The investigation of elongation of the neutral line in harmonic drive

Harmonic drive has widespread applications in power transmission for its compact size and high speed reduction ratio. Flexspline usually endures large deformation under assembly force from wave generator. In transmission state, driving force leads to multiple teeth engagement between flexspline and circular spline. Large deformation of the flexspline and contact relations between flexspline and wave generator, flexspline and circle spline make the problem more complicated than other transmission device ever. To simplify the geometry relation of flexspline, one of the assumptions in harmonic drive analysis is no elongation of neutral line, which leads to great simplification in deformation and engagement analysis of flexspline. With help of the classic relationship and finite element analysis (FEA), the rationality of the assumption is estimated in both assembly state and working state here. The geometric expressions of neutral lines are introduced first, and the elongation of the neutral lines is derived for commonly used wave generators. Then a FEA model of a flexspline in harmonic drive with eccentric double-disk roller wave generator is built, and the contact relation is defined between wave generator and flexspline. Contact analysis is carried out in assembly state and working state respectively. The elongation of the neutral line is calculated by the radial and tangential displacements. The elongation in assembly state and transmission state is compared with the original circumference length and the elongation strain is given. The research shows that the assumption is approximative in assembly state and transmission state. The elongation should be considered in harmonic drive under transmission loading.