= Floating-pinion compression margin
The \b[floating-pinion compression margin] is the amount of relative approach remaining before the less compressed contact reaches zero compression in a stated two-contact model. It turns the assumptions of a <floating-pinion balancing mode> into a quantitative admissibility check.
For $F_1=k(\delta+e+x)$ and $F_2=k(\delta-e-x)$, let equilibrium position be $x_{\rm eq}$ and define
$$
M=\delta-|e+x_{\rm eq}|.
$$
A positive $M$ means both contacts are compressed at equilibrium. If $x=x_{\rm eq}+y$ with $|y|\le A$, then $A<M$ guarantees compression throughout the bounded motion. For a steady single sinusoid and fixed $\delta$, this is the exact full-cycle condition; a general transient envelope supplies only a sufficient bound.
An original nominal example has $\delta=5\,\mathrm{\mu m}$ and $b=e+x_{\rm eq}=0.5\,\mathrm{\mu m}$, giving $M=4.5\,\mathrm{\mu m}$. A displacement amplitude $4.2\,\mathrm{\mu m}$ passes that nominal check, leaving $0.3\,\mathrm{\mu m}$ of minimum compression for the sinusoidal model.
A <floating-pinion robust contact margin> includes bounded parameter uncertainty. If $\delta\in[\delta_L,\delta_U]$ and $b\in[b_L,b_U]$, a conservative lower margin is
$$
M_L=\delta_L-\max(|b_L|,|b_U|).
$$
For $\delta=5\pm0.2\,\mathrm{\mu m}$ and $b=0.5\pm0.3\,\mathrm{\mu m}$, $M_L=4.0\,\mathrm{\mu m}$. The same amplitude $4.2\,\mathrm{\mu m}$ is no longer guaranteed admissible, although failure of the bound does not prove contact loss. Amplitude $3.8\,\mathrm{\mu m}$ leaves at least $0.2\,\mathrm{\mu m}$ under these independent interval bounds.
In the symmetric static model, $x_{\rm eq}=-2ke/(2k+k_s)$ gives
$$
M=\delta-\frac{|e|k_s}{2k+k_s},
$$
for positive mesh stiffness $k$ and nonnegative <floating-pinion centering stiffness> $k_s$. Mounting freedom can change the margin, but it also changes dynamics; maximizing this one scalar is not a complete gearbox design rule.
A <floating-pinion contact-loss check> must recompute the contact model once a force reaches zero. The historical face-gear tests provide evidence about mounting freedom and measured torque division under slow rolling, rather than a universal dynamic margin.<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}
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