Node-to-Target Formulation in Finite Element Spur Gear Problems

Abstract

In this paper, a quasistatic finite element model of a spur gear pair is developed. A node-to-target contact formulation is given, where calculations of initial gaps are based upon the actual geometry of the gear flanks rather than upon a contact node and a facet or a line segment. By using a special contact search algorithm, profile modifications and mounting errors are easily incorporated in the analysis. The problem, which also includes friction, is solved by using a nonsmooth Newton method. The static transmission error can be calculated with accuracy with a relatively small number of nodes along the gear flanks. Several examples are given in order to demonstrate the model.

Key Words:

• Gears
• Contact
• Finite element
• Static transmission error

Acknowledgments

Notes

¹This is not a requirement for the flanks on the gear.

²This is a useful formulation of Coulomb's friction law. That is, if  −  = 0, then |p _it | ≤ μp _in , but if  −  ≠ 0, then p _it  = μp _in sgn( − ).

³ [Xcirc] ^A  = [Xcirc] ^A  + û ^A .