Test Response and Nonlinear Analysis of a Turbocharger Supported on Floating Ring Bearings

2005 ◽  
Vol 127 (2) ◽  
pp. 107-115 ◽  
Author(s):  
Chris Holt ◽  
Luis San Andre´s ◽  
Sunil Sahay ◽  
Peter Tang ◽  
Gerry La Rue ◽  
...  
Keyword(s):  
Nonlinear Analysis ◽  
Equations Of Motion ◽  
Forced Response ◽  
Experimental Results ◽  
Rotor Speed ◽  
Rotor Imbalance ◽  
Feed Pressure ◽  
Nonlinear Responses ◽  
Reaction Forces ◽  
Bearing Force

Measurements of casing acceleration on an automotive turbocharger running to a top speed of 115 krpm and driven by ambient temperature pressurized air are reported. Waterfall acceleration spectra versus rotor speed show the effects of increasing lubricant inlet pressure and temperature on turbocharger rotordynamic response. A comprehensive analysis of the test data shows regimes of speed operation with two subsynchronous whirl motions (rotordynamic instabilities). Increasing the lubricant feed pressure delays the onset speed of instability for the most severe subsynchronous motion. However, increasing the lubricant feed pressure also produces larger synchronous displacements. The effect of lubricant feed temperature is minimal on the onset and end speeds of rotordynamic instability. Nevertheless, operation with a cold lubricant exhibits lower amplitudes of motion, synchronous and subsynchronous. The experimental results show the subsynchronous frequencies of motion do not lock (whip) at system natural frequencies but continuously track the rotor speed. No instabilities (subsynchronous whirl) remain for operating speeds above 90 krpm. Linear and nonlinear analysis results for the operation of a small automotive turbocharger supported on floating ring bearings are presented. A comprehensive fluid film bearing model predicting the forced response of floating ring bearings is also described. The linear rotordynamic model predicts well the rotor free–free modes and onset speed of instability using linearized bearing force coefficients. The nonlinear model incorporating instantaneous bearing reaction forces in the numerical integration of the rotor equations of motion predicts the limit cycle amplitudes with two fundamental subsynchronous whirl frequencies. Comparisons of both models to experimental results follow. The predictions evidence two unstable whirl ratios at approximately 12 ring speed and 12 ring speed plus 12 journal speed. The transient nonlinear responses reveal the importance of rotor imbalance in suppressing the subsynchronous instabilities at large rotor speeds as also observed in the experiments.

Test Response of a Turbocharger Supported on Floating Ring Bearings: Part II — Comparisons to Nonlinear Rotordynamic Predictions

2003 ◽  
Author(s):  
Chris Holt ◽  
Luis San Andre´s ◽  
Sunil Sahay ◽  
Peter Tang ◽  
Gerry La Rue ◽  
...  
Keyword(s):  
Nonlinear Analysis ◽  
Nonlinear Model ◽  
Equations Of Motion ◽  
Forced Response ◽  
Rotor Imbalance ◽  
Nonlinear Responses ◽  
Reaction Forces ◽  
Bearing Force ◽  
Linear And Nonlinear ◽  
Large Rotor

Linear and nonlinear analysis results for the operation of a small automotive turbocharger supported on floating ring bearings are presented. A comprehensive fluid film bearing model predicting the forced response of floating ring bearings is also described. The linear rotordynamic model predicts well the rotor free-free modes and onset speed of instability using linearized bearing force coefficients. The nonlinear model incorporating instantaneous bearing reaction forces in the numerical integration of the rotor equations of motion predicts the limit cycle amplitudes with two fundamental sub synchronous whirl frequencies. Comparisons of both models to experimental results follow. The predictions evidence two unstable whirl ratios at approximately 1/2 ring speed and 1/2 ring speed plus 1/2 journal speed. The transient nonlinear responses reveal the importance of rotor imbalance in suppressing the subsynchronous instabilities at large rotor speeds as also observed in the experiments.

Nonlinear Analysis of a Rigid Rotor on Magnetic Bearings

1995 ◽  
Author(s):  
C. Nataraj
Keyword(s):  
Nonlinear Analysis ◽  
Equations Of Motion ◽  
Forced Response ◽  
Magnetic Bearings ◽  
Rigid Rotor ◽  
Stability Criteria ◽  
Safe Operation ◽  
Qualitative And Quantitative ◽  
Quantitative Results ◽  
Nonlinear Equations Of Motion

A simple model of a rigid rotor supported on magnetic bearings is considered. A proportional control architecture is assumed, the nonlinear equations of motion are derived and some essential nondimensional parameters are identified. The free and forced response of the system is analyzed using techniques of nonlinear analysis. Both qualitative and quantitative results are obtained and stability criteria are derived for safe operation of the system.

Test Response of a Turbocharger Supported on Floating Ring Bearings: Part I — Assessment of Subsynchronous Motions

2003 ◽  
Author(s):  
Chris Holt ◽  
Luis San Andre´s ◽  
Sunil Sahay ◽  
Peter Tang ◽  
Gerry La Rue ◽  
...  
Keyword(s):  
Ambient Temperature ◽  
Test Data ◽  
Natural Frequencies ◽  
Comprehensive Analysis ◽  
Experimental Results ◽  
Inlet Pressure ◽  
Rotor Speed ◽  
Test Response ◽  
Feed Pressure ◽  
Feed Temperature

Measurements of casing acceleration on an automotive turbocharger running to a top speed of 115 krpm and driven by ambient temperature pressurized air are reported. Waterfall acceleration spectra versus rotor speed show the effects of increasing lubricant inlet pressure and temperature on the turbocharger rotordynamic response. A comprehensive analysis of the test data forwards regimes of speed operation with two subsynchronous whirl motions (rotordynamic instabilities). Increasing the lubricant feed pressure delays the onset speed of instability for the most severe subsynchronous motion. However, increasing the lubricant feed pressure also produces larger synchronous displacements. The effect of lubricant feed temperature is minimal on the onset and end speeds of rotordynamic instability. Nevertheless, operation with a cold lubricant exhibits lower amplitudes of motion, synchronous and subsynchronous. The experimental results show the subsynchronous frequencies of motion do not lock (whip) at system natural frequencies but continuously track the rotor speed. No instabilities (subsynchronous whirl) remain for operating speeds above 90 krpm. Bearings greatly influence turbocharger (TC) rotordynamic performance.

Analytical and Experimental Analysis of a Self-Compensating Dynamic Balancer in a Rotating Mechanism

1996 ◽  
Vol 118 (3) ◽  
pp. 468-475 ◽  
Author(s):  
Jongkil Lee ◽  
W. K. Van Moorhem
Keyword(s):  
Critical Speed ◽  
Equations Of Motion ◽  
Circular Disk ◽  
Experimental Results ◽  
Normal Operation ◽  
Rotating System ◽  
Balance System ◽  
Rotor Imbalance ◽  
Low Viscosity ◽  
The Stability

A theoretical and experimental approach was used to investigate the motion and effectiveness of a Self-Compensating Dynamic Balancer (SCDB). This is a device intended to minimize the effects of rotor imbalance and vibratory forces on a rotating system during normal operation. The basic concept of an automatic dynamic balancer has been described in many U.S. patents. The SCDB is composed of a circular disk with a groove containing massive balls and a low viscosity damping fluid. The objective of this research is to determine the motion of the balls and how this ball motion is related to the vibration of the rotating system using both theoretical and experimental methods. The equations of motion the balls were derived by the Lagrangian method. Static and dynamic solutions were derived from the analytic model. To consider dynamic stability of the motion, perturbation equations were investigated by two different methods: Floquet theory and direct computer simulation. On the basis of the results of the stability investigation, ball positions which result in a balance system are stable above the critical speed and unstable at critical speed and below critical speed. To determine the actual critical speed of the rotating system used in the experimental work, a modal analysis was conducted. Experimental results confirm the predicted ball positions. Based on the theoretical and experimental results, when the system operates below and near the first critical speed, the balls do not balance the system. However, when the system operates above the first critical speed the balls can balance the system.

scholarly journals Horizon radiation reaction forces

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Walter D. Goldberger ◽  
Ira Z. Rothstein
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Finite Size ◽  
Radiation Reaction ◽  
Effective Field ◽  
Compact Objects ◽  
Finite Size Effect ◽  
Binary Black Holes ◽  
Dissipative Effects ◽  
Reaction Forces

Abstract Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

scholarly journals Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

2006 ◽  
Author(s):  
M. Amabili ◽  
C. Touze´ ◽  
O. Thomas
Keyword(s):  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Nonlinear Responses ◽  
Nonlinear Normal ◽  
The Galerkin Method ◽  
Proper Orthogonal

The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.

Rotordynamics Performance of Hybrid Foil Bearing Under Forced Vibration Input

2017 ◽  
Author(s):  
Daejong Kim ◽  
Brian Nicholson ◽  
Lewis Rosado ◽  
Garry Givan
Keyword(s):  
Impulse Response ◽  
High Speed ◽  
Load Capacity ◽  
Supply System ◽  
Forced Response ◽  
Experimental Results ◽  
Lateral Acceleration ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Gas Supply

Foil bearings are one type of hydrodynamic air/gas bearings but with a compliant bearing surface supported by structural material that provides stiffness and damping to the bearing. The hybrid foil bearing (HFB) in this paper is a combination of a traditional hydrodynamic foil bearing with externally-pressurized air/gas supply system to enhance load capacity during the start and to improve thermal stability of the bearing. The HFB is more suitable for relatively large and heavy rotors where rotor weight is comparable to the load capacity of the bearing at full speed and extra air/gas supply system is not a major added cost. With 4,448N∼22,240N thrust class turbine aircraft engines in mind, the test rotor is supported by HFB in one end and duplex rolling element bearings in the other end. This paper presents experimental work on HFB with diameter of 102mm performed at the US Air force Research Laboratory. Experimental works include: measurement of impulse response of the bearing to the external load corresponding to rotor’s lateral acceleration of 5.55g, forced response to external subsynchronous excitation, and high speed imbalance response. A non-linear rotordynamic simulation model was also applied to predict the impulse response and forced subsynchronous response. The simulation results agree well with experimental results. Based on the experimental results and subsequent simulations, an improved HFB design is also suggested for higher impulse load capability up to 10g and rotordynamics stability up to 30,000rpm under subsynchronous excitation.

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