Tolerances and available relative motions in bolted connections

The implications of geometric and dimensional tolerances on the mechanical behavior of assemblies are often indirect or unclear. Although current tolerancing practice will generally assure that components will assemble, one may also be concerned with other aspects of the functionality of an assembly. In this paper we examine one aspect of functionality, namely the effect of statistical tolerances of location on the amount of available motion or play that can occur in bolted assemblies. A mobility formulation is proposed which allows the possible part motions to be determined in terms of one of two indices, i) the average Available Translation or Rotational Motion and ii) the Relative Mobility Area. A Monte Carlo simulation is used to perform the mobility calculations. The hole locations and tolerances are normalized, allowing the available motion of assemblies with different numbers of holes and configurations to be compared. It is shown that the geometric arrangement of holes does not significantly affect mobility. Increases in average hole to hole distance reduces available rotational motions but not translations. A decrease in available motion is shown to occur as the number of hole features increases. This decrease in quantified by means of the above indices.