In gear couplings, torsional deflection creates a varying load across the face of the gear(s). If this load distribution is uniform, then the torsional deflection of the end where torque is applied, and the free end is equal to the deflection if half the load was applied to the free end. If the load varied uniformly such that it was at maximum at the driving end and zero at the other, then the torsional deflection at the free end would be equal to a load one-third of the total applied at the free end.
From these example effects of torsional deflections, it becomes clear the torsional deflection in gear couplings creates deflections that engineers should take into account. This is because the two ends of a shaft would see deflection, even if torque applies to only one end. This can throw off encoders or other feedback mechanisms.
The above is true for the shafts of a gear coupling. Torsional deflection also affects the teeth of a gear coupling. It induces stress in the gears. If this stress becomes too great, the teeth can fail. Because stress and strain (deflection) share a relationship, the result is the greater the stress, the greater the deflection. The ability for gear teeth to recover from deformations comes from their elasticity. In most use cases, Hooke’s law applies for elasticity.
Other deflections, such as axial and radial deflections also combine to produce effects in gear couplings. While the extent of these combinations is beyond the scope of this FAQ as they involve differential equations, keep this in mind implementing gear couplings into a system.