Floating pinion
= Floating pinion
A \b[floating pinion] has mounting freedom that permits a limited position adjustment between its mating meshes. The resulting force balance can improve load division in a <split-torque transmission>. Floating does not mean unsupported: bearing and shaft constraints still transmit loads, and the allowed displacement must match the intended balancing direction.
An original symmetric scalar model illustrates the mechanism. Let two opposed mesh reactions be
$$
F_1=k(\delta+e+x),\qquad F_2=k(\delta-e-x),
$$
where $\delta$ sets mean compression, $e$ represents an initial mismatch and $x$ is the pinion's balancing displacement. Assume both contacts remain compressed. Let <floating-pinion centering stiffness> $k_s$ provide support reaction $-k_sx$, with the reaction sign chosen so that equilibrium is $F_2-F_1-k_sx=0$. Then
$$
x=-\frac{2ke}{2k+k_s},\qquad
F_1-F_2=\frac{2ke\,k_s}{2k+k_s}.
$$
With negligible centering restraint, $x\to-e$ and the reactions become equal. In the rigid-centering limit, $x\to0$ and the original imbalance remains.
For stipulated $k=100\,\mathrm{N/\mu m}$, $e=1\,\mathrm{\mu m}$ and $\delta=5\,\mathrm{\mu m}$, rigid centering gives forces $600$ and $400\,\mathrm N$. Free adjustment gives $500$ and $500\,\mathrm N$. At $k_s=200\,\mathrm{N/\mu m}$, displacement is $-0.5\,\mathrm{\mu m}$ and forces are $550$ and $450\,\mathrm N$. These describe the chosen scalar model, rather than a complete face-gear support design.
The primary 2002 rig slow-rolled pinions between two <face gears>, applied loads through hanging masses, pulleys and cables, and used tooth-root <strain gauges>. Its cantilevered pinion mount allowed a balancing displacement.<Development of Face Gear Technology for Industrial and Aerospace Power Transmission by Gregory F. Heath and others>[Summary, printed p. iii; Introduction, printed p. 1; Section VIII, torque calibration and split determination]{ref} The report's modified fixed-pinion comparison sent nearly all its load to one face-gear mesh, illustrating the effect of constraint in that tested assembly.<Development of Face Gear Technology for Industrial and Aerospace Power Transmission by Gregory F. Heath and others>[Conclusions, printed p. 84, fixed modified-idler comparison]{ref}
Finite travel, <friction>, <backlash> or loss of one contact can prevent the ideal balancing solution. At low load, the condition that both model forces are nonnegative must be checked; a <gear tooth engagement threshold> can change the equations. Position freedom can help sharing without guaranteeing identical tooth <stress> or a perfectly equal <torque> split at every operating condition.