Coupling Types - Elastic Averaging

Elastic averaging represents a subset of surface coupling types where improved accuracy is derived from the averaging of error over a large number of contacting surfaces. Contrary to kinematic design, elastic averaging is based on significantly over-constraining the solid bodies with a large number of relatively compliant members. As the system is preloaded, the elastic properties of the material allow for the size and position error of each individual contact feature to be averaged out over the sum of contact features throughout the solid body. Although the repeatability and accuracy obtained through elastic averaging may not be as high as in deterministic systems, elastic averaging design allows for higher stiffness and lower local stress when compared to kinematic couplings. In a well designed and preloaded elastic averaging coupling, the repeatability is approximately inversely proportional to the square root of the number of contact points.

Hirth or curvic couplings, used in serrated tooth circle dividers are examples of elastically averaged couplings. The serrated tooth circle divider uses two mating face gears. Both are the same diameter and have equal tooth geometry and tooth size. As the two face gears are engaged and preloaded, the teeth are lapped, the individual tooth size and position variations are averaged out over all the teeth, thus providing good repeatability