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.

On Some Problems With Modeling of Coulomb Friction in Self-Locking Speed Reducers

2014 ◽  
Author(s):  
Marek Wojtyra
Keyword(s):  
Rigid Body ◽  
Coulomb Friction ◽  
Equations Of Motion ◽  
Velocity Ratio ◽  
Friction Forces ◽  
Friction Law ◽  
Rigid Body Model ◽  
Feasible Sets ◽  
Unstable Solutions ◽  
Coulomb Friction Law

A simple mathematical model of friction in speed reducers is presented and discussed. A rigid body approach, typical for multibody simulations, is adopted. The model is based on the Coulomb friction law and exploits the analogy between reducers and wedge mechanisms. The first version of the model is purely rigid, i.e. no deflections of the mechanism bodies are allowed. Constraints are introduced to maintain the ratio between input and output velocity. It is shown that when friction is above the self-locking limit, paradoxical situations may be observed when kinetic friction is investigated. For some sets of parameters of the mechanism (gearing ratio, coefficient of friction and inertial parameters) two distinct solutions of normal and friction forces can be found. Moreover, for some combinations of external loads, a solution that satisfies equations of motion, constraints and Coulomb friction law does not exist. Furthermore, for appropriately chosen loads and parameters of the mechanism, infinitely many feasible sets of normal and friction forces can be found. Examples of all indicated paradoxical situations are provided and discussed. The second version of the model allows deflection of the frictional contact surface, and forces proportional to this deflection are applied to contacting bodies (no constraints to maintain the input-output velocity ratio are introduced). In non-paradoxical situations the obtained results are closely similar to those predicted by the rigid body model. In previously paradoxical situations no multiple solutions of friction force are found, however, the amended model does not solve all problems. It is shown that in regions for which the paradoxes were observed only unstable solutions are available. Numerical examples showing behavior of the model are provided and analyzed.

scholarly journals Crack in a solid under Coulomb friction law

2000 ◽  
Vol 45 (4) ◽  
pp. 265-290 ◽  
Author(s):  
Victor A. Kovtunenko
Keyword(s):  
Coulomb Friction ◽  
Friction Law ◽  
Coulomb Friction Law

New theoretical model of stress transfer between fibre and matrix in a uniaxially fibre-reinforced composite

1989 ◽  
Vol 425 (1868) ◽  
pp. 215-244 ◽  
Keyword(s):  
Boundary Conditions ◽  
Coulomb Friction ◽  
Stress Transfer ◽  
Matrix Crack ◽  
Matrix Interface ◽  
Friction Law ◽  
Reinforced Composite ◽  
Coulomb Friction Law ◽  
Frictional Slip ◽  
Fibre Matrix

A new analytical method has been developed that can predict the stress transfer between fibre and matrix in a uniaxially fibre-reinforced composite associated with either a single matrix crack or a fibre break. Account is taken of thermal residual stresses arising from a mismatch in thermal expansion coefficients between the fibre and matrix. In addition Poisson ratio mismatches are also taken into account. The theoretical approach retains all relevant stress and displacement components, and satisfies exactly the equilibrium equations, the interface conditions and other boundary conditions involving stresses. Two of the four stress-strain-temperature relations are satisfied exactly, whereas the remaining two are satisfied in an average sense. The required non-interface displacement boundary conditions are also satisfied in an average sense. The general representation is used to solve three types of stress transfer problem. A matrix crack and a broken fibre are analysed for the case when there is perfect bonding between fibre and matrix. The third type of problem takes account of frictional slip at the interface governed by the Coulomb friction law. The approximate analytic approach described in this paper, and the preliminary numerical predictions presented, indicate that the stress transfer between fibres and matrix in a unidirectional fibre-reinforced composite, loaded in tension, can now be investigated theoretically in more detail than before. The paper includes some discussion of singularities in the stress fields, which are smoothed by the averaging techniques employed in the analysis. The analytical approach has enabled the development of a micro-mechanical model of frictional slip at the fibre-matrix interface based on the Coulomb friction law, which is more realistic than assuming that the interfacial shear stress is a constant. Predictions are presented of the stress distributions along the fibre-matrix interface and, in particular, it is shown how the length of the frictional slip zone is related to applied strain, friction coefficient, fibre volume fraction and the difference between the test and ‘manufacturing’ temperatures. An indication is given of many other areas of composite modelling where the new theory will be applied.

scholarly journals Breakdown of the Coulomb friction law in TiC∕a-C:H nanocomposite coatings

2006 ◽  
Vol 100 (11) ◽  
pp. 114309 ◽  
Author(s):  
Y. T. Pei ◽  
P. Huizenga ◽  
D. Galvan ◽  
J. Th. M. De Hosson
Keyword(s):  
Coulomb Friction ◽  
Nanocomposite Coatings ◽  
Friction Law ◽  
Coulomb Friction Law

On Some Problems With Modeling of Coulomb Friction in Self-Locking Mechanisms

2016 ◽  
Vol 11 (1) ◽  
Author(s):  
Marek Wojtyra
Keyword(s):  
System Dynamics ◽  
Rigid Body ◽  
Coulomb Friction ◽  
Kinetic Regime ◽  
Friction Forces ◽  
Friction Law ◽  
Joint Friction ◽  
Body Model ◽  
Rigid Body Model ◽  
Coulomb Friction Law

Friction significantly influences the mechanical system dynamics, especially when self-locking property is observed. The Coulomb model is frequently adopted to represent friction in multibody analysis and simulation. It can be shown that in some extreme cases of joint friction modeling, problems with solution uniqueness and existence are encountered, even when only bilateral constraints and kinetic regime of friction are considered. These problems are studied in detail in the paper. To approach the investigated subject, a wedge mechanism, viewed as a simplified model of a speed reducer, is studied. Two different mathematical models of joint friction are used, both based on the Coulomb friction law. The first version of the model is purely rigid, i.e., no deflections of the mechanism bodies are allowed. Constraints are imposed to maintain the ratio between input and output velocity. The second version of the model allows deflection of the frictional contact surface, and forces proportional to this deflection are applied to contacting bodies (no constraints to maintain the input–output velocity ratio). Using the rigid body model, it is shown that when friction is above the self-locking limit, paradoxical situations may be observed when kinetic friction is investigated. For some sets of parameters of the mechanism (gearing ratio, friction coefficient, and inertial parameters), two distinct solutions of normal and friction forces can be found. Moreover, for some combinations of external loads, a solution that satisfies equations of motion, constraints, and the Coulomb friction law does not exist. Furthermore, for appropriately chosen loads and parameters of the mechanism, infinitely many feasible sets of normal and friction forces can be found. Investigation of the flexible body model reveals that in nonparadoxical situations the obtained results are closely similar to those predicted by the rigid body model. In previous paradoxical situations, no multiple solutions are found; however, problems with stability of solutions emerge. It is shown that in regions for which the paradoxes were observed only unstable solutions are available. The origins of paradoxical behavior are identified and discussed. The key factors determining the model performance are pointed out. Examples of all indicated problematic situations are provided and analyzed. Finally, the investigated problems are commented from more general perspectives of multibody system dynamics.

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