Stability of Sliding in a System Excited by a Rough Moving Surface

1997 ◽  
Vol 119 (4) ◽  
pp. 672-680 ◽  
Author(s):  
E. J. Berger ◽  
C. M. Krousgrill ◽  
F. Sadeghi
Keyword(s):  
Parametric Resonance ◽  
Normal Force ◽  
Surface Velocity ◽  
Force System ◽  
Periodic Surface ◽  
Linearized System ◽  
Friction Curve ◽  
The Stability ◽  
Small Periodic ◽  
Harmonic Resonance

A two-degree-of-freedom translational system has been developed to study the influence of normal force oscillations on the stability of the steady sliding position. Excited by a small, periodic surface roughness, the normal and tangential motion are coupled through a velocity-dependent friction law. The linearized system has been examined using the first-order averaging technique of Krylov and Boguliubov. In addition to the primary forced resonance, a 2:1 parametric resonance and a 1/2 sub-harmonic resonance have been encountered. Arising from velocity-dependent coupling of the normal and tangential modes and the periodic normal force variations, the parametric resonance has been found to produce locally unstable responses in some cases. Conditions for the stability of the local response based upon local friction curve slope, static normal force, system damping, and surface velocity have been derived for a broad range of frequency.

Stability of Sliding in a System Excited by a Rough Moving Surface

1995 ◽  
Author(s):  
Edward J. Berger ◽  
Charles M. Krousgrill ◽  
Farshid Sadeghi
Keyword(s):  
Parametric Resonance ◽  
Normal Force ◽  
Surface Velocity ◽  
Force System ◽  
Periodic Surface ◽  
Linearized System ◽  
Friction Curve ◽  
The Stability ◽  
Small Periodic ◽  
Harmonic Resonance

Abstract A two-degree-of-freedom translational system has been developed to study the influence of normal force oscillations on the stability of the steady sliding position. Excited by a small, periodic surface roughness, the normal and tangential motion are coupled through a velocity-dependent friction law. The linearized system has been examined using the first-order averaging technique of Krylov and Boguliubov. In addition to the primary forced resonance, a 2:1 parametric resonance and a 1/2 sub-harmonic resonance have been encountered. Arising from velocity-dependent coupling of the normal and tangential modes and the periodic normal force variations, the parametric resonance has been found to produce locally unstable responses in some cases. Conditions for the stability of the local response based upon local friction curve slope, static normal force, system damping, and surface velocity have been derived for a broad range of frequency.

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

scholarly journals Modeling and Designing a Hydrostatic Transmission With a Fixed-Displacement Motor

1998 ◽  
Vol 120 (1) ◽  
pp. 45-49 ◽  
Author(s):  
N. D. Manring ◽  
G. R. Luecke
Keyword(s):  
Order System ◽  
Axial Piston Pump ◽  
Third Order ◽  
Stability Range ◽  
Hydrostatic Transmission ◽  
Control Gain ◽  
Variable Displacement ◽  
Linearized System ◽  
The Stability ◽  
Axial Piston

This study develops the dynamic equations that describe the behavior of a hydrostatic transmission utilizing a variable-displacement axial-piston pump with a fixed-displacement motor. In general, the system is noted to be a third-order system with dynamic contributions from the motor, the pressurized hose, and the pump. Using the Routh-Hurwitz criterion, the stability range of this linearized system is presented. Furthermore, a reasonable control-gain is discussed followed by comments regarding the dynamic response of the system as a whole. In particular, the varying of several parameters is shown to have distinct effects on the system rise-time, settling time, and maximum percent-overshoot.

Experiments on the stability and transition of wind-driven water surfaces

2001 ◽  
Vol 446 ◽  
pp. 25-65 ◽  
Author(s):  
FABRICE VERON ◽  
W. KENDALL MELVILLE
Keyword(s):  
Surface Current ◽  
Field Measurements ◽  
Surface Flow ◽  
Transition To Turbulence ◽  
Surface Velocity ◽  
Small Scale ◽  
Gas Transfer ◽  
Water Surfaces ◽  
Langmuir Circulations ◽  
The Stability

We present the results of laboratory and field measurements on the stability of wind-driven water surfaces. The laboratory measurements show that when exposed to an increasing wind starting from rest, surface current and wave generation is accompanied by a variety of phenomena that occur over comparable space and time scales. Of particular interest is the generation of small-scale, streamwise vortices, or Langmuir circulations, the clear influence of the circulations on the structure of the growing wave field, and the subsequent transition to turbulence of the surface flow. Following recent work by Melville, Shear & Veron (1998) and Veron & Melville (1999b), we show that the waves that are initially generated by the wind are then strongly modulated by the Langmuir circulations that follow. Direct measurements of the modulated wave variables are qualitatively consistent with geometrical optics and wave action conservation, but quantitative comparison remains elusive. Within the range of parameters of the experiments, both the surface waves and the Langmuir circulations first appear at constant Reynolds numbers of 370 ± 10 and 530 ± 20, respectively, based on the surface velocity and the depth of the laminar shear layer. The onset of the Langmuir circulations leads to a significant increase in the heat transfer across the surface. The field measurements in a boat basin display the same phenomena that are observed in the laboratory. The implications of the measurements for air–sea fluxes, especially heat and gas transfer, and sea-surface temperature, are discussed.

Conditions of Parametric Resonance in Periodically Time-Variant Systems With Distributed Parameters

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Yong-Kwan Lee ◽  
Leonid S. Chechurin
Keyword(s):  
Parametric Resonance ◽  
Robot Manipulator ◽  
Synchronous Generator ◽  
Constant Current ◽  
Time Varying ◽  
Distributed Parameters ◽  
Time Varying Parameter ◽  
Manipulator Arm ◽  
The Stability ◽  
Systems With Distributed Parameters

Theoretical analysis of the stability problem for the control systems with distributed parameters shall be given. The approach to the analysis of such systems can be composed of two parts. First, the distributed parameter element is modeled by a frequency response function. Second, approximate conditions of parametric resonance are derived by a method of stationarization (describing functions of time-variant elements). The approach is illustrated by two examples. One is a robot-manipulator arm (distributed mechanical parameter system) controlled by a controller with a modulator/demodulator cascade (time-varying element). Another is an electromechanical transformer that consists of a constant current motor and a synchronous generator. Inductance between stator windings and the rotor of the synchronous generator serves as a periodical time-varying parameter, and a long electrical line plays the role of an element with distributed parameters. In both examples, dangerous (in terms of the first parametric resonance) regions for time-varying parameter are obtained theoretically and compared with simulation experiment.

The stability of thermal oscillations in a reactive slab: reduction to Hill’s equation

1982 ◽  
Vol 384 (1787) ◽  
pp. 455-462
Keyword(s):  
Surface Temperature ◽  
Hill’S Equation ◽  
Periodic Surface ◽  
Temperature Oscillations ◽  
Hill's Equation ◽  
Chemically Reacting ◽  
The Stability ◽  
Thermal Oscillations ◽  
Surface Temperature Variation ◽  
Time Periodic

The thermal stability of an exothermic chemically reacting slab with time-periodic surface temperature variation is examined. It is shown, on the basis of a good approximation due to Boddington, Gray and Walker, that the behaviour depends on the solutions of an ordinary differential equation of first order. The equation contains a modified amplitude, for small values of which it can be reduced to a particular form of Hill’s equation. Critical values of the Frank-Kamenetskii parameter, as a function of the amplitude ϵ and frequency ω of the surface temperature oscillations, are derived from the latter equation. For ω = 2π and 0 ≼ ϵ ≼ 2 the values are in good agreement with previously calculated ones.

scholarly journals Estimation of the Bistable Zone for Machining Operations for the Case of a Distributed Cutting-Force Model

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Tamás G. Molnár ◽  
Tamás Insperger ◽  
S. John Hogan ◽  
Gábor Stépán
Keyword(s):  
Cutting Force ◽  
Distributed Delay ◽  
Nonlinear Function ◽  
Force Model ◽  
Center Manifold Reduction ◽  
Stability Boundaries ◽  
Force System ◽  
Bistable Region ◽  
The Stability ◽  
Machining Operations

Regenerative machine tool chatter is investigated for a single-degree-of-freedom model of turning processes. The cutting force is modeled as the resultant of a force system distributed along the rake face of the tool, whose magnitude is a nonlinear function of the chip thickness. Thus, the process is described by a nonlinear delay-differential equation, where a short distributed delay is superimposed on the regenerative point delay. The corresponding stability lobe diagrams are computed and are shown numerically that a subcritical Hopf bifurcation occurs along the stability boundaries for realistic cutting-force distributions. Therefore, a bistable region exists near the stability boundaries, where large-amplitude vibrations (chatter) may arise for large perturbations. Analytical formulas are obtained to estimate the size of the bistable region based on center manifold reduction and normal form calculations for the governing distributed-delay equation. The locally and globally stable parameter regions are computed numerically as well using the continuation algorithm implemented in dde-biftool. The results can be considered as an extension of the bifurcation analysis of machining operations with point delay.

Simulation of Aurora basin, East Antarctic

2020 ◽  
Author(s):  
Liyun Zhao ◽  
Yan Zhen ◽  
Rupert Gladstone ◽  
Thomas Zwinger ◽  
John Moore
Keyword(s):  
High Resolution ◽  
Thermal Condition ◽  
Inverse Method ◽  
Flow Model ◽  
Surface Velocity ◽  
Dynamic Processes ◽  
Ice Shelf ◽  
Ice Flow ◽  
Ocean Models ◽  
The Stability

<p>The Aurora basin includes several fast-flowing glaciers (e.g. Totten and Dalton) and has large subglacial areas below sea level, which makes its study an essential part of evaluating the stability of East Antarctic against ocean warming. We use the 3D full-Stokes ice flow model Elmer/Ice to investigate the dynamic processes taking place in this basin. The spatial pattern of basal friction is deduced by inverse method from observed surface velocity. Particular focus is in the thermal condition at the bedrock. We further project the evolution of this basin during the 21st century with parameterized sub-ice shelf melting based provided by high resolution ocean models.</p>

The Stability of the Short-Period Motion of an Airframe Having Non-Linear Normal Force and Pitching Moment Curves

1960 ◽  
Vol 11 (3) ◽  
pp. 255-268
Author(s):  
P. A. T. Christopher
Keyword(s):  
Stability Theory ◽  
Phase Plane ◽  
Normal Force ◽  
Pitching Moment ◽  
Stability Criteria ◽  
Short Period ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability ◽  
Period Motion

SummaryThe analysis of the stability of second-order non-linear systems by Poincare's method of singular points in the phase plane is briefly presented and used to determine stability criteria for the short-period motion of an airframe having non-linear normal force and pitching moment curves. These results are then compared with those obtained by the application of quasilinear stability theory.

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