Dynamic Analysis of a High-Speed Rotor-Ball Bearing System Under Elastohydrodynamic Lubrication

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Yu-Yan Zhang ◽  
Xiao-Li Wang ◽  
Xiao-Qing Zhang ◽  
Xiao-Liang Yan
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Power Spectra ◽  
Elastohydrodynamic Lubrication ◽  
Lubricated Contacts ◽  
Rolling Elements ◽  
Stiffness And Damping ◽  
Bearing System

The nonlinear dynamic behaviors of a high-speed rotor-ball bearing system under elastohydrodynamic lubrication (EHL) are investigated. First, the numerical curve fittings for stiffness and damping coefficients of lubricated contacts between rolling elements and races are undertaken, and then the fitted formulae are introduced to the equations of motion of the rotor-ball bearing system to investigate its nonlinear characteristics. Furthermore, the time responses, power spectra, phase trajectories, orbit plots, and bifurcation diagrams for cases of ignoring and considering the lubrication condition in bearings are inspected and compared. The results indicate that, when lubrication is taken into account, the amplitudes of vibration displacements and velocities of the rotor system increase, and the appearance of different regions of periodic, quasi-periodic, and chaotic behavior is strongly dependent on the speed and load.

Ball bearing turbocharger vibration management: application on high speed balancer

2020 ◽  
Vol 21 (6) ◽  
pp. 619
Author(s):  
Kostandin Gjika ◽  
Antoine Costeux ◽  
Gerry LaRue ◽  
John Wilson
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Internal Combustion Engines ◽  
Ball Bearing ◽  
Squeeze Film ◽  
Design And Technology ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Bearing Loads ◽  
Stiffness And Damping

Today's modern internal combustion engines are increasingly focused on downsizing, high fuel efficiency and low emissions, which requires appropriate design and technology of turbocharger bearing systems. Automotive turbochargers operate faster and with strong engine excitation; vibration management is becoming a challenge and manufacturers are increasingly focusing on the design of low vibration and high-performance balancing technology. This paper discusses the synchronous vibration management of the ball bearing cartridge turbocharger on high-speed balancer and it is a continuation of papers [1–3]. In a first step, the synchronous rotordynamics behavior is identified. A prediction code is developed to calculate the static and dynamic performance of “ball bearing cartridge-squeeze film damper”. The dynamic behavior of balls is modeled by a spring with stiffness calculated from Tedric Harris formulas and the damping is considered null. The squeeze film damper model is derived from the Osborne Reynolds equation for incompressible and synchronous fluid loading; the stiffness and damping coefficients are calculated assuming that the bearing is infinitely short, and the oil film pressure is modeled as a cavitated π film model. The stiffness and damping coefficients are integrated on a rotordynamics code and the bearing loads are calculated by converging with the bearing eccentricity ratio. In a second step, a finite element structural dynamics model is built for the system “turbocharger housing-high speed balancer fixture” and validated by experimental frequency response functions. In the last step, the rotating dynamic bearing loads on the squeeze film damper are coupled with transfer functions and the vibration on the housings is predicted. The vibration response under single and multi-plane unbalances correlates very well with test data from turbocharger unbalance masters. The prediction model allows a thorough understanding of ball bearing turbocharger vibration on a high speed balancer, thus optimizing the dynamic behavior of the “turbocharger-high speed balancer” structural system for better rotordynamics performance identification and selection of the appropriate balancing process at the development stage of the turbocharger.

An improved model for investigating the vibration characteristics of ball bearing owing to outer race waviness under high speed

2021 ◽  
Vol 69 (2) ◽  
pp. 89-101
Author(s):  
Pingping Hou ◽  
Liqin Wang ◽  
Zhijie Xie ◽  
Qiuyang Peng
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Vibration Measurement ◽  
Vibration Frequencies ◽  
Outer Race ◽  
Response Characteristics ◽  
Lagrange’S Equation ◽  
Rolling Elements ◽  
Initial Clearance ◽  
Improved Model

In this study, an improved model for a ball bearing is established to investigate the vibration response characteristics owing to outer race waviness under an axial load and high speed. The mathematical ball bearing model involves the motions of the inner ring, outer ring, and rolling elements in the radial XY plane and axial z direction. The 2Nb + 5 nonlinear differential governing equations of the ball bearing are derived from Lagrange's equation. The influence of rotational speed and outer race waviness is considered. The outer race waviness is modeled as a superposition of sinusoidal function and affects both the contact deformation between the outer raceway and rolling elements and initial clearance. The MATLAB stiff solver ODE is utilized to solve the differential equations. The simulated results show that the axial vibration frequency occurred at l fc and the radial vibration frequencies appeared at l fc fc when the outer race waviness of the order (l) was the multiple of the number of rolling elements (k Nb) and that the principal vibration frequencies were observed at l fc fc in the radial x direction when the outer race waviness of the order (l) was one higher or one lower than the multiple of the number of rolling elements (k Nb 1). At last, the validity of the proposed ball bearing model was verified by the high-speed vibration measurement tests of ball bearings.

Dynamic Analysis of Ball Bearings Due to Clearance Effect

2009 ◽  
Author(s):  
S. H. Upadhyay ◽  
S. C. Jain ◽  
S. P. Harsha
Keyword(s):  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Peak Frequency ◽  
System Response ◽  
Ball Bearings ◽  
Outer Race ◽  
Lagrange’S Equation ◽  
Rolling Elements ◽  
Machine Systems ◽  
The Individual

In this paper, the nonlinear dynamic behavior of ball bearings due to radial internal clearance and rotor speed has been analyzed. The approach presented in this paper accounts for the contact between rolling elements and inner/outer races. The equations of motion of a ball bearing are formulated in generalized coordinates, using Lagrange’s equation considering the vibration characteristics of the individual constitute such as inner race, outer race, rolling elements. The effects of speed of rotor in which rolling element bearings shows periodic, quasi-periodic and chaotic behavior are analyzed. The results also show the intermittent chaotic behavior in the dynamic response is seen to be strongly dependent on the speed of the rotor. The results are obtained in the form of frequency responses. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The peak-to-peak frequency response of the system for each speed is obtained. The current study provides a powerful tool design and health monitoring of machine systems.

Analysis of Thermal Effect on Elastohydrodynamic Lubrication in Angular Contact Ball Bearing

2015 ◽  
Vol 741 ◽  
pp. 443-448
Author(s):  
Bao Ming Wang ◽  
Xia Lun Yun ◽  
Xing Yao Liao ◽  
Xue Song Mei
Keyword(s):  
Temperature Rise ◽  
High Speed ◽  
Ball Bearing ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Oil Viscosity ◽  
Angular Contact Ball Bearing ◽  
Scanning Method ◽  
Lubrication Performance ◽  
Thermal Ehl

Based on the theory of point contact thermal elastohydrodynamic lubrication (EHL),the mathematical models for the thermal EHL of high-speed angular contact ball bearing are established. Multi-grid method and multigrid integration method are respectively used to calculate out the film pressure and film thickness respectively,and the column-by-column scanning method is used to calculate temperature rise of isothermal EHL and thermal EHL. The calculation results show that, under the pure rolling condition, temperature rise of oil film temperature is mainly caused by the compression work and shear heat at inlet and the heat in contact zone mainly comes from the inlet and the heat conduction around; the temperature rise results in oil viscosity lower and the lubricating film thinner ,in this way it reduces the lubrication performance in contact pair.

The Non-Uniform Preloading Effect on Stiffness Behaviour of Angular Contact Ball Bearings

2012 ◽  
Author(s):  
Wenwu Wu ◽  
Jun Hong ◽  
Xiaohu Li ◽  
Yang Li ◽  
Baotong Li
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Operating Conditions ◽  
Structural Performance ◽  
Angular Contact Ball Bearing ◽  
Actual Operating ◽  
Bearing Life ◽  
Bearing Stiffness ◽  
Increasing Demand ◽  
Bearing System

With the increasing demand of higher operating speed for bearing system, more challenges have been exposed on the maintaining of the bearing performance. Preloading is an effective method to handle these challenges. Traditionally, the preloading of bearing system has been applied by uniform approaches such as rigid preload and constant preload. However, this treatment may hardly deal with the optimization of preloading problem due to the non-uniformity of the bearing stiffness becomes more apparent under high-speed operating conditions. A novel and practical approach is therefore presented in this paper to incorporate the non-uniformity effect to improve the structural performance of bearing under actual operating conditions. Firstly, the critical relationship between the stiffness behaviour and the non-uniform preload is evaluated for bearing system. The stiffness problem of angular contact ball bearing system is then formulated analytically by Jones’ model. With this approach, boundary conditions are achieved to solve the local contact deformation and predict the bearing life under non-uniform preload. Finally, both the uniform preload and the non-uniform preload cases for bearing system are simulated under various operating conditions. Comparing with traditional methods, the proposed method can provide a better solution in both stiffness and life that will enable a designer to obtain a deep insight on the optimization of bearing system.

On The Steady State and Dynamic Performance Characteristics of Floating Ring Bearings

1981 ◽  
Vol 103 (3) ◽  
pp. 389-397 ◽  
Author(s):  
Chin-Hsiu Li ◽  
S. M. Rohde
Keyword(s):  
Steady State ◽  
Linear Theory ◽  
High Speed ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Journal Bearings ◽  
Transient Problem ◽  
The Stability ◽  
Bearing System

An analysis of the steady state and dynamic characteristics of floating ring journal bearings has been performed. The stability characteristics of the bearing, based on linear theory, are given. The transient problem, in which the equations of motion for the bearing system are integrated in real time was studied. The effect of using finite bearing theory rather than the short bearing assumption was examined. Among the significant findings of this study is the existence of limit cycles in the regions of instability predicted by linear theory. Such results explain the superior stability characteristics of the floating ring bearing in high speed applications. An understanding of this nonlinear behavior, serves as the basis for new and rational criteria for the design of floating ring bearings.

Intermittent Chaotic Dynamics of Rail Axle Supported by Roller Bearings

2009 ◽  
Author(s):  
S. P. Harsha ◽  
C. ‘Nat’ Nataraj
Keyword(s):  
High Speed ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Radial Clearance ◽  
High Speed Rail ◽  
Frequency Spectra ◽  
Roller Bearings ◽  
Nonlinear Springs ◽  
Rolling Elements

In this paper, intermittent chaotic analysis of high speed rail axle supported by roller bearings has been analyzed. In the analytical formulation, the contacts between rolling elements and races are considered as nonlinear springs, whose stiffness values are obtained by using Hertzian elastic contact deformation theory. The results show the appearance of instability and chaos in the dynamic response as the speed of the axle-bearing system is changed. Period doubling and mechanism of intermittency have been observed which lead to chaos. The appearance of regions of periodic, sub-harmonic and chaotic behavior is seen to be strongly dependent on the radial clearance. Poincare´ maps, time response and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.

The Effect of Surface Waviness and Number of Rolling Elements on the Dynamic Behavior of a Rotor-Bearing System

2007 ◽  
Author(s):  
S. P. Harsha ◽  
C. Nataraj
Keyword(s):  
Chaotic Behavior ◽  
Nonlinear Dynamic Analysis ◽  
Wave Number ◽  
Surface Waviness ◽  
Nonlinear Load ◽  
Nonlinear Springs ◽  
Rotor Bearing ◽  
Rolling Elements ◽  
Bearing System ◽  
Effect Of Surface

In the paper, the effects of the number of rolling elements and wave number of surface waviness on the nonlinear dynamic analysis of a rotor-bearing system has been studied. In the analytical formulation, the contacts between rolling elements and races are considered as nonlinear springs, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The results are presented in the form of Fast Fourier Transformations (FFT) and Poincare´ maps, which show that the vibration characteristics of the rotor and its bearings change when the bearings operate in different regions of their nonlinear load deflection characteristics. The appearance of regions of periodic, sub-harmonic and chaotic behavior has been observed to be strongly dependent on number of rolling elements.

Turbulent Flow, Flexure-Pivot Hybrid Bearings for Cryogenic Applications

1996 ◽  
Vol 118 (1) ◽  
pp. 190-200 ◽  
Author(s):  
Luis San Andres
Keyword(s):  
High Speed ◽  
Energy Transport ◽  
Load Capacity ◽  
Equations Of Motion ◽  
Liquid Oxygen ◽  
Hydrodynamic Bearings ◽  
Numerical Predictions ◽  
Tilting Pad ◽  
Direct Stiffness ◽  
Stiffness And Damping

The thermal analysis of flexure-pivot tilting-pad hybrid (combination hydrostatic-hydrodynamic) bearings for cryogenic turbopumps is presented. The advantages of this type of bearing for high speed operation are discussed. Turbulent bulk-flow, variable properties, momentum and energy transport equations of motion govern the flow in the bearing pads. Zeroth-order equations for the flow field at a journal equilibrium position render the bearing flow rate, load capacity, drag torque, and temperature rise. First-order equations for perturbed flow fields due to small amplitude journal motions provide rotordynamic force coefficients. A method to determine the tilting-pad moment coefficients from the force displacement coefficients is outlined. Numerical predictions correlate well with experimental measurements for tilting-pad hydrodynamic bearings. The design of a liquid oxygen, flexure-pad hybrid bearing shows a reduced whirl frequency ratio and without loss in load capacity or reduction in direct stiffness and damping coefficients.

scholarly journals The Effect of Surface Morphology of Tapered Rolling Bearings in High-Speed Train on Grease Lubrication

Lubricants ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 76 ◽  
Author(s):  
Heli Wang ◽  
Haifeng Huang ◽  
Sibo Yu ◽  
Weijie Gu
Keyword(s):  
Surface Morphology ◽  
High Speed ◽  
Elastohydrodynamic Lubrication ◽  
Surface Damage ◽  
Mixed Lubrication ◽  
Grease Lubrication ◽  
Transit System ◽  
High Speed Trains ◽  
Rolling Elements ◽  
Forming Characteristics

With the extensive coverage of the rail transit system, ensuring the safe operation of rail vehicles is an important prerequisite. Insufficient lubrication will cause friction and wear of axle box bearings, which is directly related to ensured safety of high-speed trains. A non-Newtonian elastohydrodynamic lubrication(EHL) between tapered rolling elements and inner ring of axle box bearing in high-speed trains was established by numeric simulation. The input parameters of working conditions, including velocity, acceleration and plastic viscosity, were changed, considering the actual application and their influence trends on film-forming characteristics were analyzed. As a result, a phase of acceleration of starting or a process of braking at a low speed tends to occur mixed lubrication. Therefore, a method of optimizing surface morphology of rolling elements was adopted to improve lubrication. Based on comparison experiments, it was recommended that RMS roughness was greater than 0.03 μm and less than 0.1 μm and kurtosis was three and skewness was negative in a range of −1 to −0.5 and texture direction was parallel to rotation direction. The optimized surface promotes the transition from mixed-lubrication to full film lubrication, which alleviated the problem of surface damage due to insufficient lubrication and prolongated the service life.

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