Epicyclic or Planetary Gear Analysis
Introduction
What millennial-old technique is the basics of many of the most innovative technical breakthroughs of this moment? Robotics, 3D printing and new means of transport all have one thing in common: often they are driven by a planetary gearbox.
What is planetary gearbox?
A planetary gearbox is a gearbox with the input shaft and the output shaft aligned. A planetary gearbox is used to transfer the largest torque in the most compact form (known as torque density).
The bicycle’s acceleration hub is a great example of a planet-wheel mechanism: Have you ever wondered how you can get so much power and capabilities in such a little hub? For a three-speed hub, a one-stage planetary gear system is used, for a five-speed hub a 2-stage. Each planet gear system has a reduction state, a direct coupling and an acceleration mode.
In mathematical terms, the smallest reduction ratio is 3: 1, the largest is 10: 1. At a ratio of less than 3, the sun gear becomes too big against the planet gears. At a ratio greater than 10 the sun wheel becomes too small and the torque will drop. The ratios are usually absolute i.e. an integer number.
Whoever invented the planetary gearbox is not known, but was functionally described by Leonardo da Vinci in 1490 and has been used for centuries.
Design of Gears
Ring Gear
Module = 2.5
Number of teeth = 46
Pitch Diameter = 115 (After Calculations)
Sun Gear
Module = 2.5
Number of teeth = 14
Pitch Diameter = 35 (After Calculations)
Planetary Gears
Module = 2.5
Number of teeth = 16
Number od Gears = 4
Pitch Diameter = 40 (After Calculations)
Input Speed of the Gear = 200 rpm
Assembly
STEPS:Toolbox-ANSI Metric - Power Transmission- Select Internal Spur gear - Select Spur gear(With appropriate dimensions)
Cases
Case 1
Input motor of speed 200rpm - Sun Gear
Output - Carrier
Fixed - Ring Gear
The plot of an angular velocity of the carrier against time.
Youtube Link
Case 2
Input motor of speed 200rpm - Ring Gear
Output - Carrier
Fixed - Sun Gear
The plot of an angular velocity of the carrier against time.
Youtube Link
Case 3
Input motor of speed 200rpm - Sun Gear
Output - Ring Gear
Fixed - Carrier
The plot of an angular velocity of the carrier against time.
Youtube Link
Results and Observations
1. In the first case, the input is given to the sun gear and output is extracted at the carrier keeping the ring gear fixed, which results in the rotation of planet gear about it’s axis and enables the planetary gears to rotates .The angular velocity in this case is 280 deg/sec.
2. In the second case, the input is given to the ring gear and output is extracted at the carrier keeping the sun gear fixed. At this point we can observe peak angular velocity with 920 deg/sec , due to small size of sun and planetary gears.
3. In the third case, the input is given to sun gear , carrier is fixed and output is extracted at ring gear which results in the rotation of planet gears about their axis .Since the ring gear is bigger in diameter the angular velocity achieved is less. The angular velocity is 365.217 deg/sec.