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Many factors influence the accuracy of hole diameter measurements. We've seen in past columns the importance of operator skill in the use of rocking-type adjustable bore gages, and discussed how variations in part geometry may make even technically accurate measurements inaccurate from a part-function perspective.

One of the fundamental requirements in bore gaging is that the gage contacts be centered in the bore. Bore gages that are not properly centered measure a chord of the circle, rather than its true diameter.

Most adjustable bore gages have a centralizer that helps the operator align the gage properly. Through misuse or wear, a centralizer may be damaged, so that the reference contact is pushed off-center. As long as the centralizer is not loose, it may still be possible to master the damaged gage with a ring gage: the off-center relationship will probably carry over to workpieces, so repeatable results might be obtained. Errors in part geometry, however, could cause a lack of agreement between results from the damaged gage and an undamaged one. And if the damaged gage were to be mastered with gage blocks on a set-master, a different zero reading would be obtained. So in spite of the possibility that an adjustable bore gage with a damaged centralizer might generate accurate results, it cannot be relied upon.

Fixed-size bore gages, such as air tooling and mechanical plugs, are substantially self-centering. But after years of use, the plug may become worn, resulting in excessive clearance and poor centralization.

Checking centralization is easy for both gage types. For rocking-type gages, simply compare measurements between a master ring and a set-master of the same nominal dimension. The difference between the round and square surfaces will reveal any lack of centralization. To check a two-contact or two-jet plug, insert the gage horizontally into a master ring, allowing the master to bear the gage's weight. Measure once with the contacts or jets oriented vertically, and once horizontally. If the measurements differ, centralization is poor.

Centralization error is the difference between the true diameter and the length of the chord measured. Quality personnel occasionally specify centralization error as a percentage of the total error budget (or repeatability requirement) for a gaging operation. For example, the error budget might be ten percent of the tolerance: in addition to an allowance for centralization error, this might include influences of operator error; gage repeatability; environmental variation; and within-part variation (for example, geometry error).

Gage users should be prepared to calculate how far off the bore centerline a gage may be without exceeding the specified centralization error. We'll call the allowable distance between the bore centerline and the contact centerline the misalignment tolerance. A simple formula, based on the relationship between the legs and the hypotenuse of a right triangle, does the job:

x2 = z2 - y2
where:
x = misalignment tolerance
y = z - 1/2 centralization error
z = 1/2 nominal diameter

Let's run through an example. The nominal bore dimension is 0.5 inch, with a dimensional tolerance of 0.002 inch (±0.001 inch). Centralization error is specified at a maximum of 2 percent of the dimensional tolerance (or 0.02 × 0.002 inch = 0.00004 inch).

z = 0.5" ÷ 2 = 0.250"
y = 0.250" - (0.00004" ÷ 2) = 0.24998"
x2 = (0.250")2 - (0.24998")2
x2 = 0.0625" - 0.06249"
x2 = 0.00001"
x = 0.00316"

The gage can be misaligned slightly more than 0.003 inch off-center before it will exceed the allowable centralization error. If you run through the same exercise for a 5.0 inch nominal bore, keeping the other values constant, you'll find that misalignment can be up to 0.010 inch before centralization error exceeds 2 percent of the 0.002 inch dimensional tolerance. Thus, as bore size increases, so does the misalignment tolerance.