Stability Analysis of a Hydrodynamic Journal Bearing With Rotating Herringbone Grooves

2003 ◽  
Vol 125 (2) ◽  
pp. 291-300 ◽  
Author(s):  
G. H. Jang ◽  
J. W. Yoon
Keyword(s):  
Journal Bearing ◽  
Equations Of Motion ◽  
Fourier Series Expansion ◽  
Algebraic Equations ◽  
High Rotational Speed ◽  
Dynamic Coefficients ◽  
Stiffness Coefficients ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Herringbone Grooves

This paper presents an analytical method to investigate the stability of a hydrodynamic journal bearing with rotating herringbone grooves. The dynamic coefficients of the hydrodynamic journal bearing are calculated using the FEM and the perturbation method. The linear equations of motion can be represented as a parametrically excited system because the dynamic coefficients have time-varying components due to the rotating grooves, even in the steady state. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill’s infinite determinant of these algebraic equations. The validity of this research is proved by the comparison of the stability chart with the time response of the whirl radius obtained from the equations of motion. This research shows that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing eccentricity and with decreasing groove number, which play the major roles in increasing the average and variation of stiffness coefficients, respectively. It also shows that a high rotational speed is another source of instability by increasing the stiffness coefficients without changing the damping coefficients.

Stability Analysis of a Rotating System Due to the Effect of Ball Bearing Waviness

2002 ◽  
Vol 125 (1) ◽  
pp. 91-101 ◽  
Author(s):  
G. H. Jang ◽  
S. W. Jeong
Keyword(s):  
Parametric Excitation ◽  
Ball Bearing ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Fourier Series Expansion ◽  
Time Varying ◽  
Algebraic Equations ◽  
Rotating System ◽  
Mathieu’S Equation ◽  
The Stability

This research presents an analytical model to investigate the stability due to the ball bearing waviness in a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu’s equation, because the stiffness coefficients have time-varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill’s infinite determinant for these algebraic equations. The validity of this research is proven by comparing the stability chart with the time responses of the vibration model suggested by prior research. This research shows that the waviness in the ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 i=1,2,3,….

Stability Analysis of a Whirling Rigid Rotor Supported by FDBs Considering Five Degrees of Freedom of a General Rotor-Bearing System

2014 ◽  
Author(s):  
M. H. Lee ◽  
J. H. Lee ◽  
G. H. Jang
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time Varying ◽  
Algebraic Equations ◽  
Dynamic Coefficients ◽  
Mass Unbalance ◽  
Whirling Motion ◽  
Rotor Bearing ◽  
The Stability ◽  
Bearing System

A rotor supported by fluid dynamic bearings (FDBs) has a whirling motion by centrifugal force due to the mass unbalance or by the flexibility of shaft. This whirling motion also generates periodic time-varying oil-film reaction and dynamic coefficients even in case of the stationary grooved FDBs. This paper proposes a method to determine the stability of a whirling rotor supported by stationary grooved FDBs considering five degrees of freedom of a general rotor-bearing system. Dynamic coefficients are calculated by using the finite element method and the perturbation method, and they are represented as periodic harmonic functions by considering whirling motion. Because of the periodic time-varying dynamic coefficients, the equations of motion of the rotor supported by FDBs can be represented as a parametrically excited system. The solution of the equations of motion can be assumed as the Fourier series so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Hill’s infinite determinant is calculated by using these algebraic equations in order to determine the stability. The stability of the FDBs decreases with the increase of rotational speed. The stability of the FDBs increases with the increase of whirl radius, because the average and variation of Cxx increase faster than those of Kxx. The proposed method is verified by solving the equations of motion by using the forth Runge-Kutta method to determine the convergence and divergence of whirl radius.

A simplified thermohydrodynamic stability analysis of journal bearings

2005 ◽  
Vol 219 (3) ◽  
pp. 225-234 ◽  
Author(s):  
S Singhal ◽  
M. M. Khonsari
Keyword(s):  
Journal Bearing ◽  
Journal Bearings ◽  
Lubricating Oil ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Stiffness Coefficients ◽  
Design Charts ◽  
Operating Region ◽  
Rapid Prediction ◽  
The Stability

This work investigates the stability of a journal bearing system, including the effects of inlet viscosity. Simplified thermohydrodynamic design charts for the rapid prediction of stiffness coefficients, damping coefficients, and threshold speed have been developed. This investigation reveals that the inlet viscosity has a pronounced influence on the bearing dynamic coefficients of the lubricating oil film. This investigation also reveals that it is possible to stabilize a journal bearing either by heating the oil or by cooling the oil depending on the operating region.

Evaluation of Dynamic Coefficients of a Two-Lobe Journal Bearing Using an Electrical Analogy Approach

1996 ◽  
Vol 118 (3) ◽  
pp. 657-662 ◽  
Author(s):  
Har Prashad
Keyword(s):  
Journal Bearing ◽  
Operating Conditions ◽  
Dynamic Coefficients ◽  
Electrical Analogy ◽  
Dimensional Parameters ◽  
Capacitive Reactance ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Stability Regime ◽  
Stiffness And Damping

A theoretical approach to evaluating capacitance, resistance, capacitive reactance, and impedance of the lower and upper lobes of a two-lobe elliptical hydrodynamic journal bearing under various operating conditions is developed. It is established that the change in capacitance and resistance with the change in eccentricity ratios is nonlinear. The capacitance and resistance, thus determined, are correlated with the dynamic coefficients of bearings using an electrical analogy. It is found that the stiffness and damping coefficients are higher for two-lobe bearings as compared to those of cylindrical bearings having identical dimensional parameters and operating under similar conditions. The analysis may have the potential to diagnose the stability regime of a bearing through the bearing’s electrical parameters. The electrical analogy may be a useful alternative to conventional techniques.

Optimization of Journal Bearing Profile for Higher Dynamic Stability Limits

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Rodrigo Nicoletti
Keyword(s):  
Journal Bearing ◽  
Optimization Procedure ◽  
Control Points ◽  
Time Domain Simulation ◽  
Rotating System ◽  
Stability Margins ◽  
Dynamic Coefficients ◽  
The Stability ◽  
Stability Limits ◽  
Improve Stability

This work presents an optimization procedure to find bearing profiles that improve stability margins of rotor-bearing systems. The profile is defined by control points and cubic splines. Stability margins are estimated using bearing dynamic coefficients, and obtained solutions are analyzed as a function of the number of control points and of the Sommerfeld number at optimization. Results show the feasibility of finding shapes for the bearing that significantly improve the stability margins. Some of the obtained solutions overcome the stability margins of conventional bearings, such as the journal bearing and preloaded bearings with 0.5 and 0.67 preload. A time domain simulation of a flexible shaft rotating system supported by such bearings corroborates the results.

Linear stability analysis of finite hydrodynamic journal bearing under turbulent lubrication with coupled-stress fluid

2016 ◽  
Vol 68 (3) ◽  
pp. 386-391 ◽  
Author(s):  
Abhishek Ghosh ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Newtonian Fluid ◽  
High Speed ◽  
Journal Bearing ◽  
Slenderness Ratio ◽  
Linear Perturbation ◽  
Content Type ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Coupled Stress

Purpose Several researchers have observed that to satisfy modern day’s need, it is essential to enhance the characteristics of journal bearing, which is used in numerous applications. Moreover, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of Non-Newtonian fluids is coming more into picture. Furthermore, if turbo-machinery applications are taken into account, then it can be seen that journal bearings are used for high speed applications as well. Thus, neglecting turbulent conditions may lead to erroneous results. Hence, this paper aims to present focuses on studying the stability characteristics of finite hydrodynamic journal bearing under turbulent coupled-stress lubrication. Design/methodology/approach First, the governing equation relevant to the problem is generated. Then, the dynamic analysis is carried out by linear perturbation technique, leading to three perturbed equations, which are again discretized by finite difference method. Finally, these discretized equations are solved with the help of Gauss-Seidel Iteration technique with successive over relaxation scheme. Consequently, the film response coefficients and the stability parameters are evaluated at different parametric conditions. Findings It has been concluded from the study that with increase in value of the coupled-stress parameter, the stability of the journal may increase. Whereas, with increase in Reynolds number, the stability of the journal decreases. On the other hand, stability increases with increasing values of slenderness ratio. Originality/value Researches have been performed to study the dynamic characteristics of journal bearing with non-Newtonian fluid as the lubricant. But in the class of non-Newtonian lubricants, the use of coupled-stress fluid has not yet been properly investigated. So, an attempt has been made to perform the stability analysis of bearings with coupled-stress fluid as the advanced lubricant.

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

Morton Effect Induced Synchronous Instability in Mid-Span Rotor–Bearing Systems, Part 2: Models and Simulations

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Zenglin Guo ◽  
Gordon Kirk
Keyword(s):  
Journal Bearing ◽  
Negative Impact ◽  
System Stability ◽  
Stability Performance ◽  
Fluid Film Bearings ◽  
Morton Effect ◽  
Thermal Bending ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Thermal Imbalance

The mechanism of the Morton Effect induced synchronous instability has been discussed in Part 1, using an assumption of isotropic linear bearings. The second part of the current study will now focus on the more realistic systems, mid-span rotors supported by the hydrodynamic journal bearings. First, the models to calculate the thermal bending of the shaft and the temperature distribution across the journal surface are established. This can be used to calculate the equivalent thermal imbalance. The calculations of the temperature difference and its equivalent thermal imbalance using hydrodynamic plain journal bearing models are conducted and discussed with the comparison to the analytical results obtained in Part 1. It shows that the thermal imbalance induced by the Morton Effect may increase to the level of the mechanical imbalance and then its influence on the system stability should be included. The suggested thermal bending model also partially explains that the mid-span rotors are less liable to be influenced by the Morton Effect induced instability than are the overhung configurations, because of the restraining effect between two supports. Finally, a symmetric mid-span rotor - hydrodynamic journal bearing system is calculated to show its stability performance. The results show the inclusion of the Morton Effect may lead to an unstable operation of the system. Considering the existence of the oil film self-induced vibration due to the dynamic characteristics of fluid film bearings, the Morton Effect may make a further negative impact on the stability of the system. The simulation results of the unbalance response show that the Morton Effect changes the shapes of the whirling orbits and makes them no longer the standard elliptical orbits around the static equilibriums.

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