Power transmission in aircraft propulsion

Requirements

• Minimum weight with high power: use of alloy steels, case-hardened ground gears, thin webs and light casings.
• High reliability and safety: redundancy, high factor on fatigue life, vibration and condition monitoring; the gearbox is flight-critical.
• Operation at high speed and temperature with forced oil lubrication and cooling.
• Compact size and the correct shaft geometry, with low noise and vibration.
• Ability to carry the propeller thrust and gyroscopic loads.

Why a reduction gearbox

A gas turbine runs efficiently at 10000 to 30000 rpm, but a large propeller must turn slowly (about 1000 to 2000 rpm) so that blade tip speed stays below sonic speed for efficiency and low noise. A reduction gearbox gives this speed ratio.

Why epicyclic

Power is shared among several planet gears, so each tooth carries less load; coaxial input and output; compact and light; balanced forces on the sun and carrier give lower bearing loads.

Numerical

Sun input, ring fixed, carrier output: speed ratio $= 1 + \dfrac{z_r}{z_s}$.

$$\frac{N_{in}}{N_{out}} = \frac{12000}{1500} = 8 = 1 + \frac{z_r}{z_s} \;\Rightarrow\; \frac{z_r}{z_s} = 7$$

For example $z_s = 18$, $z_r = 126$ (planet teeth $= (126-18)/2 = 54$).

Input torque $T_{in} = \dfrac{P}{\omega} = \dfrac{1\,500\,000}{12000\times2\pi/60} = 1193.7\ \text{N m}$.

Output torque (no loss) $= T_{in}\times 8 = 9549\ \text{N m}$.

Answer: $z_r/z_s = 7$; propeller torque about 9550 N m.