Probabilistic Estimation of the Effect of Dimensional Tolerance for Turbine/Compressor Blade Attachment

Root attachments of rotating blades of a turbine or a compressor often have multiple lobes. These lobes fit into a matching groove in a rotating disk. Dimension of these lobes, in general, will not be identical for each blade. However, these dimensions will be within manufacturing tolerance. The resulting dimensional fit becomes random in statistical sense within the specified tolerance. Thus precise dimension is unknown even if it is assured to be within the specified tolerance band. This creates the possibility that for a given blade all the lobes might not be in contact i.e. there might be a gap in the joint. This also means that lobes will carry unequal load. The gap condition may be different for each blade. As the rotational speed increases, each gap will start closing and ideally will eventually close. Description of a method to assess the influence of manufacturing tolerances on the reliability of such a joint for disk-blade assembly is presented. The resulting estimated stress as a function of rotating speed and tolerance stacking is also presented. The stress result is combined with probabilistic analysis that yields the probability for stress to be within a predetermined amount thus providing a measure of success.