On the Effect of Brakes upon Railway Trains

Abstract

Xo reliable data exists, at the present time, to show the exact effect of speed upon the coefficient of friction between shoes and wheels of other materials than those described in these experiments ; such information, however, as can be secured, indicates that, while the values of the constants a and b, in the above formula, may vary for brake shoes and wheels of other materials, the general effect of speed upon the coefficient of friction is the same ; that is, the friction is greatest at very low speeds, and decreases, by the same general law, as the speed increases. The results shown in Table X, on page 172 of the third paper, uniformly indicate that, at any constant speed, the friction also diminishes, according to some law, as the time of rubbing of the brake shoe upon the wheel is extended. The extent of the experiments in this direction is somewhat too limited to determine, as fully as is to be desired, the effect of the time of continued rubbing upon the coefficient of friction. Yet it is apparent that, however long the brake shoe continues to rub upon the wheel, the friction can never become reduced to zero, and the general relation between the coefficient of friction and the time of continued rubbing must therefore be expressed by an equation similar to that for the coefficient of friction as effected by speed.

Digital Control as Source of Chaotic Behavior

“…The characteristic of the damping force between the revolving polishing tool and the fixed workpiece is a mixture of the dry and viscous friction characteristics and depends on the relative velocity v rel = Rω 0 +v between the surfaces. At low relative speeds, the combined dry and viscous friction force acting on the cylinder is locally decreasing as v rel increases [Conti, 1875;Galton, 1878]. This effect may lead to the so-called stickslip vibrations in several uncontrolled mechanical systems [Popp & Stelter, 1990].…”