Roller bearings with rational working surfaces and their manufacture

Abstract

The development of bearing production may be divided into three stages. The first dates back 500 years, to the invention of ball bearings and roller bearings by Leonardo da Vinci (1452-1519). Intent on reducing friction in machines, Leonardo had the idea of using round bodies. "I see no great difference between them, except that balls may turn in all directions and rollers only in one. However, if balls and rollers are in contact as they move, their motion will be slower, on account of the opposing frictional force." In surviving sketches, we may see the separator proposed by Leonardo for the division of the rollers. True to his principle of a compre� hensive approach to engineering problems, Leonardo suggested means of reducing friction and wear in machines that have only been implemented many years later in various countries. For example, Leonardo's rec� ipe for a metalalloy lubricant is similar in composition to the bearing material proposed by Babbitt in 1839. The second stage is associated with the theoretical developments of Heinrich Hertz (1857-1894), per� mitting the calculation of the contact area and the contactstress distribution over the contact area. In solving the contact problem, Hertz assumed that the initial gap between the contacting bodies is a quadratic function. This framework remained unchanged for around sixty years. In that period, Hertz's theory was experi� mentally confirmed, and possibilities for its practical application were explored. We should note, in particular, the contributions of N.M. Belyaev and A.N. Dinnik. Only sixty years ago, on the basis of work by Muskhe� lishvili, Vekua, Lyapunov, and others, I. Ya. Shtaerman developed solutions for the case of a circular contact area and an arbitrary initial gap and also for the case of an elliptical contact area with a biquadratic initial gap. However, like Hertz's solution, Shtaerman's approach did not apply to the contact of asymmetric bodies. Many Russian and nonRussian solutions have attempted a general solution of the contact problem. Their work is of great theoretical and practical value, since it permits the determination of the bodies' stress-strain state in different conditions. As a result, it is possible to determine the stress and strain close to the contact zone for the interaction of bodies charac� terized by nonuniform materials, nonuniform layers of material, asymmetric load, a nonuniform contact sur� face, and various profiles: a wedge, a cone, a truncated sphere, a parallelepiped, a cylinder, a torus, etc. The most general solutions may be found in (1-3) and elsewhere. In these studies, analytical expressions are given for the dimensions of the contact area and the contact stresses between roller bodies of arbitrary form. On that basis, for the first time, it is possible to pre� dictively control the contactstress distribution between the roller bodies. In the figure, we present examples of the stress distribution in the contact zone as a function