A Stability Analysis of the Wheel Shimmy

2012 ◽  
Author(s):  
Giandomenico Di Massa ◽  
Stefano Pagano ◽  
Salvatore Strano ◽  
Mario Terzo
Keyword(s):  
Stability Analysis ◽  
Degree Of Freedom ◽  
Experimental Investigations ◽  
Classical Stability ◽  
Low Degree ◽  
Oscillation Modes ◽  
Non Linear ◽  
The Stability ◽  
Three Degree Of Freedom ◽  
Wheel Shimmy

The wheel shimmy is a classical non-linear problem. The most frequently used approach to study this phenomena is based on linearized low degree of freedom models, that from one side, thanks the simplicity of the equations of the motion, allows to evaluate the stability with classical stability-analysis approach, but from the other side it limits the study about the equilibrium point. In this paper a stability-analysis, based on a three degree of freedom non-linear analytical model, is presented. Starting from the system numerical response, adopting a time-domain modal analysis method, the modal parameters were identified. The proposed procedure, through a 3 degree of freedom nonlinear representation of the castor, highlights the three main castor oscillation modes whose characteristics can then be identified with a method applicable even for experimental investigations.

Non-linear stability analysis of micropolar fluid lubricated journal bearings with turbulent effect

2019 ◽  
Vol 71 (1) ◽  
pp. 31-39
Author(s):  
Subrata Das ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Micropolar Fluid ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Turbulent Regime ◽  
Content Type ◽  
Non Linear ◽  
The Stability ◽  
Bearing System

Purpose The purpose of this paper is to investigate the effect of turbulence on the stability characteristics of finite hydrodynamic journal bearing lubricated with micropolar fluid. Design/methodology/approach The non-dimensional transient Reynolds equation has been solved to obtain the non-dimensional pressure field which in turn used to obtain the load carrying capacity of the bearing. The second-order equations of motion applicable for journal bearing system have been solved using fourth-order Runge–Kutta method to obtain the stability characteristics. Findings It has been observed that turbulence has adverse effect on stability and the whirl ratio at laminar flow condition has the lowest value. Practical implications The paper provides the stability characteristics of the finite journal bearing lubricated with micropolar fluid operating in turbulent regime which is very common in practical applications. Originality/value Non-linear stability analysis of micropolar fluid lubricated journal bearing operating in turbulent regime has not been reported in literatures so far. This paper is an effort to address the problem of non-linear stability of journal bearings under micropolar lubrication with turbulent effect. The results obtained provide useful information for designing the journal bearing system for high speed applications.

A Dynamical Model for Studying the Stability of Thermo-Solutal Convection Under the Effect of Vertical Vibration

2005 ◽  
Author(s):  
Y. P. Razi ◽  
M. Mojtabi ◽  
K. Maliwan ◽  
M. C. Charrier-Mojtabi ◽  
A. Mojtabi
Keyword(s):  
Stability Analysis ◽  
Mechanical Vibration ◽  
Stability Limit ◽  
Lewis Number ◽  
Vertical Vibration ◽  
Wave Number ◽  
Dimensionless Wave Number ◽  
Non Linear ◽  
Linear Differential ◽  
The Stability

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations: BH¨+B(π2+k2)+1H˙+(π2+k2)−k2k2+π2RaT(1+Rsinω*t*)H=k2k2+π2(NRaT)(1+Rsinω*t*)Fε*BF¨+Bπ2+k2Le+ε*F˙+π2+k2Le−k2k2+π2NRaT(1+Rsinω*t*)F=k2k2+π2RaT(1+Rsinω*t*)H where RaT is thermal Rayleigh number, R is acceleration ratio (bω2/g), Le is the Lewis number, k is the dimensionless wave-number, ε* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.

Relationship between the Steady-Handling Characteristics of Automobiles and Their Stability

1973 ◽  
Vol 15 (5) ◽  
pp. 326-328 ◽  
Author(s):  
R. S. Sharp
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Degree Of Freedom ◽  
Nonlinear Region ◽  
Handling Characteristics ◽  
Yield Information ◽  
Turning Motion ◽  
The Stability ◽  
Three Degree Of Freedom

Analyses of the steady-state handling behaviour of an automobile and the stability of its steady-turning motion, based on a three degree of freedom mathematical model, are used to show that the steady behaviour and the stability are related similarly in the nonlinear region as in the well documented linear one. It is concluded that analysis and measurement of the steady behaviour will yield information on the stability of automobiles.

Non-Linear Transient Stability Analysis of a Rigid Rotor Supported on Journal Bearings With Rectangular Dimples

2015 ◽  
Author(s):  
Ram Turaga
Keyword(s):  
Stability Analysis ◽  
Surface Texture ◽  
Transient Stability ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Pressure Curve ◽  
Rigid Rotor ◽  
Non Linear ◽  
The Stability ◽  
Transient Stability Analysis

The influence of deterministic surface texture on the sub-synchronous whirl stability of a rigid rotor has been studied. Non-linear transient stability analysis has been performed to study the stability of a rigid rotor supported on two symmetric journal bearings with a rectangular dimple of large aspect ratio. The surface texture parameters considered are dimple depth to minimum film thickness ratio and the location of the dimple on the bearing surface. Journal bearings of different Length to diameter ratios have been studied. The governing Reynolds equation for finite journal bearings with incompressible fluid has been solved using the Finite Element Method under isothermal conditions. The trajectories of the journal center have been obtained by solving the equations of motion of the journal center by the fourth-order Runge-Kutta method. When the dimple is located in the raising part of the pressure curve the positive rectangular dimple is seen to decrease the stability whereas the negative rectangular dimple is seen to improve the stability of the rigid rotor.

scholarly journals A method for identification of non-linear multi-degree-of-freedom systems

1998 ◽  
Vol 212 (4) ◽  
pp. 287-298 ◽  
Author(s):  
G Dimitriadis ◽  
J E Cooper
Keyword(s):  
System Identification ◽  
Degree Of Freedom ◽  
Accurate Identification ◽  
Wide Range ◽  
Non Linear ◽  
Linear System Identification ◽  
The Stability ◽  
Non Linear System ◽  
Identification Techniques ◽  
Flutter Testing

System identification methods for non-linear aeroelastic systems could find uses in many aeroelastic applications such as validating finite element models and tracking the stability of aircraft during flight flutter testing. The effectiveness of existing non-linear system identification techniques is limited by various factors such as the complexity of the system under investigation and the type of non-linearities present. In this work, a new approach is introduced which can identify multi-degree-of-freedom systems featuring any type of non-linear function, including discontinuous functions. The method is shown to yield accurate identification of three mathematical models of aeroelastic systems containing a wide range of structural non-linearities.

Multivariable Control Design for a Bilateral Telemanipulator

2003 ◽  
Author(s):  
Kevin B. Fite ◽  
Michael Goldfarb
Keyword(s):  
Impedance Control ◽  
Singular Values ◽  
Degree Of Freedom ◽  
Stability Robustness ◽  
Remote Environment ◽  
And Performance ◽  
The Stability ◽  
Three Degree Of Freedom ◽  
And Control ◽  
Control Methodology

This paper presents an architecture and control methodology for a multi-degree-of-freedom teleoperator system. The approach incorporates impedance control of the telemanipulator pair and formulates the system as a single feedback loop encompassing the human operator, telemanipulator, and remote environment. In so doing, multivariable Nyquist-like techniques are used to design compensation for enhanced stability robustness and performance. A measure of the transparency exhibited by the multivariable teleoperator system is attained using matrix singular values. The approach is experimentally demonstrated on a three degree-of-freedom scaled telemanipulator pair with a highly coupled environment. Using direct measurement of the power delivered to the operator to assess the system’s stability robustness, along with the proposed measure of multivariable transparency, the loop-shaping compensation is shown to improve the stability robustness by a factor of almost two and the transparency by more than a factor of five.

Efficient and Robust Approaches to the Stability Analysis of Large Multibody Systems

2007 ◽  
Vol 3 (1) ◽  
Author(s):  
Olivier A. Bauchau ◽  
Jielong Wang
Keyword(s):  
Stability Analysis ◽  
Large Scale ◽  
Equations Of Motion ◽  
Classical Stability ◽  
Linearized Stability ◽  
Signal Synthesis ◽  
Common Framework ◽  
Synthesis Procedure ◽  
The Stability ◽  
Proper Orthogonal

Linearized stability analysis methodologies that are applicable to large scale, multiphysics problems are presented in this paper. Two classes of closely related algorithms based on a partial Floquet and on an autoregressive approach, respectively, are presented in common framework that underlines their similarity and their relationship to other methods. The robustness of the proposed approach is improved by using optimized signals that are derived from the proper orthogonal modes of the system. Finally, a signal synthesis procedure based on the identified frequencies and damping rates is shown to be an important tool for assessing the accuracy of the identified parameters; furthermore, it provides a means of resolving the frequency indeterminacy associated with the eigenvalues of the transition matrix for periodic systems. The proposed approaches are computationally inexpensive and consist of purely post processing steps that can be used with any multiphysics computational tool or with experimental data. Unlike classical stability analysis methodologies, it does not require the linearization of the equations of motion of the system.

Non-linear stability analysis of floating ring bearings using Hopf bifurcation theory

2011 ◽  
Vol 225 (12) ◽  
pp. 2804-2818 ◽  
Author(s):  
A Amamou ◽  
M Chouchane
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Limit Cycles ◽  
Critical Speed ◽  
Design Parameters ◽  
Stable Limit ◽  
Non Linear ◽  
The Stability

Floating ring bearings are used to support and guide rotors in several high-speed rotating machinery applications. They are usually credited for lower heat generation and higher vibration suppressing ability. Similar to conventional hydrodynamic bearings, floating ring bearings may exhibit unstable behaviour above a certain stability critical speed. Linear stability analysis is usually applied to predict the stability threshold speed. Non-linear stability analysis, however, is needed to predict the presence and the size of stable limit cycles above the stability threshold speed or unstable limit cycles below the stability critical speed. The prediction of limit cycles is an important step in bearing stability analysis. In this article, a non-linear dynamic model is derived and used to investigate the stability of a perfectly balanced symmetric rigid rotor supported by two identical floating ring bearings near the critical stability boundaries. The fluid film hydrodynamic reactions of the floating ring bearings are modelled by applying the short bearing theory and the half Sommerfeld solution. Hopf bifurcation theory is then utilized to determine the existence and the approximate size of stable and unstable limit cycles in the neighbourhood of the stability critical speed depending on the bearing design parameters. Numerical integration of the non-linear equations of motion is then carried out in order to compare the trajectories obtained by numerical integration to those obtained analytically using Hopf bifurcation analysis. Stability boundary curves for typical bearing design parameters have been decomposed into boundaries with supercritical stable limit cycles and boundaries with subcritical unstable limit cycles. The shape and size of the limit cycles for selected bearing parameters are presented using both analytical and numerical approaches. This article shows that floating ring stability boundaries may exhibit either stable supercritical limit cycles or unstable subcritical limit cycles predictable by Hopf bifurcation.

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