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.

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.

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 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.

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.

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.

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. 

scholarly journals TRANSMITTED POWER AND ENERGY FLOW BEHAVIOR OF DEGRADING WET FRICTION CLUTCHES

2012 ◽  
pp. 286-291
Author(s):  
SHOAIB IQBAL ◽  
THIERRY JANSSENS ◽  
WIM DESMET ◽  
FARID AL- BENDER
Keyword(s):  
Energy Flow ◽  
Relative Velocity ◽  
Normal Load ◽  
Flow Behavior ◽  
Friction Material ◽  
Friction Model ◽  
Friction Torque ◽  
Phase Changes ◽  
Transmitted Power ◽  
Wet Friction

Experiments and simulations performed in the framework of accelerated-life tests of wet friction clutches reveal that with the progression of degradation of clutches, the transmitted power decreases together with a change in the energy flow behavior, mainly in the pre-lockup phase. In addition, the engagement duration increases and the relative velocity fluctuation in post-lockup phase changes. These degradation effects are due to the reduction in friction torque and the change in the relative velocity profile caused by the changing friction characteristics of the clutch friction material with degradation. Simulations are performed in a bond graph methodology incorporating an adapted form of the Generalized Maxwell Slip (GMS) friction model, which calculates the friction torque taking into account the dynamic variation in relative velocity and the normal load.

A Nonlinear Analysis Formulation for Bend Stiffeners

2007 ◽  
Vol 51 (03) ◽  
pp. 250-258 ◽  
Author(s):  
M. A. Vaz ◽  
C. A. D. de Lemos ◽  
M. Caire
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Nonlinear Analysis ◽  
Cross Section ◽  
Contact Force ◽  
Oil And Gas ◽  
Constitutive Relations ◽  
Mathematical Formulation ◽  
Power Series Expansion ◽  
Gas Production

Bend stiffeners are polymeric structures with a conical shape designed to limit the curvature of flexible risers and umbilical cables at their uppermost connections, protecting them against overbending and from accumulation of fatigue damage. Thus, they are of vital importance to deep water oil and gas production systems. This work develops a mathematical formulation and a numerical solution procedure for the geometrical and material nonlinear analysis of the riser/bend stiffener system considered as a beam bending model. The structures are separately modeled, which allows the numerical calculation of the contact force along the system arc length. The governing differential equations are derived considering geometrical compatibility, equilibrium of forces and moments, and nonlinear asymmetric material constitutive relations, which leads to a shift in the neutral axis position from the cross-section centroid. The eccentricity and the bending moment versus curvature relation for each cross section are numerically calculated and then expressed by a polynomial power series expansion. A set of four first-order nonlinear ordinary differential equations is written and four boundary conditions are specified at both ends. Once the global problem is solved, the contact force may be promptly calculated. A finite difference method is implemented in Fortran code to obtain the numerical solution. A case study is carried out where linear elastic symmetric and nonlinear elastic asymmetric constitutive models are compared and discussed. The results are presented for the riser/bend stiffener deflected configuration, angle, curvature, and contact force distribution. The results demonstrate that an accurate structural analysis of bend stiffeners depends on a precise assessment of the nonlinear asymmetric polyurethane property.

306 Study on Squeal Reduction based on Vibration Behavior of Disk Brake System

2008 ◽  
Vol 2008.83 (0) ◽  
pp. _3-6_
Author(s):  
Masayuki AZUMA ◽  
Atsuhiko SHINTANI ◽  
Tomohiro ITO ◽  
Katsuhisa FUJITA
Keyword(s):  
Brake System ◽  
Disk Brake ◽  
Vibration Behavior
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