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

Rolling friction robot fingers

A low friction, object guidance, and gripping finger device for a robotic end effector on a robotic arm is disclosed, having a pair of robotic fingers each having a finger shaft slideably located on a gripper housing attached to the end effector. Each of the robotic fingers has a roller housing attached to the finger shaft. The roller housing has a ball bearing mounted centering roller located at the center, and a pair of ball bearing mounted clamping rollers located on either side of the centering roller. The object has a recess to engage the centering roller and a number of seating ramps for engaging the clamping rollers. The centering roller acts to position and hold the object symmetrically about the centering roller with respect to the X axis and the clamping rollers act to position and hold the object with respect to the Y and Z axis

Atomic Scale Sliding and Rolling of Carbon Nanotubes

A carbon nanotube is an ideal object for understanding the atomic scale aspects of interface interaction and friction. Using molecular statics and dynamics methods different types of motion of nanotubes on a graphite surface are investigated. We found that each nanotube has unique equilibrium orientations with sharp potential energy minima. This leads to atomic scale locking of the nanotube. The effective contact area and the total interaction energy scale with the square root of the radius. Sliding and rolling of nanotubes have different characters. The potential energy barriers for sliding nanotubes are higher than that for perfect rolling. When the nanotube is pushed, we observe a combination of atomic scale spinning and sliding motion. The result is rolling with the friction force comparable to sliding.Comment: 4 pages (two column) 6 figures - one ep

Stress evaluations under rolling/sliding contacts

The state of stress beneath traction drive type of contacts were analyzed. Computing stresses and stress reversals on various planes for points beneath the surface were examined. The effect of tangential and axial friction under gross slip conditions is evaluated with the models. Evaluations were performed on an RC (rolling contact) tester configuration and it is indicated that the classical fatigue stresses are not altered by friction forces typical of lubricated contact. Higher values of friction can result in surface shear reversal that exceeds the stresses at the depth of maximum shear reversal under rolling contact

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

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

On the Normal Force and Static Friction Acting on a Rolling Ball Actuated by Internal Point Masses

The goal of this paper is to investigate the normal and tangential forces acting at the point of contact between a horizontal surface and a rolling ball actuated by internal point masses moving in the ball's frame of reference. The normal force and static friction are derived from the equations of motion for a rolling ball actuated by internal point masses that move inside the ball's frame of reference, and, as a special case, a rolling disk actuated by internal point masses. The masses may move along one-dimensional trajectories fixed in the ball's and disk's frame. The dynamics of a ball and disk actuated by masses moving along one-dimensional trajectories are simulated numerically and the minimum coefficients of static friction required to prevent slippage are computed.Comment: 24 pages, 28 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1801.09178; text overlap with arXiv:1708.0382