Transient Response of Rotor-Bearing Systems

1974 ◽  
Vol 96 (2) ◽  
pp. 682-690 ◽  
Author(s):  
R. G. Kirk ◽  
E. J. Gunter
Keyword(s):  
Transient Response ◽  
Transient Analysis ◽  
Equations Of Motion ◽  
Present System ◽  
Flexible Rotor ◽  
Machine Performance ◽  
Extensive Evaluation ◽  
Rotor Bearing ◽  
Method Of Solution ◽  
Energy Principles

The equations of motion necessary to calculate the transient response of a multimass flexible rotor supported by nonlinear, damped bearings are derived from energy principles. Rotor excitation may be the result of imbalance, internal friction, rotor acceleration, nonlinear forces due to any number of bearing or seal stations, and gyroscopic couples developed from skewed disk effects. The method of solution for transient response simulation is discussed in detail and is based on extensive evaluation of numerical methods available for transient analysis. Examples of the application of transient response for the analysis of rotor bearing systems are presented and compared to actual machine performance. Recommendations for the use and extension of the present system simulation model are discussed.

An FE Transient Response Analysis Model of a Flexible Rotor-Bearing System With Mount System to Base Shock Excitation

2007 ◽  
Author(s):  
An Sung Lee ◽  
Byung Ok Kim
Keyword(s):  
Transient Response ◽  
Transportation Systems ◽  
Integration Scheme ◽  
Response Analysis ◽  
Flexible Rotor ◽  
Analysis Model ◽  
Transient Responses ◽  
Transient Response Analysis ◽  
Rotor Bearing ◽  
Bearing System

Turbomachinery such as turbines, pumps and compressors, which are installed in transportation systems such as warships, submarines and space vehicles, etc., often perform crucial missions and are exposed to potential dangerous impact environments such as base-transferred shock forces. To protect turbomachinery from excessive shock forces, it may be needed to accurately analyze transient responses of rotors, considering the dynamics of mount designs to be applied with. In this study a generalized FE transient response analysis model, introducing relative displacements, is firstly proposed to accurately predict transient responses of a flexible rotor-bearing system with mount systems to base-transferred shock forces. In the transient analyses the state-space Newmark method of a direct time integration scheme is utilized, which is based on the average velocity concept. Results show that for the identical mount systems considered, the proposed FE-based detailed flexible rotor model yields more reduced transient vibration responses to the same shocks than a conventional simple model or a Jeffcott rotor. Hence, in order to design a rotor-bearing system with a more compact light-weighted mount system, preparing against any potential excessive shock, the proposed FE transient response analysis model herein is recommended.

Coupled Lateral and Torsional Nonlinear Transient Solver With Application to Flexible Rotor-Bearing System

2014 ◽  
Author(s):  
Jianming Cao ◽  
Tim Dimond ◽  
Paul Allaire
Keyword(s):  
Rotational Speed ◽  
Equations Of Motion ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Rotor Bearing ◽  
Nonlinear Transient ◽  
Gyroscopic Effects ◽  
Nonlinear Equations Of Motion ◽  
Torsional Analysis ◽  
Bearing System

This paper provides a time transient method for solving coupled lateral and torsional analysis of a flexible rotor-bearing system including gyroscopic effects, nonlinear short journal bearings, nonlinear short squeeze film dampers, and external nonlinear forces/torques. The rotor is modeled as linear, and the supporting components, including bearings and dampers, are modeled as nonlinear. An implicit Runge-Kutta method is developed to solve the nonlinear equations of motion with non-constant operating speed since the unbalance force and the gyroscopic effect are related to both the rotational speed and the acceleration. The developed method is compared with previous torsional analysis first to verify the nonlinear transient solver. Then the coupled lateral and torsional analysis of a flexible 3-disk rotor with nonlinear bearings and nonlinear dampers driven by a synchronous motor is approached. The acceleration effects on lateral and torsional amplitudes is presented in the analysis. The developed method can be used to study the rotor motion with non-constant rotational speed, such as during startup, shutdown, going through critical speeds, blade loss force, or other sudden loading.

Transient Response Analysis of Damped Rotor Systems by the Normal Mode Method

1975 ◽  
Author(s):  
A. J. Dennis ◽  
R. H. Eriksson ◽  
L. H. Seitelman
Keyword(s):  
Steady State ◽  
Normal Mode ◽  
Transient Response ◽  
Transient Analysis ◽  
Equations Of Motion ◽  
Forced Response ◽  
Mode Shapes ◽  
Response Analysis ◽  
Rotor Systems ◽  
Incremental Formulation

A method to determine the transient response of damped single or multi-shaft rotor systems is presented. The rotor systems are idealized as rotating concentrated masses connected by massless beams, discrete springs, and dampers. The springs may have piecewise constant springs rates to simulate the stiffening effect of parts coming in contact after displacement through an initial offset. Arbitrary forcing functions are allowed. The method employs an incremental formulation in which damping gyroscopic and nonlinear terms are treated as external loads which are lagged in time. The equations of motion are uncoupled by performing a normal mode expansion of the response solution in terms of the non-rotating, undamped eigenvectors and their associated eigenvalues; modes and natural frequencies are obtained from a standard Prohl analysis. An analytical solution is used for each step of the incremental analysis. This technique has been used to study the response of a number of rotor systems to the sudden application of a rotating imbalance load. The systems studied include a dual shaft model of a rig, a single-shaft case from the written literature and a large multi-line (multi-shaft) system. The transient analysis was run out to steady-state and close agreement obtained with results from an independent steady-state forced response analysis. Orthogonality relations between the mode shapes were observed to be critical to the quality of the results. It was observed that transient analysis of multi-line systems can be accurately predicted only if the higher frequency modes which are participating in the response are included in the normal mode solution.

Transient Response of a Support Structure Excited by an Accelerating Unbalanced Rotor

1986 ◽  
Vol 53 (2) ◽  
pp. 417-423 ◽  
Author(s):  
F. Ellyin ◽  
Z. Wolanski
Keyword(s):  
Finite Element ◽  
Transient Response ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Graphical Form ◽  
System Response ◽  
Transient Vibration ◽  
Element Discretization ◽  
Unbalanced Rotor ◽  
Method Of Solution

The transient vibration of a beam supporting an unbalanced rotor is investigated using finite element discretization techniques. The rotor speed is time dependent to simulate transients at startup. The beam is low-tuned relative to the rotor operating speed. A rigid rotor shaft mounted in an oil-film bearing is considered. The “short-bearing” approximation and nonlinear performance of the journal bearing are assumed. The method of solution for transient response is based on direct integration of the system equations of motion using finite element in time formulation. The results of numerical anlaysis are presented in graphical form and discussed. One notes significant effects of the journal bearing on the system response.

On the Transient Analysis of Rotor-Bearing Systems

1988 ◽  
Vol 110 (4) ◽  
pp. 515-520 ◽  
Author(s):  
R. Subbiah ◽  
N. F. Rieger
Keyword(s):  
Dynamic Systems ◽  
Transient Analysis ◽  
Element Model ◽  
Flexible Rotor ◽  
Rotor Systems ◽  
Response Data ◽  
Rotor Bearing ◽  
Time Marching ◽  
The Stability ◽  
The Given

The transient dynamic response of a flexible rotor in nonlinear supports has been investigated using time marching methods. Several marching techniques such as Newmark β, Wilson θ, and Houbolt have been utilized in this study of rotor-bearing dynamic systems, to examine the stability of the system, and the suitability of each technique for predicting the onset of instability. The given rotor system has been modeled both in space and time using the transfer matrix method and the Houbolt method. The transient orbital response data so obtained have been compared with those obtained by a finite element model. Differences in the order of 6 percent were found. A nonlinear representation of a finite bearing has been included in the transient matrix model and the stability characteristics of different rotor systems of varied complexity have been studied. The nonlinear results have been compared with earlier results obtained using linear bearing representations.

A Successive Merging and Condensation (SMAC) Method Applied to Transient Analysis of Multi-Shaft Rotor System

1993 ◽  
Author(s):  
Santosh Ratan ◽  
Jorge Rodriguez
Keyword(s):  
Transient Response ◽  
Transient Analysis ◽  
Rotor System ◽  
Time Step ◽  
Transient Dynamic Analysis ◽  
Numerical Examples ◽  
Linear Coupling ◽  
Rotor Systems ◽  
Coupling Constraints ◽  
Smac Method

Abstract A method for performing transient dynamic analysis of multi-shaft rotor system is proposed. The proposed methodology uses the reported Successive Merge and Condensation (SMAC) method [12] and a decoupling technique to decouple the shafts. Multi-shaft rotor systems are treated as systems of many independent single shaft rotor systems with external unknown coupling forces acting at the points of couplings. For each time step, first, the SMAC method is used to get the transient response in terms of the unknown coupling forces. This is followed by the application of the coupling constraints to calculate the coupling forces and, in turn, the response at the end of that time step. The proposed method preserves the efficiency advantages of the SMAC algorithm for single-shaft rotor system. Numerical examples to validate and illustrate the applicability of the method are given. The method is shown to be applicable to linear and non-linear coupling problems.

Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part I: Analytical Bearing Model

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Mohammad Miraskari ◽  
Farzad Hemmati ◽  
Mohamed S. Gadala
Keyword(s):  
Journal Bearing ◽  
Nonlinear Coefficient ◽  
Journal Bearings ◽  
Flexible Rotor ◽  
Dynamic Coefficients ◽  
Flexible Rotors ◽  
Rotor Bearing ◽  
Bearing Force ◽  
Derivatives Of ◽  
Bearing System

To determine the bifurcation types in a rotor-bearing system, it is required to find higher order derivatives of the bearing forces with respect to journal velocity and position. As closed-form expressions for journal bearing force are not generally available, Hopf bifurcation studies of rotor-bearing systems have been limited to simple geometries and cavitation models. To solve this problem, an alternative nonlinear coefficient-based method for representing the bearing force is presented in this study. A flexible rotor-bearing system is presented for which bearing force is modeled with linear and nonlinear dynamic coefficients. The proposed nonlinear coefficient-based model was found to be successful in predicting the bifurcation types of the system as well as predicting the system dynamics and trajectories at spin speeds below and above the threshold speed of instability.

Updating Rotor-Bearing Finite Element Models

1997 ◽  
Author(s):  
Cristinel Mares ◽  
Cecilia Surace
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Parameters Estimation ◽  
Flexible Rotor ◽  
Estimation Errors ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Measured Frequency Response ◽  
Stiffness And Damping ◽  
The Finite Element Model

Abstract In this paper, the possibility of updating the finite element model of a rotor-bearing system by estimating the bearing stiffness and damping coefficients from a few measured Frequency Response Functions using a Genetic Algorithm is investigated. The issues of identifiability and parameters estimation errors, computational costs and algorithm tuning are addressed. A simulated example of a flexible rotor supported by orthotropic bearings is used for illustrating the method.

scholarly journals Transient Response Technique Applied to Active Magnetic Bearing Machinery During Rotor Drop

1996 ◽  
Vol 118 (2) ◽  
pp. 154-163 ◽  
Author(s):  
T. Ishii ◽  
R. Gordon Kirk
Keyword(s):  
Transient Response ◽  
New Technology ◽  
Contact Point ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Flexible Rotor ◽  
Theoretical Formulation ◽  
Rolling Element ◽  
Bearing Design ◽  
Amb System

The active magnetic bearing (AMB) is a relatively new technology which has many advantages compared with conventional bearing design. In an AMB system, the rolling-element back-up bearings are indispensable to protect the magnetic bearing rotor and stator, and other stationary seals along the rotor shaft. In this paper, a theoretical formulation is proposed and solved numerically to examine the transient response of the flexible rotor, from the time just previous to when the AMB shuts down and including the rotor drop onto the back-up bearing. The backward whirl of the rotor, which may lead to the destructive damage of the machinery, has been analytically predicted at very light support damping and very high support damping. Also, the vibration due to the nonlinearity of the contact point geometry has been included in the analysis. The influence of the support damping on the displacement of the disk and also the contact force between the journal and the inner-race of the back-up bearing have been computed for various rotor system parameters. By comparing these results with the optimum support damping for the simple flexible rotor model, it is shown that this support damping optimization can be applicable for specifying the required optimum range of support damping for the back-up bearings of AMB systems.

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