Page 86 - Electric Drives and Electromechanical Systems

Chapter 3 Power transmission and sizing 79

A sun gear, which may or may not be fixed.
Several planetary gears.
Planet gear carrier.
An outer gear ring, which may not be used on all systems.

This design results in relatively low speeds between the individual gear wheels and
giving a highly efficient design. One advantage is that the gearbox has no bending
moments generated by the transmitted torque; consequently, the stiffness is consider-
ably higher than in comparable configuration. Also, they can be assembled coaxially with
the motor, leading to a more compact overall design. The relationship for a planetary
gearbox can be shown to be (Waldron and Kinzel, 1999),
u sun u carrier N ring
¼ (3.10)
u ring u carrier N sun
where u sun ; u carrier and u ring are the angular speeds of the sun gear, planet carrier and
ring with reference to ground. N ring and N sun are the number of teeth on the sun and ring
respectively. Given any two angular velocities, the third can be calculated - normally the
ring is fixed, hence u ring ¼ 0.
If one of the gearbox elements is fixed the torque relationships can be shown to be,
N ring
T ring ¼ T sun ðCarrier fixedÞ
N sun
N ring þ N sun
T carrier ¼ T sun ðRing fixedÞ (3.11)
N sun
N ring þ N sun
T carrier ¼ T ring ðSun fixedÞ
N ring

nnn
Example 3.1
A planetary gearbox has 200 teeth on its ring, and 50 teeth on its sun gear. The input to the sun
gear is 100 rev min 1 clockwise.
Determine the planet carrier speed if the ring is fixed or rotating at 5 rev min 1 either
clockwise or counter-clockwise.
Rearranging Eq. (3.10), gives

N sun u sun þ N ring u ring
u carrier ¼
N sun þ N ring
When the ring is rotated at 5 rev min 1 clockwise, the output speed is 20 rev min 1
clockwise.
When the ring is fixed, the output speed is 16 rev min 1 clockwise.
When the ring is rotated at 5 rev min 1 counter-clockwise, the output speed is 12 rev
min 1 clockwise.