Understanding and modelling the torsional stiffness of harmonic drives through finite-element method

Torsional stiffness or rigidity is a crucial characteristic in the design of transmission devices, including harmonic drives (HDs). Among the various design aspects constituting a reduction mechanism in robotic systems, torsional stiffness is an important factor for positioning accuracy and control issues. One of the major advantages of HDs is their capacity to present a high reduction ratio while maintaining a small hardware size. However, manufacturing these drives remains a complex and costly process due to the high precision of its machined components; as a result, the use of such drives is still limited only to high-end mechanical products and technologies. Given these costs, numerical analysis becomes an effective alternative for obtaining valuable data through simulations, without the need for prototypes. This article presents a finite-element model to reproduce the behaviour of the torsional stiffness of an HD. The numerical model allows an evaluation of the effects of various geometrical parameters on the torsional stiffness of the HD. The numerical model of the HD can be used for optimization purposes, i.e. to develop an HD with a high torque capacity combined with a high-rated lifespan.