Gradual development of S-shaped gears

Abstract

Search for an improved gear tooth flank shape arose from heavy industry problems rolling mills. Original involute gears suffered severe flank damages. So, better gear teeth flanks should improve contact circumstances, decrease the flank pressure, and enhance a lubrication film. This was achieved by a curved, pole symmetric path of contact by purely graphical methods. And the developed gears, proven in heavy industry applications, showed highly improved properties. Specimens of both gear geometries, which were made of tempered and nitrided alloy steel, were tested on an FZG testing machine, and results confirmed the theoretical foundations of S-gears. Then it was necessary to replace the graphical method by a numerical one and to define the tool. So, the rack profile was defined by a pole symmetric parabolic-type function, which in turn defined the path of contact and finally gears with an arbitrary number of teeth. Many applications were developed with S-gear shape, e.g., helical, crossed, and planetary gears, various worm drives, etc. S-gear concept was also used with polymer gears and high transmission ratio planetary gears. Lately, this concept was used to develop crossed helical gear drive with perpendicular shafts. Such drives are often used in centrifuge drives (e. g. Alfa-Laval) and this implementation with the module m = 5 mm uses a large driving gear with 60 teeth (with the left-handed helix angle of 30°) on the horizontal shaft and a smaller driven gear with 20 teeth (with the right-handed helix angle of 60°) on the vertical shaft. This paper is a tribute to work of Professor Jože Hlebanja (1926-2022) whose research was dedicated to gears with improved properties, namely S-gears.