Pad Pivot Research Articles

Transient Hydrodynamic Analysis of Ball Mill Multi-Pocket Pivoted Pad Hydro-static Bearing

Huge ball mill bearings experience a transient period when they are fed with raw material or their basis is impacted. The behavior of such bearings during the transient period is significant to the safety of the machine. In the present paper, the step load is used to simulate this process. Transient hydrodynamic lubricating models of a multi-pocket pivoted pad hydro-static bearing used in ball mill are established. The hydrodynamic and squeeze effects are take into account, and the models are solved using nonlinear numerical methods. The journal center trajectory, time response of the pad tilting, oil pressure in the pockets, and minimum pad film thickness during the transient period are presented. The oil flow rate evolutions out of the main pockets in all pads are exhibited. The effects of step load on bearing performance are discussed. It was found that the decrease in minimum film thickness can be quite large under the step load impact, which may lead to the damage of the bearing.

On the tilting‐pad thrust bearings hydrodynamic lubrication under combined numerical and machine learning techniques

AbstractThrust bearings are machine elements designed to support axial loads in rotating machinery. The hydrodynamic lubrication analysis of such bearings has been a major subject for many studies over the years, leading to important conclusions for design parameters that affect their optimal operating conditions. Furthermore, the last few years, the influence of the industry 4.0 concept has brought new tools that can revolutionise bearings' design. The aim of this study is to combine numerical analysis and machine learning techniques in order to identify optimal thrust bearing's hydrodynamic designs. For this purpose, the Reynolds equations are solved using the finite difference technique on a 2‐D grid of a tilting pivoted bearing's pad. The bearing pressure distribution; load carrying capacity and friction are calculated for multiple operating conditions. The data produced are used as input for the training of regression models that predict the behaviour of the thrust bearing for a wide range of loads and rotating speeds. Simple and multi‐variable, linear, polynomial and SVM regression models are compared for their accuracy to predicting the bearing's operating conditions. The major findings related with three different lubricants, a monograde SAE 30, a multi‐grade SAE 10W40 and a bio‐lubricant AWS 100 that are compared and their optimal operating conditions are suggested in terms of minimum friction force and maximum load carrying capacity for the bearing pad. AWS 100 is found to be the most suitable lubricant that provides the bearing with low operating friction and high load carrying capacity in all studied cases.

The Effect of the Pivot Stiffness on the Performances of Five-Pad Tilting Pad Bearings

The role of the pivot flexibility in tilting-pad journal bearings (TPJBs) has become essential, particularly for bearings working at high applied load and relatively high rotor speeds. Predictions from a simple bearing model with rigid pivots show incorrect estimation of the dynamic coefficients in comparison with the experimental results. Normally, the more flexible the pad pivot, the lower the dynamic coefficients because the stiffness of the pivot takes in series with the stiffness and damping of the oil film. This paper investigates the influence of pivot stiffness on the dynamic force coefficients of two different five-pad TPJBs as a function of the applied static load and excitation frequency: rocker-backed pivot and spherical pivot bearings. In order to highlight the effect of the pivot stiffness in the spherical pivot bearing, displacement restriction components and elastic copper made shims have been used. Firstly, a thermo-elasto-hydrodynamic model for the static and dynamic characteristics of the two bearings is described. This model takes into account the flexibility of both pad and pivot. The pivot stiffnesses calculated by means of the Hertz theory and those obtained by experiments have been introduced and compared in the model. The clearance profiles of two tested bearing and the shaft center loci obtained by measurement and prediction are also shown. The dynamic coefficients of the two bearings obtained from the numerical simulation were compared with the experimental results. By the analysis it can be concluded that the effect of the pivot flexibility on the clearance profile, the shaft locus and on the dynamic coefficients is very significant. More important, it is important to estimate the pivot stiffness of each single pad using experimental measurements.

Pad–Pivot Friction Effect on Nonlinear Response of a Rotor Supported by Tilting-Pad Journal Bearings

This paper presents a numerical study for nonlinear rotordynamic response with bifurcations of tilting pad journal bearings when pad–pivot friction forces are taken into account. A Stribeck friction model is employed to determine the friction coefficient for the contacts between the pads and the spherical-type pivots. The boundary/mixed/hydrodynamic friction mode is determined for each pad surface based on the instantaneous angular motion of the pads. A Jeffcott type rotor supported on 5-pad tilting pad journal bearings is used for the structural model, and finite element fluid film models are utilized to calculate the reaction forces and moments on the pads. The simulation results show that pad–pivot friction plays an important role in determining the stability of the rotor system. For the autonomous condition, the friction induces a Hopf bifurcation and generates limit cycles at high rotor spin speed (>14 krpm), which were originally stable equilibrium states with a no friction condition. For the nonautonomous condition, the 1× synchronous response becomes subsynchronous/quasiperiodic responses in the high-speed range (>14 krpm) with the appearances of Neimark-Sacker bifurcations. It is shown that the outbreak points and corresponding response types are highly dependent on the state of disk imbalance. A comparison of the linear and nonlinear models clearly illustrates the importance of retaining nonlinear forces to determine potential deleterious vibration.

Experimental research on tribological and vibration performance of water-lubricated hydrodynamic thrust bearings used in marine shaft-less rim driven thrusters

Aiming at the demand of marine shaft-less rim-driven thrusters(RDTs) for high load capacity, long life, low friction and low vibration water lubricated hydrodynamic thrust bearings(WLHTBs), three types of WLHTBs were designed and manufactured: pivot-supported, rubber-supported and fixed pads bearings. A series of experiments were carried out to study their tribological and vibration performance. Axial force, friction torque, axial displacement of the thrust collar, water temperature and vibration characteristics under different working conditions were acquired by a load cell, a torque meter, 4 proximity sensors, 2 thermometers and 3 B&K pulse sensors during a planned 200 h’ test for each bearing. The experimental results indicate that pivot and rubber-supported bearings have good lubrication and load carrying properties under different conditions. With the rotation speed of the thrust collar increases from 100 to 600 r min−1, the friction coefficient of both bearings is lower than 0.06 under the specific pressure of 0.1 MPa, and reduces similarly to lower than 0.01 under 0.5 MPa. The vibration acceleration amplitude of the rubber-supported WLHTB in X, Y and Z directions are all less than the value of pivoted and fixed pads ones under same speed and load condition. After 200 h of test, the average height and mass loss of the pivot and rubber-supported pads of each WLHTB have only reduced 35 µm/0.0232 g and 42.4 µm/0.0296 g respectively. On the contrary, the performance of the fixed pads bearing is the worst. Under the specific pressure of 0.5 MPa condition, the friction factor increases to 0.2 when the speed reaches 600 r min−1, and the outlet cooling water temperature increases to 70 °C in 20 min. The thrust collar is damaged and the pads’ polymer surfaces are burnt. The experimental research results provide an important reference for the design of WLHTBs for RDTs.

Thermal–Hydrodynamic Behaviour of Coated Pivoted Pad Thrust Bearings: Comparison between Babbitt, PTFE and DLC

The hydrodynamic lubrication and thermal analysis of tilting pad thrust bearings has been a major subject for many studies in the field of tribology. There is only a limited number of studies regarding thrust bearings with coated surfaces. The purpose of this study is to build a parametric, iterative algorithm in order to perform a complete thermal and hydrodynamic lubrication analysis for pivoted pad thrust bearings with coatings. The analytical model is mainly based on the energy, continuity and Navier–Stokes equations, which are solved numerically with the Semi-Implicit Method for Pressure Linked Equations Consistent (SIMPLEC) method. The analysis focuses on a single pivoted pad of the thrust bearing. The thermal properties of the coating material are taken into account and the resulting thermal and flow fields are solved. The basic hydrodynamic and tribological characteristics are calculated for an uncoated, a Babbitt coated, a PTFE coated and a diamond like carbon (DLC) coated pivoted pad thrust bearing. The pressure and the film thickness distribution, as well as the load capacity and the frictional forces, are determined for several pad positions and velocities of the rotor. A mineral oil lubricant is used to estimate the shear thinning or thickening effects on the pad tribological performance. The results indicate that pads coated with PTFE and DLC show lower friction forces compared to the common steel and Babbitt applications. At the same time, the DLC coating seems to affect the bearing’s flow and thermal fields less than the PTFE, making it more suitable for thrust bearings applications.

Theoretical and experimental study on the static and dynamic characteristics of tilting-pad thrust bearing

Abstract The static and dynamic characteristics of tilting-pad thrust bearing (TPTB) considering the lubricant viscosity-temperature effect and pad elastic deformation are first analyzed by theoretical thermalelastohydrodynamic (TEHD) modeling. The TPTB test rig with electric oil pump is designed and built to apply axial loads and sinusoidal hydraulic excitation due to the opening changes in the overflow valve. An Instrumental Variable Filter (IVF) algorithm is developed to identify the TPTB stiffness and damping coefficients with pad pivot stiffness considered. Compared to the experimental results, the calculated TPTB temperature is more accurate after using the TEHD model. The TPTB stiffness and damping coefficients calculated by the pressure perturbation method are reasonably close to the experimental results with low-amplitude and low-frequency hydraulic excitation.

Pad attitude adjusting moment in large multi-pocket pivoted pad used in static oil journal bearing

PurposeLarge scale is a trend of the ball mill, so the loads on their bearings become very large, bearing operating conditions turn into more severe. The moment of inertia to their pivot of the pad increase significantly, so it leads to the difficult of the pad attitude adjustment and makes the pad tilting angles time response slow, the key factor to effects attitude adjustment is the oil film moment to the pad pivot at unbalance position. the oil film moment and its effect factors must be studied in the design of the bearing used in ball mill.Design/methodology/approachModels about the lubrication of multi-pocket pivoted pad hydrostatic bearing is established, the complicated relationship of the oil flow rate between the oil pockets are taken into account. Finite differential method is used to solv the model, and theroy of finite element method is use to calculate the oil flow rate out of the pocket edges. Newton’s methods are used to determine the pressure of pockets.The pad tilting moment to its pivot is numerically analyzed.FindingsThe tilting moment to its pivot is set as an indicator of the ability for a pad to adjust its attitude. The effects of the diameter of throttling capillary and the pocket area on the attitude adjusting capacity is studied. Relations between the attitude adjustment capacity for a pad and there effects factors are presented.Practical implicationsThe methods and results have the special reference to the design and operation of multiple pockets tilted pad hydrostatic journal bearing.Originality/valueMethods to studied the pad attitude adjustment are given in the article for the multi-pocket pivot pad hydrostatic beairng.The influence factors on pad attitude adjusting capacity are discussed for a this specail kind hydrostatic bearing, the how the factors influence the pad tilting angle adjustment are presented.

Numerical study of the influence of the pivot position on the steady-state behavior of tilting-pad thrust bearings

The coordinates of the pivot pads variation of a hydrodynamic thrust bearing can result in hydrodynamic pressure field changes that forms on the surface of the pad with consequent changes in the values of the bearing performance parameters, such as power loss, load capacity and operating temperatures. The analysis was performed by computer simulation (FORTRAN), based on the numerical solution of the two-dimensional isoviscous Reynolds equation in polar coordinates by finite difference method. The simulated bearing was based on the dimensions of a KV 9 Kingsbury thrust bearing, existing on the tribology laboratory of the university. With the pivot position variation (radius r and angle θ), starting with a bearing with central pivot pads, as well as a bearing consisting of pads with pivot located in other positions, both in the radial direction and in the circumferential direction, was possible to verify some significant changes in the bearing performance parameters. It was found that the maximum load occurs in the case of pads with pivot located approximately 60% of the average circumferential length, but for a substantially longer than the average radius of radial position. On the other hand, the minimum power loss occurs due to friction in the bearings for pivoting the pads with about 67% of the average circumferential length thereof.

Characteristic Analysis and Simulated Test of Hybrid Bearing with the Introduction of Piezoelectric Controller

A novel hybrid bearing with the introduction of piezoelectric controller and tilting pads to control vibration actively is proposed in this paper, and the feasibility of this scheme is verified by theoretical calculation and experimental data. This scheme can control the vibration of bearing actively by using the electromechanical characteristics of piezoelectric ceramic transducer (PZT) components. The static internal character of PZT and static external characteristic of piezoelectric control component are analyzed, and the calculation equations of preload coefficient and driving force of the new bearing are given. The simulation setup of the new bearing is designed and developed. The data representing the relationship of displacement of pad pivot, driving force, voltage, and the simulation stiffness of liquid film are obtained in the test, and the feature parameters of piezoelectric control component are amended to analyze the relationship between preload coefficient of the bearing and driving voltage. The proposed new bearing has the function of controlling preload actively. The theoretical and experimental research results provide essential guidance for the detail design of this new bearing and also provide a new idea for the vibration control of high speed rotor systems.

Multibody dynamics of pivot slipper pad thrust bearing in axial piston machines incorporating thermal elastohydrodynamics and mixed lubrication model

A model for the calculation of multibody dynamics incorporating a transient, three-dimensional, thermal elastohydrodynamic pivot pad contact in swash plate axial piston pumps is presented. The simulation is based on the numerical solution of equations of motion, generalized Reynolds, energy and Fourier heat equations. The equation of motion of the hybrid pivot bearing is derived by Lagrangian formalism and solved in due consideration of friction in the spherical joint and piston-barrel. Mass conserving cavitation, non-Newtonian flow and a mixed friction model with consideration of real-measured surface topologies are implemented. Results for a slipper pad with retain plate are presented. The impact of the retain device on slipper pad friction and temperature are discussed.

Balancing wedge action in textured converging bearings

This study investigates a hydrodynamic lubrication mechanism of textured surfaces, termed “balancing wedge action”, found in pivoted pad bearings. The analytical model is a one-dimensional pivoted pad bearing having a single dimple on the pad and considers the equilibrium of the moment applied to the surfaces. The results show that incorporation of a dimple on the pad surface changes the convergence ratio, improving the load capacity without negative pressure. The trends of load and friction in terms of the dimple depth and location are complex depending on the pivot position. The dimple locations at the outlet side, center, and inlet could improve tribological performance.

Nonlinear dynamic behaviour of vertical and horizontal rotors in compliant liner tilting pad journal bearings: Some design considerations

Dynamic behaviour of vertical and horizontal rotors in journal bearings with line pivot pads is investigated. Two bearing designs are compared: one with white metal pads and another with compliant liner pads. The influence of elasticity of the liner on the journal orbits is investigated. Some practical aspects of the compliant liner pad design are discussed. Compliant bearing design parameters such as preload factor, pivot offset, radial clearance, viscoelasticity, and pad inclination to control the size of the journal orbit are considered.

Numerical Study of Thermohydrodynamic Characteristics of Oil Tilting-Pad Journal Bearings with a Self-Pumping Fluid Flow Circulation

A thermohydrodynamic numerical code is developed for analyzing the steadily loaded finite tilting-pad journal bearings for vertical hydropower plants. The Reynolds equation and the two-dimensional energy equation in fluid film lubrication are solved by the central difference technique with a successive overrelaxation scheme and the backward difference with an iterative technique, respectively. In the simulation, the lubricant viscosity is changed with the temperature variation (in both axial and sliding directions) and the pad deformation is brought up in calculations. Oil circulation is considered as a self-pumping fluid flow through pad side leakage via a circumferential groove. Self-lubricating approach is guaranteed the oil cooling procedure and bearing performance in hydropower plants. The effects of pad number, preload factor, pivot position, and shaft rotational speed on the bearing performance are illustrated. Power friction loss, maximum oil film temperature, circulated oil fluid flow, minimum oil film thickness, and pad tilting angle are the most important results.

유한 요소 해석을 통해 계산된 틸팅 패드 베어링의 피봇 강성과 Hertzian 접촉 모델 해석 결과 비교

Recent studies emphasize the importance of pivot stiffness in the analysis of tilting pad bearings (TPBs). The present paper develops a finite element model of the pad pivot and compares the predicted pivot stiffness to the results of Hertzian contact model calculations. Specifically, a finite element analysis generates tetrahedral mesh models with ~40,000 nodes for a ball-socket pivot and ~50,000 nodes for a rocker-back pivot. These models assume a frictionless boundary condition in the contact area. Increasing the applied loads on the pad in conjunction with increasing time steps ensures rapid convergence during the nonlinear numerical analysis. Predictions are performed using the developed finite element model for increasing the differential diameters between the pad pivot (or ball) and the bearing housing (or socket). The predictions show that the pivot contact area increases with decreasing differential diameters and increasing applied loads. Further, the maximum deformation occurring at the pivot center increases with increasing differential diameters and increasing applied loads. The pivot stiffness increases nonlinearly with decreasing differential diameters and increasing applied loads. Comparisons of results of the developed finite element model to those of Hertzian contact model calculations assuming a small contact area show that the latter model underestimates the pivot stiffnesses predicted by the finite element models of the ball-socket and rocker-back pivots, particularly for small differential diameters. This result implies the need for cautionduring the design of pivot stiffness by the Hertzian contact model.

The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings

Recent comprehensive experimental data showcasing the force coefficients of commercial size tilting pad journal bearings has brought to rest the long standing issue on the adequacy of the [K,C,M] physical model to represent frequency independent bearing force coefficients, in particular viscous damping. Most experimental works test tilting pad journal bearings (TPJBs) with large preloads, operating over a large wide range of rotor speeds, and with null to beyond normal specific loads. Predictions from apparently simple fluid film bearing models stand poor against the test data which invariably signals to theory missing pivot and pad flexibility effects, and most importantly, ignoring significant differences in bearing and pad clearances due to actual operation, poor installation and test procedures, or simply errors in manufacturing and assembly. Presently, a conventional thermo hydrodynamic bulk flow model for prediction of the pressure and temperature fields in TPJBs is detailed. The model accounts for various pivot stiffness types, all load dependent and best when known empirically, and allows for dissimilar pad and bearing clearances. The algorithm, reliable even for very soft pad-pivots, predicts frequency reduced bearing impedance coefficients and over a certain frequency range delivers the bearing stiffness, damping and virtual mass force coefficients. Good correlation of predictions against a number of experimental results available in the literature bridges the gap between a theoretical model and the applications. Predicted pad reaction loads reveal large pivot deflections, in particular for a bearing with large preloaded pads, with significant differences in pivot stiffness as a function of specific load and operating speed. The question on how pivot stiffness acts to increase (or decrease) the bearing force coefficients, in particular the dynamic stiffness versus frequency, remains since the various experimental data show contradictory results. A predictive study with one of the test bearings varies its pivot stiffness from 10% of the fluid film stiffness to an almost rigid one, 100 times larger. With certainty, bearings with nearly rigid pivot stiffness show frequency independent force coefficients. However, for a range of pad pivot stiffness, 1/10 to ten times the fluid film stiffness, TPJB impedances vary dramatically with frequency, in particular as the excitation frequency grows above synchronous speed. The bearing virtual mass coefficients become negative, thus stiffening the bearing for most excitation frequencies.

A Theory of the Hydrodynamic Film Thickness in Centrally Pivoted Oil-Lubricated Plane-Pad Thrust Bearings

An analytical model is developed in this article for pivoted, oil-lubricated rectangular plane-pad thrust bearings considering the thermal effects of oil viscosity. The model is governed by three dimensionless parameters: the pad length-to-width ratio, the location of the pad pivot, and the bearing load parameter that prescribes lubricant thermal properties and applied load. Analyses were carried out for centrally pivoted bearings of a number of pad length-to-width ratios and a number of bearing load parameters. The results suggest a theory that, for bearings with a square pad or wider, the oil viscosity thermal effect enables a centrally pivoted bearing to develop a hydrodynamic film thickness of about one half of the film thickness that would be developed under isothermal conditions with the pad pivoted at its maximum-load-capacity optimal position. This level of relative film thickness could be developed under all design conditions of practical interest. The theory is fairly general and may be applicable to fan-shaped thrust bearing assemblies with the concept of equivalent length-to-width ratio of the bearing pad. The validity of the theory is modestly evaluated and should be further validated in time through various means and in various settings.

Geometrical design parameters for journal bearings with flexure pads and compliant liners

A hydrodynamic journal bearing utilizing flexure pads with a compliant liner is studied and its performance enhanced through a parametric study. The main geometrical dimensions are varied and the affect on pad performance is analyzed. This will put more knowledge into the design and function of flexure pads. Guidelines are given to the design of the pads and are also covering the polymer liner. It is found that the use of flexure pads is an attractive alternative to pivoted pads. Pivot contact-related failure modes are eliminated and load capacity is not restricted by the force that can be transferred through the pivot contact. When combined with a polymer liner, the pad performance is enhanced further, especially when operating at thin lubricant films.

A passive Maglev vehicle with self-regulating aerostatic-aerodynamic pads

The levitation of an operating Maglev is obtained with electromagnets EMS or superconducting materials SMS. In 2003, we designed a simpler Maglev PMS, which is levitated by permanent-magnet-aluminium circuits to remove the lateral instability of permanent magnets. In this paper, we show how to increase the side stability of this Maglev using lateral aerostatic-aerodynamic pivoted pads, arranged in the gap slide-guide. The air impacts the head of the pads giving a high aerostatic lift, which is added to the aerodynamic lift. The pads self-regulate their slope, thus increasing their lift as external forces increase.

An Analytical Complete Model of Tilting-Pad Journal Bearing Considering Pivot Stiffness and Damping

Abstract Considering the freedom of pad tilting and pad translation along preload orientation, an analytical complete model, as well as mathematical method, which contains 2n+2 degrees of freedom, is presented for calculating the dynamical characteristics of tilting-pad journal bearing. Based on the motion relationship of shaft and pad, the local coordinate system, the generalized displacement, and the generalized force vector are chosen. The concise transformation of generalized displacement, generalized force, and its Jacobian matrix between the local and global coordinate systems are built up in matrix form. A fast algorithm using the Newton–Raphson method for calculating the equilibrium position of journal and pads is proposed. The eight reduced stiffness and damping coefficients can be obtained assuming that the journal and all pads are subject to harmonic vibration. Numerical results show that the reduced damping coefficients and the threshold speed can be effectively enhanced by giving suitable pad pivot stiffness and damping simultaneously, and this analytical method can be applied to analyze dynamical behavior of the tilting-pad journal bearing rotor system.