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.

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.

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.

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.

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.

Nonlinear Dynamic of a Geared Rotor System With Nonlinear Oil Film Force and Nonlinear Mesh Force

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Yahui Cui ◽  
Zhansheng Liu ◽  
Yongliang Wang ◽  
Jianhuai Ye
Keyword(s):  
Numerical Integration ◽  
Dynamic Model ◽  
Rotational Speed ◽  
Nonlinear Dynamic ◽  
Journal Bearing ◽  
Rotational Frequency ◽  
Rotor System ◽  
Dynamic Responses ◽  
Oil Film ◽  
Gear Mesh

To investigate the effect of oil film force on a geared rotor system, a short journal bearing model was applied to represent nonlinear oil film force. A dynamic model of the geared rotor oil journal bearing system was presented. The nonlinear gear mesh force and nonlinear oil film force were considered in the model. The nonlinear dynamic responses of the system were investigated by numerical integration method. This article shows that when the rotational speed is relatively low, the vibration of the system is mainly affected by nonlinear mesh force. With the increase of rotational speed, the influence of nonlinear oil film force also increases gradually, and the subsynchronous forward precession phenomena appear. When the speed increases to a certain value, the amplitude of the subsynchronous forward precession exceeds the amplitude of the rotational frequency, and the nonlinear mesh force is greatly affected by the nonlinear oil film force. However, the linear oil film force does not affect the nonlinear mesh force. The subsynchronous forward precession is difficult to be predicted by linear oil film force which was previously applied. This experiment is performed to validate the correctness of the dynamic model presented, and the numerical integration results of low speeds are validated by the experimental data.

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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