Gear torque-path load fraction

A 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,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 $10\mathrm{N}\mathrm{m}$ at $100$ and $200\mathrm{rad}{\mathrm{s}}^{-1}$ 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 $50\mathrm{rad}{\mathrm{s}}^{-1}$, their output torques are $20$ and $40\mathrm{N}\mathrm{m}$, 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 $s_2=a_2{\tau }_2$, thenEqual 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.^[ref] Report the reference shaft, sign convention, operating condition and measurement uncertainty with a torque-path fraction.