= Floating-pinion robust contact margin
A \b[floating-pinion robust contact margin] is the smallest two-contact compression margin allowed by a stated set of uncertain parameters. It strengthens a nominal <floating-pinion compression margin> by checking every admissible parameter combination, while retaining the assumptions of the underlying contact model.
Let $\delta$ be the common approach and $b=e+x_{\rm eq}$ the equilibrium imbalance in the symmetric linear model. If the admissible pairs form a set $\mathcal U$, define
$$
M_{\rm rob}=\inf_{(\delta,b)\in\mathcal U}(\delta-|b|).
$$
For displacement $y$ from equilibrium with $|y|\le A$, the smaller contact compression is at least $M_{\rm rob}-A$. Thus \b[$A<M_{\rm rob}$ guarantees positive compression] for both contacts throughout the bounded motion. Equality permits zero compression and does not guarantee maintained compressive contact.
For independent interval bounds, or a bounding rectangle containing all possible pairs,
$$
M_{\rm box}=\delta_L-\max(|b_L|,|b_U|).
$$
This is exact when every pair in the rectangle is admissible. If the rectangle includes impossible combinations, it remains a conservative lower bound on $M_{\rm rob}$.
A <correlated floating-pinion uncertainty set> can materially change the conclusion. In an original example, all quantities are in micrometres and
$$
\delta=5+u,\qquad b=0.5+u,\qquad |u|\le0.2.
$$
Here $b$ stays positive, so $\delta-|b|=4.5$ for every allowed $u$. The exact joint-set margin is $4.5\,\mathrm{\mu m}$. Treating the ranges independently instead gives $4.8-0.7=4.1\,\mathrm{\mu m}$. An amplitude $A=4.3\,\mathrm{\mu m}$ passes the joint-set guarantee with residual compression $0.2\,\mathrm{\mu m}$, but fails the rectangular sufficient test. Failure of a conservative test does not itself demonstrate contact loss.
The admissible set must come from defensible parameter bounds, including any shared mounting or thermal effects. A <covariance> estimate alone supplies no absolute bound for all realizations. If the motion amplitude also depends on uncertain parameters, a direct bound on $\delta-|b|-A$ can preserve correlations that separate worst-case bounds discard.
Floating mounting was physically motivated by face-gear load sharing. NASA's primary report describes mounting freedom and slow-roll torque-division tests; those observations motivate the contact model, but do not validate every dynamic or uncertainty assumption above.<Development of Face Gear Technology for Industrial and Aerospace Power Transmission by Gregory F. Heath and others>[Introduction, printed pp. 1–2; Conclusions, printed p. 84]{ref} Once a contact opens, a <floating-pinion contact-loss check> must use the appropriate changed force law.
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