A General Model for Two-Point Contact Dry-Friction Whip and Whirl

2012 ◽  
Author(s):  
Jason C. Wilkes
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
General Model ◽  
Dry Friction ◽  
Point Contact ◽  
Current Work ◽  
Equipment Failure ◽  
Air Bearings ◽  
Single Location ◽  
Arbitrary Phase

Numerous papers have investigated the behavior of dry-friction whip and whirl; most of them consider contact between a rotor and stator at a single location. For rotors running on multiple magnetic bearings, air bearings, or bushings, equipment failure may result in rub at more than one location. For these cases, it is important to have an analytical model that characterizes possible regions of two-point contact dry-friction whip and whirl. Until a recent publication by Childs and Kumar in 2011, there were no attempts to analytically describe the behavior of dry-friction whip and whirl at more than one location. In their work, they assume that forces at the two rotor/stator contacts are either in-phase, or out-of phase. The current work presents a method that is more general, allowing for an arbitrary phase between contact locations. In theory this method can be applied to more than two contact locations; however, a two-point contact example case is developed and compared to numerical simulations in the current work.

A General Model for Two-Point Contact Dry-Friction Whip and Whirl: Further Advancements and Experimental Test Results

2015 ◽  
Author(s):  
Jason C. Wilkes ◽  
Tim Allison
Keyword(s):  
Experimental Test ◽  
General Model ◽  
Dry Friction ◽  
Point Contact ◽  
Current Work ◽  
Test Results ◽  
Air Bearings ◽  
Test Rig ◽  
Single Location ◽  
Arbitrary Phase

Numerous papers have investigated the behavior of dry-friction whip and whirl; most of them consider contact between a rotor and stator at a single location. For rotors running on multiple magnetic bearings, air bearings, or bushings, equipment failure may result in rub at more than one location. For these cases, it is important to have an analytical model that characterizes possible regions of two-point contact dry-friction whip and whirl. The current work presents a general model to predict possible whirl regions for multi-contact dry-friction whip and whirl, allowing for an arbitrary phase between contact locations. In theory this method can be applied to more than two contact locations; however, a two-point contact example case is developed and compared to results from an experimental test rig developed to demonstrate multi-contact dry-friction whip and whirl in the current work.

Application of Dry-Friction Whip and Whirl Solution Methods to Systems With Support Asymmetry

2018 ◽  
Author(s):  
Jason C. Wilkes
Keyword(s):  
Relative Motion ◽  
General Model ◽  
Dry Friction ◽  
Current Work ◽  
General Sense ◽  
Continuous Contact ◽  
Solution Methods ◽  
Asymmetric Rotor ◽  
Two Bodies

Dry-friction whip and whirl occurs when a rotor contacts a stator across a clearance annulus. In a general sense, the relative motion between the two bodies is described by a circular precessing motion. While this problem is generally well understood, the author is unaware of any papers that discuss the problem for systems having asymmetric rotor or stator supports. The current work will investigate a general model to describe dry-friction whip and whirl for the case of continuous contact between a rotor and stator in the presence of asymmetry. This paper will show that for light asymmetry, the rotor and stator motions are elliptical; however, the relative motion between the two bodies remains circular.

The effects of geometric offsets on the dynamic responses of a Scott—Russell amplifying mechanism with flexible hinges

2009 ◽  
Vol 223 (10) ◽  
pp. 2413-2423 ◽  
Author(s):  
C-M Chen ◽  
R-F Fung
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
Dynamic Responses ◽  
Analytical Models ◽  
Dynamic Equations ◽  
Magnification Factor ◽  
Flexure Hinges ◽  
Magnification Factors ◽  
Straight Line ◽  
Deviation Factor

The dynamic equations of a micro-positioning Scott—Russell (SR) mechanism associated with two flexible hinges and an offset are developed to calculate output responses. Both rigid and flexible hinges are considered to explore the results. The main features in the kinematics of the SR mechanism are its displacement amplification and straight-line motion, which are widely needed in practical industries. The manufacturing inaccuracy of the SR mechanism definitely causes geometric offsets of flexure hinges, and affects displacement amplification and straight-line output motion. Analytical models based on kinematics and Hamilton's principle are derived to explore the variation of linearity ratio, magnification factor, and deviation factor due to various offsets and link lengths. From numerical simulations for the SR mechanism with various offsets of flexible hinges in the conditions of different link lengths, it is found that offsets of flexure hinges obviously affect the amplifying factor and linearity ratio, and appear to dominate the changes of magnification factors. Moreover, an analytical model is also used to predict magnification factors due to various offsets. Finally, some conclusions concerning the effects of offset on the performance of the SR mechanism are drawn.

The Stick Motion of a Harmonically Excited, Friction-Induced Oscillator on a Sinusoidally Traveling Surface

2006 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Dry Friction ◽  
The Other ◽  
Linear Oscillator ◽  
Analytical Prediction ◽  
Nonlinear Friction ◽  
Friction Forces

In this paper, the methodology is presented through investigation of a periodically, forced linear oscillator with dry friction, resting on a traveling surface varying with time. The switching conditions for stick motions in non-smooth dynamical systems are obtained. From defined generic mappings, the corresponding criteria for the stick motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the stick motions is illustrated. Finally, numerical simulations of stick motions are carried out to verify the analytical prediction. The achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces possessing a CO - discontinuity.

Forced Vibration of Elastic Structures With Friction Contacts

1999 ◽  
Author(s):  
Walter Sextro
Keyword(s):  
Relative Motion ◽  
Dry Friction ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Point Contact ◽  
Normal Pressure ◽  
Tangential Direction ◽  
Contact Model ◽  
Elastic Structures ◽  
Normal Forces

Abstract In many technical contacts energy is dissipated because of dry friction and relative motion. This can be used to reduce the vibration amplitudes. For example, shrouds with friction interfaces are used to reduce the dynamic stresses in turbine blades. The three-dimensional motion of the blades results in a three-dimensional relative motion of the contact planes. The developed Point-Contact-Model is used to calculate the corresponding tangential and normal forces for each contact element. This Point-Contact-Model includes the roughness of the contact surfaces, the normal pressure distribution due to roughness, the stiffness in normal and tangential direction and dry friction. An experiment with two non-Hertzian contacts is used to verify the developed contact model. The comparison between measured and calculated frequency response functions for three-dimensional forced vibrations of the elastic structures shows a very good agreement.

Analysis of Motion of the Impact-Dry-Friction Pair of Bodies and its Application to the Investigation of the Impact Dampers Dynamics

1999 ◽  
Author(s):  
František Peterka
Keyword(s):  
Analytical Solution ◽  
Numerical Simulations ◽  
Mechanical System ◽  
Relative Motion ◽  
Dry Friction ◽  
Friction Pair ◽  
Strong Nonlinearity ◽  
Friction Forces ◽  
The Impact ◽  
Analysis Of Motion

Abstract The motion with impacts and dry friction forces appears in some mechanical systems as mechanisms with clearances, (e.g., in gearings, pins, slots, guides, valve gears etc.), impact dampers, relays, forming and mailing machines, power pics etc. Such mechanisms include one or more pairs of impacting bodies, which introduce the strong nonlinearity into the system motion. The motion of the general pair of bodies with the both-sides impacts and dry friction forces is assumed (Fig.1). It can be the part of a more complex chain of masses in the mechanical system. Dead zones in the relative motion of bodies can be caused by assumed nonlinearities. The mathematical conditions controlling the numerical simulations or analytical solution of the motion are introduced. The application of this method is explained by the study of the influence of dry friction force on amplitude-frequency characteristics of four types of dynamical and impact dampers with optimised parameters.

An Improved Analytical Model of Friction and Ball Motion in Linear Ball Bearings With Application to Ball-to-Ball Contact Prediction

2018 ◽  
Author(s):  
Bo Lin ◽  
Molong Duan ◽  
Chinedum E. Okwudire ◽  
Jason S. Wou
Keyword(s):  
Analytical Model ◽  
Analytical Formula ◽  
Point Contact ◽  
Friction Model ◽  
Linear Velocity ◽  
Contact Forces ◽  
Ball Bearings ◽  
Friction Behavior ◽  
Rolling Ball ◽  
Ball Contact

The friction behavior of rolling ball machine components like linear ball bearings is very important to their functionality. For instance, differences in linear velocity of balls induces ball-to-ball contact in certain circumstances, resulting in significant increases and variations in friction. In this paper, an improved analytical formula for determining the linear velocity of balls in four-point-contact linear ball bearings is derived as a function of contact angle deviations and contact forces. The analytical formula is validated against a comprehensive friction model in the literature and shown to be in good agreement, while an oversimplified analytical model proposed by the authors in prior work is shown to be inaccurate. A case study is presented where insights gained from the derived analytical formula are used to mitigate velocity difference of balls in a linear ball bearing which otherwise would experience ball-to-ball contact.

scholarly journals Analysis of an Approximated Model for the Depletion Region Width of Planar Junctionless Transistors

Electronics ◽  
2019 ◽  
Vol 8 (12) ◽  
pp. 1436
Author(s):  
Arian Nowbahari ◽  
Avisek Roy ◽  
Muhammad Nadeem Akram ◽  
Luca Marchetti
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
Threshold Voltage ◽  
Analytical Formula ◽  
Numerical Data ◽  
Maximum Error ◽  
Depletion Region ◽  
Comsol Multiphysics ◽  
Flat Band ◽  
Junctionless Transistors

In this paper, we investigate the accuracy of the approximated analytical model currently utilized, by many researchers, to describe the depletion region width in planar junctionless transistors (PJLT). The proposed analysis was supported by numerical simulations performed in COMSOL Multiphysics software. By comparing the numerical results and the approximated analytical model of the depletion region width, we calculated that the model introduces a maximum RMS error equal to 90 % of the donor concentration in the substrate. The maximum error is achieved when the gate voltage approaches the threshold voltage ( V t h ) or when it approaches the flat band voltage ( V F B ) of the transistor. From these results, we concluded that this model cannot be used to determine accurately the flat-band and the threshold voltage of the transistor, although it represents a straightforward method to estimate the depletion region width in PJLT. By using the approximated analytical model, we extracted an analytical formula, which describes the electron concentration at the ideal boundary of the depletion region. This formula approximates the numerical data extracted from COMSOL with a relative error lower than 1 % . The proposed formula is in our opinion, as useful as the formula of the approximated analytical model because it allows for estimating the position of the depletion region also when the drain and source terminals are not grounded. We concluded that the analytical formula proposed at the end of this work could be useful to determine the position of the depletion region boundary in numerical simulations and in graphical representations provided by COMSOL Multiphysics software.

Hysteretic effects of dry friction: modelling and experimental studies

2007 ◽  
Vol 366 (1866) ◽  
pp. 747-765 ◽  
Author(s):  
Jerzy Wojewoda ◽  
Andrzej Stefański ◽  
Marian Wiercigroch ◽  
Tomasz Kapitaniak
Keyword(s):  
Numerical Simulations ◽  
Dry Friction ◽  
Experimental Studies ◽  
Friction Model ◽  
Hysteretic Effect ◽  
Motion Characteristic ◽  
Friction Models ◽  
Theoretical Analyses ◽  
Friction Modelling

In this paper, the phenomena of hysteretic behaviour of friction force observed during experiments are discussed. On the basis of experimental and theoretical analyses, we argue that such behaviour can be considered as a representation of the system dynamics. According to this approach, a classification of friction models, with respect to their sensitivity on the system motion characteristic, is introduced. General friction modelling of the phenomena accompanying dry friction and a simple yet effective approach to capture the hysteretic effect are proposed. Finally, the experimental results are compared with the numerical simulations for the proposed friction model.

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