Mesh stiffness of micro-spur gears by finite element formulations based on modified couple stress theory

Abstract

Finite element formulations developed for micro-sized structures are utilized for the determination of mesh stiffness of micro-spur gear pairs. The equations are based on Modified Couple Stress Theory developed for micro-beams. Timoshenko and Euler–Bernoulli type formulations are used separately to observe the difference. Calculations are performed for micro-gear pairs having two different module types and the stiffness of both double and single mesh regions are obtained. The results reveal the size effect on the mesh stiffness of micro-gears, and can be used in the future for more advanced gear configurations. The comparison study shows that performing calculations with classical continuum theories as well as Euler–Bernoulli type beam formulations can cause significant errors in the mesh stiffness depending on the size of micro-gears.