Response Surface Mapping and Multi-Objective Optimization of Crowning and Tapers in Water-Lubricated Thrust Bearings

2019 ◽  
Author(s):  
Xin Deng ◽  
Cori Watson ◽  
Minhui He ◽  
Roger Fittro ◽  
Houston Wood
Keyword(s):  
Film Thickness ◽  
Power Loss ◽  
Performance Metrics ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Design Variables ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Bearing Design ◽  
The Impact

Abstract Fluid film bearings for turbomachinery are designed to support the loads applied by the rotor system. Oil-lubricated bearings are widely used in high speed rotating machines. However, environmental issues and risk-averse operations have made water lubricated bearings increasingly popular. Due to different viscosity properties between oil and water, the low viscosity of water decreases film thickness significantly. Crowning and tapers are two main ways to maintain the film thickness requirements in water lubrication, but no studies about the influence of these parameters on the film thickness in water-lubricated bearings have been reported. Therefore, further understanding of the performance associated with optimizing the bearing design with different weighted performance and their relationships to bearing design variables could be invaluable to bearing design engineers. This study explores the impact of three crowning and taper design variables on the performance of one tilting pad thrust bearing using the design of experiments techniques applied to a thermoelastohydrodynamic (TEHD) bearing model. The bearing design variables analyzed in this study include the radius of the ground-in crown, taper circumferential angle offset, and the vertical taper distance at the inner and outer radii. Each of the design variables is first varied over five levels, each in central composite design. The outputs from the TEHD numerical simulations used as performance measures for each bearing design point were the minimum film thickness, the film thickness at the pivot location, maximum film pressure and power loss. Multi-objective optimization was performed. A range of weighting parameters was selected for the optimization function to find a bearing design that maintains the minimum film thickness criterion while minimizing power loss. The resulting optimum design points allowed for a comparison between the design optimization at different weightings. This study demonstrates how designers can use these approaches to view the relationships between design variables and important performance metrics to design better bearing for a wide range of applications.

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.

Multi-Objective Optimization of Composite Elliptical Submersible Pressure Hull for Minimize the Buoyancy Factor and Maximize Buckling Load Capacity

2014 ◽  
Vol 578-579 ◽  
pp. 75-82 ◽  
Author(s):  
Fathallah Elsayed ◽  
Hui Qi ◽  
Li Li Tong ◽  
Mahmoud Helal
Keyword(s):  
Parametric Design ◽  
Load Capacity ◽  
Buckling Load ◽  
Multi Objective Optimization ◽  
Element Analysis ◽  
Multi Objective ◽  
Design Variables ◽  
Wide Range ◽  
Conflicting Objectives ◽  
Sophisticated Analysis

Due to the wide range of variables involved and sophisticated analysis techniques required, optimum structural design of composite submersible pressure hull is known to be a challenge for designers. The major challenge involved in the coupled design problem is to handle multiple conflicting objectives. The problem with its proper consideration through multi-objective optimization is studied in this paper. Minimize the buoyancy factor and maximize buckling load capacity of the submersible pressure hull under hydrostatic pressure is considered as the objective function to reach the operating depth equal to 6000m. Finite element analysis of composite elliptical submersible pressure hull is performed using ANSYS parametric design language (APDL). The constraints based on the failure strength of the hulls are considered. The fiber orientation angles and the thickness in each layer, the radii of the ellipse, the ring beams and the stringers dimensions are taken as design variables. Additionally, a sensitivity analysis is performed to study the influence of the design variables up on objectives and constraints functions. Results of this study provide a valuable reference for designers of composite underwater vehicles.

The Multi-Objective Optimization for Cycloidal Gear Drive Based on the Elastohydrodynamic Lubrication Theory

2012 ◽  
Vol 591-593 ◽  
pp. 697-703 ◽  
Author(s):  
Xue Yi Qian
Keyword(s):  
Particle Swarm Optimization ◽  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Lubrication Theory ◽  
Multi Objective Optimization ◽  
Swarm Optimization ◽  
Gear Teeth ◽  
Multi Objective ◽  
Gear Drive ◽  
Minimum Film Thickness

For improving the designed quality of the cycloidal gear planetary drive, the paper derives a calculation formula of the minimum film thickness, which is between cycloidal gear teeth, based on elastohydrodynamic lubrication theory and gear geometry. A mathematical model for constrained multi-objective optimization is established and the model satisfies three constrains:maximize minimum film thickness between gear teeth( minimize the reciprocal ), minimize average value of m points’s absolute error value on active section that is between the tooth curves of positive shift optimal combination and tooth curves of rotated angle’s modification, minimize the total volume of gear drive. The paper abandons traditional designed method of the multi-objective optimization , improves two-objective particle swarm optimization and offers a new designed model for constrained three-objective optimization. The example is analyzed and the optimization program is complied using Matlab. The optimization’s process and result shows that the method of improved constrained multi-objective particle swarm optimization could effectively improve the products’ synthesize economical and technical indexes.

Integrated Design and Multi-Objective Optimization of a Single Stage Heat-Pump Turbocompressor

2013 ◽  
Author(s):  
J. Schiffmann
Keyword(s):  
Design Optimization ◽  
High Efficiency ◽  
Integrated Design ◽  
Heat Pumps ◽  
Small Scale ◽  
Multi Objective Optimization ◽  
Design Constraints ◽  
Multi Objective ◽  
Wide Range ◽  
Standard Design

Small scale turbomachines in domestic heat pumps reach high efficiency and provide oil-free solutions which improve heat-exchanger performance and offer major advantages in the design of advanced thermodynamic cycles. An appropriate turbocompressor for domestic air based heat pumps requires the ability to operate on a wide range of inlet pressure, pressure ratios and mass flows, confronting the designer with the necessity to compromise between range and efficiency. Further the design of small-scale direct driven turbomachines is a complex and interdisciplinary task. Textbook design procedures propose to split such systems into subcomponents and to design and optimize each element individually. This common procedure, however, tends to neglect the interactions between the different components leading to suboptimal solutions. The authors propose an approach based on the integrated philosophy for designing and optimizing gas bearing supported, direct driven turbocompressors for applications with challenging requirements with regards to operation range and efficiency. Using previously validated reduced order models for the different components an integrated model of the compressor is implemented and the optimum system found via multi-objective optimization. It is shown that compared to standard design procedure the integrated approach yields an increase of the seasonal compressor efficiency of more than 12 points. Further a design optimization based sensitivity analysis allows to investigate the influence of design constraints determined prior to optimization such as impeller surface roughness, rotor material and impeller force. A relaxation of these constrains yields additional room for improvement. Reduced impeller force improves efficiency due to a smaller thrust bearing mainly, whereas a lighter rotor material improves rotordynamic performance. A hydraulically smoother impeller surface improves the overall efficiency considerably by reducing aerodynamic losses. A combination of the relaxation of the 3 design constraints yields an additional improvement of 6 points compared to the original optimization process. The integrated design and optimization procedure implemented in the case of a complex design problem thus clearly shows its advantages compared to traditional design methods by allowing a truly exhaustive search for optimum solutions throughout the complete design space. It can be used for both design optimization and for design analysis.

The Finite Element Analysis and the Multi-Objective Optimization Design of Spindle Systems of CNC Gantry Machine Tools

2016 ◽  
Vol 693 ◽  
pp. 243-250
Author(s):  
Zhi Zhong Guo ◽  
Yun Shun Zhang ◽  
Shi Hao Liu
Keyword(s):  
Machine Tools ◽  
Optimization Design ◽  
Multi Objective Optimization ◽  
Element Analysis ◽  
Multi Objective ◽  
Vibration Resistance ◽  
Design Variables ◽  
Force Coupling ◽  
The Finite Element Analysis ◽  
Spindle Structure

It is discovered that the vibration resistance of spindle systems needs to be improved based on the statics analysis, modal analysis and heating-force coupling analysis of spindle systems of CNC gantry machine tools. The design variables of optimization are set according to sensitivity analysis, multi-objective and dynamic optimization design is realized and its designing scheme is gained for spindle structure. The research results show that vibration resistance can be improved without change of the quality and static property of spindle systems of CNC gantry machine tools.

scholarly journals Analytical Formula for the Ratio of Central to Minimum Film Thickness in a Circular EHL Contact

Lubricants ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 80 ◽  
Author(s):  
Petr Sperka ◽  
Ivan Krupka ◽  
Martin Hartl
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Analytical Formula ◽  
Numerical Calculations ◽  
Constant Ratio ◽  
Viscosity Coefficients ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Film Parameter ◽  
Ehl Contact

Prediction of minimum film thickness is often used in practice for calculation of film parameter to design machine operation in full film regime. It was reported several times that majority of prediction formulas cannot match experimental data in terms of minimum film thickness. These standard prediction formulas give almost constant ratio between central and minimum film thickness while numerical calculations show ratio which spans from 1 to more than 3 depending on M and L parameters. In this paper, an analytical formula of this ratio is presented for lubricants with various pressure–viscosity coefficients. The analytical formula is compared with optical interferometry measurements and differences are discussed. It allows better prediction, compared to standard formulas, of minimum film thickness for wide range of M and L parameters.

scholarly journals Power Loss Calculation in 11-Level Cascaded H-Bridge Inverter using Harmony Search Optimized Switching Scheme

2019 ◽  
Vol 8 (6) ◽  
pp. 5200-5205
Keyword(s):  
Optimization Algorithm ◽  
Power Loss ◽  
System Analysis ◽  
Search Algorithm ◽  
Optimization Technique ◽  
Harmony Search ◽  
Multilevel Inverter ◽  
Total Power ◽  
Multi Objective Optimization ◽  
Multi Objective

Power loss is the most significant parameter in power system analysis and its adequate calculation directly effects the economic and technical evaluation. This paper aims to propose a multi-objective optimization algorithm which optimizes dc source magnitudes and switching angles to yield minimum THD in cascaded multilevel inverters. The optimization algorithm uses metaheuristic approach, namely Harmony Search algorithm. The effectiveness of the multi-objective algorithm has been tested with 11-level Cascaded H-Bridge Inverter with optimized DC voltage sources using MATLAB/Simulink. As the main objective of this research paper is to analyze total power loss, calculations of power loss are simplified using approximation of curves from datasheet values and experimental measurements. The simulation results, obtained using multi-objective optimization method, have been compared with basic SPWM, optimal minimization of THD, and it is confirmed that the multilevel inverter fired using multi- objective optimization technique has reduced power loss and minimum THD for a wide operating range of multilevel inverter.

scholarly journals Resource allocation and task admission control in cloud systems

2021 ◽  
Author(s):  
Haleh Khojasteh
Keyword(s):  
Resource Allocation ◽  
Performance Metrics ◽  
Cloud Model ◽  
Blocking Probability ◽  
Arrival Rate ◽  
Cloud System ◽  
Wide Range ◽  
Priority Scheme ◽  
The Impact ◽  
And Task

The focus of this thesis is solving the problem of resource allocation in cloud datacenter using an Infrastructure-as-a-Service (IaaS) cloud model. We have investigated the behavior of IaaS cloud datacenters through detailed analytical and simulation models that model linear, transitional and saturated operation regimes. We have obtained accurate performance metrics such as task blocking probability, total delay, utilization and energy consumption. Our results show that the offered load does not offer complete characterization of datacenter operation; therefore, in our evaluations, we have considered the impact of task arrival rate and task service time separately. To keep the cloud system in the linear operation regime, we have proposed several dynamic algorithms to control the admission of incoming tasks. In our first solution, task admission is based on task blocking probability and predefined thresholds for task arrival rate. The algorithms in our second solution are based on full rate task acceptance threshold and filtering coefficient. Our results confirm that the proposed task admission mechanisms are capable of maintaining the stability of cloud system under a wide range of input parameter values. Finally, we have developed resource allocation solutions for mobile clouds in which offloading requests from a mobile device can lead to forking of new tasks in on-demand manner. To address this problem, we have proposed two flexible resource allocation mechanisms with different prioritization: one in which forked tasks are given full priority over newly arrived ones, and another in which a threshold is established to control the priority. Our results demonstrate that threshold-based priority scheme presents better system performance than the full priority scheme. Our proposed solution for clouds with mobile users can be also applied in other clouds which their users’ applications fork new tasks.

scholarly journals Resource allocation and task admission control in cloud systems

2021 ◽  
Author(s):  
Haleh Khojasteh
Keyword(s):  
Resource Allocation ◽  
Performance Metrics ◽  
Cloud Model ◽  
Blocking Probability ◽  
Arrival Rate ◽  
Cloud System ◽  
Wide Range ◽  
Priority Scheme ◽  
The Impact ◽  
And Task

The focus of this thesis is solving the problem of resource allocation in cloud datacenter using an Infrastructure-as-a-Service (IaaS) cloud model. We have investigated the behavior of IaaS cloud datacenters through detailed analytical and simulation models that model linear, transitional and saturated operation regimes. We have obtained accurate performance metrics such as task blocking probability, total delay, utilization and energy consumption. Our results show that the offered load does not offer complete characterization of datacenter operation; therefore, in our evaluations, we have considered the impact of task arrival rate and task service time separately. To keep the cloud system in the linear operation regime, we have proposed several dynamic algorithms to control the admission of incoming tasks. In our first solution, task admission is based on task blocking probability and predefined thresholds for task arrival rate. The algorithms in our second solution are based on full rate task acceptance threshold and filtering coefficient. Our results confirm that the proposed task admission mechanisms are capable of maintaining the stability of cloud system under a wide range of input parameter values. Finally, we have developed resource allocation solutions for mobile clouds in which offloading requests from a mobile device can lead to forking of new tasks in on-demand manner. To address this problem, we have proposed two flexible resource allocation mechanisms with different prioritization: one in which forked tasks are given full priority over newly arrived ones, and another in which a threshold is established to control the priority. Our results demonstrate that threshold-based priority scheme presents better system performance than the full priority scheme. Our proposed solution for clouds with mobile users can be also applied in other clouds which their users’ applications fork new tasks.

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