A novel analytical model for gear contact analysis considering edge effect

Gear contact analysis plays a critical role in gear dynamics, lubrication, and fatigue strength investigation. Numerous studies have been proposed addressing it, but most of them neglect tooth edge effects, resulting in a lack of prediction accuracy. To bridge this gap, this paper develops a novel analytical model based on the influence coefficient matrix method. The model incorporates various factors to reflect the edge effect, including deflection decay along the tooth width, the mirror rule at edge planes, local support effects at tooth ends, and local stiffness concentration at the tip. Contact pressure results from the model show strong agreement with the finite element method (FEM) for both spur and helical gears. Using this validated approach, we analyze gear load distributions and quantify the impacts of tooth modification and misalignment. The results indicate that edge effects amplify contact pressure, particularly at the tooth tip contact area. Lead crowning and tip relief effectively mitigate these effects. A local rounding is suggested at the start of relief to avoid localized stress concentration at the transition area. Gear misalignment would increase the three-dimensional face load factor, with twisting misalignment showing a more significant influence than tilting. The tooth lead modification can improve gear load distribution, in which lead slope modification has a better effect than lead crowning.