Hole Alignment Tolerance Stacking Issues

Each of two parts has K coordination holes with the intent that each hole on onepart is paired and to be pinned with a corresponding hole on the other part. Whilethe nominal hole centers for each hole pair are identical, the actual hole centers willdeviate from their nominal values in some random fashion reflecting the inherent holecentering accuracy of the drilling process. It is then of some interest to examine themaximal hole center discrepancy among K such hole pairs and to understand how thisdiscrepancy grows with K. We give a plausible and very simple model for assessingthis maximal discrepancy statistically and show that the growth of this discrepancy isslow, namely on the order of√log(K). Although this model formulation assumes theunrealistic true position part alignment on all K nominal centers, it is still useful inthat it provides a conservative assessment compared to what might be possible under“best” alignment. Furthermore, its results relate essentially linearly to the common,practical alignment procedure using primary and secondary hole pairs. The statisticaltreatment of hole center variation is compared to the worst case treatment for bothalignment procedures. While the gain of the statistical over worst case treatment issmall under true positioning it is substantial under primary/secondary hole alignment.Consequences for minimal clearance and maximal clean-out diameters are derived,assuming no or negligible hole and pin diameter variations. These results can beextended usefully to the situation when triplets of holes, one hole each on one of threeparts, need to be pinned. The above results are derived assuming equal hole centeringvariability from hole to hole. This is extended to hole centering variability that growslinearly with the distances of the nominal hole centers from some reference datum. Afurther extension deals with matching two parts where each part is built up from ksubparts with n holes each. The misalignments of the subparts relative to each otheradd dependency complications when trying to assess the maximum mismatch betweenthe K = kn holes on each assembly half.∗ P.O. Box 3707, MC 7L-22, Seattle WA 98124-2207, e-mail: [email protected]