Nonlinear Dynamics of the Rod-Fastened Jeffcott Rotor

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Qi Yuan ◽  
Jin Gao ◽  
Pu Li
Keyword(s):  
Nonlinear Dynamics ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Operating Parameters ◽  
Flexural Stiffness ◽  
The Finite Element Method ◽  
Jeffcott Rotor ◽  
Unbalance Force ◽  
Contact Surfaces ◽  
Tie Rods

Rod-fastened rotors are composed of some disks clamped together by a central tie rod or several tie rods distributed along the circumference. Due to the nonlinear flexural stiffness of the contact interfaces in disks, especially when the contact surfaces are partially separated, the dynamics of the rod-fastened rotors are potentially different from that of the solid rotors. In this paper, the nonlinear flexural stiffness of a rod-fastened Jeffcott rotor is calculated by the finite element method (FEM). Then the harmonic balance method is adopted to analyze the dynamics of the rotor. The flexural stiffness of a rod-fastened Jeffcott rotor dramatically decreased with the increase of the dimensionless load γ1 from 1 to 2.5. Thus, the dynamics of the rotor were nonlinear when it was subjected to a large unbalance force. The response of the rotating rotor contains a predominantly forward 1X component or both forward 1X component and backward 1X components. However, the rotor may settle in a state depending upon both the operating parameters and its history.

Revealing Nonlinear Dynamics Phenomena in Mooring Due to Slowly-Varying Drift

2005 ◽  
Author(s):  
Michael M. Bernitsas ◽  
Joa˜o Paulo J. Matsuura
Keyword(s):  
Nonlinear Dynamics ◽  
Limit Cycles ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Resonance Phenomenon ◽  
Nonlinear Phenomena ◽  
Mooring System ◽  
Stable Limit ◽  
Dynamic Interactions ◽  
Wave Drift

The effects of slowly-varying wave drift forces on the nonlinear dynamics of mooring systems have been studied extensively in the past 30 years. It has been concluded that slowly-varying wave drift may resonate with mooring system natural frequencies. In recent work, we have shown that this resonance phenomenon is only one of several possible nonlinear dynamic interactions between slowly-varying wave drift and mooring systems. We were able to reveal new phenomena based on the design methodology developed at the University of Michigan for autonomous mooring systems and treating slowly-varying wave drift as an external time-varying force in systematic simulations. This methodology involves exhaustive search regarding the nonautonomous excitation, however, and approximations in defining response bifurcations. In this paper, a new approach is developed based on the harmonic balance method, where the response to the slowly-varying wave drift spectrum is modeled by limit cycles of frequency estimated from a limited number of simulations. Thus, it becomes possible to rewrite the nonautonomous system as autonomous and reveal stability properties of the nonautonomous response. Catastrophe sets of the symmetric principal equilibrium, serving as design charts, define regions in the design space where the trajectories of the mooring system are asymptotically stable, limit cycles, or non-periodic. This methodology reveals and proves that mooring systems subjected to slowly-varying wave drift exhibit many nonlinear phenomena, which lead to motions with amplitudes 2–3 orders of magnitude larger than those resulting from linear resonance. A turret mooring system (TMS) is used to demonstrate the harmonic balance methodology developed. The produced catastrophe sets are then compared with numerical results obtained from systematic simulations of the TMS dynamics.

Analytical Solution for the Nonlinear Dynamics of Planetary Gears

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Harmonic Balance ◽  
Gear Tooth ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Mesh Stiffness ◽  
Planetary Gears ◽  
Parallel Finite Element ◽  
The Impact

Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. At resonance, the resulting vibration causes tooth separation leading to nonlinear effects such as jump phenomena and subharmonic resonance. This work examines the nonlinear dynamics of planetary gears by numerical and analytical methods over the meaningful mesh frequency ranges. Concise, closed-form approximations for the dynamic response are obtained by perturbation analysis. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. Correlation between the amplitude of response and external torque demonstrates that tooth separation occurs even under large torque. The harmonic balance method with arclength continuation confirms the perturbation solutions. The accuracy of the analytical and harmonic balance solutions is evaluated by parallel finite element and numerical integration simulations.

scholarly journals Effect of Detuning of Clamping Force of Tie Rods on Dynamic Performance of Rod-Fastened Jeffcott Rotor

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Haoliang Xu ◽  
Lihua Yang ◽  
Tengfei Xu ◽  
Yao Wu
Keyword(s):  
Natural Frequency ◽  
Rough Surface ◽  
Contact Stiffness ◽  
Dynamic Performance ◽  
Flexural Stiffness ◽  
Clamping Force ◽  
Term Operation ◽  
Analysis And Design ◽  
Jeffcott Rotor ◽  
Tie Rods

In view of the advantages of lightweight, high strength, easy cooling, and easy assembly, the rod-fastened rotor is widely used in the aeroengine and heavy gas turbine. However, because of assembly, stress relaxation, material creep, and other reasons, the clamping force of the tie rods will be out of tune during the long-term operation of the rotor. The detuning of the clamping force of the tie rods not only affects the contact stiffness of the contact interface but also causes the rod-fastened rotor with a certain residual shaft bow, which will affect the dynamic characteristics of the rod-fastened rotor. Based on the statistical model of rough surface contact (GW contact model), this paper presents a method to calculate the equivalent flexural stiffness of rough surface considering the detuning of the clamping force of the tie rods and gives the calculation method of the residual shaft bow deformation of the rod-fastened Jeffcott rotor with detuning of the tie rods. The effect of the preload, the rate of detuning of the tie rods, the number of detuning tie rods on the natural frequency, and the response of residual shaft bow of the rod-fastened Jeffcott rotor at a certain speed are investigated. The results show that the detuning of the tie rods makes the flexural stiffness of the rotor inconsistent along with two main stiffness directions of the rotor, which makes the natural frequency of the rotor divided into two. The negative detuning of the tie rods decreases the natural frequency of the rotor, while the positive detuning of the tie rods increases the natural frequency of the rotor. The smaller preload or the larger rate of detuning of the tie rods makes the detuning of the tie rods have a greater influence on the natural frequency of the rotor. These results will provide a theoretical reference for the dynamic analysis and design of the rod-fastened rotor.

scholarly journals A Study of the Influence of Rubbing on the Dynamics of a Flexible Disk Rotor System

1993 ◽  
Author(s):  
Fangsheng Wu ◽  
George T. Flowers
Keyword(s):  
Harmonic Balance ◽  
Dynamical Behavior ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Governing Equations ◽  
System A ◽  
Jeffcott Rotor ◽  
Inertial Moment ◽  
Flexible Disk ◽  
Rotor Model

This study is concerned with investigating the influence of lateral disk flexibility on the dynamics of a rotor system experiencing rub. A rotating, flexible continuous disk/shaft model was developed and the dynamical behavior of this system with and without rubbing was studied. The model developed in this study is similar to the Jeffcott rotor model except that the disk is treated as a laterally flexible continuous circular plate. The motion of the disk was transformed from physical coordinates to a set of generalized coordinates under which the generalized motion was uncoupled and the responses were calculated. Then the inertial moment acting on the shaft was computed and introduced into the governing equations of the shaft motion. Direct integration and the harmonic balance method were used to study the steady state motion of the system. A number of parameter variation studies were performed for varied rub clearances and disk mass influence ratios. The system responses to the rub, its occurrence and development, and the global stability of the observed responses were studied. The results show that rub can be classified into two types: light rub and heavy rub, and the light rub has the forms of forward, backward, or mixed whirling motion. The results also show that the disk flexibility may alter the critical speed to some degree and may also significantly affect the amplitude and stability of the rotor vibration.

Nonlinear Dynamics in Drilling and Boring Operations Assisted by Low Frequency Vibration

2007 ◽  
Author(s):  
George F. Moraru
Keyword(s):  
Nonlinear Dynamics ◽  
Harmonic Balance ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Drilling Process ◽  
Process Damping ◽  
Regenerative Effect ◽  
Low Frequency Vibration ◽  
Machining System

The nonlinear dynamics of the drilling process assisted by self-excited axial vibrations is analyzed. Models are developed and discussed, including regenerative effect and various phenomena contributing to the process damping in drilling and boring operations. Stability and bifurcation analysis, using several assumptions on the damping in the cutting process, are carried out using linear analysis tools or simulations. A simple predictive model based on a harmonic balance method is presented. Behavior charts are constructed using simulations. Hypothesis on the nature of the process damping and nonlinear behavior of the machining system are proved by experiments. A possible application to the gundrilling boring process in aircraft drilling and assembly process is presented.

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