Abstract
Helical bevel gears have inclined or twisted teeth on a conical surface and the common types are skew, spiral, zerol, and hypoid bevel gears. However, this study does not include hypoid bevel gears. Due to the geometric complexities of bevel gears, commonly used methods in their design are based on the concept of equivalent or virtual spur gear. The approach in this paper is based on the following assumptions, a) the helix angle of helical bevel gears is equal to mean spiral angle, b) the pitch diameter at the backend is defined as that of a helical gear, and c) the Tredgold's approximation is applied to the helical gear. Upon these premises, the contact stress capacity of helical bevel gears is formulated in explicit design parameters. The new contact stress capacity model is used to estimate the contact stress in three gear systems for three application examples and compared with previous solutions. Differences between the new estimated results and the previous solutions vary from -3% and -11%, with the new estimates being consistently but marginally or slightly lower than the previous solution values. Though the differences appear to be small, they are significant because the durability of gears is strongly influenced by the contact stress. For example, a 5% reduction in contact stress may result in almost 50% increase in durability in some steel materials. The equations developed do not apply to bevel crown gears.
Highlights
The term “helical bevel gear” is used in this paper to describe bevel gears that have inclined or twisted teeth on a conical surface
In this article we explore the possibility of formulating a contact stress capacity model for helical bevel gears that is less conservative than the AGMA model
A contact stress expression (Eq (20)) for helical bevel gears is derived based on several simplifying but realistic assumptions
Summary
The term “helical bevel gear” is used in this paper to describe bevel gears that have inclined or twisted teeth on a conical surface. The mesh point, mesh force, and line-of-action vector for spiral bevel gears are time varying quantities in 3D space They are more difficult to design and costly to manufacture because they require specialized and sophisticated machinery. ANSI/AGMA 2003-B97 [16] is a popular bevel gear design standard in the United States and provides a conservative means of estimating the contact and bending stresses in straight, zero, and spiral bevel gears [8)]. The power loss per mesh in bevel gear drives is of the order of 2% [17] which is considered negligible in this study
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