Steady-State Response of Continuous Nonlinear Rotor-Bearing Systems Using Analytical Approach

1998 ◽  
Vol 120 (4) ◽  
pp. 751-758 ◽  
Author(s):  
J. W. Zu ◽  
Z. Y. Ji
Keyword(s):  
Steady State ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Distributed Parameter ◽  
Steady State Response ◽  
State Response ◽  
Rotor Bearing ◽  
Continuous Modeling ◽  
Close Form ◽  
First Time

A continuous modeling of nonlinear rotor-bearing systems is presented in this paper. The shaft is treated as a distributed parameter system using Timoshenko beam theory. A close form, steady-state response of the system is solved analytically for the first time. For cubic nonlinear bearings, the response is composed of three components, synchronous vibration, subsynchronous, and supersynchronous vibration. The harmonic balance method is used to calculate the nonlinear bearing forces. Two examples of nonlinear rotor-bearing systems are shown to illustrate the analysis procedure and the nonlinear characteristics of the system. Solutions from simplified systems are also derived for comparison.

An Investigation in Optimal Locations by Genetic Algorithm for Balancing Flexible Rotor-Bearing Systems

2005 ◽  
Author(s):  
Tsu-Wei Lin ◽  
Yuan Kang ◽  
Chun-Chieh Wang ◽  
Chuan-Wei Chang ◽  
Chih-Pin Chiang
Keyword(s):  
Genetic Algorithm ◽  
Finite Element Method ◽  
Steady State ◽  
Hermitian Matrix ◽  
Influence Coefficient ◽  
Steady State Response ◽  
Flexible Rotor ◽  
The Finite Element Method ◽  
State Response ◽  
Rotor Bearing

This study utilizes genetic algorithm to minimize the condition number of Hermitian matrix of influence coefficient (HMIC) to reduce the computation errors in balancing procedure. Then, the optimal locations of balancing planes and sensors would be obtained as fulfilling optimization. The finite element method is used to determine the steady-state response of flexible rotor-bearing systems. The optimization improves the balancing accuracy, which can be validated by the experiments of balancing a rotor kit.

Steady-State Response and Stability of Rotating Composite Blades With Frictional Damping

1998 ◽  
Vol 120 (1) ◽  
pp. 131-139 ◽  
Author(s):  
T. N. Shiau ◽  
J. S. Rao ◽  
Y. D. Yu ◽  
S. T. Choi
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Composite Plates ◽  
Steady State Response ◽  
Friction Damping ◽  
State Response ◽  
Direct Integration Method ◽  
Composite Blades

Friction dampers are widely used to improve the performance of rotating blades. This paper is concerned with the steady state response and stability analysis of rotating composite plates in the presence of non linear friction damping. Direct Integration Method (DIM) and Harmonic Balance Method (HBM) are used to determine the steady state response due to periodic lateral external forces. In addition, an alternate procedure, Hybrid Method (HM) is proposed for this analysis to substantiate the results from DIM and HBM. The analysis shows that the steady state response is a function of friction damping magnitude as well as its location besides the excitation frequency and the rotational speed. A stability analysis of the composite blades is also made by including periodic in-plane excitation using Floquet-Liapunov theory.

An Improved Transfer Matrix Method for Steady-State Analysis of Nonlinear Rotor-Bearing Systems

2002 ◽  
Vol 124 (2) ◽  
pp. 303-310 ◽  
Author(s):  
J. W. Zu ◽  
Z. Ji
Keyword(s):  
Steady State ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Roller Bearing ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Rotating Shaft ◽  
Damping Characteristics ◽  
Rotor Bearing

An improved transfer matrix method is developed to analyze nonlinear rotor-bearing systems. The rotating shaft is described by the Timoshenko beam theory which considers the effect of the rotary inertia and shear deformation. A typical roller bearing model is assumed which has cubic nonlinear spring and linear damping characteristics. Transfer matrices for the Timoshenko shaft element, disk element, and nonlinear bearing element are derived and the global transfer matrix is formed. The steady-state response of synchronous, subharmonic, and superharmonic whirls is determined using the harmonic balance method. Two numerical examples are presented to demonstrate the effectiveness of this approach.

scholarly journals Local Sensitivity Analysis of Steady-State Response of Rotors with Rub-Impact to Parameters of Rubbing Interfaces

2021 ◽  
Vol 11 (3) ◽  
pp. 1307
Author(s):  
Minghong Jiang ◽  
Zhaoli Zheng ◽  
Yonghui Xie ◽  
Di Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Duffing Oscillator ◽  
Harmonic Balance Method ◽  
Friction Model ◽  
Design Parameters ◽  
Steady State Response ◽  
Local Sensitivity ◽  
Local Sensitivity Analysis ◽  
State Response

Local sensitivity analysis, which describes the relative importance of specific design parameters to the response of systems, is crucial for investigating dominant factors in optimal design. In this paper, local sensitivity analysis of the response of rotors with rub-impact to parameters of rubbing interfaces is carried out. The steady-state motion of the rotor is evaluated by a harmonic balance method and the sensitivity coefficients for every rotation speed over the speed range are derived analytically. Two classical models, including the Duffing oscillator and the gap model, are utilized to validate the accuracy and capability of the adopted methods and high accuracy is shown. Numerical investigations of sensitivities of steady-state response of rotors to parameters of rubbing interfaces are then carried out, based on a lumped Jeffcott rotor and a finite element model respectively. Conclusions are drawn that the response of rotors subjected to rubbing problems is more sensitive to initial clearance than other parameters of the applied friction model. With increase of initial gap, the response of rotors becomes more sensitive and the range of region subjected to rub-impact forces shrinks until the separation of rotor and stator.

Dynamic Response of a Geared Rotor-Bearing System Under Residual Shaft Bow Effect

2006 ◽  
Author(s):  
T. N. Shiau ◽  
E. K. Lee ◽  
Y. C. Chen ◽  
T. H. Young
Keyword(s):  
Steady State ◽  
Natural Frequencies ◽  
Coupling Effect ◽  
Equations Of Motion ◽  
Transmission Error ◽  
Mode Shapes ◽  
Steady State Response ◽  
State Response ◽  
Rotor Bearing ◽  
Bearing System

The paper presents the dynamic behaviors of a geared rotor-bearing system under the effects of the residual shaft bow, the gear eccentricity and excitation of gear’s transmission error. The coupling effect of lateral and torsional motions is considered in the dynamic analysis of the geared rotor-bearing system. The finite element method is used to model the system and Lagrangian approach is applied to derive the system equations of motion. The dynamic characteristics including system natural frequencies, mode shapes and steady-state response are investigated. The results show that the magnitude of the residual shaft bow, the phase angle between gear eccentricity and residual shaft bow will significantly affect system natural frequencies and steady-state response. When the spin speed closes to the second critical speed, the system steady state response will be dramatically increased by the residual shaft bow for the in-phase case. Moreover the zero response can be obtained when the system is set on special conditions.

Dynamic Analysis of a Geared Rotor-Bearing System With Viscoelastic Supports Under the Bow Effect

2007 ◽  
Author(s):  
T. N. Shiau ◽  
E. K. Lee ◽  
T. H. Young ◽  
W. C. Hsu
Keyword(s):  
Steady State ◽  
Dynamic Analysis ◽  
Loss Factor ◽  
Critical Speed ◽  
Transmission Error ◽  
Steady State Response ◽  
Critical Speeds ◽  
State Response ◽  
Rotor Bearing ◽  
Bearing System

This paper investigates the dynamic behaviors of a geared rotor-bearing system mounted on viscoelastic supports under considerations of the gear eccentricity, excitation of the gear’s transmission error and the residual shaft bow. The finite element method is used to model the system and Lagrangian approach is applied to derive the system equations of motion. The coupling effect of lateral and torsional motions is considered in the system dynamic analysis. The investigated dynamic characteristics include system natural frequencies and steady-state response. The results show that the mass, the stiffness and the loss factor of the viscoelastic support will significantly affect system critical speeds and steady-state response. Larger loss factor and more rigid stiffness of the viscoelastic supports will suppress the systematic amplitude of resonance. Parameters, which include magnitude of the residual bow and phase angle, are also considered in the investigation of their effects on system critical speeds and steady-state response. Results show that they have tremendous influence on first critical speed when the geared system mounted on stiff viscoelastic supports. The transmission error of the gear mesh is assumed to be sinusoidal with tooth passing frequency and it will induce multiple low resonant frequencies in the system response. It is observed that the excited critical speed equals to the original critical speed divided by gear tooth number.

Steady State Response and Stability of Rotating Composite Blades With Frictional Damping

1996 ◽  
Author(s):  
T. N. Shiau ◽  
J. S. Rao ◽  
Y. D. Yu ◽  
S. T. Choi
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Composite Plates ◽  
Steady State Response ◽  
Friction Damping ◽  
State Response ◽  
Direct Integration Method ◽  
Composite Blades

Friction dampers are widely used to improve the performance of rotating blades. This paper is concerned with the steady stale response and stability analysis of ratating composite plates in the presence of non linear friction damping. Direct Integration Method (DIM) and Harmonic Balance Method (HBM) are used to determine the steady state response due to periodic lateral external forces. In addition, an alternate procedure, Hybrid Method (HM) is proposed for this analysis to substantiate the results from DIM and HBM. The analysis shows that the steady state response is a function of friction damping magnitude as well as its location besides the excitation frequency and the rotational speed. A stability analysis of the composite blades is also made by including periodic in-plane excitation using Floquet-Liapunov theory.

Modeling and Analysis of Friction Rim Dampers for Blisks

2005 ◽  
Author(s):  
Denis Laxalde ◽  
Jean-Jacques Sinou ◽  
Fabrice Thouverez ◽  
Jean-Pierre Lombard
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Design Guidelines ◽  
Lumped Parameter Model ◽  
Dynamical Analysis ◽  
Steady State Response ◽  
Modeling And Analysis ◽  
State Response ◽  
Lumped Parameter

A damping strategy for blisks of turbomachinery involving a friction rim is investigated. These rims, located in grooves underside the wheel of the blisks, are held in by centrifugal loads and the energy is dissipated when relative motions between the rim and the disk occur. A method of dynamical analysis of a cyclic blisk nonlinearly coupled with a split rim is presented: the steady-state response being calculated using an multi-harmonic balance method. Numerical simulations on a lumped-parameter model are presented for several damper characteristics and several excitation configurations. From these results, the performance of this damping strategy is discussed and some design guidelines are given. Finally the influence of mistuning on the damping performances is analysed.

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