The mechanism of rolling friction II. The elastic range

Abstract

This paper discusses the mechanism of rolling friction under conditions where the deformations involved are predominantly elastic. Experiments on the rolling of a metal cylinder over a rubber surface show that interfacial slip of the type described by Reynolds is minute and totally insufficient to account for the observed resistance to rolling. It is shown quantitatively that the rolling resistance under these conditions is due to elastic hysteresis losses in the rubber. This accounts for the ineffectiveness of lubricants in reducing the rolling friction. Similar results are obtained for hard spheres rolling on rubber surfaces. If, however, a sphere is rolled in a preformed rubber groove, interfacial slip between the ball and groove may occur since the central band on the ball measures out a larger circle than the bands at the edge of the groove. A simple quantitative theory of this effect is given. This type of slip, first described by Heathcote, is very marked when the groove is deep and of curvature very close to that of the ball; under these conditions a suitable lubricant can effect a considerable reduction in the rolling resistance. For shallower grooves the differential slip is reduced and the Heathcote contribution to the observed rolling resistance becomes trivial. These conclusions are applied to the rolling friction of a hard steel sphere in the equilibrium groove formed in the surface of a softer metal (part I). If the rolling friction is attributed to the Heathcote mechanism a coefficient of friction within the ellipse of contact of the order of u = 1 to 2 must be invoked even in the presence of the best boundary lubricants. This is impossibly high. If, on the other hand, the rolling friction is attributed to hysteresis losses, large loss factors, greater than 20 %, must be invoked for example for copper surfaces. In order to resolve this difficulty a new experimental approach has been adopted in which a copper ball is rolled over an identical copper ball. Because of symmetry conditions at the region of contact both the Reynolds and the Heathcote type of slip are eliminated. The equilibrium rolling friction is found to be as high as that observed when a hard steel sphere rolls in a copper groove. It is concluded that interfacial slip contributes little to the rolling friction although it may play an important part in surface wear. Consequently, lubricants may reduce the amount of wear but have little effect on the rolling resistance. The greater part of this arises from elastic hysteresis losses within the metals themselves.

Rolling resistance modelling in the Celtic stone dynamics

“…An extension of this approach is presented in the work [10], where the generalized forms of approximations of the resulting friction force and moment as well as rolling resistance for elliptic contact shape are presented. Rolling friction is there modelled as a resistance against motion of the area of deformation over the body [11] and, ignoring the problem of rotation of the elliptical region, is consistent with the results obtained under the assumption of the linear hysteresis [12][13][14][15]. Karapetyan [16] proposed a two-parametric model of friction forces for spherical contact between a ball and planar base being a result of deformations of the contacting bodies.…”

Rolling friction of adhesive microspheres

“…The reciprocal of the quality factor is associated with the ratio of energy dissipated to the energy stored in dynamic loading, and can be viewed as a fundamental measure of mechanical dissipation [45]. In the case of rolling friction, the reciprocal of the quality factor is identical to Tabor's hysteresis loss factor [46], apart from a numerical factor of order unity [18]. Typical values for the quality factor in solids are 10 − 10 2 for polymers, 10 3 for glass and soft metals, but may vary with 8 These numbers are obtained by estimating the rolling angle and timescales from figures 3 of [5] and 7 of [10].…”

Viscoelastic characterization of an EPDM rubber and finite element simulation of its dry rolling friction

“…Figure 2 also shows the change of the ball's displacement and the change of the curve of rolling velocity versus the time, where T is the period (30 sec). On the right side one can see the contact geometry, where r is the radius of the rolling steel ball (7 mm), g is the width of the guiding groove on the driver part (8.6 mm), h is the vertical distance from the center point to the upper contact point of the ball, calculated by Equations (1) and (2):…”

“…The exact analytical calculation of the observed strains during mechanical loading of rubbery elements is a great challenge due to the complexity of the viscoelastic material models. Although some simplified analytical methods were developed to evaluate for example the friction resistance or internal heat generation in viscoelastic materials during rolling contact, they failed for more complex stress states or for repeated stresses [1][2][3][4][5][6][7][8][9]. On the other hand the finite element (FE) method is able to handle complex viscoelastic material models owing to the permanent advancement of the software and hardware background.…”