| Summary: | Tooth fillets are commonly made of circular profiles because they are easy to define analytically and have been shown to be superior from a bending perspective to the trochoid fillet. For gears that are cast, forged, or 3D printed, the tooth fillet can be any curve as long as it is capable of providing a smooth mesh without interference. For such design flexibility, the circular fillet may not necessarily be the best fillet profile from a bending stress point of view. Therefore, the first aim of this study is to develop a general mathematical model for defining the tooth fillet profile analytically for gears manufactured by non-generation cutting processes. The mathematical model employed a general fillet transition curve (GFTC) to ensure smooth transition surfaces in the fillet zone and an improved radius of curvature as well as tooth form factor compared to the circular fillet profile. The second aim of this work is to examine if increasing the order of the proposed GFTC can enhance the fillet strength of the gear tooth further. The design method is conducted for involute gear and, for the first time, non-involute gears. Various fillet design parameters and tooth numbers are examined. The results showed that by using the proposed fillet shape, the tooth fillet strength can be enhanced by 18–23% for involute gears and by 30–32% for non-involute gears. Also, the results showed that increasing the order of the fillet curves might not always improve the fillet strength of the gear teeth.
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