A Minimum Strain Energy Approach for Obtaining Optimal Unbalance Distribution in Flexible Rotors

1982 ◽  
Vol 104 (4) ◽  
pp. 875-880 ◽  
Author(s):  
T. F. Conry ◽  
P. R. Goglia ◽  
C. Cusano
Keyword(s):  
Strain Energy ◽  
Critical Speed ◽  
Optimization Problem ◽  
Equations Of Motion ◽  
Rotor System ◽  
Quadratic Program ◽  
Unique Minimum ◽  
Flexible Rotors ◽  
Minimum Strain Energy ◽  
Selection Of

A method is developed to design for optimal unbalance distribution in a rotor system which has elements that are assembled on the shaft and operates above the first critical speed. This method can also be used for computing the optimal selection of balance weights in specified planes for a rotor with a known distribution of unbalance—the classic balancing problem. The method is an optimization problem where the strain energy of the rotor and its supports are minimized subject to the constraints of the equations of motion of the rotor system at a particular balancing speed. The problem is a quadratic program that has a unique minimum.

scholarly journals Dynamical analysis of hollow-shaft dual-rotor system with circular cracks

2020 ◽  
pp. 146134842094828
Author(s):  
Yang Yongfeng ◽  
Wang Jianjun ◽  
Wang Yanlin ◽  
Fu Chao ◽  
Zheng Qingyang ◽  
...  
Keyword(s):  
Critical Speed ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Circular Crack ◽  
Rotor System ◽  
Resonance Phenomenon ◽  
Dynamical Analysis ◽  
Dynamical Response ◽  
Critical Speeds ◽  
Hollow Shaft

In this paper, we considered a dual-rotor system with crack in shaft. The influence of circular crack in hollow shaft on dynamical response was studied. The equations of motion of 12 elements dual-rotor system model were derived. Harmonic balance method was employed to solve the equations. The critical speed and sub-critical speed responses were investigated. It was found that the circular crack in hollow shaft had greater influence on the first-backward critical speed than the first-forward critical speed. Owing to the influence of crack, the vibration peaks occurred at the 1/2, 1/3 and 1/4 critical speeds of the rotor system, along with a reduction in sub-critical speeds and critical speeds. The deeper crack away from the bearing affected the rotor more significantly. The whirling orbits, the time-domain responses and the spectra were obtained to show the super-harmonic resonance phenomenon in hollow-shaft cracked rotor system.

scholarly journals Designing Strong Privacy Metrics Suites Using Evolutionary Optimization

2021 ◽  
Vol 24 (2) ◽  
pp. 1-35
Author(s):  
Isabel Wagner ◽  
Iryna Yevseyeva
Keyword(s):  
Optimization Problem ◽  
Evolutionary Optimization ◽  
Multiple Objectives ◽  
Shared Value ◽  
Vehicular Communications ◽  
Open Problems ◽  
Value Range ◽  
Genomic Privacy ◽  
Metaheuristic Optimization Algorithms ◽  
Selection Of

The ability to measure privacy accurately and consistently is key in the development of new privacy protections. However, recent studies have uncovered weaknesses in existing privacy metrics, as well as weaknesses caused by the use of only a single privacy metric. Metrics suites, or combinations of privacy metrics, are a promising mechanism to alleviate these weaknesses, if we can solve two open problems: which metrics should be combined and how. In this article, we tackle the first problem, i.e., the selection of metrics for strong metrics suites, by formulating it as a knapsack optimization problem with both single and multiple objectives. Because solving this problem exactly is difficult due to the large number of combinations and many qualities/objectives that need to be evaluated for each metrics suite, we apply 16 existing evolutionary and metaheuristic optimization algorithms. We solve the optimization problem for three privacy application domains: genomic privacy, graph privacy, and vehicular communications privacy. We find that the resulting metrics suites have better properties, i.e., higher monotonicity, diversity, evenness, and shared value range, than previously proposed metrics suites.

Secondary critical speed of flexible rotors with inertia slots

1983 ◽  
Vol 87 (1) ◽  
pp. 61-70 ◽  
Author(s):  
M. Sakata ◽  
M. Endo ◽  
K. Kishimoto ◽  
N. Hayashi
Keyword(s):  
Critical Speed ◽  
Flexible Rotors

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

Feasibility investigation of a compressor rotor supported by gas foil bearings with inhomogeneous bump foils

2021 ◽  
pp. 135065012110046
Author(s):  
Hao Li ◽  
Haipeng Geng ◽  
Bo Wang ◽  
Wei Zheng
Keyword(s):  
Critical Speed ◽  
Rotor System ◽  
Experimental Result ◽  
Test Results ◽  
Rotating Speed ◽  
Foil Bearings ◽  
Dynamic Coefficients ◽  
High Order Harmonic ◽  
Compressor Rotor ◽  
Operating Points

In this paper, a rotordynamic experiment on a compressor rotor system is presented and the feasibility of gas foil bearings with inhomogeneous bump foils is verified. A push–pull device is designed to obtain the stiffness curve and the nominal clearance of foil bearings. Operating points and dynamic coefficients of the rotor system at each rotating speed are predicted. In rotordynamic analysis, an alternative model of the impeller is proposed and the critical speed is predicted by employing the finite element method, in which the dynamic coefficients of inhomogeneous foil bearings are taken into account. Compared with the experimental result, the accuracy of the prediction for the critical speed is verified to be about 14% error. Two sets of foil bearings with 22 and 41 μm nominal clearance are manufactured and tested. Test results indicate that the vibration amplitude can be greatly reduced by diminishing the bearing clearance. When foil bearings with 22 μm clearance are used, the high-order harmonic frequencies of rotor vibration are significantly inhibited, and the amplitude of the rotating frequency is obviously restricted. Thus, the foil bearing with inhomogeneous bump foils tested in this paper can meet the speed requirement of the compressor when the nominal clearance is set at 22 μm.

Crack Driving Force in Anisotropic Media due to Non-Elastic Deformation

2004 ◽  
Vol 261-263 ◽  
pp. 75-80
Author(s):  
G.H. Nie ◽  
H. Xu
Keyword(s):  
Elastic Deformation ◽  
Driving Force ◽  
Strain Energy ◽  
Elastic Stress ◽  
Complex Function ◽  
Crack Driving Force ◽  
Special Cases ◽  
Degree Of Anisotropy ◽  
Minimum Strain Energy ◽  
Orthotropic Media

In this paper elastic stress field in an elliptic inhomogeneity embedded in orthotropic media due to non-elastic deformation is determined by the complex function method and the principle of minimum strain energy. Two complex parameters are expressed in a general form, which covers all characterizations of the degree of anisotropy for any ideal orthotropic elastic body. The stress acting on the long side of ellipse can be considered as a crack driving force and applied in failure and fatigue analysis of composites. For some special cases, the resulting solutions will reduce to the known results.

General Method for Optimizing Composite Patch Repairs

2015 ◽  
Vol 1120-1121 ◽  
pp. 670-674
Author(s):  
Abdelmadjid Ait Yala ◽  
Abderrahmanne Akkouche
Keyword(s):  
Mechanical Properties ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Optimization Problem ◽  
Composite Patch ◽  
Matlab Program ◽  
Patch Repairs ◽  
Selection Of ◽  
General Method

The aim of this work is to define a general method for the optimization of composite patch repairing. Fracture mechanics theory shows that the stress intensity factor tends towards an asymptotic limit K∞.This limit is given by Rose’s formula and is a function of the thicknesses and mechanical properties of the cracked plate, the composite patch and the adhesive. The proposed approach consists in considering this limit as an objective function that needs to be minimized. In deed lowering this asymptote will reduce the values of the stress intensity factor hence optimize the repair. However to be effective this robust design must satisfy the stiffness ratio criteria. The resolution of this double objective optimization problem with Matlab program allowed us determine the appropriate geometric and mechanical properties that allow the optimum design; that is the selection of the adhesive, the patch and their respective thicknesses.

Steady-State Performance of Squeeze Film Damper Supported Flexible Rotors

1977 ◽  
Vol 99 (4) ◽  
pp. 552-558 ◽  
Author(s):  
M. D. Rabinowitz ◽  
E. J. Hahn
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Rolling Element Bearing ◽  
Squeeze Film ◽  
Response Curves ◽  
Flexible Rotors ◽  
Steady State Operation ◽  
Bearing Life ◽  
Rolling Element ◽  
Single Mass

The synchronous steady-state operation of a centrally preloaded single mass flexible rotor supported in squeeze film bearing dampers is examined theoretically. Assuming the short bearing approximation and symmetric motions, frequency response curves are presented exhibiting the effect of relevant system parameters on rotor excursion amplitudes and unbalance transmissibilities for both pressurized and unpressurized lubricant supply. Hence, the influence of rotor flexibility, rotor mass distribution, rotor speed, bearing dimensions, lubricant viscosity, support flexibility can be readily determined, allowing for optimal rotor bearing system design. It is shown that with pressurized bearing mounts, the possibility of undesirable operation modes is eliminated and a smooth passage through the first pin-pin critical speed of the rotor is feasible, while absence of pressurization significantly limits the maximum safe unbalance in the vicinity of this critical speed. Significant decrease in transmissibility and rotor excursion amplitudes over those obtainable with rigid mounts are shown to be a practical possibility, with consequent decrease in the vibration level of the rotor mounts and prolongation of rolling element bearing life, while maintaining acceptable rotor vibration amplitudes. A design example is included to illustrate the use of the data.

A Virtual Bearing Method for Optimal Bearing Placement of Flexible Rotor Systems

2017 ◽  
Author(s):  
Shibing Liu ◽  
Bingen Yang
Keyword(s):  
Optimization Problem ◽  
Optimization Method ◽  
Rotor System ◽  
Problem Solution ◽  
Flexible Rotor ◽  
Rotor Systems ◽  
Real Coded Genetic Algorithm ◽  
Minimum Number ◽  
Distributed Transfer Function ◽  
Flexible Rotor Systems

Flexible multistage rotor systems have a variety of engineering applications. Vibration optimization is important to the improvement of performance and reliability for this type of rotor systems. Filling a technical gap in the literature, this paper presents a virtual bearing method for optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. In the development, a distributed transfer function formulation is used to define the optimization problem. Solution of the optimization problem by a real-coded genetic algorithm yields the locations and dynamic coefficients of bearings, by which the prescribed operational requirements for the rotor system are satisfied. A numerical example shows that the proposed optimization method is efficient and accurate, and is useful in preliminary design of a new rotor system with the number of bearings unforeknown.

Nonlinear Dynamic Study on Effects of Rub-Impact Caused by Oil-Rupture in a Multi-Shafts Turbine With a Squeeze Film Damper

2014 ◽  
Author(s):  
T. N. Shiau ◽  
C. R. Wang ◽  
D. S. Liu ◽  
W. C. Hsu ◽  
T. H. Young
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Rotor System ◽  
Squeeze Film ◽  
Speed Ratio ◽  
Frequency Spectra ◽  
Squeeze Film Damper ◽  
Assumed Mode Method ◽  
Nonlinear Dynamic Behavior

An investigation is carried out the analysis of nonlinear dynamic behavior on effects of rub-impact caused by oil-rupture in a multi-shafts turbine system with a squeeze film damper. Main components of a multi-shafts turbine system includes an outer shaft, an inner shaft, an impeller shaft, ball bearings and a squeeze film damper. In the squeeze film damper, oil forces can be derived from the short bearing approximation and cavitated film assumption. The system equations of motion are formulated by the global assumed mode method (GAMM) and Lagrange’s approach. The nonlinear behavior of a multi-shafts turbine system which includes the trajectories in time domain, frequency spectra, Poincaré maps, and bifurcation diagrams are investigated. Numerical results show that large vibration amplitude is observed in steady state at rotating speed ratio adjacent to the first natural frequency when there is no squeeze film damper. The nonlinear dynamic behavior of a multi-shafts turbine system goes in its way into aperiodic motion due to oil-rupture and it is unlike the usual way (1T = >2T = >4T = >8T etc) as compared to one shaft rotor system. The typical routes of bifurcation to aperiodic motion are observed in a multi-shafts turbine rotor system and they suddenly turn into aperiodic motion from the periodic motion without any transition. Consequently, the increasing of geometric or oil parameters such as clearance or lubricant viscosity will improve the performance of SFD bearing.

Sign in / Sign up

Export Citation Format

Share Document