Further analysis of pneumatic ball gauge calibration data; development of quadratic equations

Abstract

In earlier papers it was shown that an apparent pressure dependence of effective area of pneumatic ball gauges could be ascribed to non-constancy of effective area as conventionally defined. The relationship between P, the pressure measured at the gauge and F, the force due to load of weights on the ball, was generally better represented by an equation of the form P= a+ bF derived from linear least squares analysis of calibration data. It is the objective of the present paper to investigate whether the addition of a quadratic term, cF 2, would improve the agreement of calculated values of P with known calibration values. Calibration data collected for 8-ball gauges were analyzed using analysis of variance (ANOVA) to infer the significance of the quadratic term. For 7 of 8 gauges, a quadratic term significantly improved agreement between calculated and calibration values of P.