Rotor Vibration under the Coupled Effects of Mass Unbalance and Asymmetric Bearings

2016 ◽  
Vol 846 ◽  
pp. 199-204 ◽  
Author(s):  
Joseph Patrick Spagnol ◽  
Helen Wu
Keyword(s):  
Critical Speed ◽  
High Energy ◽  
Damping Matrix ◽  
Mass Unbalance ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Stiffness And Damping Coefficient ◽  
Early Fault Detection ◽  
Stiffness And Damping ◽  
Rotor Dynamic

Large unbalance in rotor-dynamic systems is typically responsible for high energy vibrations and the consequent decrease in machine life. This paper presents an analytical model developed using Lagrangian mechanics and partial differential equations (PDEs) for the purpose of early fault-detection in rotor-bearing systems. The model was validated through a Fortran based program, RDA99 developed by Adams (2010), by successfully quantifying the single-peak unbalance response of the simple 8 DOF and 12 DOF rotor-bearing mass stations over two cases. Case I uses bearings with symmetric stiffness and damping matrix. The critical speed for Case I occurred at 1690 rpm and orbital shapes of each mass station was found to be circular with forward-whirl orbits. In Case II asymmetrical bearing stiffness and damping coefficient matrices demonstrate an anisotropic system. Critical speed occurred at 1655 rpm and rotor, bearing and pedestal orbits were seen to be elliptical and changing with shaft speed. Both cases demonstrated a significant shaft bending contribution to the disk displacement.

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 Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

2021 ◽  
Author(s):  
T. A. El-Sayed ◽  
Hussein Sayed
Keyword(s):  
Equations Of Motion ◽  
Journal Bearings ◽  
Third Order ◽  
Damping Coefficients ◽  
The Third ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Rotor Stiffness ◽  
Stiffness And Damping ◽  
Bearing System

AbstractHydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they are susceptible to oil whirl instability, which may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical journal bearings is used to investigate the stability and bifurcations of rotor bearing system. Since a closed form for the finite bearing forces is not exist, nonlinear bearing stiffness and damping coefficients are used to represent the bearing forces. The bearing forces are approximated to the third order using Taylor expansion, and infinitesimal perturbation method is used to evaluate the nonlinear bearing coefficients. The mesh sensitivity on the bearing coefficients is investigated. Then, the equations of motion based on bearing coefficients are used to investigate the dynamics and stability of the rotor-bearing system. The effect of rotor stiffness ratio and applied load on the Hopf bifurcation stability and limit cycle continuation of the system are investigated. The results of this work show that evaluating the bearing forces using Taylor’s expansion up to the third-order bearing coefficients can be used to profoundly investigate the rich dynamics of rotor-bearing systems.

Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part II: Effect of Tilt-Pad Bearings and Foundation Dynamics

1987 ◽  
Vol 109 (1) ◽  
pp. 8-14 ◽  
Author(s):  
J. M. Vance ◽  
B. T. Murphy ◽  
H. A. Tripp
Keyword(s):  
Critical Speed ◽  
Natural Frequencies ◽  
State Of The Art ◽  
Dynamic Properties ◽  
Experimental Measurements ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Speed Prediction ◽  
Bearing Stiffness ◽  
Stiffness And Damping

This is the second of two papers describing results of a research project directed at verifying computer programs used to calculate critical speeds of turbomachinery. This part describes measurements made to determine the characteristics of tilt-pad bearings and foundation dynamics. Critical speeds of a 166 kg laboratory rotor on tilt-pad bearings are then compared with predictions from a state-of-the-art damped eigenvalue computer program. Measured natural frequencies of a steam turbine are also compared with computer predictions. Accuracy of critical speed prediction is shown to depend on accuracy of 1) the “free-free” rotor models, 2) the bearing stiffness and damping coefficients, and 3) the dynamic properties of the foundation, which can be represented by an impedance that must be determined by experimental measurements.

Turbomachinery Dual Rotor-Bearing System Analysis

2002 ◽  
Author(s):  
Hsiao-Wei D. Chiang ◽  
Chih-Neng Hsu ◽  
Wes Jeng ◽  
Shun-Hsu Tu ◽  
Wei-Chen Li
Keyword(s):  
Finite Element ◽  
Transfer Matrix ◽  
Critical Speed ◽  
System Analysis ◽  
Design Parameters ◽  
Critical Speeds ◽  
Rotor Design ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Bearing System

It is very common for aircraft engines to have dual rotor or even triple rotor designs. Due to the complexity of having multiple rotor design, the transfer matrix methods have used in the past to deal with multiple rotor-bearing systems. However, due to transfer matrix method’s assumptions, sometimes resulted in numerical stability problems or root-missing problems. The purpose of this paper is to develop a systematic theoretical analysis of the dynamic characteristics of turbomachinery dual rotor-bearing systems. This dual rotor-bearing system analysis will start with a finite element (FEM) rotor-bearing system dynamic model, then using different methods to verify the analysis results including critical speed map and bearing stiffness. In an inertia coordinate system, a general model of continuous dual rotor-bearing systems is established based on a lagrangian formulation. Gyroscopic moment, rotary inertia, bending and shear deformations have been included in the model. From a point of view of the systematic approach, a solution of the finite element method is used to calculate the critical speeds by several different methods, which in turn can help to verify this dual rotor-bearing system approach. The effects of the speed ratio of dual rotors on the critical speed will be studied, which in turn can be used as one of the dual rotor design parameters. Also, both critical speeds are in effect functions of dual rotor speeds. Finally, the bearing stiffness between high speed and low speed shafts not only affect the critical speeds of the dual rotor system, but also affect the mode shapes of the system. Therefore, the bearing stiffness in between is of even greater importance in turbomachinery dual rotor or multiple rotor design.

Based on One-Dimensional Model to Calculate the Critical Speed

2012 ◽  
Vol 203 ◽  
pp. 427-431
Author(s):  
Jun Feng Wang ◽  
Kang Sun
Keyword(s):  
Critical Speed ◽  
Early Stage ◽  
Reference Value ◽  
Dimensional Model ◽  
Lumped Mass ◽  
One Dimensional ◽  
Rotor Bearing ◽  
Continuous Mass ◽  
Stiffness And Damping ◽  
Bearing System

Use the simple geometric features of a one-dimensional model to calculate the rotor critical speed, the shaft use the beam element to simulate, considering the shear deformation, continuous mass, the rotation inertia and gyro effect, bearing simplified as linear stiffness and damping element, disc use the lumped mass element to simulate, considering the mass and the effect of inertia, finite element method is applied, established the rotor-bearing system dynamics model, through the example to validate, the results show that the model is the advantage of calculation on a smaller scale, solution speed and high precision, easy to adjust the parameters for the model, suitable for large needs to adjust the parameters in the early stage of design and analysis of the rotor-bearing system, it has great reference value for the design and analysis of rotor dynamics.

The Effect of Cavitation on the Vibration Behaviour of Nonlinear Rotor Bearing Systems

2006 ◽  
Author(s):  
Duc Pham ◽  
Ningsheng Feng ◽  
Eric Hahn
Keyword(s):  
Dynamic Properties ◽  
Fluid Film ◽  
Stable Operation ◽  
Rotor Bearing ◽  
Reaction Forces ◽  
Bearing Stiffness ◽  
Operation Stability ◽  
Bearing Force ◽  
Air Ingress ◽  
Stiffness And Damping

Rotor bearing systems frequently utilise hydrodynamic bearings whose dynamic properties are generally influenced by the bearing reaction forces (which determine the bearing stiffness and damping coefficients). These reaction forces are frequently unknown and are generally determined from the solution of the Reynolds equation using rotor motion measurements as input. Of interest is the attainable accuracy of such bearing force determinations, and for experimental evaluation, a test rig was fabricated, the design specification of which required that the rotor system run stably over its operating speed range. This paper describes the commissioning of this rig for stability purposes with the aid of natural frequency analyses, noting the required design modifications to ensure stable operation. Stability was found to be significantly influenced by the extent of the continuous fluid film in the hydrodynamic circumferentially grooved bearings. It was concluded that the assumption of a 180 degree film extent was totally inappropriate even though the bearing ends were open to the atmosphere, whereas the assumption of fluid film break up at the lubricant saturation vapour pressure proved appropriate for stability predictions provided one ensured that the bearings were flooded. Preliminary bearing force evaluations proved inconclusive, primarily because the self aligning bearings nevertheless experienced angular misalignment; and because there was uncertainty as to how much air was entrained in the bearings, in spite of attempts to prevent air ingress.

Finite Element and Modal Analyses of Rotor-Bearing Systems Under Stochastic Loading Conditions

1984 ◽  
Vol 106 (1) ◽  
pp. 80-89 ◽  
Author(s):  
E. Hashish ◽  
T. S. Sankar
Keyword(s):  
Finite Element ◽  
Simple Procedure ◽  
Stochastic Loading ◽  
Rotor Bearing ◽  
Random Disturbances ◽  
Element Technique ◽  
Stiffness And Damping ◽  
The Mathematical Model ◽  
Rotor Dynamic ◽  
Spatial Support

A flexible rotor bearing system is represented in detail utilizing the state of the art finite element technique. The mathematical model takes into account the gyroscopic moments, rotary inertia, shear deformation, internal viscous damping, hysteretic damping, linear as well as nonlinear stiffness, and damping for the finite bearing and the bearing support flexibility. Using a simple Timoshenko element and recognizing an analogy between the motion planes, a procedure is given that requires a construction of only three symmetric 4×4 matrices. As an application, the different effects of the bearing lining flexibility and the bearing support flexibility on the rotor stability behavior is studied and discussed. The necessary relation for general modal analysis is simply restated and integrated into the conventional spectral approach, thus developing a simple procedure for the calculation of the stochastic response of a general rotor dynamic system. An application to a light rotor bearing featuring a general spatial support and subjected to random disturbances is illustrated.

A Microturbine Rotor-Bearing System Analysis

2002 ◽  
Author(s):  
Hsiao-Wei D. Chiang ◽  
Chih-Neng Hsu ◽  
Wes Jeng ◽  
Shun-Hsu Tu ◽  
Wei-Chen Li
Keyword(s):  
Finite Element ◽  
Critical Speed ◽  
System Analysis ◽  
Modal Testing ◽  
System Dynamic Model ◽  
Fem Model ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Bearing System ◽  
Engine Life

A microturbine of 12-pound thrust was developed for the Unmanned Aerial Vehicle (UAV) applications. Recent tests of the microturbines reveal problems associated with rear ball bearing integrity after extended run times. The microturbine rotor design originally calls for a critical speed margin of at least 15∼20% to prevent excessive vibrations. However, the microturbine was using an existing turbocharger rotor component with unknown margins. Therefore, the purpose of this paper is to perform both theoretical and experimental analyses of the dynamic characteristics of the 12-pound thrust microturbine rotor-bearing system. This rotor-bearing system analyses will start with a finite element (FEM) rotor-bearing system dynamic model, then using modal testing and dynamic engine test to verify the analysis results including critical speed map and bearing stiffness. In this paper, the rotor-bearing system dynamic model will be established under an inertia coordinate system. Through finite element method, this model can be used to predict natural frequencies, critical speed map, and bearing stiffness. Also, under free-free condition, a modal testing will be performed, and its results are used to compare with the FEM model. Then the gyroscopic moment effects are included in the FEM model to calculate the critical speed map. Finally the critical speed map is used to compare with the results of the dynamic experiments of the 12-pound thrust microturbine engine and the bearing stiffness is estimated through an optimization approach. Examination of the microturbine engine and recent product developments indicate that thrust performance and engine life goals can be improved to upgrade the present design. With the rotor-bearing system analysis, the goal of increasing the current engine life and improved performance is sought as a practical goal for the microturbine design.

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