= Gear torque-path load fraction
A \b[gear torque-path load fraction] specifies how a stated total transmitted <torque> is divided among paths of a <split-torque transmission>. With all branch torques referred to the same shaft coordinate,
$$
\lambda_j=\frac{\tau_j}{\sum_\ell\tau_\ell}.
$$
For positive total torque and nonnegative contributions, the fractions lie between zero and one and sum to one. If a path carries reverse or circulating <power>, the signed ratio requires a different interpretation; it need not lie in that interval.
The common coordinate is essential. Two branches carrying $10\,\mathrm{N\,m}$ at $100$ and $200\,\mathrm{rad\,s^{-1}}$ carry powers $1000$ and $2000\,\mathrm W$. Their equal raw torques do not imply equal power shares. If ideal gearing brings both contributions to a common output speed $50\,\mathrm{rad\,s^{-1}}$, their output torques are $20$ and $40\,\mathrm{N\,m}$, giving fractions $1/3$ and $2/3$.
For parallel elastic paths with the same twist coordinate and zero gaps, $\tau_j=K_j\theta$ gives $\lambda_j=K_j/\sum_\ell K_\ell$. In that model a stiffness ratio $2:3$ gives fractions $0.4$ and $0.6$, regardless of the total torque while the same linear branches remain active. Gaps and a <floating pinion> can change that allocation.
A sensor ratio also needs a <measurement model>. If two channels obey $s_1=a_1\tau_1$ and $s_2=a_2\tau_2$, then
$$
\lambda_1=\frac{s_1/a_1}{s_1/a_1+s_2/a_2}.
$$
Equal torques with sensitivities $a_1=2$ and $a_2=1$ give raw signals in the ratio $2:1$; the raw signal fraction $2/3$ is not the torque fraction $1/2$. Cross-talk and changing tooth-load distributions may require a fuller calibration model.
The primary face-gear program reported approximately $48\%/52\%$ division at the input pinions and a different split between its idlers. The report also explains why tooth strain was not an invariant direct proxy for transmitted load.<Development of Face Gear Technology for Industrial and Aerospace Power Transmission by Gregory F. Heath and others>[Section VIII, printed pp. 71–78; Conclusions, printed p. 84, torque calibration, reported splits and strain/load limitations]{ref} Report the reference shaft, sign convention, operating condition and <measurement uncertainty> with a torque-path fraction.
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