There is considerable geometric variability of raw castings and weldments before any machining of surfaces that assemble with other components. Consequently, considerable time often is spent identifying successful set-up adjustments at the machining fixtures for such parts in a way to ensure that every machined surface will be complete. The proposed Set-Up-Map© is a point-space subset of R6 where each of the six orthogonal coordinates correspond to one of the rigid-body displacements in three dimensional space: three translations and three rotations. Any point within the Set-Up-Map (S-Map) corresponds to a small body displacement (SBD) of the part that satisfies the condition that each feature will lie within its associated tolerance zone after machining. S-Maps are derived from previous work on Tolerance Maps© (T-Maps), which represent feature deviations allowed by a given tolerance zone. Each raw casting or weldment is scanned, and the point-cloud data fitted to individual features, to determine how much each to-be-machined (TBM) feature deviates from nominal specifications. Each local T-Map is formed from a library, then shifted to be centered on its corresponding scanned feature on each casting; it becomes a local S-Map primitive. Each of these local S-Maps is then transformed to a single global reference frame. The intersection of these S-Map primitives in the global frame gives the allowable small body displacements that satisfy the positioning requirements for all TBM features. Since T-Maps are convex objects, a half-space intersection method is used to generate an S-Map. Any point within the S-Map represents a viable small body displacement specific to the global coordinate system established on the part. In the case that as-cast or as-welded features deviate from what is acceptable, the S-Map will be the empty set. Consequently, in addition to reducing the time for setup in a fixture, S-Maps can serve as a valuable diagnostic to determine that a part should be either scrapped or reworked.

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