Fast Modelling of Bending Stresses in Dimensionless Gear Teeth using BEM

V.A. Spitas, T.N. Costopoulos, and C.A. Spitas (Greece)


Spur gears, bending stress, BEM, dimensionless gears, tabular method.


A new fast method of modeling spur gear teeth to be used in bending stress calculation problems is considered. The real bending stress values are calculated by linear interpolation from tabulated ones obtained from Boundary Element Analysis on dimensionless teeth. The dimensionless tooth model has the advantage that its worst loading case can be described and determined accurately by the use of only four parameters, i.e. the number of teeth, the addendum modification, the thickness at pitch and the contact ratio of the gear pair. The first three describe the geometry of a 20o involute gear tooth in a unique way and the fourth is used to determine the Highest Point of Single Tooth Contact (HPSTC), where the worst loading conditions occur on every tooth mesh cycle. A set of analytical equations is used to modulate the actual full-scale real gear stress problem into the dimensionless teeth-meshing model and then they can be solved in the reverse order to yield the actual stress values. Following the proposed methodology, the actual tooth fillet stresses can be computed in a way that is faster compared to the existing numerical methods and more accurate compared to the existing analytical or empirical methods.

Important Links:

Go Back