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A face gear is a gear whose working teeth occupy an annular face and mesh with a mating cylindrical pinion. A common arrangement turns the drive through approximately a right angle; other shaft angles and tapered configurations are possible. Its working surface geometry must maintain compatible tooth contact, rather than simply placing ordinary cylindrical teeth on a flat disk.

Tooth counting still supplies an ideal speed relation. If the pinion has $N_p$ teeth and the face gear $N_f$, equality of tooth-passage rates givesAn original 20-tooth pinion driving a 100-tooth face gear at $1500$ revolutions per minute therefore gives $300$ revolutions per minute at the output. Rotation signs require a stated orientation of the two different shaft axes; the scalar minus sign for an external parallel-axis spur gear pair cannot be copied without that convention.

The annular layout also explains a geometric design issue. With $N$ tooth positions, angular spacing is $2\pi /N$, while arc spacing on a ring of radius $r$ isFor $N=80$, radii $40$ and $60\mathrm{mm}$ give arc spacings about $3.142$ and $4.712\mathrm{mm}$. This radial change does not prescribe two interchangeable gear modules; it shows why a generated face-tooth surface cannot be understood as a single extruded cylindrical tooth profile.

A primary 2002 program built a scaled-power split-torque transmission with two opposed face gears, two input pinions and two idlers.^[ref] Multiple meshes make the geometry useful for distributing and recombining load, but also make alignment and compatibility important.

A bench rotation check can test the tooth-count ratio. A gear contact marking test, dimensional inspection and load-sensitive measurements address different questions about the manufactured surfaces and their operation. Correct output speed alone does not establish an acceptable gear contact pattern, tooth stress or gear efficiency.

A 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 bewhere $\delta$ 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 $-k_{s}x$, with the reaction sign chosen so that equilibrium is $F_2-F_1-k_{s}x=0$. ThenWith negligible centering restraint, $x\to -e$ and the reactions become equal. In the rigid-centering limit, $x\to 0$ and the original imbalance remains.

For stipulated $k=100N/\mu \mathrm{m}$, $e=1\mu \mathrm{m}$ and $\delta =5\mu \mathrm{m}$, rigid centering gives forces $600$ and $400\mathrm{N}$. Free adjustment gives $500$ and $500\mathrm{N}$. At $k_s=200N/\mu \mathrm{m}$, displacement is $-0.5\mu \mathrm{m}$ 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.^[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.^[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.

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.

Gregory F. Heath is a mechanical engineer whose documented research includes rotorcraft transmissions and face gear technology. His2010 author biography describes him as an associate technical fellow at Boeing Rotorcraft-Mesa and a technical integrator for an advanced rotorcraft-drive program.^[ref]

Heath coauthored Development of Face Gear Technology for Industrial and Aerospace Power Transmission by Gregory F. Heath and others with Robert R. Filler and Jie Tan. Their2002 report documents a250-horsepower proof-of-concept split-torque transmission using concentric face gears. The tests examined whether floating input pinions could divide the load nearly evenly between parallel transmission paths.^[ref]

The mechanical question is more demanding than obtaining the desired gear ratio. If two parallel paths have unequal geometry or effective stiffness, one can carry more torque than intended. In an ideal equal-speed example, dividing a100N·m input into50N·m in each path also divides input power equally. A60/40N·m split preserves the total transmitted torque but raises the larger path's load20% above the intended50N·m share. A floating pinion supplies freedom intended to improve load balance; the report's apparatus and measurements tested how that mechanism behaved in a manufactured transmission.

Heath also coauthored the later gear-pitting detection study with Paula J. Dempsey, David G. Lewicki and Perumal Shanthakumaran, linking transmission development with experimental assessment of damage indicators.^[ref]

Jie Tan coauthored Development of Face Gear Technology for Industrial and Aerospace Power Transmission by Gregory F. Heath and others with Gregory F. Heath and Robert R. Filler. Its2002 title page identifies Tan with The Boeing Company in Mesa, Arizona. The work investigated concentric face gears and floating pinions as a means of distributing transmitted torque between parallel paths.^[ref]

The report is useful because its apparatus revealed that different load divisions in one split-torque transmission need not agree. While input-pinion mesh division was close to48/52, the idlers were reported near57/43. The authors related the idler imbalance to how backlash had been set using strain indications, and discussed the limitations of inferring the split from those indications alone.^[ref]

In an illustrative100-unit load normalization, a57-unit path is14% above the intended50-unit equal share. A geometric gear ratio can remain correct despite that unequal internal loading. Tan's coauthored study therefore provides a concrete connection between transmission geometry, adjustment and experimentally inferred forces, rather than treating the desired speed ratio as a complete description of mechanical performance.

Robert R. Filler is a coauthor of experimental mechanical-engineering work on face gear transmissions. The2002 report with Gregory F. Heath and Jie Tan identifies all three with The Boeing Company in Mesa, Arizona. Their report documents design, manufacture and testing of a scaled250-horsepower proof-of-concept split-torque transmission.^[ref]

The experiment made load balance measurable. The input pinions were slow-rolled under torque supplied through weights, pulleys and cables, while tooth-root strain gauges recorded deformation associated with load. Measurement calibration was needed to convert those indications into an estimate of the torque division. The reported full two-pinion/two-idler configuration gave approximately48% and52% at the upper and lower input-pinion meshes.^[ref]

For an illustrative normalization to100N·m total input torque, those fractions correspond to48 and52N·m. The larger branch is4% above an ideal50N·m equal share, even though the two branches differ by4N·m. The distinction matters when comparing a measured torque split with the load intended for each path. Filler's documented contribution is as a coauthor of the experimental transmission study; the result depends on the complete tested arrangement.