Efficiency Prediction of Splash-Lubricated Bevel Gear Drives via Energy-Equivalent Spur Gear Transformation

Abstract

Accurate efficiency prediction of splash-lubricated bevel gear drives is challenging due to the continuously varying pitch radius along the conical face width and the absence of closed-form analytical formulations tailored to conical geometries. This study presents a novel energy-equivalent transformation that converts a partially immersed bevel gear into an equivalent spur gear while preserving the hydrodynamic energy associated with oil churning. By defining the face width along the cone generatrix and deriving a radius-weighted integral representation of the immersed region, an equivalent spur diameter is obtained for both partial and full immersion conditions. The transformed geometry enables the direct application of established spur-gear loss models to evaluate meshing, bearing, seal, and splash lubrication losses within a unified framework. A rated-condition efficiency evaluation procedure is developed in which the load torque is determined from a consistent power balance equation, ensuring physical compatibility between transmitted power and total losses. The resulting formulation provides a geometrically rigorous and computationally efficient method for predicting total efficiency of bevel gear drives operating under oil-bath lubrication. The proposed approach bridges the gap between conical gear geometry and spur-based analytical loss modeling, offering a practical tool for efficiency estimation, preliminary design, and optimization of bevel gear transmissions in splash-lubricated environments.