Optimum Journal Bearing Parameters for Minimum Rotor Unbalance Response in Synchronous Whirl

1982 ◽  
Vol 104 (2) ◽  
pp. 339-344 ◽  
Author(s):  
R. B. Bhat ◽  
J. S. Rao ◽  
T. S. Sankar
Keyword(s):  
Optimal Design ◽  
Optimization Techniques ◽  
Oil Viscosity ◽  
Hydrodynamic Bearings ◽  
Unbalance Response ◽  
Design Variables ◽  
Tilting Pad ◽  
Bearing Design ◽  
Stiffness And Damping ◽  
Lower Limits

Optimization techniques are employed to design hydrodynamic bearings for minimum unbalance response of rotors in synchronous whirl. The analysis for the unbalance response considers the effects of direct and cross coupled coefficients of stiffness and damping in the bearings. A parametric study of the unbalance response is carried out to show the influence of bearing parameters on the response and to demonstrate the merits of applying optimization techniques in bearing design. The bearing parameters optimized are the diameter, clearance, and the oil viscosity. In addition to setting upper and lower limits on the foregoing design variables, the Sommerfeld number is also constrained to be within a certain range for the operational speeds of the rotor. The quantity minimized is the maximum unbalance response of the rotor in the operational speed range. Plain cylindrical, grooved, elliptical, and four shoe tilting pad type bearings are considered in the optimal design of the rotor bearing system. The results indicate that an optimal design of hydrodynamic bearings can reduce the unbalance response of rotors.

Vibration Analysis of Statically Indeterminate Rotors With Hydrodynamic Bearings

1998 ◽  
Vol 120 (4) ◽  
pp. 781-788 ◽  
Author(s):  
N. S. Feng ◽  
E. J. Hahn
Keyword(s):  
Vibration Analysis ◽  
Operating Conditions ◽  
System Stability ◽  
Hydrodynamic Bearings ◽  
Hydrodynamic Bearing ◽  
Unbalance Response ◽  
Tilting Pad ◽  
The Stability ◽  
Rotor Bearings ◽  
Stiffness And Damping

In statically indeterminate rotor bearings systems, where the rotor is supported by one or more hydrodynamic bearings, the reactions at each hydrodynamic bearing, and hence its stiffness and damping properties depend not only on the bearing type, the operating conditions and the bearing dimensions but also on the relative lateral alignment between the journal and the bearing housing; the alignment, therefore, has a significant influence on the system stability and unbalance response. Additional complications arise if nonsymmetric bearing types such as elliptic or tilting pad bearings are present. An iterative procedure is outlined which enables the bearing reactions to be determined at any speed, thereby enabling even large systems such as turbomachinery to be rapidly analyzed in conjunction with existing linear rotor bearing vibration analysis software. Sample numerical examples show how misalignment and bearing type can affect the natural frequencies, the stability threshold, and the unbalance response of such statically indeterminate systems.

Structural Analysis and Optimal Design of Lightweight Skate for Loading and Unloading

2013 ◽  
Vol 785-786 ◽  
pp. 1258-1261
Author(s):  
In Pyo Cha ◽  
Hee Jae Shin ◽  
Neung Gu Lee ◽  
Lee Ku Kwac ◽  
Hong Gun Kim
Keyword(s):  
Topology Optimization ◽  
Structural Analysis ◽  
Optimal Design ◽  
Optimization Techniques ◽  
Normal Operation ◽  
Stress And Strain ◽  
Initial Model ◽  
Design Variables ◽  
Model Set ◽  
Main Frame

Topology optimization and shape optimization of structural optimization techniques are applied to transport skate the lightweight. Skate properties by varying the design variables and minimize the maximum stress and strain in the normal operation, while reducing the volume of the objective function of optimal design and Skate the static strength of the constraints that should not degrade compared to the performance of the initial model. The skates were used in this study consists of the main frame, sub frame, roll, pin main frame only structural analysis and optimal design was performed using the finite element method. Simplified initial model set design area and it compared to SM45C, AA7075, CFRP, GFRP was using the topology optimization. Strength does not degrade compared to the initial model, decreased volume while minimizing the stress and strain results, the optimum design was achieved efficient lightweight.

Multiple Design Objectives in Hydrodynamic Journal Bearing Optimization

1984 ◽  
Vol 106 (1) ◽  
pp. 54-60 ◽  
Author(s):  
S. M. Metwalli ◽  
G. S. A. Shawki ◽  
M. O. A. Mokhtar ◽  
M. A. A. Seif
Keyword(s):  
Journal Bearing ◽  
Design Procedure ◽  
Oil Viscosity ◽  
Novel Approach ◽  
Design Variables ◽  
Loss Maximum ◽  
Hydrodynamic Journal Bearing ◽  
Bearing Design ◽  
Maximum Minimum ◽  
Selection Of

A novel approach is presented to optimize the finite journal bearing performance under steady loading conditions. Closed form expressions representing the behavior of the bearing as explicit functions of the design variables are utilized. Different competing objectives are assumed to suit various design applications. A method of multiplying objectives and raising to different exponents has been adopted. The basic competing objectives are minimum power loss, maximum-minimum film thickness, minimum side leakage, minimum temperature rise, and minimum bearing size. A journal bearing design procedure for optimum performance is thus devised for the selection of optimum bearing length, clearance, and oil viscosity. A numerical example is also presented.

Turbulent Flow, Flexure-Pivot Hybrid Bearings for Cryogenic Applications

1996 ◽  
Vol 118 (1) ◽  
pp. 190-200 ◽  
Author(s):  
Luis San Andres
Keyword(s):  
High Speed ◽  
Energy Transport ◽  
Load Capacity ◽  
Equations Of Motion ◽  
Liquid Oxygen ◽  
Hydrodynamic Bearings ◽  
Numerical Predictions ◽  
Tilting Pad ◽  
Direct Stiffness ◽  
Stiffness And Damping

The thermal analysis of flexure-pivot tilting-pad hybrid (combination hydrostatic-hydrodynamic) bearings for cryogenic turbopumps is presented. The advantages of this type of bearing for high speed operation are discussed. Turbulent bulk-flow, variable properties, momentum and energy transport equations of motion govern the flow in the bearing pads. Zeroth-order equations for the flow field at a journal equilibrium position render the bearing flow rate, load capacity, drag torque, and temperature rise. First-order equations for perturbed flow fields due to small amplitude journal motions provide rotordynamic force coefficients. A method to determine the tilting-pad moment coefficients from the force displacement coefficients is outlined. Numerical predictions correlate well with experimental measurements for tilting-pad hydrodynamic bearings. The design of a liquid oxygen, flexure-pad hybrid bearing shows a reduced whirl frequency ratio and without loss in load capacity or reduction in direct stiffness and damping coefficients.

HYDRODYNAMIC THRUST BEARINGS WITH POLYMER LINING

Tribologia ◽  
2016 ◽  
Vol 268 (4) ◽  
pp. 225-237 ◽  
Author(s):  
Michał WODTKE
Keyword(s):  
Polymeric Materials ◽  
Industrial Applications ◽  
Hydrodynamic Bearings ◽  
Thrust Bearings ◽  
Sliding Surfaces ◽  
Current State ◽  
Tilting Pad ◽  
History Of ◽  
Bearing Design ◽  
Experimental Researches

Polymeric linings of sliding surfaces of the hydrodynamic bearings have been used successfully for over 50 years. Despite of their long history of operation and research, they have not become widespread in industrial applications. This fact may be surprising, considering the conclusions that have been published concerning bearing operation and design. This paper summarizes the current state of the art of the tilting-pad thrust bearings with a polymer lining of pad sliding surfaces. Bearing design and the most commonly used polymeric materials are described. The results of the latest theoretical and experimental researches by both bearing manufacturers and at scientific centres are presented. Observed properties of the bearings with polymer lining were compared to the properties of the bearings covered with Babbitt, which is the most frequently material used as lining for hydrodynamic bearings.

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.

scholarly journals Effects of Tilting Pad Journal Bearing Design Parameters on the Pad-Pivot Friction and Nonlinear Rotordynamic Bifurcations

2020 ◽  
Vol 10 (16) ◽  
pp. 5406
Author(s):  
Sitae Kim ◽  
Sangwon Byun ◽  
Junho Suh
Keyword(s):  
Journal Bearing ◽  
Design Parameters ◽  
Stribeck Curve ◽  
Nonlinear Properties ◽  
Design Variables ◽  
Mass Eccentricity ◽  
Tilting Pad ◽  
Bearing Design ◽  
Set Up ◽  
Tilting Pad Journal Bearing

This study numerically analyzes and investigates the effects of the bearing design parameters of a tilting pad journal bearing (TPJB) on the pad-pivot friction-induced nonlinear rotordynamic phenomena and bifurcations. The bearing parameters were set to the pad preload, pivot offset, spherical pivot radius, and bearing length to diameter (L/D) ratio. The Stribeck curve model (SCM) model was applied at the contact surface between the pad and the pivot, which varied to the boundary-mixed-fluid friction state depending on the friction condition. The rotor-bearing model was set up with a symmetrical five-pad TPJB system supporting a Jeffcott type rigid rotor. The fluid repelling force generated in the oil film between each pad and the shaft was calculated using a finite element method. The simulation recurrently conducted the transient numerical integration to obtain the Poincaré maps and phase states of the journal and pad with various bearing design variables, then the nonlinear properties of each condition were analyzed by expressing the bifurcation diagrams. As a result, the original findings of this study are: (1) The pad preload and pivot offset significantly influenced the emergence of Hopf bifurcations and the associated limit cycles. In contrast, (2) the pivot radius and L/D ratio contributed relatively less to the friction-induced instability. Resultantly, (3) all the effects diminished when the rotor operated under the larger mass eccentricity of the disc.

Optimal Design of a Pilot OTEC Power Plant in Taiwan

1991 ◽  
Vol 113 (4) ◽  
pp. 294-299 ◽  
Author(s):  
C. H. Tseng ◽  
K. Y. Kao ◽  
J. C. Yang
Keyword(s):  
Power Plant ◽  
Optimal Design ◽  
Optimization Model ◽  
Large Scale ◽  
Design Procedure ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Thermal Energy Conversion ◽  
Design Variables ◽  
Ocean Thermal Energy

In this paper, an optimal design concept has been utilized to find the best designs for a complex and large-scale ocean thermal energy conversion (OTEC) plant. The OTEC power plant under this study is divided into three major subsystems consisting of power subsystem, seawater pipe subsystem, and containment subsystem. The design optimization model for the entire OTEC plant is integrated from these subsystems under the considerations of their own various design criteria and constraints. The mathematical formulations of this optimization model for the entire OTEC plant are described. The design variables, objective function, and constraints for a pilot plant under the constraints of the feasible technologies at this stage in Taiwan have been carefully examined and selected. The numerical optimization method called Sequential Quadratic Programming (SQP) is selected to obtain the optimum results. The main purpose of this paper is to demonstrate the design procedure with the optimization techniques for engineering and economics in the OTEC plant so that anyone else can build upon their models according to their needs.

Response Surface Mapping and Multi-Objective Optimization of Tilting Pad Bearing Designs

2017 ◽  
Author(s):  
Michael Branagan ◽  
Neal Morgan ◽  
Brian Weaver ◽  
Houston Wood
Keyword(s):  
Film Thickness ◽  
Power Loss ◽  
Performance Metrics ◽  
Optimization Methods ◽  
Fluid Film ◽  
Design Variables ◽  
Tilting Pad ◽  
Bearing Design ◽  
Central Composite

Fluid film bearings for turbomachinery are designed to support the loads applied by the rotor system, often at high speeds when power loss in the bearing becomes significant and bearing temperatures can reach levels that can be detrimental to the long-term reliability of the support system. These requirements of supportive bearings require an intimate understanding of how bearing design variables affect their overall performance. Ideal bearings minimize power loss to increase machine efficiency and maintain low operating temperatures to ensure long-term reliability while meeting other design criteria such as minimum film thickness to provide proper support and avoiding high fluid pressures that can be harmful to the bearing structure. However, real world designs are often forced to sacrifice some of these design goals in order to preserve others. Therefore, further understanding of the relative opportunity costs associated with optimizing the bearing design with differently weighted performance metrics and their relationships to bearing design variables is invaluable to design engineers. This study explores the impact of eight bearing design variables on the performance of two tilting pad journal bearings supporting an eight-stage centrifugal compressor using design of experiments techniques applied to an established thermoelastohydrodynamic (TEHD) bearing model of tilting pad bearing performance. The bearing design variables analyzed include the radial clearance, pad arc spacing, pad axial length, pivot offset, preload, working fluid viscosity and viscosity index, and the number of pads. Each of the design variables — excluding the number of pads which was realistically constrained — were first varied over five levels each in a central composite design. These central composite designs were repeated for each of three values for number of pads. The responses obtained from the TEHD numerical simulations for each bearing design point were power loss, maximum pad temperature, minimum film thickness, and maximum fluid film pressure. The results from the central composite studies were fit with a multivariate least-squares regression model and a secondary series of experimental design studies were simulated around potential optimum design points to obtain a learning set to initialize direct optimization methods. Two direct multi-objective optimization methods, a sequential quadratic programming method and a multi-island genetic algorithm, were performed using Isight, a commercial software. A range of weighting parameters were selected for the optimization functions to find bearing designs that minimized power loss and pad temperature while maintaining pressure and film thickness criteria within acceptable design ranges for fluid film bearings. The resulting optimum design points allowed for a comparison between the design optimization approaches. The various strengths and weaknesses of the different methods are discussed. This study demonstrates how designers can use these approaches to view the relationships between design variables and important performance metrics to design better bearings for a wide range of applications.

scholarly journals A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils

2021 ◽  
Vol 26 (2) ◽  
pp. 34
Author(s):  
Isaac Gibert Martínez ◽  
Frederico Afonso ◽  
Simão Rodrigues ◽  
Fernando Lau
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Volume Fraction ◽  
Optimization Techniques ◽  
Free Form ◽  
Aerodynamic Shape Optimization ◽  
Sequential Approach ◽  
Airfoil Surface ◽  
Aerodynamic Shape ◽  
Design Variables

The objective of this work is to study the coupling of two efficient optimization techniques, Aerodynamic Shape Optimization (ASO) and Topology Optimization (TO), in 2D airfoils. To achieve such goal two open-source codes, SU2 and Calculix, are employed for ASO and TO, respectively, using the Sequential Least SQuares Programming (SLSQP) and the Bi-directional Evolutionary Structural Optimization (BESO) algorithms; the latter is well-known for allowing the addition of material in the TO which constitutes, as far as our knowledge, a novelty for this kind of application. These codes are linked by means of a script capable of reading the geometry and pressure distribution obtained from the ASO and defining the boundary conditions to be applied in the TO. The Free-Form Deformation technique is chosen for the definition of the design variables to be used in the ASO, while the densities of the inner elements are defined as design variables of the TO. As a test case, a widely used benchmark transonic airfoil, the RAE2822, is chosen here with an internal geometric constraint to simulate the wing-box of a transonic wing. First, the two optimization procedures are tested separately to gain insight and then are run in a sequential way for two test cases with available experimental data: (i) Mach 0.729 at α=2.31°; and (ii) Mach 0.730 at α=2.79°. In the ASO problem, the lift is fixed and the drag is minimized; while in the TO problem, compliance minimization is set as the objective for a prescribed volume fraction. Improvements in both aerodynamic and structural performance are found, as expected: the ASO reduced the total pressure on the airfoil surface in order to minimize drag, which resulted in lower stress values experienced by the structure.

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