Conversion of a piston–cylinder dimensional dataset to the effective area of a mechanical pressure generator

Recent developments in diameter metrology at NIST have improved the dimensional characterization of piston-cylinder assemblies (PCAs) to unprecedented precision. For the newest generation of PCAs, the standard uncertainty in the measurement of the outer diameter is 12 nm, while uncertainty in the measurement of the inner diameter is 14 nm. With a high-accuracy dimensional dataset in hand, the task of determining the pressure generated by a specific PCA is reduced to converting the diameter (and straightness and roundness) to an effective area (and distortion coefficient). The details on how this was performed for the artifact PCA2062 are described. PCA2062 was dimensioned in 2017 and 2020; the area repeated within <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>0.2</mml:mn> <mml:mo>×</mml:mo> <mml:msup><mml:mn>10</mml:mn> <mml:mrow><mml:mo>-</mml:mo> <mml:mn>6</mml:mn></mml:mrow> </mml:msup> <mml:mo>⋅</mml:mo> <mml:msub><mml:mi>A</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:mrow> </mml:math> . The calculation produced estimates of fall rate and rotation decay that agreed with experimental observations within 12 %. The fall rate is proportional to the square of the gap width; therefore, the agreement between calculation and measurement validates the dimensional estimate of the gap width within (36 ± 42) nm, where the 42 nm standard uncertainty is governed by the present state of flow theory. The piston gage model is buttressed by three comparison tests against a laser barometer, which support a view that PCA2062 is linear and reproducible within 0.2 μPa Pa^-1. Finally, an estimate of uncertainty in the effective area of a dimensioned artifact is provided: as expected, the diameter measurement is the main culprit, but there are open questions regarding the flow model that preclude an accurate evaluation of the distortion coefficient. For the 530 kPa operating range of PCA2062, distortion is not a significant problem, but the effect would be dominant in assemblies operating at 1 MPa and above.