scholarly journals Celtic Stone Dynamics Revisited Using Dry Friction and Rolling Resistance

2012 ◽  
Vol 19 (5) ◽  
pp. 1115-1123 ◽  
Author(s):  
J. Awrejcewicz ◽  
G. Kudra
Keyword(s):  
Stress Distribution ◽  
Dry Friction ◽  
Rolling Resistance ◽  
Optimization Methods ◽  
Approximate Model ◽  
Integral Model ◽  
Normal Stress Distribution ◽  
Friction Forces ◽  
Contact Shape ◽  
Celtic Stone

The integral model of dry friction components is built with assumption of classical Coulomb friction law and with specially developed model of normal stress distribution coupled with rolling resistance for elliptic contact shape. In order to avoid a necessity of numerical integration over the contact area at each the numerical simulation step, few versions of approximate model are developed and then tested numerically. In the numerical experiments the simulation results of the Celtic stone with the friction forces modelled by the use of approximants of different complexity (from no coupling between friction force and torque to the second order Padé approximation) are compared to results obtained from model with friction approximated in the form of piecewise polynomial functions (based on the Taylor series with hertzian stress distribution). The coefficients of the corresponding approximate models are found by the use of optimization methods, like as in identification process using the real experiment data.

scholarly journals A new approximate model of tyre accounting for both deformed state and dry friction forces in the contact spot on the background of the coupled model

2018 ◽  
Vol 211 ◽  
pp. 08003 ◽  
Author(s):  
Alexey A. Kireenkov ◽  
Dmitry V. Nushtaev ◽  
Sergey I. Zhavoronok
Keyword(s):  
Numerical Simulation ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Numerical Models ◽  
Coupled Model ◽  
Approximate Model ◽  
Contact Spot ◽  
Engineering Practice ◽  
Friction Forces ◽  
Deformed State

A new approximate model of the tire rolling accounting for coupled longitudinal and lateral sliding as well as the spinning and the deformed state resulting in elastic forces is proposed. The main goal of this investigation consists in the construction of simple models with a few of degrees of freedom allowing one to implement them analytically in the engineering practice, primarily for the estimation of the rolling stability and for the prognosis of the instable rolling so-called ”shimmy phenomenon” and to numerical simulation of the transient dynamics of rolling wheels with sliding effects. Such a model could become useful at the earlier stages of the engineering design instead of complex numerical models that are usually resource consuming. The known models of the shimmy phenomenon are usually based on the nonholonomic condition of the steady rolling and consider as the main cause of instability only the tire deformation while the sliding and spinning are assumed to vanish, i. e. the dry friction effects are neglected. Another type of models consists in the ”rigid wheel” assumption, in other words only the dry friction effects are accounted on the background of the coupled dry friction theory whereas the deformed state effects are neglected. Such a theory is based on the complete accounting of the combined kinematics due to simultaneous sliding and spin and shows its efficiency for slightly deformed wheels and the unsteady rolling regimes. Our goal consists in the formulation of the combined model that takes into account as well as the deformed state as the dry friction effects. This model is based on the solution of some model problems for the tire using solid finite element simulation or various shell theories, the computing of a set of specific generalized rigidity factors for the tire model, and on the accounting for the shape of the contact spot and the contact pressure distribution after the numerical simulation of the tire-road contact interaction in quasi-statics. As a result, we obtain a model with only a few degrees of freedom but more general that the Keldysh’s or Klimov’s ones.

TANGENS HYPERBOLICUS APPROXIMATIONS OF THE SPATIAL MODEL OF FRICTION COUPLED WITH ROLLING RESISTANCE

2011 ◽  
Vol 21 (10) ◽  
pp. 2905-2917 ◽  
Author(s):  
GRZEGORZ KUDRA ◽  
JAN AWREJCEWICZ
Keyword(s):  
Initial Conditions ◽  
Rolling Resistance ◽  
Special Kind ◽  
Integral Model ◽  
Real Problem ◽  
Complete Set ◽  
Celtic Stone ◽  
Model Of Friction ◽  
First Time ◽  
Circular Contact

In this paper, for the first time, the complete set of Tangens hyperbolicus approximations of model of dry friction coupled with rolling resistance for circular contact area between interacting bodies is proposed. The developed approximations are compared with corresponding Padé approximants of the first and second order well known from the literature and with the numerical solution of the exact integral model as well. It is shown that Tangens hyperbolicus approximants are closest to the exact solution. Then the approximated models are applied to the celtic stone dynamics, however with the significant simplifying assumption of circular contact between stone and the table, presenting differences between them again. Certain specific approximations and regularizations of the friction and rolling resistance models enabling and facilitating their application to the real problem are shown. The analysis of the response dependence on initial conditions is performed by the use of a special kind of diagram.

Stress in Bonded Adherends for Single Lap Joints

1996 ◽  
Vol 12 (03) ◽  
pp. 167-171
Author(s):  
G. Bezine ◽  
A. Roy ◽  
A. Vinet
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Numerical Model ◽  
Stress Distribution ◽  
Normal Stress ◽  
Lap Joints ◽  
Axial Loads ◽  
Normal Stress Distribution ◽  
Single Lap Joints ◽  
Element Technique

A finite-element technique is used to predict the shear stress and normal stress distribution in adherends for polycarbonate/polycarbonate single lap joints subjected to axial loads. Numerical and photoelastic results are compared so that a validation of the numerical model is obtained. The influences on stresses of the overlap length and the shape of the adherends are studied.

Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Damping Ratio ◽  
Strong Dependence ◽  
Time Integration ◽  
Single Mode ◽  
Stick Slip ◽  
Friction Forces ◽  
Equivalent Damping ◽  
Damping Characteristics ◽  
Parameter Values

Abstract The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.

Normal stress distribution adjacent to optimum holes in composite plates

1994 ◽  
Vol 29 (4) ◽  
pp. 393-398 ◽  
Author(s):  
R. Ramesh Kumar ◽  
G. Venkateswara Rao ◽  
K.S. Suresh
Keyword(s):  
Stress Distribution ◽  
Normal Stress ◽  
Composite Plates ◽  
Normal Stress Distribution

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.

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.

Dry-Friction Whip and Whirl Predictions for a Rotor-Stator Model With Rubbing Contact at Two Locations

2011 ◽  
Author(s):  
Dara W. Childs ◽  
Dhruv Kumar
Keyword(s):  
Analytical Solutions ◽  
Dry Friction ◽  
Supported Housing ◽  
Precession Frequency ◽  
Rigid Rotor ◽  
Clearance Ratio ◽  
Running Speed ◽  
Nonlinear Simulation ◽  
Friction Forces ◽  
Nonlinear Connections

The present work investigates the phenomena of whip and whirl for a rigid rotor contacting at two bearing locations. The idea originated with a paper by Clark et al. in 2009 on an anemometer undergoing dry friction whip and whirl. The anemometer rotor was supported by two Teflon® bushings within an elastically supported housing. The dry-friction forces arose at the bushings. Prior models for dry friction whirl and whip have considered rub at one non-support location. The present analytical model consists of a rigid rotor connected to a rigid stator at two rubbing contact locations. Analytical solutions are developed for the following normal reaction forces at the contact locations: (1) In phase, and (2) 180 degrees out of phase. Analytical solutions are only possible for the same RCl (Radius to Clearance ratio) at the two rub locations and define regions where dry-friction whirl is possible plus indication possible boundaries between whirl and whip. These solutions are similar to Black’s in 1968. A flexible-rotor/flexible-stator model with nonlinear connections at the bearings was developed to more correctly establish the range of possible solutions. The nonlinear connections at the rub surface are modeled using Hunt and Crossley’s 1975 contact model with coulomb friction. Dry friction simulations are performed for the following rotor center of gravity (C.G.) configurations: (1) Centered, (2) 3/4 contact-span location and (3) Overhang location outside the contacts. Results from the in-phase analytical solutions and the nonlinear simulations agree to some extent with the rotor mass centered and at 3/4 location in that whirl-to-whip transitions occur near the pinned rotor-stator bounce frequency. For the overhung mass case, the nonlinear simulation predicts whip at different frequencies for the two contact locations. Neither analytical solution modes predicts this outcome. No out-of-phase solutions could be obtained via time-transient simulations. Dry-friction whirling is normally characterized as supersynchronous precession with a precession frequency equal to running speed times RCl. Simulation predictions for models with different RCl mimic whirling. Simulation predictions show increasing backward precessional (BP) frequency with increasing rotor speeds. However, individual contact velocities show slipping at all conditions. Slipping is greater at one location than the other, netting a “whirl-like” motion. For the overhung model with different RCl ratios, apart from whipping at different frequency the two contacts also whirl at different frequencies corresponding to the RCl at the respective contacts. Simulations predict a different running speed for the “jump up” in precession frequency associated with a transition from whirl-to-whip with increasing running speed than for the jump-down in precession frequency for whirl-to-whip in a speed-decreasing mode.

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