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.

Analytical Method of Response of Piping System With Nonlinear Support

2000 ◽  
Vol 122 (4) ◽  
pp. 437-442
Author(s):  
Shigeru Aoki ◽  
Takeshi Watanabe
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Analytical Method ◽  
Mode Shapes ◽  
Piping System ◽  
Steady State Response ◽  
Response Curves ◽  
State Response ◽  
Damping Characteristics ◽  
Nonlinear Support

This paper deals with steady-state response of the piping system with nonlinear support having hysteresis damping characteristics. Considering the energy loss for contact with a support, an analytical method of approximate solution for the beam, a one-span model of the piping system, with quadrilateral hysteresis loop characteristics is presented. Some numerical results of the approximate solution for the response curves and the mode shapes are shown. [S0094-9930(00)00204-3]

Sensitivity Analysis for the Steady-State Response of Damped Linear Elastodynamic Systems Subject to Periodic Loads

1990 ◽  
Author(s):  
Daniel A. Tortorelli
Keyword(s):  
Steady State ◽  
Vibration Amplitude ◽  
Equations Of Motion ◽  
Steady State Response ◽  
Analysis Techniques ◽  
Direct Differentiation ◽  
State Response ◽  
Need To Evaluate ◽  
The Time Domain ◽  
General Response

Abstract Adjoint and direct differentiation methods are used to formulate design sensitivities for the steady-state response of damped linear elastodynamic systems that are subject to periodic loads. Variations of a general response functional are expressed in explicit form with respect to design field perturbations. Modal analysis techniques which uncouple the equations of motion are used to perform the analyses. In this way, it is possible to obtain closed form relations for the sensitivity expressions. This eliminates the need to evaluate the adjoint response and psuedo response (these responses are associated with the adjoint and direct differentiation sensitivity problems) over the time domain. The sensitivities need not be numerically integrated over time, thus they are quickly computed. The methodology is valid for problems with proportional as well as non-proportional damping. In an example problem, sensitivities of steady-state vibration amplitude of a crankshaft subject to engine firing loads are evaluated with respect to the stiffness, inertial, and damping parameters which define the shaft. Both the adjoint and direct differentiation methods are used to compute the sensitivities. Finite difference sensitivity approximations are also calculated to validate the explicit sensitivity results.

Periodic Steady State Response and Fatigue Analysis of a Nonlinear City Bus Model

2009 ◽  
Author(s):  
George Valsamos ◽  
Christos Theodosiou ◽  
Sotirios Natsiavas
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Nonlinear Models ◽  
Equations Of Motion ◽  
High Stress ◽  
Direct Determination ◽  
Accurate Information ◽  
Steady State Response ◽  
State Response ◽  
Periodic Steady State

Dynamic response related to fatigue prediction of an urban bus is investigated. First, a quite complete model subjected to road excitation is employed in order to extract sufficiently reliable and accurate information in a fast way. The bus model is set up by applying the finite element method, resulting to an excessive number of degrees of freedom. In addition, the bus suspension units involve nonlinear characterstics. A step towards alleviating this difficulty is the application of an appropriate coordinate transformation, causing a drastic reduction in the dimension of the final set of the equations of motion. This allows the application of a systematic numerical methodology leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. Next, typical results were obtained for excitation resulting from selected urban road profiles. These profiles have either a known form or known statistical properties, expressed by an appropriate spatial power spectral density function. In all cases examined, the emphasis was put on investigating ride response. The main attention was focused on identifying areas of the bus suspension and frame subsystems where high stress levels are developed. This information is based on the idea of a nonlinear transfer function and provides the basis for applying suitable criteria in order to perform analyses leading to prediction of fatigue failure.

scholarly journals Dynamic Response of a Thick Piezoelectric Circular Cylindrical Panel: An Exact Solution

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Atta Oveisi ◽  
Mohammad Gudarzi ◽  
Seyyed Mohammad Hasheminejad
Keyword(s):  
Steady State ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Cylindrical Panel ◽  
Mode Shapes ◽  
Steady State Response ◽  
Two Dimensional ◽  
Finite Element Software ◽  
State Response ◽  
Thick Shells

One of the interesting fields that attracted many researchers in recent years is the smart structures. The piezomaterials, because of their ability in converting both mechanical stress and electricity to each other, are very applicable in this field. However, most of the works available used various inexact two-dimensional theories with certain types of simplification, which are inaccurate in some applications such as thick shells while, in some applications due to request of large displacement/stress, thick piezoelectric panel is needed and two-dimensional theories have not enough accuracy. This study investigates the dynamic steady state response and natural frequency of a piezoelectric circular cylindrical panel using exact three-dimensional solutions based on this decomposition technique. In addition, the formulation is written for both simply supported and clamped boundary conditions. Then the natural frequencies, mode shapes, and dynamic steady state response of the piezoelectric circular cylindrical panel in frequency domain are validated with commercial finite element software (ABAQUS) to show the validity of the mathematical formulation and the results will be compared, finally.

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.

Analysis of an Accelerating Rotor-Bearing System With Flexible Damped Supports

1998 ◽  
Author(s):  
Euro L. Casanova ◽  
Luis U. Medina
Keyword(s):  
Steady State ◽  
Numerical Integration ◽  
Equations Of Motion ◽  
Peak Amplitude ◽  
Graphical Form ◽  
Jeffcott Rotor ◽  
Rotor Bearing ◽  
Flexible Supports ◽  
Steady State Predictions ◽  
Bearing System

This paper deals with the dynamics of an accelerating unbalanced Jeffcott rotor-bearing system mounted on damped, flexible supports. The general equations of motion for such a system are presented and discussed. The rotor response was predicted, via numerical integration, for various cases in runup and rundown conditions and presented in graphical form. The effects of acceleration on the rotor peak amplitude and the speed at which the peak occurs is discussed and compared to steady state predictions.

scholarly journals Structural Damage Detection Using Slopes of Longitudinal Vibration Shapes

2015 ◽  
Author(s):  
W. Xu ◽  
W. D. Zhu ◽  
S. A. Smith
Keyword(s):  
Steady State ◽  
Damage Detection ◽  
Structural Damage ◽  
Longitudinal Vibration ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Noise Robustness ◽  
Steady State Response ◽  
Structural Damage Detection ◽  
State Response

While structural damage detection based on flexural vibration shapes, such as mode shapes and steady-state response shapes under harmonic excitation, has been well developed, little attention is paid to that based on longitudinal vibration shapes that also contain damage information. This study originally formulates a slope vibration shape for damage detection in bars using longitudinal vibration shapes. To enhance noise robustness of the method, a slope vibration shape is transformed to a multiscale slope vibration shape in a multiscale domain using wavelet transform, which has explicit physical implication, high damage sensitivity, and noise robustness. These advantages are demonstrated in numerical cases of damaged bars, and results show that multiscale slope vibration shapes can be used for identifying and locating damage in a noisy environment. A three-dimensional (3D) scanning laser vibrometer is used to measure the longitudinal steady-state response shape of an aluminum bar with damage due to reduced cross-sectional dimensions under harmonic excitation, and results show that the method can successfully identify and locate the damage. Slopes of longitudinal vibration shapes are shown to be suitable for damage detection in bars and have potential for applications in noisy environments.

Sign in / Sign up

Export Citation Format

Share Document