Multiple solutions of stick and separation type in the Signorini model with Coulomb friction

2005 ◽  
Vol 85 (9) ◽  
pp. 673-680 ◽  
Author(s):  
P. Hild
Keyword(s):  
Multiple Solutions ◽  
Coulomb Friction ◽  
Signorini Model

Threshold of Multiple Stick-Slip Chaos for an Archetypal Self-Excited SD Oscillator Driven by Moving Belt Friction

2017 ◽  
Vol 27 (01) ◽  
pp. 1750009 ◽  
Author(s):  
Z. X. Li ◽  
Q. J. Cao ◽  
A. Léger
Keyword(s):  
Multiple Solutions ◽  
Coulomb Friction ◽  
Homoclinic Orbits ◽  
The Self ◽  
External Excitation ◽  
Stick Slip ◽  
Sd Oscillator ◽  
Excited System ◽  
Analytical Expressions ◽  
Natural Characteristics

In this paper, we investigate the multiple stick-slip chaotic motion of an archetypal self-excited smooth and discontinuous (SD) oscillator driven by moving belt friction, which is constructed with the SD oscillator and the classical moving belt. The friction force between the mass and the belt is modeled as a Coulomb friction for this system. The energy introduction or dissipation during the slip and stick modes in the system is analyzed. The analytical expressions of homoclinic orbits of the unperturbed SD oscillator are derived by using a special coordinate transformation without any pronominal truncation to retain the natural characteristics, which allows us to utilize the Melnikov’s method to obtain the chaotic thresholds of the self-excited SD oscillator in the presence of the damping and external excitation. Numerical simulations are carried out to demonstrate the multiple stick-slip dynamics of the system, which show the efficiency of the prediction for stick-slip chaos of the perturbed self-excited system. The results presented herein this paper demonstrate the complicated dynamics of stick-slip periodic solutions, multiple stick-slip chaotic solutions and also coexistence of multiple solutions for the perturbed self-excited SD oscillator.

Some Consequences of Coulomb Friction in Modeling Longitudinal Traction

1990 ◽  
Vol 18 (1) ◽  
pp. 13-65 ◽  
Author(s):  
W. W. Klingbeil ◽  
H. W. H. Witt
Keyword(s):  
Shear Force ◽  
Coulomb Friction ◽  
Interfacial Shear ◽  
Force Generation ◽  
Behavior Patterns ◽  
Inflation Pressure ◽  
Friction Law ◽  
The Coefficient Of Friction ◽  
Coulomb Friction Law ◽  
Perfect Adhesion

Abstract A three-component model for a belted radial tire, previously developed by the authors for free rolling without slip, is generalized to include longitudinal forces and deformations associated with driving and braking. Surface tractions at the tire-road interface are governed by a Coulomb friction law in which the coefficient of friction is assumed to be constant. After a brief review of the model, the mechanism of interfacial shear force generation is delineated and explored under traction with perfect adhesion. Addition of the friction law then leads to the inception of slide zones, which propagate through the footprint with increasing severity of maneuvers. Different behavior patterns under driving and braking are emphasized, with comparisons being given of sliding displacements, sliding velocities, and frictional work at the tire-road interface. As a further application of the model, the effect of friction coefficient and of test variables such as load, deflection, and inflation pressure on braking stiffness are computed and compared to analogous predictions on the braking spring rate.

An Overview of Risk-Based EEE Counterfeit Part Detection Based on SAE AS6171

2018 ◽  
Author(s):  
Michael H. Azarian
Keyword(s):  
Risk Assessment ◽  
Multiple Solutions ◽  
Test Equipment ◽  
Assessment Methodology ◽  
Test Plan ◽  
Specific Test ◽  
Risk Assessment Methodology

Abstract As counterfeiting techniques and processes grow in sophistication, the methods needed to detect these parts must keep pace. This has the unfortunate effect of raising the costs associated with managing this risk. In order to ensure that the resources devoted to counterfeit detection are commensurate with the potential effects and likelihood of counterfeit part usage in a particular application, a risk based methodology has been adopted for testing of electrical, electronic, and electromechanical (EEE) parts by the SAE AS6171 set of standards. This paper provides an overview of the risk assessment methodology employed within AS6171 to determine the testing that should be utilized to manage the risk associated with the use of a part. A scenario is constructed as a case study to illustrate how multiple solutions exist to address the risk for a particular situation, and the choice of any specific test plan can be made on the basis of practical considerations, such as cost, time, or the availability of particular test equipment.

Multiple Solutions Approach (MSA): Conceptions and Practices of Primary School Teachers in Ghana

2016 ◽  
Vol 2 (2) ◽  
pp. 333
Author(s):  
Michael Johnsn Nabie ◽  
Kolawole Raheem ◽  
John Bijou Agbemaka ◽  
Rufai Sabtiwu
Keyword(s):  
Primary School ◽  
Multiple Solutions ◽  
School Teachers ◽  
Primary School Teachers
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