Friction/Vibration Coupling Due to Viscoelastic Interaction of Rough Surfaces of Two Disks in Frictional Contact

2003 ◽  
Author(s):  
Kambiz Farhang ◽  
Aik-Liang Lim
Keyword(s):  
Contact Force ◽  
Dynamic Instability ◽  
Rough Surfaces ◽  
Normal Load ◽  
Mathematical Formulation ◽  
Negative Slope ◽  
Axial Position ◽  
Disk System ◽  
Macro Scale ◽  
Approximate Equations

Approximate equations describing contact of rough surfaces are implemented in the equations of motion for frictional interaction of two disks in relative rotational motion. The approximate equations are nonlinear functions of the relative axial position of the two disks and provide coupling between their compressive and rotary motion. A set of two coupled nonlinear ordinary differential equations is obtained. The mathematical formulation propounded in this paper connects the tribological events at micron-scale and the macroscopic scale vibration response of the two-disk system. This is accomplished by a visco-elastic account of interaction at the micron scale, its statistical quantification through the approximate analytical representation of the statistical expectation of contact force and the introduction of the contact force into the macro-scale dynamics of the two-disk system. Steady-state analysis of the system supports observed behavior of many mechanical systems with friction. It is shown that, as a result of coupling of the macro-system’s dynamics and contact, there are combinations of parameters at the microand macro-scale that yield negative slope in friction force/sliding speed, a well known source of dynamic instability. This results in an effective negative damping that tends to reduce with decrease in the normal load and/or increase in structural damping of the system.

A Non-Phenomenological Account of Friction/Vibration Interaction in Rotary Systems

2004 ◽  
Author(s):  
Kambiz Farhang ◽  
Aik-Liang Lim
Keyword(s):  
Contact Force ◽  
Dynamic Instability ◽  
Normal Load ◽  
Mathematical Formulation ◽  
Friction Torque ◽  
Negative Slope ◽  
Disk System ◽  
Disk Brake ◽  
Macro Scale ◽  
Phenomenological Account

The mathematical formulation relates the tribological events at micron-scale and the macroscopic scale vibration response of a two-disk brake system. This is accomplished by a visco-elastic account of interaction at the micron scale, its statistical quantification through the approximate analytical representation of the statistical expectation of contact force and the introduction of the contact force into the macro-scale dynamics of the two-disk system. Steady-state analysis of the system establishes the relation between friction torque and speed and supports observed behavior of many mechanical systems with friction. It is shown that, as a result of coupling of the macro-system’s dynamics and contact, there are combinations of parameters at the micro- and macro-scale that yield negative slope in friction torque/sliding speed relation, a well known source of dynamic instability. This results in an effective negative damping that tends to reduce with decrease in the normal load and/or increase in structural damping of the system.

Derivation of Friction Torque-Speed Relation Due to Viscoelastic Contact in a Two-Disk Brake

2004 ◽  
Author(s):  
Kambiz Farhang ◽  
Aik-Liang Lim
Keyword(s):  
Contact Force ◽  
Dynamic Instability ◽  
Normal Load ◽  
Mathematical Formulation ◽  
Friction Torque ◽  
Brake System ◽  
Negative Slope ◽  
Coupled Equations ◽  
Disk Brake ◽  
Macro Scale

Using a nonlinear model of a two disk brake system, coupled equations of motion are found for their frictional interaction. The mathematical formulation relates the tribological events at micron-scale and the macroscopic scale vibration response of a two-disk brake system. This is accomplished by a visco-elastic account of interaction at the micron scale, its statistical quantification through the approximate analytical representation of the statistical expectation of contact force and the introduction of the contact force into the macro-scale dynamics of the two-disk system. Steady-state analysis of the system establishes the relation between friction torque and speed and supports observed behavior of many mechanical systems with friction. It is shown that, as a result of coupling of the macro-system’s dynamics and contact, there are combinations of parameters at the micro-and macro-scale that yield negative slope in friction torque/sliding speed relation, a well known source of dynamic instability. This results in an effective negative damping that tends to decrease with decrease in the normal load and/or increase in structural damping of the system.

Stribeck Effect in the Frictional Viscoelastic Contact of Rough Surfaces

2008 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Contact Force ◽  
Dynamic Instability ◽  
Normal Load ◽  
Mathematical Formulation ◽  
Friction Torque ◽  
Brake System ◽  
Negative Slope ◽  
Disk System ◽  
Coupled Equations ◽  
Disk Brake

Using a nonlinear model of a two disk brake system, coupled equations of motion are found for their frictional interaction. The mathematical formulation relates the tribological events at micron scale and the macroscopic scale vibration response of a two-disk brake system. This is accomplished by a viscoelastic account of interaction at the micron scale, its statistical quantification through the approximate analytical representation of the statistical expectation of contact force and the introduction of the contact force into the macroscale dynamics of the two-disk system. Steady-state analysis of the system establishes the relation between friction torque and speed and supports observed behavior of many mechanical systems with friction. It is shown that, as a result of coupling of the macrosystem’s dynamics and contact, there are combinations of parameters at the micro- and macroscale that yield negative slope in friction torque/sliding speed relation, a well known source of dynamic instability. This results in an effective negative damping that tends to decrease with decrease in the normal load and/or increase in structural damping of the system.

A Multi-Scale Account of Friction-Vibration Interaction

2008 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Contact Force ◽  
Dynamic Instability ◽  
Normal Load ◽  
Mathematical Formulation ◽  
Friction Torque ◽  
Brake System ◽  
Negative Slope ◽  
Coupled Equations ◽  
Disk Brake ◽  
Macro Scale

Using a nonlinear model of a two disk brake system, coupled equations of motion are found for their frictional interaction. The mathematical formulation relates the tribological events at micron scale and the macroscopic scale vibration response of a two-disk brake system. This is accomplished by a viscoelastic account of interaction at the micron scale, its statistical quantification through the approximate analytical representation of the statistical expectation of contact force and the introduction of the contact force into the macro-scale dynamics of the two-disk system. Steady-state analysis of the system establishes the relation between friction torque and speed and supports observed behavior of many mechanical systems with friction. It is shown that, as a result of coupling of the macro-system’s dynamics and contact, there are combinations of parameters at the micro- and macro-scale that yield negative slope in friction torque/sliding speed relation, a well known source of dynamic instability. This results in an effective negative damping that tends to decrease with decrease in the normal load and/or increase in structural damping of the system.

A Non-Phenomenological Account of Friction/Vibration Interaction in Rotary Systems

2005 ◽  
Vol 128 (1) ◽  
pp. 103-112 ◽  
Author(s):  
Kambiz Farhang ◽  
Aik-Liang Lim
Keyword(s):  
Contact Force ◽  
Dynamic Instability ◽  
Normal Load ◽  
Mathematical Formulation ◽  
Friction Torque ◽  
Brake System ◽  
Negative Slope ◽  
Disk System ◽  
Coupled Equations ◽  
Disk Brake

Using a nonlinear model of a two disk brake system, coupled equations of motion are found for their frictional interaction. The mathematical formulation relates the tribological events at micron scale and the macroscopic scale vibration response of a two-disk brake system. This is accomplished by a viscoelastic account of interaction at the micron scale, its statistical quantification through the approximate analytical representation of the statistical expectation of contact force and the introduction of the contact force into the macroscale dynamics of the two-disk system. Steady-state analysis of the system establishes the relation between friction torque and speed and supports observed behavior of many mechanical systems with friction. It is shown that, as a result of coupling of the macrosystem’s dynamics and contact, there are combinations of parameters at the micro- and macroscale that yield negative slope in friction torque/sliding speed relation, a well known source of dynamic instability. This results in an effective negative damping that tends to decrease with decrease in the normal load and/or increase in structural damping of the system.

scholarly journals Identification of Friction/Vibration Interaction between Solids

2008 ◽  
Vol 5 (1) ◽  
pp. 62 ◽  
Author(s):  
J. A. Abdo ◽  
N. Al-Rawahi
Keyword(s):  
Friction Force ◽  
Dynamic Instability ◽  
Loss Modulus ◽  
Rough Surfaces ◽  
Mathematical Formulation ◽  
Negative Slope ◽  
Nonlinear Ordinary Differential Equations ◽  
Friction Forces ◽  
Phenomenological Account ◽  
Voigt Model

 Dry-friction forces have been shown to depend not only on the characteristics of the surface in contact but also on the dynamic interaction of the contacting bodies. A viscoelastic mathematical model that accounts for the interaction at micro-scale of rough surfaces is developed. The mathematical formulation relates the tribological events at microscopic and macroscopic scales vibration response of a "mass on moving belt". The viscoelastic properties are presented by combining loss modulus with Young's modulus to obtain a differential operator on the interference, reminiscent of the Kelvin-Voigt model. The analysis of the system establishes the relation between friction force and speed and supports observed behavior of many systems with friction. The derivations do not rely on a phenomenological account of friction, which requires a presumed friction coefficient. Instead the friction force is accounted for as a result of interaction of the rough surfaces. This has led to a set of nonlinear ordinary differential equations that directly relate the vibration of the system to the surface parameters. It is shown that, as a result of coupling of the macrosystem's dynamics and contact, there are combinations of parameters at micro- and macroscale that yield negative slope in friction force/sliding speed relation, a well known source of dynamic instability. 

A Contact Model of Nominally Flat Rough Surfaces Based on a Visco-Elasto-Adhesive Interaction

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
W. Cheng ◽  
K. Farhang
Keyword(s):  
Closed Form ◽  
Contact Force ◽  
Rough Surfaces ◽  
Mathematical Formulation ◽  
Power Laws ◽  
Adhesive Interaction ◽  
Time Rate ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Rate Dependent

Approximate closed-form equations are derived for normal contact force between nominally flat rough surfaces in dry contact. The formulation is based on the asperity-level interaction in which adhesive forces between two asperities and elastic and rate-dependent forces are included. The elastic and time rate-dependent portion of force is derived using a viscoelastic interaction of the two asperities. Statistical consideration of rough surfaces then furnishes the mathematical formulation of total normal force due to adhesion, elastic, and rate-dependent properties of the solids in contact. The probabilistic formulation of contact force leads to integral equations. From these are derived approximate closed-form expressions that relate the microscale properties of the surfaces to the macroscale behavior in the form of the total normal contact force between the surfaces. The approximate equations for visco-elasto-adhesive contact of rough surfaces illustrate the dependence of the contact force on the time rate of approach based on a combination of 1/6, 1/3, and 1 power laws.

Contact of Rough Surfaces: Combined Elastic and Rate-Dependent Effects

2008 ◽  
Author(s):  
Ali Sepehri ◽  
Kambiz Farhang
Keyword(s):  
Half Plane ◽  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Approximation Error ◽  
Tangential Velocity ◽  
Contact Forces ◽  
Tangential Contact ◽  
Force Components ◽  
Approximate Equations

Approximate closed form equations are found for normal and tangential contact forces of rough surfaces in dry friction. Using a viscoelastic asperity behavior, mathematical formulae are derived for normal and tangential components of the contact force that depend not only on the separation of the two surfaces but also the rate of approach and relative sliding. The tangential force over a half-plane, corresponding to the moving direction, is found accounting for the directionality of the tangential component of asperity forces. A statistical approach is forwarded in which dependence of the asperity normal and tangential contact force on relative tangential velocity of two asperities can presented as corrective factors in the mathematical description of normal and tangential force components. These are force directionality corrective coefficient and force-velocity directionality corrective coefficient. Two sets of approximate equations are found for each of the normal and half-plane tangential force components. The simplest forms of the approximate equations achieve accuracy to within five (5) percent error, while other forms yield approximation error within 0.2 percent.

Combined Force and Moment in a Three Dimensional Model of Elastic Contact of Nominally Flat Rough Surfaces

2008 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Half Plane ◽  
Contact Force ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Three Dimensional Model ◽  
Tangential Contact ◽  
Applied Forces ◽  
Approximate Equations

In this paper we consider the contact between two rectangular rough surfaces that provide normal and tangential contact force as well as contact moment to counteract the net moment imposed by the applied forces. The surfaces are permitted to develop slight angular misalignment and thereby contact moment is derived. Through this scheme it is possible to also define elastic contribution to friction since the half-plane tangential contact force on one side of an asperity is no longer balanced by the half-plane tangential force component on the opposite side. The elastic friction force however is shown to be of a much smaller order than the contact normal force. Approximate closed form equations are found for contact force and moment as functions of separation, asperity radius of curvature sum, mean plane slope and nominal contact dimension. The approximate equations are shown to give error within seven percent.

Leakage Prediction in Mechanical Seals Under Hydrostatic Operating Condition

2007 ◽  
Author(s):  
S. Elhanafi ◽  
K. Farhang
Keyword(s):  
Closed Form ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Rough Surfaces ◽  
Mechanical Seals ◽  
Operating Condition ◽  
Form Equation ◽  
Macro Scale ◽  
The Mean

This paper considers leakage in mechanical seals under hydrostatic operating condition. A contact model based on the Greenwood and Williamson contact of rough surfaces is developed for treating problems involving mechanical seals in which both the micron scale roughness of the seal face and its macro scale profile are used to obtain either a closed-form equation or a nonlinear equation relating mean plane separation to the mass flow rate. The equations involve the micron scale geometry of the rough surfaces and physical parameter of the seal and carriage. Under hydrostatic condition, it is shown that there is an approximate closed-form solution in which mass flow rate in terms of the mean plane separation, or alternatively, the mean plane separation in terms of the leakage mass flow rate is found. Equations pertaining to leakage in nominally flat seal macro profile is considered and closed form equation relating to leakage flow rate to pressure difference is obtained that contain macro and micron geometries of the seal.

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