, the Finite Element (FE) model of rotor system is developed, where the local nonlinear support forces produced by MR damper and its coupling effects with the rotor are considered. A hybrid numerical method is proposed to solve the nonlinear FE motion equations of the MR damper-rotor system. To validate the proposed model, a rotor test bench with two dual-coil MR dampers is constructed, upon which experimental studies on the dynamic characteristics of MR damper-rotor system are carried out. The effects of different system parameters, including rotational speed, excitation current and amount of unbalance, on nonlinear dynamic behaviors of MR damper-rotor system are evaluated. The results show that the system may appear chaos, jumping, and other complex nonlinear phenomena, and the level of the nonlinearity can be effectively alleviated by applying suitable excitation current and oil supply pressure.

The influence of the preload on the nonlinear dynamic performance of the rod-fastened Jeffcott rotor system

For a rod-fastened Jeffcott rotor (RFJR) system, this paper establishes a nonlinear dynamic model considering contact interface, preload, unbalanced mass, nonlinear oil film force, and gives the dynamic equation of the rotor system. Then the fourth-order Runge–Kutta method is applied to study the nonlinear dynamics and bifurcation characteristics of the RFJR system. The bifurcation diagram, time-domain vibration waveform, frequency spectrum, phase trajectory, and Poincare section are applied to investigate the influence of the preload on the nonlinear dynamic performance of the rotor system. The results show that the preload affects the instability speed of the synchronous periodic solution of the RFJR system, the rotor system’s first critical speed, and the rotor system’s vibration amplitude passing the first critical speed. Whether the preload of the rotor is saturated or not has a very different effect on the vibration characteristics of the RFJR system. Assuming the fastening force of the tie rods is uneven, it will make the combined rotor have a certain initial bending deformation. At this time, the detuning rate of the tie rod will affect the rotor system’s nonlinear dynamic performance. In addition, the phase angle between the initial bending deformation and the mass eccentricity of the rotor also has a certain impact on the nonlinear dynamic characteristics of the combined rotor. The results obtained in this paper will provide a reference for understanding the nonlinear dynamics of the combined rotor and further research.

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.

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.