Stiff Testing Machines, Stick Slip Sliding, and the Stability of Rock Deformation

2013 ◽  
pp. 93-102 ◽  
Author(s):  
Neville G. W. Cook
Keyword(s):  
Rock Deformation ◽  
Stick Slip ◽  
The Stability

Friction Induced Vibrations in Aircraft Disk Brakes

1997 ◽  
Author(s):  
Lisle B. Hagler ◽  
Per G. Reinhall
Keyword(s):  
Friction Coefficient ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Rotational Model ◽  
Stick Slip ◽  
Numeric Simulation ◽  
Constant Friction ◽  
The Stability ◽  
Rotor Stiffness ◽  
Friction Induced Vibration

Abstract This paper presents a detailed analysis of the dynamic behavior of a single rotor/stator brake system. Two separate mathematical models of the brake are considered. First, a non-rotational model is constructed with the purpose of showing that friction induced vibration can occur in the stator without assuming stick-slip behavior and a velocity dependent friction coefficient. Self-induced vibrations are analyzed via the application of the method of multiple scales. The stability boundaries of the primary resonance, as well as the super-harmonics and sub-harmonics are determined. Secondly, rotational effects are investigated by considering a mathematical brake model consisting of a spinning rotor engaging against a flexible stator. Again, a constant friction coefficient is assumed. The stability of steady whirl is determined as a function of the system parameters. We demonstrate that only forward whirl is stable for no-slip motion of the rotor. The interactions between chatter, squeal, and rotor whirl are investigated through numeric simulation. It is shown that rotor whirl can be an important source of the torsional oscillations (squeal) of the stator and that the settling time to no-slip decreases as the ratio of the stator to rotor stiffness is increased.

Thermal Instability of Sliding and Oscillations Due to Frictional Heating Effect

1988 ◽  
Vol 110 (1) ◽  
pp. 69-72 ◽  
Author(s):  
I. L. Maksimov
Keyword(s):  
Thermal Instability ◽  
Initial Conditions ◽  
Frictional Heating ◽  
Interface Temperature ◽  
Heating Effect ◽  
Stick Slip ◽  
Instability Development ◽  
The Stability ◽  
Sliding Dynamics ◽  
Sliding Instability

The stability of sliding has been studied, taking into account frictional heating effect and friction coefficient dependence upon the interface temperature and sliding velocity. The collective—thermal and mechanical—sliding instability has been found to exist; instability emergence conditions and dynamics (both in linear and nonlinear stages) have been determined. It is shown that both the threshold and the dynamics of thermofrictional instability differ qualitatively from the analogous characteristics of “stick-slip” phenomenon. Namely, the oscillational instability behavior due to the energy exchange between thermal and mechanical modes has been found to occur under certain initial conditions; the velocities range has been determined for which collective sliding instability may occur whereas the stick-slips would be not possible. The nonlinear analysis of instability evolution has been carried out for pairs with the negative thermal-frictional sliding characteristics, the final stage of sliding dynamics has been described. It is found that stable thermofrictional oscillations can occur on the nonlinear stage of sliding instability development; the oscillations frequency and amplitude have been determined. The possibility has been discussed of the experimental observation of new dynamical sliding phenomena at low temperatures.

scholarly journals Stability of PDF Controller With Stick-Slip Friction Device

1997 ◽  
Vol 119 (3) ◽  
pp. 486-490 ◽  
Author(s):  
Jia-Yush Yen ◽  
Chih-Jung Huang ◽  
Shu-Shung Lu
Keyword(s):  
Control Algorithm ◽  
Controller Design ◽  
System Model ◽  
Pole Placement ◽  
Order System ◽  
Stick Slip ◽  
Precision Control ◽  
Experimental Works ◽  
The Stability ◽  
Control Accuracy

This paper presents the precision control of drive devices with significant stick-slip friction. The controller design follows the Pseudo-Derivative Feedback (PDF) control algorithm. Using the second order system model, the PDF controller offers arbitrary pole placement. In this paper, the stability proof for the controller with stick-slip friction is presented. On the basis of this proof, the stability criteria are derived. The paper also includes both the computer simulation and the experimental works to confirm the theoretical result. The experiments conducted on a Traction Type Drive Device (TTDD) shows that control accuracy of as high as ±1 arc – second is achieved.

scholarly journals Mitigation of Torsional Vibrations in Drilling Systems using Adaptive Nonlinear Control System

2020 ◽  
Vol 9 (4) ◽  
pp. 3317-3321
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
String Model ◽  
Stick Slip ◽  
Rock Interaction ◽  
Performance Specifications ◽  
Level Model ◽  
Multi Level ◽  
The Stability ◽  
Level Training

The reason for this work is to plan a robust yield feedback control way to deal with dispense with torque stick-slip vibrations in boring frameworks. Current industry controllers generally neglect to dispose of stick-slip vibrations, particularly when different torque flex modes assume a job in maniacal assault. In terms of build controller production, a real trainingstring system performs a multi-level model work such as torque mechanics. The proposed controller design is artfully distorted at optimizing the stability with respect to the uncertainty of the nonlinear bit-rock interaction. Based on heroes and intentions. Besides, a closed loop strength examination of the nonlinear preparing string model is displayed. This controller structure system offers a few points of interest contrasted with existing controllers. To begin with, just surface estimations are utilized, barring the requirement for entire estimations underneath it. Second, multi-level training-string dynamics are effectively handled in ways to access state-training controllers. Third, stability is explicitly provided with respect to bit-rock contact uncertainty and closed-loop performance specifications include controller design. The results of the study report confirm that stick-slip vibrations are actually eliminated in realistic drilling scenarios using a controller designed to achieve this state-ofcontrol control.

Influencing Factors on Stick-Slip Behavior of a Ball Screw Driven Elevation Mechanism for MLRS

2012 ◽  
Vol 271-272 ◽  
pp. 958-968
Author(s):  
Young Hyu Choi ◽  
Sung Hyun Jang ◽  
Ji Han Oh
Keyword(s):  
Mathematical Model ◽  
Ball Screw ◽  
Force Model ◽  
Stick Slip ◽  
Single Degree Of Freedom ◽  
Stribeck Effect ◽  
The Stability ◽  
Friction Parameters ◽  
The Mathematical Model ◽  
Rocket System

As an MLRS (Multiple Launch Rocket System) cage is moved with a uniform speed through an elevation mechanism for MRLS operated using ball screws, its stick-slip behavior can be observed by the friction in a ball screw actuator. In this study, a single-degree of freedom mathematical model of an MLRS elevation system is designed and its stick-slip behavior is analyzed using a friction force model considering the Stribeck effect. The stability of a vibration system is analyzed through deriving an equation of normalized motion for the mathematical model and the influences of mechanical parameters and friction parameters on the vibration response and stability are theoretically analyzed.

The Study of the Triaxial Rheological Test of the Argillaceous Siltstone in Malin Mine

2012 ◽  
Vol 446-449 ◽  
pp. 2125-2131 ◽  
Author(s):  
Qi Shu Bai ◽  
Yuan You Xia ◽  
Xin Xi Liu ◽  
Zi Han Yang
Keyword(s):  
Coal Industry ◽  
Surrounding Rock ◽  
Rock Deformation ◽  
Creep Characteristics ◽  
Reasonable Evidence ◽  
Roadway Support ◽  
The Stability ◽  
Argillaceous Siltstone ◽  
Rheological Test ◽  
The Relationship

Abstract. Coal being one of the main energy resources in China. Coal industry plays an important role in the domestic economy. Roadway support is a key technology in coal mining, and the mechanical properties of surrounding rock directly affect the stability of roadways and their supporting structure. In order to solve the problem of gateway support for C8 coal seam, In terms of the rheological data got from the argillaceous siltstone samples and the influence that loading history has on rock deformation, it employs Burgers model to reflect the creep characteristics of rock. The analytical results demonstrate that the creep test curves of rock sample basically tallies with the theoretical curves and Burgers clearly describes the creep characteristics of rocks. The relationship between surrounding rock stress and surrounding rock deformation provides roadway support with reasonable evidence.

Impact of dilatant strengthening and energy dissipation on fault slip stability

2021 ◽  
Author(s):  
Antoine Jacquey ◽  
Manolis Veveakis ◽  
Ruben Juanes
Keyword(s):  
Energy Dissipation ◽  
Fluid Pressure ◽  
Fault Slip ◽  
Numerical Continuation ◽  
Dissipated Energy ◽  
Dynamic Evolution ◽  
Coupling Scheme ◽  
Aseismic Slip ◽  
Stick Slip ◽  
The Stability

<p>The temporal and spatial distribution of fluid pressure and temperature within a fault core are key determinants of the onset and nature (seismic or aseismic) of fault slip. Laboratory and field observations indicate that transient localization of fluid pressure and temperature often go hand in hand with strain localization upon seismic rupture: as slip occurs on a fault plane, temperature increases due to dissipated energy and fluid pressure decreases due to dilatant strengthening. An accurate description of this thermo-hydro-mechanical multiphysics coupling controlling slip mechanisms is therefore essential to characterize the stability of fault slip.</p><p>Here, we present results from analytical and numerical analyses of the stability of fault slip adopting a thermo-hydro-mechanical coupling scheme together with a rate-dependent plasticity formulation. In particular, we focus on the relevance of dilatant strengthening competing with energy dissipation as driving processes for stick-slip events and aseismic slip. We analyze the multiple steady states of the system and their respective stability by means of a numerical continuation technique, and we describe the dynamic evolution of deformation, fluid pressure and temperature fields by considering an associated transient problem.</p><p>The results presented here provide insights into the stability criterion for aseismic slip and the dynamic evolution of slip instability as a function of the physical (thermal and hydraulic) properties of the fault material and the boundary conditions (tectonic stresses and off-fault fluid pressure and temperature conditions). We identify two mechanisms for periodic slip, one driven by elastic loading and the other by multiphysics oscillations. We discuss the implications of these results for characterizing the transition from stable aseismic slip to unstable seismic slip in the context of natural and induced seismicity.</p>

Fault healing plays a key role in creating the spectrum of tectonic faulting styles from seismic to aseismic slip

2020 ◽  
Author(s):  
Chris Marone
Keyword(s):  
Potential Energy ◽  
Stress Drop ◽  
Elastic Strain ◽  
Stability Boundary ◽  
Fault Slip ◽  
Slow Slip ◽  
Stick Slip ◽  
Slow Earthquakes ◽  
The Stability ◽  
Fault Healing

<p>Tectonic faults fail in a broad spectrum of modes ranging from aseismic creep to fast, ordinary, earthquakes modulated by elastodynamic rupture processes. Laboratory friction experiments with repetitive stick-slip failure have reproduced this complete range of modes with failure durations spanning several orders of magnitude. These works show that the frictional weakening rate with slip (i.e., the rheological critical stiffness <em>k<sub>c</sub> =σ<sub>n</sub>(b-a)/D<sub>c</sub></em>, where <em>σ<sub>n</sub></em> is effective fault normal stress, <em>D<sub>c</sub></em> is the friction critical slip distance and <em>(b-a)</em> represents the friction rate parameter) is the primary control on the mode of slip, but higher-order effects are also important including variation of <em>k<sub>c</sub>  </em>with slip velocity.  Far from the stability boundary, stick-slip occurs when the rate of elastic unloading with slip <em>k</em> is small compared to the frictional weakening rate (i.e., <em>k</em><<<em>k<sub>c</sub></em>). Potential energy, in the form of stored elastic strain, drives rapid fault acceleration. Near the stability boundary, when <em>k ~ k<sub>c</sub></em>, lab experiments document slow and quasi-dynamic failure events, consistent with the observation that earthquake stress drop is negligible for slow earthquakes. Lab data show that stick-slip stress drop decreases systematically as <em>k/k<sub>c</sub></em> approaches 1 from below. There are two possible scenarios for slow slip near the stability boundary, although they are degenerate in most cases. 1) Fault slip relieves elastic stresses prior to failure and thus the potential energy needed to drive fast rupture is absent. 2) Elastic strain accumulates but the fault rheology is velocity strengthening or otherwise inconsistent with rapid slip, for example because the frictional weakening rate <em>k<sub>c</sub></em>  is low.  In Scenario 1, slip can occur early in the seismic cycle, as creep, or later in the cycle when shear stress reaches a critical value for precursory slip.  In either case, slip occurs because the rate of fault healing is low compared to the stressing rate. A low rate of fault healing can also explain Scenario 2 because the friction state evolution parameter <em>b</em> scales directly with the rate of fault healing and <em>k<sub>c</sub></em>. Given that the friction parameter <em>a</em> is positive definite, the frictional healing rate (<em>b</em>) sets the scale of <em>k<sub>c</sub></em> for a given value of <em>D<sub>c</sub></em>. Thus, while these two scenarios for slow slip appear distinct they both derive from the rate of fault healing.  Exceptions would involve faults that are strongly velocity weakening <em>(b-a)</em> >>0 yet have negligible healing rates (<em>b</em> ~ 0), which is indeed rare.  The rate of fault healing is expected to vary with mineralogy, effective stress, temperature and other factors. Thus, while we expect a systematic variation of seismic style with depth, associated with changes in <em>k<sub>c</sub></em>, we should not be surprised to find a spectrum of faulting styles throughout the lithosphere, including a range of styles at a given location.  Discoveries of seismic tremor, low frequency earthquakes, and other modes of fault slip are challenging our views of tectonic faulting and they highlight the need for close connections between field observations, detailed laboratory work and theoretical studies of friction and faulting.</p>

The contact line of an evaporating droplet over a solid wedge and the pinned–unpinned transition

2016 ◽  
Vol 791 ◽  
pp. 519-538 ◽  
Author(s):  
Seok Hyun Hong ◽  
Marco A. Fontelos ◽  
Hyung Ju Hwang
Keyword(s):  
Differential Equation ◽  
Contact Line ◽  
Contact Angles ◽  
Liquid Interface ◽  
Stick Slip ◽  
Small Perturbations ◽  
Stability And Instability ◽  
The Stability ◽  
Stick Slip Motion ◽  
Slip Motion

We compute the equilibrium contact angles for an evaporating droplet whose contact line lies over a solid wedge. The stability of the liquid interface is also considered and an integro-differential equation for small perturbations is deduced. The analysis of this equation yields criteria for stability and instability of the contact line, where the instability represents transition from the pinned to unpinned contact line representative of stick–slip motion.

Friction-Induced Squeak of Ceramic-on-Ceramic Hip Implants: A Stability Design Criteria

2012 ◽  
Author(s):  
Mark Sidebottom ◽  
Manish Paliwal
Keyword(s):  
Computer Aided Design ◽  
Acoustic Analysis ◽  
Femoral Stem ◽  
Coupled System ◽  
Stick Slip ◽  
Audio Data ◽  
Mathematical Analyses ◽  
The Stability ◽  
Parametric Analyses ◽  
Ceramic On Ceramic

Friction-induced squeaking has been reported in 1–10% of patients who have a ceramic on ceramic total hip replacement, which is a subject of annoyance. The goal of this study was to investigate the possible factors attributing to the hip squeak, and understand the underlying phenomenon. The investigation involved acoustic, modal, and mathematical analyses. Acoustic analysis involved extracting and analyzing audio data from the videos files of squeaking ceramic hips. The audio data was transformed from the time to frequency domain using Fast Frequency Transform (FFT) using MATLAB. This allowed the identification of the squeal frequencies. Modeling involved 3-D rendering of the hip implant (femoral stem, head, cup liner, and the cup shell) using computer-aided-design software. Mathematical analysis involved the investigation of the role of the frictional stick-slip phenomenon of the metal shell and ceramic liner on squeal using a 2-DOF mathematical model. Mass, stiffness properties, and coefficient of friction of the components were incorporated to study the limit cycle using MATLAB/Simulink, which is an indicator of the stability of the system. Modal (Numerical) analysis involved the evaluation of the modal frequencies of the components using ANSYS, to investigate their contribution to squeal. Acoustic analysis of the squeal frequencies showed that the range of squeal frequencies of the coupled system ranged from 1500–3000 Hz, which concurred well with the literature. Modal Analysis showed the metallic shell’s resonant frequency at 4600 Hz. The parametric analyses using the 2-dof model showed that a stable system was approached as the stiffness of the liner was increased. The increase in mass of the shell resulted in larger limit-cycles. Increased stiffness of the shell proved to stabilize the system for most loading conditions.

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