Analysis of an Accelerating Rotor-Bearing System With Flexible Damped Supports

1998 ◽  
Author(s):  
Euro L. Casanova ◽  
Luis U. Medina
Keyword(s):  
Steady State ◽  
Numerical Integration ◽  
Equations Of Motion ◽  
Peak Amplitude ◽  
Graphical Form ◽  
Jeffcott Rotor ◽  
Rotor Bearing ◽  
Flexible Supports ◽  
Steady State Predictions ◽  
Bearing System

This paper deals with the dynamics of an accelerating unbalanced Jeffcott rotor-bearing system mounted on damped, flexible supports. The general equations of motion for such a system are presented and discussed. The rotor response was predicted, via numerical integration, for various cases in runup and rundown conditions and presented in graphical form. The effects of acceleration on the rotor peak amplitude and the speed at which the peak occurs is discussed and compared to steady state predictions.

Dynamic Response of a Geared Rotor-Bearing System Under Residual Shaft Bow Effect

2006 ◽  
Author(s):  
T. N. Shiau ◽  
E. K. Lee ◽  
Y. C. Chen ◽  
T. H. Young
Keyword(s):  
Steady State ◽  
Natural Frequencies ◽  
Coupling Effect ◽  
Equations Of Motion ◽  
Transmission Error ◽  
Mode Shapes ◽  
Steady State Response ◽  
State Response ◽  
Rotor Bearing ◽  
Bearing System

The paper presents the dynamic behaviors of a geared rotor-bearing system under the effects of the residual shaft bow, the gear eccentricity and excitation of gear’s transmission error. The coupling effect of lateral and torsional motions is considered in the dynamic analysis of the geared rotor-bearing system. The finite element method is used to model the system and Lagrangian approach is applied to derive the system equations of motion. The dynamic characteristics including system natural frequencies, mode shapes and steady-state response are investigated. The results show that the magnitude of the residual shaft bow, the phase angle between gear eccentricity and residual shaft bow will significantly affect system natural frequencies and steady-state response. When the spin speed closes to the second critical speed, the system steady state response will be dramatically increased by the residual shaft bow for the in-phase case. Moreover the zero response can be obtained when the system is set on special conditions.

Dynamic Analysis of a Spur Geared Rotor-Bearing System with Nonlinear Gear Mesh Stiffness

2014 ◽  
Vol 945-949 ◽  
pp. 853-861 ◽  
Author(s):  
Ying Chung Chen ◽  
Chung Hao Kang ◽  
Siu Tong Choi
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Element Model ◽  
Dynamic Responses ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Lagrange’S Equation ◽  
Rotor Bearing ◽  
Gear Mesh Stiffness ◽  
Bearing System

The gear mesh stiffnesses have been regarded as constants in most previous models of geared rotor-bearing systems. In this paper, a dynamic analysis of a spur geared rotor-bearing system with nonlinear gear mesh stiffness is presented. The nonlinear gear mesh stiffness is accounted for by bending, fillet-foundation and contact deflections of gear teeth. A finite element model of the geared rotor-bearing system is developed, the equations of motion are obtained by applying Lagrange’s equation, and the dynamic responses are computed by using the fourth-order Runge-Kutta numerical method. Numerical results indicate that the proposed gear mesh stiffness provides a realistic dynamic response for spur geared rotor-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.

Chaotic Motions of a Dual-Spin Body

1998 ◽  
Vol 65 (1) ◽  
pp. 150-156 ◽  
Author(s):  
A. C. Or
Keyword(s):  
Steady State ◽  
Numerical Integration ◽  
Coulomb Friction ◽  
Equations Of Motion ◽  
Homoclinic Tangency ◽  
Chaotic Attractors ◽  
Chaotic Motions ◽  
Homoclinic Points ◽  
Melnikov’S Method

The dynamics of a dual-spinner subject to the action of an internal oscillatory torque and Coulomb friction between the two linked bodies is investigated. The conditions for existence of transverse homoclinic points and homoclinic tangency of chaotic motions are obtained using Melnikov’s method. Through long-term numerical integration of the equations of motion, steady-state chaotic attractors are also found and studied numerically by varying the forcing amplitude.

Coupled Lateral and Torsional Nonlinear Transient Rotor–Bearing System Analysis With Applications

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Jianming Cao ◽  
Paul Allaire ◽  
Timothy Dimond
Keyword(s):  
Rotational Speed ◽  
System Analysis ◽  
Equations Of Motion ◽  
Squeeze Film ◽  
Rotor Bearing ◽  
Nonlinear Transient ◽  
Gyroscopic Effects ◽  
Nonlinear Equations Of Motion ◽  
Torsional Analysis ◽  
Bearing System

This paper provides a time transient method for solving coupled lateral and torsional analysis of a flexible rotor–bearing system including gyroscopic effects, nonlinear short journal bearings, nonlinear short squeeze film dampers (SFDs), and external nonlinear forces/torques. The rotor is modeled as linear, and the supporting components, including bearings and dampers, are modeled as nonlinear. An implicit Runge–Kutta method is developed to solve the nonlinear equations of motion with nonconstant operating speed since the unbalance force and the gyroscopic effect are related to both the rotational speed and the acceleration. The developed method is compared with a previous torsional analysis first to verify the nonlinear transient solver. Then the coupled lateral and torsional analysis of an example flexible three-disk rotor, perhaps representing a compressor, with nonlinear bearings and nonlinear dampers driven by a synchronous motor is approached. The acceleration effects on lateral and torsional amplitudes of vibration are presented in the analysis. The developed method can be used to study the rotor motion with nonconstant rotational speed such as during startup, shutdown, going through critical speeds, blade loss force, or other sudden loading.

Dynamic Analysis of a Motorized Spindle With Externally Pressurized Air Bearings

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Chundong Xu ◽  
Shuyun Jiang
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Forced Response ◽  
Air Bearings ◽  
Motorized Spindle ◽  
Static And Dynamic Characteristics ◽  
Rotating Speed ◽  
Rotor Bearing ◽  
Bearing System

The purpose of this paper is to investigate the dynamic characteristics of a motorized spindle with externally pressurized air bearings. The externally pressurized air bearings consist of a journal bearing and a double pad thrust bearing with orifice restrictors. The equations of motion for the rotor-bearing system are established considering five degrees-of-freedom (DOF). The perturbation method and the finite difference method are introduced to calculate the static and dynamic characteristics of the air bearings; and the effects of the rotating speed and tilt angle of the rotor on the dynamic characteristics of the air bearings are analyzed. With the dynamic coefficients of the air bearings and the 5DOF rotor-dynamic model obtained, the stability, the unbalance response, and the forced response of the rotor-bearing system are investigated. Finally, the static and dynamic characteristics of the spindle are verified by an experimental study.

scholarly journals Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

2021 ◽  
Author(s):  
T. A. El-Sayed ◽  
Hussein Sayed
Keyword(s):  
Equations Of Motion ◽  
Journal Bearings ◽  
Third Order ◽  
Damping Coefficients ◽  
The Third ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Rotor Stiffness ◽  
Stiffness And Damping ◽  
Bearing System

AbstractHydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they are susceptible to oil whirl instability, which may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical journal bearings is used to investigate the stability and bifurcations of rotor bearing system. Since a closed form for the finite bearing forces is not exist, nonlinear bearing stiffness and damping coefficients are used to represent the bearing forces. The bearing forces are approximated to the third order using Taylor expansion, and infinitesimal perturbation method is used to evaluate the nonlinear bearing coefficients. The mesh sensitivity on the bearing coefficients is investigated. Then, the equations of motion based on bearing coefficients are used to investigate the dynamics and stability of the rotor-bearing system. The effect of rotor stiffness ratio and applied load on the Hopf bifurcation stability and limit cycle continuation of the system are investigated. The results of this work show that evaluating the bearing forces using Taylor’s expansion up to the third-order bearing coefficients can be used to profoundly investigate the rich dynamics of rotor-bearing systems.

Parametric Study of Stability Criteria for Rotor Bearing Model With Viscoelastic Support

2017 ◽  
Author(s):  
S. Chandraker ◽  
J. K. Dutt ◽  
H. Roy
Keyword(s):  
Classical Method ◽  
Equations Of Motion ◽  
Weight Ratio ◽  
High Strength ◽  
Point Of View ◽  
Stability Criteria ◽  
Engineering Structures ◽  
Rotor Bearing ◽  
The Stability ◽  
Bearing System

In the last few decades, intensive research has been carried out on viscoelastic materials. Among them, most importantly polymers and composites thereof find extensive applications in engineering structures and rotors primarily due to quite high strength to weight ratio in comparison with metals. In dynamic modeling of rotor bearing system, incorporation of damping is very important as stationary (external) damping always helps in stability, however rotary damping (internal) promotes instability of rotors above a certain speed. Therefore for modeling point of view, it is very important to consider both internal or external damping effect. For this reason, the dissipation mechanism has been handled in such a way that it provides proper forces irrespective of its presence in a stationary or a rotary frame. Also in present work, both classical method and operator multiplier method are suggested to derive the equations of motion. The analysis also shows the stability zones of the rotor bearing system for various parametric values of different viscoelastic supports. It is found that choosing a right viscoelastic support can increase the stability criteria of the system to some extent.

Response Analysis of a General Asymmetric Rotor-Bearing System

1980 ◽  
Vol 102 (1) ◽  
pp. 147-157 ◽  
Author(s):  
T. Inagaki ◽  
H. Kanki ◽  
K. Shiraki
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Field Measurements ◽  
Transverse Mass ◽  
Response Analysis ◽  
Mass Moment ◽  
Rotor Bearing ◽  
Asymmetric Rotor ◽  
Bearing System

This paper presents an analytical method for the evaluation of the synchronous response of a general asymmetric rotor-bearing system. In the analysis, slightly asymmetric shaft stiffness in bending and shearing, which distribute along the rotor, and asymmetric transverse mass moment of inertia are considered. The dynamic properties of bearings and pedestals are assumed to be anisotropic and coupled in each direction. The equations of motion with periodic time dependent coefficients are solved by the Harmonic Balance Method and formulated to the transfer matrix. These solutions include the “Modified Holzer-Myklestad-Prohl Method by Lund & Orcutt” as a special case. The results of the analysis are confirmed by a simple model test and field measurements of large turbosets.

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