Radial Clearance Research Articles

A dynamic model considering the time-varying friction moment of a flexible rotor system

PurposeBearing friction moments are important factors that affect the vibrations of rotor systems. The bearing friction moments are related to the dimension parameters, lubrication conditions and manufacturing errors of support bearings. This work studies the effects of the bearing friction moments on the vibrations of rotor systems.Design/methodology/approachThe rotor is separated into several shaft elements for formulating a flexible rotor. The time-varying friction moment (TFM) is affected by the time-varying contact loads. The vibrations of FRS from the TFM and Palmgren's friction moment (PFM) calculation methods are compared. Moreover, the effects of the rotor offset and radial clearance on the frequency-amplitude characteristics of FRS are studied.FindingsThe TFM method is more consistent with the actual operation mechanisms. The rotor offset and radial clearance can significantly affect the nonlinear vibrations of FRS. This work provides a new reference and research method for the vibration analysis of rotor systems considering the friction effects.Originality/valueThe elastohydrodynamic lubrication (EHL), elastic hysteresis and differential sliding are considered. A flexible rotor system (FRS) dynamic model considering the TFM is proposed. The vibrations of FRS from the TFM calculation method and empirical calculation formula are compared. The effects of the rotor offset and radial clearance on the frequency–amplitude characteristics of FRS are studied.

Static and Dynamic Characteristics of Nonmetallic Labyrinth Seals Based on Fluid–Solid–Thermal Coupling

In this paper, static and dynamic characteristics of a labyrinth seal were studied by fluid–solid–thermal coupling analysis (FSTCA). Deformation and stress distribution of nonmetallic labyrinth seals (i.e., PEEK and PEEK-CA30) were further analyzed to investigate the effects on leakage and rotor stability compared to that of metallic material (i.e., AL alloy). The results show that a higher pressure drop of airflow at the last tooth along the airflow direction suggested a more remarkable energy conversion to kinetic energy. Airflow velocity at the tooth root was obviously lower than that at the tooth tip because of vortex in tooth cavity. Maximum deformation of the seal occurred at tip of the first tooth, while equivalent stress mainly distributed at the root. Both axial and radial deformations led to deformations of seal cavities and upward movements of the teeth, resulting in greater radial clearances. PEEK-CA30 had the lower radial and axial maximum deformations compared to PEEK and AL alloy, which in turns caused a lower leakage with increasing inlet temperature and inlet/outlet pressure ratio and a higher effective damping coefficient under different vortex frequencies, indicating a better seal performance and a better stability of rotor system. The equivalent stress for AL alloy deeply depended on inlet temperature of airflow due to higher elasticity modulus, higher thermal conductivity and higher thermal expansion coefficient, which made the seal more likely to fail under higher inlet temperature.

Intelligent Diagnostics of Radial Internal Clearance in Ball Bearings with Machine Learning Methods

This article classifies the dynamic response of rolling bearings in terms of radial internal clearance values. The value of the radial internal clearance in rolling-element bearings cannot be described in a deterministic manner, which shows the challenge of its detection through the analysis of the bearing’s dynamics. In this article, we show the original approach to its intelligent detection through the analysis of short-time intervals and the calculation of chosen indicators, which can be assigned to the specific clearance class. The tests were carried out on a set of 10 brand new bearings of the same type (double row self-aligning ball bearing NTN 2309SK) with different radial internal clearances corresponding to individual classes of the ISO-1132 standard. The classification was carried out based on the time series of vibrations recorded by the accelerometer and then digitally processed. Window statistical indicators widely used in the diagnosis of rolling bearings, which served as features for the machine learning models, were calculated. The accuracy of the classification turned out to be unsatisfactory; therefore, it was decided to use a more advanced method of time series processing, which allows for the extraction of subsequent dominant frequencies into experimental modes (Variational Mode Decomposition (VMD)). Applying the same statistical indicators to the modes allowed for an increase in classification accuracy to over 90%.

Effect of internal excitation induced by non-uniform contact of roller bearings on nonlinear vibration and stability of rotor system under combined loads

The misalignment of roller bearing rings will results in moment load, together with the unbalance and external loads, forming the combined dynamic loads. The complex combined load can cause non-uniform contact of rollers and rings, which reduces the bearing’s life and significantly affect the vibration of rotor systems. This paper mainly studies the roller bearing internal contact performances under combined loads and the influence of internal excitation on the nonlinear vibration of rotor systems. First, the “slices” method is used to establish the mechanical model of roller bearings, which considers the radial clearance and nonlinear Hertz contact. The obtained time-varying bearing nonlinear support reaction is introduced into the rotor concentrated mass model, and a roller bearing–rotor system dynamic model is proposed. Further, the system’s complex nonlinear vibrations, such as bifurcation and chaos, are analyzed by spectrum, orbits, bifurcation, and Poincare map. The roller bearing contact performances and stability under the influence of ring tilt angle, rotational speed, and unbalance, are analyzed by contact load statistical features. Finally, based on a rolling bearing–rotor test rig, the vibration experiment considering the combined load was performed, and the experiment results are compared with simulation results to verify the proposed model and conclusions.

THERMAL ASSESSMENT ON TRIBOLOGICAL PROPERTIES OF TURBOCHARGER JOURNAL BEARING

High speed rotation of turbocharger rotor shaft could lead to significant frictional losses generated in journal bearing, which in turn affects the engine minimum speed. Therefore, this study is to mathematically predict the frictional behaviour for a turbocharger journal bearing, considering lubricant film formation and thermal effect. A mathematical model is initially derived from a 2-D Reynolds equation based on finite difference method and Modified Newton Raphson’s Method. Then, a reduced energy equation is integrated, to consider thermal effect. The mathematical model is validated with measured friction power of a typical automotive turbocharger obtained from literature. Through the analysis, it is shown that thermal analysis assumption correlates better with literature experimental data. The significant temperature rise in lubricant leads to the reduction of viscosity as well as the frictional power losses of the turbocharger. A parametric study using Taguchi methodis then conducted to optimize parameters, such as bearing width, type of engine oil used as lubricant and bearing radial clearance, for minimizing the friction power loss. The effect of bearing width is found to contribute the most to the frictional power loss, followed by the lubricant oil and lastly, the radial clearance of the bearing.

Mixed Lubrication Analysis of Scrolls Lubricated With CO2/Oil Mixture Based on a Homogeneous Model

Abstract The tribological performance of scrolls lubricated with CO2/oil mixture is investigated using a combination of the mixed lubrication model and the homogeneous model. The physical characteristics of the CO2/oil mixture were established prior to using the lubrication model. Then the evolution of the lubrication condition during the meshing process of scrolls was investigated, and the impact of radial clearance and refrigerant on the tribological behavior was assessed. The lubrication condition of the tribo-pair deteriorates as the meshing point moves toward the center of the scrolls. The effects of radial clearance and refrigerant mass fraction on friction and lubrication are strongly influenced by the meshing position. In addition, the presence of refrigerant leads to less hydrodynamic pressure and more asperity contact.

Experimental validation of IS2062 deep drawing component

Deep drawing isa leading manufacturing method in which a sheet metal blank is radially stretched into a die by action of a punch to produce various parts of automobiles, computers, electronic items and many other things used in day-to-day life. Optimization of sheet metal forming process parameters was important to reduce the cost of manufacturing a product. Forming a defect-free drawn part is always a challenging task. This work presents analysis and experimental identification of the deep drawing process in order to avoid earring effect and Stretcher strain defect. In our present work, low carbon structural steel (IS2062, Carbon 0.17 to 0.19 wt%) is used for deep drawing application. Factors mainly influencing the friction coefficient, blank holder force, and die nose radius, which are the sheet metal process characteristics that exhibit deformation behaviour. In an experiment, radial clearance between the die and the punch was taken as 0.15 mm on each side. Deep drawing operation was carried out on a 1200 ton hydraulic press with a servo controlled mechanism, a 3 stage forming process was taken and values were compared with the FEA, A cylindrical cup with a LDR of 1.8 has been successfully created experimentally.

THE CALCULATION OF A MULTISTAGE TURBOMOLECULAR VACUUM PUMP

The dependencies of the main characteristics of a turbomolecular pump operating in the molecular regime of gas flow on the number of stages and their geometrical parameters are considered. Programs developed using the Monte Carlo method in a three-dimensional formulation, taking into account the influence of radial and axial clearances, make it possible to trace the full trajectory of each molecule through the entire flow path of the pump, as well as calculate the gas evolution flows. Determining the probabilities of molecules passing in the forward and reverse directions made it possible to establish the influence of the geometric parameters of the stages and their location in the flow path on the main characteristics of the pump.

Thin films in hydrodynamic lubrication regime: The Osiris friction setup.

A model hydrodynamic lubrication tribometer consisting of two hydrodynamic journal bearings working under thin film conditions was developed to investigate the mechanisms of hydrodynamic friction with low-viscosity fluids and the role of surface effects. A small nominal radial clearance of about 5 µm was considered between the two surfaces. This fully instrumented setup provides in situ information on the sheared fluid film in terms of simultaneous measurements of film thickness; localization and extension of the cavitation zone, with a resolution of 30°; nominal friction torques up to 0.5 Nm, with an accuracy of 0.05 mNm; temperature; and the position of the shaft for velocities up to 12 000 rpm. To illustrate the capability of the Osiris tribometer, thin hydrodynamic film measurements were performed on smooth surfaces. The results are presented here, and the thermal effects, acceleration, and inertia contributions are discussed. Finally, the influence of the surface topography using textured surfaces was demonstrated and the role of adsorbed layers on the surface due to fluid formulation was highlighted.

Geometric design and performance analysis of conical-rotor screw vacuum pump with adjustable flow field clearances

Structure rotor takes a great effect on the performance of screw vacuum pump. An optimized design for conical rotor profiles with adjustable flow field clearances is proposed. Mathematical models of cross-section profiles and helix of conical rotor are established. Meshing model can generate directly by the profiles with stable circumferential clearance, tooth clearance, tooth side clearance and radial clearance. Effects of offset distance involute, deflection angle of epicycloid, the radial offset distances of addendum and dedendum circles on the clearances are analyzed. Mathematical models for working chamber volume, tooth width, pumping speed and shaft power of the vacuum pump are established. Furthermore, the calculated pumping speed and shaft power are verified by comparing the experimental measured results. Effects of rotor structure parameters on the geometric characteristics and working performance of the vacuum pump are revealed as well as the comparisons with the fixed-pitch and variable-pitch cylindrical screw vacuum pumps. Results show that shaft power of the conical rotor pump are smaller than those of the two cylindrical pumps under similar actual pumping speeds, resulting in superior performances.

Vibration analysis of shaft-cylindrical roller-bearing-pedestal system considering damage by Runge–Kutta algorithm

The raceway damage of the bearing restricts the operation stability of the system. Therefore, in the case of damage, simulating vibration response and predicting the performance of the shaft-cylindrical roller-bearing-pedestal system have high research value. According to the structural characteristics and the force transfer relationship, a dynamic model of the shaft-cylindrical roller-bearing-pedestal system is established in this paper. Then, the vibration response of the system is simulated by Runge–Kutta algorithm and measured by experiment. Finally, the effects of load and speed, damage size, and radial clearance on the dynamic performance are investigated. The simulation and measurement results indicate that the load F and the speed N can promote the enhancement of the vibration acceleration signal. As the damage length continues to increase, the ring in the Poincaré map begins to break, and the system transits from quasi-periodic to chaotic motion. The vibration signal is more affected by the damage size than by the damage location. When the radial clearance increases from 5 × 10−6 m to 15 × 10−6 m, the PTP value increases from 23.83 m·s−2 to 61.36 m·s−2.

Dynamic characteristics of asymmetrically supported cylindrical roller bearing–rotor coupled system considering variable compliance vibration

This article provides a dynamic model of a cylindrical roller bearing–rotor system by combining the finite element method of the rotor and the interaction between the components of the bearing to study the dynamic response of the rotor with asymmetric support mode. The shaft is discretized by beam elements with five degrees of freedom. The bearing inner ring is consolidated with the journal of the shaft. The simulation results show that variable compliance vibration can stimulate resonance of the rotor in the sub-critical speed region. The variable compliance vibration of the rolling bearings does not occur synchronously on both sides of the asymmetric supported rotor. The increase in radial load and clearance exacerbates variable compliance vibration, while rotor imbalance has a smaller impact on variable compliance vibration. Usually, the presented coupled model can be applied to the comprehensive analysis of the vibration characteristics of all components in any cylindrical roller bearing–rotor system.

Transient heat transfer and temperatures in closed compressor rotors

During transient gas turbine operating cycles, the radial clearance between the rotating blades and the stationary casing is governed by the thermal stresses and radial growth of the compressor discs. Robust and accurate prediction of the temperature and heat transfer inside compressor cavities is critical to controlling these clearances and the design of reliable and efficient engines. This paper presents a fully predictive model to determine disc temperatures and shroud heat fluxes for a closed disc cavity (rotating cylindrical annulus), simulating an engine compressor. This is the first published reduced-order modelling of compressor cavities during engine transients in literature and the most detailed publication of transient experimental data in this context. Due to the conjugate nature of the heat transfer, a conduction model of the compressor disc and a model of the flow and heat transfer in the cavity between the co-rotating discs are included. The conduction was computed using a two-dimensional finite element solver, and the disc heat transfer was calculated assuming conductive laminar Ekman layers on the disc surfaces. Correlations for free convection on flat plates are used to model the heat transfer on the inner and outer radii of the rotating cavity. The transient core temperatures were calculated in a quasi-steady manner, with the heat transfer at every time step predicted assuming zero net heat flow. The model was validated using new transient data collected from the Compressor Cavity Rig at the University of Bath. The model shows consistent agreement with all experimental cases, providing insight into the conjugate relationship between the disc and shroud heat transfer, revealing that disc heat transfer is sustained long after there is no convective heat transfer from the shroud. This approach has direct application to practical thermo-mechanical codes, contributing to the design of next-generation, net-zero aerospace architectures.

Effect of the radial gap size on the deterministic flow in a centrifugal pump due to impeller-tongue interactions

The research on the flow in centrifugal pumps is quite broad and covers most of the relevant issues. However, most of the studies are focused on the steady behaviors and less literature is available for the dynamic interactions. Unsteady mechanisms for energy transfer and sources of impeller-tongue interaction can be identified in centrifugal pumps using the deterministic decomposition of the flow. Probably, the most important effect to be considered is the radial gap or spacing between the impeller exit diameter and the volute tongue radial location. The numerical dataset of a full 3D URANS model in a centrifugal pump has been employed to study in detail the effect of the radial gap size in the unsteady fluctuations of the velocity field within the pump, using the deterministic analysis as the main novelty. The numerical model developed by the authors has been already tested towards the prediction of the unsteady pressure field inside the volute, at the impeller exit. The new results presented here allow to see the impact of both geometrical and operating parameters on the flow discharge and momentum exchange. In particular, four different radial gaps (23.2%, 17.0%, 11.4% and 8.8% of the impeller diameter) operated at five different flow rates (from 20% to 160% of the nominal rate) have been numerically resolved and analyzed. The deterministic analysis reveals the major impact of the radial clearance on the blade-to-blade flow patterns within the impeller, especially at low flow rates. Unsteady viscous interaction induces radial velocity fluctuations that can be as high as a 40% of the time-averaged value. Moreover, this non-linear term can be perceived up to 1.5 times higher in the case of radial gap reductions from 23.2% to 8.8% of the impeller diameter. There is not a prevailing effect of the radial gap on that velocity component, and a pure temporal term dependence is found. On the contrary, the influence of the gap on the tangential component, responsible for the unsteady evolution of the impeller torque, is found to be the key parameter. Therefore, the fluctuations of the flow blockage are found to be the consequence of the impeller flow patterns and the fluctuations of the torque are to be assigned to the radial gap influence. All the post-processing routines have provided a precise picture of all the classic unsteady mechanisms involved: jet-wake pattern interaction, acoustic wave propagations and recirculating cells at off-design conditions. Hence, deterministic analysis is a useful tool to analyze the flow inside centrifugal pumps and it envisages the introduction of deterministic flow variables as objective functions for design optimization algorithms.

Numerical Analysis of Turbulence Effect for Coupled Journal-Thrust Water-Lubricated Bearing With Micro Grooves

Abstract The purpose of this study is to assess the role of turbulence on the lubrication performances of coupled journal-thrust water-lubricated bearing with micro grooves using a numerical model. The results of the simulation model are compared to the published experimental data to verify the validity of the numerical model. The load capacity, maximum film pressure, and local Reynolds number variations with the rotating speed, eccentricity, radial clearance, axial geometric gap, and micro groove depth for coupled journal-thrust water-lubricated bearing are examined. Furthermore, the calculated results under the turbulent flow are compared with those under laminar flow for coupled and separate bearings. The results show that the turbulence effect can improve the lubrication performances by enlarging fluid pressure and load capacity of the coupled journal-thrust bearing and the laminar flow assumption is no longer applicable to the actual operating conditions of the water-lubricated bearings at a high rotation speed. In addition, optimal micro groove depths for both journal bearing and thrust bearing exist to reach the peak of the load capacity while the optimal micro groove depths for journal bearing and thrust bearing are not the same.

An Analysis of the Influence of Surface Roughness and Clearance on the Dynamic Behavior of Deep Groove Ball Bearings Using Artificial Neural Networks.

The deep groove ball bearing is one of the most important components of the rotary motion system and is the research subject in this paper. After factory assembly, new ball bearings need to pass quality control. The conventional approach relies on measuring the vibration amplitudes for each unit and sorting them into classes according to the vibration level. In this paper, based on experimental research, models are created to predict the vibration class and analyze the dynamic behavior of new ball bearings. The models are based on artificial neural networks. A feedforward multilayer perceptron (MLP) was applied, and a backpropagation learning algorithm was used. A specific method of training groups of artificial neural networks was applied, where each network provided an answer to the input within the group, and the final answer was the mean value of the answers of all networks in the group. The models achieved a prediction accuracy of over 90%. The main aim of the research was to construct models that are able to predict the vibration class of a new ball bearing based on the geometric parameters of the bearing rings. The models are also applied to analyze the influence of surface roughness of the raceways and the internal radial clearance on bearing vibrations.

Experimental and CFD analysis of static and dynamic rotor stabilities in three-annular seals

At the sealing pressures of 1.25, 2.5, 5, 7.5 or 10 bar and at a rotation speed of zero to 8000 rpm, using experiment and CFD simulation, the static and dynamic stabilities of two three-annular seal basic designs were investigated. Those were the design with identical radial clearances at each annulus (ThASIC) and the one with 2 times larger radial clearance at the second annulus (ThASDC) in the presence of two axial dimensions for the connecting cavities of 1 and 3 mm. A possible mode of self-excited radial oscillations of a non-rotating shaft in a three-annular seal has been available from the experiments, and the explanation of this phenomenon occurrence has been given. The influences of the axial sizes of the connecting cavities and the clearance of the second annulus on the velocity distributions along the length and circumference of the seal have been studied. The analysis of the response amplitudes for a possible imbalance and wall motion orbit depending on the frequency of rotation with direct synchronous whirl of the shaft has shown that with an increase in the sealing pressure, the critical rotation speed and amplitude increases in the ThASDC design and the critical rotation speed decreases in the ThASIC design. The smallest whirl amplitude and a more centered position are typical for the ThASDC design with the enlarged connecting cavity of l2,4= 3 mm. The analysis of each annulus contribution to the magnitudes of hydrodynamic forces has been carried out, and depending on the sealing pressure and the seal design, the dynamic stiffness and damping coefficients have been got. The effect of the friction factor fsθ on the circumferential flow for different three-annular seal designs has been obtained. Its impact on the dynamic stability of the rotor (ThAS-RR design) and stator (ThAS-SR and ThAS-SRS designs) ribs, which were located in the connecting cavities of the three-annular seal, has been studied. The dynamic coefficients of stiffness, damping, and leakage for five different designs (ThASIC, ThASDC, ThAS-RR, ThAS-SR, and ThAS-SRS) of the three-annular seals have been compared. Due to the flow hydrodynamics analysis, the formation mechanisms for the decentering and destabilizing forces in the three-annular seals have been explained.

Dynamic modeling and vibration analysis of offshore wind turbine rotor system with insulated bearing under inclined shaft current damage

The offshore wind turbine is a device that uses the wind energy on the ocean to generate electricity. The voltage generated by offshore wind turbine can break down the insulated bearing and cause inclined shaft current damage. To explore the dynamic characteristics and influencing factors of offshore wind turbine rotor system, a dynamic model of offshore wind turbine rotor system is proposed. The insulating coating, inclined shaft current damage and contact characteristics are considered in the model. Through numerical simulation, the mapping relationship between vibration response and damage length is studied, the influence of the interaction between inclination angle and radial clearance on vibration response is analyzed, and the influence of the mass of insulating coating and speed on vibration response is discussed. The practicability of the model is proved by the experiment of physical prototype. The results show that, as the length of the shaft current damage increases from 10 × 10−5 m to 50 × 10−5 m, the strength of the vibration response increases. The coupling of the inclination angle of the shaft current damage and the radial clearance jointly promotes the enhancement of the vibration response. The enhancement effect of radial clearance is more significant than that of inclination angle. The increase of speed worsens the state of operation, and the state transitions from stable quasi-period to chaos.

Mathematical modeling and dynamic analysis of insulated bearing-steel pedestal system under shaft current damage

The insulated bearing may be damaged when operating under the action of current. Firstly, a novel dynamic model of insulated bearing-steel pedestal system with shaft current damage is proposed, and the model is solved based on the Runge-Kutta algorithm. Then, the model is verified by the experimental results. Based on the solution results of the dynamic model, the influence of mass and damage on the vibration signal is analyzed, the effect of damage on the stability of the insulated bearing-steel pedestal system is studied, and the influence of radial clearance on the vibration characteristics of the insulated bearing-steel pedestal system is discussed. The results indicate that, the vibration acceleration signal of the pedestal shows a positive correlation with the mass m i and the mass m o. As the length of damage increases, a few points begin to leave the quasi-periodic ring, and the quasi-periodic ring in Poincaré map gradually breaks. The coupling effect of shaft current damage and radial clearance makes the insulated bearing-steel pedestal system easier to enter an unstable motion state.

Research on the vibration characteristics of the ball bearing considering the uncertain bearing-shaft interference fit

Due to the exist of the inevitable dimensional tolerance and assembling errors in the ball bearing, the interference amounts between the inner ring and the connected shaft are uncertain but bounded, which could directly affect the dynamics performance of the rotor-ball bearing system. Whereas, most of the works on the field of dynamics in a ball bearing have considered the varying compliance (VC) vibration as deterministic vibration and there are few quantitative studies considering the uncertain factors. Therefore, in this paper, an uncertain ball bearing-rotor dynamic model is presented based on the Chebyshev interval method. Firstly, the uncertain interference amounts between the bearing inner ring and the connected shaft are modeled by the Chebyshev interval method. Then the radial clearance and actual interference amounts of ball bearing are derived by the bearing-shaft interference fit model. The time-dependent ball-raceway contact probability is formulated and the influence of the average and deviation coefficient of the initial interference amounts on the vibration behaviors of the rotor under various rotational speeds are investigated based on the double degrees of freedom (2-DOF) ball bearing system. The numerical cases show that the amounts of the bearing-shaft interference fit are uncertain and could be affected by rotational speed, which have an obvious influence on the dynamic performance of the rotor-ball bearing system. Reasonable design of the interference amounts could reduce the dispersion of the displacement and time-varying stiffness. The numerical results obtained by the present study are compared to the Monte Carlo simulation (MCS), which show the validity of the study.