As Mahr Federal’s director of precision gauges, **George Schuetz** explains, circular geometry gauging means more than just roundness.

Roundness is far from the only circular geometry specification that machinists may be required to meet, and therefore to inspect. Let us look at some of the other parameters. As we describe them, refer to the figure to see how each is indicated on part print callouts.

Roundness involves no datum: it is evaluated relative to the part profile itself using one of the four methods: Maximum Inscribed Circle, Minimum Circumscribed Circle, Least Squares Centre, or Minimum Radial Separation. Eccentricity, in contrast, is measured relative to a datum, which is the centre of part rotation, as established by the spindle of the geometry gauge (or by a part feature defined as the datum that has been canted on the spindle). Eccentricity is the distance between the centres of the reference circle used to calculate out-of-roundness, and the datum. As the part rotates 180° around the datum axis, the centre of the reference circle is displaced by twice the eccentricity value: hence, concentricity is twice eccentricity. Both eccentricity and concentricity may be measured for features lying in a single plane or in two planes.

Circular runout, another datum-referenced measurement, measures the radial separation of two concentric circles whose common centre is the datum, and which entirely enclose the part profile. Circular runout is the result of the combination of two form-error factors: out-of-roundness, and out-of-concentricity. The two factors may be additive or may cancel each other out, depending on vector directions. Circular flatness (of a flange, for example) may be specified at an indicated radius, and measured in a circular trace. This is a datum-free measurement that uses either a minimum-zone or a least squares calculation, similar to those used in roundness measurements.

Circular flatness can be used as the basis for plane parallelism measurements. Care must be taken, however, in reading and interpreting callouts correctly. The statement “A is parallel to B” (within a specified tolerance) implies that surface B is the datum. Any out-of-flatness present in this surface is ignored, while out-of-flatness in surface A is included in the calculation. The gauge user cannot treat the two surfaces interchangeably. If one excludes out-of-flatness of both surfaces, the measurement is defined as parallelism plane runout.

In order to measure a number of squareness related parameters, a vertical datum axis must first be established by measuring the roundness of the part at two planes, thus creating a part axis between the centres of the two reference circles. After normalising the part axis to the gauge spindle’s axis of rotation, the horizontal surface in question is gauged at a specified radius, and normalised to the datum axis. Perpendicularity includes the out-of-flatness of the horizontal surface, while perpendicularity plane runout ignores out-of-flatness. Squareness is defined as half the plane runout value, in other words, it measures only from the centre of the part’s rotation to the indicated radius, while perpendicularity plane runout measures the deviation across the entire circle.

All of the parameters above can be measured on so-called “roundness” gauges, which do not provide a means for precision vertical movement of the gauge head. “Cylindricity” gauges, on the other hand, incorporate precision reference surfaces in the gauge head positioning axes, permitting measurements of a number of additional parameters.

Cylindricity is a useful parameter that provides an overall assessment of part roundness, taper, and straightness. Because it is not possible to measure every point on a three-dimensional surface, part profiles are taken at a number of planes, then combined into a single cylindricity value. Statistical analysis, and experience, may be required to establish the number of sample profiles needed for an accurate measurement.

Cylindricity gauges can also be used to measure the straightness of an ID or OD surface on a vertically oriented workpiece, by keeping the part stationary and traversing the gauge head up or down. Straightness can then be used as the basis for linear parallelism measurements, comparing opposed ID or OD surfaces, or comparing an ID surface to an OD surface.

The main point is that numerous parameters have been developed in order to control the functionality of parts across a wide range of possible configurations and applications. Make no assumptions when gauging part geometry: be sure you understand what the parameter means before you try to measure it.