scholarly journals Bifurcation and Chaos Analysis of Gear Pair System Based on Crack Rotor-Bearing System with Rub-Impact Effect

2018 ◽  
Vol 201 ◽  
pp. 01008
Author(s):  
Cai-Wan Chang-Jian ◽  
Cheng-Chi Wang ◽  
Li-Ming Chu
Keyword(s):  
Power Spectra ◽  
Operating Conditions ◽  
Speed Ratio ◽  
Bifurcation Diagrams ◽  
Systematic Analysis ◽  
Diverse Range ◽  
Impact Effect ◽  
Rotor Bearing ◽  
System Power ◽  
Bearing System

This study performs a systematic analysis of the dynamic behavior of a crack rotor-bearing system with rub-impact effect. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless damping coefficient, the dimensionless unbalance parameter and the dimensionless rotational speed ratio as control parameters. The analysis methods employed in this study include the dynamic trajectories of the crack rotor-bearing system, power spectra, Poincaré maps and bifurcation diagrams. Lyapunov exponent and fractal dimensional analysis are also used to identify the onset of chaotic motion. The numerical results reveal that the system exhibits a diverse range of periodic, sub-harmonic, quasi-periodic and chaotic behaviors. The results presented in this study provide an understanding of the operating conditions under which undesirable dynamic motion takes place in a crack rotor-bearing system and therefore serve as a useful source of reference for engineers in designing and controlling such systems.

The bifurcation and chaos of a gear pair system based on a strongly non-linear rotor—bearing system

2010 ◽  
Vol 224 (9) ◽  
pp. 1891-1904 ◽  
Author(s):  
C-W Chang-Jian
Keyword(s):  
Operating Conditions ◽  
Speed Ratio ◽  
Gear Pair ◽  
Chaotic Motions ◽  
Systematic Analysis ◽  
Gear Mesh ◽  
Non Linear ◽  
Rotor Bearing ◽  
Linear Effects ◽  
Bearing System

A systematic analysis of the dynamic behaviours of a gear pair system based on a rotor—bearing system under strongly non-linear effects (i.e. non-linear suspension effect, non-linear oil-film force, non-linear rub-impact force, and non-linear gear mesh force) is presented in this study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless unbalance coefficient, the dimensionless damping coefficient, and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is specified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents, and fractal dimension of the system. There exists various forms of periodic, quasi-periodic, and chaotic motions at different bifurcation parameters. The simulation results also found that highly non-periodic motions do exist in gear—rotor—bearing systems under those non-linear effects. The results presented in this study provide a better understanding of the operating conditions under which undesirable dynamic motion takes place in a gear—bearing system; they would therefore serve as a useful source of reference for engineers in designing and controlling such systems.

scholarly journals Couple-Stress Fluid Improves Dynamic Response of Gear-Pair System Supported by Journal Bearings

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Cai-Wan Chang-Jian ◽  
Shiuh Ming Chang ◽  
Hsieh-Chung Hsu
Keyword(s):  
Rotational Speed ◽  
Couple Stress ◽  
Dynamic Responses ◽  
Couple Stress Fluid ◽  
Speed Ratio ◽  
Systematic Analysis ◽  
Diverse Range ◽  
Gear Mesh ◽  
Highly Nonlinear ◽  
Bearing System

A systematic analysis of the dynamic behavior of a gear-bearing system with nonlinear suspension, couple-stress fluid flow effect, nonlinear oil-film force, and nonlinear gear mesh force is performed in the present study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless rotational speed ratio as a control parameter. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents and fractal dimension of the gear-bearing system. The numerical results reveal that the system exhibits a diverse range of periodic, subharmonic, quasiperiodic, and chaotic behaviors. The couple-stress fluid would be a useful lubricating fluid to suppress nonlinear dynamic responses and improve the steady of the systems. The results presented in this study provide some useful insights into the design and development of a gear-bearing system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes.

Gear Dynamics Analysis With Turbulent Journal Bearings Under Quadratic Damping and Nonlinear Suspension—Bifurcation and Chaos

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Cai-Wan Chang-Jian
Keyword(s):  
Turbulent Flow ◽  
Power Spectra ◽  
Speed Ratio ◽  
Control Parameters ◽  
Bifurcation And Chaos ◽  
Systematic Analysis ◽  
Gear Mesh ◽  
Damping Effect ◽  
Quadratic Damping ◽  
Bearing System

This study performs a systematic analysis of the dynamic behavior of the gear for the gear-bearing system with the turbulent flow effect, quadratic damping effect, nonlinear suspension effect, nonlinear oil-film force, and complicated gear mesh force. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless unbalance coefficient and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents, and fractal dimension of the gear-bearing system. The ignorance of quadratic damping effect for turbomachineries especially in turbulent cases may cause significant errors. The proposed simulation model and theory may provide some useful information for engineers in designing or controlling some turbomachineries particularly in turbulent flow cases.

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.

Analysis of Rotor Bearing Systems With Uncertainties: A Fuzzy Approach

2009 ◽  
Author(s):  
Singiresu S. Rao ◽  
Yazhao Qiu
Keyword(s):  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operating Conditions ◽  
Fourth Power ◽  
Fuzzy Approach ◽  
Restoring Force ◽  
Analysis And Design ◽  
Highly Sensitive ◽  
Rotor Bearing ◽  
Bearing System

The components of most structural and mechanical systems exhibit considerable variations or uncertainties in their properties and the performance characteristics of such systems are subject to uncertainties. In the case of a rotor bearing system, the nonlinear bearing restoring force is usually represented as a third or fourth power of displacement or as a piecewise linear function of displacement. The coefficients of these models are acquired from experiments and approximations, and will vary considerably during the operation of the bearing. Hence it is more reasonable to treat them as uncertain values. Other bearing parameters such as the inertial properties of concentrated disks, distributed mass and damping of the rotating assemblies are also uncertain due to manufacturing and assembly errors and imprecise operating conditions. It is known that the vibration response of a rotor is highly sensitive to small fluctuations or variations in the bearing parameters. Therefore, any realistic analysis and design of rotor-bearing systems must take the uncertainties into account. In this paper, a methodology is presented for the fuzzy analysis of nonlinear rotor-bearing systems along with numerical results to demonstrate the computational feasibility of the methodology.

A Fuzzy Approach for the Analysis of Rotor-Bearing Systems With Uncertainties

2011 ◽  
Author(s):  
Singiresu S. Rao ◽  
Yazhao Qiu
Keyword(s):  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operating Conditions ◽  
Fourth Power ◽  
Fuzzy Approach ◽  
Restoring Force ◽  
Analysis And Design ◽  
Highly Sensitive ◽  
Rotor Bearing ◽  
Bearing System

The components of most structural and mechanical systems exhibit considerable variations or uncertainties in their properties and the performance characteristics of such systems are subject to uncertainties. In the case of a rotor bearing system, the nonlinear bearing restoring force is usually represented as a third or fourth power of displacement or as a piecewise linear function of displacement. The coefficients of these models are acquired from experiments and approximations, and will vary considerably during the operation of the bearing. Hence it is more reasonable to treat them as uncertain values. Other bearing parameters such as the inertial properties of concentrated disks, distributed mass and damping of the rotating assemblies are also uncertain due to manufacturing and assembly errors and imprecise operating conditions. It is known that the vibration response of a rotor is highly sensitive to small fluctuations or variations in the bearing parameters. Therefore, any realistic analysis and design of rotor-bearing systems must take the uncertainties into account. In this paper, a methodology is presented for the fuzzy analysis of nonlinear rotor-bearing systems along with numerical results to demonstrate the computational feasibility of the methodology.

scholarly journals A Model To Estimate Synchronous Vibration Amplitude For Detection of Unbalance in Rotor-Bearing System

2021 ◽  
Vol 26 (2) ◽  
pp. 161-169
Author(s):  
I.M. Jamadar
Keyword(s):  
Mathematical Model ◽  
Vibration Amplitude ◽  
Numerical Technique ◽  
Operating Conditions ◽  
Box Behnken Design ◽  
Unbalanced Rotor ◽  
Mass Eccentricity ◽  
Rotor Bearing ◽  
Different Levels ◽  
Bearing System

A numerical technique for detection of unbalance magnitude of a rotor-bearing system is proposed and verified by experimental analysis. Dimensional analysis is used for development of mathematical model of an unbalanced rotor-bearing system following rigid rotor approach. A developed mathematical model is solved by factorial regression analysis method using the experimental data obtained by a Box-Behnken design. The proposed approach integrates the rotor parameters, disc parameters, bearing parameters and operating conditions with the synchronous vibration amplitude. Confirmation experiments are conducted using Taguchi design methodology with unbalance mass, rotor speed, mass eccentricity and radial load as parameters with different levels assigned to them.

A pilot web former designed to study retention-formation relationships

2010 ◽  
Vol 25 (2) ◽  
pp. 185-194
Author(s):  
Anna Svedberg ◽  
Tom Lindström
Keyword(s):  
Pilot Scale ◽  
Operating Conditions ◽  
Montmorillonite Clay ◽  
Speed Ratio ◽  
Good Reproducibility ◽  
Total Solids ◽  
Retention Aids ◽  
Solids Content ◽  
Relationship Of ◽  
The Relationship

Abstract A pilot-scale fourdrinier former has been developed for the purpose of investigating the relationship between retention and paper formation (features, retention aids, dosage points, etc.). The main objective of this publication was to present the R-F (Retention and formation)-machine and demonstrate some of its fields of applications. For a fine paper stock (90% hardwood and 10% softwood) with addition of 25% filler (based on total solids content), the relationship between retention and formation was investigated for a microparticulate retention aid (cationic polyacrylamide together with anionic montmorillonite clay). The retention-formation relationship of the retention aid system was investigated after choosing standardized machine operating conditions (e.g. the jet-to-wire speed ratio). As expected, the formation was impaired when the retention was increased. Since good reproducibility was attained, the R-F (Retention and formation)-machine was found to be a useful tool for studying the relationship between retention and paper formation.

Applications of vibro-acoustic measurement and analysis in conjunction with tribological parameters to assess surface fatigue wear developed in the roller-bearing system

2021 ◽  
pp. 135065012098246
Author(s):  
Shashikant Pandey ◽  
Muniyappa Amarnath
Keyword(s):  
Roller Bearing ◽  
Operating Conditions ◽  
Rolling Contact ◽  
Stribeck Curve ◽  
Fatigue Wear ◽  
Surface Fatigue ◽  
Rolling Element ◽  
Measurement And Analysis ◽  
Contact Surfaces ◽  
Bearing System

Rolling-element bearings are the most commonly used components in all rotating machinery. The variations in the operating conditions such as an increase in the number of operating cycles, load, speed, service temperature, and lubricant degradation result in the development of various defects such as pitting, spalling, scuffing, scoring, etc. The defects that appeared on rolling contact surfaces cause surface deterioration and change in the vibration and sound levels of the bearing system. The present experimental investigations are aimed at assessing the surface fatigue wear that appears on the contact surfaces of roller bearings. The studies considered the estimation of specific film thickness, analysis of surface fatigue wear developed on the rolling-element surfaces, surface roughness analysis, grease degradation analysis using Fourier transform infrared radiation, and vibration and sound signal measurement and analysis. The results obtained from the experimental investigation provide a good correlation between surface wear, vibration, and sound signals with a transition in the lubrication regimes in the Stribeck curve.

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