An improved method of solving contact trajectory boundary for Spiral bevel gear

A method of solving contact trajectory boundary is developed for spiral bevel gear. Tooth surfaces of pinion and gear are projected to axial cross section based on rotation transformation, vector operation is used to distinguish whether contact point belongs to tooth surface or not. Distances between contact point and every boundary of tooth surface are calculated, if the minimum distance is less than preset value, this contact point is considered to be contact trajectory boundary. Starting from initial point of TCA, contact point approaches contact trajectory boundary by adaptive step size, when currently step size is greater than preset step size, the value of the last contact point is used as initial value for new contact point, otherwise initial value is calculated by particle swarm optimization with penalty function, this method can improve the solving speed greatly while keeping stable. Finally, the validity and practicability of this method are proved by a numerical example.