Evaluating Size with the Geometric Tolerance Command

Many geometric tolerance commands contain a size tolerance. This page describes how the geometric tolerance command computes measured size values and measured local size values.

Size Specifications

The geometric tolerance command supports only a few size specifications. There is a separate size command for more complicated size specifications. For information, see "Using the Size Command".

Under ASME, the geometric tolerance command uses the following size specification. The unrelated actual mating envelope (UAME) controls the feature surface in the plus-material direction, and the local sizes control the feature surface in the minus-material direction. The local sizes are opposed-point sizes unless the feature is a cylinder, and you have the CIRCULAR_ELEMENTS local size option. That said, the geometric tolerance command does not report local sizes unless you turn on local size reporting, because many measurement systems have insufficient accuracy to verify that the local sizes comply with the size tolerance.

Under ISO, most size tolerances are envelope sizes as defined in ISO 14405-1. This means the plus-material direction is controlled by a mating envelope size, and the minus-material direction is controlled by opposed-point local sizes. However, when ISO 17450-3 applies, as discussed in "Deriving the Toleranced Feature", then the size tolerance is a no-modifiers (default) size. This means the size tolerance does not control any mating envelope, and the only sizes are the two-point local sizes.

Global Size

Anytime the size specification includes a mating envelope size, the size tolerance has a global size. ISO tolerances call this GLOBAL SIZE in the Edit window, while ASME tolerances call this UAME in the Edit window. The only time the size tolerance does not have a global size is when ISO 17450-3 applies as discussed above.

If your considered feature does not have surface data, the global size is the MEAS size of the input feature.

If your considered feature has surface data, and your feature math option is LSQ (least squares), the global size is the size of the (unconstrained) least squares best fit.

If your considered feature has surface data, and your feature math option is DEFAULT, the global size is the size of the inscribed or circumscribed best fit, whichever of the two is external to the material. Since traditional inscribed and circumscribed fits are notoriously unstable, PC-DMIS uses a constrained least squares algorithm to compute the inscribed or circumscribed fit in a stable way.

As discussed in "Specification Versus Verification" in "Introduction to Geometric Tolerances and Feature Control Frames", we offer both LSQ and DEFAULT feature math options because different measurement systems have different amounts of measurement uncertainty. If your measurement system is precise and accurate enough to measure the feature's form error—if the measurement uncertainty is much smaller than the form error—then it makes sense to use DEFAULT math. If the measurement uncertainty is larger than the form error, then you should use LSQ math. For more information, see "Specification Versus Verification".

Local Size

If ISO 17450-3 applies as discussed above, then the size specification is the default ISO size specification (no modifiers), meaning there are only local sizes and no global size. The geometric tolerance command reports both the maximum and the minimum local size.

If ISO 174509-3 does not apply, and if your considered feature has surface data, you have the option to report local sizes. This is primarily useful when your feature math option is DEFAULT, because the geometric tolerance command reports only the worst local size in the internal to material direction. When combined with DEFAULT feature math, the global size controls the surface in the external to material direction while the local size controls the surface in the internal to material direction. By contrast, the LSQ feature math has a least-squares global size, which does not control the surface deviations in either direction, and so the surface will be uncontrolled in the external to material direction.

For ISO size tolerances, and for ASME size tolerances on spheres and widths, the local sizes are evaluated using opposed points. Each local size is essentially a two-point caliper measurement. Please ensure your measured points all have a directly opposed point, or the measurement accuracy may suffer. This is especially challenging on spheres.

For ASME size tolerances on cylinders, you have a choice of using the OPPOSED_POINTS interpretation or the CIRCULAR_ELEMENTS interpretation. These interpretations are specified in ASME Y14.5.1 - 2019. The opposed points interpretation behaves as just described.

The circular elements interpretation requires that the surface data was measured in circular cross sections. It best-fits a circle to each cross section; the sizes of the circles are the local sizes. When the feature math type is LSQ, the circles are computed using least squares. When the feature math type is DEFAULT, the circles are inscribed or circumscribed, whichever of the two is internal to the material. Since traditional inscribed and circumscribed fits are notoriously unstable, PC-DMIS uses a constrained least squares algorithm to compute the inscribed or circumscribed fit in a stable way.

It does not make sense to report local sizes unless your measurement system is precise and accurate enough to measure the feature's form error.

Bonus Calculations

Some geometric tolerances have a maximum material condition modifier (MMC) or least material condition modifier (LMC). This means that as the unrelated mating envelope size (or unrelated minimum material envelope size for LMC) deviates from the MMC (or LMC), additional tolerance or "bonus" tolerance is added to the tolerance in the feature control frame, yielding a total tolerance. For DEFAULT feature math, the measured bonus tolerance is the difference between an inscribed or circumscribed best fit and one of the limits of size. Since traditional inscribed and circumscribed fits are notoriously unstable, PC-DMIS uses a constrained least squares algorithm to compute the inscribed or circumscribed fit in a stable way. For LSQ feature math, the measured bonus tolerance is the difference between the least squares global size and one of the limits of size.

Measured bonus tolerance is calculated in the following way.

In every case, the bonus is limited so it is never negative, and never exceeds the total size tolerance (the upper boundary of size minus the lower boundary of size).

Report

Without Local Size

When you are not reporting local size, the size label of the report looks like this:

The header bar shows the dimension ID of the tolerance, the dimension units (MM or IN), the size specification, the math type (LSQ in this case), and the standard (ASME Y14.5 in this case). The table below shows the measured sizes of each sphere.

With Global and Local Sizes

When you are reporting global sizes and local sizes, the size label has extra rows, with LS added as a suffix for the worst local sizes. For example, "SPH1 - LS". For ASME tolerances on cylinders, the header bar also says whether the local size interpretation is OPPOSED or CIRCULAR. When reporting global sizes and local sizes, the report looks like this:

Without Global Size

When ISO 17450-3 applies, there is no global size reported. Instead, MIN and MAX are added as a suffix for the worst local sizes in both directions. The report looks like this: