Constrained Design Optimization of Rotor-Tilting Pad Bearing Systems

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Costin D. Untaroiu ◽  
Alexandrina Untaroiu
Keyword(s):  
Design Optimization ◽  
Power Loss ◽  
Optimization Design ◽  
Optimization Approach ◽  
Design Variables ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Automatic Optimization ◽  
Tilting Pad Bearings ◽  
Bearing System

Design of a rotor-bearing system is a challenging task due to various conflicting design requirements, which should be fulfilled. This study considers an automatic optimization approach for the design of a rotor supported on tilting-pad bearings. A numerical example of a rotor-bearing system is employed to demonstrate the merits of the proposed design approach. The finite element method is used to model the rotor-bearing system, and the dynamic speed-dependent coefficients of the bearing are calculated using a bulk flow code. A number of geometrical characteristics of the rotor simultaneously with the parameters defining the configuration of tilting pad bearings are considered as design variables into the automatic optimization process. The power loss in bearings, stability criteria, and unbalance responses are defined as a set of objective functions and constraints. The complex design optimization problem is solved using heuristic optimization algorithms, such as genetic, and particle-swarm optimization. Whereas both algorithms found better design solutions than the initial design, the genetic algorithms exhibited the fastest convergence. A statistical approach was used to identify the influence of the design variables on the objective function and constraint measures. The bearing clearances, preloads and lengths showed to have the highest influence on the power loss in the chosen design space. The high performance of the best solution obtained in the optimization design suggests that the proposed approach has good potential for improving design of rotor-bearing systems encountered in industrial applications.

Automatic Design Optimization of Rotors Supported on Tilting Pad Bearings

2009 ◽  
Author(s):  
Costin D. Untaroiu ◽  
Alexandrina Untaroiu ◽  
Amir Younan ◽  
Paul E. Allaire
Keyword(s):  
Design Optimization ◽  
High Performance ◽  
Optimization Design ◽  
Industrial Applications ◽  
Design Approach ◽  
Automatic Design ◽  
Design Variables ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Bearing System

This study considers the optimization of a rotor supported on bearings using an automatic design approach. A finite element approach is used to model the rotor-bearing system and the dynamic speed-dependent coefficients of the bearing are calculated using a bulk flow code. A numerical example of a rotor-bearing system is employed to demonstrate the merits of the present design approach. A few geometric characteristics of the rotor together with the parameters defining the configuration of tilting pad bearing are considered as design variables into the automatic optimization process. The power loss in bearings, stability criteria, and unbalance responses are defined as a set of objective functions and constraints. The complex design optimization problem is solved using heuristic optimization algorithms, such as genetic, and particle-swarm optimization. Whereas both algorithms found better design solutions than the initial design, the genetic algorithms exhibited the fastest convergence. The high performance of the best solution obtained in the optimization design suggests that the proposed approach has good potential for improving design of rotor-bearing systems encountered in industrial applications.

Reliability-based design optimization of electromagnetic shielding structure using neural networks and real-coded genetic algorithm

2014 ◽  
Vol 228 (18) ◽  
pp. 3471-3481 ◽  
Author(s):  
Heeralal Gargama ◽  
Sanjay K Chaturvedi ◽  
Awalendra K Thakur
Keyword(s):  
Genetic Algorithm ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Design Optimization ◽  
Electromagnetic Shielding ◽  
Optimization Approach ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Design Variables ◽  
Real Coded Genetic Algorithm

The conventional approaches for electromagnetic shielding structures’ design, lack the incorporation of uncertainty in the design variables/parameters. In this paper, a reliability-based design optimization approach for designing electromagnetic shielding structure is proposed. The uncertainties/variability in the design variables/parameters are dealt with using the probabilistic sufficiency factor, which is a factor of safety relative to a target probability of failure. Estimation of probabilistic sufficiency factor requires performance function evaluation at every design point, which is extremely computationally intensive. The computational burden is reduced greatly by evaluating design responses only at the selected design points from the whole design space and employing artificial neural networks to approximate probabilistic sufficiency factor as a function of design variables. Subsequently, the trained artificial neural networks are used for the probabilistic sufficiency factor evaluation in the reliability-based design optimization, where optimization part is processed with the real-coded genetic algorithm. The proposed reliability-based design optimization approach is applied to design a three-layered shielding structure for a shielding effectiveness requirement of ∼40 dB, used in many industrial/commercial applications, and for ∼80 dB used in the military applications.

scholarly journals Nonlinear Dynamics Analysis of Tilting Pad Journal Bearing-Rotor System

2011 ◽  
Vol 18 (1-2) ◽  
pp. 45-52 ◽  
Author(s):  
Jiayang Ying ◽  
Yinghou Jiao ◽  
Zhaobo Chen
Keyword(s):  
Nonlinear Dynamics ◽  
System Dynamics ◽  
Journal Bearing ◽  
Rotor System ◽  
Moment Of Inertia ◽  
Dynamics Analysis ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Tilting Pad Journal Bearing ◽  
Bearing System

The nonlinear dynamics theory is increasingly applied in the dynamics analysis of tilting pad journal bearing-rotor system. However, extensive work on system dynamics done previously neglects the influence caused by the moment of inertia of the pad. In this paper, a comparison is made between the responses of the rotor in the bearings with and without pad inertia effect. Taking the Jeffcott rotor system as an example, the characteristics of bearing-rotor system, such as bifurcation diagram, cycle response, frequency spectrum, phase trajectories, and Poincaré maps, were attained within a certain rotation rate range. The pivotal oil-film force of tilting pad journal bearing was calculated by database method. The results directly demonstrate that considering the influence of the pad moment of inertia, system dynamics characteristics are found more complicated when rotor-bearing system works around natural frequency and system bifurcation is observed forward when rotor-bearing system works on high-speed range.

Stability of Rotor-Bearing Systems With Generalized Support Flexibility and Damping and Aerodynamic Cross-Coupling

1975 ◽  
Vol 97 (3) ◽  
pp. 461-469 ◽  
Author(s):  
R. E. Warner ◽  
A. I. Soler
Keyword(s):  
Cross Coupling ◽  
Frequency Dependent ◽  
Oil Film ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Single Mass ◽  
Tilting Pad Bearings

This paper examines stability of the flexible single mass rotor, acted on by motion induced forces due to aero-dynamic cross-coupling and supported most generally by oil film tilting pad bearings which are in turn mounted on flexible, damped supports. Plotted results include the frequency dependent spring and damping coefficients for the 4-pad tilting pad bearing, damping coefficients for the 360-deg squeeze bearing and stability plots of rotor-bearing systems including aerodynamic cross-coupling, the 4-pad tilting pad bearing and the 150-deg partial arc bearing with various support arrangements.

Geometry Optimization of Hybrid Tilting-Pad Journal Bearings

2007 ◽  
Author(s):  
Ilmar Ferreira Santos ◽  
Bo Uldall Kristiansen
Keyword(s):  
Angular Velocity ◽  
Geometry Optimization ◽  
Injection Pressure ◽  
Hydrodynamic Condition ◽  
Damping Factor ◽  
Operational Conditions ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Run Up ◽  
Bearing System

Radial tilting-pad bearings under hybrid lubrication conditions are industrially used in heavy horizontal machines. One single orifice is normally designed and machined in the middle of the pad. Through such an orifice pressurized lubricant is injected and the rotor-bearing system is hydrostatically lubricated during start-up and run-up conditions. Nevertheless, at a pre-defined angular velocity the hydrostatic lubrication is turned-off and the rotor-bearing system operates under hydrodynamic condition. The main focus of the present work is to investigate the feasibility of using the hydrostatic lubrication as an auxiliary mechanism to improve rotor stability and increase damping reserve of rotor-bearing systems. The geometry of the bearing, namely number of orifices, their positioning over the pad surface and their diameters, are optimized using the damping factor of the rotor-bearing system as weighting functional. The dependency of the optimal parameters on the rotor angular velocity and injection pressure (operational conditions) is discussed and the limits of an increase in damping reserve via geometry optimization are elucidated.

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.

scholarly journals Numerical Simulation of Nonlinear Oil Film Forces of Tilting-Pad Guide Bearing in Large Hydro-unit

2000 ◽  
Vol 6 (5) ◽  
pp. 345-353 ◽  
Author(s):  
Li-Feng Ma ◽  
Xin-Zhi Zhang
Keyword(s):  
Reynolds Equation ◽  
Nonlinear Simulation ◽  
Motion Patterns ◽  
Damping Coefficients ◽  
Nonlinear Motion ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Angular Velocities ◽  
Stiffness And Damping ◽  
Bearing System

A new numerical method is proposed for predicting the nonlinearity of tilting-pad guide bearing oilfilm force in the rotor-bearing system in a large hydro-unit. Nonlinear displacement and velocity of the journal center, as well as nonlinear tilting angles and angular velocities of the pads in non-stationary Reynolds equation are taken into account. This method is also suited for other small rotor-bearing system. As an example, the response due to a momentarily created unbalance is Calculated. The nonlinear motion patterns of the pad and journal whirling orbit are obtained. Finally, the nonlinear orbit is compared to the linear one that could be calculated from linear stiffness and damping coefficients. It is shown that there are important differences between those two orbits and that the nonlinear simulation is more accurate.

Nonlinear dynamic analysis of a rotor-bearing system with porous tilting pad bearing support

2018 ◽  
Vol 94 (2) ◽  
pp. 1391-1408 ◽  
Author(s):  
Yihua Wu ◽  
Kai Feng ◽  
Yun Zhang ◽  
Wanhui Liu ◽  
Wenjun Li
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Bearing System

Reliability-based design optimization of 3D orthogonal woven composite automobile shock tower

2021 ◽  
pp. 002199832110476
Author(s):  
Zhao Liu ◽  
Lei Zhang ◽  
Ping Zhu ◽  
Mushi Li
Keyword(s):  
Design Optimization ◽  
Composite Structures ◽  
Optimization Design ◽  
Optimization Procedure ◽  
Woven Composite ◽  
Reliability Based Design Optimization ◽  
Multi Scale ◽  
Reliability Based Design ◽  
Design Variables ◽  
3D Orthogonal Woven

Three-dimensional orthogonal woven composites are noted for their excellent mechanical properties and delamination resistance, so they are expected to have promising prospects in lightweight applications in the automobile industry. The multi-scale characteristics and inherent uncertainty of design variables pose great challenges to the optimization procedure for 3D orthogonal woven composite structures. This paper aims to propose a reliability-based design optimization method for guidance on the lightweight design of 3D orthogonal woven composite automobile shock tower, which includes design variables from material and structure. An analytical model was firstly set up to accurately predict the elastic and strength properties of composites. After that, a novel optimization procedure was established for the multi-scale reliability optimization design of composite shock tower, based on the combination of Monte Carlo reliability analysis method, Kriging surrogate model, and particle swarm optimization algorithm. According to the results, the optimized shock tower meets the requirements of structural performance and reliability, with a weight reduction of 37.83%.

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