978 - 0 - 521 - 76170 - 3 - Noncircular Gears : Design and Generation

Designers have tried for many years to apply noncircular gears in automatic machines and instruments. The obstacle was the lack of effective methods of generation of noncircular gears similar to those applied for the generation of circular gears. However, researchers have continued the investigation of application of noncircular gears – see the earlier works by Burmester (Burmester, 1888), Golber (Golber, 1939), Temperley (Temperley, 1948), or Boyd (Boyd, 1940) – and manufacturers have intensified their efforts for improvement of the generation of noncircular gears (Fellows, 1924; Bopp & Reuther G.m.b.H., 1938). Due to the lack of exact methods of generation of noncircular gears, the efforts were first directed to the development of methods based on the meshing of generating tools with master gears. Figure 1.1.1 shows the Fellows’ approach where the noncircular master gear 1 is in mesh with a master rack (Fellows, 1924). The rack cutter and gear being generated are denoted by 3 and 4, respectively. Bopp and Reuther’s approach (Fig. 1.1.2) is based on the simulation of meshing of a noncircular master worm gear c with a worm f that is identical to the hob d; a is the spur noncircular gear being generated; the cam b and the follower e form the cammechanism designated for simulation of the required variable distance between c and f (Bopp & Reuther G.m.b.H., 1938). Weight g maintains the continuous contact between the cam and the follower. However, both approaches were difficult to apply due to the necessity of manufacturing noncircular master gears, which was expensive and time-consuming. The breakthrough of generation of noncircular gears happened in years 1949– 1951, wherein enveloping methods of generation of noncircular gears were developed based on generation by a rack cutter, hob, or a shaper (Litvin et al., 1949 to 1951). Such methods were based on obtaining the gear tooth surface as the envelope to the family of tool surfaces and are based on the following ideas: