scholarly journals Multiobjective Optimization of Rotor-Bearing System With Critical Speeds Constraints

1991 ◽  
Author(s):  
Ting Nung Shiau ◽  
Jer Rong Chang
Keyword(s):  
Multiobjective Optimization ◽  
Expansion Method ◽  
Weighting Method ◽  
Cross Sectional ◽  
Design Algorithm ◽  
Critical Speeds ◽  
Design Variables ◽  
Rotor Bearing ◽  
Polynomial Expansion Method ◽  
Bearing System

An efficient optimal design algorithm is developed to individually or simultaneously minimize the total weight of shaft and the transsmitted forces at the bearings which play very important roles in designing a rotor-bearing system under the constraints of critical speeds. The cross sectional area of shaft, the bearing stiffness, and the positions of bearings and disks are chosen as the design variables. The dynamic characteristics are determined by applying the generalized polynomial expansion method and the sensitivity analysis is also investigated. For multiobjective optimization, the weighting method (WM), the goal programming method (GPM), and the fuzzy method (FM) are applied. The results show that the present multiobjective optimization algorithm can greatly reduce both the weight of shaft and the forces at the bearings with critical speeds constraints.

Multi-objective Optimization of Rotor-Bearing System With Critical Speed Constraints

1993 ◽  
Vol 115 (2) ◽  
pp. 246-255 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang
Keyword(s):  
Critical Speed ◽  
Expansion Method ◽  
Multi Objective Optimization ◽  
Weighting Method ◽  
Cross Sectional ◽  
Design Algorithm ◽  
Multi Objective ◽  
Design Variables ◽  
Rotor Bearing ◽  
Bearing System

An efficient optimal design algorithm is developed to minimize, individually or simultaneously, the total weight of the shaft and the transmitted forces at the bearings. These factors play very important roles in designing a rotor-bearing system under the constraints of critical speeds. The cross-sectional area of the shaft, the bearing stiffness, and the positions of bearings and disks are chosen as the design variables. The dynamic characteristics are determined by applying the generalized polynomial expansion method and the sensitivity analysis is also investigated. For multi-objective optimization, the weighting method (WM), the goal programming method (GPM), and the fuzzy method (FM) are applied. The results show that the present multi-objective optimization algorithm can greatly reduce both the weight of the shaft and the forces at the bearings with critical speed constraints.

Multi-objective Optimization of a Flexible Rotor in Magnetic Bearings With Critical Speeds and Control Current Constraints

1997 ◽  
Vol 119 (1) ◽  
pp. 186-195 ◽  
Author(s):  
Ting Nung Shiau ◽  
Chun Pao Kuo ◽  
Jiunn Rong Hwang
Keyword(s):  
Expansion Method ◽  
Magnetic Bearings ◽  
Multi Objective Optimization ◽  
Flexible Rotor ◽  
Weighting Method ◽  
Cross Sectional ◽  
Critical Speeds ◽  
Multi Objective ◽  
Design Variables ◽  
Single Objective

This paper presents the single objective optimization and the multi-objective optimization for a flexible rotor system with magnetic bearings. The weight of rotor shaft and the transmitted forces at the magnetic bearings are minimized either individually or simultaneously under the constraints on the critical speeds and the control currents of magnetic bearings. The design variables are the cross-sectional area of the shaft, the bias currents of magnetic bearings, and the positions of the disk and the magnetic bearings. The dynamic characteristics are analyzed using the generalized polynomial expansion method and the sensitivity analysis is also studied. For single objective optimization, the method of feasible directions (MFD) is applied. For multi-objective optimization, the weighting method (WM), the goal programming method (GPM), and the fuzzy method (FM) are employed. It is found that the system design can be significantly affected by the choices of the bias currents of magnetic bearings, the position of the disk with unbalance, and the magnetic bearings. The results also show that a better compromised design can always be obtained for multi-objective optimization.

scholarly journals Multiobjective Optimization of a Flexible Rotor in Magnetic Bearings With Critical Speeds and Control Current Constraints

1994 ◽  
Author(s):  
Ting Nung Shiau ◽  
Chun Pao Kuo ◽  
Jiunn Rong Hwang
Keyword(s):  
Expansion Method ◽  
Magnetic Bearings ◽  
Multi Objective Optimization ◽  
Flexible Rotor ◽  
Weighting Method ◽  
Cross Sectional ◽  
Critical Speeds ◽  
Multi Objective ◽  
Design Variables ◽  
Single Objective

This paper presents the single objective optimization and the multi-objective optimization for a flexible rotor system with magnetic bearings. The weight of rotor shaft and the transmitted forces at the magnetic bearings are minimized either individually or simultaneously under the constraints on the critical speeds and the control currents of magnetic bearings. The design variables are the cross-sectional area of the shaft, the bias currents of magnetic bearings, and the positions of the disk and the magnetic bearings. The dynamic characteristics are analyzed using the generalized polynomial expansion method and the sensitivity analysis is also studied. For single objective optimization, the method of feasible directions (MFD) is applied. For multi-objective optimization, the methods including the weighting method (WM), goal programming method (GPM), and the fuzzy method (FM) are employed. It is found that the system design can be significantly affected by the choices of the bias currents of magnetic bearings, the position of the disk with unbalance and the magnetic bearings. The results also show that a better compromized design can always be obtained for multi-objective optimization.

Multilevel Optimization of Rotor Bearing System With Dynamic Behavior Constraints

2000 ◽  
Author(s):  
T. N. Shiau ◽  
H. J. Lee ◽  
Y. J. Tsai
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Technique ◽  
Maximum Amplitude ◽  
Expansion Method ◽  
Axial Position ◽  
Multilevel Optimization ◽  
Weighting Method ◽  
Design Variables ◽  
Transmitted Force ◽  
Rotor Bearing

The main purpose of this study is to investigate the multilevel optimization of rotor-bearing systems. The design variables include the shaft inner radius, the bearings stiffness, and the axial position of the bearings and disks. The design objectives are minimization of the shaft weight and transmitted force to the bearings. Constraints are placed on the critical speeds, the maximum shaft bending stress, and the maximum amplitude of the steady state response. In the multilevel optimization, three levels are considered and each level includes a single objective and/or multiobjective with various design variables and constraints. For each level, the method of feasible direction (MFD) is used. In addition, the weighting method (WM) is used for multiobjective optimization. The dynamic analysis is carried out using the generalized polynomial expansion method. The results show that the shaft weight and transmitted forces can be simultaneously reduced with the multilevel technique and are better than those obtained using the multiobjective optimization technique with only a single level.

scholarly journals Optimum Weight Design of a Rotor Bearing System With Dynamic Behavior Constraints

1989 ◽  
Author(s):  
Ting Nung Shiau ◽  
Jon Li Hwang
Keyword(s):  
Dynamic Behavior ◽  
Optimization Technique ◽  
Penalty Function Method ◽  
Efficient Design ◽  
Cross Sectional ◽  
Design Algorithm ◽  
Optimum Weight ◽  
Rotor Bearing ◽  
Weight Design ◽  
Bearing System

An efficient design algorithm for optimum weight design of a rotor bearing system with dynamic behavior constraints is investigated. The constraints include the restrictions on stresses, unbalance response, and/or critical speeds. The system dynamic behaviors are analyzed by the finite element method. And the exterior penalty function method is used as the optimization technique to minimize the system weight. The system design variables are the cross-sectional areas of the shaft and the stiffnesses of the bearings. The sensitivity analysis of the system parameters is also investigated. The example of a single spool rotor bearing system is employeed to demonstrate the merits of the design algorithm with different combination of dynamic behavior constraints. At the optimum stage, it is shown that the weight of rotor system can be significantly reduced. Moreover, the optimum design weights are quite difference for various combinations of dynamic behavior constraints.

Effective Evaluation of Rotordynamic Performance Within Rotor-Bearing System Design Bounds

2021 ◽  
Author(s):  
Zhusan Luo ◽  
Carl L. Schwarz
Keyword(s):  
System Design ◽  
Operating Conditions ◽  
Performance Parameters ◽  
Critical Speeds ◽  
Effective Evaluation ◽  
Analytical Results ◽  
Design Variables ◽  
Rotor Bearing ◽  
Current Design ◽  
Bearing System

Abstract This paper presents a study on the effective evaluation of rotordynamic performance for multiple analysis cases within rotor-bearing system design bounds. The variations in rotordynamic design variables and operating conditions are usually considered in a rotordynamic analysis. This can provide useful information about the current design, potential for modification, and the capability of off-design operation. Typical design bounds of a tilting pad journal bearing are discussed to show the complexity of multiple design cases and a demand for a method to postprocess the analytical results. Rotordynamic performance is conventionally assessed by examining undamped critical speed maps, damped modes, stability, and unbalance responses. Evaluating rotordynamic performance for multiple cases is a tedious task for both rotordynamicists and reviewers. A new approach is studied to effectively extract, present and evaluate analytical results. A theoretical study shows the analytical results can be synthesized to determine key performance parameters. It is proposed that the amplification factors at critical speeds can be converted to equivalent logarithmic decrements. Based on the two studies, a new rotordynamic performance diagram is created to present damped modes, critical speeds and relevant acceptance criteria. With this informative diagram, one can quickly and effectively evaluate the acceptability and robustness of multiple design cases. This diagram can also convey the trends of key performance parameters, comparisons between cases, and the sensitivities of key performance parameters to design variables more clearly and concisely. This synthesizing approach and the rotordynamic performance diagram may be useful in modifying an existing design, determining a proper off-design operation range, and investigating rotordynamic issues.

Optimum Weight Design of a Rotor Bearing System With Dynamic Behavior Constraints

1990 ◽  
Vol 112 (4) ◽  
pp. 454-462 ◽  
Author(s):  
Ting Nung Shiau ◽  
Jon Li Hwang
Keyword(s):  
Dynamic Behavior ◽  
Optimization Technique ◽  
Penalty Function Method ◽  
Efficient Design ◽  
Cross Sectional ◽  
Design Algorithm ◽  
Optimum Weight ◽  
Rotor Bearing ◽  
Weight Design ◽  
Bearing System

An efficient design algorithm for optimum weight design of a rotor bearing system with dynamic behavior constraints is investigated. The constraints include restrictions on stresses, unbalance response, and/or critical speeds. The system dynamic behaviors are analyzed by the finite element method. The exterior penalty function method is used as the optimization technique to minimize the system weight. The system design variables are the cross-sectional areas of the shaft and the stiffnesses of the bearings. The sensitivity analysis of the system parameters is also investigated. The example of a single spool rotor bearing system is employed to demonstrate the merits of the design algorithm with different combinations of dynamic behavior constraints. At the optimum stage, it is shown that the weight of the rotor system can be significantly reduced. Moreover, the optimum design weights are quite different for various combinations of dynamic behavior constraints.

A fast multiobjective optimization approach to S-duct scoop inlets design with both inflow and outflow

2018 ◽  
Vol 233 (9) ◽  
pp. 3381-3394
Author(s):  
Lifang Zeng ◽  
Dingyi Pan ◽  
Shangjun Ye ◽  
Xueming Shao
Keyword(s):  
Multiobjective Optimization ◽  
Total Pressure ◽  
Optimization Method ◽  
Navier Stokes ◽  
Integral Model ◽  
Optimization Approach ◽  
Navier Stokes Equation ◽  
Cross Sectional ◽  
Design Variables ◽  
Computational Fluid Dynamics Analysis

A fast multiobjective optimization method for S-duct scoop inlets considering both inflow and outflow is developed and validated. To reduce computation consumption of optimization, a simplified efficient model is proposed, in which only inflow region is simulated. Inlet pressure boundary condition of the efficient model is specified by solving an integral model with both inflow and outflow. An automated optimization system integrating the computational fluid dynamics analysis, nonuniform rational B-spline geometric representation technique, and nondominated sorting genetic algorithm II is developed to minimize the total pressure loss and distortion at the exit of diffuser. Flow field is numerically simulated by solving the Reynolds-averaged Navier–Stokes equation coupled with k–ω shear stress transport turbulence model, and results are validated to agree well with previous experiment. S-duct centreline shape and cross-sectional area distribution are parameterized as the design variables. By analyzing the results of a suggested optimal inlet chosen from the obtained Pareto front, total pressure recovery has increased from 97% to 97.4%, and total pressure distortion DC60 has decreased by 0.0477 (21.7% of the origin) at designed Mach number 0.7. The simplified efficient model has been validated to be reliable, and by which the time cost for the optimization project has been reduced by 70%.

Improving Rotordynamic Performance of an Axial Flow Compressor With Two-Lobe Bearings Using Nonlinear Constraint Parameter Optimization

2011 ◽  
Author(s):  
Henning Ressing ◽  
Sebastian Kukla
Keyword(s):  
Parameter Optimization ◽  
Dynamic Performance ◽  
Axial Flow ◽  
Rotor Dynamics ◽  
Nonlinear Constraint ◽  
Design Variables ◽  
Rotor Bearing ◽  
Flow Compressor ◽  
Rotor Dynamic ◽  
Bearing System

Bearings are a key factor in achieving a good rotor dynamics performance for turbo machinery. Large compressors, steam and gas turbines for industrial applications are generally equipped with journal bearings either as tilting pad or multi-lobe bearing type. Here bearing parameters such as bearing geometry, bearing load or oil viscosity significantly alter bearing behavior and influence the rotor dynamics of the entire rotor-bearing system. In order to find an optimal set of bearing parameters for a given rotor-bearing system a nonlinear parameter optimization approach is employed. The rotor-bearing system is parameterized using bearing width, clearance and preload as design variables, since they represent design parameters that can be modified without significantly influencing the rotor design as a whole. The set of design variables is further constraint to stay within feasible limits of bearing design. The objective function is defined as a quantitative measure of rotor dynamic performance evaluating the distance from required separation margins with respect to rotor critical speeds based on API 617 7th Ed. In order to compute the objective function based on the design variables the bearing code ALP3T, solving Reynolds equations for the bearing fluid film, is used to compute the required stiffness and damping coefficients as input to the rotor dynamics program. The rotor dynamics performance is then evaluated using the rotor dynamics code SR3 based on the transfer matrix method. Both programs have been developed by the University of Braunschweig and are defacto industry standard within the German turbo machinery industry. The two programs are coupled and the nonlinear constraint optimization problem is solved using MATLAB’s optimization toolbox. The feasibility of this method is discussed based on an example of an axial flow compressor using two-lobe bearings. It is shown that a significant improvement in rotor dynamic performance can be achieved when compared to previous bearing selections for similar compressor designs and that the approach is suitable for a real-life engineering environment.

Generalized Polynomial Expansion Method for the Dynamic Analysis of Rotor-Bearing Systems

1991 ◽  
Author(s):  
Ting Nung Shiau ◽  
Jon Li Hwang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Expansion Method ◽  
Polynomial Expansion ◽  
The Finite Element Method ◽  
Rotor Systems ◽  
Generalized Polynomial ◽  
Rotor Bearing ◽  
Polynomial Expansion Method ◽  
Element Method

The determination of critical speeds and modes and the unbalance response of rotor-bearing systems is investigated with the application of a technique called the generalized polynomial expansion method (GPEM). This method can be applied to both linear and nonlinear rotor systems, however, only linear systems are addressed in this paper. Three examples including single spool and dual rotor systems are used to demonstrate the efficiency and the accuracy of this method. The results indicate a very good agreement between the present method and the finite element method (FEM). In addition, computing time will be saved using this method in comparison with the finite element method.

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