An analytical approach for the determination of helical gear tooth geometry

Purpose: This paper aims to present an analytical approach for the determination of helical gear tooth geometry and introduces the necessary parameters. Tooth geometry including tooth chamfer, involute curve, root fillet, helix as well as tooth microgeometry can be obtained using the presented approach. Design/methodology/approach: The presented analytical approach involves deriving the equivalent equations at the transverse plane rather than the normal plane. Moreover, numerical evaluation of microgeometry modifications is presented for tooth profile, tooth lead and flank twist. Findings: An analytical approach is presented and equations are derived and explained in detail for helical gear tooth geometry calculation, including tooth microgeometry. Method 1, which was presented by Lopez and Wheway (1986) for obtaining the root fillet, is examined and it is proven that it does not work accurately for helical gears, but rather it works perfectly in the case of spur gears. Changing the normal plane parameters in Method 1 to the transverse plane ones does not give correct results. Two alternative methods, namely, Methods 2 and 3, are developed in the current research for the calculation of the tooth root fillet of helical gears. The presented methods and also the numerical evaluation presented for microgeometry modification are examined against the geometry obtained from Windows LDP software. The results show very good agreement, and it is feasible to apply the approach using the presented equations. Originality/value: In the gear design process, it is important to model the correct gear tooth geometry and deliver all related dimensions and calculations accurately. However, the determination of helical gear tooth geometry has not been presented adequately by equations to facilitate gear modelling. The detailed helical gear tooth root has been enveloped using software tools that can simulate the cutter motion. Deriving those equations, presented in this article, provides gear design engineers and researchers with the possibility to model helical gears and perform design calculations in a structured, applicable and accurate method. © 2023, Emerald Publishing Limited.