Reducing Lateral Vibrations of a Rotor Passing Through Critical Speeds by Acceleration Scheduling

A method is presented for reducing the lateral response of an imbalanced rotor accelerating or decelerating through its first lateral bending critical speed by using a variable acceleration rate. A lumped parameter model along with a numerical integration scheme is used to simulate the response of a simply supported, single disk rotor during fast acceleration and deceleration through critical speed. The results indicate that the maximum response and/or the total vibrational energy of a rotor passing through the critical speed can be reduced significantly by using a variable acceleration schedule. That is, reducing the acceleration rate after the nominal critical speed is passed. These predictions were verified experimentally for a single disk rotor.

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A Critical Examination of the Hysteresis in Wells Turbines Using CFD and Lumped Parameter Models

Volume 10: Ocean Renewable Energy ◽

10.1115/omae2019-96518 ◽

2019 ◽

Author(s):

T. Ghisu ◽

F. Cambuli ◽

P. Puddu ◽

I. Virdis ◽

M. Carta ◽

...

Keyword(s):

Turbine Blades ◽

Unsteady Aerodynamics ◽

Lumped Parameter Model ◽

Hysteretic Behavior ◽

Critical Examination ◽

Wells Turbine ◽

Lumped Parameter ◽

Lumped Parameter Models ◽

Acceleration And Deceleration ◽

The Common

Abstract The hysteretic behavior of OWC-installed Wells turbines has been known for decades. The common explanation invokes the presence of unsteady aerodynamics due to the continuously varying incidence of the flow on the turbine blades. This phenomenon is neither new nor unique to Wells turbines, as an aerodynamic hysteresis is present in rapidly oscillating airfoils and wings, as well as in different types of turbomachinery, such as wind turbines and helicopter rotors, which share significant similarities with a Wells turbine. An important difference is the non-dimensional frequency: the hysteresis appears in oscillating airfoils only at frequencies orders of magnitude larger than the ones Wells turbines operate at. This work contains a reexamination of the phenomenon, using both CFD and a lumped parameter model, and shows how the aerodynamic hysteresis in Wells turbines is negligible, and how the often measured differences in performance between acceleration and deceleration are caused by the capacitive behavior of the OWC system.

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The Mechanism on Prediction of Transient Maximum Amplitude for Tuned and Mistuned Blisks

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4046761 ◽

2020 ◽

Vol 142 (5) ◽

Author(s):

Luohui Ouyang ◽

Hai Shang ◽

Hua Chen ◽

Qingzhen Bi ◽

Li-Min Zhu

Keyword(s):

Damping Ratio ◽

Maximum Amplitude ◽

Element Model ◽

Forced Response ◽

Lumped Parameter Model ◽

Fundamental Parameter ◽

Reduced Order ◽

Lumped Parameter ◽

Engine Order ◽

Acceleration And Deceleration

Abstract Blisks are subjected to frequent acceleration and deceleration, which leads to a transient forced response; however, there is limited understanding of this response. In this work, the mechanism on prediction of transient maximum amplitude is found. An analytical link is proposed between the transient maximum amplitude and a fundamental dimensionless parameter which combines the damping ratio, natural frequency, acceleration, and engine order of the system to reveal the mechanism of the transient maximum amplitude. Therefore, the transient maximum amplitudes of tuned and mistuned blisks are predicted analytically. First, a lumped parameter model is used to study the mechanism of the transient maximum amplitude for a tuned blisk, and an approximated analytical expression is derived between the fundamental parameter and the transient amplification factor of a 1DOF (degree-of-freedom) model. The relationship is also applicable to a reduced order, tuned finite element model (FEM). Second, the mechanism of the transient response for a mistuned blisk is studied in the decoupled modal space of the blisk, based on the 1DOF transient relationship. The transient maximum amplitude in a reduced order, mistuned FEM is predicted. Two lumped parameter models and a FEM are employed to validate the prediction.

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A Study of Shaft Vibration Based on Transfer Matrix

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.365-366.339 ◽

2013 ◽

Vol 365-366 ◽

pp. 339-343

Author(s):

Chang Tan ◽

Zhi Ling Guo ◽

Rui Kun Zhou

Keyword(s):

Numerical Simulation ◽

Transfer Matrix ◽

Critical Speed ◽

Lumped Parameter Model ◽

Lumped Parameter ◽

The Common ◽

Shaft Vibration ◽

Set Up

This paper first analyze the method of transfer matrix, set up the lumped parameter model. then figure out the common transfer matrix of shaft. Take some shaft as an example, using matlab calculate the critical speed and analyze the result. The analysis can provide basis and method for shaft vibration numerical simulation.

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Modeling and Control of Coupled Torsional and Lateral Vibrations in Drill Strings

Volume 2: Diagnostics and Detection; Drilling; Dynamics and Control of Wind Energy Systems; Energy Harvesting; Estimation and Identification; Flexible and Smart Structure Control; Fuels Cells/Energy Storage; Human Robot Interaction; HVAC Building Energy Management; Industrial Applications; Intelligent Transportation Systems; Manufacturing; Mechatronics; Modelling and Validation; Motion and Vibration Control Applications ◽

10.1115/dscc2015-9714 ◽

2015 ◽

Cited By ~ 1

Author(s):

Liu Hong ◽

Jaspreet Singh Dhupia

Keyword(s):

Sliding Mode ◽

Good Control ◽

Friction Torque ◽

Lumped Parameter Model ◽

Oil Well ◽

Lateral Instability ◽

Stick Slip ◽

Rock Interaction ◽

Lateral Vibrations ◽

Lumped Parameter

Excessive vibrations of the drill strings, e.g., the stick-slip vibration, are the primary cause of premature failures and drilling inefficiencies in oil well drilling. To investigate and suppress such vibrations, this paper studies the dynamics of drill strings using a lumped parameter model, in which both the torsional stick-slip and lateral vibrations are taken into consideration. The friction torque due to the downhole bit-rock interaction, which plays a key role in stick-slip vibration, is modeled as a hysteretic dry friction function. Simulated results of this developed model are shown to have a close qualitative agreement with the field observations in terms of stick-slip vibrations. Afterwards, a sliding mode controller is applied to mitigate the undesired vibrations of drill strings. A good control performance in suppressing the stick-slip phenomenon is demonstrated for the proposed controller. However, numerical simulations also demonstrate that the control action can excite lateral instability in the system, which can result in impacts between the drill collars and the borehole wall due to the large amplitude in lateral vibrations. Thus, a proper choice of the control parameters is essential to suppress the vibrations in the drill strings. The developed lumped parameter model describing the coupled torsional and lateral response in the controlled drill strings presented in this paper can be used to aid in offline tuning of those control variables.

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Numerical Study of Forward and Backward Whirling of Drill-String

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4037318 ◽

2017 ◽

Vol 12 (6) ◽

Cited By ~ 9

Author(s):

Marcin Kapitaniak ◽

Vahid Vaziri ◽

Joseph Páez Chávez ◽

Marian Wiercigroch

Keyword(s):

Chaotic Behavior ◽

Initial Conditions ◽

Numerical Study ◽

Experimental Studies ◽

Drill String ◽

Lumped Parameter Model ◽

Drilling Rig ◽

Lateral Vibrations ◽

Lumped Parameter ◽

Theoretical Predictions

This work presents a numerical investigation of the undesired lateral vibrations (whirling) occurring in drill-strings, which is one of the main sources of losses in drilling applications. The numerical studies are conducted using a nonsmooth lumped parameter model, which has been calibrated based on a realistic experimental drilling rig. The numerical investigations are focused on identifying different types of whirling responses, including periodic and chaotic behavior, which have been previously observed experimentally. As a result, the parameter space is divided into different regions showing dynamically relevant responses of the model, with special interest on the influence of the mass and angular velocity of the drill-string system. In particular, the study reveals the coexistence of various types of whirling motion for a given set of parameters and their sensitivity to initial conditions. The obtained theoretical predictions confirm previous experimental studies carried out by the authors, which provides a solid basis for a better understanding of whirling phenomena in drill-string applications.

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Modeling of Spur and Helical Gear Planetary Drives With Flexible Ring Gears and Planet Carriers

Journal of Mechanical Design ◽

10.1115/1.2359468 ◽

2006 ◽

Vol 129 (1) ◽

pp. 95-106 ◽

Cited By ~ 47

Author(s):

V. Abousleiman ◽

P. Velex ◽

S. Becquerelle

Keyword(s):

Equations Of Motion ◽

Three Dimensional ◽

Lumped Parameter Model ◽

Integration Scheme ◽

Ring Gear ◽

Time Step ◽

Contact Algorithm ◽

Lumped Parameter ◽

Epicyclic Gear ◽

Internal Gear

A model is presented which enables the simulation of the three-dimensional static and dynamic behavior of planetary/epicyclic spur and helical gears with deformable parts. The contributions of the deflections of the ring gear and the carrier are introduced via substructures derived from 3D finite element models. Based on a modal condensation technique, internal gear elements are defined by connecting the ring-gear substructure and a planet lumped parameter model via elastic foundations which account for tooth contacts. Discrete mesh stiffness and equivalent normal deviations are introduced along the contact lines, and their values are recalculated as the mating flank positions vary with time. A constraint mode substructuring technique is used to simulate the planet carrier as a superelement which is connected to the planet center. Planetary/epicyclic gear models are completed by assembling lumped parameter sun gear/planet elements along with shaft elements, lumped stiffness, masses and inertias. The corresponding equations of motion are solved by combining a time-step integration scheme and a contact algorithm for all simultaneous meshes. Several quasistatic and dynamic results are given which illustrate the potential of the proposed hybrid model and the interest of taking into account ring gear and carrier deflections.

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