Beyond the Paired t-Test: Equivalence-Based Validation of Centrifugal Stress Models for Solid, Tapered-Web, and Gaussian Flywheel Discs

Comparing the fatigue lives of competing flywheel shapes first requires trusted stress models. This study validates axisymmetric plane-stress models of three bore-less discs, each with a 0.2 m radius and a 25 mm rim: a constant-thickness solid disc in structural steel, a linearly tapered web (50 mm at the hub) in carbon steel, and a Gaussian profile (30.2 mm at the hub) in ASTM Class 30 cast iron. At 522.57 rad/s, each model was compared at 40 radial positions with its matching published solution and, independently, with a converged two-dimensional axisymmetric finite element analysis (FEA). Agreement was judged by the area-under-the-curve (AUC) difference, point-wise errors, the paired t-test, and the two one-sided tests (TOST) procedure with a ±5% equivalence margin, with confidence intervals corrected for serial correlation through an effective sample size and a moving-block bootstrap. All comparisons passed the 15% AUC limit (largest deviation 4.83%), yet the t-test misjudged two cases: it rejected the solid disc despite mean offsets of only −0.04 and +0.12 MPa, and accepted the tapered-web hoop stress (p = 0.314) although the curves differed by 11.92 MPa at the rim. Correlation-corrected TOST and a point-wise envelope check found the solid and Gaussian discs equivalent to their references and the tapered web not equivalent. The FEA agreed with all three models to within 1.2% of peak stress but differed from the tapered-web reference by up to 12.0 MPa, showing that the discrepancy comes from the reference's neglect of the thickness-gradient term. With all discs in the same steel, the tapered web had the highest energy shape factor (0.718, against 0.631 and 0.606). Validation should pair AUC with point-wise errors and a correlation-aware equivalence test, and should separate agreement with a reference from model accuracy

flywheel disc, centrifugal stress, model validation, area under the curve

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