The epicyclic gear train experiment determines the velocity ratio and holding torque of a planetary gear train and verifies that its input, output and holding torques sum to zero. Epicyclic trains deliver large speed reductions in a compact, coaxial package — the mechanism inside automatic gearboxes, differentials and wind-turbine drives.
Aim of the experiment
To determine the velocity ratio and the holding (fixing) torque of an epicyclic gear train, and to verify the torque relationship between its members.
Theory
In an epicyclic (planetary) gear train, the axes of some gears move. A central sun gear meshes with planet gears carried on an arm (carrier), which in turn mesh with an outer annulus (ring) gear. Because the planets both spin and revolve, the velocity ratio is found by the tabular (or algebraic) method rather than by simple gear ratios.
For torque, in steady running the algebraic sum of the three external torques is zero:
Tinput + Toutput + Tholding = 0
and, neglecting friction, power in equals power out (Tinωin = −Toutωout). The holding torque is the reaction needed to fix one member.
Apparatus required
- Epicyclic gear train apparatus (sun, planet and annulus gears with a carrier arm)
- Arrangement to apply input torque and measure output and holding torques (spring balances / weights and a brake)
- Tachometer
Procedure
- Fix one member (e.g. the annulus) and note the configuration.
- Apply a known input torque and measure the output speed to obtain the velocity ratio.
- Measure the holding torque from the reaction on the fixed member.
- Verify the torque balance Tin + Tout + Thold ≈ 0 and compare the measured velocity ratio with the tabular calculation.
Result
The measured velocity ratio agrees with the tabular-method value, and the three torques sum to approximately zero, confirming the torque relationship.
Applications
Epicyclic gear trains are used in automatic transmissions, differentials, hoists, and wind-turbine and helicopter gearboxes. The experiment complements the flywheel and governor practicals. See related definitions in the engineering lab glossary.
Frequently asked questions
What is an epicyclic gear train?
It is a gear system in which planet gears rotate on their own axes while also revolving around a central sun gear, carried by an arm — giving large, compact, coaxial speed reductions.
How is the velocity ratio of an epicyclic train found?
By the tabular (or algebraic) method, which tracks the rotations of each gear when the arm and gears are moved in steps, because simple gear-ratio rules do not apply to moving axes.
Why do the torques in an epicyclic train sum to zero?
In steady running with no acceleration, the external torques on the input, output and fixed members must balance, so their algebraic sum is zero.
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