Stability Analysis on Rotor Systems Supported by Self-acting Tilting-pad Gas Bearings with Frequency Effects

The recent research on stability of gas bearing-rotor systems still mostly adopts the same method as in oil-lubricated bearing-rotor systems.The dynamic coefficients of gas bearings in the case that the perturbation frequencies are same as the rotating speed are used to carry out the stability analysis of rotor systems.This method does not contact the frequency characteristics of dynamic stiffness and damping coefficients of gas bearings with the dynamical behaviors of rotor systems.Furthermore,the effects of perturbation frequencies on the stability of systems are not taken into account.In this paper,the dynamic stiffness and damping coefficients of tilting-pad gas bearings are calculated by the partial derivative method.On the base of solution of dynamic coefficients,two computational models are produced for stability analysis on rotor systems supported by tilting-pad gas bearings according to whether the degrees of the freedom of pads tilting motions are included in the equations of motion or not.In the condition of considering the frequency effects of dynamic coefficients of tilting-pad gas bearings,the corresponding eigenvalues of the rigid and first five vibration modes of the system with the working speeds of 8-30 kr/min are computed through iteratively solving the equations of motion of rotor-system by using two computational models,respectively.According to the obtained eigenvalues,the stability of rotor system is analyzed.The results indicate that the eigenvalues and the stability of rotor system obtained by these two computational models are well agreement each other.They all can more accurately analyze the stability of rotor systems supported by tilting-pad gas bearings.This research has important meaning for perfecting the stability analysis method of rotor systems supported by gas bearings.

Establishment of the thermo-mechanical coupling model of axle box bearings with track irregularity excitation and analysis of its temperature characteristics

As an important component of the running gear of high-speed trains,axle box bearings can cause lubricating grease failure and damage to bearing components under continuous high-temperature operation,which will affect the normal operation of highspeed trains.Therefore,bearing temperature is one of the key parameters to be monitored in the online monitoring system for trains.Based on the thermal network method,this paper establishes a thermal network model for the axle box bearing,considering the radial thermal deformation of the double-row tapered roller bearing components caused by the oil film characteristics and the temperature variations of the lubricating grease.A thermo-mechanical coupling model for the grease-lubricated double-row tapered roller axle box bearing of high-speed trains with track irregularity excitation is established.The correctness of the model is verified using the test bench data,and the temperature of the bearing at different rotational speeds,loads,fault sizes,and ambient temperatures are investigated.

Design and optimization of fluid lubricated bearings operated with extreme working performances——a comprehensive review

Fluid lubricated bearings have been widely adopted as support components for high-end equipment in metrology,semiconductor devices,aviation,strategic defense,ultraprecision manufacturing,medical treatment,and power generation.In all these applications,the equipment must deliver extreme working performances such as ultraprecise movement,ultrahigh rotation speed,ultraheavy bearing loads,ultrahigh environmental temperatures,strong radiation resistance,and high vacuum operation,which have challenged the design and optimization of reliable fluid lubricated bearings.Breakthrough of any related bottlenecks will promote the development course of high-end equipment.To promote the advancement of high-end equipment,this paper reviews the design and optimization of fluid lubricated bearings operated at typical extreme working performances,targeting the realization of extreme working performances,current challenges and solutions,underlying deficiencies,and promising developmental directions.This paper can guide the selection of suitable fluid lubricated bearings and optimize their structures to meet their required working performances.

A Hybrid Approach for Predicting the Remaining Useful Life of Bearings Based on the RReliefF Algorithm and Extreme Learning Machine

Accurately predicting the remaining useful life(RUL)of bearings in mining rotating equipment is vital for mining enterprises.This research aims to distinguish the features associated with the RUL of bearings and propose a prediction model based on these selected features.This study proposes a hybrid predictive model to assess the RUL of rolling element bearings.The proposed model begins with the pre-processing of bearing vibration signals to reconstruct sixty time-domain features.The hybrid model selects relevant features from the sixty time-domain features of the vibration signal by adopting the RReliefF feature selection algorithm.Subsequently,the extreme learning machine(ELM)approach is applied to develop a predictive model of RUL based on the optimal features.The model is trained by optimizing its parameters via the grid search approach.The training datasets are adjusted to make them most suitable for the regression model using the cross-validation method.The proposed hybrid model is analyzed and validated using the vibration data taken from the public XJTU-SY rolling element-bearing database.The comparison is constructed with other traditional models.The experimental test results demonstrated that the proposed approach can predict the RUL of bearings with a reliable degree of accuracy.

Intelligent Fault Diagnosis Method of Rolling Bearings Based on Transfer Residual Swin Transformer with Shifted Windows

Due to their robust learning and expression ability for complex features,the deep learning(DL)model plays a vital role in bearing fault diagnosis.However,since there are fewer labeled samples in fault diagnosis,the depth of DL models in fault diagnosis is generally shallower than that of DL models in other fields,which limits the diagnostic performance.To solve this problem,a novel transfer residual Swin Transformer(RST)is proposed for rolling bearings in this paper.RST has 24 residual self-attention layers,which use the hierarchical design and the shifted window-based residual self-attention.Combined with transfer learning techniques,the transfer RST model uses pre-trained parameters from ImageNet.A new end-to-end method for fault diagnosis based on deep transfer RST is proposed.Firstly,wavelet transform transforms the vibration signal into a wavelet time-frequency diagram.The signal’s time-frequency domain representation can be represented simultaneously.Secondly,the wavelet time-frequency diagram is the input of the RST model to obtain the fault type.Finally,our method is verified on public and self-built datasets.Experimental results show the superior performance of our method by comparing it with a shallow neural network.

Research on heat dissipation characteristics of magnetic fluid bearings under multiple field coupling effects

This paper analyzes the sources of heat losses in magnetic fluid bearings,proposes various cou-pling relationships of physical fields,divides the coupled heat transfer surfaces while ensuring the continuity of heat flux density,and analyzes the overall heat dissipation pathways of the bearings.By changing parameters such as input current,rotor speed,and inlet oil flow rate,the study applies a multi-physics field coupling method to investigate the influence of different parameters on the temper-ature field and heat dissipation patterns of the bearings,which is then validated through experi-ments.This research provides a theoretical basis for the optimal design of magnetic fluid bearing sys-tems.

Vibration Suppression for Active Magnetic Bearings Using Adaptive Filter with Iterative Search Algorithm

Active Magnetic Bearing(AMB) is a kind of electromagnetic support that makes the rotor movement frictionless and can suppress rotor vibration by controlling the magnetic force. The most common approach to restrain the rotor vibration in AMBs is to adopt a notch filter or adaptive filter in the AMB controller. However, these methods cannot obtain the precise amplitude and phase of the compensation current. Thus, they are not so effective in terms of suppressing the vibrations of the fundamental and other harmonic orders over the whole speed range. To improve the vibration suppression performance of AMBs,an adaptive filter based on Least Mean Square(LMS) is applied to extract the vibration signals from the rotor displacement signal. An Iterative Search Algorithm(ISA) is proposed in this paper to obtain the corresponding relationship between the compensation current and vibration signals. The ISA is responsible for searching the compensating amplitude and shifting phase online for the LMS filter, enabling the AMB controller to generate the corresponding compensation force for vibration suppression. The results of ISA are recorded to suppress vibration using the Look-Up Table(LUT) in variable speed range. Comprehensive simulations and experimental validations are carried out in fixed and variable speed range, and the results demonstrate that by employing the ISA, vibrations of the fundamental and other harmonic orders are suppressed effectively.

Research on the Influence of Raceway Waviness on the Vibration Characteristics of Deep Groove Ball Bearings

The dynamics model of a 2-degree-of-freedom deep groove ball bearing is established by incorporating the raceway surface waviness model comprising multiple sinusoidal functions superposition.The model is solved using the fourth-order Runge-Kutta method to obtain the vibration characteristics including displacement,velocity,acceleration,and frequency of the bearing.Validation of the model is accomplished through comparison with theoretical vibration frequencies.The influence of the amplitude of waviness of the inner and outer ring raceway surfaces of deep groove ball bearings on the vibration displacement,peak-to-peak vibration displacement and root-mean-square vibration acceleration is analyzed,and the results show that as the amplitude of the inner and outer ring raceway surfaces waviness increases,all the vibration characteristic indexes increase,indicating that the vibration amplitude of the bearings as well as the energy of the waviness-induced shock waveforms increase with the increase of the amplitude of the waviness.

Bearing Fault Diagnosis Based on the Markov Transition Field and SE-IShufflenetV2 Model

A bearing fault diagnosis method based on the Markov transitionfield(MTF)and SEnet(SE)-IShufflenetV2 model is proposed in this paper due to the problems of complex working conditions,low fault diagnosis accuracy,and poor generalization of rolling bearing.Firstly,MTF is used to encode one-dimensional time series vibration sig-nals and convert them into time-dependent and unique two-dimensional feature images.Then,the generated two-dimensional dataset is fed into the SE-IShufflenetV2 model for training to achieve fault feature extraction and classification.This paper selects the bearing fault datasets from Case Western Reserve University and Paderborn University to experimentally verify the effectiveness and superiority of the proposed method.The generalization performance of the proposed method is tested under the variable load condition and different signal-to-noise ratios(SNRs).The experimental results show that the average accuracy of the proposed method under different working conditions is 99.2%without adding noise.The accuracy under different working conditions from 0 to 1 HP is 100%.When the SNR is 0 dB,the average accuracy of the proposed method can still reach 98.7%under varying working conditions.Therefore,the bearing fault diagnosis method proposed in this paper is characterized by high accuracy,strong anti-noise ability,and generalization.Moreover,the proposed method can also overcome the influence of variable working conditions on diagnosis accuracy,providing method support for the accurate diagnosis of bearing faults under strong noise and variable working conditions.

Life-Cycle Bearing Capacity for Pre-Stressed T-beams Based on Full-Scale Destructive Test

To investigate the evolution of load-bearing characteristics of pre-stressed beams throughout their service life and to provide a basis for accurately assessing the actual working state of damaged pre-stressed concrete T-beams,destructive tests were conducted on full-scale pre-stressed concrete beams.Based on the measurement and ana-lysis of beam deflection,strain,and crack development under various loading levels during the research tests,combined with the verification coefficient indicators specified in the codes,the verification coefficients of bridges at different stages of damage can be examined.The results indicate that the T-beams experience complete,incom-plete linear,and non-linear stages during the destructive test process.In the complete linear elastic stage,both the deflection and bottom strain verification coefficients comply with the specifications,indicating a good structural load-bearing capacity no longer adheres to the code’s requirements.In the non-linear stage,both coefficients exhi-bit a sharp increase,resulting in a further decrease in the structure’s load-bearing capacity.According to the pro-visions of the current code,the beam can be in the incomplete linear stage when both values fall within the code’s specified range.The strain verification coefficient sourced from the compression zone at the bottom of theflange is not recommended for assessing the bridge’s load-bearing capacity.

Dynamic Simulation Study of Friction and Lubrication on ICE Bearings

Friction and lubrication simulation analysis of internal combustion engine bearings are studied. A series of software implementary precepts for mathematical modeling, to analytic calculating and realizing simulation outcome are brought forward. As a dynamic simulating technique is introduced into the process of engine bearing design, simulation models of the oil film are built and the emulational analysis of the shaft center track is carried out. A software program package “Engine Bearing Friction and Lubrication Dynamic Simulation System” is developed to realize the real time simulation of the working status of bearing during the design process. Through developing virtualized products, the defects of the product design can be found in time and improve the products at once. Thus the purpose of predicting and controlling the cost, quality and design period of the products can be achieved.

An Overview of Performance Characteristics, Experiencesand Trends of Aerospace Engine Bearings Technologies

In this paper, the operating conditions, technical requirements, performance characteristics, design ideas, application experiences and development trends of aerospace engine bearings, including material technology, integration design and reliability, are reviewed. The development history of aerospace engine bearing is recalled briefly at first. Then today＇s material technologies and the high bearing performances of the bearings obtained through the new materials are introduced, which play important roils in the aeroengine bearing developments. The integration design ideas and practices are explained to indicate its significant advantages and importance to the aerospace engine bearings. And the reliability of the shaft-bearing system is pointed out and treated as the key requirement with goals for both engine and bearing. Finally, as it is believed that the correct design comes from practice, the pre-qualification rig testing conducted by FAG Aerospace GmbH ＆ Co. KG is briefly illustrated as an example. All these lead to the development trends of aerospace engine bearings from different aspects.

Quasi-static Analysis of Thrust-loaded Angular Contact Ball Bearings Part Ⅰ:Theoretical Formulation

Ball bearings play an important role in various rotating machineries,but the complicated kinematic and tribological features of ball bearings make many aspects of their operating behaviors still inconclusive.Most theoretical analyses of ball bearings up to date are based on either the hypothesis of race control or other empirical models to determine the ball motion of ball bearings,but none of these strategies can reveal and consequently employ the intrinsic coupling mechanism between the spin and the tangential traction of contacting bodies rolling upon one another.To remedy the deficiency of current analytical models for ball bearing analysis,the rolling contact theory is employed to establish an explicit link between motions and interactions within ball bearings.A differential slip model is established to precisely define the slip component due to the significant curvature of the common contact patches between the ball and inner/outer raceways.The creepage and the spin ratio are formulated to accurately define the relative rigid motion between the ball and the inner/outer raceway.Then a quasi-static analytical model is established that can accurately determine the motions of the balls and races of the ball bearing.It can also give a vivid description of the slip and traction distributions within the contact area.The analytical model can be effectively used to analyze the operational conditions and tribological features of solid-lubricated ball bearings.It can also be used optimize the construction of ball bearings for specific applications.

Application of Computational Fluid Dynamics and Fluid Structure Interaction Techniques for Calculating the 3D Transient Flow of Journal Bearings Coupled with Rotor Systems

Journal bearings are important parts to keep the high dynamic performance of rotor machinery. Some methods have already been proposed to analysis the flow field of journal bearings, and in most of these methods simplified physical model and classic Reynolds equation are always applied. While the application of the general computational fluid dynamics （CFD）-fluid structure interaction （FSI） techniques is more beneficial for analysis of the fluid field in a journal bearing when more detailed solutions are needed. This paper deals with the quasi-coupling calculation of transient fluid dynamics of oil film in journal bearings and rotor dynamics with CFD-FSI techniques. The fluid dynamics of oil film is calculated by applying the so-called ＂dynamic mesh＂ technique. A new mesh movement approacb is presented while the dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. The proposed mesh movement approach is based on the structured mesh. When the joumal moves, the movement distance of every grid in the flow field of bearing can be calculated, and then the update of the volume mesh can be handled automatically by user defined function （UDF）. The journal displacement at each time step is obtained by solving the moving equations of the rotor-bearing system under the known oil film force condition. A case study is carried out to calculate the locus of the journal center and pressure distribution of the journal in order to prove the feasibility of this method. The calculating results indicate that the proposed method can predict the transient flow field of a journal bearing in a rotor-bearing system where more realistic models are involved. The presented calculation method provides a basis for studying the nonlinear dynamic behavior of a general rotor-bearing system.

Unbalance Vibratory Displacement Compensation for Active Magnetic Bearings

As the dynamic stiffness of radial magnetic bearings is not big enough, when the rotor spins at high speed, unbalance displacement vibration phenomenon will be produced. The most effective way for reducing the displacement vibration is to enhance the radial magnetic bearing stiffness through increasing the control currents, but the suitable control currents are not easy to be provided, especially, to be provided in real time. To implement real time unbalance displacement vibration compensation, through analyzing active magnetic bearings （AMB） mathematical model, the existence of radial displacement runout is demonstrated. To restrain the runout, a new control scheme-adaptive iterative learning control （A1LC） is proposed in view of rotor frequency periodic uncertainties during the startup process. The previous error signal is added into AILC learning law to enhance the convergence speed, and an impacting factor/3 influenced by the rotor rotating frequency is introduced as learning output coefficient to improve the rotor control effects, As a feed-forward compensation controller, AILC can provide one tmknown and perfect compensatory signal to make the rotor rotate around its geometric axis through power amplifier and radial magnetic bearings. To improve AMB closed-loop control system robust stability, one kind of incomplete differential PID feedback controller is adopted. The correctness of the AILC algorithm is validated by the simulation of AMB mathematical model adding AILC compensation algorithm through MATLAB soft. And the compensation for fixed rotational frequency is implemented in the actual AMB system. The simulation and experiment results show that the compensation scheme based on AILC algorithm as feed-forward compensation and PID algorithm as close-loop control can realize AMB system displacement minimum compensation at one fixed frequency, and improve the stability of the control system. The proposed research provides a new adaptive iterative/earning control algorithm and control strategy for AMB displacement minimum compensation, and provides some references for time-varied displacement minimum compensation.

Quasi-static Analysis of Thrust-loaded Angular Contact Ball Bearings Part Ⅱ:Results and Discussion

Ball bearings are widely employed mechanical components characterized by high precision and quality,and usually play important roles in various rotary machines and mechanisms.Many advanced applications require a deep understanding of their various kinematic and tribological characteristics that are essential to predict the fatigue endurance,relieve the vibration and minimize the power dissipation of ball bearings in particular applications.An angular contact ball bearing under a specified operating condition is simulated with the quasi-static/creepage analytical model proposed in the preceding article.The results demonstrate that the ball bearing is a statically determinate system.That the balls spin on both inner and outer races means the ball is controlled by neither the inner nor the outer raceway.The friction between the ball and raceway renders the inner and outer contact angles unequal.The larger the coefficient of friction is,the larger the angle deviation.The tangential traction perpendicular to the rolling direction due to the spin induces a gyro-like rotation of the ball with respect to the raceway even if no inertial effects are considered.The tangential elastic compliance of contacting surfaces gives rise to locked areas within the contact patch and transforms the sliding lines from circles into spirals.The differential slip due to the close conformity of the ball and raceway makes the sliding and traction distributions asymmetric,which will influence the location of the spinning center of the ball with respect to the raceway.The quasi-static/creepage model can be used to reveal the operating behaviors of ball bearings running under steady conditions and to optimize the design of ball bearings for specific applications.

DYNAMIC BEHAVIOR OF A CRACKED FLEXIBLE ROTOR SUPPORTED ON JOURNAL BEARINGS

The dynamic behavior of a cracked flexible rotor supported on three kinds ofjournal bearings is presented. Numerical experiments show that nonsynchronous responseswill happen due to the rotor crack, and the amplitudes of the nonsynchronous componentsbecome larger with the increase of crack. On the other hand, the fluid forces of journalbearings can suppress the nonsynchronous response. The (1/2) × or (3/2) × harmoniccomponent rarely appears for small crack near the rotating speed ratio Ω = 2Ωc or Ω =(2/3)Ωc. In the case of supercritical rotating speed, the additional 0× harmonic component is increased as the crack increases. The bearing parameters affect greatly the occur-rence of the nonsynchronous responses by means of exerting innuence on the critical spedand the stabi1ity of the system.

Development of a modified Mooney-Rivlin constitutive model for rubber to investigate the effects of aging and marine corrosion on seismic isolated bearings

In this study, aging and marine corrosion tests of a large number of rubber material and rubber bearings have been carried out. The constitutive Mooney-Rivlin model parameters for a rubber isolated bearing have been determined. By applying the least-square method to the experimental data, the relationships between the aging time and the marine corrosion time with the constants in the constitutive model for a rubber beating have been derived. Next, the Mooney-Rivlin model has been modified accordingly. Further, using the modified Mooney-Rivlin model and the Abaqus software, the performance of the rubber isolated bearings has been simulated. The simulation results have been compared to the experimental results so as to verify the accuracy of the modified model. The comparison shows that the maximum errors for the vertical and horizontal stiffnesses are 16.8% and 0.49%, respectively. Since these errors are considered acceptable, the accuracy of the modified constitutive model can be considered verified. The results of this study can provide theoretical support for the performance study on rubber isolated bearings under the complex ocean environment and the life-cycle performance evaluation of bridges and other offshore structures.

Characteristics of the Main Journal Bearings of an Engine Based on Non-linear Dynamics

Many simple nonlinear main journal bearing models have been studied theoretically, but the connection to existing engineering system has not been equally investigated. The consideration of the characteristics of engine main journal bearings may provide a prediction of the bearing load and lubrication. Due to the strong non-linear features in bearing lubrication procedure, it is difficult to predict those characteristics. A non-linear dynamic model is described for analyzing the characteristics of engine main journal bearings. Components such as crankshaft, main journals and con rods are found by applying the finite element method. Non-linear spring/dampers are introduced to imitate the constraint and supporting functions provided by the main bearing and oil film. The engine gas pressure is imposed as excitation on the model via the engine piston, con rod, etc. The bearing reaction force is calculated over one engine cycle, and meanwhile, the oil film thickness and pressure distribution are obtained based on Reynolds differential equation. It can be found that the maximum bearing reaction force always occurs when the maximum cylinder pressure arises in the cylinder adjacent to that bearing. The simulated minimum oil film thickness, which is 3 μm, demonstrates the reliability of the main journal bearings. This non-linear dynamic analysis may save computing efforts of engine main bearing design and also is of good precision and close connection to actual engine main journal bearing conditions.

Effect of Manufacturing Errors on Static Characteristics of Externally Pressurized Spherical Air Bearings

Externally pressurized spherical air bearings are the key component of the three-axis air bearing table, and the manufacturing errors of the bearing affects the performance of the air bearing table. However, the manufacturing errors are unavoidable, and the pursuit to enhance the manufacturing accuracy will increase the cost greatly. In order to provide some theoretical guideline for the tolerance choice in the design of the externally pressurized spherical air bearings with inherent compensation, the effects of several manufacturing errors on the static characteristics of the air bearing are studied. Due to the complex geometry of the computational domain, an unstructured meshing technology is used for mesh generation. A finite-volume method is adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations. A modified SIMPLE algorithm which is suitable for compressible flows is applied to solve the discretized governing equations. The effects of the dimension error and the roundness error of the ball head and the ball socket on the static characteristics are investigated. The investigation result shows that the positive dimension error and the oblate spheroid-type roundness error of the ball head as well as the negative dimension error and the prolate spheroid-type roundness error of the ball socket can improve the bearing capacity and static stiffness of the air bearings by reducing the mass flow. The calculation method proposed in this paper fits well for the general principle, which can be extended to the characteristics analysis of other air bearings.