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 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.

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.

Non-linear dynamic analysis of bearing—rotor system lubricating with couple stress fluid

2008 ◽  
Vol 222 (4) ◽  
pp. 599-616 ◽  
Author(s):  
C-W Chang-Jian ◽  
C-K Chen
Keyword(s):  
Dynamic Analysis ◽  
Chaotic Motion ◽  
Couple Stress ◽  
Couple Stress Fluid ◽  
Speed Ratio ◽  
Non Linear ◽  
System Life ◽  
The Stability ◽  
Suitable System ◽  
Bearing System

The current study performs a dynamic analysis of a rotor supported by two couple stress fluid film journal bearings with non-linear suspension. The dynamics of the rotor centre and bearing centre are studied. The analysis of the rotor—bearing system is investigated under the assumptions of a couple-stress lubricant and a short journal bearing approximation. The displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The analysis methods employed in this study include the dynamic trajectories of the rotor centre and the bearing centre, Poincaré maps, and bifurcation diagrams. The Lyapunov exponent analysis is also used to identify the onset of chaotic motion. Numerical results show that the stability of the system varies with the non-dimensional speed ratios. Specifically, it is found that the system is quasi-periodic at a small speed ratio ( s = 0.5). At speed ratios of s = 0.6–0.7, the system is periodic. At s = 0.8–1.9, the system is quasi-periodic, but the system is periodic at s = 2.0–2.6. However, the system exhibits chaotic motion at the speed ratios s = 2.7–2.74. At the speed ratios s = 2.75–3.16, the system becomes periodic. At s = 3.17–3.30, the system is unstable. The Poincaré map has a particular form at s = 3.17, indicative of a chaotic motion. At s = 3.31–6.0, the system finally becomes periodic. The results also confirm that the stability of the system varies with the non-dimensional speed ratios s and l∗. The results of this study allow suitable system parameters to be defined such that undesirable behaviour of the rotor centre can be avoided and the bearing system life extended as a result.

Dynamic analysis of a helical geared rotor-bearing system with composite rotating shafts

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ying-Chung Chen ◽  
Xu Feng Cheng ◽  
Siu-Tong Choi
Keyword(s):  
Composite Material ◽  
Dynamic Analysis ◽  
Dynamic Characteristics ◽  
Mesh Stiffness ◽  
Content Type ◽  
Gear Mesh ◽  
Rotor Bearing ◽  
Rotating Shafts ◽  
Gear Mesh Stiffness ◽  
Bearing System

Purpose This study aims to study the dynamic characteristics of a helical geared rotor-bearing system with composite material rotating shafts. Design/methodology/approach A finite element model of a helical geared rotor-bearing system with composite material rotating shafts is developed, in which the rotating shafts of the system are composed of composite material and modeled as Timoshenko beam; a rigid mass is used to represent the gear and their gyroscopic effect is taken into account; bearings are modeled as linear spring-damper; and the equations of motion are obtained by applying Lagrange’s equation. Natural frequencies, mode description, lateral responses, axial responses, lamination angles, lamination numbers, gear mesh stiffness and bearing damping coefficients are investigated. Findings The desired mechanical properties could be constructed using different lamination numbers and fiber included angles by composite rotating shafts. The frequency of the lateral module decreases as the included angle of the fibers and the principal shaft of the composite material rotating shaft increase. Because of the gear mesh stiffness increase, the resonance frequency of the coupling module of the system decreases, the lateral module is not influenced and the steady-state response decreases. The amplitude of the steady-state lateral and axial responses gradually decreases as the bearing damping coefficient increases. Practical implications The model of a helical geared rotor-bearing system with composite material rotating shafts is established in this paper. The dynamic characteristics of a helical geared rotor-bearing system with composite rotating shafts are investigated. The numerical results of this study can be used as a reference for subsequent personnel research. Originality/value The dynamic characteristics of the geared rotor-bearing system had been reported in some literature. However, the dynamic analysis of a helical geared rotor-bearing system with composite material rotating shafts is still rarely investigated. This paper shows some novel results of lateral and axial response results obtained by different lamination angles and different lamination numbers. In the future, it makes valuable contributions for further development of dynamic analysis of a helical geared rotor-bearing system with composite material rotating shafts.

Non-linear dynamic behaviour of rotor—bearing system trained by bevel gears

2008 ◽  
Vol 222 (4) ◽  
pp. 617-627 ◽  
Author(s):  
M Li
Keyword(s):  
Equilibrium Points ◽  
Rotor System ◽  
Design Stage ◽  
Oil Film ◽  
Bevel Gears ◽  
Linear Dynamic ◽  
Non Linear ◽  
Rotor Bearing ◽  
Stability And Bifurcations ◽  
Bearing System

The vibrations of parallel geared rotor—bearing system have been intensively discussed; however, little attention has been paid to the dynamic analysis of angled bevel-geared system supported on journals. In the present work, the non-linear dynamics of a bevel-geared rotor system on oil film bearings is studied. First, the dynamic model is developed under some assumptions, such as rigid rotors, short-bearings, small teeth errors, and so forth. Then, the non-linear dynamic behaviours of both the balanced and unbalanced rotor system are analysed, respectively, in which the equilibrium points, limit cycles, their stability, and bifurcations are paid more attention. Numerical results show that in the bevel-geared rotor system under the action of non-linear oil film forces there exists a series of complex non-linear dynamic phenomena of rotor orbits, such as Hopf bifurcation, torus-doubling bifurcation, and jump phenomenon. All these features can help us to understand the dynamic characteristics of bevel-geared rotor—bearing system at design stage and during running period. Finally, some concerned problems during the investigation are also present.

Dynamic Analysis of a Spur Geared Rotor-Bearing System with Nonlinear Gear Mesh Stiffness

2014 ◽  
Vol 945-949 ◽  
pp. 853-861 ◽  
Author(s):  
Ying Chung Chen ◽  
Chung Hao Kang ◽  
Siu Tong Choi
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Element Model ◽  
Dynamic Responses ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Lagrange’S Equation ◽  
Rotor Bearing ◽  
Gear Mesh Stiffness ◽  
Bearing System

The gear mesh stiffnesses have been regarded as constants in most previous models of geared rotor-bearing systems. In this paper, a dynamic analysis of a spur geared rotor-bearing system with nonlinear gear mesh stiffness is presented. The nonlinear gear mesh stiffness is accounted for by bending, fillet-foundation and contact deflections of gear teeth. A finite element model of the geared rotor-bearing system is developed, the equations of motion are obtained by applying Lagrange’s equation, and the dynamic responses are computed by using the fourth-order Runge-Kutta numerical method. Numerical results indicate that the proposed gear mesh stiffness provides a realistic dynamic response for spur geared rotor-bearing system.

Optimum Design of Rotor-Bearing Systems Considering the Nonlinear Effects of Bearing Fluid Forces

2005 ◽  
Author(s):  
Zhaobo Chen ◽  
Yinghou Jiao ◽  
Songbo Xia ◽  
Wenhu Huang
Keyword(s):  
Optimum Design ◽  
Fitness Function ◽  
Evolutionary Process ◽  
Nonlinear Effects ◽  
Radial Clearance ◽  
Chaotic Motions ◽  
Fluid Forces ◽  
Adaptive Procedures ◽  
Rotor Bearing ◽  
Bearing System

Genetic algorithms (GAs) are adaptive procedures that find solution to problems by an evolutionary process that mimics natural selection. In this paper, methods based on GAs have been developed and presented for design optimization of journal bearings in nonlinear rotor system. The GA uses a 30-bit chromosome to represent the bearing radial clearance, aspect ratio and lubricant viscosity, with 10-bit for each design variable. The instability onset speed of the system is taken as the fitness function in GA, in which the nonlinear effects of the bearing fluid forces are considered. The instability onset speed is defined in two different cases, that is, periodic and quasi-periodic or chaotic motions. To verify the effectiveness of the suggested method, a rigid rotor-bearing system is taken as an example to be optimized. The different crossover probabilities, mutation probabilities and population sizes are employed to analyze their influences on GA so that a set of appropriate parameters are chosen to be used in the final calculation. The results are compared with those obtained by numerical simulation. It is shown that the proposed algorithm is effective in the optimum design of rotor-bearing system.

Dynamic Analysis of a Geared Rotor-Bearing System with Time-Varying Gear Mesh Stiffness and Pressure Angle

2013 ◽  
Vol 284-287 ◽  
pp. 461-467
Author(s):  
Ying Chung Chen ◽  
Chung Hao Kang ◽  
Siu Tong Choi
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Responses ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Pressure Angle ◽  
Proposed Model ◽  
Rotor Bearing ◽  
Gear Mesh Stiffness ◽  
Bearing System

The dynamic analysis of a geared rotor-bearing system with time-varying gear mesh stiffness and pressure angle is presented in this paper. Although there are analyses for both of the gear and rotor-bearing system dynamics, the coupling effect of the time-varying mesh and geared rotor-bearing system is deficient. Therefore, the pressure angle and contact ratio of the geared rotor-bearing system are treated as time-varying variables in the proposed model while they were considered as constant in previous models. The gear mesh stiffness is varied with different contact ratios of the gear pair in the meshing process. The nonlinear equations of motion for the geared rotor-bearing system are obtained by applying Lagrange’s equation and the dynamic responses are computed by using the Runge-Kutta numerical method. Numerical results of this study indicated that the proposed model provides realistic dynamic response of a geared rotor-bearing system.

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