 Floating-pinion compression margin

The 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 $x_{\mathrm{eq}}$ and defineA positive $M$ means both contacts are compressed at equilibrium. If $x=x_{\mathrm{eq}}+y$ 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 $\delta =5\mu \mathrm{m}$ and $b=e+x_{\mathrm{eq}}=0.5\mu \mathrm{m}$, giving $M=4.5\mu \mathrm{m}$. A displacement amplitude $4.2\mu \mathrm{m}$ passes that nominal check, leaving $0.3\mu \mathrm{m}$ 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 isFor $\delta =5\pm 0.2\mu \mathrm{m}$ and $b=0.5\pm 0.3\mu \mathrm{m}$, $M_L=4.0\mu \mathrm{m}$. The same amplitude $4.2\mu \mathrm{m}$ is no longer guaranteed admissible, although failure of the bound does not prove contact loss. Amplitude $3.8\mu \mathrm{m}$ leaves at least $0.2\mu \mathrm{m}$ under these independent interval bounds.

In the symmetric static model, $x_{\mathrm{eq}}=-2ke/(2k+k_s)$ givesfor 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.^[ref]