Rolling friction of a viscous sphere on a hard plane

A first-principle continuum-mechanics expression for the rolling friction coefficient is obtained for the rolling motion of a viscoelastic sphere on a hard plane. It relates the friction coefficient to the viscous and elastic constants of the sphere material. The relation obtained refers to the case when the deformation of the sphere $\xi$ is small, the velocity of the sphere $V$ is much less than the speed of sound in the material and when the characteristic time $\xi/V$ is much larger than the dissipative relaxation times of the viscoelastic material. To our knowledge this is the first ``first-principle'' expression of the rolling friction coefficient which does not contain empirical parameters.Comment: 6 pages, 2 figure

Rolling friction of a hard cylinder on a viscous plane

The resistance against rolling of a rigid cylinder on a flat viscous surface is investigated. We found that the rolling-friction coefficient reveals strongly non-linear dependence on the cylinder's velocity. For low velocity the rolling-friction coefficient rises with velocity due to increasing deformation rate of the surface. For larger velocity, however, it decreases with velocity according to decreasing contact area and deformation of the surface.Comment: 7 pages, 3 figure

Rolling as a continuing collision

We show that two basic mechanical processes, the collision of particles and rolling motion of a sphere on a plane, are intimately related. According to our recent findings, the restitution coefficient for colliding spherical particles \epsilon, which characterizes the energy loss upon collision, is directly related to the rolling friction coefficient \mu_{roll} for a viscous sphere on a hard plane. We quantify both coefficients in terms of material constants which allow to determine either of them provided the other is known. This relation between the coefficients may give rise to a novel experimental technique to determine alternatively the coefficient of restitution or the coefficient of rolling friction

Rolling friction for hard cylinder and sphere on viscoelastic solid

We calculate the friction force acting on a hard cylinder or spherical ball rolling on a flat surface of a viscoelastic solid. The rolling friction coefficient depends non-linearly on the normal load and the rolling velocity. For a cylinder rolling on a viscoelastic solid characterized by a single relaxation time Hunter has obtained an exact result for the rolling friction, and our result is in very good agreement with his result for this limiting case. The theoretical results are also in good agreement with experiments of Greenwood and Tabor. We suggest that measurements of rolling friction over a wide range of rolling velocities and temperatures may constitute an useful way to determine the viscoelastic modulus of rubber-like materials.Comment: 7 pages, 6 figure

Jamming transition in a two-dimensional open granular pile with rolling resistance

We present a molecular dynamics study of the jamming/unjamming transition in two-dimensional granular piles with open boundaries. The grains are modeled by viscoelastic forces, Coulomb friction and resistance to rolling. Two models for the rolling resistance interaction were assessed: one considers a constant rolling friction coefficient, and the other one a strain dependent coefficient. The piles are grown on a finite size substrate and subsequently discharged through an orifice opened at the center of the substrate. Varying the orifice width and taking the final height of the pile after the discharge as the order parameter, one can devise a transition from a jammed regime (when the grain flux is always clogged by an arch) to a catastrophic regime, in which the pile is completely destroyed by an avalanche as large as the system size. A finite size analysis shows that there is a finite orifice width associated with the threshold for the unjamming transition, no matter the model used for the microscopic interactions. As expected, the value of this threshold width increases when rolling resistance is considered, and it depends on the model used for the rolling friction.Comment: 9 pages, 6 figure

Effect of Friction on Dense Suspension Flows of Hard Particles

We use numerical simulations to study the effect of particle friction on suspension flows of non-Brownian hard particles. By systematically varying the microscopic friction coefficient $\mu_p$ and the viscous number $J$, we build a phase diagram that identifies three regimes of flow: Frictionless, Frictional Sliding, and Rolling. Using energy balance in flow, we predict relations between kinetic observables, confirmed by numerical simulations. For realistic friction coefficient and small viscous numbers (below $J\sim 10^{-3}$) we show that the dominating dissipative mechanism is sliding of frictional contacts, and we characterize asymptotic behaviors as jamming is approached. Outside this regime, our observations support that flow belongs to the universality class of frictionless particles. We discuss recent experiments in the context of our phase diagram.Comment: 8 page

Behavior of aircraft antiskid breaking systems on dry and wet runway surfaces: A slip-ratio-controlled system with ground speed reference from unbraked nose wheel

An experimental investigation was conducted at the Langley aircraft landing loads and traction facility to study the braking and cornering response of a slip ratio controlled aircraft antiskid braking system with ground speed reference derived from an unbraked nose wheel. The investigation, conducted on dry and wet runway surfaces, utilized one main gear wheel, brake, and tire assembly of a DC-9 series 10 airplane. During maximum braking, the average ratio of the drag force friction coefficient developed by the antiskid system to the maximum drag force friction coefficient available was higher on the dry surface than on damp and flooded surfaces, and was reduced with lighter vertical loads, higher yaw angles, and when new tire treads were replaced by worn treads. Similarly, the average ratio of side force friction coefficient developed by the tire under antiskid control to the maximum side force friction coefficient available to a freely rolling yawed tire decreased with increasing yaw angle, generally increased with ground speed, and decreased when tires with new treads were replaced by those with worn treads

Role of friction in asymmetrical rolling

Розглянуті методи визначення коефіцієнта тертя при прокатуванні стосовно умов несиметричного прокатування на валках різного діаметру, що обертаються з однаковими кутовими швидкостями. Запропонована гіпотетична крива зміни коефіцієнта тертя при прокатуванні порошків, з врахуванням існування тертя ковзання і тертя спокою. Запропоновано на ділянці дуги контакту, де сила тертя відповідає неповній силі тертя коефіцієнт тертя приймати рівним коефіцієнту тертя спокою. Ця ділянка відповідатиме зоні прилипання. Показано, що при розглянутій схемі несиметричної прокатки в зоні відставання на малому валку сила тертя виштовхує метал з валків, а в зоні випередження напрямок і величина сили тертя на великому валку залежатиме від параметрів прокатування.Purpose. Methodology of estimation the friction coefficient is discussed relative to asymmetrical rolling for powders using rollers of different diameters that rotate with similar angle velocities. Design/methodology/approach Experimental methods and analytical dependencies used for measuring the friction coefficient for various patterns of rolling are considered. The method of forward slip, the method of measurement of friction coefficient via the diagram of radial pressure upon the roll, and the method of roller-pin testing on standard friction machines are validated as useful for application to conditions of asymmetrical rolling on rollers of various diameters that rotate with similar angle velocities. A hypothetical curve of the friction coefficient variation at powder rolling is suggested that accounted for the presence of slipping friction and friction at rest. At the above pattern of asymmetrical rolling, the friction force of the smaller roller extrudes the metal out of the rolls within the lag zone, while in the zone of slippage on the delivery side, the friction force on the major roll shall depend on the rolling conditions.Рассмотрены методы определения коэффициента трения при прокатке применительно к условиям несимметричной прокатки на валках разного диаметра вращающихся с одинаковыми угловыми скоростями. Предложена гипотетическая кривая изменения коэффициента трения при прокатке порошков, с учётом существования трения скольжения и трения покоя. Предложено на участке дуги контакта, где сила трения соответствует неполной силе трения коэффициент трения принимать равным коэффициенту трения покоя. Этот участок будет соответствовать зоне прилипания. Показано, что при рассмотренной схеме несимметричной прокатки в зоне отставания на малом валке сила трения выталкивает металл из валков, а в зоне опережения направление и величина силы трения на большом валке будет зависеть от параметров прокатки

On a mechanical lens

In this paper, we consider the dynamics of a heavy homogeneous ball moving under the influence of dry friction on a fixed horizontal plane. We assume the ball to slide without rolling. We demonstrate that the plane may be divided into two regions, each characterized by a distinct coefficient of friction, so that balls with equal initial linear and angular velocity will converge upon the same point from different initial locations along a certain segment. We construct the boundary between the two regions explicitly and discuss possible applications to real physical systems

Slowing-Down in the Radiator and Cherenkov Radiation Angular Distributions from Relativistic Heavy Ions at FAIR, SPS and LHC energies

An adaptive learning algorithm using laser velocity meter is proposed for the process control of tandem cold mills. This method is used for on-line adaptive learning calculation of deformation resistance of strip and rolling friction models. The reverse calculation values of deformation resistance and friction coefficient as variables of non-linear equations can be obtained by introducing the measured rolling force and forward slip into the calculation model individually. Using Newton-Raphson iterative calculation to solve the non-linear equations, the reverse calculation values can be calculated. The actual forward slip obtained from the measured strip rolling speed using laser meter makes it possible that the deformation resistance of strip and friction coefficient can be uncoupled for model adaptive learning calculation. The inverse calculation and adaptive learning can improve whole control system of tandem cold mills significantly