Coefficients Of Bearings Research Articles

Influence of Spiral Angle on the Performance of Spiral Oil Wedge Sleeve Bearing

Spiral angel is an important structure parameter of spiral oil wedge sleeve bearing, which produces greater impact on bearing performance. Based on JFO boundary condition, the generalized Reynolds equations considering four slip conditions are established. Using the concept of partial derivatives, stiffness and damping coefficients of sleeve bearing are calculated. The results show that carrying capacity and friction drag of oil film decrease, temperature rise decreases first and then increases, and end leakage rate, stiffness, and damping coefficients generally increase first and then decrease with the increase of spiral angle. The carrying capacity, friction drag, temperature rise, stiffness, and damping coefficients are smaller and the end leakage rate is higher considering wall slip and JFO condition compared with reckoning with no slip and Reynolds boundary condition.

Influences of journal with 3D form errors on dynamic coefficients of hydrodynamic bearings yielded to JFO boundary conditions

The dynamic characteristics of the journal with form error are analyzed, including normalized stiffness and damping coefficients. A new expression for journal surface with form error is presented, which is capable of formulating any types of form errors on the journal, and the dimensionless Reynolds equation is renewed and solved suffering from the Jakobsson, Floberg, and Olsson boundary conditions. The results show that form errors do have a significant influence on the dynamic performance of journal bearings and that the uncertainty attribute of form error could result in variations of dynamic properties so significantly that the system might operate in an entirely different way. Therefore, it is necessary to take more operating information into account, such as the elaborate state of the journal surface, in order to predict the bearing performance more accurately.

Identification of Dynamic Characteristics of Hybrid Bump-Metal Mesh Foil Bearings

The stability of oil-free high-speed turbo-machinery can be effectively improved by increasing the damping characteristic of the gas foil bearing (GFB). Novel hybrid bump-metal mesh foil bearings (HB-MFBs) have been previously developed. Prior experimental results show that the parallel combination of bump structure and metal mesh not only can improve the structure stiffness but also provide better damping property compared with the bump-type foil structure. To investigate the dynamic behavior of floating HB-MFBs and promote its application, this study measured the dynamic force coefficients of HB-MFBs on a rotating test rig. The vibrations of HB-MFBs with different mesh densities (40%, 32.5%, and 25%) and a generation І bump-type foil bearing (BFB) with similar size are measured under static and impact loads to estimate the bearing characteristics. Static load test results show that the linear stiffness decreases when the air film is generated (from 0 rpm to 20 krpm) but increases gradually with speed (from 20 krpm to 30 krpm, and 40 krpm). Moreover, the dynamic force coefficients of HB-MFBs indicate the significant influence of metal mesh density on bearing dynamic characteristics. The growth in block density increases the dynamic stiffness and damping coefficients of bearing. The comparison of HB-MFB (32.5% and 40%) and BFB emphasizes the good damping characteristics of HB-MFB.

A numerical method for solution of the discharge coefficients in externally pressurized gas bearings with inherent orifice restrictors

To study the discharge coefficients of aerostatic bearings, a new numerical method which combines the method of “separation of variables” for solution of laminar boundary-layer equations and analytical solution of Reynolds equation is proposed. The discharge coefficients are suitable for solution of Reynolds equation. The influences of flow and geometry parameters on discharge coefficients are investigated and the results indicate that there exists parameters insensitive and sensitive regions in discharge coefficient analysis. Further research shows that flow and geometry parameters affect discharge coefficient by influencing the pressure ratio (pr/ps) and discharge coefficient tends to be constant when pressure ratio is approximately less than 0.6, which is the reason that there exists the parameters insensitive and sensitive regions.

A modified adaptive backstepping method for shaft deflection tracking control of magnetically suspended momentum wheel with nonlinear magnetic torque

A modified adaptive backstepping tracking method is proposed to improve the tracking performance of the magnetic bearing system with nonlinear magnetic toque. For a magnetically suspended momentum wheel, two dimensional gyroscopic torque can be produced when the rotor shaft is actively deflected by the active magnetic bearing. High precision rapid tracking control of shaft deflection is desiderated to provide high precision and wide bandwidth outputting torque. The nonlinearity of magnetic bearing is analyzed initially, and the stiffness coefficients of magnetic bearing can be treated as bounded continuous functions with respect to deflection angles. A fuzzy function based adaptive law is proposed to estimate the stiffness coefficients. Combining with a modified backstepping method, the proposed control strategy can deal with the nonlinearity efficiently when the shaft deflects rapidly, and its stability is proved by Lyapunov stability theory. To validate the effectiveness of this method, numerous simulations are performed and the results indicate that this method improves the tracking precision when tracking high frequency reference deflection angles.

Feasibility study of a turbocharger rotor supported by air foil bearings with diameter of 17 mm focusing on rotordynamic performance

This paper presents the feasibility study of an oil-free turbocharger with journal bearing diameter of 17 mm. Rotordynamic performance of a turbocharger rotor, supported by two identical bump-type foil journal bearings and a pair of foil thrust bearings, is predicted and tested. High-pressure cold nitrogen is adopted to drive the turbocharger rotor. In rotordynamic analysis, the critical speeds and logarithmic decrement of the turbocharger rotor are predicted by employing the finite element method, in which the stiffness and damping coefficients of foil journal bearings and aerodynamic cross-coupled stiffness of the turbine are taken into account. Compared with experimental results, the accuracy of the prediction for rotordynamic analysis is verified for 7.82% marginal error of the critical speed. During the experiment, three foil journal bearings with different nominal clearances are manufactured and tested. The maximum stable operating speed reaches 105,000 r/min for this 17-mm-diameter oil-free turbocharger rotor system. Test results indicate the nominal clearance has a negative influence on threshold speed of sub-synchronous motions. When the nominal clearance is relatively small, the foil journal bearing could not lift off due to a large starting torque, while sub-synchronous motions would emerge under a large nominal clearance because of the reduced stiffness and damping coefficients of foil journal bearings.

Investigation on Axial Displacement Fault Mechanism Based on Dynamic Characteristic Coefficients Identification of Tilting-Pad Thrust Bearing

To prevent the thrust bearing damage faults, the thrust bearing pad temperature and the static axial displacement variation are usually monitored and cared about, but axial vibration caused by axial dynamic excitation can also result in the severe rubbing. An electric oil pump system with overflow valve is designed on a similar industrial centrifugal compressor test-rig to apply the axial low-frequency excitation from 3 to 7 Hz, and the axial and radial vibration response amplitudes are analyzed. Then, the stiffness and damping coefficients of tilting-pad thrust bearing (TPTB) are identified by instrumental variable filter (IVF) algorithm to reveal the mechanism of TPTB dynamic characteristics affecting axial vibration. Finally, a fault case about surge and the rubbing of thrust bearing is studied. Compared with axial vibration, radial vibration does not directly correlate to axial excitation, and the axial frequency spectrum is an effective method to diagnose axial displacement faults; the static axial load, the dynamic excitation amplitude and the excitation frequency all exert influence on thrust bearing dynamic characteristics and axial vibration response. The research results can guide the design of thrust bearings and help to diagnose the axial displacement faults, while the test device and method can be used to measure the static and dynamic characteristics of thrust bearings.

Identification of dynamic coefficients of the journal bearing considering velocity slip of cavitation zone in the rotating spindle unit

A rotating spindle unit, supported by the journal bearings, is developed to improve the cavitation erosion resistance of the journal bearing as well as the spindle dynamic performance. The turbulent lubrication model considering velocity slip in cavitation zone is derived, and the static and dynamic parameters of the journal bearing are obtained. An identification algorithm is further derivated to identify simultaneously the 16 dynamic coefficients of the two journal bearings in the spindle unit. The available experimental results reveal that the journal bearing coefficients are well predicted and estimated by the present model, and the estimated bearing parameters by regularization solution are in good agreement with the assumed values, while it has opposite effect by directed solution for discrete ill-posed problems. It is concluded that the identification accuracy of bearing parameters is governed by the displacement error, and the percentage deviation of dynamic coefficients decreases with the decrease of the displacement error.

Comparison of Perturbed Reynolds Equation and CFD Models for the Prediction of Dynamic Coefficients of Sliding Bearings

The accuracy and utility of rotordynamic models for machinery systems are greatly affected by the accuracy of the constituent dynamic bearing models. Primarily, the dynamic behavior of bearings is modeled as linear combination of mass, damping, and stiffness coefficients that are predicted from a perturbed Reynolds equation. In the present paper, an alternative method using Computational Fluid Dynamics (CFD) with a moving boundary is used to predict the dynamic coefficients of slider bearings and the results are compared with the more commonly employed perturbed Reynolds equation model. A linear slider bearing geometry is investigated and the results serve as precursors to similar investigations involving the more complex journal bearing geometries. Time and frequency domain methods for the estimation of dynamic coefficients are shown to give comparable results. For CFD with a moving boundary, temporal inertia is found to have a significant effect for a reduced, squeeze Reynolds number less than one. The temporal inertia effect is captured through an added mass coefficient within the dynamic model of the bearing.

Commissioning of a Novel Test Apparatus for the Identification of the Dynamic Coefficients of Large Tilting Pad Journal Bearings

This paper describes the commissioning of a novel test bench for the static and dynamic characterization of large tilting pad journal bearings, realized within a collaboration of the Department of Civil and Industrial Engineering of the University of Pisa, BHGE and AM Testing.The adopted test bench configuration has the test article (TA) floating at the mid-span of a rotor supported by two rolling bearings. The TA is statically loaded vertically upwards by a hydraulic actuator and excited dynamically by two orthogonal hydraulic actuators with multiple frequency sinusoidal forces. The test rig is capable of testing bearings with a diameter from 150 to 300 mm. It includes very complex mechanical, hydraulic, electrical and electronic components, and needs, for the whole plant, about 1 MW of electric power.The commissioning of the testing system involved several aspects and presented various issues. This work focuses on measuring systems and data acquisition of high-frequency data (forces, accelerations and relative displacements) and on data processing for the identification of the bearing dynamic coefficients. The identification procedure is based on the linearity assumption and the principle of superposition, operating in the frequency domain with the fast Fourier transforms of the applied forces and displacement signals. First results, referred to a 4-pad bearing, are in satisfactory agreement with theoretical ones.

Prediction of Stiffness and Damping of Gas Foil Journal Bearing for High-Speed Rotor

Contamination-free bearings such as gas bearings are an alternate solution in various high-speed turbomachinery such as turboexpander and turbocharger. The major limitation of gas bearing is its low dynamic characteristics such as stiffness and damping. Gas foil bearings (GFBs) are the bearings with elastic spring-like structure in between the runner and the bearing base. These elastic structures in GFB help to tailor the dynamic coefficients of bearing by modifying foil material and its geometry. A bump type GFB is quite popular among tribologists due to its ease of fabrication and assembly compared to other types of GFB. In a bump type GFBs, the overall bearing stiffness is due to stiffness the bump foil, top foil, and the pressurized bearing gas. The overall damping inside the bearing is due to coulombs friction between (i) top and bump foil and (ii) bump foil and the bearing base. A number of numerical techniques have been successfully developed to predict the static characteristic, unlike the dynamic characteristics. This paper discusses a perturbation technique to predict the dynamic characteristic such as overall stiffness and damping of a bump type gas foil bearing. Finite difference formulation is used to determine four stiffness and four damping coefficients. The four coefficients include two direct and two cross-coupled coefficients. The influence of foil material and its geometry over the dynamic characteristics are also discussed in the paper.

A numerical procedure for evaluating physical parameters of ergonomic assessment for cart pushing/pulling tasks

Manual Material Handling (MMH), by pushing or pulling carts, is a common task that characterizes any manufacturing or service operation, and there is always a significant human input to those operations in terms of physical load.The physical load represents the effect of input forces during MMH operations that depend on the interaction between material handling equipment and the working environment.Many times MMH represents a critical issue related to human-machine interaction due to the carts can work in environment with parameters different from those used in designing, subjecting workers to risk of musculoskeletal disorders.The aim of this work, developed in collaboration with Fiat Chrysler Automobiles (FCA), is to develop a new procedure that allows estimating the initial and the maintenance forces necessary to push or pull carts, knowing the characteristics of the cart and the environment in which it works, in order to preventively assess the ergonomic indexes according to ISO 11228-2.The procedure is based on multibody simulations. The cart is modeled by Computer Aided Design (CAD) code and, then, imported in a multibody code where numerical simulations are performed in order to calculate the forces. In the multibody code static and dynamic friction coefficients of bearing of wheels are assigned, together with parameters of contact between wheels and floor.Changing the pivot angle of two floating wheels, several simulations have been carried out.Moreover, considering a cart used at the assembly line of the FCA plant of Pomigliano d’Arco (Naples), experimental tests have been performed in order to validate the procedure by comparing numerical results with the experimental ones.

Theoretical research of dynamic characteristics of Tc bearing of measurement while drilling

In this paper, through analyzing Tc bearing by the theory of Hydrodynamic lubrication, the unsteady Reynolds equation of Tc bearing under the dynamic-state condition is initially established. The formula of Tc bearing’s liquid-film dimensionless stiffness coefficient and damping coefficient is derived. Furthermore, two kinds of the distribution curves of Tc bearing’s liquid-film dimensionless stiffness coefficient, damping coefficient against Tc bearing’s eccentricity ratio and width-diameter ratio are displayed respectively, and the stability criterion of liquid film is worked out and the angular speed of instability of bearing shaft is calculated. Overall, conclusions are drawn: downhole system improves the entire system’s stability by enhancing the stiffness of bearing shaft itself. The improvement of the stability of bearing shaft itself, which can be done by altering the structure of Tc bearing and adopting better spiral flutes and ellipse groove can strengthen the whole system’s stability. The high width-diameter ratio of Tc bearing increases the liquid film’s stiffness coefficient and damping coefficient of Tc bearing. The rotational rate of rotary table is lower than half of that of the supporting system of Tc bearing.

Performance of a novel foil journal bearing with surface micro-grooved top foil

To improve the performance of foil bearing including load capacity and stability, the surface micro groove structure on top foil is proposed, which is possible with the development of surface micro machining process. The micro groove structure on top foil can be processed by laser surface process, chemical etching, mechanical grinding, etc. This paper proposes a novel bump-type gas foil journal bearing with surface micro-grooved top foil and investigates the influence of micro groove depth on bearing performance theoretically. A modified pressure governing equation is established with the consideration of gas rarefaction, and the performance of the bearing is analyzed based on numerical simulation. By considering the variation of top foil thickness for surface micro groove, the load capacities with and without gas rarefaction considered are obtained by finite difference method, where the 2D thick plate model is adopted for the top foil. By employing the perturbation method, the force coefficients of this type foil bearing are calculated. The results indicate this novel foil journal bearing with surface micro-grooved top foil can decrease the end leakage and increase pressure around load domain efficiently. The load capacity and dynamic properties are improved. Moreover, with the increment of micro groove depth, the load capacity and direct stiffness are reinforced further. For the foil journal bearing with a micro groove depth of 8 µm on top foil, the load capacity and direct stiffness increase by about 11.89% and 11.87%, respectively, compared with traditional foil journal bearing.

Determination of stiffness coefficient of stern shaft bearing

In this article the authors solve the problem of determining a stiffness coefficient of stern shaft bearing with mechanical and geometrical parameters of the ship shafting and stern bearings. The influence of the stiffness coefficient on transverse and parametric vibrations is investigated. The dependence of the Ship’s Shafting of tension state and deformation of stern bearing is shown. The equation for determining the stiffness coefficient is obtained. The numerical value of the stiffness coefficient of feed bearings of some types of vessels is presented.

THE RELATIONSHIP BETWEEN STIFFNESS LOSSES AND LOSSES IN BEARINGS OF ROPE BLOCKS

Purpose. To determine the efficiency of rope blocks, it is necessary to determine the stiffness coefficient of the ropes of blocks, taking into account the classification group of the mechanism and the wrapping angle of a block by a rope. At this one should use well-tested values of the efficiency coefficients of the rope blocks, taking into account the wrapping angle of a block by a rope and the analytically found friction coefficients of the rolling bearings given to the trunnion. Methodology. The work presents the analytical method of determining the coefficient of bearing resistance of the block when it is rotated by both the inner and outer cages, as well as the design scheme of the bearing of the block. Findings. The analysis of the lubrication method effect, the operating mode of the mechanism and the wrapping angle of a block by a rope on losses in bearings was carried out for rope blocks. The corresponding comparative tables of losses are given. Analysis of the obtained calculation results allows us to establish: 1) the main resistance affecting the cable blocks efficiency is the resistance in bearings; 2) the second largest component is the stiffness losses, depending on the operating mode, the wrapping angle of a block by a rope, the type of bearing lubrication; 3) the block efficiency when rotating the inner cage is higher than rotating the outer one by about 3% with thick lubrication and 1M mode; 4) in the sequential location of assemblies with a rolling bearing, it is necessary to strive for the design of the assembly in which the inner cage rotates; 5) with the number of blocks up to 5, one can use the recommended definitions of block bearings in the literature with an error in the efficiency value of up to 10%. Originality. The authors obtained values of resistances in the rolling bearings of the rope blocks and stiffness losses due to the girth of the block by the rope. In this case, dependences were used to determine the coefficient of rolling friction, obtained using the Hertz analytic dependences on determination of contact stresses and deformations, as well as the experimental values of the coefficient of rolling friction for the blocks. Practical value. The resistance values obtained by the authors can be used for refined calculations of the mechanisms of machines.

Bending fault evaluation for the HP-IP rotor system of the nuclear steam turbine based on the dynamic model

With considering the unbalance mass-fluid film bearings-rotor elements, a dynamics model for the nuclear half-speed 1000 MW saturated steam turbine with No. Dongfang HN1089 is constructed. By solving of the Reynolds Equation and the dynamics model, the oil pressure distribution and dynamic coefficients of the fluid film bearings, and the unbalance response of the rotor, are obtained. The method for evaluating the bending fault based on the dynamics model is proposed, in which the bending parameter is transformed as the unbalance mass. A case on the bending fault evaluation for HN1089 is carried out. The results show that the response sensitivity of HN1089 on the unbalance mass is about 1/6 that of the thermal power units with the same capacity (1000 MW); and it is difficult to decrease the excited response from the bending fault even to add the maximum unbalance mass. In actual, the removing stress in the partial zone and turning method are applied to deal with the HP-IP rotor bending fault, and the response of the repaired rotor is 0.033 m by the actual field test. The results show the model and the method for evaluating the bending fault are accurate and reasonable, which will provide the important theoretical guide for fast and accurately dealing with such bending fault in the steam turbine rotor system.

Model-based interpolation-iteration method for bearing coefficients identification of operating flexible rotor-bearing system

The requirement of bearing coefficients identification based on flexible rotor-bearing systems has stimulated the investigation of bearing forces over the years, whereby in industry high speed balancing machines and flexible rotor-bearing test rigs can be used to measure the dynamic force coefficients of bearings. However, the actual rotor vibration at the bearing nodes cannot be measured or simply calculated by the data acquired from a single measurement station outside of the bearing. To solve this problem, a double-section interpolation-iteration method to identify the dynamic coefficients has been developed which uses previously identified coefficients to predict new vibration vectors from a finite element model and then updates the vibration vectors at the bearings to recalculate the coefficients. Numerical investigations on the estimation error, convergence, and robustness against noise were carried out, and the specific measurement process and method are presented. Simulation results show that this method has high confidence intervals in the identification of both direct stiffness and damping coefficients. Moreover, the experimental work, in which an active magnetic bearing was used to excite a flexible test rig supported by tilting pad bearings, was also carried out to validate the method, with the vibration shape predicted by the identified results matching the test data very well and the first forward mode parameters also matching the results from sine-swept identification.

A direct numerical approach to compute the nonlinear rotordynamic coefficient of the noncircular gas journal bearing

Gas bearings are extensively used in several industrial applications to support the rotating load at high speed due to its favorable characteristics. The numerical computation of the gas film damping and stiffness coefficients is a difficult task due to nonlinearity in the Reynolds equation for compressible lubricant. In the present work, a numerical method based on the finite element method is developed for the direct computation of gas film damping and stiffness coefficients. In this method, a double partial differential equation approach has been used to compute the dynamic characteristics. Further, the numerical results presented shows that the bearing ellipticity ratio significantly affects the nonlinear trajectory of the journal.

Stiffness and damping coefficients for journal bearing using the 3D transient flow calculation

The dynamic coefficients of journal bearing are necessary components in the analysis of linear stability and response of rotating dynamic systems. We propose a new method for the numerical identification of bearing support force coefficients in flexible rotor-bearing systems based on the 3D transient flow calculation. The CFD commercial software FLUENT is mainly used in this simulation, which employs a finite volume method for the discretization of the Navier-Stokes equations. To determine the dynamic coefficients, a new mesh movement approach is presented to update the volume mesh when the journal moves during the 3D transient flow calculation of a journal bearing. Existing dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. Measurements and identification are performed on a test rotor supported on a pair of identical two-lobe fluid film bearings, and the results obtained from the CFD methods agree well with experimental results. The results indicate that the methods proposed in this paper can predict the dynamic coefficients of the journal bearing in a rotor-bearing system effectively, and provide a further tool for stability analysis.