Calculation of Dynamic Coefficients in a Hydrodynamic Bearing Considering Five Degrees of Freedom for a General Rotor-Bearing System

1999 ◽  
Vol 121 (3) ◽  
pp. 499-505 ◽  
Author(s):  
G. H. Jang ◽  
Y. J. Kim
Keyword(s):  
Degrees Of Freedom ◽  
Disk Drive ◽  
Spindle Motor ◽  
Hydrodynamic Bearing ◽  
Thrust Bearings ◽  
Dynamic Coefficients ◽  
Rotor Bearing ◽  
The Moment ◽  
Wedge Effect ◽  
Bearing System

A complete method is presented to calculate the stiffness and the damping coefficients in a hydrodynamic bearing considering five degrees of freedom for a general rotor-bearing system. Perturbation equations are obtained from Reynolds equation by assuming the small amplitude motion of a bearing center, and are solved by the finite element method. Their characteristics due to eccentricity and misalignment are investigated for herringbone groove journal and thrust bearings in the spindle motor of a hard disk drive. This research shows that the dynamic coefficients increase with increasing the misalignment as well as the eccentricity due to the wedge effect. It also shows that the moment coefficients, which have been neglected in most of the previous analyses, are of significant magnitude in a journal bearing and have even bigger values for the thrust bearing when they are compared with the ball bearing in the same type of a spindle motor.

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.

Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part I: Analytical Bearing Model

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Mohammad Miraskari ◽  
Farzad Hemmati ◽  
Mohamed S. Gadala
Keyword(s):  
Journal Bearing ◽  
Nonlinear Coefficient ◽  
Journal Bearings ◽  
Flexible Rotor ◽  
Dynamic Coefficients ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Bearing Force ◽  
Derivatives Of ◽  
Bearing System

To determine the bifurcation types in a rotor-bearing system, it is required to find higher order derivatives of the bearing forces with respect to journal velocity and position. As closed-form expressions for journal bearing force are not generally available, Hopf bifurcation studies of rotor-bearing systems have been limited to simple geometries and cavitation models. To solve this problem, an alternative nonlinear coefficient-based method for representing the bearing force is presented in this study. A flexible rotor-bearing system is presented for which bearing force is modeled with linear and nonlinear dynamic coefficients. The proposed nonlinear coefficient-based model was found to be successful in predicting the bifurcation types of the system as well as predicting the system dynamics and trajectories at spin speeds below and above the threshold speed of instability.

Dynamic Coefficients of the Coupled Journal and Thrust Bearings Considering Five Degrees of Freedom for a General Rotor-Bearing System

2007 ◽  
Author(s):  
G. H. Jang ◽  
S. H. Lee ◽  
H. W. Kim
Keyword(s):  
Degrees Of Freedom ◽  
Thrust Bearing ◽  
Numerical Differentiation ◽  
Reynolds Equations ◽  
Thrust Bearings ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Translational Displacement ◽  
Finite Displacements ◽  
Perturbation Equations

This paper proposes a method to calculate the stiffness and the damping coefficients of the coupled journal and thrust bearings considering tilting motion. The Reynolds equations and their perturbation equations are derived by linearization of bearing reaction with respect to the general five degrees of freedom, i.e. the tilting displacement and angular velocity as well as the translational displacement and velocity. Reynolds equations and their perturbation equations are transformed to the finite element equations by considering the continuity of pressure and flow at the interface between the journal and the thrust bearings. It also includes the Reynolds boundary condition in the numerical analysis to simulate the cavitation phenomena. The stiffness and the damping coefficients of the proposed method are compared with those of the numerical differentiation of the loads with respect to finite displacements and velocities of bearing center. It shows that the proposed method can calculate the dynamic coefficients of a coupled journal and thrust bearing more accurately and efficiently than the differentiation method.

scholarly journals Dynamic Analysis of Integrally Geared Compressors with Varying Workloads

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Ming Zhang ◽  
Zhinong Jiang ◽  
Jinji Gao
Keyword(s):  
Critical Load ◽  
Axial Force ◽  
High Efficiency ◽  
Dynamic Responses ◽  
Dynamic Behaviors ◽  
Meshing Stiffness ◽  
Dynamic Coefficients ◽  
Coupling System ◽  
Rotor Bearing ◽  
Bearing System

Integrally geared compressors are characterized by compact and high efficiency machines, which are widely used in modern processing industries. As an important part of integrally geared compressors, a geared rotor-bearing system exhibits complicated dynamic behaviors. When running at rated speeds, a coupling system likely produces resonance with an adjusted workload, and a critical load phenomenon occurs. The dynamic coefficients of bearings, axial force and torque, and gear meshing stiffness vary with workload because of the interaction between rotors. In this study, a dynamic model of a geared rotor-bearing system influenced by the dynamic coefficients of bearings, axial force and torque, and gear meshing stiffness is developed. The dynamic responses of the coupling system are calculated and analyzed by using a typical five-shaft integrally geared compressor as an example. The effects of different parameters on the dynamic behaviors of the proposed system are also considered in the discussion. The geared rotor-bearing system is further investigated to examine the failure mechanism of the critical load.

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.

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