Gaging "Relational" Dimensions

George Schuetz, Mahr Federal Inc.

 Specifications often require inspection of dimensional relationships between two features, or between two dimensions on the same feature.  For example, a TIR (total indicator reading or total indicated runout) specification defines a relationship between the outside diameter of a part feature, and the part's axis.  The taper of a conical part is another relational specification, which is checked by comparing diameters at two known heights.  Other examples include distance between centers, ID or OD ovality, and parallelism.

 Compared to single-dimension specifications (such as diameter), these "relational" specifications can be challenging to inspect.  Not only do they involve multiple measurements; they also require that separate measurement results be somehow combined in a mathematical relationship.  This might be as simple as subtracting the minimum reading from the maximum reading, as in the case of ovality, or so complex as to require trigonometry, as in the case of taper measurements.

 Of the three standard gaging methods available for these tasks—indicator gaging, electronic gaging, and air gaging—air possesses the best combination of properties for most applications.  Dial indicators are somewhat bulky, restricting the close spacing of contacts.  And to combine the results of two or more measurements, the operator must usually perform mathematical calculations.  While electronic gaging amplifiers can be readily programmed to combine signals from multiple contacts and calculate results directly, many electronic gage contacts are too long to be placed in tooling for inside dimension measurements.

 The type of air gage known as a dual-circuit air comparator (also known as a differential, or balanced, gage) has a circuit working on either side of a bellows in such a way that the gage reads zero when pressure in both circuits is equal, while any differential between the circuits is displayed as variation from zero.  With appropriate tooling, this arrangement allows the gage to combine signals from multiple jets, to generate relational dimension results directly.  In addition, air jets are quite small, permitting great flexibility in gage design, especially for inside measurements.

 The diagrams show schematically how jets are arranged in tooling to measure various relational dimensions.  As shown in (A), a conical taper gage places pairs of jets on separate circuits, to compare two diameters at known heights.  Gage (B) measures wall thickness variation, or eccentricity of ID to OD.  The tooling in (C) measures bore squareness, while ignoring bore diameter and taper.  Two such tools could be combined in a single fixture to measure bend and twist of two bores relative to one another, or bore parallelism in two planes.

 Gage (D) measures the center distance between bores by comparing distances between opposite walls of the bores, while ignoring changes in bore diameter.  Gage (E) measures ovality by comparing two diameters in the same plane, at 90 degrees to one another.  And gage (F) measures parallelism by comparing part thickness at two locations.
 Another common "relational" inspection task (not shown) is the measurement of clearance between mating parts, as in fuel injector and bearing assemblies.  We can't squeeze a gage between the assembled components to measure clearance directly, but we can measure two unassembled parts simultaneously, using one gage circuit for the ID component, and the other for the OD component.  The gage will thus display the "match" or clearance.  Should it indicate that clearance is out of tolerance, we can leave the OD part on the tooling, and inspect a number of ID parts until we find a proper match.

 It is often useful to obtain simple, single-dimension measurements simultaneously with relational measurements.  For example, in addition to inspecting wall thickness variation in (B), we may also want to measure the outside diameter.  Air gaging excels at this task.  In all the examples, additional jets could be installed in the tooling, adjacent to the ones shown.  These new jets would run on separate air circuits to a second comparator, to perform simultaneous measurements of diameters (in diagrams A through E), or thickness (F).  In many cases, the tolerance for the "relational" dimension will be significantly tighter than the tolerance for the "simple" dimension.  If this is the case, we can specify different levels of magnification for the two gages, each one suited to the range and resolution required.