Self-Excited Oscillations in Sliding With a Constant Friction Coefficient—A Simple Model

1996 ◽  
Vol 118 (4) ◽  
pp. 819-823 ◽  
Author(s):  
G. G. Adams
Keyword(s):  
Simple Model ◽  
Steady State Solution ◽  
Partial Loss ◽  
Positive Real ◽  
Stick Slip ◽  
Complex Modes ◽  
Constant Friction ◽  
Modes Of Vibration ◽  
The Coefficient Of Friction ◽  
Loss Of Contact

The sliding of two surfaces with respect to each other involves many interacting phenomena. In this paper a simple model is presented for the dynamic interaction of two sliding surfaces. This model consists of a beam on elastic foundation acted upon by a series of moving linear springs, where the springs represent the asperities on one of the surfaces. The coefficient of friction is constant. Although a nominally steady-state solution exists, an analysis of the dynamic problem indicates that the steady solution is dynamically unstable for any finite speed. Eigenvalues with positive real parts give rise to self-excited motion which continues to increase with time. These self-excited oscillations can lead either to partial loss-of-contact or to stick-slip. The mechanism responsible for the instability is a result of the interaction of certain complex modes of vibration (which result from the moving springs) with the friction force of the moving springs. It is expected that these vibrations play a role in the behavior of sliding members with dry friction.

Self-Excited Oscillations in Sliding With a Constant Friction Coefficient

1995 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Dry Friction ◽  
Steady State Solution ◽  
Dynamic Interaction ◽  
Positive Real ◽  
Finite Speed ◽  
Sliding Surfaces ◽  
Complex Modes ◽  
Constant Friction ◽  
Modes Of Vibration ◽  
The Coefficient Of Friction

Abstract The sliding of two surfaces with respect to each other involves many interacting phenomena. In this paper a simple model is presented for the dynamic interaction of two dry sliding surfaces. This model consists of a beam on elastic foundation acted upon by a series of moving linear springs, where the springs represent the asperities on one of the surfaces. The coefficient of friction is constant. Although a nominally steady-state solution exists, an analysis of the dynamic problem indicates that the steady solution is dynamically unstable for any finite speed. Eigenvalues with positive real parts give rise to self-excited motion which continues to increase with time. The mechanism responsible for the instability is a result of the interaction of certain complex modes of vibration (which result from the moving springs) with the friction force of the moving springs. It is expected that these vibrations play a role in the behavior of sliding members with dry friction.

Dynamic Instabilities in the Sliding of Two Layered Elastic Half-Spaces

1998 ◽  
Vol 120 (2) ◽  
pp. 289-295 ◽  
Author(s):  
G. G. Adams
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Positive Real ◽  
Stick Slip ◽  
Dynamic Stresses ◽  
Dynamic Motion ◽  
Sliding Motion ◽  
Complex Eigenvalues ◽  
Wide Range ◽  
Loss Of Contact

Two flat layered elastic half-spaces, of different material properties, are pressed together and slide against each other with a constant coefficient of friction. Although a nominally steady-state solution exists, an analysis of the dynamic motion yields complex eigenvalues with positive real parts, i.e., a flutter instability. These results demonstrate that self-excited (unstable) motion occurs for a wide range of material combinations. The physical mechanism responsible for this instability is that of slip-wave destabilization. The influence of the properties of the layers on the destabilization of sliding motion is investigated. These dynamic instabilities lead either to regions of stick-slip or to areas of loss-of-contact. Finally the dynamic stresses at the interfaces between the layers and the semi-infinite bodies are determined and compared to the nominally steady-state stresses. These dynamic stresses are expected to play an important role in delamination.

Self-Excited Oscillations of Two Elastic Half-Spaces Sliding With a Constant Coefficient of Friction

1995 ◽  
Vol 62 (4) ◽  
pp. 867-872 ◽  
Author(s):  
G. G. Adams
Keyword(s):  
Coefficient Of Friction ◽  
Material Properties ◽  
Constant Coefficient ◽  
Dry Friction ◽  
Steady State Solution ◽  
Interfacial Slip ◽  
Positive Real ◽  
Stick Slip ◽  
Wide Range ◽  
Loss Of Contact

Two flat isotropic elastic half-spaces, of different material properties, are pressed together and slide against each other with a constant coefficient of friction. Although a nominally steady-state solution exists, an analysis of the dynamic problem demonstrates that the steady solution can be dynamically unstable. Eigenvalues with positive real parts give rise to self-excited motion which occurs for a wide range of material pairs, coefficients of friction, and sliding velocities (including very low speeds). These self-excited oscillations are generally confined to the region near the interface and can lead either to regions of loss of contact or to areas of stick slip. The mechanism responsible for the instability is essentially one of destabilization of interfacial (slip) waves. It is expected that these vibrations might play an important role in the behavior of sliding members with dry friction.

Vibration and Analysis of Multi-Disk Friction Systems

1998 ◽  
Author(s):  
Henric Larsson ◽  
Kambiz Farhang
Keyword(s):  
Frictional Contact ◽  
Vibration Characteristics ◽  
Lumped Parameter Model ◽  
Stick Slip ◽  
Friction Forces ◽  
Lumped Parameter ◽  
Modes Of Vibration ◽  
The Coefficient Of Friction ◽  
Slip Region ◽  
Stiffness And Damping

Abstract The paper presents a lumped parameter model of multiple disks in frictional contact. The contact elastic and dissipative characteristics are represented by equivalent stiffness and damping parameters in the axial as well as the torsional directions. The formulation accounts for the coupling betwen the axial and angular motions by viewing the contact normal force to be the result of axial behavior of the system. The frictional contact of two disks in contact is modeled in two dynamic states (i.e. sticking and slipping state) having individual lumped parameter models and the conditions that control the switching between the two states are established. The friction forces are represented by assuming the coefficient of friction to be a function of the sliding velocity, varying exponentially from its static value at zero relative velocity to its kinetic value at high velocities. A computer simulation of an eight-rotor disk assembly is presented. The torsional vibration characteristics and how it is liked to the axial modes of vibration is analyzed. The vibration characteristics in the transient, steady-state and stick-slip region is compared. In the stick-slip region, the angular velocity of the interfaces in frictional contact is depicted and the sticking and slipping states are defined. It is shown that the duration of slip is approximately constant and the duration of stick increases almost exponentially until a final sticking is achieved.

Micro/Nano-Tribological Behavior of Octadecyltrichlorosilane on Silicon as a Coating for MEMS

2005 ◽  
Author(s):  
J. Barriga ◽  
B. Ferna´ndez ◽  
E. Abad ◽  
B. Coto
Keyword(s):  
Liquid Phase ◽  
Vapour Phase ◽  
Stick Slip ◽  
Force Microscopy ◽  
Angle Measurements ◽  
Atomic Force ◽  
Contact Angle Measurements ◽  
Assembled Monolayers ◽  
The Coefficient Of Friction ◽  
Semicontact Mode

Despite progresses achieved in the technology of MEMS, the tribological problem continues being an unresolved matter. Wear and stick-slip phenomena are many times the origin of failure of these devices. The application of self-assembled monolayers (SAMs) in liquid phase seems to be a solution to this problems. SAMs of octadecyltrichlorosilane (CH3(CH2)17SiCl3, OTS) were attached to Si(100) oxidized in liquid phase. Contact angle measurements were used for characterizing the grade of hydrophobicity. The topography of the coating was obtained with an Atomic Force Microscopy (AFM) in semicontact mode. The images showed the presence of particles related to the polymerization of the precursor molecule during the formation process of the SAMs. Creating the film of lubricant in vapour phase would avoid this undesirable effect. Tribological tests were carried out with a microtribometer in linear reciprocating movement with a ball of 2 mm of diameter (100Cr6 and Si3N4) and load of some milinewtons. Results were compared with those obtained for silicon oxidized without any coating. The coefficient of friction (COF) and wear (substrate and ball) were studied under different test conditions.

scholarly journals Experimental Study on the Transition between Static and Kinetic Frictions of Steel/Shale Pairs

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Qin Lian ◽  
Chunxu Yang ◽  
Jifei Cao
Keyword(s):  
Friction Coefficient ◽  
Normal Load ◽  
Critical Distance ◽  
Dynamic Friction ◽  
Stick Slip ◽  
Dynamic Friction Coefficient ◽  
The Coefficient Of Friction ◽  
The Difference ◽  
Stick Slip Motion ◽  
Insight Into

The transition between static and kinetic frictions of steel/shale pairs has been studied. It was found that the coefficient of friction decreased exponentially from static to dynamic friction coefficient with increasing sliding displacement. The difference between static and dynamic friction coefficients and the critical distance Dc under the dry friction condition is much larger than that under the lubricated condition. The transition from static to dynamic friction coefficient is greatly affected by the normal load, quiescent time, and sliding velocity, especially the lubricating condition. Maintaining continuous lubrication of the contact area by the lubricant is crucial to reduce or eliminate the stick-slip motion. The results provide an insight into the transition from static to dynamic friction of steel/shale pairs.

Tribological Investigation of Copper (Cu) and Copper Oxide (CuO) Nanoparticles Based Nanolubricants for Machine Tool Slideways

2014 ◽  
Author(s):  
Saravanakumar Nesappan ◽  
Nallasamy Palanisamy ◽  
Mahesh Chandran
Keyword(s):  
Electron Microscope ◽  
Machine Tool ◽  
Copper Oxide ◽  
Elevated Temperatures ◽  
Stick Slip ◽  
Base Oil ◽  
Weight Composition ◽  
The Coefficient Of Friction ◽  
Oxide Particles ◽  
Mineral Lubricant

The present study intends to evaluate the tribological characteristics of Copper (Cu) and Copper oxide (CuO) based nanolubricant for its use in machine tool slideways. Different sizes of copper and copper oxide particles were chosen and physical characterisation were carried out using scanning electron microscope (SEM) and transmission electron microscope (TEM). The nanolubricants were prepared by adding various proportions (0.1%, 0.25%, 0.4% wt) of the particles in Polyalphaolefin (PAO) base oil with lecithin and oleic acid surfactants. Friction and stick-slip characteristics of the nanolubricants were assessed using pin-on-block reciprocating friction monitor simulating the actual loading conditions prevailing in machine tool slideways. Studies were also conducted under elevated temperatures to ascertain the performance of particles at higher temperatures. Extreme pressure properties of the lubricants were studied using Four Ball Tester. The results of the experiments were compared with ISO VG 32 oil, a conventional mineral lubricant meant for machine tool slideways and it was found that the tribological properties nanolubricants using both the nanoparticles were considerably better. The coefficient of friction found to be decreased by 2.5% and 17.5% for copper particles with 0.1% weight composition in ambient temperature and elevated temperature respectively. Whereas for copper oxide particles with 0.1% weight composition a reduction of 14.25% and 10% were obtained.

Frictional Vibrations

1955 ◽  
Vol 22 (2) ◽  
pp. 207-214
Author(s):  
David Sinclair
Keyword(s):  
Coefficient Of Friction ◽  
Equations Of Motion ◽  
Static Friction ◽  
Uniform Motion ◽  
Friction Characteristic ◽  
Stick Slip ◽  
The Coefficient Of Friction ◽  
Brake Lining ◽  
Solid Bodies ◽  
Frictional Vibrations

Abstract Frictional vibrations, such as stick-slip motion and automobile-brake squeal, which occur when two solid bodies are rubbed together, are analyzed mathematically and observed experimentally. The conditions studied are slow uniform motion and relatively rapid simple harmonic motion of brake lining over a cast-iron base. The equations of motion show and the observations confirm that frictional vibrations are caused primarily by an inverse variation of coefficient of friction with sliding velocity, but their form and occurrence are greatly dependent upon the dynamical constants of the mechanical system. With a constant coefficient of friction, the vibration initiated whenever sliding begins is rapidly damped out, not by the friction but by the “natural” damping of all mechanical systems. The coefficient of friction of most brake linings and other organic materials was essentially invariant with velocity, except that the static coefficient was usually greater than the sliding coefficient. Most such materials usually showed a small decrease in coefficient with increasing temperature. The persistent vibrations resulting from the excess static friction were reduced or eliminated by treating the rubbing surfaces with polar organic compounds which produced a rising friction characteristic.

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.

A Study of the Stick-Slip Motion of Machine Tool Feed Drives

1969 ◽  
Vol 184 (1) ◽  
pp. 543-560 ◽  
Author(s):  
R. Bell ◽  
M. Burdekin
Keyword(s):  
Cast Iron ◽  
Simple Model ◽  
Machine Tools ◽  
Dynamic Measurements ◽  
Stick Slip ◽  
Feed Drive ◽  
Feed Drives ◽  
Stick Slip Motion ◽  
Lubricant Viscosity ◽  
Slip Motion

The phenomenon of ‘stick-slip’ oscillations of the feed drives of machine tools is an important problem in the design of certain types of machine tools. The factors contributing to this particular type of instability are studied both experimentally and analytically with the aid of a simple model based on dynamic measurements. The experimental work is restricted to a scraped cast iron-cup ground cast iron slideway interface. The principal experimental variables are lubricant viscosity and the natural frequency of the drive. The dynamic observations provide evidence and data that enable the use of a simple model rather than the more usual application of an involved analysis. The consideration of analytical and experimental results allows further understanding of the mechanism of feed drive instability to be developed.

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