From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Analysis of stresses in helical fabroil gears, outlining assumptions and formulas for comparative figures.
| Identifier | ExFiles\Box 136\1\ scan0316 | |
| Date | 12th April 1940 | |
| 1155 Rm{William Robotham - Chief Engineer}/JRS 2/CK{Mr Clark} 12-4-40 Treatment of Helical Fabroil Gears Since it is propsed to investigate the stresses in various fabroil gears including one with a tooth thicker than half the pitch the Lewis formula cannot be used. This treatment necessarily involves certain assumptions but it should give comparative figures for the various tooth forms. The assumptions made are. 1)The whole load is carried by one tooth 2)The load is carried along the tip of the tooth The first of these is afterwards modified. Referring to figure 1. Wn= W/Cos.ψ It is better to consider the load on the tooth not as the inclined load Wt in fig. 2 but as its 2 components, Wn causing a bending stress and Wc causing a compression stress, on the tooth materials. Wc=Wn tan. ø = W tan. ø / cos.ψ . If "h" is the total height of the tooth the bending moment on the teeth is Wnh = Wh/Cos.ψ The resisting moment of the weakest section is b/Cos.ψ . (tx^2)/6 . f where f is the safe stress. ∴ Wh/Cos.ψ = b/Cos.ψ . (tx^2)/6 . f or f= 6Wh/(btx^2) The perpendicular component produces a compressive stress whose average is Wc / (b/Cos.ψ tx) = (W tan. ø / Cos.ψ) / (b/Cos.ψ tx) = W tan. ø / b tx Maximum tensile strength produced is: ft= 6Wh/(btx^2) - W tan. ø / btx This stress is allowing for conditions worse than can possibly exist and a suitable modification is to divide this stress by the number of teeth in contact assuming that the load is equally distributed over this number. Contact in involute gears takes place only along the line tangent to the 2 base circles and only on the portion of this line lying between the 2 addendam circles i.e. contact takes place from M to N. | ||