Few problems with regularized Coulomb law

Ligier, Jean-Louis; Bonhôte, Philippe

doi:10.1051/meca/2014075

Cited by 5 publications

(3 citation statements)

References 19 publications

(19 reference statements)

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“…Similar types of Coulomb friction regularization (sometimes involving the arctangent function) have also been used in dynamical simulations involving friction [44][45][46]. Many regularizations (including ours) involve a frictional force that rises monotonically from zero at zero velocity to the kinetic friction force [47][48][49][50], while others (e.g. [51]) allow for a nonmonotonic behavior near zero velocity, to simulate the effect of a static friction coefficient that is greater than the kinetic friction coefficient, and allow for stick-slip transitions.…”

Section: Modelmentioning

confidence: 99%

Intermittent sliding locomotion of a two-link body

Alben,

Puritz

2020

Preprint

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We study the possibility of efficient intermittent locomotion for two-link bodies that slide by changing their interlink angle periodically in time. We find that the anisotropy ratio of the sliding friction coefficients is a key parameter, while solutions have a simple scaling dependence on the friction coefficients' magnitudes. With very anisotropic friction, efficient motions involve coasting in low-drag states, with rapid and asymmetric power and recovery strokes. As the anisotropy decreases, burst-and-coast motions change to motions with long power strokes and short recovery strokes, and roughly constant interlink angle velocity on each. These motions are seen in the spaces of sinusoidal and power-law motions described by two and five parameters, respectively. Allowing the duty cycle to vary greatly increases the motions' efficiency compared to the case of symmetric power and recovery strokes. Allowing further variations in the concavity of the power and recovery strokes only improves the efficiency further when friction is very anisotropic. Near isotropic friction, a variety of optimally efficient motions are found with more complex waveforms. Many of the optimal sinusoidal and power-law motions are similar to those that we find with an optimization search in the space of more general periodic functions (truncated Fourier series). When we increase the resistive force's power law dependence on velocity, the optimal motions become smoother, slower, and less efficient, particularly near isotropic friction. I. INTRODUCTIONIn this paper we study the optimal kinematics for intermittent locomotion by simple (two-link) bodies sliding on rough surfaces. Intermittent locomotion occurs when propulsive forces are applied (very) nonuniformly in time, perhaps for only a brief interval [1]. Such locomotion is often divided into two phases, termed burst and coast, power and recovery, or thrust and drag, for example. Much previous work has studied the optimal kinematics of bodies swimming in fluids, at low, intermediate (O(1)), and high Reynolds numbers (i.e. inverse viscosities). Bodies in fluids experience velocity-dependent drag forces that can penalize more rapid and intermittent motions to some degree.At low Reynolds number, for example, it can be shown that the most efficient swimming motions exert constant mechanical power [2], or have a constant stroke speed [3]. At higher Reynolds numbers, fluid drag typically scales as velocity squared, and steadier swimming speeds and propulsive forces may be more efficient for drag-based locomotion [4][5][6][7]. Interestingly, for undulatory high-Reynolds-number swimmers, intermittent (e.g. "burst-and-coast") swimming can be more efficient than steady swimming [8], in part because of boundary layer thinning during steady swimming

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Section: Modelmentioning

confidence: 99%

Intermittent sliding locomotion of a two-link body

Alben,

Puritz

2020

Preprint

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“…In the regularised approaches, known also as penalty or complaint methods, the contact force is assumed as a continuous function of penetration of contacting bodies [7][8][9]. The frictional forces are then often formulated by the use of regularised Coulomb's model of friction [10][11][12][13]. The regularisation can be a result of a need of simplification of the model but also very often corresponds to the physical nature of a real object (compliance of the bodies, microslips, etc.…”

Section: Introductionmentioning

confidence: 99%

Application of a special class of smooth models of the resultant friction force and moment occurring on a circular contact area

Kudra

Awrejcewicz

2016

Arch Appl Mech

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Some special cases of a larger class of smooth models of the resultant friction force occurring on a planar contact area are developed and presented. These models are constructed under assumptions of classical Coulomb's law of friction on each element of contact and instantaneous transition between two modes: fully developed sliding and rigid stick state without local slips and deformations of the contact area. They are able to model cases of different values of static and kinetic friction factors. The considered models are very effective tools for fast and reliable numerical simulations of mechanical systems with frictional contacts. They are applied in modelling and numerical analysis of a special kind of mechanical system, i.e. a kind of a pendulum with special frictional driving. The rotational joint of the pendulum is elastically suspended in the motion plane. The pendulum is driven by circular frictional contact with a rotating disk. Examples of self-excited bifurcation and chaotic dynamics as well as stick-slip behaviour of the pendulum are presented.

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“…Coulomb friction law results in more realistic responses in the microslip regime [23], this is unlikely to be important for the brake dynamics due to the rigid body model that is used. To summarise, as Stewart aptly states, "the physics points to real discontinuities, and there is little advantage numerically in smoothing the discontinuity" [22].…”

Section: Numerically Modelling Friction and Rigid Bodiesmentioning

confidence: 99%

A piston braking model for the L1d CFD code

Byrne¹

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The L1d computational fluid dynamics code is used to model numerous shock tunnel facilities worldwide. A number of free-piston driven shock tunnel facilities, such as the T4 Stalker tube at the University of Queensland, utilises a piston-braking system to prevent facility damage. However, the braking system may have some effects on the piston dynamics during operation. The L1d code currently does not account for the brake dynamics and the friction force created through the piston-brake interface. It was hypothesised that including this may lead to more accurate predictions, which would benefit any institution that models shock tunnel facilities using a piston-brake system. This thesis developed a numerical model to understand the piston-brake dynamics. The model was validated against L1d for a configuration neglecting brake dynamics. The model was then used with brake dynamics to investigate the effect on piston motion for numerous shock tunnel flow conditions and friction coefficient configurations. Simulations suggested that the friction force generated by the brakes had a slight effect on the piston motion, but was too insignificant to warrant including it in the L1d code.

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Few problems with regularized Coulomb law

Cited by 5 publications

References 19 publications

Intermittent sliding locomotion of a two-link body

Intermittent sliding locomotion of a two-link body

Application of a special class of smooth models of the resultant friction force and moment occurring on a circular contact area

A piston braking model for the L1d CFD code

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