Representing stresses that arise in parallel assemblies that contain imperfect geometry allowed by tolerances

This paper concerns the role of geometric imperfections on assemblies in which the location of a target part is dependent on supports at two features. In some applications, such as a turbo-machine rotor that is supported by a series of parts at each bearing, it is the interference or clearance at a functional target feature, such as at the blades that must be controlled. The first part of the paper relates the limits of location for the target part to geometric imperfections of other parts when stacked-up in parallel paths. In other applications where parts are flexible, deformations are induced when parts in parallel are assembled together by clamping. Presuming that perfectly manufactured parts have been designed to fit perfectly together and produce zero deformations, the clamping-induced deformations result entirely from the imperfect geometry produced during manufacture. The magnitudes and types of these deformations are a function of part dimensions and material stiffnesses, and they are limited by design tolerances that control manufacturing variations. The last part of the paper relates the limits on stresses in parts to functional tolerance limits that must be set at the beginning of a tolerance analysis of parts in any assembly.