scholarly journals Dynamic Analysis of a Rotor-Bearing-SFD System with the Bearing Inner Race Defect

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Junhong Zhang ◽  
Xin Lu ◽  
Jiewei Lin ◽  
Liang Ma ◽  
Jun Wang
Keyword(s):  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Elastohydrodynamic Lubrication ◽  
Hertzian Contact ◽  
System Stability ◽  
Time Frequency ◽  
Runge Kutta Method ◽  
Rolling Element ◽  
Rotor Bearing ◽  
Inner Race

In this paper, the dynamic behavior of a rotor-bearing-SFD system with the inner race defect of bearing is investigated. The contact force between the rolling element and the race is calculated in Hertzian contact and elastohydrodynamic lubrication condition. The supporting force of the SFD is simulated by integrating the pressure distribution derived from Reynolds’s equation. The equations of motion of the rotor-bearing-SFD system are derived and solved using the fourth-order Runge-Kutta method. The dynamic behavior and the fault characteristics are analyzed with two configurations of the SFD: (1) mounted on the unfaulted bearing and (2) mounted on the faulty bearing. According to the analysis of time-frequency diagram, waterfall plot, and spectral diagram, the results show that the characteristics of inner race defects on bearing frequencies are related to the characteristic multiple frequency of the inner race defect and the fundamental frequency. The speed and defect width have different influence on the distribution and amplitude of frequency. The SFD can enhance the system stability under the bearing fault but the enhancement decreases with the increasing speed. Meanwhile, the beneficial effect of the SFD varies according to the mounted position in the rotor system.

scholarly journals Dynamic behavior of the nonlinear planetary gear model in nonstationary conditions

2020 ◽  
pp. 095440622094104
Author(s):  
Ahmed Hammami ◽  
Ayoub Mbarek ◽  
Alfonso Fernández ◽  
Fakher Chaari ◽  
Fernando Viadero ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Nonlinear Effects ◽  
Hertzian Contact ◽  
Mesh Stiffness ◽  
Planetary Gearbox ◽  
Time Frequency ◽  
Run Up ◽  
Nonlinear Equations Of Motion

The nonlinear effects in gearboxes are a key concern to describe accurately their dynamic behavior. This task is difficult for complex gear systems such as planetary gearboxes. The main aim of this work is to provide responses to overcome this difficulty especially in nonstationary operating regimes by investigating a back-to-back planetary gearbox in steady conditions and in the run-up regime. The nonlinear Hertzian contact of teeth pair is modeled in stationary and nonstationary run-up regime. Then it is incorporated in to a torsional model of the planetary gearbox through different mesh stiffness functions. In addition, motor torque and external load variation are taken into account. The nonlinear equations of motion of the back-to-back planetary gearbox are computed through the Newmark- β algorithm combined with the method of Newton–Raphson. An experimental validation of the proposed numerical model is done through a test bench for both stationary and run-up regimes. The vibration characteristics are extracted and correlated to speed and torque. Time–frequency analysis is implemented to characterize the transient regime during the run-up.

The Dynamic Behavior of a Rolling Element Auxiliary Bearing Following Rotor Impact

2001 ◽  
Vol 124 (2) ◽  
pp. 406-413 ◽  
Author(s):  
M. O. T. Cole ◽  
P. S. Keogh ◽  
C. R. Burrows
Keyword(s):  
Dynamic Behavior ◽  
Angular Acceleration ◽  
Element Model ◽  
Magnetic Bearing ◽  
Rolling Element Bearing ◽  
Linear Matrix ◽  
Rolling Element ◽  
Non Linear ◽  
In Series ◽  
Inner Race

The dynamic behavior of a rolling element bearing under auxiliary operation in rotor/magnetic bearing systems is analyzed. When contact with the rotor occurs, the inner race experiences high impact forces and rapid angular acceleration. A finite element model is used to account for flexibility of the inner race in series with non-linear ball stiffnesses arising from the ball-race contact zones. The dynamic conditions during rotor/inner race contact, including ball/race creep, are deduced from a non-linear matrix equation. The influences of bearing parameters are considered together with implications for energy dissipation in the bearing.

Nonlinear Dynamics Behaviors of Ball Screws with Preload Considered

2012 ◽  
Vol 510 ◽  
pp. 304-309 ◽  
Author(s):  
Yong Jiang Chen ◽  
Wen Cheng Tang ◽  
Shi Gen Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Behavior ◽  
Analytical Model ◽  
Rotational Speed ◽  
Nonlinear Dynamic ◽  
Hertzian Contact ◽  
Ball Screw ◽  
Contact Deformation ◽  
Rolling Element ◽  
Equations Of Motions

In order to improve the vibration problem arise when rotational speed of a ball screw is increased, an analytical model is proposed to study the nonlinear dynamic behavior of the ball screw with preload considered. The contact force of each rolling element described according to nonlinear Hertzian contact deformation and the re-circulating mechanism has been taken in to account. A end-type ball screw is selected as an example, the methods of Runge-Kutta-fehlberg is used to solve the equations of motions numerically. It was found that the preload can be useful in controlling the vibration of the system,but the inhibit effect is not proportional to it,in the light of different type of ball screw, corresponding prevention preload is recommended.

Vibration Response of Rolling Element Bearings in a Rotor Bearing System to a Local Defect Under Radial Load

2005 ◽  
Vol 128 (2) ◽  
pp. 252-261 ◽  
Author(s):  
A. Choudhury ◽  
N. Tandon
Keyword(s):  
Theoretical Model ◽  
Vibration Response ◽  
Local Defect ◽  
Radial Load ◽  
Rolling Element ◽  
Spectral Components ◽  
Rotor Bearing ◽  
Defect Frequency ◽  
Inner Race ◽  
Bearing System

In the present investigation, a theoretical model has been developed to obtain the vibration response due to a localized defect in various bearing elements in a rotor-bearing system under radial load conditions. The rotor-bearing system has been modeled as a three degrees-of-freedom system. The model predicts significant components at the harmonics of characteristic defect frequency for a defect on the particular bearing element. In the case of a defect on the inner race or a rolling element, the model predicts sidebands about the peaks at defect frequencies, at multiples of shaft and cage frequencies, respectively. The model has also predicted some additional components at harmonics of shaft and cage frequencies due to a local defect on the inner race and a rolling element, respectively. The expressions for all these spectral components have also been derived. Typical numerical results for an NJ 204 bearing have been obtained and plotted. The amplitude of the component at defect frequency, for an outer race defect, is found to be much higher as compared to those due to inner race defect or a rolling element defect of the same size and under similar conditions of load and speed. The results of vibration measurements on roller bearings with simulated local defects have also been presented to experimentally validate the theoretical model proposed. It can be observed from the results that the spectral components predicted by the theoretical model find significant presence in the experimental spectra. Comparison of the normalized analytical values of the spectral components with their experimental values shows fair agreement for most of the cases considered. Probable area of the generated excitation pulses has been calculated and the effects of pulse area variation on the experimental results have been studied.

Hydrodynamic support and dynamic response for an inner-piloted bearing cage

2003 ◽  
Vol 217 (1) ◽  
pp. 19-28 ◽  
Author(s):  
D R Ashmore ◽  
E J Williams ◽  
S McWilliam
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Rolling Element Bearing ◽  
Computationally Efficient ◽  
Support Mechanism ◽  
Rolling Element ◽  
Element Bearing ◽  
Analytical Expressions ◽  
Inner Race ◽  
Generalized Reynolds Equation

Although many attempts have been made to model rolling-element bearings with inner-piloted cages, they all simplify the hydrodynamic cage-support mechanism. This can mean that some cage behaviour is inadequately explained, such as cage lap. This paper presents the development of a new three-dimensional analysis of the hydrodynamic support for an inner-piloted cage for a rolling-element bearing incorporating starved-film conditions. The solution of the generalized Reynolds equation along with a continuity equation leads to analytical expressions for the hydrodynamic forces. The equations of motion for the cage are then integrated numerically using the Newmark beta method to predict the cage response. The availability of analytical hydrodynamic force expressions means that the numerical integration process is computationally efficient. The influence of key parameters such as the level of lubrication and the angular velocity of the inner race are investigated.

scholarly journals Identification of Bearing Faults using Wavelet Transform

2019 ◽  
Vol 8 (4) ◽  
pp. 9829-9833
Keyword(s):  
Condition Monitoring ◽  
Specific Problem ◽  
Wavelet Packet ◽  
Outer Race ◽  
Time Frequency ◽  
Machine Element ◽  
Rolling Element ◽  
Increasing Demand ◽  
Application Specific ◽  
Inner Race

This research is concerned with description of a scheme for bearing’s localized defect detection based on wavelet packet transform (WPT). WPT provides a high resolution time-frequency distribution from which periodic structural ringing due to repetitive force impulses, generated upon the passing of each rolling element on the defect, are detected. The objective of this work is to emphasis on the outer race defect, inner race defect and ball defect. In modern industrial scenario, there is increasing demand for automatic condition monitoring that reduce the gap between digital model and actual product. With reliable condition monitoring, faults such as machine element failures could be identified in their early-stages and further damage to the system could be prevented. Successful monitoring is a complex and application-specific problem, but a generic tool would be useful in preliminary analysis of new signals and in verification of known theories.

Instability Threshold and Stability Boundaries of Rotor-Bearing Systems

1996 ◽  
Vol 118 (1) ◽  
pp. 115-121 ◽  
Author(s):  
W. J. Chen
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Optimization Techniques ◽  
Instability Threshold ◽  
System Stability ◽  
Stability Boundaries ◽  
Practical Applications ◽  
Design Variables ◽  
Rotor Bearing ◽  
The Stability

A direct numerical method for the determination of instability threshold and stability boundaries of flexible rotor-bearing systems is presented. The proposed procedure can also be used to improve the system stability by considering the design variables as operating parameters. The finite element method is utilized in the formulation of system equations of motion. The numerical algorithm is based on nonlinear optimization techniques. Two examples are presented to illustrate the feasibility, desirability, and ability of the proposed algorithm. A simple journal bearing system is used for the parametric study. An industrial high-speed compressor is employed to demonstrate the ability of this algorithm to deal with practical applications. The stability boundaries calculated from this algorithm are in agreement with the experimental results.

Mathematical Model for Rotor Bearing System by Considering the Effect of Shaft Dynamics and Localized Bearing Defects

2016 ◽  
Author(s):  
N. Upadhyay ◽  
M. Jules ◽  
P. K. Kankar ◽  
B. R. Nana Nbendjo
Keyword(s):  
Equations Of Motion ◽  
Mathematical Formulation ◽  
Dynamic Environment ◽  
Hertzian Contact ◽  
System Response ◽  
Restoring Force ◽  
System Behaviour ◽  
Bearing Defects ◽  
Rotor Bearing ◽  
Bearing System

This work is focused on development of model for unbalanced rotor bearing system to predict system behaviour in dynamic environment. In this model, nonlinearity is introduced due to two factors, namely, clearance of bearing and localized bearing races defects. The contact between the races and balls is considered as Hertzian contact which results in nonlinear restoring force due to elastic deformation in contact zone. In the mathematical formulation, the shaft is considered as rotating Timoshenko beam, supported on two ball bearings. After modelling of shaft corresponding equations representing the system behaviour has been formulated. The governing equations of motion are solved by Sixth order Runge-Kutta method. Bifurcation plots have been plotted to understand the state of the system in healthy condition and due to localized defects on races of the bearings. The Frequency spectrum and phase trajectory diagrams are also plotted for better understanding of the system response.

A Theoretical Model to Predict the Vibration Response of Rolling Bearings in a Rotor Bearing System to Distributed Defects Under Radial Load

1999 ◽  
Vol 122 (3) ◽  
pp. 609-615 ◽  
Author(s):  
N. Tandon ◽  
A. Choudhury
Keyword(s):  
Theoretical Model ◽  
Vibration Response ◽  
Radial Load ◽  
Outer Race ◽  
Rolling Element ◽  
Spectral Components ◽  
Rotor Bearing ◽  
Defect Frequency ◽  
Inner Race ◽  
Bearing System

A theoretical model to predict the vibration response of rolling element bearing in a rotor bearing system to distributed defects under radial load has been developed. The rotor bearing system has been considered as a three degrees of freedom model. The distributed defects considered are, the waviness of outer and inner races, and off size rolling element. The model predicts discrete spectrum with specific frequency components for each order of waviness. For outer race waviness, the spectrum has components at outer race defect frequency and its harmonics. In the case of inner race waviness, the waviness orders equal to number of rolling elements and its multiples give rise to spectral components at inner race defect frequency and its multiples. Other orders of waviness generate sidebands at multiples of shaft frequency about these peaks. The model predicts the amplitudes of the spectral components due to outer race waviness to be much higher as compared to those due to inner race waviness. In the case of an off-size rolling element, the model predicts discrete spectra having significant components at multiples of cage frequency. [S0742-4787(00)00603-2]

A Simplified Model for Structural Vibrations in Ball Bearings

1994 ◽  
Author(s):  
Kambiz Farhang ◽  
Kapil Mehra ◽  
Jayanta Datta
Keyword(s):  
Linear Model ◽  
Equations Of Motion ◽  
Linear Representation ◽  
Accurate Estimate ◽  
Rolling Element Bearing ◽  
Hertzian Contact ◽  
Outer Ring ◽  
Rolling Bearings ◽  
Geometrical Properties ◽  
Rolling Element

Abstract More often than not, in studies involving dynamics and vibration of rotor systems, the bearings within a rotor system are treated as linear components. However, it is well understood that bearing systems are nonlinear due to both their geometrical properties and Hertzian contact between their components. This paper develops a linear formulation to approximate the vibration behavior of rolling bearings. A study of the approximation in the linear representation for rolling bearings is presented in which the effects of preload, lubricant viscosity and outer ring mass on the accuracy of the linear representation are determined. The equations of motion governing the vibrations of rolling element bearing are found to be a set of second-order, nonlinear ordinary differential equations with position periodic coefficients. These equations are linearized about nominal values of the position vectors of the rolling element and the outer ring center. The linearized equations of motion are solved to obtain the small perturbations (displacements) from the nominal positions. The results show that the linear model representation is applicable for bearings with preload. Existence of damping and/or greater outer ring mass enhance the approximation provided by the linear model. Most importantly, the linear representation provides a conservative estimate of the rolling element motion and very accurate estimate of the outer ring motion.

Sign in / Sign up

Export Citation Format

Share Document