Principal accomplishments in the scientific theory of gearing

Abstract

An in-depth analysis of the accomplishments in the theory of gearing has been undertaken by the author. The main results of the performed analysis are outlined in the paper in a chronological order. Two periods of time are proposed to be considered: pre-Eulerian and post-Eulerian time of the evolution of the gear art. No principal accomplishments in the theory of gearing were attained in the pre-Eulerian period of evolution of gearing. It is stated that scientific theory of gearing is originated from the publication by Leonhard Euler of two of his famous papers (1760). The main theorem of parallel-axes gearing, or, in other words, the “conjugate action law”, is loosely attributed to R. Willis (1841), which is not correct. Ch. Camus was the first (1733), who has carried out a research on this subject, however he failed to formulate this law of gearing correctly. In the final form the theorem was known to L. Euler and to F. Savaryr. Therefore, it is proposed to refer to the main theorem of parallel-axes gearing as to the “Camus-Euler-Savaryr theorem of gearing” (or just as to the “CES-theorem of gearing”, for simplicity). A huge mistake in the theory of gearing was committed by T. Olivier (1842). The effect of this mistake onto the evolution of the theory of gearing is discussed. Contributions by G. Grant (1887), and by V. Shishkovt (1948), that is, his well-known equation of contact, n·VΣ=0, are outlined. Introduced in around 2008, concept of the operating base pitch in a gear pair considered in detail. Latest accomplishments in the theory of gearing are summarized and briefly discussed in the paper. These accomplishments form the foundation of the self-consistent scientific theory of gearing (Radzevich, S.P., 2012, 2018). The scientific theory of gearing is not threatened with destruction, but only superstructure and development are extected (every scientific theory features this property).