Coefficients Of Bearings Research Articles

A review: Enhancing tribological properties of journal bearings composite materials

Abstract Tribology is the science of studying friction, wear, and lubrication. Composite materials consist of two or more constituents (phases): the discontinuous phase represents the reinforcement and the continuous phase represents the matrix. Journal bearing is manufactured from various composite materials. This article reviews the literature on improving the tribological properties of journal bearings made of composite materials (polymer matrix composite materials and metal matrix composite materials) by dividing the previous studies into six primary sections depending on the kinds of composite materials. An efficient method was utilized to solve the problems of composite journal bearings in water lubrication such as wear resistance, reduced friction, and increased service life of journal bearings in various applications especially in ships. The impact of composite materials, which were added through thermoplastic such as polytetrafluoroethylene (PTFE), polyether-ether-ketone, POM, and PA66, thermoset such as epoxy, polyester, and phenolic reinforced with fibers, and thermoplastic with thermoset (PTFE/epoxy composite) to reduce wear rate and coefficient of friction, and also the addition of nanomaterials to composite journal bearing to enhance the tribological properties in various applications were examined. The last section used metal matrix composite reinforced to other metal or alloy to give the attractive mechanical properties used to improve wear resistance and friction coefficient of journal bearing. The novelty of this article lies in the comprehensive analysis of various composite materials and their effect on the tribological properties of journal bearings, providing future insights into bearing design and optimization to improve performance.

Identification of dynamic coefficients of gas foil bearings by simulated excitation based on coupled fields

The dynamic coefficients (dynamic stiffness coefficient and dynamic damping coefficient) of gas foil bearings (GFBs) are important for transient dynamics calculation and stability analysis of the GFBs-rotor system. Although the perturbation method can be used to calculate the dynamic coefficients, it can only consider a single whirl ratio. Moreover, the whirl ratio is assumed and not practical. Therefore, this paper proposes an identification method of dynamic coefficients of GFBs by simulated excitation. Firstly, based on single journal-single GFB model considering gas-structure interaction by coupled fields, harmonic excitations were applied to the rotor to obtain the shaft orbit. Next, frequency response function method and equivalence coefficient method were used to identify dynamic coefficients. The former method is suitable for the case where response and excitation are same frequency, namely linear problem. The latter method is fit for the situation in which the response has multiple frequency components, namely nonlinear problem. Finally, examples were carried out, and the results from different methods were compared and analyzed. This research work lays a theoretical foundation for the design of the GFBs-rotor system.

Lumped parameters models for the stability analysis of rotors supported on gas bearings

In this paper different lumped parameters models are presented for the stability analysis of rotors supported on gas bearings. The analysis is carried out taking into account the damping and stiffness coefficients of journal bearings, calculated with the perturbation method. Lumped parameters models of different complexity are discussed for the description of the main rigid modes of the spindle. In case of symmetric systems, it is shown that the complexity of the model can be reduced by halving the number of the degrees of freedom. The analogy with the single mass approach is demonstrated. The considerations discussed in the paper are preliminary for the stability analysis of more complex systems, such as the ones with non-fixed bushes.

Effects of lubricant rheology and flow turbulence on the dynamic properties of hydrodynamic bearing

The present numerical investigation, which takes into account the coexisted consequence of the turbulence domain and non-Newtonian flow rheology, predicts the dynamic properties of a finite hydrodynamic bearing. Under the proper flow boundary conditions, the turbulence (linear) and non-Newtonian hypotheses have revised the Continuity and Navier–Stokes equation. The finite element approach is acclimated to calculate the clearance extent of the finite hydrodynamic bearing using the Galerkin approach and a sturdy iteration strategy. The cylindrical coordinate's versions of continuity and momentum equations are bestowed for the lubricant field of the finite hydrodynamic bearing, postulating the turbulence domain and non-Newtonian flow rheology. Dynamic properties of a finite hydrodynamic bearing have been enumerated using cross-coupled and direct lubricant-film bearing coefficients, whirl ratio and critical mass at various eccentricity ratios for different ranges of Reynolds numbers and different values of flow behavior index of the non-Newtonian rheological model. In comparison to perfect turbulence and non-Newtonian rheological status, the mixed regime demonstrated improved properties. The direct and cross-coupled lubricant-film bearing coefficients are improved by 12.28% and 20.85% respectively while critical mass is enhanced by 20.55% at selected values of Reynolds number and power-law index. The proposed severe fluid film domain improves the stability of finite hydrodynamic bearings significantly.

Calibration of Oil Film Thickness Acoustic Reflection Coefficient of Bearing under Multiple Temperature Conditions

Rolling mill bearings are prone to wear, erosion, and other damage characteristics due to prolonged exposure to rolling forces. Therefore, regular inspection of rolling mill bearings is necessary. Ultrasonic technology, due to its non-destructive nature, allows for measuring the oil film thickness distribution within the bearing during disassembly. However, during the process of using ultrasonic reflection coefficients to determine the oil film thickness and distribution state of rolling mill bearings, changes in bearing temperature due to prolonged operation can occur. Ultrasonic waves are susceptible to temperature variations, and different temperatures of the measured structure can lead to changes in measurement results, ultimately distorting the results. This paper proposes using density and sound speed compensation methods to address this issue. It simulates and analyzes the oil film reflection coefficients at different temperatures, ultimately confirming the feasibility and effectiveness of this approach. The paper establishes a functional relationship between bearing pressure and reflection coefficients, oil film thickness, and reflection coefficients. This allows for the compensation of reflection coefficients under any pressure conditions, enhancing the accuracy of oil film thickness detection. The proposed method provides technical support for the maintenance of plate rolling processes in the steel industry.

Propagation of Uncertainty in Experimental Dynamic Coefficients of Fluid Film Journal Bearings

Abstract The stiffness and damping coefficients of fluid film bearings play a key role in predicting levels of vibration and stability margins in high-performance industrial rotating machinery. However, variability in the coefficients calculated by numerical bearing codes creates inaccuracies in the rotodynamic predictions. Therefore, there is a strong need for accurate experimental measurement of bearing coefficients for validation purposes. This work examines new propagation uncertainty strategies in bearing coefficients estimation, and for the first time examines the effect of the nonlinearity of the dynamic coefficients on the experimental uncertainty estimated by the Taylor Series Method. The Montecarlo method is presented as a more accurate approach to estimating experimental uncertainty. The results of the analyses are compared to published values from previously reported studies. This paper also proposes a novel method to convert the random behavior in the output of a sensor in the time domain to the frequency domain. It is found this conversion is quite beneficial for the accuracy of the coefficients; in one example, uncertainty estimations of ±84% are reduced to just ±6%, when using the proposed method. This work also reveals that the uncertainty estimations from the Taylor Series Method are not entirely reliable, without additional checks of nonlinearity, and that converting data to the frequency domain, by using the novel method here, is useful for achieving smaller uncertainty estimations than with traditional methodology.

Calculation and Analysis of Equilibrium Position of Aerostatic Bearings Based on Bivariate Interpolation Method

The solution of equilibrium positions is a critical component in the calculation of the dynamic characteristic coefficients of aerostatic bearings. The movement of the rotor in one direction leads to bidirectional variations in the air film force, resulting in low efficiency when using conventional calculation methods. It can even lead to iterative divergence if the initial value is improperly selected. This study concentrates on the orifice throttling aerostatic bearings and proposes a novel method called the bivariate interpolation method (BIM) to calculate the equilibrium position. The equilibrium equation for the rotor under the combined influence of air film forces, gravity, and external loads is established. A calculation program based on the finite difference method is developed to determine the equilibrium position. The process of solving the equilibrium position and the convergence is compared with the secant method and the search method. Furthermore, the variation trend of the equilibrium position and stiffness when the external loads changes are studied based on the BIM. Finally, the correctness of the BIM to solve the equilibrium position is proved by comparing it with the experiment results. The calculation results indicate that the BIM successfully resolves the problem of initial value selection and exhibits superior computational efficiency and accuracy. The equilibrium position initially moves away from the direction of the external load as the load increases, and then this gradually approaches the load direction. The main stiffness increases with increases in the external load, while the variation in cross stiffness depends on the direction of the external load.

Magnetic-controlled friction behavior of a water-lubricated magnetorheological rubber bearing under boundary lubrication

To solve the issue of the non-adjustable friction coefficient of water-lubricated bearings in operation, a water-lubricated rubber bearing is designed based on magnetorheological (MR) rubbers in this study. The experimental platform measured the friction coefficients with different magnetic fields and low speed. The friction coefficient of the MR rubber bearing peaks in boundary lubrication. The friction coefficient of the bearings is controlled by the magnetic field, resulting in a reduction of the friction coefficient up to 36%. The theoretical analysis combines the magnetic-dipole model and the theory of friction trinomials. It revealed that the magnetic-controlled modulus of elasticity and loss factor of MR rubber bearings affect the friction coefficient, with the modulus of elasticity factor dominating.

Parameter Optimization of Friction Pendulum Bearings Based on the Adaptive Genetic Algorithm Considering the Overall Evolutionary Status

Improper design of friction pendulum bearings can lead to poor seismic reduction performance and may result in the failure of local vulnerable components. And the parameter design of friction pendulum bearings mainly relies on experience and verification calculations at present. This paper proposes an adaptive genetic algorithm considering the overall evolution state of the population, adjusting crossover and mutation probabilities adaptively based on individual fitness and population diversity. Compared to traditional algorithms, it exhibits better global search capabilities and convergence efficiency. Combining the improved genetic algorithm with finite element models, a parameter optimization method is proposed. The parameters of friction pendulum bearings are optimized. In response to the situation in this paper, the optimal friction coefficient of the friction pendulum bearing is determined to be 0.01 and the optimal equivalent radius is 3.3 m. This can provide a reference for the design of seismic isolation devices.

Numerical investigation on the rotordynamics of a high-speed air compressor supported by gas foil bearings

Gas foil bearings are particularly suitable for supporting rotors of hydrogen fuel cell air compressors. Based on Reynolds equation and elastic mechanics theory, a fluid-structure interaction model of gas foil bearings is introduced. A series of perturbation equations are developed and solved to obtain stiffness and damping coefficients of the foil bearings at different rotational speeds. A lumped model of the bearing-rotor system is developed and the rotor stability is analysed by innovatively applying Riccati transfer matrix method. The natural frequencies of the rotor are calculated and then the Campbell diagram is plotted. Subsequently, the critical speeds and the corresponding vibration modes are obtained. The predicted values of the proposed model are highly consistent with the reported experimental results and finite element results, indicating the accuracy of the model. Based on the calculation of rotor unbalance response, further investigation on the effects of unbalance parameters on unbalance response is conducted. The results obtained in this paper could provide theoretical reference for the design of foil bearing supported rotors.

Finite element analyses of rotor/bearing system using second-order journal bearings stiffness and damping coefficients

The rotor-bearing system is a crucial component of rotating machinery, such as turbines, pumps, compressors, and turbogenerators, which are widely used in various advanced engineering fields. This work presented a methodology for studying the behavior of an elastic Jeffcott rotor supported by two similar fluid film journal bearings. A finite element model using consistent matrix formulation was employed to simulate the shaft, including the external load, with four degrees of freedom per node. The small perturbation method was used to evaluate the second-order bearing coefficients of a journal bearing of finite length. These coefficients were further integrated with the finite element model to evaluate the dynamic response of the flexible rotors. Moreover, the system equations of motion were presented in dimensional form. The results of the second-order bearing coefficients analysis agreed with nonlinear analysis when the speed was less than the threshold speed, while there was a pronounced difference in second-order analysis when the speed was above the threshold speed. The behavior of the rotor-bearing system was studied using dynamic response and orbit diagrams, revealing that changes in rotational speed significantly affected the rotor’s stability.

A Contribution to Experimental Identification of Frequency-Dependent Dynamic Coefficients of Tilting-Pad Journal Bearings with Centered and Off-Centered Pivot

Linearized dynamic bearing parameters and models are of essential interest for rotordynamic analyses in machine design. This paper experimentally studies the impact of pad preload and pivot offset on the frequency-dependent characteristics of dynamic stiffness (K) and damping coefficients (C) of a KC-model for tilting-pad journal bearings. For this purpose, two four-pad test bearing configurations (preload m=0.17, pivot offset 0.5 and preload m=0.47, pivot offset 0.6) that differ highly with respect to the pad design parameters are investigated. Contributing effects on the results due to geometric differences are excluded as far as possible, as only one aligning ring and one pivot support design is used. The tests are conducted on a high-performance test rig for surface speeds up to 140 m/s and excitation frequencies of 500 Hz. Significant deviations between the two bearings are identified that generally match theoretically predicted differences and, therefore, contribute to the validation of dynamic bearing modeling.

Modelling and Simulation of Aerodynamic Cylindrical Bearings Using ANSYS Hydrodynamic Bearing Element Types

Modern power engine concepts and environmental restrictions demand oil-free lubrication of rotors, for example, by gas bearings. However, the stiffness and damping properties ruling the rotor’s dynamics are poorly documented for aerodynamic bearings and simple calculation methods are lacking. Based on the similarity between aerodynamic and hydrodynamic journal bearings, it is investigated to what extent the hydrodynamic bearing element types of the commercial FE program ANSYS are also suitable for air bearings. Within these elements, the compressibility of the gas is neglected. After verification of the ANSYS hydrodynamic element types with literature data for cylindrical hydrodynamic bearings, the stiffness and damping coefficients of a cylindrical aerodynamic bearing are calculated by using the ANSYS hydrodynamic element types. In the examined speed range, the results agree well with literature data that consider gas compressibility. Therefore, the FE elements designed for hydrodynamical journal bearings may also be used for simulating cylindrical aerodynamic bearings. The presented calculation approach provides a compact and easy-to-use method for rotordynamic simulations with cylindrical aerodynamic bearings in a single development environment.

Assessing the fatigue wear effect on traction coefficient and dynamic performance of roller bearing

Rolling element bearings are commonly employed in rotating machinery to support rotating shafts. These machinery elements are vulnerable to failure due to increased friction and heat, which cause progressive wear on the rolling interaction surfaces of the bearing. The failure of bearings causes an unpredicted shutdown of equipment, leading to an increase in downtime and financial losses. Various condition monitoring techniques have been developed for periodic assessment of failure in roller-bearing systems. The focus of this work is to establish a relationship between surface fatigue wear, film thickness [Formula: see text], asperity load ratio [Formula: see text], lubricant film stiffness [Formula: see text] and traction coefficient [Formula: see text] parameters. A periodic assessment of the above-mentioned parameters was made on the test bearing, which was subjected to a fatigue test for 2000 h. The results acquired from the experimental study highlighted that, as surface fatigue wear on the bearing interaction surfaces and lubricant degradation occurred with an increase in fatigue load cycles, the asperity load ratio [Formula: see text] and traction coefficient [Formula: see text] parameters showed a gradual rise in trend which further resulted in a difference in the dynamic behaviour of the bearing system.

A Simplified Model for the On-Line Identification of Bearing Direct-Dynamic Parameters Based on Algebraic Identification (AI)

In this paper, a mathematical model is presented to identify the direct dynamic coefficients (kxx, kzz, cxx, czz) of a pressurized bearing in a rotor-bearing system. The presented mathematical model for online identification is the result of the application of the algebraic identification approach to a two-degree-of-freedom rotor-bearing model. The proposed identification model requires only the vibration response as the input data. The performance of the model was assessed by theoretically and experimentally testing the proposed identifier at different shaft frequencies and, for the experimental test, a pressurized bearing that has hydrodynamic and hydrostatic characteristics at a support pressure of 10 psi was considered. The working fluid is Chevron GST 32 oil. The results show negligible differences between the vibration response of the experimental rotor and those obtained numerically using the identified direct dynamic coefficients of the pressurized bearing. In addition, it is observed that the algebraic identifier determines the identified parameters in a time less than 0.2 s. The proposed identifier can be used in other types of bearings, which is a great advantage over other identifiers.

Calculation of Dynamic Coefficients of Air Foil Journal Bearings Using Time-Domain Identification

Dynamic coefficients of a bearing are basic elements of rotor dynamics analysis. At present, there are still some issues in the calculation of the dynamic coefficient of air foil bearing. In this paper, the dynamic coefficients of the air foil bearing are calculated by time-domain identification. This method does not need to linearize the system equations, so it is generally applicable to different models for air foil bearings. Using the established method, this paper verified the calculation results using the foil model with axial uniform deformation for the first time, and the influence of the foil model on the dynamic coefficients was studied. The calculation results of the foil models with axial uniform deformation and axial independent deformation have significant differences. Furthermore, the accuracy of the dynamic coefficient method for different disturbance amplitudes was compared. The results indicate that the dynamic coefficient method has good accuracy over a large disturbance range.

Dynamic Behavior of a Tilting-Pad Thrust Bearing Operating Under a Hybrid Lubrication Regime

Abstract The present contribution aims to evaluate the effects of the oil pressure injection on the dynamic behavior of a hybrid-lubricated tilting-pad thrust bearing. First, a thermohydrodynamic model is applied to determine the equilibrium position as dictated by pressure and temperature distributions resulting from both hydrodynamic and hybrid lubrication regimes. Subsequently, the perturbation and frequency reduction methods are applied to determine the stiffness and damping coefficients of the bearing for various operational conditions. The results show that the dynamic force coefficients are strongly dependent on the operational conditions of the bearing, such as static load and rotating speed, as well as the perturbation frequency, for both lubrication regimes. The quantification of the injection pressure influence on the force coefficients of hybrid-lubricated thrust bearings is the main original contribution of this work.

Mechanical Behaviors and Numerical Simulation Analysis of a New Isolation System

Finite element analysis is one of the key steps in evaluating the effectiveness of an isolation system. The aim of this paper is to research the mechanical properties of sliding and rolling friction systems and their application for isolating frame structures. A hybrid seismic isolation system is proposed, which aims to protect the superstructure by reducing dynamic response. The effect of different parameters on the friction coefficient of the isolation bearing was tested using a compression-shear testing machine, and the results showed that various parameters significantly affected the friction coefficient. In addition, a numerical analysis finite element model was established using SAP2000 software to compare the seismic isolation performance of the hybrid isolation system with that of traditional seismic-resistant structures. The results showed that the composite isolation system not only effectively reduced inter-story shear and acceleration, but also slightly enhanced the seismic isolation effect as the friction coefficient decreased.

Probabilistic Seismic Sensitivity Analyses of High-Speed Railway Extradosed Cable-Stayed Bridges

It is known that the extradosed cable-stayed bridge, a hybrid bridge, possesses the virtues of both classic cable-stayed bridges and girder bridges in mechanical behaviors. In this paper, the sensitivity of seismic fragility demand parameters (SFDP) of a high-speed railway extradosed cable-stayed bridge is studied systematically along with the consideration of structural parameter uncertainty. Based on the probability distribution and correlation of random parameters, the Latin hypercube sampling method is adopted herein. The dynamic 3D finite element model of the employed bridge is established by using powerful and attractive OpenSEES nonlinear software. A nonlinear incremental dynamic analysis is performed to consider the randomness of structural parameters using sampling analysis. Some important conclusions are drawn indicating that the structural design parameter uncertainty predominantly has influence on the SFDP for fragility analysis of bridge structures. The design parameters of extradosed cable-stayed bridges are categorized and identified as primary, secondary and insensitive parameters. The high sensitivity parameters of extradosed cable-stayed bridges for fragility analysis include friction coefficient of bearing, concrete bulk density, damping ratio, peak compressive strength of confined concrete, component size and peak strain of confined concrete. Additionally, the strength and strain of unconfined concrete cannot be ignored. Furthermore, the uncertainty of structural design parameters fails to be responsible for the cable force responses due to larger girder stiffness. The structural design parameter uncertainty has a significant influence on the responses of extradosed cable-stayed bridges for seismic fragility analysis.

A time-varying instantaneous frequency fault features extraction method of rolling bearing under variable speed

Under variable speed, the time-frequency analysis (TFA) method for processing rolling bearing vibration signal is susceptible to noise, which cannot extract accurate time-frequency features. Plus, the special meaning of each time-frequency feature remains unclear. Based on the dynamic characteristics of rolling bearing and combined with the improved multisynchrosqueezing transform (IMSST), empirical Fourier decomposition (EFD), and generalized demodulation (GD), a time-varying instantaneous frequency fault features extraction method of rolling bearing under variable speed is proposed in this paper. Firstly, the instantaneous frequency (IF) trajectory of the rotating shaft is accurately represented by the better time-frequency resolution of IMSST, and the demodulation phase function for GD is constructed by combining the fault characteristic coefficient (FCC) of the rolling bearing. Then, the components in the signal that match the demodulation phase function are mapped into constant IF components. Through adaptive EFD and inverse demodulation, the time-varying IF components satisfying the conditions are separated. Finally, based on the Hilbert transform (HT) and adaptive time-frequency spectrum (ATFS), a high-quality time-frequency representation (TFR) is reconstructed to extract the time-varying IF fault features and identify the defect type of rolling bearing. The simulation and measured signal analysis results show that the proposed method can accurately extract fault features of rolling bearings with different defects under variable speed and identify fault types, thus maximally avoiding the influence of noise and interference components.