Dynamic Response Analysis of Rotor-Bearing Systems With Cracked Shaft

2002 ◽  
Vol 124 (4) ◽  
pp. 690-696 ◽  
Author(s):  
M. A. Mohiuddin ◽  
Y. A. Khulief
Keyword(s):  
Large Scale ◽  
Crack Detection ◽  
Equations Of Motion ◽  
Response Analysis ◽  
Reduced Order ◽  
Stepped Shaft ◽  
Rotor Bearing ◽  
Element Approach ◽  
Detection Schemes ◽  
Cracked Shaft

A general dynamic model for a large-scale rotor-bearing system with a cracked shaft is introduced. A finite shaft element with a crack is developed using a consistent finite element approach. The model accommodates shafts with tapered portions, multiple disks and anisotropic bearings. The formulation is applicable to rotor-bearing systems with different practical design configurations including intermediate bearings, shaft overhang, and stepped shaft assemblies. A reduced order form of equations of motion is obtained by invoking the actual non-planar (complex) modal transformations. The time-response due to different excitations are calculated, and comparisons are presented to establish the validity and efficiency of the reduced order model. It is hoped that the developed computational scheme offers an efficient and essential core module in establishing other specialized crack detection schemes for rotor-bearing systems.

The Motion Formalism for Flexible Multibody Systems

2021 ◽  
Author(s):  
Olivier Bauchau ◽  
Valentin Sonneville
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Solution Process ◽  
Flexible Multibody Systems ◽  
Structural Elements ◽  
Governing Equations ◽  
Euclidean Group ◽  
Reduced Order ◽  
Flexible Multibody ◽  
Element Approach

Abstract This paper describes a finite element approach to the analysis of flexible multibody systems. It is based on the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) recognizes that these are members of the Special Euclidean group thereby coupling their displacement and rotation components, and (3) resolves all tensors components in local frames. The goal of this review paper is not to provide an in-depth derivation of all the elements found in typical multibody codes but rather to demonstrate how the motion formalism (1) provides a theoretical framework that unifies the formulation of all structural elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, and (4) prevents the occurrence of singularities.

Detection of Cracks in Mistuned Bladed Disks Using Reduced-Order Models and Vibration Data

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced-order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the uncracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reduced-order) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

Response Analysis of a General Asymmetric Rotor-Bearing System

1980 ◽  
Vol 102 (1) ◽  
pp. 147-157 ◽  
Author(s):  
T. Inagaki ◽  
H. Kanki ◽  
K. Shiraki
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Field Measurements ◽  
Transverse Mass ◽  
Response Analysis ◽  
Mass Moment ◽  
Rotor Bearing ◽  
Asymmetric Rotor ◽  
Bearing System

This paper presents an analytical method for the evaluation of the synchronous response of a general asymmetric rotor-bearing system. In the analysis, slightly asymmetric shaft stiffness in bending and shearing, which distribute along the rotor, and asymmetric transverse mass moment of inertia are considered. The dynamic properties of bearings and pedestals are assumed to be anisotropic and coupled in each direction. The equations of motion with periodic time dependent coefficients are solved by the Harmonic Balance Method and formulated to the transfer matrix. These solutions include the “Modified Holzer-Myklestad-Prohl Method by Lund & Orcutt” as a special case. The results of the analysis are confirmed by a simple model test and field measurements of large turbosets.

Detection of Cracks in Mistuned Bladed Disks Using Reduced Order Models and Vibration Data

2011 ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the un-cracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reducedorder) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated, and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

Coupled Lateral and Torsional Vibrations of a Cracked Rotor

2004 ◽  
Author(s):  
Jerzy T. Sawicki ◽  
George Y. Baaklini ◽  
Andrew L. Gyekenyesi
Keyword(s):  
Crack Detection ◽  
Vibration Spectrum ◽  
Equations Of Motion ◽  
Structural Response ◽  
Crack Model ◽  
Cracked Rotor ◽  
Lateral Vibrations ◽  
Crack Problems ◽  
Torsional Excitation ◽  
Cracked Shaft

Rotor crack problems present a significant safety and loss hazard in nearly every application of modern turbomachinery, particularly in the power generation industry. However, early crack detection is not easily achieved during the operation of machinery. The difficulty is based on the fact that a crack produces an undetectable change in the overall structural response. This paper analyzes the coupling of torsional and lateral vibrations for an unbalanced cracked rotor. The rotor equations of motion for a system with cracked shaft, obtained using Lagrangian dynamics, show coupling and nonlinear interaction between the torsional and lateral vibrations. To investigate the effect of a transverse surface crack on the dynamic rotor response the breathing crack model was employed. By applying an external torsional excitation together with the excitation due to unbalance, signature responses were observed in the rotor vibration spectrum at sum and difference frequencies. These signature responses were due to the nonlinear effect of the crack. The observed phenomena, analytically defined here, offers a new methodology concerning crack detection and prognosis in rotors.

Dynamic Analysis of Multibody Rotor-Bearing System

1997 ◽  
Author(s):  
M. A. Mohiuddin ◽  
Y. A. Khulief
Keyword(s):  
Large Scale ◽  
Shear Stiffness ◽  
Dynamic Responses ◽  
Torsional Stiffness ◽  
Reduced Order Models ◽  
The Finite Element Method ◽  
Reduced Order ◽  
Rotor Bearing ◽  
Gyroscopic Effects ◽  
Bearing System

Abstract A multibody formulation of a rotor-bearing system of interconnected flexible and rigid components is presented. The elastic shaft is modelled by the finite element method where shear stiffness, torsional stiffness and the gyroscopic effects are considered. An application to a large-scale rotor-bearing system is presented. Complex modal transformations were invoked to obtain a reduced-order dynamic model. The dynamic responses due step and impulse excitations were obtained using both the full-order and the reduced-order models. Comparisons are presented to verify the validity and accuracy of the reduced-order modal form.

Online condition monitoring for detection of crack in the shaft using vibration analysis method

2018 ◽  
Vol 70 (7) ◽  
pp. 1193-1200 ◽  
Author(s):  
Bhumi Ankit Shah ◽  
Dipak P. Vakharia
Keyword(s):  
Vibration Analysis ◽  
High Speed ◽  
Crack Detection ◽  
Transverse Crack ◽  
Second Harmonic ◽  
Harmonic Component ◽  
Reverse Direction ◽  
Response Analysis ◽  
Content Type ◽  
Cracked Shaft

Purpose The purpose of this study is to identify the crack in the shaft at incipient stage. Transverse crack is the most common type of crack found on the periphery of the shaft. The changes in dynamic behaviour of the rotor at high speed are enormous. The reliable operation of the machinery is paramount for the safety of individual and plant. Condition-based maintenance monitors the mechanical and operational condition of the machine. During such inspection, if any unhealthy symptoms are detected, then affected part is identified and taken out for the maintenance at most appropriate time. Design/methodology/approach Simulating the transverse crack of different depth and location is the most challenging part of the experimental analysis. To optimize the total experimental cost for simulation of crack in the shaft, inverted crack is proposed to be produced in shaft and investigation shall be carried out for of early crack detection in shaft using vibration analysis. The set of experiments has been conducted on healthy shaft, inverted cracked shaft and actual cracked shaft. Inverted crack methodology provides flexibility of simulating crack of any size and at any location, and it can be reconfigured for several times to obtain various set of results. Findings To derive objective of the study, steady state response analysis and transient response analysis are performed on the experiment test rig. Vibration signals are acquired from the bearing locations to detect the crack. The paper addresses the influence of the inverted crack on critical speed of the shaft and deviation of first and second harmonic component of the shaft because of introduction of inverted crack. The resultant Nyquist plots, orbit plots and frequency plots are compared with the baseline data (obtained with the healthy shaft) to identify the crack. Originality/value The present study focuses on methodology by which inverted crack is developed in the healthy shaft, which resembles the behaviour of actual crack, and it shall be used to study the changes in rotor stiffness caused by transverse crack. The experimental results obtained using the inverted crack shaft have same vibration characteristics but in reverse direction as it would have occurred with the cracked shaft.

Maximum Unbalance Responses of a Gear-Coupled Two-Shaft Rotor-Bearing System

2003 ◽  
Author(s):  
An Sung Lee ◽  
Jin Woong Ha
Keyword(s):  
Analytical Solutions ◽  
Numerical Approach ◽  
Turbine Engines ◽  
Response Analysis ◽  
Gas Turbine Engines ◽  
Unbalance Response ◽  
Rotor Bearing ◽  
Element Approach ◽  
Bearing System ◽  
General Method

A general method is presented for obtaining the unbalance response orbit of a gear-coupled two-shaft rotor-bearing system, based on the finite element approach. Specifically, analytical solutions of the maximum and minimum radii of the orbit are proposed. The method has been applied to the unbalance response analysis of a 600 kW turbo-chiller rotor-bearing system, having a bull-pinion speed increasing gear. Bumps in the unbalance responses have been observed at the first torsional natural frequency because of the coupling between the lateral and torsional dynamics due to gear meshing. In addition, the analytical solutions have been validated with results obtained by a full numerical approach. The proposed method can be generally applied to an analysis of the unbalance response orbits of dual-shaft rotor-bearing systems coupled by bearings as well, which are often found in aerospace gas turbine engines.

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