Exact analytical algebraic expressions for mathematical modeling of face-milling spiral bevel gears

Face-milling spiral bevel gears are widely used in gear transmission systems because they generally exhibit better transmission characteristics than straight bevel gears. When solving gear surface equations using the conjugate principle, numerical techniques are commonly used because of their inherent accuracy. However, in this study, an alternative method is proposed in which the gear surface equation is derived mathematically and is then solved using an analytical approach. An illustrative case study is presented to substantiate the efficacy and applicability of the recommended methodology. The computational results confirm the effectiveness and robustness of the proposed algebraic expressions as an alternative analytical framework for spiral bevel gear tooth surface modeling.