A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings: Part I—Single Pad Analysis

1990 ◽  
Vol 112 (2) ◽  
pp. 169-176 ◽  
Author(s):  
L. L. Earles ◽  
A. B. Palazzolo ◽  
R. W. Armentrout
Keyword(s):  
Finite Element ◽  
Current Method ◽  
Journal Bearings ◽  
Radius Of Curvature ◽  
Approximate Methods ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Tilting Pad ◽  
Element Approach ◽  
General Method

A general method of incorporating pad flexibility effects into tilting pad isothermal bearing analysis is developed. The pad assembly approach is extended using 2-dimensional finite elements to determine pad deformations of a single pad. The pad deformations are represented by a single degree of freedom, the change in the pad radius of curvature, thus the current method is an approximate approach. The equations to calculate frequency reduced coefficients for a single pad are presented. Synchronously reduced coefficients for a single pad are in agreement with previous curved beam approximate methods and a more rigorous iterative approach. The finite element pad model provides more versatility in modeling nonuniform pad dimensions and the skewed boundary conditions which occur at the spherical pivot-pad socket interfaces.

scholarly journals Rocking motion of slender elastic body on rigid floor

1986 ◽  
Vol 19 (1) ◽  
pp. 18-27 ◽  
Author(s):  
T. Ichinose
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Angular Momentum ◽  
Elastic Body ◽  
Vibration Mode ◽  
Simple Relationship ◽  
Element Analysis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Rocking Motion

A single degree of freedom (SDOF) model is presented to describe the rocking behaviour of a slender elastic body on a rigid floor. This model assumes the vibration mode to be a linear combination of flexural and rocking modes. A finite element analysis is also presented, in which following features are observed to support the assumptions of the proposed SDOF model: (1) There exists a simple relationship between the magnitudes of flexural and rocking modes, which relation can be derived from the equilibrium of moment. (2) Angular momentum is conserved at the instances of uplifting and landing.

A Finite-Element-Based Method to Determine the Spatial Stiffness Properties of a Notch Hinge

1998 ◽  
Vol 123 (1) ◽  
pp. 141-147 ◽  
Author(s):  
Shilong Zhang ◽  
Ernest D. Fasse
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Joint Stiffness ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stiffness Properties ◽  
Six Degree Of Freedom ◽  
Flexural Hinges

Notch hinges are flexural hinges used to make complex, precise mechanisms. They are typically modeled as single degree-of-freedom hinges with an associated joint stiffness. This is not adequate for all purposes. This paper computes the six degree-of-freedom stiffness properties of notch hinges using finite element methods. The results are parameterized in terms of meaningful design parameters.

FOLDING OF A TYPE OF DEPLOYABLE ORIGAMI STRUCTURES

2012 ◽  
Vol 12 (06) ◽  
pp. 1250054 ◽  
Author(s):  
YAO CHEN ◽  
JIAN FENG
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Jacobian Matrix ◽  
Element Analysis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Element Simulation ◽  
Rigid Plane ◽  
Configuration Changes ◽  
Good Agreement

Some types of rigid origami possess specific geometric properties. They have a single degree of freedom, and can experience large configuration changes without cut or being stretched. This study presents a numerical analysis and finite element simulation on the folding behavior of deployable origami structures. Equivalent pin-jointed structures were established, and a Jacobian matrix was formed to constrain the internal mechanisms in each rigid plane. A nonlinear iterative algorithm was formulated for predicting the folding behavior. The augmented compatibility matrix was updated at each step for correcting the incompatible strains. Subsequently, finite element simulations on the deployable origami structures were carried out. Specifically, two types of generalized deployable origami structures combined by basic parts were studied, with some key parameters considered. It is concluded that, compared with the theoretical values, both the solutions obtained by the nonlinear algorithm and finite element analysis are in good agreement, the proposed method can well predict the folding behavior of the origami structures, and the error of the numerical results increases with the increase of the primary angle.

Time-Domain Finite-Element Solutions for Single-Degree-of-Freedom Systems with Time-Dependent Parameters

1980 ◽  
Vol 22 (1) ◽  
pp. 29-33 ◽  
Author(s):  
J. E. T. Penny ◽  
G. F. Howard
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Time Domain ◽  
Time Dependent ◽  
Algebraic Equations ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stiffness Properties ◽  
Linear Algebraic Equations ◽  
External Forces

The motion of systems in which mass, damping, and stiffness properties are known functions of time is described in terms of time-domain finite elements. The response of such systems to external forces is determined by generating matrices, the coefficients of which are functions of the varying parameters. The original differential equations are then replaced by sets of linear algebraic equations which are solved numerically. Examples of the use of the method are given.

On the Frequency Dependency of Tilting-Pad Journal Bearings

2019 ◽  
Author(s):  
Laurence F. Wagner
Keyword(s):  
Journal Bearings ◽  
Operating Conditions ◽  
Experimental Investigations ◽  
Single Degree Of Freedom ◽  
Frequency Dependency ◽  
Exciting Frequency ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Rotational Damping ◽  
Tilting Pad Journal Bearings

Abstract Controversy regarding the dynamic modeling of tilting-pad journal bearings (TPJB) has existed for years, with the question of the effective stiffness and damping properties, and the requirement for consideration of frequency dependency, being of great concern. There is a partial disconnect between the results of theoretical and many experimental investigations. This paper attempts to examine this issue in more of a macro sense; broadening the scope of the geometric and operating domains, and in turn expanding an understanding of related frequency effects. The investigation hinges on a single-pad, single degree-of-freedom (DOF) model that represents various geometries and operating conditions for a full bearing. The results clearly show that the dynamic coefficients must be dependent upon the “exciting” frequency, and that the dependency is primarily associated with the pad rotational damping.

Unbalance Response of Rotors Considering the Distributed Bearing Stiffness and Damping

1994 ◽  
Author(s):  
A. S. Sekhar ◽  
B. S. Prabhu
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Journal Bearings ◽  
Principle Of Virtual Work ◽  
Unbalance Response ◽  
Tilting Pad ◽  
Bearing Stiffness ◽  
Element Technique ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

Usually while modelling rotor-bearing systems the bearings are treated as point supports. In the present paper, using the finite element technique, the unbalance response of rotors is studied by considering distributed bearing stiffness and damping. The bearing stiffness and damping terms are derived by the principle of virtual work. Unbalance responses of rotors with bearing distributed effects are compared with the model using point supports and for different supports Viz., cylindrical journal bearings, tilting pad journal bearings, offset and three lobe journal bearings.

A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings: Part II—Assembled Bearing and System Analysis

1990 ◽  
Vol 112 (2) ◽  
pp. 178-182 ◽  
Author(s):  
L. L. Earles ◽  
A. B. Palazzolo ◽  
R. W. Armentrout
Keyword(s):  
Finite Element ◽  
System Analysis ◽  
Journal Bearings ◽  
Complex Eigenvalue ◽  
Finite Element Approach ◽  
Rotor Bearing ◽  
Element Approach ◽  
Bearing System

Pad flexibility effects are studied in an actual bearing. This flexibility is shown to decrease the predicted instability onset speed of the rotor bearing system. The use of complex eigenvalue dependent bearing coefficients as compared with using synchronously reduced coefficients is seen to produce a more significant decrease in the instability onset speed. Further reductions in the instability onset speed are obtained by including pivot stiffness in the complex eigenvalue dependent bearing coefficients.

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